# from Rho and Prescott, PLoS Comput Biol 2012 # to be run in XPP # 2-D model plus noise (to get oscillations near the bifurcation) and adaptation (to getting bursting) (see Figs 3-5) # DIFFERENTIAL EQUATIONS dv/dt = (Istim+sqrt(Qi)*ni-gna*minf(V)*(V-Vna)-gk*w*(V-VK)-gl*(V-Vl)-gadapt*z*(v-VK))/cap dw/dt = phi_w*(winf(V)-w)/tauw(V) dz/dt = (1/(1+exp((beta_z-v)/gamma_z))-z)/tauz # TO IMPLEMENT NOISE wiener ni param Qi=1 # noise amplitude is adjusted by varying Qi. Remove noise by setting to 0 # FUNCTIONS AND PARAMETERS minf(v)=.5*(1+tanh((v-beta_m)/gamma_m)) winf(v)=.5*(1+tanh((v-beta_w)/gamma_w)) tauw(v)=1/cosh((v-beta_w)/(2*gamma_w)) param Istim=0 param vna=50,vk=-100,vl=-70 param gk=20,gl=2,gna=20 param beta_m=-1.2,gamma_m=18 param beta_w=-13,gamma_w=10 # beta_w = -21 for transient spiking; beta_w = -13 for repetitive spiking param phi_w=.15 param cap=2 param gadapt=0.5,tauz=300,beta_z=0,gamma_z=4 # this implements a spike-dependent form of adaptation... activated only as V crosses 0 mV # INITIAL CONDITIONS V(0)=-70 w(0)=0.000025 z(0)=0 # ALWAYS USE EULER! - Actually this is only true for noise @ total=10000,dt=.05,xlo=-100,xhi=60,ylo=-.125,yhi=.6,xp=v,yp=w @ meth=euler @ MAXSTOR=1000000,bounds=10000 done