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spike_fitting.jl
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### A Pluto.jl notebook ###
# v0.18.4
using Markdown
using InteractiveUtils
# ╔═╡ d24e4576-b066-11ec-3cd9-55bf3d0f89a1
begin
using CSV
using Plots
using DataFrames
using DifferentialEquations
end
# ╔═╡ fd3fcbe9-f028-48fb-b454-bb41e19c3ad1
PC038_S12 = CSV.read("neuron firing data/csv/PC038_S12.csv",DataFrame)
# ╔═╡ 76f65b0a-ef0a-487a-85dd-37ead71c19ca
begin
plot(PC038_S12[!,"t"] .* 1000,PC038_S12[!,"Y"],xlabel="time in ms",ylabel="V in mV")
savefig("sweep.png")
end
# ╔═╡ 82d49652-668e-4490-bba6-a28a3386edb5
plot(PC038_S12[!,"t"] .* 1000,PC038_S12[!,"C"],xlabel="time in ms",ylabel="Applied Current pA")
# ╔═╡ 238950da-0ab0-493d-b1fc-b54cb1968a36
begin
## Constants
const C_m = 100.0 # μF/cm², membrane capacitance
const G_NaMax = 40 # mS/cm², maximum conductivity of Na channel
const G_KMax = 35 # mS/cm², maximum conductivity of K channel
const G_L = 0.3 # mS/cm², leak conductivity
const V_r = -68 # mV, resting potential
const V_Na = 40 # mV, Nernst voltage for Na
const V_K = -77 # mV, Nernst voltage for K
const V_L = -54.387 # mV, Nernst voltage for leak
## Function Definitions
α_n(dV) = (0.1 - 0.01*dV)/(exp(1 - 0.1*dV)- 1)
β_n(dV) = 0.125/(exp(0.0125*dV))
α_m(dV) = (2.5 - 0.1*dV)/(exp(2.5 - 0.1*dV)- 1)
β_m(dV) = 4/(exp(dV/18))
α_h(dV) = 0.07/(exp(0.05*dV))
β_h(dV) = 1/(exp(3 - 0.1*dV)+ 1)
# Steady states
n_∞(dV) = α_n(dV)/(α_n(dV)+β_n(dV))
m_∞(dV) = α_m(dV)/(α_m(dV)+β_m(dV))
h_∞(dV) = α_h(dV)/(α_h(dV)+β_h(dV))
end
# ╔═╡ a31dd320-e814-4728-968a-7e529c9781e4
begin
# Injected Current Function
I_inj(t) = 150 * (531.25 <= t <= 1531.2)
end
# ╔═╡ 248b583c-1557-4399-9fa4-816a352fe39e
function HH_model(u,p,t)
n, m, h, Vm = u
# Update transfer rate coefficients, n, m, and h
V_diff = Vm - V_r # difference between the rest voltage and membrane voltage
dn = α_n(V_diff)*(1-n) - β_n(V_diff)*n
dm = α_m(V_diff)*(1-m) - β_m(V_diff)*m
dh = α_h(V_diff)*(1-h) - β_h(V_diff)*h
# Update cell membrane voltage, Vm
G_K = G_KMax * n^4 # Sodium conductance
G_Na = G_NaMax * h * m^3 # Potasium conductance
dVm = (I_inj(t) + (V_Na - Vm)*G_Na + (V_K - Vm)*G_K + (V_L - Vm)*G_L)/C_m
[dn; dm; dh; dVm]
end
# ╔═╡ a549f336-5498-4529-a5b6-bf6778a5d286
begin
## Run Model:
u0 = [n_∞(0); m_∞(0) ; h_∞(0); -65.1]
tspan = (0.0,2000.0)
prob = ODEProblem(HH_model, u0, tspan)
sol = solve(prob, saveat=0.01);
end
# ╔═╡ 3fd06541-fdad-4772-aa29-f71fa6d33690
begin
p1 = plot(sol.t, sol[4,:], legend=false, ylabel="Voltage [mV]")
plot!(PC038_S12[!,"t"] .* 1000,PC038_S12[!,"Y"])
p2 = plot(sol.t, I_inj.(sol.t), legend=false, lc=:red, ylabel="Current [pA]")
p3 = plot(sol.t, sol[1:3,:]', label=["n" "m" "h"], legend=:topright,
xlabel="Time [ms]", ylabel="Fraction Active")
l = grid(3, 1, heights=[0.4, 0.2 ,0.4])
plot(p1, p2, p3, layout = l, size=(800,500), lw=2)
#savefig("simulation2.png")
end
# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
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# ╔═╡ 00000000-0000-0000-0000-000000000002
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