hh_equations

hh_equations - fit the experimentally-measured curves One...

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Hodgkin-Huxley model of the AP Here are the equations from which you can calculate n , n , m , m , and h , h , where n ( V ) = 0.01( V + 60) exp( ( V + 60)/10) 1 n ( V ) = 0.125exp( ( V + 70)/80) m ( V ) = 0.1( V + 45) exp( ( V + 45)/10) 1 m ( V ) = 4exp( ( V + 70)/18) h ( V ) = 0.07exp( ( V + 70)/20) h ( V ) = 1 exp( ( V + 40)/10) + 1 From these rate constants, the expressions for the asymptotic (infinity) values and time constants for the state variables can be calculated thusly: n ( V ) = n ( V ) n ( V ) + n ( V ) and n ( V ) = 1 n ( V ) + n ( V ) Analogous expressions can be written for m, and h. IMPORTANT NOTE: the expressions for α n and α m have singularities, i.e. generate divide-by-zero errors when V = -60 mV and -45 mV, respectively. This has no theoretical significance, but just arises from the particular functions that were chosen to
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Unformatted text preview: fit the experimentally-measured curves. One way to deal with this is to include an ifstatement that detects when the voltage parameter is near the bad voltage (-45 or -60 mV), and for these cases, return the limit of α as V approaches that value. For α n the limit is 0.1, and for α m the limit is 1. Example MATLAB code: %% m_inf if (abs(v(i) + 45) <=0.01) a_m(i) = 1; else a_m(i) = (-0.1*(v(i) + 45))/(exp(-(v(i) + 45)/10) - 1); end; %% n_inf if (abs(v(i) + 60) <=0.01) a_n(i) = .1; else a_n(i) = (-0.01*(v(i) + 60))/(exp(-(v(i) +60)/10) - 1); end;...
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