{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# コンダクタンスベースモデル\n", "## Hodgkin-Huxleyモデル\n", "**Hodgkin-Huxleyモデル** (HH モデル)は, ニューロンの膜興奮を表現する,初めに導出された数理モデルである {cite:p}`Hodgkin1952-gy`\\footnote{HodgkinおよびHuxleyの論文の図をカラー化して分かりやすくした論文 {cite:p}`Hopper2022-xj` がある.}.HodgkinおよびHuxleyはヤリイカの巨大神経軸索に対して**電位固定法**(voltage-clamp)を用いた実験を行い, 実験から得られた観測結果を元にモデルを構築した {cite:p}`Schwiening2012-pi`.HHモデルには等価な電気回路モデルがあり, **膜の並列等価回路モデル** (parallel conductance model)と呼ばれている.膜の並列等価回路モデルでは, ニューロンの細胞膜をコンデンサ, 細胞膜に埋まっているイオンチャネルを可変抵抗 (動的に変化する抵抗) として置き換える.\n", "\n", "**イオンチャネル** (ion channel)は特定のイオン(例えばナトリウムイオンやカリウムイオンなど)を選択的に通す膜輸送体の一種である.それぞれのイオンの種類において, 異なるイオンチャネルがある (同じイオンでも複数の種類のイオンチャネルがある).また, イオンチャネルにはイオンの種類に応じて異なる**コンダクタンス**(抵抗の逆数で電流の「流れやすさ」を意味する)と**平衡電位**(equilibrium potential)がある.HHモデルでは, ナトリウム(Na$^{+}$)チャネル, カリウム(K$^{+}$)チャネル, 漏れ電流(leak current)のイオンチャネルを仮定する.漏れ電流のイオンチャネルは当時特定できなかったチャネルで, 膜から電流が漏れ出すチャネルを意味する.なお, 現在では漏れ電流の多くはCl$^{-}$イオン(chloride ion)によることが分かっている." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "それでは, 等価回路モデルを用いて電位変化の式を立ててみよう.上図において, $C_m$は細胞膜のキャパシタンス(膜容量), $I_{m}(t)$は細胞膜を流れる電流(外部からの入力電流), $I_\\text{Cap}(t)$は膜のコンデンサを流れる電流, $I_\\text{Na}(t)$及び $I_K(t)$はそれぞれナトリウムチャネルとカリウムチャネルを通って膜から流出する電流, $I_\\text{L}(t)$は漏れ電流である.このとき, \n", "\n", "$$\n", "\\begin{equation}\n", "I_{m}(t)=I_\\text{Cap}(t)+I_\\text{Na}(t)+I_\\text{K}(t)+I_\\text{L}(t) \n", "\\end{equation}\n", "$$\n", "\n", "という仮定をしている.膜電位を$V(t)$とすると, Kirchhoffの第二法則 (Kirchhoff's Voltage Law)より, \n", "\n", "$$\n", "\\begin{equation}\n", "\\underbrace{C_m\\frac {dV(t)}{dt}}_{I_\\text{Cap} (t)}=I_{m}(t)-I_\\text{Na}(t)-I_\\text{K}(t)-I_\\text{L}(t)\n", "\\end{equation}\n", "$$\n", "\n", "となる.Hodgkinらはチャネル電流$I_\\text{Na}, I_K, I_\\text{L}$が従う式を実験的に求めた.\n", "\n", "$$\n", "\\begin{align}\n", "I_\\text{Na}(t) &= \\bar{g}_{\\text{Na}}\\cdot m^{3}h(V-E_{\\text{Na}})\\\\\n", "I_\\text{K}(t) &= \\bar{g}_{\\text{K}}\\cdot n^{4}(V-E_{\\text{K}})\\\\\n", "I_\\text{L}(t) &= \\bar{g}_{\\text{L}}(V-E_{\\text{L}})\n", "\\end{align}\n", "$$\n", "\n", "ただし, $\\bar{g}_{\\text{Na}}, \\bar{g}_{\\text{K}}$はそれぞれNa$^+$, K$^+$の最大コンダクタンスである (ここで上付き棒は上限値であることを示す).$\\bar{g}_{\\text{L}}$はオームの法則に従うコンダクタンスで, Lコンダクタンスは時間的に変化はしないと仮定する.また, $m$はNa$^+$コンダクタンスの活性化パラメータ, $h$はNa$^+$コンダクタンスの不活性化パラメータ, $n$はK$^+$コンダクタンスの活性化パラメータであり, ゲートの開閉確率を表している.よって, HHモデルの状態は$V, m, h, n$の4変数で表される.これらの変数は以下の$x$を$m, n, h$に置き換えた3つの微分方程式に従う. \n", "\n", "$$\n", "\\begin{equation}\n", "\\frac{dx}{dt}=\\alpha_{x}(V)(1-x)-\\beta_{x}(V)x\n", "\\end{equation}\n", "$$\n", "\n", "ただし, $V$の関数である$\\alpha_{x}(V),\\ \\beta_{x}(V)$は$m, h, n$によって異なり, 次の6つの式に従う.