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Biological Sciences
Jason Brown

NERVOUS SYSTEMS SLIDE 2: NEURONS  Neurons have four major components: o Dendrites – Collects electrical signals from other kinds of cells or from the environment. Can connect via dendrite to dendrite, sensory cells via dendrites, or dendrites are free ended connecting with chemicals in the environment (ex. pain neuron, inflammation) o Cell body – Integrates incoming signals and generates outgoing signal to axon. Neurons can either send a signal or not send a signal, can’t send out a half signal o Axon – Conducts electrical signals to the presynaptic terminals o Presynaptic terminals – Transmit electrical signals to the next neuron, muscle, or gland.  There are 2 basic kinds of potentials that neurons can use: o Graded potential: restricted to the cell body and dendrites o Action potential: the signal occurs at the length of the axon and the presynaptic terminals SLIDE 3: IONIC COMPOSOTION OF BODY FLUIDS: SEAWATER ≈ECF ≠ ICF  The nature of electrical signal is such that they result from the membrane being polarized, there’s a charge separation across the plasma membrane of a neuron, and that membrane potential can vary considerably.  How is there a membrane potential to begin with and how do you modify the membrane potential?  The extracellular fluid (ECF) of all animals is rich in sodium and chloride. This is because they evolved in seawater.  Intracellular fluids (ICF) are poor in sodium and chloride of most animals. There’s lots of potassium and proteins in the ICF. SLIDE 4: IONIC COMPOSITION OF BODY FLUIDS: DOUBLE DONNAN EFFECT  Why isn’t the ICF the same composition as the ECF? If it was the same composition as the ECF you wouldn’t have to expend energy to maintain difference in concentration so why not have a sodium and chloride rich ICF?  The answer is summed up by the Double Donnan Effect.  On the left you have ICF; on the right you have ECF which could be interstitial fluid or hemolymph.  If we start with the ICF and ECF both being rich in sodium and chloride, we see a problem.  The problem is that there’s something present in ICF which aren’t present in the ECF at similar concentrations, and those things are proteins.  Most proteins, under physiological pH, have a net negative charge. So we have a negatively charged thing in the ICF, but it’s not present at nearly the same concentration, if present at all, in the ECF.  The second important point is that the proteins that are present in the ICF are not membrane permeable and are trapped in the ICF.  This leads to donnan equilibrium, which says if you have a charged particle trapped on one side of the membrane, it’s going to effect the distribution of all the other charged particles that can permeate the membrane.  This means that because the negatively charged proteins are present only in the ICF, the chloride is excluded from the inside of the cell due to repelling from the proteins. At the same time sodium and potassium are attracted into the cell.  The distribution of the ions thus shifts because of the presence of the impermeable negatively charged species.  The mathematics of the Double Donnan Effect tells us that because the distribution of these ions occur in such a way that the repulsion of chloride and attraction of sodium and potassium leads to a situation where the total number of solutes in the ICF becomes much greater than the number of solutes in the ECF, meaning you now have an osmotic gradient set up.  Remember animals try to keep the osmotic gradient between ECF and ICF to prevent movement of water, but due to the redistribution of ions due to the negatively charged proteins, water is drawn into the cell.  This process isn’t sustainable; the cell can’t be constantly taking in water because it affects cell volume and concentrations. The cells evolved to solve this problem by pumping out ions from their ICF to their ECF.  You’ll find in plasma membrane of all cells, there are sodium potassium ATPase. This pumps out 3 sodium, and pumps in 2 potassium. This pumps out more ions than it’s pumping in, and minimizes the osmotic gradient between the two fluids.  In addition, the green boxes you see are the sodium transporters, which sodium uses to get through. Cells are generally not as permeable as sodium.  They pump sodium out, and it has no way to get back in. So the positively charged species are trapped on the other side of the membranes.  The potassium channels are still present so a lot of potassium that’s pumped into the cell can leak back out.  By pumping sodium out and having a membrane impermeable to sodium, the net effect is that is that we rebalanced the osmotic gradient. Also because you’re pumping out 3 sodium for every 2 potassium, it also attracts chloride to come out of the cell.  The general effect is that you have roughly equal concentration of solutes on both side of the membrane, but the composition of the fluids is different. The ECF becomes exclusively sodium and chloride, but the ICF becomes depleted in sodium and chloride and much more enriched in potassium.  Every cell has this composition where sodium and chloride dominate the ECF, and potassium and proteins dominate the ICF. This occurs in every cell because they contain proteins with a negative charge. SLIDE 5: IONIC COMPOSITION OF BODY FLUIDS  So every cell has protein and potassium rich ICF, and the sodium and chloride rich ECF is separated by a narrow membrane. The plasma membrane is about 7-8 nanometers thick.  The membrane plays 2 roles in terms of electrochemistry of a neuron. It is considered both the resistor, and the capacitor. This means if you have 2 electrically charged fluids, they’re restricted from freely crossing the membrane because they can’t pass through the lipid bilayer and their passage is restricted to where ever there are ion channels to allow them to pass through.  So the membrane offers resistance to the flow of charge across the membrane because those charges can only pass through the ion channel  It is also a capacitor because it acts to insulate any charges that build up on one side of the membrane from any charges that build up on the other side.  