conv_rate = 1/tau

change to timescale tau to match paper

Author: mjowen

diagrams.jl

@@ -122,27 +122,27 @@ savefig("results/diagrams/actionPotential.pdf")
 # Limit cycles
 plotTime = 1.0
 # Start - Tracking
-params = (g_Na_sf=1.0, g_K_sf=1.0, g_L_sf=1.0, conv_rate=2.5)
+params = (g_Na_sf=1.0, g_K_sf=1.0, g_L_sf=1.0, τ=0.4)
 prob_de = ODEProblem(Model.ode!, Model.ic, (0.,1000.0), params, reltol=1e-8, abstol=1e-10)
 sol = DifferentialEquations.solve(prob_de, Tsit5(), maxiters=1e7, saveat=10.0)
 sol = Tools.aligned_sol(sol[end], prob_de, plotTime)
 plot(sol, label="Start - Tracking", idxs=(1); plotParams...)
 
 # Start - Standard
-params = (g_Na_sf=1.0, g_K_sf=1.0, g_L_sf=1.0, conv_rate=2.5)
+params = (g_Na_sf=1.0, g_K_sf=1.0, g_L_sf=1.0, τ=0.4)
 prob_de = ODEProblem(Model.ode!, Model.ic, (0.,1000.0), params, reltol=1e-8, abstol=1e-10)
 sol = Tools.aligned_sol(Model.ic, prob_de, plotTime)
 plot!(sol, label="Start - Standard", idxs=(1); plotParams...)
 
 # End - Small perturbation
-params = (g_Na_sf=1.1, g_K_sf=1.0, g_L_sf=1.0, conv_rate=2.5)
+params = (g_Na_sf=1.1, g_K_sf=1.0, g_L_sf=1.0, τ=0.4)
 prob_de = ODEProblem(Model.ode!, Model.ic, (0.,1000.0), params, reltol=1e-8, abstol=1e-10)
 sol = DifferentialEquations.solve(prob_de, Tsit5(), maxiters=1e7, saveat=10.0)
 sol = Tools.aligned_sol(sol[end], prob_de, plotTime)
 plot!(sol, label="End - Small Perturbation", idxs=(1); plotParams...)
 
 # End - Large perturbation
-params = (g_Na_sf=1.5, g_K_sf=1.2, g_L_sf=0.8, conv_rate=2.5)
+params = (g_Na_sf=1.5, g_K_sf=1.2, g_L_sf=0.8, τ=0.4)
 prob_de = ODEProblem(Model.ode!, Model.ic, (0.,1000.0), params, reltol=1e-8, abstol=1e-10)
 sol = DifferentialEquations.solve(prob_de, Tsit5(), maxiters=1e7, saveat=10.0)
 sol = Tools.aligned_sol(sol[end], prob_de, plotTime)

model.jl

@@ -54,8 +54,8 @@ function ode!(dz, z, p, t=0)
 	dz[2] = alpha_m*(1-m)-beta_m*m
 	dz[3] = alpha_h*(1-h)-beta_h*h
 	dz[4] = alpha_n*(1-n)-beta_n*n
-	dz[5] = 2.5*(-(i_Na)/(1000*F) - (nai-nai_target)/20.0)
-	dz[6] = 2.5*(-(i_K+i_Leak)/(1000*F) - (ki-ki_target)/20.0)
+	dz[5] = (1/0.4)*(-(i_Na)/(1000*F) - (nai-nai_target)/20.0)
+	dz[6] = (1/0.4)*(-(i_K+i_Leak)/(1000*F) - (ki-ki_target)/20.0)
 
 	dz
 end
@@ -110,8 +110,8 @@ function ode_cont!(dz, z, p, t=0)
 	dz[2] = alpha_m*(1-m)-beta_m*m
 	dz[3] = alpha_h*(1-h)-beta_h*h
 	dz[4] = alpha_n*(1-n)-beta_n*n
-	dz[5] = 2.5*(-(i_Na)/(1000*F) - (nai-nai_target)/20.0)
-	dz[6] = 2.5*(-(i_K+i_Leak)/(1000*F) - (ki-ki_target)/20.0)
+	dz[5] = (1/0.4)*(-(i_Na)/(1000*F) - (nai-nai_target)/20.0)
+	dz[6] = (1/0.4)*(-(i_K+i_Leak)/(1000*F) - (ki-ki_target)/20.0)
 
 	dz
 end

noble_conc.jl

@@ -13,7 +13,7 @@ function noble_conc!(dz, z, p, t=0)
 	ko = 3.8
 
 	# Parameters
-	@unpack g_Na_sf, g_K_sf, g_L_sf, conv_rate = p
+	@unpack g_Na_sf, g_K_sf, g_L_sf, τ = p
 
     # States
 	V, m, h, n, nai, ki = z
@@ -54,20 +54,20 @@ function noble_conc!(dz, z, p, t=0)
 	dz[2] = alpha_m*(1-m)-beta_m*m
 	dz[3] = alpha_h*(1-h)-beta_h*h
 	dz[4] = alpha_n*(1-n)-beta_n*n
-	dz[5] = conv_rate*(-(i_Na)/(1000*F) - (nai-nai_target)/20.0)
-	dz[6] = conv_rate*(-(i_K+i_Leak)/(1000*F) - (ki-ki_target)/20.0)
+	dz[5] = (1/τ)*(-(i_Na)/(1000*F) - (nai-nai_target)/20.0)
+	dz[6] = (1/τ)*(-(i_K+i_Leak)/(1000*F) - (ki-ki_target)/20.0)
 
 	dz
 end
 
 # parameter values
-params = (g_Na_sf=1.0, g_K_sf=1.0, g_L_sf=1.0, conv_rate=1.0)
+params = (g_Na_sf=1.0, g_K_sf=1.0, g_L_sf=1.0, τ=1.0)
 
 # initial condition
 z0 = [-87.0, 0.01, 0.8, 0.01, 30, 160]
 
 # tune the convergence rate
-params = @set params.conv_rate=2.5
+params = @set params.τ=0.4
 
 # Want to converge in close to 100 seconds
 prob_de = ODEProblem(noble_conc!, z0, (0.,200.0), params, reltol=1e-8, abstol=1e-10)