transcripts/3GC721pNRLE.json

[{"text": "MICHALE FEE: OK, good\nmorning, everyone.", "start": 12.896, "duration": 2.964}, {"text": "OK, so today we are\ngoing to continue", "start": 15.86, "duration": 4.95}, {"text": "the process of building\nour equivalent circuit", "start": 20.81, "duration": 2.79}, {"text": "model of a neuron.", "start": 23.6, "duration": 2.46}, {"text": "This model was actually\ndeveloped in the late '40s", "start": 26.06, "duration": 4.98}, {"text": "and early '50s by Alan\nHodgkin and Andrew", "start": 31.04, "duration": 2.31}, {"text": "Huxley, who started working on\nthe problem of understanding", "start": 33.35, "duration": 4.83}, {"text": "how neurons make\naction potentials.", "start": 38.18, "duration": 2.5}, {"text": "And so they studied\nthe squid giant axon,", "start": 40.68, "duration": 3.63}, {"text": "which is actually a\nvery cool preparation,", "start": 44.31, "duration": 2.03}, {"text": "because that axon is actually\nabout a millimeter across,", "start": 46.34, "duration": 4.18}, {"text": "and so you can stick\nwires inside of it.", "start": 50.52, "duration": 3.78}, {"text": "And they did a bunch of\nvery cool experiments", "start": 54.3, "duration": 3.32}, {"text": "to figure out how these\ndifferent ionic conductances", "start": 57.62, "duration": 3.748}, {"text": "and how these different\ncomponents of the circuit", "start": 61.368, "duration": 2.042}, {"text": "work together to make\nan action potential.", "start": 63.41, "duration": 4.95}, {"text": "So that's what we're\ngoing to continue doing,", "start": 68.36, "duration": 3.94}, {"text": "we're going to\nessentially continue", "start": 72.3, "duration": 2.96}, {"text": "describing and motivating\nthe different components", "start": 75.26, "duration": 2.79}, {"text": "of this circuit.", "start": 78.05, "duration": 1.21}, {"text": "So today, we're going to\nget through the process", "start": 79.26, "duration": 4.73}, {"text": "of introducing a\nvoltage-measuring device,", "start": 83.99, "duration": 4.29}, {"text": "a current source, a\ncapacitor, a conductance,", "start": 88.28, "duration": 3.33}, {"text": "and we're going to start\nintroducing a battery, OK?", "start": 91.61, "duration": 5.32}, {"text": "OK.", "start": 96.93, "duration": 0.5}, {"text": "So here's what we want\nto accomplish today.", "start": 97.43, "duration": 4.83}, {"text": "So we want to understand how\nkind of at the simplest level", "start": 102.26, "duration": 3.81}, {"text": "how neurons respond\nto injected currents,", "start": 106.07, "duration": 4.71}, {"text": "we want to understand\nhow membrane", "start": 110.78, "duration": 1.56}, {"text": "capacitance and membrane\nresistance allows neurons", "start": 112.34, "duration": 3.78}, {"text": "to integrate their\ninputs over time,", "start": 116.12, "duration": 2.55}, {"text": "and to filter their inputs or\nsmooth their inputs over time--", "start": 118.67, "duration": 4.2}, {"text": "and that particular model is\ncalled a resistor capacitor", "start": 122.87, "duration": 3.75}, {"text": "model or an RC\nmodel of a neuron.", "start": 126.62, "duration": 4.88}, {"text": "We're going to go through how\nto derive the differential", "start": 131.5, "duration": 2.64}, {"text": "equations that describe that\nmodel-- it's actually quite", "start": 134.14, "duration": 3.54}, {"text": "simple, but some\nof you may not have", "start": 137.68, "duration": 2.58}, {"text": "been through that before,\nso I want to go through it", "start": 140.26, "duration": 2.52}, {"text": "step by step so we\ncan really understand", "start": 142.78, "duration": 2.25}, {"text": "where that comes from.", "start": 145.03, "duration": 2.27}, {"text": "And we're going to learn to\nbasically look at a current--", "start": 147.3, "duration": 4.635}, {"text": "a pattern of current\ninjection, and we", "start": 151.935, "duration": 1.845}, {"text": "should be able to\nintuitively see", "start": 153.78, "duration": 3.0}, {"text": "how the voltage of\nthat neuron responds.", "start": 156.78, "duration": 5.08}, {"text": "And we're going to\nstart working on where", "start": 161.86, "duration": 3.09}, {"text": "the batteries of a neuron\nactually come from, OK?", "start": 164.95, "duration": 4.33}, {"text": "OK.", "start": 169.28, "duration": 0.62}, {"text": "So-- all right.", "start": 169.9, "duration": 1.59}, {"text": "So-- all right.", "start": 171.49, "duration": 3.27}, {"text": "So we're going to basically\ntalk about the following sort", "start": 174.76, "duration": 4.585}, {"text": "of thought experiment, OK?", "start": 179.345, "duration": 1.995}, {"text": "The following conceptual idea.", "start": 181.34, "duration": 1.65}, {"text": "We're going to take\na neuron and we're", "start": 182.99, "duration": 2.31}, {"text": "going to put it in a\nbath of sailing, OK?", "start": 185.3, "duration": 2.79}, {"text": "A saltwater solution that\nrepresents the extracellular", "start": 188.09, "duration": 2.76}, {"text": "solution that neurons--", "start": 190.85, "duration": 3.45}, {"text": "extracellular\nsolution in the brain.", "start": 194.3, "duration": 2.47}, {"text": "And we're going to put an\nelectrode into that neuron", "start": 196.77, "duration": 2.87}, {"text": "so that we can inject\ncurrent, and we're", "start": 199.64, "duration": 2.07}, {"text": "going to put another\nelectrode into the neuron", "start": 201.71, "duration": 2.41}, {"text": "so that we can\nmeasure the voltage,", "start": 204.12, "duration": 1.64}, {"text": "and we're going to study\nhow this neuron responds--", "start": 205.76, "duration": 3.78}, {"text": "how the voltage of the neuron\nresponds to current injections,", "start": 209.54, "duration": 3.41}, {"text": "OK?", "start": 212.95, "duration": 1.9}, {"text": "Now why is it that we\nwant to actually do that?", "start": 214.85, "duration": 3.27}, {"text": "Why is that an interesting or\nimportant experiment to do?", "start": 218.12, "duration": 5.39}, {"text": "Anybody have any\nidea why we would", "start": 223.51, "duration": 2.37}, {"text": "want to actually measure\nvoltage and current", "start": 225.88, "duration": 3.117}, {"text": "for a neuron in the brain?", "start": 228.997, "duration": 1.083}, {"text": "Yes?", "start": 234.73, "duration": 0.5}, {"text": "AUDIENCE: Be able to use the\nmathematical model [INAUDIBLE]", "start": 235.23, "duration": 2.82}, {"text": "provided for us?", "start": 238.05, "duration": 0.94}, {"text": "MICHALE FEE: OK, but\nit's more than just", "start": 238.99, "duration": 3.14}, {"text": "so that we can describe\nit mathematically, right?", "start": 242.13, "duration": 3.63}, {"text": "It's because these things--", "start": 245.76, "duration": 1.65}, {"text": "something about\nvoltage and current", "start": 247.41, "duration": 1.71}, {"text": "are actually relevant to\nhow a neuron functions.", "start": 249.12, "duration": 3.91}, {"text": "Yes?", "start": 253.03, "duration": 0.5}, {"text": "AUDIENCE: Like the\nresistance inside?", "start": 253.53, "duration": 2.61}, {"text": "MICHALE FEE: Yeah.", "start": 256.14, "duration": 0.99}, {"text": "So that's an important\nquantity, but we're", "start": 257.13, "duration": 2.1}, {"text": "looking for something\nmore fundamental,", "start": 259.23, "duration": 1.89}, {"text": "like why is it\nactually important", "start": 261.12, "duration": 2.13}, {"text": "that we understand how voltage\nchanges when a neuron has", "start": 263.25, "duration": 4.05}, {"text": "current injected into it?", "start": 267.3, "duration": 1.69}, {"text": "Habiba?", "start": 268.99, "duration": 0.5}, {"text": "AUDIENCE: Equals [INAUDIBLE]\ndifferent like ion channels,", "start": 269.49, "duration": 2.39}, {"text": "a different set of\nvoltages [INAUDIBLE]..", "start": 271.88, "duration": 3.975}, {"text": "MICHALE FEE: Exactly.", "start": 275.855, "duration": 0.875}, {"text": "So ion channels are\nsensitive to voltage,", "start": 276.73, "duration": 3.49}, {"text": "and the way they function\ndepends very critically", "start": 280.22, "duration": 3.68}, {"text": "on voltage.", "start": 283.9, "duration": 0.93}, {"text": "So many-- if not\nmost-- ion channels", "start": 284.83, "duration": 3.72}, {"text": "are voltage sensitive and are\ncontrolled by voltage, OK?", "start": 288.55, "duration": 6.0}, {"text": "And that's exactly why.", "start": 294.55, "duration": 1.52}, {"text": "So nearly every aspect of\nwhat neurons do in the brain", "start": 296.07, "duration": 4.21}, {"text": "as you're walking around looking\nat things and doing things", "start": 300.28, "duration": 5.16}, {"text": "is controlled by\nvoltage, and that", "start": 305.44, "duration": 1.89}, {"text": "goes through the voltage\nsensitivity of buying channels,", "start": 307.33, "duration": 4.01}, {"text": "OK?", "start": 311.34, "duration": 0.73}, {"text": "But what is it that changes\nthe voltage in a neuron?", "start": 312.07, "duration": 3.63}, {"text": "Yes?", "start": 322.03, "duration": 0.5}, {"text": "AUDIENCE: The action potential.", "start": 322.53, "duration": 2.09}, {"text": "MICHALE FEE: That's\non the output side.", "start": 324.62, "duration": 3.17}, {"text": "Yes?", "start": 327.79, "duration": 0.5}, {"text": "AUDIENCE: Is it\nion concentration?", "start": 328.29, "duration": 2.2}, {"text": "MICHALE FEE: Good.", "start": 330.49, "duration": 1.01}, {"text": "That's correct.", "start": 331.5, "duration": 1.8}, {"text": "I'm looking for something\na little bit different.", "start": 333.3, "duration": 3.78}, {"text": "Habiba?", "start": 337.08, "duration": 0.5}, {"text": "AUDIENCE: Do you have\npumps or [INAUDIBLE]..", "start": 337.58, "duration": 1.99}, {"text": "MICHALE FEE: Yeah, those\nare all good answers.", "start": 339.57, "duration": 2.718}, {"text": "Not quite what I'm looking for.", "start": 342.288, "duration": 1.292}, {"text": "AUDIENCE: [INAUDIBLE]", "start": 343.58, "duration": 2.74}, {"text": "MICHALE FEE: Yes.", "start": 346.32, "duration": 1.56}, {"text": "So the answer is that\nthe voltage of a neuron", "start": 347.88, "duration": 4.17}, {"text": "changes because--", "start": 352.05, "duration": 3.22}, {"text": "the reason current is important\nis because the reason voltage", "start": 355.27, "duration": 3.99}, {"text": "changes in a neuron is because\nother cells are injecting", "start": 359.26, "duration": 4.02}, {"text": "current into our neuron.", "start": 363.28, "duration": 2.31}, {"text": "Sensory inputs are injecting\ncurrent into our neuron, OK?", "start": 365.59, "duration": 4.8}, {"text": "Everything that a neuron\nreceives, all the information", "start": 370.39, "duration": 3.66}, {"text": "that a neuron receives from\nother neurons in the network", "start": 374.05, "duration": 3.33}, {"text": "and from the outside world\ncomes from currents being", "start": 377.38, "duration": 3.36}, {"text": "injected into that neuron, OK?", "start": 380.74, "duration": 3.45}, {"text": "And so it's really\nimportant that we understand", "start": 384.19, "duration": 2.01}, {"text": "how the neuron transforms that\ncurrent input from other cells", "start": 386.2, "duration": 5.61}, {"text": "and from the sensory periphery\ninto voltage changes that", "start": 391.81, "duration": 4.98}, {"text": "then change the behavior\nof ion channels.", "start": 396.79, "duration": 2.88}, {"text": "Is that clear?", "start": 399.67, "duration": 1.05}, {"text": "That link of current\ninputs to voltage output", "start": 400.72, "duration": 4.59}, {"text": "is really crucial,\nand that's why we're", "start": 405.31, "duration": 1.86}, {"text": "doing this experiment, OK?", "start": 407.17, "duration": 1.92}, {"text": "OK, and that's this\npoint right here.", "start": 412.39, "duration": 3.49}, {"text": "OK, so one of the\nfirst things we're", "start": 415.88, "duration": 1.5}, {"text": "going to see when we go\nthrough this analysis", "start": 417.38, "duration": 2.94}, {"text": "is that neurons can\nperform analog integration.", "start": 420.32, "duration": 2.85}, {"text": "They can perform numerical\nintegration over time, OK?", "start": 423.17, "duration": 4.1}, {"text": "That's pretty cool.", "start": 427.27, "duration": 1.86}, {"text": "Voltage is that integral over\ntime of the injected current.", "start": 429.13, "duration": 5.34}, {"text": "To first order.", "start": 434.47, "duration": 1.56}, {"text": "It's the simplest\nbehavior of a neuron.", "start": 436.03, "duration": 2.222}, {"text": "So if you measure the\nvoltage of a neuron", "start": 438.252, "duration": 1.708}, {"text": "and you turn on current and\nyou turn the current on,", "start": 439.96, "duration": 3.45}, {"text": "the voltage of a\nneuron will ramp up,", "start": 443.41, "duration": 3.21}, {"text": "integrating that\ninput over time, OK?", "start": 446.62, "duration": 2.7}, {"text": "Pretty cool.", "start": 449.32, "duration": 1.17}, {"text": "So we're going to\nsee how that happens,", "start": 450.49, "duration": 2.1}, {"text": "why that happens biophysically.", "start": 452.59, "duration": 3.84}, {"text": "OK.", "start": 456.43, "duration": 0.57}, {"text": "So let's come back to\nour neuron in the dish.", "start": 457.0, "duration": 3.0}, {"text": "Let me just explain a little\nbit how you would actually", "start": 460.0, "duration": 2.7}, {"text": "do this experiment.", "start": 462.7, "duration": 0.94}, {"text": "So these electrodes are\nlittle pieces of glass tubing.", "start": 463.64, "duration": 3.15}, {"text": "So you take a fine glass\ntube about a millimeter", "start": 466.79, "duration": 2.27}, {"text": "across you heat it up in\nthe middle over a flame,", "start": 469.06, "duration": 2.91}, {"text": "and you pull it apart when\nit melts in the middle,", "start": 471.97, "duration": 2.64}, {"text": "and it makes a very sharp point.", "start": 474.61, "duration": 2.73}, {"text": "You break off the fine little\nthread of glass that's left,", "start": 477.34, "duration": 4.8}, {"text": "and you have a tube that narrows\ndown to a very sharp point,", "start": 482.14, "duration": 3.3}, {"text": "but it's still a tube, and\nyou can literally just--", "start": 485.44, "duration": 2.935}, {"text": "there are some cells, like in\nthe old days people studied", "start": 488.375, "duration": 2.375}, {"text": "large neurons and in\nsnails where the cells are", "start": 490.75, "duration": 3.453}, {"text": "a millimeter across, you\ncan take an electrode", "start": 494.203, "duration": 1.917}, {"text": "and literally just by hand\npoke it into the cell.", "start": 496.12, "duration": 2.52}, {"text": "And then you fill that\nelectrode with a salt solution,", "start": 498.64, "duration": 4.23}, {"text": "and then you put a wire in\nthe back of that electrode,", "start": 502.87, "duration": 2.64}, {"text": "and you hook it up\nto an amplifier.", "start": 505.51, "duration": 1.93}, {"text": "Now we want to measure\nthe voltage in the cell.", "start": 507.44, "duration": 2.73}, {"text": "Remember, voltage is\nalways voltage difference.", "start": 510.17, "duration": 3.619}, {"text": "We're always measuring\nthe difference", "start": 513.789, "duration": 1.591}, {"text": "between the voltage in one place\nand the voltage somewhere else.", "start": 515.38, "duration": 3.46}, {"text": "So this amplifier\nhas two inputs.", "start": 518.84, "duration": 2.61}, {"text": "It's called a\ndifferential amplifier,", "start": 521.45, "duration": 2.18}, {"text": "and we're going to hook\nthe electrode that's", "start": 523.63, "duration": 2.19}, {"text": "in the cell to\nthe plus terminal,", "start": 525.82, "duration": 1.86}, {"text": "we're going to put\na wire in the bath,", "start": 527.68, "duration": 1.94}, {"text": "hook it to the minus\nterminal, and this amplifier", "start": 529.62, "duration": 2.08}, {"text": "is measuring the difference\nbetween the voltage", "start": 531.7, "duration": 2.61}, {"text": "inside the cell and the\nvoltage outside the cell, OK?", "start": 534.31, "duration": 3.18}, {"text": "Any questions about that?", "start": 537.49, "duration": 2.2}, {"text": "So we're going to take the other\nhalf of that piece of glass", "start": 539.69, "duration": 2.78}, {"text": "that we pulled, fill\nit with salt solution,", "start": 542.47, "duration": 2.675}, {"text": "stick it in the cell, and\nwe're going to hook it up", "start": 545.145, "duration": 2.125}, {"text": "to a current source.", "start": 547.27, "duration": 1.83}, {"text": "Now our current source is\nbasically just a battery, OK?", "start": 549.1, "duration": 4.17}, {"text": "But it's got some\nfancy electronics", "start": 553.27, "duration": 2.17}, {"text": "such that the current that flows\nis equal to whatever value you", "start": 555.44, "duration": 4.73}, {"text": "set, OK?", "start": 560.17, "duration": 4.85}, {"text": "And of course,\nremember, that voltage", "start": 565.02, "duration": 1.955}, {"text": "is in units of volts and\ncurrent is charge per second.", "start": 566.975, "duration": 4.815}, {"text": "Charge is coulombs, so\ncoulombs per