<latrotox@gmail.com> The Spark of Life: Electrical Basis of the Action Potential, ….A Triumph of Biophysics* and the Most Important Parallel Electrical Circuit you’ll ever need to know Metro IB Physics - 4 Spring 2017 Stan Misler <latrotox@gmail.com> *Application of physical principles, including mathematical model building, to understanding basic biological phenomenon (excitability, sensory transduction, molecular biology); organ imaging; and organ replacement with physical apparati

1. Introduction: Getting to the “heart” of the matter via Emily Dickenson Tell all the truth, but tell it slant, Success in circuit (electrical circuit) lies. Too bright for our infirm delight, The truth’s superb surprise. As lightning to the children eased, With explanation kind, The truth must dazzle gradually, Or everyone be blind.

1. The Action Potential of the cell membrane The action potential (AP) is a brief change in the voltage across a biological membrane, DVm, in response to a stimulus. The AP, which propagates down a nerve or muscle at a speed of up to 10s of meters per s, is based on brief changes in permeability (movement) of ions (Na, K, Ca) across the cell membrane. The AP can be set off by flow of current from another region of the cell, application of chemical transmitters on the outside of the cell or membrane deformation all of which may bring Vm to a threshold voltage ~-45 mv. The AP (a) enables rapid communication between nerve cells at synapses to produce movement, thought or emotions; (b) stimulates contraction of muscle; and (c) releases hormones (e.g., adrenalin and insulin) by endocrine (hormone secreting) cells. The AP can be best understood by analyzing an equivalent circuit consisting of several current sources (conductance pathways g, each with its own ionic battery E), and a capacitor Cm, all in parallel.

2. Action potentials and ion channels The currents underlying the AP flow through ion selective channels (tunneling devices) consisting of open pores in proteins that span the cell membrane, a bilayer of lipids separating two solutions of ions, one intracellular (the cytoplasm inside the cell) and the other extracellular (the fluid outside the cell). In electrical terms the transmembrane channel represents an electrical conductance g (= 1/R) while the surrounding lipid bilayer represents a capacitor in parallel. The heads of the lipids nearest the solutions form the parallel plates of the capacitor and the tails of the lipid form the dielectric. Each battery E, which is in series with a conductance g, results from a concentration difference of an ionic species across the membrane. Together these pathways give rise to an overall voltage across the membrane Vm The AP can be set off by a stimulus (e.g., small current pulse) that charges the membrane capacitance and brings the Vm to a less inside negative voltage, the threshold allowing sequential openings of more channels. This further changes the voltage across the membrane in total often by as much as 120 mV (from inside negative 80 mV to inside positive 40 mv) over 1msec.

How do we know that conductance changes are ionic and not electronic or semiconductor like? Change external concentrations of ions

3. Analysis of the equivalent circuit representing the action potential Kirchoff’s current law states that at any node in a circuit the sum of the current entering the node equals the sum of the current leaving it = A law of conservation of charge Conductances are both voltage and time dependent

4. Dueling ionic conductances: sequential opening of Na, K conductances underlie the AP. To show this calculate the membrane potential Vm under each condition where dVm/dt -> 0 Regenerative and sequential opening (“gating”) of channels underlying the AP. The more Na channels that are opened initially at the voltage threshold (~-40 mv), the more the inward current to charge the capacitor to a more positive potential and open more Na channels. However the closer the Vm gets to the value of the Na battery (E) the Vm exceeds threshold for opening K channels. Over time both types open channels inactivate returning Vm to rest

5. The battery of a conductance channel: Equilibrium condition Movement of ion (e.g., K) across a patch of membrane down a concentration gradient leaves a counterion (e.g., Cl) behind thus setting up a local space charge region near the membrane, which opposes further build up of charge difference on either side across that patch of membrane and gives a stable equilibrium potential across the membrane 3-Mar 8-Mar 2 1 P3 Exit 5 mM KCl 130 mM KCl

Steady state condition: putting two current sources in parallel -> continuous current flow through dueling channels

6. Gating of Conductance channel opening of tail of channel in response to electrostatic movement of wing -> exposure of transmembrane channel pore and movement of ions across selectivity filter Your text here

7. Conclusion Maneuvers (chemicals released by neighboring nerve cells, membrane stretch or injection of current), which charge membrane capacitance from rest Vm (-70 to -90 mv) to a threshold of -40 mv open voltage sensitive Na channels that transiently brings Vm towards + 60 mV. At these Vms voltage sensitive K channels slowly open returning Vm towards rest. This sequential change in open channels produces voltage impulse or action potential that propagates along the excitable cell. If the cell membrane contains voltage activated channels carrying Ca the influx of Ca into the cell will set off cell secretion (in nerve terminals or endocrine cells) or cell contraction (e.g., in heart) Early but transient opening of Na channels bringing inward Na current Later but more sustained opening of K channels evoking outward K currents

Alternative representations of Propagating Action potential impulse Alternative representations of Propagating Action potential impulse. (Left) Observation of space dependence of Vm at fixed time to (Right) Observation of time dependence of Vm at a given location xo

Steady state condition: continuous current flow through dueling channels

How do we know that during the AP membrane conductances change but capacitance does not? Wheatstone Bridge experiment