Download 1. Introduction: Getting to the “heart”

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
<[email protected]>
*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
5 mM KCl
3-Mar
2
2
8-Mar
2
2
8-Mar
1
1
P3
P3
Exit
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.
(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