second,", "start": 571.79, "duration": 3.36}, {"text": "and that's equal to the unit\nof current, which is amperes.", "start": 575.15, "duration": 4.31}, {"text": "All right.", "start": 579.46, "duration": 0.6}, {"text": "Now let's take a closer look\nat our little spherical neuron,", "start": 580.06, "duration": 4.71}, {"text": "our little neuron.", "start": 584.77, "duration": 1.2}, {"text": "We've chopped all the\ndendrites and axons off,", "start": 585.97, "duration": 2.02}, {"text": "so it's just a little\nsphere, and you can basically", "start": 587.99, "duration": 2.87}, {"text": "model a neuron just like any\nother cell as a spherical shell", "start": 590.86, "duration": 5.61}, {"text": "of insulating material, OK?", "start": 596.47, "duration": 3.27}, {"text": "In this case, a lipid bilayer.", "start": 599.74, "duration": 2.31}, {"text": "This is a phospholipid bilayer.", "start": 602.05, "duration": 3.0}, {"text": "Phospholipids are just little\nfat molecules that have a polar", "start": 605.05, "duration": 3.72}, {"text": "head on one side-- that means\nthey're soluble in water", "start": 608.77, "duration": 2.76}, {"text": "on this side, and they\nhave a non-polar tail,", "start": 611.53, "duration": 3.09}, {"text": "so they don't like to be\nin contact with water,", "start": 614.62, "duration": 2.16}, {"text": "and the two polar\ntails go end to end--", "start": 616.78, "duration": 3.63}, {"text": "sorry, the non-polar\ntails go end to end,", "start": 620.41, "duration": 2.49}, {"text": "the polar heads face\nout into the water.", "start": 622.9, "duration": 3.42}, {"text": "Does that makes sense?", "start": 626.32, "duration": 1.16}, {"text": "And they are very closely\npacked together so", "start": 627.48, "duration": 2.85}, {"text": "that ions can't pass\nthrough that membrane,", "start": 630.33, "duration": 2.55}, {"text": "so it's insulating.", "start": 632.88, "duration": 2.43}, {"text": "It's very thin, it's only\nabout 23 angstroms across, OK?", "start": 635.31, "duration": 4.98}, {"text": "An angstrom is about the\nsize of a hydrogen atom.", "start": 640.29, "duration": 4.81}, {"text": "They're very thin, OK?", "start": 645.1, "duration": 1.93}, {"text": "OK, we have saline inside.", "start": 650.03, "duration": 1.84}, {"text": "What is saline?", "start": 651.87, "duration": 1.85}, {"text": "What is it in our model?", "start": 653.72, "duration": 1.785}, {"text": "Remember on Tuesday what--", "start": 659.22, "duration": 1.662}, {"text": "AUDIENCE: A wire.", "start": 660.882, "duration": 0.708}, {"text": "MICHALE FEE: Good.", "start": 661.59, "duration": 0.75}, {"text": "It's a wire and we have saline\noutside, which is also a wire.", "start": 662.34, "duration": 4.75}, {"text": "So we have two wires separated\nby an insulator, what is that?", "start": 667.09, "duration": 4.07}, {"text": "That's a capacitor, because\nit's two conductors separated", "start": 676.1, "duration": 3.43}, {"text": "by an insulator, OK?", "start": 679.53, "duration": 1.83}, {"text": "So an electrical component\nthat behaves like a capacitor--", "start": 681.36, "duration": 6.085}, {"text": "like if you were to\nbuild one of those,", "start": 687.445, "duration": 1.625}, {"text": "you would take like a\npiece of aluminum foil,", "start": 689.07, "duration": 3.27}, {"text": "put a piece of paper on it, put\nanother piece of aluminum foil", "start": 692.34, "duration": 2.88}, {"text": "next to it, and\nattach wires to that,", "start": 695.22, "duration": 2.85}, {"text": "and you would squeeze the\nstack of aluminum foil paper", "start": 698.07, "duration": 3.51}, {"text": "and aluminum foil together, and\nthat becomes a capacitor, OK?", "start": 701.58, "duration": 3.87}, {"text": "And it has a symbol that\nlooks like this electrically.", "start": 705.45, "duration": 4.31}, {"text": "So this is now our equivalent\ncircuit of this model neuron,", "start": 709.76, "duration": 5.6}, {"text": "OK?", "start": 715.36, "duration": 0.61}, {"text": "It's very simple.", "start": 715.97, "duration": 1.27}, {"text": "It's a capacitor\nwith one wire here", "start": 717.24, "duration": 2.57}, {"text": "that represents the inside of\nthe cell, another wire that", "start": 719.81, "duration": 4.16}, {"text": "represents the\noutside of the cell.", "start": 723.97, "duration": 4.19}, {"text": "We have a current\nsource that connects", "start": 728.16, "duration": 2.52}, {"text": "the outside of the cell\nto the inside of the cell.", "start": 730.68, "duration": 3.03}, {"text": "When we turn on\nthe current source,", "start": 733.71, "duration": 1.47}, {"text": "it takes charges\nfrom inside of here", "start": 735.18, "duration": 4.08}, {"text": "and sticks them\nthrough the electrode", "start": 739.26, "duration": 3.45}, {"text": "and pumps them into the cell.", "start": 742.71, "duration": 2.28}, {"text": "Does that makes sense?", "start": 744.99, "duration": 2.91}, {"text": "This is our-- this is sort\nof a simplified symbol", "start": 747.9, "duration": 5.06}, {"text": "for a voltage-measuring device.", "start": 752.96, "duration": 2.73}, {"text": "The voltage difference\nbetween the inside of the cell", "start": 755.69, "duration": 2.94}, {"text": "and the outside of the cell\nis what we're measuring here,", "start": 758.63, "duration": 3.03}, {"text": "and that difference is called\nthe membrane potential.", "start": 761.66, "duration": 3.27}, {"text": "It's the voltage difference\nbetween the inside", "start": 764.93, "duration": 3.63}, {"text": "and the outside of the\nmembrane, all right?", "start": 768.56, "duration": 2.91}, {"text": "Any questions about that?", "start": 771.47, "duration": 1.5}, {"text": "Yes?", "start": 772.97, "duration": 0.7}, {"text": "AUDIENCE: There's a narrow\nresistance for [INAUDIBLE]..", "start": 773.67, "duration": 2.3}, {"text": "MICHALE FEE: What's that?", "start": 775.97, "duration": 0.757}, {"text": "AUDIENCE: The resistance for--", "start": 776.727, "duration": 1.193}, {"text": "MICHALE FEE: Yes,\nbut we're going", "start": 777.92, "duration": 0.69}, {"text": "to do it one piece at a time.", "start": 778.61, "duration": 1.39}, {"text": "So we're going to\nstart with a capacitor.", "start": 780.0, "duration": 1.96}, {"text": "The resistor will\ncome in a few slides.", "start": 781.96, "duration": 2.38}, {"text": "Yes?", "start": 787.75, "duration": 1.348}, {"text": "AUDIENCE: So the [INAUDIBLE].", "start": 789.098, "duration": 1.437}, {"text": "MICHALE FEE: Exactly.", "start": 797.455, "duration": 0.875}, {"text": "So we've simplified our\nneurons so that it's", "start": 798.33, "duration": 2.46}, {"text": "just an insulating shell, OK?", "start": 800.79, "duration": 3.51}, {"text": "No ion channels, no\ncurrent anywhere else.", "start": 804.3, "duration": 2.79}, {"text": "If we want to inject current\ninto this simple model neuron,", "start": 807.09, "duration": 3.93}, {"text": "we have to inject it through\nthis electrode here, OK?", "start": 811.02, "duration": 3.68}, {"text": "So we're just going down\nto the very simplest case,", "start": 814.7, "duration": 5.03}, {"text": "because this is already\nkind of interesting enough", "start": 819.73, "duration": 3.05}, {"text": "to understand just by itself.", "start": 822.78, "duration": 1.41}, {"text": "Yes?", "start": 824.19, "duration": 0.806}, {"text": "AUDIENCE: So if the cell's\nacting as a capacitor,", "start": 824.996, "duration": 2.174}, {"text": "is their energy stored\nin their myelin?", "start": 827.17, "duration": 3.805}, {"text": "MICHALE FEE: The\nenergy is stored", "start": 830.975, "duration": 1.375}, {"text": "in the electric field\nthat crosses the bilayer,", "start": 832.35, "duration": 1.92}, {"text": "and I'll get to\nthat in a second.", "start": 834.27, "duration": 1.375}, {"text": "Any other questions?", "start": 839.48, "duration": 1.05}, {"text": "OK, great questions.", "start": 840.53, "duration": 2.338}, {"text": "All right, so what happens\nwhen we inject current", "start": 842.868, "duration": 2.042}, {"text": "into our neuron?", "start": 844.91, "duration": 0.78}, {"text": "As I said, the current\nsource is pulling charges", "start": 845.69, "duration": 4.05}, {"text": "from the outside and pumping\nthem into the inside,", "start": 849.74, "duration": 4.196}, {"text": "all right?", "start": 853.936, "duration": 2.736}, {"text": "So what happens when goes on?", "start": 856.672, "duration": 6.498}, {"text": "So what we're doing is we\nare injecting current-- let's", "start": 863.17, "duration": 2.66}, {"text": "say this is our capacitor.", "start": 865.83, "duration": 1.75}, {"text": "There are charges, there\nare ions on the inside", "start": 867.58, "duration": 5.35}, {"text": "that are just up against the\ninside of the cell membrane.", "start": 872.93, "duration": 3.45}, {"text": "There are charges\non the outside, OK?", "start": 876.38, "duration": 3.87}, {"text": "And when we inject a charge\nfrom the outside to the inside--", "start": 880.25, "duration": 3.31}, {"text": "let's put one of those\ncharges right here.", "start": 883.56, "duration": 2.15}, {"text": "And we're going to push it\ninto this cell, when you inject", "start": 885.71, "duration": 2.75}, {"text": "a charge, you get\nan excessive charge", "start": 888.46, "duration": 3.64}, {"text": "on the inside of the\ncell membrane, OK?", "start": 892.1, "duration": 3.96}, {"text": "And what does that do?", "start": 896.06, "duration": 1.2}, {"text": "You now have more positive\ncharges inside than outside,", "start": 897.26, "duration": 4.86}, {"text": "like-charges repel--", "start": 902.12, "duration": 2.38}, {"text": "so it pushes one\nof those charges", "start": 904.5, "duration": 2.27}, {"text": "away from the outside\nof the membrane.", "start": 906.77, "duration": 3.683}, {"text": "Does that makes sense?", "start": 910.453, "duration": 0.917}, {"text": "OK, that's kind of interesting.", "start": 913.88, "duration": 1.52}, {"text": "We took a charge, we pushed\nit in, and a charge comes out.", "start": 915.4, "duration": 8.25}, {"text": "Right?", "start": 923.65, "duration": 1.02}, {"text": "We have a current flowing.", "start": 924.67, "duration": 1.62}, {"text": "We have charges coming\nin and charges leaving.", "start": 926.29, "duration": 3.07}, {"text": "We have a current flowing\nthrough an insulator.", "start": 929.36, "duration": 2.77}, {"text": "How is that possible?", "start": 932.13, "duration": 2.38}, {"text": "It's a capacitive current, OK?", "start": 934.51, "duration": 2.24}, {"text": "No charges are actually\npassing through the insulator,", "start": 936.75, "duration": 3.9}, {"text": "but it looks like you\nhave a current flowing.", "start": 940.65, "duration": 3.42}, {"text": "That's called a\ncapacitive current.", "start": 944.07, "duration": 2.4}, {"text": "And we represent that in\nour diagram by a current", "start": 946.47, "duration": 4.85}, {"text": "I sub C, capacitive current that\nflows through the capacitor.", "start": 951.32, "duration": 4.32}, {"text": "Pretty cool, right?", "start": 955.64, "duration": 1.3}, {"text": "You have a current flowing\nthrough an insulator.", "start": 956.94, "duration": 2.21}, {"text": "That's what a capacitor is.", "start": 959.15, "duration": 3.03}, {"text": "OK.", "start": 962.18, "duration": 1.29}, {"text": "Now notice that you\nhave a charge imbalance.", "start": 963.47, "duration": 2.82}, {"text": "You have three positive\ncharges here and only", "start": 966.29, "duration": 2.82}, {"text": "one positive charge here.", "start": 969.11, "duration": 2.35}, {"text": "So there is an excess of two\npositive charges on the inside.", "start": 971.46, "duration": 2.87}, {"text": "That's because we added a\npositive charge to the inside", "start": 974.33, "duration": 3.0}, {"text": "and took away a positive\ncharge from the outside,", "start": 977.33, "duration": 2.31}, {"text": "so that leaves a charge\nimbalance of 2, OK?", "start": 979.64, "duration": 4.04}, {"text": "What do you get between positive\ncharge and negative charge", "start": 983.68, "duration": 3.73}, {"text": "if you hold them\nnext to each other?", "start": 987.41, "duration": 2.04}, {"text": "What is there in between?", "start": 989.45, "duration": 2.61}, {"text": "AUDIENCE: It's attraction.", "start": 992.06, "duration": 1.422}, {"text": "MICHALE FEE: Good,\nit's attraction,", "start": 993.482, "duration": 1.458}, {"text": "but what is it that\ncauses that attraction?", "start": 994.94, "duration": 2.07}, {"text": "Remember yesterday, we talked\nabout a something on a charge", "start": 997.01, "duration": 3.87}, {"text": "produces a force, what is it?", "start": 1000.88, "duration": 1.298}, {"text": "AUDIENCE: Electric field.", "start": 1002.178, "duration": 1.042}, {"text": "MICHALE FEE: Good.", "start": 1003.22, "duration": 0.75}, {"text": "So there's an electric\nfield between the positive--", "start": 1003.97, "duration": 3.6}, {"text": "the excess positive charges here\nand the excess negative charges", "start": 1007.57, "duration": 3.66}, {"text": "here, OK?", "start": 1011.23, "duration": 1.56}, {"text": "That's an electric\nfield, all right?", "start": 1012.79, "duration": 3.0}, {"text": "And that electric\nfield stores energy.", "start": 1015.79, "duration": 2.35}, {"text": "How do you know there's\nenergy in this system, though?", "start": 1018.14, "duration": 2.54}, {"text": "What could you do to\ndemonstrate that there is", "start": 1020.68, "duration": 2.19}, {"text": "energy stored in that system?", "start": 1022.87, "duration": 3.76}, {"text": "Any ideas?", "start": 1026.63, "duration": 0.83}, {"text": "You have two plates, two\nmetal plates, let's say,", "start": 1027.46, "duration": 2.95}, {"text": "in the metal version of this.", "start": 1030.41, "duration": 1.76}, {"text": "Separated by an insulator.", "start": 1032.17, "duration": 1.98}, {"text": "What would happen if you\npulled away the insulator?", "start": 1034.15, "duration": 4.13}, {"text": "Those two things would do\nthat again, but louder--", "start": 1038.28, "duration": 2.49}, {"text": "boom.", "start": 1040.77, "duration": 0.87}, {"text": "What does that take\nto make that sound?", "start": 1041.64, "duration": 3.959}, {"text": "Energy, OK?", "start": 1045.599, "duration": 1.711}, {"text": "So there's energy stored\nin that electric field.", "start": 1050.04, "duration": 3.34}, {"text": "So there's a charge imbalance,\nthere's an electric field.", "start": 1053.38, "duration": 2.45}, {"text": "What does an electric field over\nsome distance correspond to?", "start": 1055.83, "duration": 5.098}, {"text": "AUDIENCE: A voltage difference.", "start": 1060.928, "duration": 1.292}, {"text": "MICHALE FEE: A voltage\ndifference, OK?", "start": 1062.22, "duration": 3.004}, {"text": "Now, there's a charge imbalance\nand a voltage difference,", "start": 1068.46, "duration": 3.19}, {"text": "and they're proportional\nto each other.", "start": 1071.65, "duration": 2.41}, {"text": "So there's a\nproportionality constant", "start": 1074.06, "duration": 2.45}, {"text": "that's called the\ncapacitance, all right?", "start": 1076.51, "duration": 3.32}, {"text": "If you can put a lot of charge\nand have a small voltage", "start": 1079.83, "duration": 5.16}, {"text": "difference, that's\na big capacitor.", "start": 1084.99, "duration": 2.25}, {"text": "Now you can get a big capacitor\njust by having a big area.", "start": 1087.24, "duration": 2.5}, {"text": "You can see, you can have a lot\nof charges with a small voltage", "start": 1089.74, "duration": 3.38}, {"text": "difference if you have big\nplates on your capacitor, OK?", "start": 1093.12, "duration": 5.49}, {"text": "So the capacitance is actually\nproportional to the area", "start": 1098.61, "duration": 3.15}, {"text": "of the plates,\nand it's inversely", "start": 1101.76, "duration": 1.5}, {"text": "proportional to the\ndistance between them.", "start": 1103.26, "duration": 2.8}, {"text": "It's a very thin\nmembrane, which means", "start": 1106.06, "duration": 3.2}, {"text": "you can get a lot of\ncapacitance in a tiny area, OK?", "start": 1109.26, "duration": 4.44}, {"text": "That's pretty cool.", "start": 1113.7, "duration": 3.23}, {"text": "All right, any questions?", "start": 1116.93, "duration": 2.98}, {"text": "So charge is coulombs, and there\nare 6 times 10 to the charges", "start": 1119.91, "duration": 4.17}, {"text": "in a coulomb, the\nelemental charges, electron", "start": 1124.08, "duration": 2.94}, {"text": "or monovalent ion charges.", "start": 1127.02, "duration": 4.888}, {"text": "Voltage is in units of\nvolts, and the capacitance", "start": 1131.908, "duration": 2.042}, {"text": "is in units of farads.", "start": 1133.95, "duration": 1.32}, {"text": "Any questions?", "start": 1138.72, "duration": 2.3}, {"text": "All right.", "start": 1141.02, "duration": 1.62}, {"text": "So we have our relation between\nvoltage difference and charge", "start": 1142.64, "duration": 4.7}, {"text": "difference.", "start": 1147.34, "duration": 