Let’s assume we have a membrane that’s exclusively permeable to potassium (the orange channels you see here are potassium channels). If that’s the case, because there’s lots of potassium in the ICF relative to ECF, the potassium will move by diffusion from the ICF to the ECF.  Typically if that occurred, it would attract a negatively charged component to follow along. The main negatively charged species in the ICF are the proteins which aren’t membrane permeable.  This develops a charge separation process membrane where the outside of the membrane is a little positively charged, and the inside becomes a little negatively charged.  Eventually potassium is going to stop because it will build up negative charges along the membrane and will start pulling potassium back into the cell due to the developing electric gradient. SLIDE 6: RESTING MEMBRANE POTENTIAL: NERNST EQUATION  At what point do these 2 gradients balance each other out?  Modeling this mathematically, the Nernst equation allows us to calculate the equilibrium potential. This allows us to calculate how much of a charge separation can form across the membrane before that charge separation equally balances out the concentration gradients.  So the question is how negatively charged does the inside of the membrane have to get for the inward pull of potassium to equally balance the outward movement of potassium down its diffusion gradient.  In the Nernst equation, the (z) stands for the charge on the ion species we’re talking about. The [X]out is the concentration of some ion on the outside, and [X]in is the concentration of the same ion in the ICF.  If you take the numbers you see on the right example if you take potassium and plug it into the equation, you can calculate how much of a charge separation can occur across the plasma membrane, before the electric gradient and chemical gradient balance each other out.  So you plug in all the constants, assume the temperature is 301 Kelvin for example, and the charge for potassium is positive so for (z) you put (1) because it’s one positive charge. So you plug in the concentrations and you calculate the equation and you get -88 millivolts.  This means that potassium will keep diffusing out of the cell from ICF to ECF until there’s an 88 millivolt difference in charge across the membrane, at which point that charge withdrawing potassium back in at the same rate that potassium is diffusing out of the cell.  This is the electric difference in passive form for the concentration gradient and electric gradient to be perfectly balanced so there’s no net movement across the membrane. SLIDE 7 RESTING MEMBRANE POTENTIAL: NERNST EQUATION  You can do this for any of these other ions example for sodium the value is +57 millivolts  Since sodium is more concentrated in the ECF, it will keep moving into the cell until the inside of the cell is 57 millivolts more positively charged than outside, at which point the electrostatic repulsion of sodium will balance its desire to come down its concentration gradient.  The Nernst equation allows you to calculate the equilibrium potential for INDIVIDUAL IONS only.  The higher the concentration gradient, example you change ICF potassium from 400-600, you get a larger electric gradient before the two things come to balance. SLIDE 8 RESTING MEMBRANE POTENTIAL: NERNST EQUATION  Because the plasma membrane is so thin, it doesn’t take many ions crossing the membrane to establish a potential difference across that membrane.  Example, if you have 400 mM of potassium in the ICF, it will take very few ions to establish an electric gradient so the concentrations won’t change because the number of ions that move across the membrane are negligible and won’t have an effect on the concentrations of the interstitial and intercellular fluids.  The Nernst equation is useful if the membrane is only permeable to a single ion, but in reality it’s permeable to several ions. The 3 that are most important for figuring out membrane potential are potassium, sodium, and chloride. SLIDE 9 RESTING MEMBRANE POTENTIAL: GOLDMAN EQUATION  How do you take the concentration differences of all the ions and put them together to figure out the membrane potential?  The Goldman equation allows us to calculate membrane potential across the cell membrane.  The (P) you see her stands for permeability of ions, how permeable is the membrane to these 3 different ions. Example ( ) is permeability of potassium.  Other ions like calcium can be added to this equation but these 3 ions (Na, K, Cl) are the dominant ions that effect membrane potential.  As mentioned before, even if ions move across the membrane the concentrations don’t change much, so the concentrations of inside and outside of the cell are relatively fixed. This leaves us with the permeability of the membrane to these ions being the largest determinant of membrane potential. SLIDE 10 RESTING MEMBRANE POTENTIAL: GOLDMAN EQUATION  Most membranes are very permeable to potassium, moderately permeable to chloride, and not permeable at all to sodium. So for potassium is 100x more permeable than sodium, and chloride is 10x more permeable than sodium and these are the permeability constants you see here as 100, 1, 10 for potassium, sodium, and chloride. These are relative numbers.  When you take all the numbers and calculate you’ll come up with a value of -74 mV  Given the concentration of these ions here, they’ll distribute themselves across the membranes that there will be a -74 mV negative charge on the inside of the membrane relative to the outside.  The permeability of a cell at rest is determined by leakage channels. These channels permit ions to move in and out by following their gradient. These channels are open all the time.  Another thing to note is that at this value of membrane potential, in this case -74 mV, none of the 3 ions are at equilibrium.  Example if you look at chloride on slide 8, the equilibrium potential is -86 mV, so if we have a -74 mV membrane potential at rest, the chloride will keep moving into the cell until it’s -86 mV inside the cell. So if you make the membrane more permeable to chloride, it will come in until the cell’s membrane potential is -86 mV.  