A patch of squid giant axon membrane ( , ) is held space-clamped (no spatial spread)…

PHYSICS · Multi-part · Fermi University Physics · Biophysics & Medical Physics · Bioelectricity, the senses and the physics of the body · Bioelectricity, the senses and the physics of the body

Forces, Machines and Signals, Ch The nerve impulse

Problem

A patch of squid giant axon membrane (

R_m = 1.5\,\mathrm{k\Omega\,cm^2}

\tau = R_mC_m = 1.5\,\mathrm{ms}

) is held space-clamped (no spatial spread) and stepped with a steady current density

I

t=0

, so its depolarisation obeys the passive charging curve

V(t) = IR_m\left(1-e^{-t/\tau}\right)

. Take the threshold for firing, once active channels engage, as

V_{\rm th} = 15\,\mathrm{mV}

. ((a)) For

I = 12\,\mu\mathrm{A\,cm^{-2}}

, find the steady-state depolarisation

IR_m

and the time

t_{\rm th}

at which

V(t)

first reaches

V_{\rm th}

. ((b)) Find the rheobase current

I_{\rm rheo}

, the smallest current for which

V(t)

can ever reach

V_{\rm th}

(i.e. as

t\to\infty

). ((c)) For

I = 8\,\mu\mathrm{A\,cm^{-2}}

, state whether threshold is ever reached, however long the pulse, and explain why in terms of

I_{\rm rheo}

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