1.43}, {"text": "And what we're\ngoing to do is we're", "start": 1148.77, "duration": 2.23}, {"text": "going to calculate this\ncapacitive current.", "start": 1151.0, "duration": 3.48}, {"text": "How do you think\nwe would calculate", "start": 1154.48, "duration": 2.28}, {"text": "the capacitive current?", "start": 1156.76, "duration": 1.02}, {"text": "Well, the capacitive\ncurrent is just", "start": 1161.31, "duration": 3.34}, {"text": "the rate at which the charge\nimbalance is changing, right?", "start": 1164.65, "duration": 5.25}, {"text": "Current is just charge\nper unit of time.", "start": 1169.9, "duration": 3.26}, {"text": "OK?", "start": 1173.16, "duration": 0.5}, {"text": "So we're going to calculate the\ncapacitive current as the time", "start": 1173.66, "duration": 3.68}, {"text": "rate of change of the charge--", "start": 1177.34, "duration": 1.56}, {"text": "and I've dropped\nthe deltas here.", "start": 1178.9, "duration": 2.67}, {"text": "So capacitive current\nis dQ/dt, all right?", "start": 1181.57, "duration": 4.91}, {"text": "And remember that Q is just\nCV, so the capacitive current", "start": 1186.48, "duration": 4.245}, {"text": "is just C dV/dt, and\nthe Vm here represents", "start": 1190.725, "duration": 3.765}, {"text": "the membrane potential, OK?", "start": 1194.49, "duration": 2.64}, {"text": "So the capacitive current\nthrough a membrane", "start": 1197.13, "duration": 3.63}, {"text": "is just the capacitance\ntimes the time rate of change", "start": 1200.76, "duration": 3.36}, {"text": "of the membrane potential.", "start": 1204.12, "duration": 3.75}, {"text": "Any questions?", "start": 1207.87, "duration": 2.168}, {"text": "OK.", "start": 1210.038, "duration": 0.932}, {"text": "Pretty straightforward.", "start": 1210.97, "duration": 1.96}, {"text": "Now what we're\ngoing to do now is", "start": 1212.93, "duration": 2.51}, {"text": "we're going to relate\nthe injected charge", "start": 1215.44, "duration": 4.17}, {"text": "to the-- sorry, the injected\ncurrent to the capacitor.", "start": 1219.61, "duration": 3.12}, {"text": "And what does Kirchhoff's\ncurrent law tell us?", "start": 1222.73, "duration": 2.95}, {"text": "It tells us that the amount of\ncurrent going into this wire", "start": 1225.68, "duration": 3.29}, {"text": "has to be equal to the amount\nof current leaving that wire.", "start": 1228.97, "duration": 3.86}, {"text": "OK?", "start": 1232.83, "duration": 0.5}, {"text": "So we can write that\ndown as follows.", "start": 1233.33, "duration": 2.39}, {"text": "The difference in sign here is\nbecause the electrode current", "start": 1235.72, "duration": 3.6}, {"text": "is defined as positive\ninward, the capacitive current", "start": 1239.32, "duration": 3.54}, {"text": "is defined as positive outward.", "start": 1242.86, "duration": 4.108}, {"text": "OK?", "start": 1246.968, "duration": 0.5}, {"text": "So you can see that\nwe just calculated", "start": 1254.95, "duration": 3.0}, {"text": "the capacitive\ncurrent, it's C dV/dt,", "start": 1257.95, "duration": 2.16}, {"text": "so we can just\nplug that in here,", "start": 1260.11, "duration": 2.07}, {"text": "and now we see this\nvery simple relation", "start": 1262.18, "duration": 2.19}, {"text": "between the injected\ncurrent and the voltage.", "start": 1264.37, "duration": 3.88}, {"text": "And again, the current\nhas unit of amperes,", "start": 1274.75, "duration": 2.21}, {"text": "which is coulombs per second.", "start": 1276.96, "duration": 1.32}, {"text": "OK, so we have that.", "start": 1280.8, "duration": 2.31}, {"text": "Now we have a\ndifferential equation", "start": 1283.11, "duration": 1.83}, {"text": "that describes the relation\nbetween current and voltage,", "start": 1284.94, "duration": 2.46}, {"text": "we can just integrate\nit to get the solution.", "start": 1287.4, "duration": 5.19}, {"text": "So that membrane\npotential will just", "start": 1292.59, "duration": 2.34}, {"text": "be some initial membrane\npotential at time 0", "start": 1294.93, "duration": 4.2}, {"text": "plus 1 over C integral over\ntime of the injected current.", "start": 1299.13, "duration": 6.06}, {"text": "Just integrate both sides.", "start": 1310.89, "duration": 1.41}, {"text": "You get V here, you get\nintegral of I there,", "start": 1312.3, "duration": 3.06}, {"text": "and divide both sides\nby C. Any questions?", "start": 1315.36, "duration": 8.848}, {"text": "It's either really\nconfusing or really obvious.", "start": 1324.208, "duration": 4.362}, {"text": "Yeah?", "start": 1328.57, "duration": 0.5}, {"text": "Everybody OK?", "start": 1329.07, "duration": 1.66}, {"text": "All right, good.", "start": 1330.73, "duration": 1.28}, {"text": "Now what is this?", "start": 1332.01, "duration": 0.9}, {"text": "What is the integral\nof current over time?", "start": 1332.91, "duration": 4.96}, {"text": "AUDIENCE: It's\ncharge [INAUDIBLE]", "start": 1337.87, "duration": 1.66}, {"text": "MICHALE FEE: Good.", "start": 1339.53, "duration": 0.75}, {"text": "It's the amount of charge\nyou injected between time", "start": 1340.28, "duration": 3.0}, {"text": "0 and time t, right?", "start": 1343.28, "duration": 2.4}, {"text": "And what is the amount of charge\nyou inject-- if I tell you", "start": 1345.68, "duration": 5.07}, {"text": "that I injected an amount of\ncharge delta Q, how much did", "start": 1350.75, "duration": 4.44}, {"text": "I change the voltage?", "start": 1355.19, "duration": 0.94}, {"text": "Delta V is delta Q over\nC, and that's exactly.", "start": 1363.38, "duration": 2.58}, {"text": "So the voltage is just\nthe starting voltage", "start": 1365.96, "duration": 2.91}, {"text": "plus delta voltage.", "start": 1368.87, "duration": 2.87}, {"text": "Does that makes sense?", "start": 1371.74, "duration": 2.38}, {"text": "This integral here is just--", "start": 1374.12, "duration": 2.88}, {"text": "that part is just\nthe amount of charge", "start": 1377.0, "duration": 2.43}, {"text": "you injected divided by C gives\nyou the change in the voltage.", "start": 1379.43, "duration": 3.66}, {"text": "So the voltage is just the\nstarting voltage plus delta V,", "start": 1383.09, "duration": 5.25}, {"text": "OK?", "start": 1388.34, "duration": 1.21}, {"text": "Yes?", "start": 1389.55, "duration": 0.5}, {"text": "AUDIENCE: [INAUDIBLE]", "start": 1390.05, "duration": 1.838}, {"text": "MICHALE FEE: What's that?", "start": 1391.888, "duration": 1.042}, {"text": "AUDIENCE: [INAUDIBLE]", "start": 1392.93, "duration": 0.983}, {"text": "MICHALE FEE: Oh.", "start": 1393.913, "duration": 0.667}, {"text": "Because this equation\nhere just came from here.", "start": 1394.58, "duration": 5.76}, {"text": "That was our charge--", "start": 1400.34, "duration": 1.51}, {"text": "our relation between charge\nbalance and voltage difference.", "start": 1401.85, "duration": 4.28}, {"text": "Yeah?", "start": 1406.13, "duration": 0.5}, {"text": "If it's not clear, just\nplease ask, thank you.", "start": 1410.41, "duration": 2.41}, {"text": "OK.", "start": 1415.99, "duration": 1.01}, {"text": "There we go.", "start": 1417.0, "duration": 0.73}, {"text": "So what is the\ninterval constant?", "start": 1417.73, "duration": 7.31}, {"text": "It's just some constant\ntimes time, right?", "start": 1425.04, "duration": 2.94}, {"text": "So our voltage is just\nsome initial voltage", "start": 1427.98, "duration": 3.27}, {"text": "plus the injected current\nover C times time.", "start": 1431.25, "duration": 4.51}, {"text": "And so you can see where\nthis comes from, right?", "start": 1435.76, "duration": 2.24}, {"text": "When you turn the\ncurrent on, the voltage", "start": 1438.0, "duration": 2.34}, {"text": "just increases\nlinearly over time", "start": 1440.34, "duration": 3.81}, {"text": "with a slope that's given\nby the current divided", "start": 1444.15, "duration": 4.44}, {"text": "by the capacitance.", "start": 1448.59, "duration": 1.566}, {"text": "OK?", "start": 1450.156, "duration": 0.5}, {"text": "All right, any questions?", "start": 1458.782, "duration": 4.038}, {"text": "You guys are being very quiet.", "start": 1462.82, "duration": 1.49}, {"text": "This is the point where\nI start feeling nervous,", "start": 1464.31, "duration": 3.0}, {"text": "I went too fast.", "start": 1467.31, "duration": 1.0}, {"text": "Yes?", "start": 1468.31, "duration": 0.8}, {"text": "AUDIENCE: You continually\ndraw the curve for a while--", "start": 1469.11, "duration": 2.25}, {"text": "MICHALE FEE: Yep.", "start": 1471.36, "duration": 0.708}, {"text": "AUDIENCE: [INAUDIBLE]", "start": 1472.068, "duration": 2.012}, {"text": "MICHALE FEE: Yes, it does.", "start": 1474.08, "duration": 1.75}, {"text": "And it breaks at\nabout a volt or so.", "start": 1475.83, "duration": 7.09}, {"text": "Because the electric\nfield gets so strong,", "start": 1482.92, "duration": 2.55}, {"text": "it literally just\nrips the atoms apart", "start": 1485.47, "duration": 3.09}, {"text": "in the molecules of\nthe lipid bilayer.", "start": 1488.56, "duration": 1.795}, {"text": "Yes?", "start": 1493.95, "duration": 0.5}, {"text": "AUDIENCE: Why do you [INAUDIBLE]", "start": 1494.45, "duration": 1.378}, {"text": "MICHALE FEE: Sorry,\nI shouldn't say--", "start": 1495.828, "duration": 1.542}, {"text": "it doesn't rip the atoms apart,\nit rips the molecules apart.", "start": 1497.37, "duration": 4.37}, {"text": "You need much higher\nelectric fields to do that.", "start": 1501.74, "duration": 2.91}, {"text": "Yes?", "start": 1504.65, "duration": 0.81}, {"text": "AUDIENCE: [INAUDIBLE]", "start": 1505.46, "duration": 5.268}, {"text": "MICHALE FEE: Oh.", "start": 1510.728, "duration": 0.667}, {"text": "Because we're integrating\nfrom time 0 to time t.", "start": 1511.395, "duration": 6.045}, {"text": "We want to know the\nvoltage at time t, OK?", "start": 1517.44, "duration": 4.02}, {"text": "We're starting at 0, we're\nintegrating the current", "start": 1521.46, "duration": 2.64}, {"text": "from time 0 to time t,\nwhich is where we're wanting", "start": 1524.1, "duration": 5.56}, {"text": "to know the voltage, right?", "start": 1529.66, "duration": 1.33}, {"text": "So you have to integrate\nthe current from 0 to t.", "start": 1530.99, "duration": 3.02}, {"text": "We can't use t in here.\nt is the endpoint.", "start": 1534.01, "duration": 5.33}, {"text": "Yeah.", "start": 1539.34, "duration": 0.64}, {"text": "Does that makes sense?", "start": 1539.98, "duration": 0.998}, {"text": "Good question, thank you.", "start": 1540.978, "duration": 1.042}, {"text": "OK, everybody all right?", "start": 1550.18, "duration": 1.41}, {"text": "I'm going to stand here until\nI hear one more question.", "start": 1551.59, "duration": 4.18}, {"text": "Yes?", "start": 1555.77, "duration": 0.5}, {"text": "AUDIENCE: [INAUDIBLE]", "start": 1556.27, "duration": 4.213}, {"text": "MICHALE FEE: Oh, here.", "start": 1560.483, "duration": 0.917}, {"text": "Because it's a\ncurrent of value I0.", "start": 1561.4, "duration": 4.44}, {"text": "Great question.", "start": 1565.84, "duration": 1.95}, {"text": "Yes?", "start": 1567.79, "duration": 0.5}, {"text": "AUDIENCE: So to maintain this\nconstant current [INAUDIBLE]", "start": 1568.29, "duration": 3.22}, {"text": "the amount of [INAUDIBLE]\nyou're pumping it and--", "start": 1571.51, "duration": 3.76}, {"text": "MICHALE FEE: Yes.", "start": 1575.27, "duration": 1.14}, {"text": "That's right.", "start": 1576.41, "duration": 0.63}, {"text": "This-- OK, I should have\nmaybe been more clear.", "start": 1577.04, "duration": 2.88}, {"text": "This current source has a\nknob on it that I get to set.", "start": 1579.92, "duration": 4.23}, {"text": "I get to like--", "start": 1584.15, "duration": 2.52}, {"text": "there would be an\napp now, and I'd", "start": 1586.67, "duration": 1.47}, {"text": "pull out my current\nsource app and I", "start": 1588.14, "duration": 2.22}, {"text": "type in 10 milliamps, boom.", "start": 1590.36, "duration": 1.578}, {"text": "And this thing-- because\nthere's a Bluetooth connection", "start": 1591.938, "duration": 2.292}, {"text": "to this thing, and it like sets\nthis thing to 10 milliamps,", "start": 1594.23, "duration": 3.18}, {"text": "and it just keeps pumping\n10 milliamps until you tell", "start": 1597.41, "duration": 2.55}, {"text": "it to do something else, OK?", "start": 1599.96, "duration": 4.16}, {"text": "Yes?", "start": 1604.12, "duration": 0.5}, {"text": "AUDIENCE: [INAUDIBLE] make the\nright direction instead of it", "start": 1604.62, "duration": 3.07}, {"text": "being constant current\nstate that usually--", "start": 1607.69, "duration": 2.617}, {"text": "MICHALE FEE: Oh, OK.", "start": 1610.307, "duration": 0.833}, {"text": "AUDIENCE: --that would\ncreate some weird kind of--", "start": 1611.14, "duration": 2.86}, {"text": "MICHALE FEE: Sure.", "start": 1614.0, "duration": 1.15}, {"text": "Yeah.", "start": 1615.15, "duration": 0.5}, {"text": "What would that be, actually?", "start": 1615.65, "duration": 1.23}, {"text": "If you put in a linear\nramp in current?", "start": 1616.88, "duration": 2.805}, {"text": "It would be a parabolic\nvoltage profile.", "start": 1619.685, "duration": 2.715}, {"text": "Yeah, very good.", "start": 1622.4, "duration": 1.2}, {"text": "That's exactly it.", "start": 1623.6, "duration": 1.23}, {"text": "This current profile that\nyou-- this voltage profile", "start": 1624.83, "duration": 4.8}, {"text": "is literally just the numerical\nintegral of this function.", "start": 1629.63, "duration": 4.03}, {"text": "So all you have to\ndo is look at this", "start": 1633.66, "duration": 1.67}, {"text": "and integrate it in\nyour head, and you can", "start": 1635.33, "duration": 2.16}, {"text": "see what the voltage does, OK?", "start": 1637.49, "duration": 3.18}, {"text": "Great.", "start": 1640.67, "duration": 0.75}, {"text": "That's exactly right.", "start": 1641.42, "duration": 1.56}, {"text": "So let's do another example.", "start": 1642.98, "duration": 1.3}, {"text": "Let's put in a current pulse.", "start": 1644.28, "duration": 2.0}, {"text": "So we start at zero current,\nwe step it up to I0,", "start": 1646.28, "duration": 2.88}, {"text": "we hold it there for tau,\nthen we turn the current off.", "start": 1649.16, "duration": 3.42}, {"text": "So let's start our\nneuron right here.", "start": 1652.58, "duration": 2.1}, {"text": "What's going to happen?", "start": 1654.68, "duration": 1.782}, {"text": "What's your name?", "start": 1656.462, "duration": 0.708}, {"text": "I'm going to ask you\nto do this problem.", "start": 1657.17, "duration": 2.25}, {"text": "What-- yeah.", "start": 1659.42, "duration": 0.79}, {"text": "AUDIENCE: Sammy.", "start": 1660.21, "duration": 0.668}, {"text": "MICHALE FEE: Sammy.", "start": 1660.878, "duration": 0.792}, {"text": "What's this voltage going to do?", "start": 1661.67, "duration": 2.778}, {"text": "AUDIENCE: So I'd say constant.", "start": 1664.448, "duration": 1.482}, {"text": "MICHALE FEE: Good.", "start": 1665.93, "duration": 0.75}, {"text": "Because it's zero current.", "start": 1666.68, "duration": 1.503}, {"text": "Then what's going to happen?", "start": 1668.183, "duration": 1.167}, {"text": "AUDIENCE: And it's\ngoing to [INAUDIBLE]", "start": 1669.35, "duration": 1.26}, {"text": "MICHALE FEE: Good.", "start": 1670.61, "duration": 0.75}, {"text": "AUDIENCE: [INAUDIBLE]", "start": 1671.36, "duration": 1.77}, {"text": "MICHALE FEE: Good.", "start": 1673.13, "duration": 1.164}, {"text": "AUDIENCE: And then the\n[INAUDIBLE] go back to constant", "start": 1674.294, "duration": 3.361}, {"text": "at that point.", "start": 1677.655, "duration": 0.965}, {"text": "MICHALE FEE: Awesome.", "start": 1678.62, "duration": 1.08}, {"text": "That's it.", "start": 1679.7, "duration": 0.67}, {"text": "It's that simple.", "start": 1680.37, "duration": 2.87}, {"text": "OK?", "start": 1683.24, "duration": 2.515}, {"text": "Good.", "start": 1685.755, "duration": 2.795}, {"text": "All right.", "start": 1688.55, "duration": 0.57}, {"text": "Now somebody brought\nup resistors.", "start": 1689.12, "duration": 1.62}, {"text": "Who brought up ion conductances?", "start": 1690.74, "duration": 2.28}, {"text": "Somebody mentioned that.", "start": 1693.02, "duration": 1.68}, {"text": "So that's the next thing\nwe're going to add.", "start": 1697.33, "duration": 2.01}, {"text": "This is sort of the zero\norder model of a neuron.", "start": 1699.34, "duration": 4.24}, {"text": "It has the simplest view and\nit's often not so bad, OK?", "start": 1703.58, "duration": 4.46}, {"text": "For short periods of time.", "start": 1708.04, "duration": 1.96}, {"text": "But neurons actually have\nion channels, all right?", "start": 1710.0, "duration": 3.68}, {"text": "Allow current to flow\nthrough the membrane.", "start": 1713.68, "duration": 2.86}, {"text": "So we're going to start\ntoday by analyzing", "start": 1716.54, "duration": 1.76}, {"text": "the case of the simplest\nkind of ion channel", "start": 1718.3, "duration": 2.58}, {"text": "which