1. PHYSIOLOGY 1 Lecture 11 Membrane Potentials

2. n Objectives: Student should know –1. The basic principals of electricity –2. Membrane channels –3. Electrical-chemical gradient –4. Factors that determine resting membrane potential –5. Ion concentrations inside and outside cell –6. Ohm’s law, Nernst equation, Goldman equation –7. Polarity - role

3. Membrane Potentials n A. The body as a whole is electrically neutral n B. All of the cells of body have an electrical potential across their membrane (Voltage difference) known as the membrane potential n C. Membrane potentials develop because of differing ion concentrations between the inside and outside of the cell

4. Membrane Potentials

5. n Principals of electricity - Potential difference is determined by the difference in charge between two points n 1. Units of electrical potential are in volts (V) or for biological system millivolts (mV) 1 V = 1000mV n 2. Voltage is always measured between two points (Potential difference)

6. Membrane Potentials n B. Current - flow of electrical charges from one point to another n 1. Like charges repel unlike attract n 2. Ions tend to move from areas of greater concentration to areas of least concentration n 3. Movement of a positive ion from one side of a membrane to the other implies a negative charge is left behind

8. Membrane Potentials n C. Current Flow n Ohm’s Law - I = E / R, R = resistance n I = current flow, E = electrical potential –1. Cell - Aqueous solution + good conductor (Ions and water) –2. Lipid membrane - A few charged groups can not carry current - high electrical resistance - good insulator –3. ECF and ICF - both have low electrical resistance

9. Membrane Potentials n Resting Membrane Potential –1. By convention - ECF (outside of the cell) is assigned a voltage of zero –2. Polarity of the membrane is stated in terms of the sign of the excess charge inside of the cell

10. Membrane Ion Channels n Types of Channels –1. Leak channels - Open all of the time - slow leak of ions n a. Sodium, potassium & chlorine n b. Membrane 75% more permeable to K+ than Na+ n c. Accounts for 95% of the resting membrane potential

11. Membrane Ion Channels n 2. Na+K+ATPase Pump n a. Unequal transport of positive ions makes the ICF more negative than it would be from diffusion alone - 2 K+ inside and 3 Na+ to outside n b. Electrogenic pump n c. Accounts for 5% of resting membrane potential

12. Membrane Potentials Ion Gradients n The ion gradients have two forms. –1. Chemical Concentration Gradient –2. Electrical concentration gradient –(Charge buildup and charge differential) –Together these form what is known as the electrochemical gradient

13. Resting Membrane Potential n 1. In all cells a potential difference across the membrane exists –a. Inside is negative (Na+K+ATPase) –b. Membrane potentials usually within -40 to -90 mv n 2. A cell with a resting membrane potential is said to be polarized n 3. Both the inside and the outside of the cell are electrically neutral

14. Resting Membrane Potential n B. Factors that determine the resting membrane potential –Selective permeability of the of the plasma membrane –Leak channels –Na+K+ATPase pump –Differences in ion concentrations

15. Membrane Potentials

16. Resting Membrane Potential n 2. Many substances are in the cell but the mobile ions Na+, K+, Ca++ and Cl- play the most important roles n 3. ECF - Cl- helps to balance Na+ n ICF - Proteins (Neg charge) balance K+

17. Resting Membrane Potential n 4. Selective membrane permeability –a. At rest - Slightly permeable to Na+, 75 times more permeable to K+, and freely permeable to Cl- –b. K+ moves down it’s concentration gradient more easily & faster than Na+ –c. Movement of a K+ out leaves a negative charge behind

18. Resting Membrane Potential n d. Why no equilibrium? –Na+K+ATPase pump - stabilizes resting membrane potential by maintaining diffusion gradients for Na+ and K+ –Concentration gradient – Limit to ability of Na+K+ATPase pump n c. Cl- Movement out = movement in - no contribution to membrane potential

19. Equilibrium Potential n Equilibrium potential or electrochemical potential at which ion movements in both directions across the membrane are exactly balanced (net movement = zero) n 1. Ion flux = 0 implies no net ion movement n 2. The value of the equilibrium potential (Nernst potential) for any ion depends on the concentration gradient across the membrane for that ion

20. Equilibrium Potential n 4. The greater the concentration gradient the greater the equilibrium potential n 5. The equilibrium potential for one ion can be different in magnitude and direction from those of other ions n 6. Given the ion concentration gradient the Nernst potential for any ion can be calculated. The Nernst equation is used to determine the electrochemical potential for any ion across the biological membrane.

21. Equilibrium Potential n Nernst Equation n E(x) = RT/ZF log [x]inside/[x]outside n R = Gas constant n T = Temp. degrees Kelvin n Z = Charge on ion (Valance) n F = Faraday’s constant

22. Membrane Potentials Nernst’s Equation n A more useful form of the Nernst’s equation is - n E(x) = -61mV log [X]inside / [X]outside n or n = 61 mV log [X]outside / [X]inside

23. Membrane Potentials Nernst’s Equation - Examples n Example 1 - Calculate the electrochemical potential for Na+ n E Na+ = -61mV log [14]/[140] n log of 0.10 = -1 n then n E Na+ = 61 mV

24. Membrane Potentials Nernst’s Equation - Examples n Example 2 - Calculate the electrochemical potential for K+ n E K+ = -61mV log [140]/[4] n log of 35 = 1.5441 n then n E K+ = - 94 mV

25. Membrane Potentials Nernst Equation - Examples

26. Membrane Potentials Resting Membrane Potential n In reality a living cell contains a great number of ionic species. Most of these can and do move in and out of the cell others such as proteins can not without help. The net movement of all ionic currents across the membrane determines the resting membrane potential.

27. Membrane Potentials Resting Membrane Potential n The net current flow ( I ) across the membrane is given by; n I(x) = g(x) {Em - E(x)} n Where - g(x) is ion conductance n Em is resting membrane Pot. n E(x) is the Nernst’s Pot.

28. Membrane Potentials Resting Membrane Potential n At rest the membrane potential is not changing, then the sum of all currents must equal zero. n Thus n I Na+ + I K+ + I Cl- + … = 0

29. Membrane Potentials Resting Membrane Potential n Therefore n g Na+ [Em -E Na+ ] + g K+ [Em - E K+ ] + g Cl- [Em - E Cl- ] + … = 0

30. Membrane Potentials Resting Membrane Potential n Solving for Em yields the Goldman equation which gives the resting membrane potential

31. Membrane Potentials Resting Membrane Potential n Goldman Equation n Em = [g Na+ /(g Na+ + g K+ + g Cl- )] E Na+ n + [g K+ /(g Na+ + g K+ + g Cl- )] E K+ n + [g Cl- /(g Na+ + g K+ + g Cl- )] E Cl- n + … n Thus the resting membrane potential is a summation of all of the ion potentials times their percentage of the total ion conductance

32. Membrane Potentials Resting Membrane Potential n Since K+ conductance is almost 75 times that of Na+. The resting membrane potential is much closer to the Nernst’s potential for K+ than it is to the Nernst’s potential for Na+. n Why would K+ conductance predominate?

33. Excitable Cells n A. Nerve and muscle cells are excitable (Em < -40 mV) –1. Electrochemical impulses are transient and rapid changes in Em –2. Two forms of electrochemical impulses n B. Electrochemical signals –1. Graded potentials - short distance –2. Action potentials - long distance