\n", "\n", "$$\n", "\\begin{equation}\n", "\\begin{array}{ll}\n", "\\alpha_{m}(V)=\\dfrac {0.1(V+40)}{1-\\exp (-0.1(V+40))}, &\\beta_{m}(V)=4\\exp {(-(V+65)/18)}\\\\\n", "\\alpha_{h}(V)=0.07\\exp {(-0.05(V+65))}, & \\beta_{h}(V)=1/(1+{\\exp {\\left(-0.1(V+35)\\right)}})\\\\\n", "\\alpha_{n}(V)={\\dfrac {0.01(V+55)}{1-\\exp {\\left(-0.1(V+55)\\right)}}},& \\beta_{n}(V)=0.125\\exp {(-0.0125(V+65))} \n", "\\end{array}\n", "\\end{equation}\n", "$$\n", "\n", "これまでに説明した式を用いてHHモデルを実装する.まず必要なパッケージを読み込む." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "using Parameters: @unpack # or using UnPack\n", "using PyPlot\n", "rc(\"axes.spines\", top=false, right=false)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "abstract type Layer end\n", "abstract type Neuron <: Layer end\n", "abstract type SpikeNeuron <: Neuron end\n", "\n", "abstract type Synapse <: Layer end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "変更しない定数を保持する `struct` の `HHParameter` と, 変数を保持する `mutable struct` の `HH` を作成する.定数は次のように設定する. \n", "\n", "$$\n", "\\begin{equation}\n", "\\begin{array}{l}\n", "C_m=1.0\\ \\mu\\textrm{F/cm}^2, \\bar{g}_{\\text{Na}}=120\\ \\textrm{mS/cm}^2, \\bar{g}_{\\text{K}}=36\\ \\textrm{mS/cm}^2, \\bar{g}_{\\text{L}}=0.3\\ \\textrm{mS/cm}^2\\\\\n", "E_{\\text{Na}}=50.0\\ \\textrm{mV}, E_{\\text{K}}=-77\\ \\textrm{mV}, E_{\\text{L}}=-54.387\\ \\textrm{mV} \n", "\\end{array}\n", "\\end{equation}\n", "$$\n" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "@kwdef struct HHParameter{FT}\n", " Cm::FT = 1 # 膜容量(uF/cm^2)\n", " gNa::FT = 120; gK::FT = 36; gL::FT = 0.3 # Na+, K+, leakの最大コンダクタンス(mS/cm^2)\n", " ENa::FT = 50; EK::FT = -77; EL::FT = -54 # Na+, K+, leakの平衡電位(mV)\n", "end\n", "\n", "@kwdef mutable struct HH{FT} <: SpikeNeuron\n", " num_neurons::UInt16\n", " dt::FT = 1e-3\n", " param::HHParameter = HHParameter{FT}()\n", " v::Vector{FT} = fill(-65, num_neurons)\n", " m::Vector{FT} = fill(0.05, num_neurons) \n", " h::Vector{FT} = fill(0.6, num_neurons)\n", " n::Vector{FT} = fill(0.32, num_neurons)\n", "end" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "function update!(neuron::HH, Iext::Vector)\n", " @unpack num_neurons, dt, v, m, h, n = neuron\n", " @unpack Cm, gNa, gK, gL, ENa, EK, EL = neuron.param\n", " @inbounds for i = 1:num_neurons\n", " αm = 0.1(v[i]+40)/(1 - exp(-0.1(v[i]+40)))\n", " βm = 4exp(-(v[i]+65)/18)\n", " αh = 0.07exp(-0.05*(v[i]+65))\n", " βh = 1/(1 + exp(-0.1*(v[i]+35)))\n", " αn = 0.01(v[i]+55)/(1 - exp(-0.1(v[i]+55)))\n", " βn = 0.125exp(-0.0125(v[i]+65))\n", " \n", " m[i] += dt * (αm *(1 - m[i]) - βm * m[i])\n", " h[i] += dt * (αh *(1 - h[i]) - βh * h[i])\n", " n[i] += dt * (αn *(1 - n[i]) - βn * n[i])\n", " \n", " INa = gNa * m[i]^3 * h[i] * (v[i] - ENa)\n", " IK = gK * n[i]^4 * (v[i] - EK)\n", " IL = gL * (v[i] - EL)\n", " \n", " v[i] += dt / Cm * (Iext[i] - INa - IK - IL)\n", " end\n", " return v\n", "end\n", "\n", "(layer::Layer)(x) = update!(layer, x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "次に変数を更新する関数`update!`を書く.