is the kind of ion channel\nyou get when you take a needle", "start": 1720.88, "duration": 2.73}, {"text": "and you poke a hole\nin the membrane, OK?", "start": 1723.61, "duration": 4.06}, {"text": "It's called the leak\nor a hole, all right?", "start": 1727.67, "duration": 4.36}, {"text": "And we're going to analyze\nwhat our neuron does", "start": 1732.03, "duration": 2.65}, {"text": "when you do that.", "start": 1734.68, "duration": 0.73}, {"text": "So what we're going to find\nis that the ion channel--", "start": 1735.41, "duration": 5.08}, {"text": "a leak conductance, it can\nbe represented in our model", "start": 1740.49, "duration": 3.91}, {"text": "simply by a resistor, OK?", "start": 1744.4, "duration": 4.67}, {"text": "And we're going to have our\ncapacitive current, membrane", "start": 1749.07, "duration": 3.15}, {"text": "capacitive current, and a\nmembrane ionic current that's", "start": 1752.22, "duration": 4.08}, {"text": "due to ions flowing through ion\nchannels in the membrane, OK?", "start": 1756.3, "duration": 4.4}, {"text": "And that current will be--", "start": 1764.41, "duration": 1.66}, {"text": "we're going to call that\nour leak resistance,", "start": 1766.07, "duration": 3.06}, {"text": "and that current will\nbe our leak current, OK?", "start": 1769.13, "duration": 6.6}, {"text": "So now, Kirchhoff's\ncurrent law tells us what?", "start": 1775.73, "duration": 2.76}, {"text": "That the leak current plus\nthe capacitive current", "start": 1778.49, "duration": 3.57}, {"text": "has to equal the injected\ncurrent, all right?", "start": 1782.06, "duration": 3.668}, {"text": "We know the capacitive\ncurrent is just C dV/dt,", "start": 1790.71, "duration": 3.15}, {"text": "so we just plug that\nin, and now we have I", "start": 1793.86, "duration": 2.28}, {"text": "leak plus C dV/dt equals the\ninjected electrode current.", "start": 1796.14, "duration": 4.02}, {"text": "That is called membrane\nionic current, that", "start": 1802.79, "duration": 3.09}, {"text": "is called membrane\ncapacitive current,", "start": 1805.88, "duration": 2.62}, {"text": "and that is our\nelectrode current.", "start": 1808.5, "duration": 2.73}, {"text": "There's a sign convention\nin neuroscience,", "start": 1811.23, "duration": 4.5}, {"text": "which is that membrane\nionic currents that", "start": 1815.73, "duration": 2.87}, {"text": "are outward from the\ninside of the cell", "start": 1818.6, "duration": 2.25}, {"text": "to the outside of the cell\nmembrane are positive in sign.", "start": 1820.85, "duration": 4.56}, {"text": "Positive charges leaving the\ncell have a positive sign.", "start": 1825.41, "duration": 4.31}, {"text": "It's just convention, it\ncould have been the other way.", "start": 1829.72, "duration": 3.29}, {"text": "But you have to choose\nsomething, so that's what--", "start": 1833.01, "duration": 4.12}, {"text": "I think it was Hodgkin\nand Huxley, actually,", "start": 1837.13, "duration": 2.73}, {"text": "who decided that.", "start": 1839.86, "duration": 2.13}, {"text": "Inward currents, positive\ncharges entering the cell", "start": 1841.99, "duration": 2.7}, {"text": "through the membrane going\nthis way from extracellular", "start": 1844.69, "duration": 2.46}, {"text": "to intracellular, are\ndefined as negative.", "start": 1847.15, "duration": 4.383}, {"text": "Electrode currents,\nthe other way.", "start": 1851.533, "duration": 1.417}, {"text": "Electrode current--\ninward current is--", "start": 1852.95, "duration": 2.46}, {"text": "into the cell is positive.", "start": 1855.41, "duration": 2.072}, {"text": "OK, so we're going to poke\na hole in our membrane", "start": 1860.86, "duration": 2.58}, {"text": "and we're going to model that\nion channel using Ohm's law.", "start": 1863.44, "duration": 5.42}, {"text": "So the leak current is just\nmembrane potential divided", "start": 1868.86, "duration": 3.3}, {"text": "by resistance, leak resistance.", "start": 1872.16, "duration": 3.06}, {"text": "So what do we get if\nwe plug this into our--", "start": 1879.95, "duration": 2.9}, {"text": "I leak plus I capacitance?", "start": 1882.85, "duration": 2.2}, {"text": "Capacitive equals\ninjected current.", "start": 1885.05, "duration": 2.52}, {"text": "We get V membrane potential,\nVm over RL plus C dV/dt", "start": 1887.57, "duration": 5.07}, {"text": "equals injected current, OK?", "start": 1892.64, "duration": 3.655}, {"text": "We multiply both sides by\nresistance, we get V plus RC--", "start": 1899.07, "duration": 6.39}, {"text": "that why it's\ncalled an RC model--", "start": 1905.46, "duration": 2.86}, {"text": "dV/dt equals leak\nresistance times", "start": 1908.32, "duration": 3.94}, {"text": "the injected current, all right?", "start": 1912.26, "duration": 4.1}, {"text": "Now that's looking a\nlittle complicated,", "start": 1916.36, "duration": 2.38}, {"text": "but we're going to\nsimplify things now.", "start": 1918.74, "duration": 3.2}, {"text": "Tau-- I'm sorry, RC is\nresistance times capacitance,", "start": 1921.94, "duration": 4.03}, {"text": "and it turns out, that\nhas units of time.", "start": 1925.97, "duration": 3.3}, {"text": "And so we're going\nto call that tau--", "start": 1929.27, "duration": 3.84}, {"text": "got a little ahead of myself.", "start": 1933.11, "duration": 1.657}, {"text": "That's called tau,\nwe're going to make", "start": 1934.767, "duration": 1.583}, {"text": "that substitution in a minute.", "start": 1936.35, "duration": 2.57}, {"text": "But first we're going to\ncalculate the steady state", "start": 1938.92, "duration": 2.25}, {"text": "solution to that\nlittle equation, OK?", "start": 1941.17, "duration": 2.88}, {"text": "So bear with me, hang\non, it's all going", "start": 1944.05, "duration": 2.487}, {"text": "to make sense in a minute.", "start": 1946.537, "duration": 1.083}, {"text": "Does anyone know how to\ncalculate the steady state", "start": 1950.947, "duration": 2.083}, {"text": "solution of a\ndifferential equation?", "start": 1953.03, "duration": 2.62}, {"text": "Yes?", "start": 1955.65, "duration": 0.5}, {"text": "AUDIENCE: [INAUDIBLE]", "start": 1956.15, "duration": 1.14}, {"text": "MICHALE FEE: Good.", "start": 1957.29, "duration": 0.75}, {"text": "What's your name?", "start": 1958.04, "duration": 0.57}, {"text": "AUDIENCE: Rebecca.", "start": 1958.61, "duration": 0.75}, {"text": "MICHALE FEE: Rebecca.", "start": 1959.36, "duration": 1.55}, {"text": "So you said the derivative--", "start": 1960.91, "duration": 1.96}, {"text": "so let's do that.", "start": 1962.87, "duration": 1.4}, {"text": "Set dV/dt equal to 0.", "start": 1964.27, "duration": 1.58}, {"text": "And what do you find?", "start": 1968.55, "duration": 2.09}, {"text": "Sorry, we flashed\nthe answer up there.", "start": 1970.64, "duration": 1.85}, {"text": "What do you get if you\nsaid dV/dt equals 0?", "start": 1972.49, "duration": 3.636}, {"text": "AUDIENCE: [INAUDIBLE]", "start": 1976.126, "duration": 1.734}, {"text": "MICHALE FEE: Good.", "start": 1977.86, "duration": 0.93}, {"text": "So you inject some\ncurrent, we're", "start": 1978.79, "duration": 2.9}, {"text": "going to hold the current\nconstant, let's say, OK?", "start": 1981.69, "duration": 2.84}, {"text": "We've put some current in\nand we hold it constant.", "start": 1984.53, "duration": 4.19}, {"text": "The voltage will change,\nand eventually things", "start": 1988.72, "duration": 2.49}, {"text": "will settle down and\nthe dV/dt will go to 0.", "start": 1991.21, "duration": 4.42}, {"text": "At that point, we\nknow the voltage.", "start": 1995.63, "duration": 2.55}, {"text": "It's just RL times Ie.", "start": 1998.18, "duration": 3.66}, {"text": "What is the voltage equals\nresistance times current?", "start": 2001.84, "duration": 3.18}, {"text": "What is that?", "start": 2005.02, "duration": 1.087}, {"text": "AUDIENCE: Ohm's law.", "start": 2006.107, "duration": 0.833}, {"text": "MICHALE FEE: Ohm's law.", "start": 2006.94, "duration": 2.25}, {"text": "It's just when we inject\ncurrent, a bunch of stuff", "start": 2009.19, "duration": 4.6}, {"text": "happens, and when\nthe dust settles,", "start": 2013.79, "duration": 3.93}, {"text": "the voltage difference is\njust the injected current", "start": 2017.72, "duration": 3.86}, {"text": "divided by the resistance.", "start": 2021.58, "duration": 3.51}, {"text": "Does that makes sense?", "start": 2025.09, "duration": 1.33}, {"text": "Yes?", "start": 2026.42, "duration": 0.5}, {"text": "AUDIENCE: Where is [INAUDIBLE]", "start": 2026.92, "duration": 5.647}, {"text": "MICHALE FEE: Well, right\nnow we just took a needle", "start": 2032.567, "duration": 2.083}, {"text": "and poked a hole in our cell.", "start": 2034.65, "duration": 2.73}, {"text": "So--", "start": 2037.38, "duration": 1.07}, {"text": "AUDIENCE: How big the hole is?", "start": 2038.45, "duration": 1.25}, {"text": "MICHALE FEE: Yep, exactly.", "start": 2039.7, "duration": 1.79}, {"text": "It's how big the hole is.", "start": 2041.49, "duration": 2.04}, {"text": "Now cells-- real cells\ndo have leak channels.", "start": 2043.53, "duration": 4.42}, {"text": "They're actually\nion channels that", "start": 2047.95, "duration": 3.68}, {"text": "leak kind of any\nion that's in there.", "start": 2051.63, "duration": 2.96}, {"text": "It's not very common.", "start": 2054.59, "duration": 3.708}, {"text": "And you'll see why in a minute.", "start": 2058.298, "duration": 1.292}, {"text": "Actually, that's not quite true.", "start": 2062.87, "duration": 3.269}, {"text": "There are ion channels that\nlook essentially like leaks,", "start": 2066.139, "duration": 4.941}, {"text": "and it turns out\nthat the ion channels", "start": 2071.08, "duration": 4.309}, {"text": "that many neurotransmitter\nreceptors like", "start": 2075.389, "duration": 4.201}, {"text": "glutamate and acetylcholine,\nthe ion channels actually", "start": 2079.59, "duration": 4.379}, {"text": "look like little leaks.", "start": 2083.969, "duration": 1.381}, {"text": "They pass multiple ions that\nmakes them look like leaks.", "start": 2085.35, "duration": 4.86}, {"text": "OK.", "start": 2095.69, "duration": 0.82}, {"text": "So in steady state, the membrane\npotential goes to RL times Ie,", "start": 2096.51, "duration": 5.7}, {"text": "and we call that voltage\nsomething special, V infinity,", "start": 2102.21, "duration": 4.47}, {"text": "because it's the voltage that\nthe system reaches at time", "start": 2106.68, "duration": 4.26}, {"text": "equals infinity, OK?", "start": 2110.94, "duration": 3.82}, {"text": "Any questions about that?", "start": 2114.76, "duration": 1.09}, {"text": "OK.", "start": 2118.57, "duration": 0.5}, {"text": "So we're going to just rewrite\nthis equation as Vm plus tau", "start": 2119.07, "duration": 5.58}, {"text": "dV/dt equals V infinity.", "start": 2124.65, "duration": 2.02}, {"text": "And that equation we're\ngoing to see over and over", "start": 2126.67, "duration": 3.5}, {"text": "and over again in this class\nin many different contexts, all", "start": 2130.17, "duration": 3.88}, {"text": "right?", "start": 2134.05, "duration": 0.5}, {"text": "It's a first order linear\ndifferential equation", "start": 2134.55, "duration": 2.28}, {"text": "and it's very powerful, so I\nwant you to get used to it.", "start": 2136.83, "duration": 5.87}, {"text": "So what does this mean?", "start": 2142.7, "duration": 3.4}, {"text": "So let's rewrite this\nequation a little bit.", "start": 2146.1, "duration": 2.31}, {"text": "Let's move this term\nto the other side", "start": 2148.41, "duration": 3.65}, {"text": "and divide both sides by\ntau, and here's what you get.", "start": 2152.06, "duration": 3.0}, {"text": "dV/dt equals minus\n1 over tau V minus--", "start": 2155.06, "duration": 4.89}, {"text": "times V minus V infinity.", "start": 2159.95, "duration": 3.885}, {"text": "OK?", "start": 2163.835, "duration": 2.795}, {"text": "Now let's take a look at what\nthe derivative dV/dt looks", "start": 2166.63, "duration": 3.89}, {"text": "like as a function of voltage.", "start": 2170.52, "duration": 1.28}, {"text": "Yes?", "start": 2171.8, "duration": 0.5}, {"text": "AUDIENCE: So why\ncouldn't we have said", "start": 2172.3, "duration": 1.583}, {"text": "we didn't mean to [INAUDIBLE].", "start": 2173.883, "duration": 2.377}, {"text": "MICHALE FEE: V infinity\nis defined as RL times Ie.", "start": 2180.22, "duration": 5.334}, {"text": "AUDIENCE: Oh, so\nthat's a [INAUDIBLE]..", "start": 2185.554, "duration": 1.796}, {"text": "MICHALE FEE: It's a definition.", "start": 2187.35, "duration": 1.41}, {"text": "Sorry, I should have put\nlike three lines there", "start": 2188.76, "duration": 3.14}, {"text": "to indicate that\nit's the definition.", "start": 2191.9, "duration": 1.71}, {"text": "AUDIENCE: OK.", "start": 2193.61, "duration": 0.88}, {"text": "MICHALE FEE: Yeah.", "start": 2194.49, "duration": 0.75}, {"text": "Sorry, that's a very\nimportant question.", "start": 2195.24, "duration": 2.45}, {"text": "What's your name?", "start": 2197.69, "duration": 0.986}, {"text": "AUDIENCE: Rishi.", "start": 2198.676, "duration": 0.894}, {"text": "MICHALE FEE: Rishi.", "start": 2199.57, "duration": 0.54}, {"text": "OK.", "start": 2200.11, "duration": 0.5}, {"text": "I'm going to make an\nattempt to remember names.", "start": 2200.61, "duration": 2.765}, {"text": "So is everyone clear about that?", "start": 2206.09, "duration": 2.03}, {"text": "V infinity is defined\nas the resistance", "start": 2208.12, "duration": 4.3}, {"text": "times this injected current.", "start": 2212.42, "duration": 1.66}, {"text": "So the injected current, when we\ninject current into our neuron,", "start": 2214.08, "duration": 4.7}, {"text": "you're changing V infinity, OK?", "start": 2218.78, "duration": 3.37}, {"text": "You're controlling it.", "start": 2222.15, "duration": 1.953}, {"text": "Does that makes sense?", "start": 2224.103, "duration": 0.917}, {"text": "OK.", "start": 2228.57, "duration": 0.62}, {"text": "So let's look at how\nthe derivative changes", "start": 2229.19, "duration": 2.848}, {"text": "as a function of voltage,\nit's very simple.", "start": 2232.038, "duration": 1.792}, {"text": "Bear with me.", "start": 2233.83, "duration": 0.7}, {"text": "All of this is\ngoing to crystallize", "start": 2234.53, "duration": 2.49}, {"text": "in your mind in one beautiful\nconstruct very shortly.", "start": 2237.02, "duration": 4.2}, {"text": "Yes?", "start": 2241.22, "duration": 0.843}, {"text": "AUDIENCE: [INAUDIBLE]", "start": 2242.063, "duration": 3.381}, {"text": "MICHALE FEE: Yep.", "start": 2245.444, "duration": 2.116}, {"text": "Resistance times capacitance\nhas units time, OK?", "start": 2247.56, "duration": 5.72}, {"text": "And so we call it tau.", "start": 2253.28, "duration": 1.47}, {"text": "Tau is just a constant, OK?", "start": 2254.75, "duration": 2.97}, {"text": "So hang on, bear with me.", "start": 2257.72, "duration": 2.89}, {"text": "The derivative is a\nfunction of voltage.", "start": 2260.61, "duration": 3.94}, {"text": "And at V equals V infinity,\nthe derivative is 0, right?", "start": 2264.55, "duration": 5.3}, {"text": "That's the definition\nof the infinity,", "start": 2273.42, "duration": 2.11}, {"text": "it's the voltage at which\nthe derivative is 0.", "start": 2275.53, "duration": 4.046}, {"text": "Yeah?", "start": 2279.576, "duration": 2.814}, {"text": "And the voltage is less than\nV infinity, the derivative", "start": 2282.39, "duration": 7.1}, {"text": "is positive, right?", "start": 2289.49, "duration": 3.78}, {"text": "When the voltage is\nbelow the infinity,", "start": 2293.27, "duration": 2.4}, {"text": "the derivative of\nvoltage is positive.", "start": 2295.67, "duration": 2.25}, {"text": "So what is the voltage doing?", "start": 2297.92, "duration": 2.9}, {"text": "It's approaching V infinity.", "start": 2300.82, "duration": 2.17}, {"text": "If the voltage is\nabove V infinity,", "start": 2302.99, "duration": 3.1}, {"text": "voltage greater than V infinity,\nthe derivative is negative.", "start": 2306.09, "duration": 4.5}, {"text": "So voltage does what?", "start": 2310.59, "duration": 2.365}, {"text": "AUDIENCE: [INAUDIBLE]", "start": 2312.955, "duration": 0.875}, {"text": "MICHALE FEE: Yes, but it's--", "start": 2313.83, "duration": 1.04}, {"text": "AUDIENCE: Approaches--", "start": 2314.87, "duration": 0.917}, {"text": "MICHALE FEE: It\napproaches V infinity.", "start": 2315.787, "duration": 2.073}, {"text": "So no matter where\nvoltage is, it's", "start": 2317.86, "duration": 2.0}, {"text": "always approaching V infinity.", "start": 2319.86, "duration": 1.44}, {"text": "If it's below V infinity,\nthe slope is positive,", "start": 2321.3, "duration": 2.61}, {"text": "and it approaches V infinity.", "start": 2323.91, "duration": 1.83}, {"text": "If it's above V infinity,\nthe slope is negative,", "start": 2325.74, "duration": 4.26}, {"text": "and it approaches V\ninfinity from above.", "start": 2330.0, "duration": 3.24}, {"text": "Pretty