 for taking so long we usually run one lecture for every four we usually run the entire lecture so we don't need to swap the recordings. Again my name is Henry Lester and the most recent time that I taught this course was in fall of 2013 and then last year I was on the sabbatical so things are a bit rusty plus the fact that I'm wearing an old pair of glasses I can see you raise your hand but may not recognize you. My background as Ralph said includes biophysics and electrophysiology and I also hold a joint appointment at the is visiting scientist at the Janelia research campus and that wonderful video of a zebrafish's brain lighting up its neurons that Ralph showed you was developed at that campus in the lab where I have the joint appointment so what we're going to do today is rather special because we are going to accompany evolution and the points that Ralph made with a simple probably the simplest possible lecture in this course we're going to derive from first principles the ionic bases of neuroscience so if somebody should ask you at a cocktail party how do you remember the sodium and potassium and reversal and roasting potentials and energy potentials and all that you'll say oh I can derive it very easily and here's how we're going to do it right we're going to go over today we're going to be we're going to end at around 1215 for which I apologize so what is the most abundant molecule in an organism anybody want to guess somebody said pizza no what did you say water that's correct okay so by far the most abundant molecule in an organism is water I should not have done that we'll go back and put in water water does anybody disagree with that okay unanimous very good so we will go on to the next point and we'll actually calculate from first principles from the stuff that you learned in chem one the abundance of water the molecular weight of water H2O is around 18 its density as you know is about one kilogram per liter because a kilogram a liter weighs a kilogram so the concentration of water in an aqueous solution is 1000 grams per liter divided by 18 grams per liter or 55 moles per liter or 55 molar and all the other molecules in the body or at least a hundred times less concentrated so we need to pay attention to the properties of water and these properties include the hydration and the salvation of various ions and molecules by water we will discuss that point during today's talk now let's think about the typical ion concentrations extracellular concentration in the cerebrospinal fluid or in the blood in the intracellular concentration the major monovial and ions sodium potassium and chloride have these concentrations and to some extent they are reversed in the intracellular in the cytosol in the intracellular solution for sodium and for potassium and for chloride the divalent ions magnesium is roughly within a factor of four about as concentrated outside is inside calcium is much more concentrated outside than inside other ions have varying concentrations as well we're going to derive all of this from first principles today okay how we're going to do that well we're going to take advantage of the fact that we evolved from seawater so here is the concentration of the ions in seawater lots of sodium a bit of potassium some chloride some divalent ions and some other ions actually the extracellular solution blood is a diluted version of seawater in its major ions here's a factor of three here's a factor of two and a half here's a factor of five factor of five a much larger factor and then the phosphate and the protons the protons are roughly as concentrated in the blood as in seawater that is we live at pH 7 intracellular is different and we're going to derive that fact right now so first first point is that all this just came from being in seawater in blood is a dilute version of seawater now the next thing that organisms have done in order to get themselves some energy and in order to compartmentalize molecules is that they have membranes membranes provide a barrier to diffusion around cells and they form compartments the typical membrane consists of lipids with fatty acids and a polar tail so this is like a layer of oil and molecules especially ions do not easily diffuse through lipids do not diffuse through membranes so we have hydrophobic molecules that do diffuse right through membranes we have a small uncharged polar molecules like water that don't diffuse very well through membranes we have large uncharged polar molecules that diffuse very poorly and ions not at all so all a lot of these concepts come from the text that you might have used in by eight by nine which is alberts or it's more modern version so membranes do a good job of compartmentalizing especially of ions and the the moral of today's lecture the overwhelming result of today's lecture is that specialized proteins channels and transporters do control the permeation of many ions so we go from a completely separate compartments to communicating compartments let's talk about then a cell that has evolved in seawater and has no concentration gradients of ions between the outside and the inside so the external monovialin cations or in blood have high sodium low potassium mostly sodium on the outside a little bit of potassium and on the inside mostly sodium and a little bit of potassium this cell cannot do much of interest so we'd like to the first thing we'd like to do the first thing nature has done is to store energy in a concentration gradient but because we are animals and not plants we don't live in cardboard boxes the way plants do plants have cell walls we don't have cell walls so we need to keep the osmotic pressure the same inside and outside the cell so to store energy in a concentration gradient without osmotic stress we simply reverse the ratio of