NeuroPhysiology and Membrane Potentials. The Electrochemical Gradient

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1 NeuroPhysiology and Membrane Potentials Communication by neurons is based on changes in the membrane s permeability to ions This depends on the presence of specific membrane ion channels and the presence of electrochemical gradients. The gradients in ion concentration creates a flow of ions which in turn creates electrical currents. The resulting charge separation across the membrane creates a voltage according to the law of Ohm. Current (flow) = Voltage / Resistance 1 The Electrochemical Gradient Electrostatic gradient principles: Like charges repulse each other; Unlike charges attract. Chemical gradient: Down the concentration gradient 2 1

2 The Chemical Gradient 3 The Equilibrium and Membrane Potential Assume the following conditions A single cell Low [K ] outside High [K ] inside No channels for K whatsoever There is no electrical gradient (other charged elements are present to create neutrality) What will happen? 4 2

3 Now insert a few K leakage channels into the cell. What will happen? There is initially no electrical gradient ; the only force is the chemical gradient K will diffuse down the concentration gradient As more K leaves the cell, an electrical gradient becomes established ; a new force comes into play What is the direction of these two forces? 5 Initially K moves outwards, down the chemical concentration gradient However, for every charge leaving, we create a charge deficit on the inside ( or we create a negative surplus charge) and add a charge on the outside. This is the beginning of the electrical gradient : negative ( ) inside versus positive ( ) outside. The more K ions move out, the greater the electrical gradient becomes! 6 3

4 Thus we now have an inward and outward force Outward = chemical gradient ( a force merely based on concentration differences) Inward = electrical force ( a force merely based on opposite charges attracting each other) When 2 forces are in opposite direction, the net direction is the sum of the 2 forces. Initially, the chemical force is the greatest. But the electrical force gains momentum! 7 The charge difference across the membrane is called a membrane potential. ( like a battery ) [K ] Charge potential gradients are expressed in Volts. For a cell, the inside of the cell is used as reference (in this case, the membrane potential created is a negative one) Equilibrium is when the chemical force of driving K ions out equals the electrical force that pulls K back in. [K ] The membrane potential where we have equilibrium for K is called the K Equilibrium Potential. At this point, there is NO NET FLUX for K across the membrane! 8 4

5 The sign of a Membrane potential indicates the charge of the inside versus the outside. Since every ion has a specific channel and distribution, it has its own Equilibrium potential! The Nernst Equation provides us with the Equilibrium Potential for an ion. At 37 C, this equals [K ] [K ] E x = {60/z}. log {[X in ]/[X out ]} E x = Equilibrium Potential ( in mv ) for ion X X in, X out = inside, outside concentration Z = valence (total charge and sign of the ion) 9 E x = {60/z}. log {[X in ]/[X out ]} The Nernst Equation for K becomes thus X in = 140 mm X out = 5 mm Z = 1 E x = {60/1}. log {[140]/[5]} E x = {60/1}. log {28} [K ] [K ] E K = 86.8 mv E x = {60/1}. ( 1.447) = 86.8 mv Thus, if the membrane potential of a cell reaches 86.8 mv, there will be NO NET FLUX for K across the membrane! 10 5

6 E x = {60/z}. log {[X in ]/[X out ]} [Na ] The Nernst Equation for Na becomes thus X in = 15 mm X out = 150 mm Z = 1 E x = {60/1}. log {[15]/[105]} E x = {60/1}. log {0.1} [Na ] E Na = 60 mv E x = {60/1}. (1) = 60 mv Thus, if the membrane potential of a cell reaches 60 mv, there will be NO NET FLUX for Na across the membrane! 11 E x = {60/z}. log {[X in ]/[X out ]} E x 60 mv?? mv 87 mv 12 6

7 When a cell has a permeability (channel) for an ion, that ion will move in and out of the cell according to the electrochemical gradient If no other forces are present, movement of that ion will create a membrane potential and the ion will come to an equilibrium with respect to moving ( equal move in and equal move out) at a certain membrane potential. The Nernst Equation determines at what membrane potential equilibrium will be reached for a specific ion! Or in other words, if a cell had only 1 specific ion channel present, then the membrane potential of the cell would be equal to the equilibrium potential for that ion. 13 BUT. A cell is surrounded by several ions and each ion has leakage channels present in the membrane. So what determines the actual existing membrane potential (voltage difference across the membrane ) for a cell? The actual membrane potential is determined by the relative presence of the different ion channels. The membrane potential of a cell will always move closer towards the equilibrium potential for that ion with the most channels open! 14 7