cool, right?", "start": 2333.24, "duration": 1.47}, {"text": "So V is always just\nrelaxing toward V infinity.", "start": 2334.71, "duration": 4.98}, {"text": "And how does it get there?", "start": 2339.69, "duration": 1.29}, {"text": "Does it go linearly?", "start": 2340.98, "duration": 1.65}, {"text": "Well, you can see\nthat the slope--", "start": 2342.63, "duration": 1.68}, {"text": "the rate at which\nit approaches V", "start": 2344.31, "duration": 1.74}, {"text": "infinity is proportional to how\nfar away it is from V infinity.", "start": 2346.05, "duration": 4.58}, {"text": "And so it doesn't just go vroom,\nboom, crash into V infinity,", "start": 2350.63, "duration": 3.34}, {"text": "it kind of slowly\napproaches V infinity, OK?", "start": 2353.97, "duration": 8.39}, {"text": "Anybody know what that\nfunction is called?", "start": 2362.36, "duration": 3.53}, {"text": "AUDIENCE: Exponential.", "start": 2365.89, "duration": 1.0}, {"text": "MICHALE FEE: It's an\nexponential, good.", "start": 2366.89, "duration": 3.54}, {"text": "And it approaches with\na timescale of tau.", "start": 2370.43, "duration": 6.49}, {"text": "So if tau is small,\nit approaches quickly.", "start": 2376.92, "duration": 3.51}, {"text": "If tau is long, it\napproaches slow.", "start": 2380.43, "duration": 2.17}, {"text": "You can see that if tau is\nbig, the derivatives are small.", "start": 2382.6, "duration": 5.37}, {"text": "If tau is small, the derivatives\nare bigger, all right?", "start": 2387.97, "duration": 4.034}, {"text": "Any questions about that?", "start": 2400.28, "duration": 1.455}, {"text": "Yes?", "start": 2401.735, "duration": 1.245}, {"text": "AUDIENCE: So a\ntau usually is a--", "start": 2402.98, "duration": 2.231}, {"text": "MICHALE FEE: Sorry,\nsay it again?", "start": 2405.211, "duration": 1.375}, {"text": "AUDIENCE: --times\nequals to tau--", "start": 2406.586, "duration": 1.704}, {"text": "MICHALE FEE: Yes.", "start": 2408.29, "duration": 0.708}, {"text": "AUDIENCE: --is V\ninfinity plus 1 over e.", "start": 2408.998, "duration": 3.092}, {"text": "MICHALE FEE: At time tau, the--", "start": 2412.09, "duration": 3.556}, {"text": "AUDIENCE: Times V0.", "start": 2415.646, "duration": 1.374}, {"text": "MICHALE FEE: At time tau--", "start": 2417.02, "duration": 1.5}, {"text": "at time 0, the difference\nbetween V infinity-- sorry, V", "start": 2418.52, "duration": 3.48}, {"text": "and V infinity is\nV0 minus V infinity.", "start": 2422.0, "duration": 3.33}, {"text": "At time tau, that\ninitial difference", "start": 2425.33, "duration": 2.49}, {"text": "drops by about a third.", "start": 2427.82, "duration": 1.5}, {"text": "AUDIENCE: OK.", "start": 2429.32, "duration": 0.69}, {"text": "MICHALE FEE: About 1 over e,\nwhich I think is 2.7-something,", "start": 2430.01, "duration": 4.21}, {"text": "OK?", "start": 2434.22, "duration": 0.83}, {"text": "So in 1 tau, this\nvoltage difference", "start": 2435.05, "duration": 2.55}, {"text": "falls by about a--\ndrops by about a third.", "start": 2437.6, "duration": 2.65}, {"text": "And in another tau, it\ndrops by another third,", "start": 2440.25, "duration": 2.77}, {"text": "it keeps going, OK?", "start": 2443.02, "duration": 3.95}, {"text": "All right.", "start": 2446.97, "duration": 0.5}, {"text": "So let's just write down\nthe general solution.", "start": 2447.47, "duration": 3.606}, {"text": "The general solution\nfor the case", "start": 2451.076, "duration": 2.274}, {"text": "where you have constant\ncurrent, that voltage difference", "start": 2453.35, "duration": 9.35}, {"text": "from the voltage at\ntime t to V infinity", "start": 2462.7, "duration": 2.67}, {"text": "is just equal to the initial\nvoltage difference times e", "start": 2465.37, "duration": 2.77}, {"text": "to the minus t over tau, OK?", "start": 2468.14, "duration": 3.635}, {"text": "So if t is equal to tau, then\nthis is e to the minus 1,", "start": 2474.55, "duration": 5.4}, {"text": "so the voltage difference will\nbe 1/3 of the original voltage", "start": 2479.95, "duration": 3.78}, {"text": "difference.", "start": 2483.73, "duration": 0.9}, {"text": "Is that clear?", "start": 2484.63, "duration": 2.66}, {"text": "OK.", "start": 2487.29, "duration": 0.5}, {"text": "So now let's see what this\nlooks like in our neuron.", "start": 2487.79, "duration": 4.14}, {"text": "We have our neuron, we\nhave a current pulse,", "start": 2491.93, "duration": 2.39}, {"text": "we have zero current,\nwe turn the current", "start": 2494.32, "duration": 2.94}, {"text": "on to I0 at this time, we\nhold the current constant,", "start": 2497.26, "duration": 3.71}, {"text": "and we turn current off at\nthis time right here, OK?", "start": 2500.97, "duration": 4.69}, {"text": "So what does the voltage do?", "start": 2505.66, "duration": 2.82}, {"text": "Let's go step by step.", "start": 2508.48, "duration": 2.1}, {"text": "The first thing\nis that voltage--", "start": 2510.58, "duration": 1.89}, {"text": "sorry-- the current controls\nwhat in that equation?", "start": 2512.47, "duration": 3.525}, {"text": "The current controls V infinity.", "start": 2518.902, "duration": 4.168}, {"text": "So we can plot V\ninfinity immediately,", "start": 2523.07, "duration": 2.03}, {"text": "because V infinity is\njust the resistance", "start": 2525.1, "duration": 2.34}, {"text": "times the injected current.", "start": 2527.44, "duration": 1.36}, {"text": "So what does V\ninfinity look like?", "start": 2528.8, "duration": 1.42}, {"text": "It's constant here, and then\nwhat happens to V infinity?", "start": 2533.23, "duration": 3.678}, {"text": "AUDIENCE: Increases.", "start": 2536.908, "duration": 2.632}, {"text": "MICHALE FEE: It increases,\nthat's correct, but--", "start": 2539.54, "duration": 2.408}, {"text": "AUDIENCE: It'll\njust be [INAUDIBLE]..", "start": 2541.948, "duration": 1.542}, {"text": "MICHALE FEE: Good.", "start": 2543.49, "duration": 0.75}, {"text": "It will just be the\nresistance times the current.", "start": 2544.24, "duration": 2.08}, {"text": "Resistance is a constant, so V\ninfinity will just go up here,", "start": 2546.32, "duration": 4.566}, {"text": "right?", "start": 2550.886, "duration": 0.5}, {"text": "Good.", "start": 2551.386, "duration": 0.5}, {"text": "It'll go up, and then it\nstays constant at R times I.", "start": 2551.886, "duration": 7.414}, {"text": "And then at this\npoint, the current", "start": 2559.3, "duration": 2.75}, {"text": "goes back to 0, so V infinity\nis resistance time 0,", "start": 2562.05, "duration": 5.37}, {"text": "so V infinity drops back to 0.", "start": 2567.42, "duration": 3.88}, {"text": "Does that makes sense?", "start": 2571.3, "duration": 1.42}, {"text": "That's V infinity, that's\nnot the voltage of the cell.", "start": 2572.72, "duration": 4.44}, {"text": "That's the steady state\nvoltage of the cell.", "start": 2577.16, "duration": 3.72}, {"text": "So now what does voltage\nof the cell actually do?", "start": 2580.88, "duration": 3.89}, {"text": "So let's start our\nvoltage here at 0.", "start": 2587.47, "duration": 3.868}, {"text": "What happens?", "start": 2591.338, "duration": 0.542}, {"text": "Good.", "start": 2595.72, "duration": 1.02}, {"text": "What is it doing?", "start": 2596.74, "duration": 1.73}, {"text": "AUDIENCE: Approaching\nfrom infinity.", "start": 2598.47, "duration": 1.5}, {"text": "MICHALE FEE: Good.", "start": 2599.97, "duration": 0.78}, {"text": "It approaches.", "start": 2600.75, "duration": 1.21}, {"text": "So V at every point\nis relaxing toward V", "start": 2601.96, "duration": 5.69}, {"text": "infinity exponentially, right?", "start": 2607.65, "duration": 3.64}, {"text": "And that looks like--", "start": 2611.29, "duration": 1.08}, {"text": "at some time constant, and that\nlooks like this, all right?", "start": 2612.37, "duration": 7.31}, {"text": "Now what happens here?", "start": 2619.68, "duration": 2.505}, {"text": "AUDIENCE: [INAUDIBLE]", "start": 2622.185, "duration": 0.975}, {"text": "MICHALE FEE: Good.", "start": 2623.16, "duration": 0.75}, {"text": "Because V infinity\nsuddenly change to 0,", "start": 2623.91, "duration": 3.27}, {"text": "and so V relaxes toward\nV infinity exponentially", "start": 2627.18, "duration": 3.39}, {"text": "with some time constant.", "start": 2630.57, "duration": 1.56}, {"text": "OK?", "start": 2637.366, "duration": 0.5}, {"text": "Any questions?", "start": 2641.22, "duration": 1.177}, {"text": "OK.", "start": 2647.87, "duration": 0.5}, {"text": "Now this-- that is our\nRC model neuron, OK?", "start": 2652.08, "duration": 6.61}, {"text": "Resistance times\ncapacitance-- they", "start": 2658.69, "duration": 1.63}, {"text": "got a resistor and a\ncapacitor, but the solutions", "start": 2660.32, "duration": 4.06}, {"text": "are just exponential decays\ntoward some steady state", "start": 2664.38, "duration": 3.36}, {"text": "solution.", "start": 2667.74, "duration": 2.75}, {"text": "Now it turns out\nthat an RC system,", "start": 2670.49, "duration": 4.62}, {"text": "a first order linear system\nacts like a filter, OK?", "start": 2675.11, "duration": 5.54}, {"text": "So remember, our neuron\nthat just has a capacitor", "start": 2680.65, "duration": 4.86}, {"text": "is an integrator, it\nintegrates over time.", "start": 2685.51, "duration": 3.15}, {"text": "When you add a\nresistor, this thing--", "start": 2688.66, "duration": 3.3}, {"text": "it's kind of integrating\nhere, but then it", "start": 2691.96, "duration": 2.25}, {"text": "gets tired and stops\nintegrating, OK?", "start": 2694.21, "duration": 3.42}, {"text": "It relaxes to some steady state.", "start": 2697.63, "duration": 4.23}, {"text": "So this actually\nlooks like a filter.", "start": 2701.86, "duration": 3.89}, {"text": "It takes time to\nrespond to something.", "start": 2705.75, "duration": 4.07}, {"text": "So that system responds well to\nthings that are changing slowly", "start": 2709.82, "duration": 5.73}, {"text": "in time, and it responds\nvery weakly to things that", "start": 2715.55, "duration": 3.6}, {"text": "are changing rapidly in time.", "start": 2719.15, "duration": 2.26}, {"text": "So here's an example--", "start": 2721.41, "duration": 1.16}, {"text": "I'll put together\nthis demonstration.", "start": 2722.57, "duration": 3.78}, {"text": "In red is the injected current.", "start": 2726.35, "duration": 1.93}, {"text": "So if you have long pulses\nof injected current,", "start": 2728.28, "duration": 3.77}, {"text": "the time constant of this\ngarners about 10 milliseconds--", "start": 2732.05, "duration": 3.24}, {"text": "I think this is probably a--", "start": 2735.29, "duration": 1.64}, {"text": "what is that, a 50 or\n100-millisecond pulse?", "start": 2736.93, "duration": 2.82}, {"text": "80--", "start": 2739.75, "duration": 0.5}, {"text": "AUDIENCE: Nanofarads.", "start": 2740.25, "duration": 0.875}, {"text": "MICHALE FEE: Yeah.", "start": 2741.125, "duration": 1.1}, {"text": "You can see that in\nblue is the voltage,", "start": 2742.225, "duration": 2.165}, {"text": "it relaxes toward V infinity.", "start": 2744.39, "duration": 3.28}, {"text": "And then the current goes\noff, it relaxes back.", "start": 2747.67, "duration": 2.33}, {"text": "And you can see that the\nvoltage is responding very well", "start": 2750.0, "duration": 3.51}, {"text": "to the current injection.", "start": 2753.51, "duration": 1.71}, {"text": "But now let's make\nreally short pulses", "start": 2755.22, "duration": 3.2}, {"text": "that are much shorter than tau.", "start": 2758.42, "duration": 2.34}, {"text": "You can see that\nthe voltage starts", "start": 2760.76, "duration": 3.87}, {"text": "relaxing toward V infinity,\nbut it doesn't get very far,", "start": 2764.63, "duration": 2.397}, {"text": "and all of a sudden the\ncurrent's turned off", "start": 2767.027, "duration": 1.833}, {"text": "and it relaxes back.", "start": 2768.86, "duration": 1.68}, {"text": "And so you can plot the\npeak voltage response", "start": 2770.54, "duration": 2.91}, {"text": "as a function of the\nwidth of these pulses,", "start": 2773.45, "duration": 2.77}, {"text": "and you can see that for long\npulses, it responds very well,", "start": 2776.22, "duration": 4.43}, {"text": "but for short pulses--", "start": 2780.65, "duration": 1.87}, {"text": "really responds at all.", "start": 2782.52, "duration": 1.79}, {"text": "And that's called a\nlow pass filter, OK?", "start": 2784.31, "duration": 3.87}, {"text": "It responds well to\nslowly-changing things,", "start": 2788.18, "duration": 3.66}, {"text": "but barely responds to\nrapidly-changing things.", "start": 2791.84, "duration": 3.37}, {"text": "So it's passing low frequencies,\nlow pass filter, OK?", "start": 2795.21, "duration": 5.441}, {"text": "All right.", "start": 2803.34, "duration": 0.73}, {"text": "Any questions?", "start": 2804.07, "duration": 0.69}, {"text": "That was a lot of\nstuff all at once.", "start": 2804.76, "duration": 1.78}, {"text": "Yes?", "start": 2806.54, "duration": 0.5}, {"text": "AUDIENCE: I'm just curious,\nlike on what order is", "start": 2807.04, "duration": 2.86}, {"text": "the capacitance for nanofarads?", "start": 2809.9, "duration": 3.13}, {"text": "MICHALE FEE: OK.", "start": 2813.03, "duration": 1.07}, {"text": "It's 10 nanofarads per--", "start": 2814.1, "duration": 3.66}, {"text": "1 microfarads per\nsquare centimeter.", "start": 2817.76, "duration": 2.23}, {"text": "10 nanofarads per\nsquare millimeter, OK?", "start": 2819.99, "duration": 3.963}, {"text": "We're going to get to\nthat in a second, that's", "start": 2823.953, "duration": 1.917}, {"text": "a great question.", "start": 2825.87, "duration": 1.24}, {"text": "We're going to get to what\nthe actual numbers look like", "start": 2827.11, "duration": 2.84}, {"text": "for real neurons, OK?", "start": 2829.95, "duration": 3.24}, {"text": "I think you had a question.", "start": 2833.19, "duration": 1.45}, {"text": "AUDIENCE: [INAUDIBLE]", "start": 2834.64, "duration": 2.455}, {"text": "MICHALE FEE: Sorry,\nsay it again?", "start": 2837.095, "duration": 1.375}, {"text": "AUDIENCE: Past [INAUDIBLE]?", "start": 2838.47, "duration": 1.4}, {"text": "Is that [INAUDIBLE]\nreacts to [INAUDIBLE]??", "start": 2839.87, "duration": 2.925}, {"text": "MICHALE FEE: What happens\nis it reacts to it,", "start": 2842.795, "duration": 1.875}, {"text": "but because it's\nchanging kind of linearly", "start": 2844.67, "duration": 2.97}, {"text": "at these short times,\nit doesn't get very far.", "start": 2847.64, "duration": 2.58}, {"text": "If the current stays\non for a long time,", "start": 2850.22, "duration": 1.84}, {"text": "you can see it has exactly\nthe same profile here,", "start": 2852.06, "duration": 3.23}, {"text": "but it just has time\nto reach V infinity.", "start": 2855.29, "duration": 2.512}, {"text": "Here, it doesn't have\ntime to reach V infinity,", "start": 2857.802, "duration": 1.958}, {"text": "it just gets a little bit away\nfrom 0 and then it decays back.", "start": 2859.76, "duration": 6.83}, {"text": "Yes?", "start": 2866.59, "duration": 0.76}, {"text": "AUDIENCE: Are there other sorts\nof filters for non-responses", "start": 2867.35, "duration": 2.812}, {"text": "like [INAUDIBLE]?", "start": 2870.162, "duration": 2.768}, {"text": "MICHALE FEE: You can build\ndifferent kinds of filters", "start": 2872.93, "duration": 2.76}, {"text": "from circuits of neurons,\nbut neurons themselves", "start": 2875.69, "duration": 3.3}, {"text": "tend to be high pass filters.", "start": 2878.99, "duration": 4.17}, {"text": "You can-- sorry,\nlow pass filters.", "start": 2883.16, "duration": 2.2}, {"text": "You can make-- so you can put in\ndifferent kinds of ion channels", "start": 2885.36, "duration": 5.48}, {"text": "that change the\nproperties of neurons,", "start": 2890.84, "duration": 3.24}, {"text": "but sort of to first\norder, you should think", "start": 2894.08, "duration": 2.1}, {"text": "of neurons as low pass filters.", "start": 2896.18, "duration": 1.86}, {"text": "Yeah?", "start": 2901.976, "duration": 0.984}, {"text": "AUDIENCE: Can you\nshow the [INAUDIBLE]", "start": 2902.96, "duration": 8.322}, {"text": "MICHALE FEE: I\nwrote it like this--", "start": 2911.282, "duration": 1.458}, {"text": "you can write it as V equals V\ninfinity plus this other stuff,", "start": 2912.74, "duration": 3.24}, {"text": "but I wrote it like this because\nwhat you should really be", "start": 2915.98, "duration": 2.64}, {"text": "seeing here is that the\nvoltage difference from--", "start": 2918.62, "duration": 3.99}, {"text": "time between the voltage and V\ninfinity decays exponentially.", "start": 2922.61, "duration": 5.62}, {"text": "So the distance you are\nfrom V infinity decays", "start": 2928.23, "duration": 3.14}, {"text": "exponentially, OK?", "start": 2931.37, "duration": 2.604}, {"text": "It makes it more\nobvious that you're", "start": 2936.72, "duration": 1.66}, {"text": "decaying toward V infinity, OK?", "start": 2938.38, "duration": 4.535}, {"text": "Yes?", "start": 