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1 Resting membrane potential Inside of each cell is negative as compared with outer surface: negative resting membrane potential (between -30 and -90 mv) Examination with microelectrode (Filled with KCl solution Same mobility, There is not disturbing diffusion potential) Resting membrane potential, All living cells maintain a potential difference across their cell membranes. The inside usually negative relative to the outside. Squid (cuttle-fish or calamary) giant axon Prepared muscle cells Physics Biophysics 3 November 2015 Membrane potential The electrical potential difference (voltage) across a cell's plasma membrane. V resting = mv Why is the membrane potential formed? Unequal distribution of ions on two sides of the membrane: in the cell high K + and low Na + concentration Constantly active K-Na pump: Na + moves out, K + moves in Selectively permeable membrane: the cell membrane is more permeable for Potassium ions than Sodium ions Non-diffusible ions (proteins and nucleic acids) with negative charge are in the cell Intracellular [Na + ] 10 mm [K + ] 140 [Ca 2+ ] <10-3 [Cl - ] 3-4 [A - ] 140 Extracellular [Na + ] 120 mm [K + ] 2,5 [Ca 2+ ] 2 [Cl - ] 120

2 Forces controlling the movements of charged particles Drive forces : 1) The difference of the ions concentration - Concentration gradient (diffusion: moving the particles from a high concentration area to a low one): Chemical potential 2) Charge difference between two sides of the membrane electrical gradient: Electric potential Electro-chemical potential the combination (sum) of the chemical and the electric potential. In equilibrium the change of free energy of the chemical and electrical concentration gradient equal and different direction. The resting membrane potential can be calculated. The origin of the resting membrane potential Bernstein potassium hypothesis Nernst-equlibrium potential (electro-chemical potential) Donnan equlibrium: the membrane is impermeable for some components (e.g. intracellular proteins). Goldman-Hodgkin-Katz equation: The membrane potential is the result of a compromise between the various equlibrium potentials, each weighted by the membrane permeability and absolute concentration of the ions. Bernstein s potassium hypothesis (1902) Nernst equation 1 Chemical potential Wchem = NRT ln X 2 X N = number of moles associated with the concentration gradient R = gas constant T = absolute temperature X 1 /X 2 = concentration gradient Electrical potential Welectr = NzFE N = number of moles of the charged particles z=valency F = Faraday s number E= strength of the electric field (V)

3 Equlibrium potential Ionic concentrations inside and outside of a muscle cell Nernst equation: What membrane potential (E) balances the concentration gradient (X 1 /X 2 ). E = RT zf ln X X 1 The inward and outward flows of the ions are balanced (net current = zero equilibrium = stable, balanced, or unchanging system). 2 Na + : 120 mm K + : 2.5 mm Cl : 120 mm [K + ] E mv = 58/1 log (139/2.5) = mv [Na + ] E mv = 58/1 log (20/120) = mv [Cl ] E mv = 58/1 log (3.8/120) = mv Na + : 20 mm K + : 139 mm Cl : 3.8 mm = 30.8 mv Measured resting potential E mv = 92mV Donnan potential Passive transport The Nernst equation is not suitable for determining the membrane potential. The calculated values differ from the measured values. Behavior of the ions are not independent. It is not a closed system. Donnan equilibrium is created for membrane what is permeable for ions and nonpermeable for proteins. low concentration of small permeable anions Steady-state with mv is the potential difference. cation concentration The cell resting membrane potential is not based on Donnan equilibrium predominantly. www2.sci.u szeged.hu/.../iv.%20a%20membrantrans... donnan en.svg

4 Goldman-Hodgkin-Katz equation Equlibrium potential [K + ] E mv = -58/1 log (139/2.5) = mv K + =2.5 mm K + =139 mm mv Vm membrane potential R universal gas constant T temperature F Faraday s constant p relative permeabilities [ ] o is the concentration in the extracellular fluid [ ] i is the concentration in the intraracellular fluid E mv = mv no net movement (equilibrium) E mv > mv K + moving out E mv < mv K + moving in battery A voltage value of the ion for which the balance between the concentration gradient. Leakage through the cell membrane amembrane potential is not equal with any of the equlibrium potentials for the different ions E mv K + = mv < E mv = - 92mV E mv Na + = mv > E mv Cl = mv > the ions are trying to get (move) through the membrane K + is trying to get out leakage Na + is trying to get in Cl is trying to get in

5 It can be developed on the membrane of nerve cells or muscle cells Typical for a given cell type Required stimulation above the voltage threshold : a momentary reversal of membrane potential ( 70 mv to + 40 mv) that will be followed by the restoration of the original membrane potential after a certain time period (1 400ms). s happens in different phases. s are triggered by the depolarization of the membrane (local disturbances) if it can reach a critical value (voltage threshold). s are all or none phenomena any stimulation above the voltage threshold results in the same action potential response. any stimulation below the voltage threshold will not result action potential response. 0. Resting phase 1. Rising phase The voltage gated sodium channels will open-up if the voltage threshold was reached by the stimulus. Na + will move into the cell. the inner surface of the cell will be positively charged. Equlibrium situation 2

6 3. Overshoot The movement of the Na + will slow down EmV_Na + = mv (Nernst equlibrium potential) Na + channels will start to form an inactive conformation K + channels are starting to open up 4. Falling phase All the voltage gated K + channels are open K + move out from the cell Sodium channels are closed down (inactivation) refractory period 5. Falling phase 6. Resting phase The movement of the K + ions will slow down EmV_K + = mv (Nernst equlibrium potential) The K + channels will get into a closed conformation The numerous and slowly inactivating K + channels will cause some hyperpolarisation Hyperpolarization

7 REFRACTORY PERIOD Absolute refractory period The formation of a new AP is totaly blocked. Relative refractory period Larger depolarisation is needed than the threshold to initialize an AP.

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