# Modified Morris-Lecar model # modified from ml_salka.ode dV/dt = (i_dc-gna*minf(V)*(V-Vna)-gk*y*(V-VK)-gl*(V-Vl)-gsub*z*(V-Vsub))/c dy/dt = phi_y*(yinf(V)-y)/tauy(V) dz/dt = phi_z*(zinf(V)-z)/tauz(V) param c=2 # HERE IS EVERYTHING YOU NEED TO KNOW ABOUT THE STIMULuS # DC OFFSET # this is controlled by i_dc param i_dc=0 ## noise not included here. ## To add it, uncomment lines below by removing one "#" per line, and add "i_noise" to line 3 (dv/dt=...) above ## NOISE ## This is modeled as an Ornstein-Uhlenbeck process, gives new noise on each trial ## Here is the Wiener variable #wiener nz ## With scale=0 you get no noise ## effects of changing dt are automatically controlled for in XPP ## However, variance of i_noise also depends on tau_inoise (variance = sigma^2*tau/2) ## Therefore, if you want to keep the same variance, you must manually change sigma_inoise if you change tau_inoise #di_noise/dt=-1/tau_inoise*(i_noise-i_avg)+sigma*nz #param sigma=0, tau_inoise=5, i_avg=0 ## frozen noise can be repeated on multiple trials by saving i_noise to a .tab file and playing it back ## see xpp documentation about tables # HERE IS EVERYTHING YOU NEED TO KNOW ABOUT INTRINSIC CURRENTS # Initial conditions V(0)=-70 y(0)=0.000025 z(0)=0 # if you want to make sure initial conditions are at steady state # run trial with no stim, then select "initial conditions/last" from main menu... this will start you at the conditions at the end of your previous trial # FAST INWARD CURRENT (INa or activation variable) # This is assumed to activate instantaneously with changes in voltage # voltage-dependent activation curve is described by m minf(V)=.5*(1+tanh((V-beta_m)/gamma_m)) # maximal conductance and reversal potential param beta_m=-1.2, gamma_m=18 param gna=20, vna=50 # DELAYED RECTIFIER CURRENT (IKdr or recovery variable) # this current activates more slowly than INa, but is still faster than Isub or Iadapt (not included here) # In this code, activation of IKdr is controlled by y yinf(V)=.5*(1+tanh((V-beta_y)/gamma_y)) tauy(V)=1/cosh((V-beta_y)/(2*gamma_y)) # in the 2D model, varying beta_w shifts the w activation curve (w=y here) and can convert the neuron between class 1, 2, and 3 param beta_y=-10, gamma_y=10 # maximal conductance and reversal potential param gk=20, vk=-100, phi_y=0.15 # LEAK CURRENT (Il) # just a passive leak conductance param gl=2, vl=-70 # SLOW SUBTHRESHOLD INWARD OR OUTWARD CURRENT (Isub) zinf(V)=.5*(1+tanh((V-beta_z)/gamma_z)) tauz(V)=1/cosh((V-beta_z)/(2*gamma_z)) param beta_z=-21, gamma_z=15 # parameters below are for outward current param gsub=7, Vsub=-100, phi_z=0.15 # for inward current, change to gsub=3, Vsub=50, phi_z=0.5 # these parameters for Isub correspond to those used in Figure 4 of the paper # slow adaptation is not included in this 3D model. # following parameters control duration of simulation and axes of default plot @ total=100000,dt=.1,xlo=-100,xhi=60,ylo=-.125,yhi=.6,xp=v,yp=y @ meth=euler @ MAXSTOR=1000000 done