ソルバーとしては陽的Euler法または4次のRunge-Kutta法を用いる.以下ではEuler法を用いている.Juliaではforループを用いて1つのニューロンごとにパラメータを更新する方がベクトルを用いるよりも高速である." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Hodgkin-Huxleyモデルのシミュレーションの実行\n", "いくつかの定数を設定してシミュレーションを実行する." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " 1.305416 seconds (2.52 M allocations: 67.188 MiB, 2.45% gc time, 63.97% compilation time)\n" ] } ], "source": [ "T = 450 # ms\n", "dt = 0.01 # ms\n", "nt = Int(T/dt) # number of timesteps\n", "num_neurons = 1 # number of neurons\n", "time = (1:nt)*dt # time array\n", "Ie = repeat(10 * ((time .> 50) - (time .> 200)) + 35 * ((time .> 250) - (time .> 400)), 1, num_neurons) # injection current\n", "varr, gatearr = zeros(nt, num_neurons), zeros(nt, 3, num_neurons) # 記録用\n", "\n", "hh_neurons = HH{Float32}(num_neurons=num_neurons, dt=dt) # modelの定義\n", "\n", "# simulation\n", "@time for t = 1:nt\n", " v = hh_neurons(Ie[t, :])\n", " varr[t, :] = v\n", " gatearr[t, :, :] .= [hh_neurons.m; hh_neurons.h; hh_neurons.n]\n", "end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "ニューロンの膜電位 `v`, ゲート変数 `m, h, n`, 刺激電流 `Ie`の描画をする." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Figure(PyObject
)" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "PyObject Text(0.5, 24.0, 'Times (ms)')" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fig, axes = subplots(3,1, figsize=(5, 3), height_ratios=[1, 1, 0.5], constrained_layout=true) \n", "axes[1].set_title(\"Hodgkin-Huxley model\")\n", "axes[1].plot(time, varr[:, 1], color=\"black\"); axes[1].set_ylabel(\"V (mV)\")\n", "\n", "labellist=[\"m\" \"h\" \"n\"] \n", "for i in 1:3\n", " axes[2].plot(time, gatearr[:, i, 1], label=labellist[i])\n", "end; \n", "axes[2].set_ylabel(\"Gating Value\"); axes[2].legend(loc=\"center left\", bbox_to_anchor=(1, 0.5))\n", "axes[3].plot(time, Ie[:, 1], color=\"black\"); \n", "axes[3].set_ylabel(\"Current\\n\"*L\"($\\mu$A/cm$^2$)\"); axes[3].set_xlabel(\"Times (ms)\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "次項で用いるために発火回数を求める.ここでは膜電位が0を超えた点を数えることで,簡易的に求める." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Num. of spikes : 27\n" ] } ], "source": [ "function get_num_spikes(varr)\n", " spike = (varr[1:end-1, :] .< 0) .& (varr[2:end, :] .> 0)\n", " return sum(spike, dims=1)\n", "end\n", "\n", "num_spikes = get_num_spikes(varr)\n", "println(\"Num. of spikes : \", num_spikes[1])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "50msから200msまでで11回, 250msから400msまでで16回発火しているので発火回数は計27回であり,この結果は正しい." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Connor-Stevensモデル\n", "HHモデルはイカの巨大軸索の活動を再現したものであるが,脊椎動物のニューロンの神経活動を再現するためにHHモデルを修正したモデル (modified Hodgkin-Huxley model) が提案されてきた.その一種である,**Connor-Stevensモデル** はHHモデルに2つ目のカリウム電流(A型カリウム電流)を追加し,低い発火率でも活動を維持できる(振動を維持できる)ようにしたものである {cite:p}`Connor1971-rs,Connor1977-qo`.