2946.8, "duration": 1.15}, {"text": "AUDIENCE: If you were to arrange\nlike the physical properties", "start": 2947.95, "duration": 2.542}, {"text": "of the neuron itself,\nyou [INAUDIBLE]", "start": 2950.492, "duration": 5.378}, {"text": "MICHALE FEE: Not-- not really.", "start": 2955.87, "duration": 1.53}, {"text": "Not simply.", "start": 2957.4, "duration": 1.02}, {"text": "You can put in\ncertain ion channels", "start": 2958.42, "duration": 3.63}, {"text": "that could make a neuron less\nresponsive at low frequencies,", "start": 2962.05, "duration": 7.9}, {"text": "OK?", "start": 2969.95, "duration": 0.5}, {"text": "So you can make them kind of\nresponsive to some middle range", "start": 2970.45, "duration": 4.17}, {"text": "of frequencies\nthat won't respond", "start": 2974.62, "duration": 2.645}, {"text": "to very high\nfrequencies and they", "start": 2977.265, "duration": 1.375}, {"text": "won't respond much to\nvery low frequencies,", "start": 2978.64, "duration": 4.4}, {"text": "but for the most\npart, again, just", "start": 2983.04, "duration": 2.04}, {"text": "you should-- at this point,\nlet's just think of them", "start": 2985.08, "duration": 2.25}, {"text": "as low pass filters.", "start": 2987.33, "duration": 2.88}, {"text": "We're going to start\nadding fancy stuff", "start": 2990.21, "duration": 2.73}, {"text": "to our neuron that's going\nto make it more complicated.", "start": 2992.94, "duration": 5.17}, {"text": "So don't get too\nhung up on this.", "start": 2998.11, "duration": 2.96}, {"text": "All right, let me\njust make this point.", "start": 3001.07, "duration": 2.924}, {"text": "This one right\nhere, V equals tau--", "start": 3003.994, "duration": 3.636}, {"text": "V plus tau dV/dt equals V\ninfinity appears everywhere,", "start": 3007.63, "duration": 4.03}, {"text": "it's ubiquitous in physics,\nchemistry, biology, we'll", "start": 3011.66, "duration": 6.26}, {"text": "be using it in multiple\ndifferent contexts", "start": 3017.92, "duration": 2.46}, {"text": "in different parts of\nthe class, and in--", "start": 3020.38, "duration": 4.41}, {"text": "computation, OK?", "start": 3024.79, "duration": 2.13}, {"text": "And even slightly more\ncomplicated versions of this,", "start": 3026.92, "duration": 5.85}, {"text": "like the Michaelis-Menten\nequations in chemistry,", "start": 3032.77, "duration": 4.73}, {"text": "you can kind of understand\nthem in simple terms.", "start": 3037.5, "duration": 2.38}, {"text": "If you like have\na handle on this,", "start": 3039.88, "duration": 3.41}, {"text": "other slightly more\ncomplicated things", "start": 3043.29, "duration": 1.98}, {"text": "become much more intuitive, OK?", "start": 3045.27, "duration": 4.09}, {"text": "All right, so try\nto really make sure", "start": 3049.36, "duration": 3.9}, {"text": "that you understand\nthis equation", "start": 3053.26, "duration": 3.99}, {"text": "and how we derived it, OK?", "start": 3057.25, "duration": 5.0}, {"text": "OK, let's talk about\nthe origin of this--", "start": 3062.25, "duration": 2.79}, {"text": "the timescale of a neuron.", "start": 3065.04, "duration": 1.47}, {"text": "So the tau of a neuron--", "start": 3066.51, "duration": 1.86}, {"text": "of most neurons is about\n100 milliseconds to--", "start": 3068.37, "duration": 3.09}, {"text": "sorry, 10 milliseconds\nto 100 milliseconds,", "start": 3071.46, "duration": 2.19}, {"text": "kind of in that range.", "start": 3073.65, "duration": 1.6}, {"text": "And it comes from the values\nof resistance and capacitance", "start": 3075.25, "duration": 3.35}, {"text": "of a neuron.", "start": 3078.6, "duration": 1.39}, {"text": "So a resistor-- the\nresistance of a neuron--", "start": 3079.99, "duration": 4.67}, {"text": "range of 100 million ohms, OK?", "start": 3084.66, "duration": 5.11}, {"text": "And the capacitance is about\n10 to the minus 10 ohms", "start": 3089.77, "duration": 3.74}, {"text": "or about 100 picofarads.", "start": 3093.51, "duration": 4.13}, {"text": "And you multiply those\ntwo things together", "start": 3097.64, "duration": 2.14}, {"text": "and you get a time constant\nof about 10 milliseconds, OK?", "start": 3099.78, "duration": 5.13}, {"text": "So what that means is if you\ninject current into a neuron,", "start": 3104.91, "duration": 4.6}, {"text": "it takes about 10 to\n100 milliseconds for it", "start": 3109.51, "duration": 2.91}, {"text": "to fully respond to\nthat step of current.", "start": 3112.42, "duration": 5.59}, {"text": "The voltage will\njump up and relax", "start": 3118.01, "duration": 2.25}, {"text": "to the new V infinity in about\n10 to 100 milliseconds, OK?", "start": 3120.26, "duration": 5.25}, {"text": "So let's take a\nlittle bit closer", "start": 3125.51, "duration": 1.68}, {"text": "look at the resistance-- what\nthis resistance in capacitance", "start": 3127.19, "duration": 3.81}, {"text": "looks like in a neuron.", "start": 3131.0, "duration": 3.42}, {"text": "So we've described the\nrelation between leak current", "start": 3134.42, "duration": 4.28}, {"text": "and voltage as current equals\nvoltage over resistance,", "start": 3138.7, "duration": 6.15}, {"text": "but rather than using resistance\nto think about currents flowing", "start": 3144.85, "duration": 4.96}, {"text": "through a membrane, it's\nmuch more useful, usually,", "start": 3149.81, "duration": 3.48}, {"text": "to think about something\ncalled conductance,", "start": 3153.29, "duration": 2.44}, {"text": "and conductance is just\n1 over resistance, OK?", "start": 3155.73, "duration": 3.82}, {"text": "So conductance, G-- and we use\nthe simple G for conductance--", "start": 3159.55, "duration": 4.24}, {"text": "it's equal to 1 over resistance.", "start": 3163.79, "duration": 1.83}, {"text": "So now we can write\nOhm's law as I", "start": 3165.62, "duration": 2.34}, {"text": "equals G times V. Resistance\nhas units of ohms, G--", "start": 3167.96, "duration": 7.86}, {"text": "conductance has units of\ninverse ohms or siemens", "start": 3175.82, "duration": 2.91}, {"text": "is the SI unit for conductance.", "start": 3178.73, "duration": 4.2}, {"text": "So if we have\nconductances, if we", "start": 3182.93, "duration": 3.41}, {"text": "have two-- let's say two ion\nchannels in the membrane,", "start": 3186.34, "duration": 4.06}, {"text": "they operate in parallel.", "start": 3190.4, "duration": 1.43}, {"text": "Current flows through\nthem separately, right?", "start": 3191.83, "duration": 3.295}, {"text": "They're not in series, like\nit flows through one and then", "start": 3195.125, "duration": 2.375}, {"text": "flows through the other, right?", "start": 3197.5, "duration": 1.57}, {"text": "They are in parallel--\nthe current can flow", "start": 3199.07, "duration": 3.08}, {"text": "through both like\nthis up in parallel.", "start": 3202.15, "duration": 4.06}, {"text": "And we can write down the\ncurrent using Kirchhoff's law,", "start": 3206.21, "duration": 3.95}, {"text": "the total current\nis just the sum", "start": 3210.16, "duration": 2.04}, {"text": "of the current through those two\nseparate conductances, right?", "start": 3212.2, "duration": 3.93}, {"text": "Now the total current is--", "start": 3216.13, "duration": 2.01}, {"text": "we can just expand this\nin terms of the inductance", "start": 3218.14, "duration": 2.7}, {"text": "of each one of those.", "start": 3220.84, "duration": 0.91}, {"text": "So the total current is G1\ntimes the voltage difference", "start": 3221.75, "duration": 5.81}, {"text": "plus G2 times the\nvoltage difference", "start": 3227.56, "duration": 3.12}, {"text": "for this conductance.", "start": 3230.68, "duration": 2.93}, {"text": "So the total current is just--", "start": 3233.61, "duration": 1.88}, {"text": "you factor out the V, the total\ncurrent is just G1 plus G2,", "start": 3235.49, "duration": 4.23}, {"text": "so we can write down the total\nconductance as just G1 plus G2.", "start": 3239.72, "duration": 6.19}, {"text": "Does that makes sense?", "start": 3245.91, "duration": 1.38}, {"text": "So conductances in\nparallel add together.", "start": 3247.29, "duration": 2.94}, {"text": "So if we have a piece\nof membrane that's", "start": 3253.563, "duration": 1.667}, {"text": "got some ion channels\nin it-- or holes,", "start": 3255.23, "duration": 3.63}, {"text": "and we add another piece of\nmembrane that kind of has", "start": 3258.86, "duration": 2.22}, {"text": "the same density\nof ion channels,", "start": 3261.08, "duration": 2.36}, {"text": "you have twice the\nholes, twice the current,", "start": 3263.44, "duration": 2.64}, {"text": "and twice the conductance.", "start": 3266.08, "duration": 1.42}, {"text": "So we can write the current\nas conductance times membrane", "start": 3273.23, "duration": 3.17}, {"text": "potential, but we can\nrewrite that conductance", "start": 3276.4, "duration": 2.61}, {"text": "as the area times that\nconductance per unit area,", "start": 3279.01, "duration": 4.67}, {"text": "and that's called specific\nmembrane conductance--", "start": 3283.68, "duration": 3.52}, {"text": "in this case, it's a leak,\nso we call it specific leak", "start": 3287.2, "duration": 2.34}, {"text": "conductance, and it has units\nof conductance per area.", "start": 3289.54, "duration": 4.44}, {"text": "We multiply that by the area and\nwe get that total conductance.", "start": 3297.7, "duration": 5.37}, {"text": "Any questions about this?", "start": 3303.07, "duration": 1.26}, {"text": "No?", "start": 3309.077, "duration": 0.5}, {"text": "So you can see that\nwe can now plot", "start": 3312.92, "duration": 4.27}, {"text": "the current through the membrane\nas a function of voltage.", "start": 3317.19, "duration": 4.75}, {"text": "This is called a\nIV current plotted", "start": 3321.94, "duration": 3.14}, {"text": "as a function of voltage.", "start": 3325.08, "duration": 1.09}, {"text": "You can see that the\ncurrent is linear", "start": 3326.17, "duration": 2.707}, {"text": "as a function of voltage, right?", "start": 3328.877, "duration": 1.333}, {"text": "That's just Ohm's law.", "start": 3330.21, "duration": 3.02}, {"text": "And you can see that for a\nlow conductance, G is small,", "start": 3333.23, "duration": 2.95}, {"text": "so the slope is small.", "start": 3336.18, "duration": 2.2}, {"text": "For a high conductance,\nyou get a lot", "start": 3338.38, "duration": 2.38}, {"text": "of current for a little bit\nof voltage, and so the--", "start": 3340.76, "duration": 2.7}, {"text": "deeper, OK?", "start": 3343.46, "duration": 1.61}, {"text": "So if you plot current versus\nvoltage, you get a curve,", "start": 3345.07, "duration": 3.51}, {"text": "and the slope of that curve is\njust equal to the conductance,", "start": 3348.58, "duration": 5.834}, {"text": "all right?", "start": 3354.414, "duration": 2.386}, {"text": "OK.", "start": 3356.8, "duration": 0.54}, {"text": "Now let's look at capacitance.", "start": 3357.34, "duration": 2.86}, {"text": "The total current through these\ntwo capacitors in parallel", "start": 3360.2, "duration": 4.4}, {"text": "is just the current through\none capacitor plus the current", "start": 3364.6, "duration": 2.54}, {"text": "through the other.", "start": 3367.14, "duration": 1.02}, {"text": "We can write the current through\neach capacitor separately.", "start": 3368.16, "duration": 2.64}, {"text": "I total equals C1\ndV/dt plus C2 dV/dt.", "start": 3370.8, "duration": 5.28}, {"text": "Factor out the dV/dt and you get\nthat the total current is just", "start": 3376.08, "duration": 2.97}, {"text": "C1 plus C2 dV/dt.", "start": 3379.05, "duration": 2.27}, {"text": "So the total capacitance is\nthe sum of the capacitances.", "start": 3381.32, "duration": 4.09}, {"text": "So if you have a\npatch of membrane,", "start": 3385.41, "duration": 2.16}, {"text": "you measure the capacitance, if\nyou put another one next to it,", "start": 3387.57, "duration": 3.52}, {"text": "you'll get the sum of\nthose two capacitances.", "start": 3391.09, "duration": 2.73}, {"text": "So the capacitance\nalso scales with area.", "start": 3393.82, "duration": 2.855}, {"text": "So we can write down the\ntotal membrane capacitance", "start": 3399.27, "duration": 3.32}, {"text": "as capacitance per unit area\ntimes the area of the cell,", "start": 3402.59, "duration": 5.91}, {"text": "right?", "start": 3408.5, "duration": 1.88}, {"text": "And the area of a cell is\nlike the-- if it's a sphere,", "start": 3410.38, "duration": 3.27}, {"text": "it's 4 pi r squared\nwhere is the radius, OK?", "start": 3413.65, "duration": 5.37}, {"text": "All right.", "start": 3419.02, "duration": 0.5}, {"text": "And here's the-- this\nC sub m is called", "start": 3419.52, "duration": 3.24}, {"text": "this specific\nmembrane capacitance,", "start": 3422.76, "duration": 2.82}, {"text": "and it's 10 nanofarads per\nsquare millimeter, all right?", "start": 3425.58, "duration": 6.0}, {"text": "OK, now, I want to show\nyou something really cool.", "start": 3431.58, "duration": 3.28}, {"text": "We have a cell that has\na membrane with some--", "start": 3434.86, "duration": 3.59}, {"text": "this cell has some time\nconstant-- remember,", "start": 3438.45, "duration": 1.95}, {"text": "10 milliseconds.", "start": 3440.4, "duration": 1.99}, {"text": "Now you might think,\noh, the capacitance", "start": 3442.39, "duration": 3.89}, {"text": "of the cell depends on\nhow big it is, right?", "start": 3446.28, "duration": 2.88}, {"text": "And so the time\nconstant will change", "start": 3449.16, "duration": 1.98}, {"text": "depending on how big the\ncell is, you might think.", "start": 3451.14, "duration": 3.51}, {"text": "But let's actually\ncalculate the time", "start": 3454.65, "duration": 1.59}, {"text": "constant from this capacitance\nand this conductance, OK?", "start": 3456.24, "duration": 4.99}, {"text": "So here we go.", "start": 3461.23, "duration": 1.08}, {"text": "Time constant C. R is just 1\nover the conductance, right?", "start": 3462.31, "duration": 6.42}, {"text": "So the time constant\nis capacitance", "start": 3468.73, "duration": 1.77}, {"text": "divided by conductance--\ntotal capacitance", "start": 3470.5, "duration": 2.49}, {"text": "divided by total conductance.", "start": 3472.99, "duration": 2.91}, {"text": "But you can rewrite this\ncapacitance as capacitance", "start": 3475.9, "duration": 2.96}, {"text": "per unit area\ntimes area, you can", "start": 3478.86, "duration": 2.28}, {"text": "rewrite that conductance\nas conductance per unit", "start": 3481.14, "duration": 3.81}, {"text": "area times the area of the\ncell, and the areas cancel.", "start": 3484.95, "duration": 5.68}, {"text": "And so the time constant\nis just that capacitance", "start": 3490.63, "duration": 3.96}, {"text": "per unit area of the membrane\ndivided by the conductance", "start": 3494.59, "duration": 3.18}, {"text": "per unit area of the membrane.", "start": 3497.77, "duration": 2.11}, {"text": "And what that means is that\nthe time constant of a cell--", "start": 3499.88, "duration": 3.59}, {"text": "nothing to do with the cell.", "start": 3503.47, "duration": 1.91}, {"text": "The time constant is the\nmembrane time constant,", "start": 3505.38, "duration": 3.49}, {"text": "and it's a property\nonly of the membrane.", "start": 3508.87, "duration": 2.295}, {"text": "That's pretty cool, right?", "start": 3514.11, "duration": 1.16}, {"text": "Any questions about that?", "start": 3523.126, "duration": 1.454}, {"text": "Now in a more\ncomplicated neuron where", "start": 3533.6, "duration": 2.82}, {"text": "you have a soma and\ndendrites and axons,", "start": 3536.42, "duration": 3.06}, {"text": "different parts of the cell\ncan have different conductance", "start": 3539.48, "duration": 5.83}, {"text": "per unit area-- like\nmore ion channels", "start": 3545.31, "duration": 2.25}, {"text": "out here on the dendrite\nand maybe fewer on the soma.", "start": 3547.56, "duration": 3.45}, {"text": "And so one part of a cell can\nhave a different membrane time", "start": 3551.01, "duration": 3.69}, {"text": "constant than some other\npart of the cell, OK?", "start": 3554.7, "duration": 4.17}, {"text": "But again, it's a\nproperty of the membrane.", "start": 3558.87, "duration": 2.01}, {"text": "Any questions about that?", "start": 3567.478, "duration": 1.042}, {"text": "Yes?", "start": 3568.52, "duration": 0.774}, {"text": "AUDIENCE: So in that case,\nlike different time constants,", "start": 3569.294, "duration": 3.011}, {"text": "do you have to like consider\nflow between different areas?", "start": 3572.305, "duration": 2.845}, {"text": "MICHALE FEE: You sure do.", "start": 3575.15, "duration": 1.43}, {"text": "Absolutely.", "start": 3576.58, "duration": 0.91}, {"text": "That's one of the\ninteresting things about--", "start": 3577.49, "duration": 4.17}, {"text": "when cells have multiple--", "start": 3581.66, "duration": 1.782}, {"text": "they have different\nproperties, you", "start": 3583.442, "duration": 1.458}, {"text": "have current