sodium and potassium so on the outside we have lots of sodium a little bit of potassium on the inside we have high potassium and a little bit of sodium and in fact that is what has happened and you can derive this from first principles by remembering that sodium that seawater is mostly sodium chloride now we do that well there are specialized proteins specialized proteins consist primarily of the sodium pump which splits ATP to make a concentration gradient of sodium and potassium the sodium pump pumps sodium out of the cell and potassium into the cell it's a fascinating complex protein a machine on its own that splits ATP to pump ions it therefore produces a gradient of potassium and another one of sodium there are additional pumps in a cell that are driven by ATP there's the sodium potassium pump that I just told you about a very important calcium pump that keeps calcium outside cells less than calcium inside cells and will derive that from first principles as well so there are these complex proteins that split ATP the universal energy currency of life to make concentration gradients now electricity is the language of the nervous system you all know that and so what we would like to do what nature has done many times is to convert the concentration gradient into an electrical potential and the way to do that the way nature has done that is that nature has evolved permeability to just one of those two ions to potassium and so nature has put potassium channels in the cell membrane the result then is that because potassium is more concentrated on the inside than on the outside a little bit of potassium leaks out through that permeability to potassium that little bit of potassium leaking out causes a lost positive charge inside the cell that leads to a negatively charge it to a negative internal membrane potential so from first principles from the fact that we evolved from seawater we derived the fact that we have an internal net negative membrane potential how large is that net internal negative potential for to do that to calculate that we use the Nernst potential okay now for your first quiz in this course who developed the Nernst potential good so what Nernst said is that the energy of discharging the concentration gradient for potassium ions so has to equal the energy of moving the potassium ions through the potential difference potassium doesn't leak out forever it stops leaking out when it reaches an equilibrium in which these two energies are the same now from chem one let's go back and talk about the difference between a channel which is the way potassium is leaking out of the cell and the pump which has set up the gradients in the first place so a channel you can think of as an open pore and for each time the poor opens hundreds or thousands of ions flow through the open channel a transporter or a pump has some complex conformational changes sometimes linked to hydrolysis in which just a few ions move for every conformational change now let's go back and calculate the Nernst potential you learned a little bit about this you still use OGC in chem one okay so you learned about various electrode potentials in chem one we're going to talk about a different electrochemical phenomenon here but the principle of moving charge and balancing it with an electrical potential is the same so let's derive the Nernst potential we'll do it in chemistry units first what we've said is that the energy the free energy lost by that potassium ion as it diffuses out of the cell matches the electrical potential so Delta G then is equal to RT universal gas constant times the temperature times the log of the chemical gradient for potassium you remember that all these free energies are proportional to logs so that's the chemical potential interoptions and the energy of moving the charge is simply equal to the charge on the potassium ion times Faraday's constant times that potential difference for which we are trying to solve so at equilibrium of course Delta G equals zero these two terms balance out and therefore the voltage is equal to minus RT over the charge on the ion times Faraday's constant times the log of the potassium concentrations and for this case we know that Z is plus one that charge on the potassium ion and so for an e-fold change of potassium concentration in which the inside is greater than the outside that's what holds for the cell we get a potential difference of minus RT over F and we have R and we have T and we have F and so an e-fold difference and here is RT over F now one point that we have to change from chemistry to electrophysiology is that you remember this figure from OGN it's the mechanical equivalent of heat and so we change from calories to joules 4.18 joules per calorie so RT over F for an e-fold difference in concentration between the inside and the outside is 25 millivolts and so if we have e-fold more potassium inside than outside we'll have a resting potential of 25 millivolts we could do this in units for those who are more comfortable in physics R equals Avogadro's constant times K which is Boltzmann's constant and F equals Avogadro's constant times the charge on the electrode so if we do the same calculation in physics units we also come up with 25 millivolts and that's what a semiconductor junction for instance rectifies that e-fold per 25 millivolts and we're familiar with the statement that room at room temperature and Adam has an energy of about 25 milli electron volts so in fact in a cell the difference in concentration is more like tenfold than e-fold and this gives us to a needs us to a membrane potential of about 58 millivolts so from first principles from knowing that water that sea water is sodium chloride that blood is a dilute concentration of sodium chloride we have derived the fact that neurons have