ここでパラメータは{cite:p}`Dayan2005-ib`に記載のものを使用する.\n", "\n", "$$\n", "\\begin{equation}\n", "\\begin{array}{l}\n", "C_m=1.0\\ \\mu\\textrm{F/cm}^2,\\\\ \n", "\\bar{g}_{\\text{Na}}=120\\ \\textrm{mS/cm}^2, \\bar{g}_{\\text{K}}=20\\ \\textrm{mS/cm}^2, \\bar{g}_{\\text{A}}=47.7\\ \\textrm{mS/cm}^2, \\bar{g}_{\\text{L}}=0.3\\ \\textrm{mS/cm}^2\\\\\n", "E_{\\text{Na}}=55.0\\ \\textrm{mV}, E_{\\text{K}}=-72\\ \\textrm{mV}, E_{\\text{A}}=-75\\ \\textrm{mV},E_{\\text{L}}=-17\\ \\textrm{mV} \n", "\\end{array}\n", "\\end{equation}\n", "$$\n", "\n", "$$\n", "\\begin{equation}\n", "\\begin{array}{ll}\n", "\\alpha_m=\\dfrac{0.38(V+29.7)}{1-\\exp (-0.1(V+29.7))} & \\beta_m=15.2 \\exp (-(V+54.7)/18) \\\\\n", "\\alpha_h=0.266 \\exp (-0.05(V+48)) & \\beta_h=3.8 /(1+\\exp (-0.1(V+18))) \\\\ \n", "\\alpha_n=\\dfrac{0.02(V+45.7)}{1-\\exp (-0.1(V+45.7))} & \\beta_n=0.25 \\exp (-0.0125(V+55.7))\n", "\\end{array}\n", "\\end{equation}\n", "$$\n", "\n", "$$\n", "\\begin{equation}\n", "\\frac{dx}{dt}=\\frac{x_\\infty-x}{\\tau_x}\\ (x=a, b)\n", "\\end{equation}\n", "$$\n", "\n", "$$\n", "\\begin{equation}\n", "\\begin{array}{l}\n", "a_{\\infty}=\\left(\\dfrac{0.0761 \\exp [(V+94.22)/31.84]}{1+\\exp ((V+1.17)/28.93)}\\right)^{\\frac{1}{3}}\\\\\n", "\\tau_a=0.3632+1.158 /(1+\\exp ((V+55.96)/20.12)) \\\\\n", "b_{\\infty}=\\left[1+\\exp ((V+53.3)/14.54)\\right]^{-4}\\\\\n", "\\tau_b=1.24+2.678 /(1+\\exp [(V+50)/16.027])\n", "\\end{array}\n", "\\end{equation}\n", "$$" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "@kwdef struct CSParameter{FT}\n", " Cm::FT = 1 # 膜容量(uF/cm^2)\n", " gNa::FT = 120; gK::FT = 20; gA::FT = 47.7; gL::FT = 0.3 # Na+, K+, KA, leakの最大コンダクタンス(mS/cm^2)\n", " ENa::FT = 55; EK::FT = -72; EA::FT = -75; EL::FT = -17 # Na+, K+, KA, leakの平衡電位(mV)\n", "end\n", "\n", "@kwdef mutable struct CS{FT} <: SpikeNeuron\n", " num_neurons::UInt16\n", " dt::FT = 1e-3\n", " param::CSParameter = CSParameter{FT}()\n", " v::Vector{FT} = fill(-65, num_neurons)\n", " m::Vector{FT} = fill(0.05, num_neurons) \n", " h::Vector{FT} = fill(0.6, num_neurons)\n", " n::Vector{FT} = fill(0.32, num_neurons)\n", " a::Vector{FT} = fill(0.66, num_neurons)\n", " b::Vector{FT} = fill(0.22, num_neurons)\n", "end" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "update! (generic function with 2 methods)" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function update!(neuron::CS, Iext::Vector)\n", " @unpack num_neurons, dt, v, m, h, n, a, b = neuron\n", " @unpack Cm, gNa, gK, gA, gL, ENa, EK, EA, EL = neuron.param\n", " @inbounds for i = 1:num_neurons\n", " αm = 0.38(v[i]+29.7)/(1 - exp(-0.1(v[i]+29.7)))\n", " βm = 15.2exp(-(v[i]+54.7)/18)\n", " αh = 0.266exp(-0.05*(v[i]+48))\n", " βh = 3.8/(1 + exp(-0.1*(v[i]+18)))\n", " αn = 0.02(v[i]+45.7)/(1 - exp(-0.1(v[i]+45.7)))\n", " βn = 