There’s a huge disequilibrium for sodium, if you make the cell more permeable to sodium, it will keep flooding into the cell until the interior became +57 mV. The mechanism applies for potassium.  So all 3 ions are at disequilibrium. This is important because by changing the permeability of the cell membrane to any of these 3 ions, we can generate a change in the membrane potential of that cell. SLIDE 11 GRADED POTENTIALS: DEPOLARIZATION AND HYPERPOLARIZAION  The resting potential is roughly -70 mV. At rest the cell is largely permeable to potassium, moderately permeable to chloride and relatively impermeable to sodium.  From the resting potential, if you open up sodium channels, sodium will keep rushing into the cell and cause the membrane potential to slowly move towards 0. So in this picture it moved from -70 to around - 60 because positively charged sodium is rushing inside the cell.  If you opened potassium or chloride channels, the opposite occurs.  If you open potassium channels and since lots of potassium ions are in the ICF, it floods out of the cell and makes the interior of the cell more negative and hyper-polarization occurs until it reaches -88 mV because at that point potassium will start going into the cell at the same rate.  If you open chloride channels and since lots of chloride ions are in the ECF, it floods into the cell making it more negatively charged until you get a membrane potential of -86 mV at which point it will start going out at the same rate.  All you have to do is change the permeability of the cell membrane to an ion, and just slight movement of the ions across the membrane will change the membrane potential resulting in either depolarization or hyper-polarization. SLIDE 12 GRADED POTENTIALS: SUMMATION  Remember that dendrites receive electric signals, and then they get integrated at the cell body.  Axon hillock is a region of the neuron. Whether or not a neuron fires an electric signal depends on the membrane potential in the axon hillock.  Once the membrane potential in the axon hillock reaches the threshold potential, the neuron sends a signal down its axon.  So in the beginning the resting potential is -70 mV. Let’s assume that one of the neurons fires a signal that causes sodium channels to open. Sodium starts rushing into the cell and depolarization that occurs may spread to the region of the axon hillock and cause that region to have a slight increase in membrane potential to around -40 mV.  Let’s say another neuron fires a signal that causes sodium channels to open in another region of the axon hillock and spreads across which further increases the membrane potential of the axon hillock to around - 20 mV.  Then a signal stimulates opening of chloride channels, and chloride rushes into the cell and spread across the axon hillock and cause that region to hyperpolarize.  So stimulus coming from all these areas opening up all these channels, changing the membrane potentials which can spread and ultimately effect the membrane potential of the axon hillock. Once the membrane potential of the axon hillock region reaches a threshold potential, in this case -10, the axon hillock will go through an action potential where there’s major depolarization followed by hyperpolarization and then return to rest.  This action potential gets propagated down the entire length of the axon.  So essentially, we have graded potentials, the small changes of membrane potential of various regions of cell body and dendrites, spreading to the axon hillock and once the membrane potential of this region reaches a threshold you get an action potential.  All the signals, whether inhibitory causing hyperpolarization, or excitatory causing depolarization, all the signals coming in are integrated at the axon hillock. The net effect is the sufficient depolarization in this region causes a trigger of action potential.  Graded potential can happen in small incremental values while action potential is an “all-or-none” process where major depolarization and repolarization occurs. SLIDE 13 GRADED POTENTIALS: DECREMENTAL TRANSMISSION  The graded potentials that occur can spread only for a small region. If you depolarize a site for example with sodium, those sodium ions that rush in the interior of the cell. Because these sodium ions are positively charged, when they start to spread, they are trapped in the negative charges on the interior of the membrane surrounding the site of depolarization.  As the sodium ions move, the membrane has slight permeability to sodium so some of the sodium ions leak across the membrane out of the neuron and repolarize the membrane.  At a certain distance from the site, there won’t be any depolarization because by the time you get to that distance, most of the sodium ions have leaked out and there won’t be any depolarization at that site.  This is called decremental transmission. Where ever there’s a site of depolarization, that depolarization stops no more than 2 mm from the initial site of depolarization. It can’t spread because the intensity of depolarization decreases as you move away from the site of depolarization.  This means that if you stimulate a neuron to open a bunch of sodium channels at a particular site, sodium rushes in, and it can spread no more than 2 mm, so if the axon hillock isn’t more than roughly 2 mm away, the depolarization that occurs at the site can effect on the membrane potential of the axon hillock.  Because the depolarization at a particular site can’t spread across the length of the whole axon, which can range from a few millimeters to several centimeters or even meters, you need something else to happen, and this thing is the action potential.  As long as the dendrites aren’t more than 2-3 mm away from the axon hillock, the membrane potential will be effected and once you reach a threshold, a signal is propagated in such a way that it doesn’t decrease along the whole length of the axon as it moves down the axon. SLIDE 14 ACTION POTENTIAL: AXON HILLOCK  The axon hillock allows us to initiate a single that runs down the length of the axon.  The formation and propagation of an action potential at the axon hillock or the axon is the result of voltage-gated channels.  These channels change their con
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