Introduction to Biophysics Lecture 25 Active ion pumping, neural pulses

All animal cells have sodium anomaly of this type. Actual (measured) for squid giant axon, actual membrane potential is -60 mV. Ion Interior concentration, mM exterior concentration, mM Nernst potential K+ 400 20 -75 mV Na+ sodium anomaly 50 440 +54 mV Cl- 52 560 -59 mV All animal cells have sodium anomaly of this type.

j q,i = zi e ji = (V - iNernst )gi Ohmic conductance hypothesis (explores nonequilibrium steady state when Nernst potential is not equal transmembrane potential, good only close to resting conditions): j q,i = zi e ji = (V - iNernst )gi j - (number of ions per unit area) is positive if the net flux is outward gi - conductance per area,1/m2, note it will be different for different ions.

gK+  25gNa+  2gCl- (resting) Active pumping maintains steady-state membrane potential while avoiding large osmotic pressure 1. Analyzed gNa+ , 1948 use of radioactive Na+ Nerve and muscle cells behave ohmically under nearly resting conditions gK+  25gNa+  2gCl- (resting) In 1951, keep identical solutions on both sides ( = 0, all ions) and V = 0, cell nevertheless transports Na! j Na = (V - NaNernst )gNa + jNapump Exterior K+ and ATP (metabolism is required to maintain) jNapump

Na⁺/K⁺-ATPase (1955) Will work if purified protein is inserted into artificial membrane. Tightly coupled machine wastes not ATP. Coupled transport.

Living cell maintains a steady state indefinitely every ion must: 1) impermeant (macromolecules) or 2) in Nernst equilibrium (Cl) or 3) actively pumped (Na, K) These ions which are actively pumped must separately have their Ohmic leakage exactly matched by their active pumping rates. -jKOhmic = jKpump = -2/3 jNapump = -2/3 (-jNaOhmic) -2/3(V - NaNernst )gNa = (V - KNernst )gK V = (2 gNa NaNernst + 3gK KNernst ) / (2 gNa + 3gK) The ion species with the greatest conductance per area (K+) mostly determines the resting membrane potential which will be close to the Nernst potential of this ion. During nerve impulse, due to dramatic change in Na conductance, trasmembrane potential reverses to be close to that of Na.

Function of nerve cell Sensing stimulation from preceding cells outputs (in dendrite) Computation of the appropriate output signal Transmission (without loss of intensity) of the output signal along the axon

Passive spread Peak height is proportional to stimulus strength

Action potential

Properties of the action potential all-or-none response, peak potential is independent of the strength of the initial stimulus (as soon as it is sufficient to cross the threshold) and distance from the site of stimulation. Moves with constant speed 0.1-120 m/s Reserves its shape (independent of the stimulus) as it travels produces afterhyperpolarization Refractory period

More realistic model of cell membrane: Quasi steady state approximation omits gated ion conductance and active ion pumping. d()/ dt = I/C capacitive current C=C*A , C10-2 (F/m2)

Quasi steady state approximation omits gated ion conductance and active ion pumping. Start with steady state and shut down pumps. System will evolve slowly do Donnan equilibrium. 0 – potential difference across the membrane shortly after shutting down the pumps. Condition to avoid charge pile up:

Figure 12.4 (Schematic; circuit diagram.) Caption: See text. 0 Figure 12.4 (Schematic; circuit diagram.) Caption: See text.

Reading: Nelson 11.1, 11.2, 12.1.1 Homework: Compare the free energy gain from hydrolyses of one ATP molecule with the cost of running the Na/K pump through a cycle. Problems 11.3, 11.4, page 504 Example on page 512 (find membrane potential shortly after shutting off ion pumps).