0.25exp(-0.0125(v[i]+55.7))\n", " \n", " a∞ = ((0.0761exp((v[i]+94.22)/31.84))/(1+exp((v[i]+1.17)/28.93)))^(1/3)\n", " τa = 0.3632+1.158/(1+exp((v[i]+55.96)/20.12))\n", " b∞ = (1+exp((v[i]+53.3)/14.54))^(-4)\n", " τb = 1.24+2.678/(1+exp((v[i]+50)/16.027))\n", " \n", " m[i] += dt * (αm *(1 - m[i]) - βm * m[i])\n", " h[i] += dt * (αh *(1 - h[i]) - βh * h[i])\n", " n[i] += dt * (αn *(1 - n[i]) - βn * n[i])\n", " a[i] += dt * (a∞ - a[i]) / τa\n", " b[i] += dt * (b∞ - b[i]) / τb\n", " \n", " INa = gNa * m[i]^3 * h[i] * (v[i] - ENa)\n", " IK = gK * n[i]^4 * (v[i] - EK)\n", " IA = gA * a[i]^3 * b[i] * (v[i] - EA)\n", " IL = gL * (v[i] - EL)\n", " \n", " v[i] += dt / Cm * (Iext[i] - INa - IK - IA - IL)\n", " end\n", " return v\n", "end" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " 0.493828 seconds (2.14 M allocations: 38.829 MiB, 38.81% compilation time)\n" ] } ], "source": [ "T = 450 # ms\n", "dt = 0.01 # ms\n", "nt = Int(T/dt) # number of timesteps\n", "num_neurons = 1 # number of neurons\n", "time = (1:nt)*dt # time array\n", "Iext_cs = repeat(10 * ((time .> 50) - (time .> 200)) + 20 * ((time .> 250) - (time .> 400)), 1, num_neurons) # injection current\n", "varr_cs = zeros(nt, num_neurons) # 記録用\n", "\n", "cs_neurons = CS{Float32}(num_neurons=num_neurons, dt=dt) # modelの定義\n", "\n", "# simulation\n", "@time for t = 1:nt\n", " v = cs_neurons(Iext_cs[t, :])\n", " varr_cs[t, :] = v\n", "end" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Figure(PyObject
)" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "PyObject Text(0.5, 24.0, 'Times (ms)')" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fig, axes = subplots(2,1, figsize=(4, 2), height_ratios=[1, 0.5], constrained_layout=true) \n", "axes[1].set_title(\"Connor-Stevens model\")\n", "axes[1].plot(time, varr_cs[:, 1], color=\"black\"); axes[1].set_ylabel(\"V (mV)\")\n", "axes[2].plot(time, Iext_cs[:, 1], color=\"black\"); \n", "axes[2].set_ylabel(\"Current\\n\"*L\"($\\mu$A/cm$^2$)\"); axes[2].set_xlabel(\"Times (ms)\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## F-I曲線\n", "HHモデルにおいて,入力電流に対する発火率がどのように変化するかを調べる.次のコードのように入力電流を徐々に増加させたときの発火率を見てみよう." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "fi_curve (generic function with 1 method)" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "function fi_curve(NeuronType; num_neurons=200, T=1000, dt=0.04,\n", " current_range = [1, 30])\n", " nt = Int(T/dt) # number of timesteps\n", " Iext_range = Array{Float32}(range(current_range..., length=num_neurons)) # injection current\n", " neurons = NeuronType{Float32}(num_neurons=num_neurons, dt=dt) # modelの定義\n", " varr_fi = zeros(Float32, nt, num_neurons) # 記録用\n", "\n", " # simulation\n", " for t = 1:nt\n", " v = neurons(Iext_range)\n", " varr_fi[t, :] = v\n", " end\n", " num_spikes = get_num_spikes(varr_fi)\n", " rate = num_spikes/T*1e3;\n", " threshold = Iext_range[findfirst(rate .