a resting potential of minus 58 millivolts due to having more internal potassium than sodium we didn't really have to remember anything except physics one and one there's a little bit of slate of hand here what is the selective advantage how did we evolve the fact that the membrane is permeable to potassium at rest rather than to sodium at rest well actually here the selective advantage is fairly straightforward because a small inward leak of sodium would change the internal sodium by fractionally more than a small outward leak would change the internal potassium so the internal potassium concentration is around 140 millimolar internal sodium concentration is around 10 a leak of 10 millimolar would double the sodium concentration and therefore for cause a 17 millivolt change in the resting potential but a similar outward leak in potassium would be by 10 millimolar would decrease potassium from 140 millimolar to 130 millimolar which would be less than it twofold change in the Nernst potential and so the fact that seawater has a high concentration of sodium and the low concentration of potassium has led organisms to have a high internal concentration of potassium and to use potassium channels to maintain things at rest rather than sodium channels so cell function is more stable when the resting permeability is to potassium and sure enough the nervous system has evolved hundreds of genes for potassium channels which manipulate resting potentials and near resting potentials but has been very sparing about developing sodium and calcium channels which produce a tremendous load on a cell what I just told you several dozen potassium channels well by now it's several hundred but only about 10 sodium channels so at rest you could say potassium channels are metabolically free they don't actually cause a cell to lose energy and that's quite important because the sodium potassium pump maintaining these iron gradients actually splits about two-thirds of the brain's ATP so keeping all of those ions happy and keeping the resting potential happy is a major function of metabolism in the brain and a major use of ATP well what about other monovalent ions your let's remember seawater also has a lot of chloride so under what circumstances do neurons use chloride fluxes well actually nature appears to have had a bit of trouble making a permeability pathway that distinguishes among anions using protein side chains so there's really no anion pair that corresponds to the potassium and sodium pair as a result few cells actually do use anions to set the resting potential but transient violations of that occur because most post-synaptic synaptic inhibitory channels do use anion fluxes and they're primarily chloride the resting potential the major job of the cell is done with sodium potassium cations rather than anions could neurons utilize plasma membrane proton fluxes after all seawater has a pH of 7 our blood has a pH of 7 well probably not there simply are not enough protons concentration of 10 to the minus 7 to make a bulk flow which is required for robustly maintaining the ion concentration gradients however proton gradients do work for very small organelles and for very small cells so small organelles will see do use proton gradients and bacteria of course and mitochondria do use proton gradients but for a big neuron it's impractical so from first principles we can eliminate chloride because you can't proteins don't accurately discriminate between anion pairs and protons there are just too few of them to make a bulk flow what about divalent cations and at the beginning of this talk I told you that cells maintain calcium at very low levels well actually we live things made a commitment more than a billion years ago to use high energy phosphate bonds for energy storage therefore cells contain high internal phosphate split from ATP or used to make ATP but calcium phosphate is insiable at pH near where we live so cells can't actually have a internal a high internal calcium of concentration if they did they would get kidney stones which are calcium phosphate and inside every cell so typically cells go to a lot of trouble to maintain the internal calcium concentration at less than 10 to the minus eighth molar so simply you can derive from first principles the fact we use ATP as an energy currency therefore we have to keep internal calcium low well what about magnesium what's the selective advantage that cells don't use magnesium fluxes now this is a little trickier but it's a very interesting scientific question you have to consider the atomic scale structure of a potassium channel and so let's see if we can bring that up here if you happen to have a molecular viewer on your computer doesn't everybody have a molecular viewer on your computer this is pymol but you could use Swiss protein as well so we will show the cartoon potassium channel and will emphasize the colors by chain area there are it's a tetramer there are four identical subunits and the conducting pore through which the potassium ions flow is in the middle and these little dots in the middle of the pore are each potassium ions actually here they're rubidium ions which are easier to image in x-ray crystallography so this is a potassium channel and there is a another picture of it in candel and the important point about this picture here we have static view here we have the potassium ions in the pore all right now I said we needed to think about water potassium ions are hydrated outside the channel by water they're hydrated outside the cell and inside the cell by water they really love to be hydrated but they lose those waters of hydration when they go through the channel because the channel tricks the potassium ions into thinking they are still in water by substituting carbonyl groups for the waters