8 A cell has a bunch more K leakage channels than it has Na leakage channels Thus the M.P. will drift towards the equilibrium potential for K, which is 86 mv If K was the only ion moving across the membrane, the M.P. would be 87 mv. BUT Na moves in and out as well. Assume you have a cell with many many K channels. What will the M.P. be? Now throw in a few Na channels. What will happen to the movement of Na and how will this effect the M.P.? 15 With only K channels, the M.P. will equal the E k = 87 mv [K ] If we throw in a few Na channels, the existing M.P. will have an effect on Na movement. Analyze the forces working on Na Chemical force = Electrical force = Net force = Inward Inward Inward [K ] [Na ] E K = 86.8 mv [Na ] 16 8

9 Na will thus move inwards. However, remember that the number of Nachannels are far less than those for K. Inward minor flux of Na adds some Positive charge to the inside and makes the M.P. a little less negative, more positive. Thus, even though we have lots of K channels, the presence of some Na channels deviates the M.P. from the Equilibrium Potential for K. That is why the recorded Membrane potential of nerves equal 70 mv. [K ] [K ] [Na ] E K = 86.8 mv MP = 70 mv [Na ] 17 Ions always try to reach their equilibrium potential. The more open channels present for that ion, the more the membrane potential will drift towards the ion s equilibrium potential. Question : At this resting membrane potential, are K and Na at equilibrium? [K ] [K ] [Na ] Answer : NO because the MP is not equal to either E.P. Consequence : both ions will show net movement across the membrane E K = 86.8 mv MP = 70 mv [Na ] 18 9

10 How will Na and K move? K : Chemical force : outward Electrical force : inward but less than it was at equilibrium since the MP is less negative than at EP. The net force is thus WARDS Na : Chemical force : inwards Electrical force : inwards Net force : inwards [K ] [K ] [Na ] MP = 70 mv [Na ] 19 Thus Na moves in and K move out at a resting membrane potential of 70 mv! [K ] This means that the Na and K gradient will vanish if nothing is done about it. In addition, the membrane potential will become 0 mv when this occurs. The cell prevents this by the action of the Na/K pump! This pumps moves K back in and Na back out ( both against their concentration gradients) and reestablishes, maintains the gradients, keeping the membrane potential steady. [Na ] [K ] [K ] [Na ] MP = 70 mv [Na ] 20 10

11 Question : If a cell had equal numbers of Na and K leakage channels, what would the resting membrane potential become? In this case, the membrane potential will drift to the average between the two Equilibrium potentials : [Na ] MP = (E k E Na ) /2 = ( ) /2 " " = (27)/2 = 13.5 mv [K ] [K ] [K ] [Na ] [Na ] 21 Question : Is the Equilibrium Potential a set number or can it change? Let s look at the Nernst Equation again. E x = {60/z}. log {[X in ]/[X out ]} Which of the parameters in this equation are subject to change? The internal concentration of a cell is pretty much fixed on a short term basis, but the external ( interstitual fluid.. plasma ) one can be changed rapidly. For example : Intravenous injections of ions or injecting drugs that kill the Na/K pump, and thus messes with the ion gradients

12 Question : How do we know what direction an ion will move Remember that IF the M.P. is equal to the E.P. for an ion, then that ion will show no NET movement. Let s look at the Nernst Equation again. Also Remember that the concentration gradient for an ion, under normal conditions, never changes! So, the chemical force will always remain fairly constant. Since the electrical force depends on the electrical potential, this force is the one that changes quite frequently. This is the one we have to analyze. Finally, this force can grow larger, smaller, be equal to zero, or change direction. 23 Example : Movement of K ( E k = 87 mv) ( MP = 70 mv) (CF = chemical force ; EF = electrical force) 100 mv 87 mv 0 mv 30 mv C.F. E.F. IN IN Zero N.F. IN Zero 24 12