flowing\nbetween them,", "start": 3584.9, "duration": 2.04}, {"text": "but you have to understand\nthis kind of basic stuff", "start": 3586.94, "duration": 3.45}, {"text": "before you even get anywhere\nclose to understanding a more", "start": 3590.39, "duration": 2.91}, {"text": "complicated neuron, right?", "start": 3593.3, "duration": 1.94}, {"text": "OK.", "start": 3598.67, "duration": 1.96}, {"text": "So we're going to add a\nnew component to our model.", "start": 3600.63, "duration": 3.925}, {"text": "It's a battery, and it's\ngoing to solve one really", "start": 3607.37, "duration": 4.71}, {"text": "fatal problem with this model.", "start": 3612.08, "duration": 2.97}, {"text": "What's the problem\nwith this model?", "start": 3615.05, "duration": 2.94}, {"text": "Can anyone see--", "start": 3617.99, "duration": 0.8}, {"text": "I'm kind of showing\nit right here.", "start": 3618.79, "duration": 1.78}, {"text": "What happens to this neuron\nif I turn the current off?", "start": 3625.37, "duration": 4.91}, {"text": "It goes back to zero.", "start": 3630.28, "duration": 1.05}, {"text": "And in order to get the voltage\nto go different from zero,", "start": 3636.24, "duration": 2.55}, {"text": "I have to inject current\nthrough my current source.", "start": 3638.79, "duration": 4.67}, {"text": "Without me, the experimenter\nwith an electrode in it", "start": 3643.46, "duration": 3.39}, {"text": "injecting current, this neuron\nliterally just sits at zero", "start": 3646.85, "duration": 3.27}, {"text": "and stays there, all right?", "start": 3650.12, "duration": 3.09}, {"text": "It's actually a good model\nof a dead neuron, OK?", "start": 3653.21, "duration": 2.96}, {"text": "So in order to change that, we\nneed to add a battery here, OK?", "start": 3659.17, "duration": 5.175}, {"text": "And that battery is going\nto power this thing up,", "start": 3668.15, "duration": 3.12}, {"text": "so now it can change\nits own voltage.", "start": 3671.27, "duration": 2.44}, {"text": "And then things start\ngetting really interesting.", "start": 3676.71, "duration": 2.52}, {"text": "So how can these\nbatteries allow a neuron", "start": 3679.23, "duration": 2.64}, {"text": "to change its own voltage?", "start": 3681.87, "duration": 2.08}, {"text": "Well, the way a neuron controls\nits own voltage is it has ion", "start": 3683.95, "duration": 4.55}, {"text": "channels-- conductances--", "start": 3688.5, "duration": 2.22}, {"text": "that have little knobs\non them that the cell", "start": 3690.72, "duration": 3.0}, {"text": "can control called voltage.", "start": 3693.72, "duration": 5.42}, {"text": "So these conductances\nare voltage-dependent,", "start": 3699.14, "duration": 3.18}, {"text": "and now the cell\nconnects these batteries", "start": 3702.32, "duration": 2.88}, {"text": "to its inside wire at different\ntimes in different ways.", "start": 3705.2, "duration": 5.97}, {"text": "So let's say we want to\nmake an action potential.", "start": 3711.17, "duration": 2.43}, {"text": "So we have a battery that's\ngot a positive voltage,", "start": 3713.6, "duration": 2.78}, {"text": "we have a battery that's\ngot a negative voltage,", "start": 3716.38, "duration": 2.61}, {"text": "and we make an action potential\nby connecting the back", "start": 3718.99, "duration": 4.77}, {"text": "to the inside of the cell by\nturning on this conductance,", "start": 3723.76, "duration": 4.32}, {"text": "and then we're going\nto connect the battery", "start": 3728.08, "duration": 2.85}, {"text": "with a negative\nvoltage to our cell,", "start": 3730.93, "duration": 2.19}, {"text": "and we're going to do\nthat one after the other.", "start": 3733.12, "duration": 2.4}, {"text": "So watch this.", "start": 3735.52, "duration": 1.62}, {"text": "We're going to connect\nthe positive battery", "start": 3739.72, "duration": 2.16}, {"text": "and the voltage\nis going to go up;", "start": 3741.88, "duration": 2.005}, {"text": "we're going to turn off\nthe positive battery,", "start": 3743.885, "duration": 1.875}, {"text": "connect the negative battery,\nthe voltage goes down;", "start": 3745.76, "duration": 3.29}, {"text": "and then we're going to\nturn off both batteries,", "start": 3749.05, "duration": 3.02}, {"text": "and the voltage\njust relaxes, OK?", "start": 3752.07, "duration": 4.54}, {"text": "Cool, right?", "start": 3756.61, "duration": 1.19}, {"text": "So now the neuron can\ncontrol its own voltage.", "start": 3757.8, "duration": 4.38}, {"text": "But before we do that, we need\nto put batteries in our neuron,", "start": 3762.18, "duration": 4.734}, {"text": "OK?", "start": 3766.914, "duration": 2.036}, {"text": "All right.", "start": 3768.95, "duration": 0.5}, {"text": "So anybody know what the-- yes?", "start": 3769.45, "duration": 3.206}, {"text": "AUDIENCE: [INAUDIBLE]\nWhat does that [INAUDIBLE]", "start": 3772.656, "duration": 7.852}, {"text": "MICHALE FEE: Good, we're\ngoing to get to that.", "start": 3780.508, "duration": 1.917}, {"text": "That was-- exact next question.", "start": 3782.425, "duration": 2.575}, {"text": "What is it that makes\na battery in a neuron?", "start": 3785.0, "duration": 3.546}, {"text": "Yeah?", "start": 3788.546, "duration": 0.934}, {"text": "AUDIENCE: Well I mean, like,\nyou have like something, right?", "start": 3789.48, "duration": 2.964}, {"text": "Even in like--", "start": 3792.444, "duration": 0.786}, {"text": "MICHALE FEE: Good.", "start": 3793.23, "duration": 0.29}, {"text": "AUDIENCE: --concentration\ngradient--", "start": 3793.52, "duration": 1.16}, {"text": "MICHALE FEE: Good.", "start": 3794.68, "duration": 0.75}, {"text": "AUDIENCE: --so that\ngive us a [INAUDIBLE]", "start": 3795.43, "duration": 2.04}, {"text": "MICHALE FEE: Here.", "start": 3797.47, "duration": 0.75}, {"text": "You give the rest\nof the lecture.", "start": 3798.22, "duration": 2.49}, {"text": "That's exactly right.", "start": 3800.71, "duration": 1.89}, {"text": "OK?", "start": 3802.6, "duration": 0.54}, {"text": "Well concentration gradients.", "start": 3803.14, "duration": 2.62}, {"text": "There's one more thing we need.", "start": 3805.76, "duration": 2.51}, {"text": "Concentration gradients\nby themselves don't do it.", "start": 3808.27, "duration": 3.06}, {"text": "We need ion channels that are\npermeable only to certain ions,", "start": 3811.33, "duration": 4.87}, {"text": "OK?", "start": 3816.2, "duration": 0.5}, {"text": "And that's what we're\ngoing to do now.", "start": 3816.7, "duration": 1.583}, {"text": "So you need\nconcentration gradients", "start": 3820.84, "duration": 2.03}, {"text": "and ion-selective\npermeability, OK?", "start": 3822.87, "duration": 2.49}, {"text": "So we're going to\ngo through that.", "start": 3825.36, "duration": 3.01}, {"text": "So let's take a beaker,\nfill it with water,", "start": 3828.37, "duration": 3.5}, {"text": "have a membrane,\ndividing it into two.", "start": 3831.87, "duration": 2.7}, {"text": "We're going to have an\nelectrode on one side,", "start": 3834.57, "duration": 2.1}, {"text": "we measure the voltage\ndifference-- sorry,", "start": 3836.67, "duration": 2.16}, {"text": "we have an electron\non both sides,", "start": 3838.83, "duration": 1.44}, {"text": "we hook it up to our\ndifferential amplifier,", "start": 3840.27, "duration": 2.04}, {"text": "and measure the voltage\ndifference on the two sides,", "start": 3842.31, "duration": 2.79}, {"text": "OK?", "start": 3845.1, "duration": 1.29}, {"text": "Then we're going to put--", "start": 3846.39, "duration": 3.355}, {"text": "we're going to take a--", "start": 3853.05, "duration": 1.53}, {"text": "we're going to buy some\npotassium chloride from sigma,", "start": 3854.58, "duration": 4.24}, {"text": "we're going to take\na spoonful of it", "start": 3858.82, "duration": 1.58}, {"text": "and dump it into this\nside of the beaker.", "start": 3860.4, "duration": 3.06}, {"text": "Stir it up, and now you're going\nto have lots of potassium ions", "start": 3863.46, "duration": 4.17}, {"text": "and chloride ions on this\nside of the beaker, right?", "start": 3867.63, "duration": 2.35}, {"text": "Now we're going to\ntake a needle and poke", "start": 3872.85, "duration": 2.7}, {"text": "a hole in that membrane.", "start": 3875.55, "duration": 2.11}, {"text": "That becomes a leak,\na leak channel.", "start": 3877.66, "duration": 3.8}, {"text": "It's a non-specific--\na non-selective pore", "start": 3881.46, "duration": 3.48}, {"text": "that passes any iron, OK?", "start": 3884.94, "duration": 4.167}, {"text": "So what's going to happen?", "start": 3889.107, "duration": 1.083}, {"text": "AUDIENCE: [INAUDIBLE]", "start": 3894.375, "duration": 2.335}, {"text": "MICHALE FEE: Good.", "start": 3896.71, "duration": 0.78}, {"text": "The ions are going to diffuse.", "start": 3897.49, "duration": 2.207}, {"text": "From where to where?", "start": 3899.697, "duration": 0.833}, {"text": "Somebody else.", "start": 3900.53, "duration": 1.14}, {"text": "AUDIENCE: To the\nlower concentration.", "start": 3901.67, "duration": 1.8}, {"text": "MICHALE FEE: To the lower\nconcentration, good.", "start": 3903.47, "duration": 1.917}, {"text": "So some of those ions are going\nto diffuse from here to here.", "start": 3905.387, "duration": 2.843}, {"text": "And we can plot the potassium--\nlet's focus on potassium now.", "start": 3908.23, "duration": 3.902}, {"text": "We're going to plot-- we\ncan plot the potassium", "start": 3912.132, "duration": 1.958}, {"text": "concentration on\nthis side over time", "start": 3914.09, "duration": 2.62}, {"text": "and on this side over time.", "start": 3916.71, "duration": 1.91}, {"text": "By the way, this\nside of the beaker", "start": 3918.62, "duration": 2.91}, {"text": "is going to represent the\ninside of the neuron, which", "start": 3921.53, "duration": 2.37}, {"text": "has lots of\npotassium, and this is", "start": 3923.9, "duration": 2.01}, {"text": "going to represent the\noutside of our neuron, which", "start": 3925.91, "duration": 2.34}, {"text": "has very little potassium, OK?", "start": 3928.25, "duration": 3.09}, {"text": "So if we plot that potassium\nconcentration on this side,", "start": 3931.34, "duration": 3.94}, {"text": "it's going to\nincrease over time.", "start": 3935.28, "duration": 1.88}, {"text": "It's going to take a long--", "start": 3937.16, "duration": 1.32}, {"text": "and the concentration\nhere will decrease", "start": 3938.48, "duration": 2.13}, {"text": "and eventually they'll meet\nin the middle somewhere.", "start": 3940.61, "duration": 3.63}, {"text": "They'll become equal.", "start": 3944.24, "duration": 3.005}, {"text": "And that's going to take\na really long time, right?", "start": 3947.245, "duration": 2.125}, {"text": "Because it takes a\nlong time for this half", "start": 3949.37, "duration": 2.58}, {"text": "of this spoonful of\npotassium chloride", "start": 3951.95, "duration": 1.86}, {"text": "to diffuse to the other side.", "start": 3953.81, "duration": 2.386}, {"text": "Yeah?", "start": 3956.196, "duration": 2.874}, {"text": "OK.", "start": 3959.07, "duration": 2.73}, {"text": "Now let's get a\ndifferent kind of needle,", "start": 3961.8, "duration": 4.79}, {"text": "a very special needle.", "start": 3966.59, "duration": 1.47}, {"text": "It's really small\nand poke a hole", "start": 3968.06, "duration": 3.15}, {"text": "in the membrane that\nis only big enough", "start": 3971.21, "duration": 2.64}, {"text": "to pass potassium ions\nbut not chloride ions.", "start": 3973.85, "duration": 2.91}, {"text": "So what's going to happen now?", "start": 3979.68, "duration": 1.25}, {"text": "Yeah?", "start": 3986.49, "duration": 0.5}, {"text": "Somebody-- yes?", "start": 3986.99, "duration": 3.93}, {"text": "AUDIENCE: Half of it\nflows to the other side--", "start": 3990.92, "duration": 2.36}, {"text": "MICHALE FEE: Good.", "start": 3993.28, "duration": 0.75}, {"text": "AUDIENCE: [INAUDIBLE]", "start": 3994.03, "duration": 3.61}, {"text": "MICHALE FEE: Good.", "start": 3997.64, "duration": 1.44}, {"text": "So some potassium ions are going\nto diffuse through this pore", "start": 3999.08, "duration": 6.06}, {"text": "and go to the other side.", "start": 4005.14, "duration": 3.32}, {"text": "And what's going to happen\nis if we plot the potassium", "start": 4008.46, "duration": 2.31}, {"text": "concentration here, it\nwill decrease-- sorry--", "start": 4010.77, "duration": 3.18}, {"text": "over here it will\nincrease a little bit,", "start": 4013.95, "duration": 2.43}, {"text": "and the potassium\nconcentration on this side", "start": 4016.38, "duration": 2.04}, {"text": "will decrease a little bit,\nbut then it will stop changing,", "start": 4018.42, "duration": 3.45}, {"text": "and it will never\ncome to equilibrium.", "start": 4021.87, "duration": 3.82}, {"text": "It will also take a very short\ntime for that equilibrium", "start": 4025.69, "duration": 2.96}, {"text": "to happen, because\njust a few potassium", "start": 4028.65, "duration": 1.86}, {"text": "ions need to go to the\nother side before it stops.", "start": 4030.51, "duration": 4.37}, {"text": "So why does the concentration\nstop changing here?", "start": 4034.88, "duration": 3.48}, {"text": "Well, it's because\nthe potassium current", "start": 4038.36, "duration": 3.03}, {"text": "from this side to this\nside goes to zero,", "start": 4041.39, "duration": 2.93}, {"text": "and it goes to\nzero very quickly.", "start": 4044.32, "duration": 1.375}, {"text": "So why is that?", "start": 4051.07, "duration": 0.81}, {"text": "Well, one hint to the\nanswer to that question", "start": 4054.86, "duration": 6.53}, {"text": "comes if we look at the voltage\ndifference between the two", "start": 4061.39, "duration": 2.91}, {"text": "sides.", "start": 4064.3, "duration": 0.5}, {"text": "So what you see is that the\nvoltage difference started", "start": 4064.8, "duration": 3.22}, {"text": "at 0, and when we poked\nthat hole, all of a sudden", "start": 4068.02, "duration": 6.23}, {"text": "there was a rapidly-developing\nvoltage difference", "start": 4074.25, "duration": 2.67}, {"text": "across the two sides, OK?", "start": 4076.92, "duration": 3.55}, {"text": "Why does that\nvoltage go negative?", "start": 4084.21, "duration": 4.14}, {"text": "Anybody?", "start": 4088.35, "duration": 2.45}, {"text": "What happened when these\npositive charges started", "start": 4090.8, "duration": 3.14}, {"text": "diffusing from this\nside to this side?", "start": 4093.94, "duration": 4.175}, {"text": "AUDIENCE: Didn't\nyou say it can bond", "start": 4098.115, "duration": 1.5}, {"text": "to the positive and\nnegative charge [INAUDIBLE]", "start": 4099.615, "duration": 4.864}, {"text": "MICHALE FEE: Basically this\nis like a capacitor, right?", "start": 4104.479, "duration": 2.46}, {"text": "And some charges diffused\nfrom here to here,", "start": 4106.939, "duration": 3.991}, {"text": "some positive charges\ndiffused from here to here,", "start": 4110.93, "duration": 2.849}, {"text": "that charges up this side, and\nso the voltage is positive.", "start": 4113.779, "duration": 3.87}, {"text": "We put positive charge--\nmore positive charges here,", "start": 4117.649, "duration": 2.551}, {"text": "the voltage here goes up, OK?", "start": 4120.2, "duration": 3.715}, {"text": "So if the voltage here is\nhigher than the voltage here--", "start": 4127.31, "duration": 7.219}, {"text": "we're plotting V1 minus\nV2, the voltage here", "start": 4134.529, "duration": 3.601}, {"text": "is lower than the\nvoltage here, and so this", "start": 4138.13, "duration": 4.29}, {"text": "is going negative, OK?", "start": 4142.42, "duration": 3.369}, {"text": "And that voltage difference,\nthat negative voltage here,", "start": 4149.25, "duration": 3.84}, {"text": "positive voltage here,\nwhat does that do?", "start": 4153.09, "duration": 3.79}, {"text": "It repels, it makes--\nthe positive side", "start": 4156.88, "duration": 2.97}, {"text": "starts repelling which ions?", "start": 4159.85, "duration": 3.25}, {"text": "It's repelling positive ions.", "start": 4163.1, "duration": 2.509}, {"text": "So it keeps more potassium\nions from diffusing", "start": 4165.609, "duration": 4.231}, {"text": "through the hole.", "start": 4169.84, "duration": 2.823}, {"text": "Does that makes sense?", "start": 4172.663, "duration": 0.917}, {"text": "Blank stares.", "start": 4183.83, "duration": 1.41}, {"text": "Are we OK?", "start": 4185.24, "duration": 1.57}, {"text": "OK, good.", "start": 4186.81, "duration": 1.9}, {"text": "And it continues to drop until\nit reaches a constant voltage,", "start": 4188.71, "duration": 4.859}, {"text": "and that's called the\nequilibrium potential, OK?", "start": 4193.569, "duration": 2.476}, {"text": "The voltage changes until\nit comes to equilibrium,", "start": 4196.045, "duration": 3.075}, {"text": "and that voltage difference\nis called the equilibrium", "start": 4199.12, "duration": 2.64}, {"text": "potential.", "start": 4201.76, "duration": 2.4}, {"text": "And that voltage