of hydration so that's really wonderful evolution it's very important but it says that in order to have a robust flux through a channel a potassium ion needs to lose its waters of hydration so that needs to happen very quickly likewise here is the atomic scale structure of a sodium channel now a sodium channel as we'll learn it's not a tetramer it has only one chain but it looks as though it has four internal homology repeats and inside the pore of a sodium channel here are those carbonyl groups that trick the sodium ion into thinking it's still in water so again here is the water like pathway from the in the plane of the membrane in which the ions feel very comfortable now we need a permeant ion needs to exchange waters of hydration rather rapidly sodium and potassium can do this every nanosecond or so calcium can do this every five nanoseconds or so and so they can flow through single channels at rates that are rather large magnesium cannot exchange waters of hydration very well it takes a whole 10 microseconds for a magnesium ion to exchange its water of hydration so it's the most charged dense canion it holds its waters of hydration most tightly and therefore we can't use it for bulk flow through membranes there are a few principles exceptions in which there are transporters but no channels for magnesium so from basic physical chemistry we now know how it is that cells do not use magnesium fluxes now that was really arcane biophysics wasn't it the fact that magnesium ions don't lose their waters of hydration actually it turns out that this arcane biophysics produces a well-known phenomenon in the flux through a sodium a glutamate receptor called the NMDA receptor we will come back to this point when we talk about learning in memory but under most conditions that NMDA receptor is stuck by plugged by a magnesium ion which cannot exchange its waters of hydration and instead gets stuck in the pore under certain circumstances that NMDA receptor loses its magnesium ion it gets pushed into the cytoplasm the result is that sodium and calcium flow there's a cascade of evidence of events that produce some of the changes associated with learning in memory so this arcane biophysics in which magnesium cannot exchange its waters of hydration turns out to be very important in the Drake equation okay so what we've talked about are primary active transport sodium pumps calcium pumps in addition cells have what you might call secondary active transport having gone to such trouble to produce sodium gradients by splitting ATP a cell can now use those sodium gradients driving other exchange transporters to move metabolites in and out of cells very much the way an old-fashioned dam would build up a pond and then you could drive everything in the factory in a mill from water that flows down that pond and gets connected to the machines so the sodium pump and the calcium pump allow cells to have co-transporters and exchangers that drive other ions and small molecules in and out of the cell all right so what's the message for today that cells have evolved elaborate processes for pumping out intracellular sodium and calcium and these gradients can be used in two ways they are used for uphill exchange to control the concentrations of other small molecules that's the mill pond argument but also now that cells have made such great investments in keeping the intracellular concentrations of sodium and calcium low cells can now use small local changes in those concentrations a little bolus here and there for signaling and in fact that's the basis for signaling in the nervous system I think we'll skip this image oh well yes in addition to the fact that cells can drive can use the concentration gradient to drive other small molecules we have a very important phenomenon in neuroscience and that is neurotransmitter transporters in which the sodium coupled cell membrane serotonin transporter or dopamine transporter takes up serotonin or dopamine after it's been released and entire industries as well as entire drug abuse cultures have arisen out of molecules that block neurotransmitter transporters probably the most successful antidepressant molecules the SSRIs Prozac Zoloft block serotonin transporters and some drugs of abuse such as cocaine and amphetamine also block dopamine transporters so these are secondary transporters driven by the sodium gradient but typically we don't pay any attention to trademarks in this course so where there's a little beaver crossed out here you don't have to remember trademarks you may need to remember trivial names such as the fact that prozac is also called fluoxetine but trademarks don't matter how do these pumps work well you can read about them in candel because we vastly run out of time and so what I've said today is that there are three classes of proteins that transport ions across membranes there are active transport there's passive transport either carrier mediated or a channel protein and the active transporters split ATP the ion coupled transporters just use the fact that the active transporters have worked and the ion channels that flux many ions per event so these proteins have evolved in a natural perhaps necessary a way to provide that the resting potential arises via selective permeability to potassium this also needs leads to the Nernst potential and now transient breakdowns in that process in membrane potential are used as nerve signals and then get repaired right away by the pump as well as the fact that neuronal and non-neuronal cells also signal via transient influxes of sodium and calcium how much of the genome is devoted to the proteins I talked about today about five percent around twelve hundred and fifty genes my office hours are today and Friday red door one fifteen to two p.m. we'll see you on Wednesday