difference\nis a battery, OK?", "start": 4204.16, "duration": 6.5}, {"text": "And I'm going to--", "start": 4210.66, "duration": 0.84}, {"text": "we're going to\nexplain a little bit--", "start": 4211.5, "duration": 2.43}, {"text": "I think it's in the next\nlecture, the one that's", "start": 4213.93, "duration": 2.76}, {"text": "on tape that explains how\nyou actually can justify", "start": 4216.69, "duration": 4.17}, {"text": "representing that as a battery.", "start": 4220.86, "duration": 1.95}, {"text": "But right now, I'm\ngoing to show you", "start": 4222.81, "duration": 2.4}, {"text": "how to calculate what that\nvoltage difference actually", "start": 4225.21, "duration": 3.6}, {"text": "is-- what's the size\nof the battery, how", "start": 4228.81, "duration": 2.1}, {"text": "big is the battery, OK?", "start": 4230.91, "duration": 3.49}, {"text": "So you can see that when ions--", "start": 4234.4, "duration": 2.67}, {"text": "positive ions defuse to this\nside, this voltage goes up,", "start": 4237.07, "duration": 2.88}, {"text": "you have a voltage gradient that\ncorresponds to a field pointing", "start": 4239.95, "duration": 4.26}, {"text": "in this direction.", "start": 4244.21, "duration": 2.25}, {"text": "And that electric field pushes\nagainst the ions-- remember,", "start": 4246.46, "duration": 3.7}, {"text": "we talked about drift\nin an electric field,", "start": 4250.16, "duration": 2.4}, {"text": "so when those ions are\ntrying to diffuse across,", "start": 4252.56, "duration": 2.57}, {"text": "that electric field is\nliterally dragging them back", "start": 4255.13, "duration": 3.87}, {"text": "to this side, right?", "start": 4259.0, "duration": 5.16}, {"text": "So we have a current flowing\nthis way from diffusion,", "start": 4264.16, "duration": 4.32}, {"text": "and we have a current\nflowing that way from being", "start": 4268.48, "duration": 3.51}, {"text": "dragged in the electric field.", "start": 4271.99, "duration": 1.42}, {"text": "And so we can calculate that\nvoltage difference because", "start": 4273.41, "duration": 6.19}, {"text": "at equilibrium, the current\nflowing this way from diffusion", "start": 4279.6, "duration": 3.3}, {"text": "has to equal the current\nflowing that way from drift", "start": 4282.9, "duration": 5.95}, {"text": "in an electric field, OK?", "start": 4288.85, "duration": 1.41}, {"text": "So one way to\ncalculate this is we're", "start": 4290.26, "duration": 3.78}, {"text": "going to calculate the\ncurrent due to drift,", "start": 4294.04, "duration": 3.45}, {"text": "current due to\ndiffusion, add those up,", "start": 4297.49, "duration": 2.11}, {"text": "and that's equal to the\ntotal, and at equilibrium,", "start": 4299.6, "duration": 2.87}, {"text": "that has to equal to 0, right?", "start": 4302.47, "duration": 3.86}, {"text": "So what I'm showing\nyou now is just", "start": 4306.33, "duration": 4.11}, {"text": "sort of the\nframework for how you", "start": 4310.44, "duration": 1.59}, {"text": "would calculate this using this\ndrift and diffusion equation.", "start": 4312.03, "duration": 6.84}, {"text": "So we have Ohm's\nlaw that tells us", "start": 4318.87, "duration": 3.33}, {"text": "how the voltage\ndifference produces", "start": 4322.2, "duration": 3.03}, {"text": "a current due to drift, and we\nhave Fick's law that tells us", "start": 4325.23, "duration": 3.69}, {"text": "how much current is\ndue to diffusion,", "start": 4328.92, "duration": 3.6}, {"text": "and you can set the sum of\nthose two things to equal zero,", "start": 4332.52, "duration": 5.76}, {"text": "all right?", "start": 4338.28, "duration": 1.308}, {"text": "And so this is the\nway it would look.", "start": 4339.588, "duration": 1.542}, {"text": "I don't expect you to follow\nanything on this slide", "start": 4341.13, "duration": 3.96}, {"text": "just except to see that it\ncan be done in this way, OK?", "start": 4345.09, "duration": 4.05}, {"text": "So you don't even have\nto write this down, OK?", "start": 4349.14, "duration": 5.1}, {"text": "So the drift current\nis proportion-- it's", "start": 4354.24, "duration": 2.46}, {"text": "some constant times voltage.", "start": 4356.7, "duration": 3.21}, {"text": "Fisk's law is some constant\ntimes that concentration", "start": 4359.91, "duration": 4.44}, {"text": "gradient, remember that.", "start": 4364.35, "duration": 1.785}, {"text": "And we just set those two things\nequal and solve for delta V,", "start": 4366.135, "duration": 4.613}, {"text": "and that's what you find.", "start": 4370.748, "duration": 1.042}, {"text": "What you find is the delta V\nis just some constant times", "start": 4371.79, "duration": 2.88}, {"text": "the log of the difference\nin concentrations", "start": 4374.67, "duration": 3.66}, {"text": "on the inside and outside, OK?", "start": 4378.33, "duration": 4.664}, {"text": "Now it turns out, there's a\nway of calculating this that's", "start": 4382.994, "duration": 3.226}, {"text": "much simpler and\nmore elegant, and I'm", "start": 4386.22, "duration": 2.76}, {"text": "going to show you\nthat calculation, OK?", "start": 4388.98, "duration": 4.15}, {"text": "Yes?", "start": 4393.13, "duration": 0.509}, {"text": "AUDIENCE: And so like\nthe concentrations inside", "start": 4393.639, "duration": 1.958}, {"text": "and outside, like at the\n[INAUDIBLE] beginning of the--", "start": 4395.597, "duration": 2.785}, {"text": "MICHALE FEE: Yes,\nat the beginning.", "start": 4398.382, "duration": 1.458}, {"text": "And the answer is that the\nconcentrations don't change", "start": 4399.84, "duration": 3.24}, {"text": "very much through this\nprocess, so you can even", "start": 4403.08, "duration": 2.64}, {"text": "ignore that change, OK?", "start": 4405.72, "duration": 3.15}, {"text": "All right, everybody got this?", "start": 4408.87, "duration": 2.29}, {"text": "All right.", "start": 4411.16, "duration": 0.5}, {"text": "So here's how we're\ngoing to calculate", "start": 4411.66, "duration": 1.86}, {"text": "an alternative\nway of calculating", "start": 4413.52, "duration": 1.59}, {"text": "this voltage difference,\njust really beautiful.", "start": 4415.11, "duration": 4.55}, {"text": "We're going to use the\nBoltzmann equation.", "start": 4419.66, "duration": 1.76}, {"text": "The Boltzmann equation\ntells the probability", "start": 4421.42, "duration": 3.87}, {"text": "of a particle\nbeing in two states", "start": 4425.29, "duration": 3.06}, {"text": "as a function of the energy\ndifference between those two", "start": 4428.35, "duration": 2.93}, {"text": "states.", "start": 4431.28, "duration": 0.5}, {"text": "And one of those states is going\nto correspond to a particle", "start": 4431.78, "duration": 2.78}, {"text": "being on the left side of the\nbeaker or inside of our cell,", "start": 4434.56, "duration": 4.14}, {"text": "and that particle being\noutside of our cell", "start": 4438.7, "duration": 3.072}, {"text": "or on the other\nside of the beaker.", "start": 4441.772, "duration": 1.458}, {"text": "And those two, left\nside and right side,", "start": 4443.23, "duration": 2.55}, {"text": "have different energies, OK?", "start": 4445.78, "duration": 2.82}, {"text": "So our system has two\nstates, a high-energy state", "start": 4448.6, "duration": 3.39}, {"text": "and a low-energy state.", "start": 4451.99, "duration": 1.47}, {"text": "Boltzmann equation just\nsays the probability", "start": 4453.46, "duration": 2.058}, {"text": "of being in state 1 divided\nby the probability of being", "start": 4455.518, "duration": 2.292}, {"text": "in state 2 is just e to the\nminus energy difference divided", "start": 4457.81, "duration": 4.24}, {"text": "by kT.", "start": 4462.05, "duration": 0.5}, {"text": "k is the Boltzmann\nconstant, T is temperature--", "start": 4465.21, "duration": 2.61}, {"text": "this is the same kT\nthat we talked about", "start": 4467.82, "duration": 1.89}, {"text": "in the last lecture.", "start": 4469.71, "duration": 0.84}, {"text": "Now, you can see if the\ntemperature is very low,", "start": 4473.45, "duration": 3.05}, {"text": "all those particles are--", "start": 4476.5, "duration": 1.2}, {"text": "if the temperature is 0,\nthey're not being jostled,", "start": 4477.7, "duration": 2.16}, {"text": "they're just sitting\nthere quietly.", "start": 4479.86, "duration": 2.49}, {"text": "They can't move, they\ncan't get into state 1,", "start": 4482.35, "duration": 2.37}, {"text": "they just sit in state 2, OK?", "start": 4484.72, "duration": 3.3}, {"text": "So the probability of\nbeing in state 1 divided", "start": 4488.02, "duration": 1.95}, {"text": "by the probability of\nbeing in state 2 is 0, OK?", "start": 4489.97, "duration": 4.28}, {"text": "If kT is 0, this is\na very big number,", "start": 4494.25, "duration": 3.4}, {"text": "e to the minus big number is 0.", "start": 4497.65, "duration": 1.88}, {"text": "Now let's say that\nwe heat things up", "start": 4502.04, "duration": 1.77}, {"text": "a bit so that now kT gets big.", "start": 4503.81, "duration": 3.48}, {"text": "So the Katie actually gets\napproximately the same size", "start": 4507.29, "duration": 5.4}, {"text": "as the energy difference\nbetween our two states.", "start": 4512.69, "duration": 3.96}, {"text": "So now some of\nthose particles can", "start": 4516.65, "duration": 1.55}, {"text": "get jostled over into state 1.", "start": 4518.2, "duration": 3.25}, {"text": "And we can write down--", "start": 4525.21, "duration": 1.92}, {"text": "we can just calculate--", "start": 4527.13, "duration": 1.56}, {"text": "you can see now that the\nprobability of being in state 1", "start": 4528.69, "duration": 2.49}, {"text": "is--", "start": 4531.18, "duration": 0.84}, {"text": "divided by the probability\nof being in state 2", "start": 4532.02, "duration": 1.95}, {"text": "is bigger than 0 now.", "start": 4533.97, "duration": 1.92}, {"text": "You can actually\njust calculate it.", "start": 4535.89, "duration": 1.83}, {"text": "If the energy difference\nis just twice kT, then", "start": 4537.72, "duration": 4.05}, {"text": "energy difference,\n2kT divided by kT,", "start": 4541.77, "duration": 4.11}, {"text": "that ratio of probabilities\nis just e to the minus 2, OK?", "start": 4545.88, "duration": 4.428}, {"text": "If the energy difference is\nbigger, then you can see,", "start": 4553.55, "duration": 3.69}, {"text": "that probability\nratio is smaller.", "start": 4557.24, "duration": 1.86}, {"text": "The probability\nof being a state 1", "start": 4559.1, "duration": 1.53}, {"text": "goes to 0 if you\nincrease that energy.", "start": 4560.63, "duration": 3.385}, {"text": "If you make that\nenergy difference very", "start": 4564.015, "duration": 1.625}, {"text": "small at temperature\nkT, you'd see", "start": 4565.64, "duration": 2.94}, {"text": "that if the energy difference\nis about the same as kT,", "start": 4568.58, "duration": 4.57}, {"text": "then the probability\nof being at state 1", "start": 4573.15, "duration": 1.68}, {"text": "is equal to the\nprobability in state 2.", "start": 4574.83, "duration": 1.83}, {"text": "Those particles just\njostle back and forth", "start": 4576.66, "duration": 2.79}, {"text": "between the two states.", "start": 4579.45, "duration": 2.43}, {"text": "OK, so we're ready to do this.", "start": 4581.88, "duration": 2.53}, {"text": "Ratio of probabilities\nis e to the minus energy", "start": 4584.41, "duration": 2.4}, {"text": "difference over KT.", "start": 4586.81, "duration": 1.06}, {"text": "What's the energy of a\nparticle here versus here?", "start": 4587.87, "duration": 3.08}, {"text": "Well, that's a charged\nparticle, the energy difference", "start": 4590.95, "duration": 2.25}, {"text": "is just given by the\nvoltage difference.", "start": 4593.2, "duration": 2.85}, {"text": "So energy is charged\ntimes voltage where", "start": 4596.05, "duration": 2.85}, {"text": "Q is the charge of an ion.", "start": 4598.9, "duration": 2.136}, {"text": "The ratio of probabilities\nis e to the--", "start": 4601.036, "duration": 2.674}, {"text": "Q times voltage\ndifference over kT.", "start": 4603.71, "duration": 2.325}, {"text": "Take the log of\nboth sides, solve", "start": 4610.33, "duration": 2.07}, {"text": "for the voltage difference,\nV in minus V out", "start": 4612.4, "duration": 2.91}, {"text": "equals minus kT over Q times the\nlog of the probability ratio,", "start": 4615.31, "duration": 5.13}, {"text": "but the probability is\njust this concentration.", "start": 4620.44, "duration": 5.16}, {"text": "And so we can write\nthis as delta V--", "start": 4625.6, "duration": 3.75}, {"text": "the voltage difference\nis equal to kT", "start": 4629.35, "duration": 3.56}, {"text": "over Q, which is 25 millivolts,\ntimes the log of the ratio", "start": 4632.91, "duration": 5.43}, {"text": "of potassium concentration\noutside to potassium", "start": 4638.34, "duration": 3.12}, {"text": "concentration inside.", "start": 4641.46, "duration": 2.54}, {"text": "And that's exactly\nthe same equation", "start": 4644.0, "duration": 2.16}, {"text": "that we get if you do that much\nmore complicated derivation", "start": 4646.16, "duration": 4.5}, {"text": "based on Fick's law and\nOhm's law, balancing Fick's", "start": 4650.66, "duration": 4.41}, {"text": "law and Ohm's law, OK?", "start": 4655.07, "duration": 3.72}, {"text": "And this is equilibrium\npotential here,", "start": 4658.79, "duration": 2.13}, {"text": "not electric field.", "start": 4660.92, "duration": 3.2}, {"text": "OK, so let's take a look\nat potassium concentrations", "start": 4664.12, "duration": 2.49}, {"text": "in a real cell.", "start": 4666.61, "duration": 2.09}, {"text": "This is actually from\nsquid giant axon.", "start": 4668.7, "duration": 1.77}, {"text": "400 millimolar inside.", "start": 4670.47, "duration": 1.98}, {"text": "So 20 millimolar outside, so\nthere's a lot of potassium", "start": 4672.45, "duration": 3.75}, {"text": "inside of a cell, not\nvery much outside.", "start": 4676.2, "duration": 3.39}, {"text": "Plug those into our equation.", "start": 4679.59, "duration": 1.77}, {"text": "kT over Q is 25,000\nmillimolar-- temperature", "start": 4681.36, "duration": 2.73}, {"text": "at room temperature.", "start": 4684.09, "duration": 2.89}, {"text": "The log of that concentration\nratio is minus 3,", "start": 4686.98, "duration": 3.33}, {"text": "so ek is minus 75 millivolts.", "start": 4690.31, "duration": 2.12}, {"text": "That means if we start\nwith a lot of potassium", "start": 4692.43, "duration": 1.98}, {"text": "inside of our cell, open up a\npotassium-selective channel,", "start": 4694.41, "duration": 5.7}, {"text": "what happens?", "start": 4700.11, "duration": 1.17}, {"text": "Potassium diffuses out\nthrough that channel", "start": 4701.28, "duration": 4.73}, {"text": "and the voltage goes\nto minus 75 millivolts.", "start": 4706.01, "duration": 4.45}, {"text": "How do you know it's negative?", "start": 4710.46, "duration": 1.35}, {"text": "Like, I always can't remember\nwhether this is concentration", "start": 4711.81, "duration": 3.0}, {"text": "inside or outside, outside\nover inside, I don't know.", "start": 4714.81, "duration": 3.01}, {"text": "But the point is, you don't\nactually have to know,", "start": 4717.82, "duration": 2.145}, {"text": "because you can just\nlook at it and see", "start": 4719.965, "duration": 1.625}, {"text": "the answer what sign it is.", "start": 4721.59, "duration": 2.49}, {"text": "If you have positive ions--", "start": 4724.08, "duration": 1.85}, {"text": "a high concentration of positive\nions inside, they diffuse out,", "start": 4725.93, "duration": 4.87}, {"text": "the voltage inside of the\ncell when positive ions leave", "start": 4730.8, "duration": 4.17}, {"text": "is going to do what?", "start": 4734.97, "duration": 2.66}, {"text": "It's going to go down, so\nthat's why it's minus, OK?", "start": 4737.63, "duration": 4.41}, {"text": "So-- the battery\nand in those video", "start": 4742.04, "duration": 4.46}, {"text": "modules that I\nrecorded for you, it's", "start": 4746.5, "duration": 2.82}, {"text": "going to explain how you\nactually incorporate that", "start": 4749.32, "duration": 2.94}, {"text": "into a battery in\nour circuit model.", "start": 4752.26, "duration": 3.78}, {"text": "And so we've done\nall of these things,", "start": 4756.04, "duration": 1.84}, {"text": "we've looked at how membrane\ncapacitance and resistance", "start": 4757.88, "duration": 2.39}, {"text": "allows neurons to\nintegrate over time,", "start": 4760.27, "duration": 2.85}, {"text": "we've learned how to write down\nthe differential equations,", "start": 4763.12, "duration": 2.62}, {"text": "we're now able to just\nlook at a current input", "start": 4765.74, "duration": 2.78}, {"text": "and figure out the\nvoltage change,", "start": 4768.52, "duration": 2.01}, {"text": "and we now understand where\nthe batteries in a neuron", "start": 4770.53, "duration": 2.79}, {"text": "come from.", "start": 4773.32, "duration": 1.79}]