> 1)[2]]\n", " return Iext_range, rate, threshold\n", "end" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "Iext_range_hh, rate_hh, threshold_hh = fi_curve(HH, current_range = [1, 25])\n", "Iext_range_cs, rate_cs, threshold_cs = fi_curve(CS, current_range = [1, 25]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "発火率を計算して結果を描画する." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Figure(PyObject
)" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "PyObject Text(0.5, 0.020835, 'Input current ($\\\\mu$A/cm$^2$)')" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fig, axes = subplots(1,2, figsize=(4, 2),constrained_layout=true) \n", "axes[1].set_title(\"Type I (CS model)\")\n", "axes[1].text(threshold_cs+1, 0, L\"$I_{\\theta}$=\"*string(round(threshold_cs, digits=2)))\n", "axes[1].plot(Iext_range_cs[:], rate_cs[1, :]); \n", "axes[1].set_ylabel(\"Firing rate (Hz)\")\n", "\n", "axes[2].set_title(\"Type II (HH model)\")\n", "axes[2].text(threshold_hh+1, 0, L\"$I_{\\theta}$=\"*string(round(threshold_hh, digits=2)))\n", "axes[2].plot(Iext_range_hh[:], rate_hh[1, :]); \n", "fig.supxlabel(L\"Input current ($\\mu$A/cm$^2$)\", size=10)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "このような曲線を**frequency-current (F-I) 曲線** (または neuronal input/output (I/O) 曲線)と呼ぶ.$I_\\theta$は閾値電流を意味する(ここでは発火率が1Hz以上になる点を閾値と設定している).F-I曲線の種類に応じてType IおよびIIに分けられる\\footnote{Type IIIニューロンも存在する}." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 全か無かの法則の反例\n", "ニューロンは電流が流入することで膜電位が変化し, 膜電位がある一定の閾値を超えると活動電位が発生する, というのはニューロンの活動電位発生についての典型的な説明である.膜電位が閾値を超えるか超えないかで活動電位の発生が決まるという法則を, **全か無かの法則** (all-or-none principle) と呼ぶ.後に説明するLIFモデルなどは,全か無かの法則に従って神経活動のモデル化を行っている.しかし,この全か無かの法則の法則は必ずしも成立するわけではない.反例として **抑制後リバウンド** (Postinhibitory rebound; PIR)という現象がある.抑制後リバウンドは過分極性の電流の印加を止めた際に膜電位が静止膜電位に回復するのみならず, さらに脱分極をして発火をするという現象である.この時生じる発火を**リバウンド発火** (rebound spikes)と呼ぶ.この現象が生じる要因として**アノーダルブレイク** (anodal break, またはanode break excitation; ABE)や,遅いT型カルシウム電流 (slow T-type calcium current) が考えられている {cite:p}`Chik2004-ka`.HH モデルはこのうちアノーダルブレイクを再現できるため, シミュレーションによりどのような現象か確認してみよう.これは入力電流を変更するだけで行える." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " 0.439759 seconds (2.11 M allocations: 39.755 MiB, 7.73% gc time)\n" ] } ], "source": [ "T = 450 # ms\n", "dt = 0.01 # ms\n", "nt = Int(T/dt) # number of timesteps\n", "num_neurons = 1 # number of neurons\n", "time = (1:nt)*dt # time array\n", "Ie = repeat(10 * (-(time .> 50) + (time .> 200)) + 20* (-(time .> 250) + (time .> 400)), 1, num_neurons) # injection current\n", "varr, gatearr = zeros(nt, num_neurons), zeros(nt, 3, num_neurons) # 記録用\n", "\n", "hh_neurons = HH{Float32}(num_neurons=num_neurons, dt=dt) # modelの定義\n", "\n", "# simulation\n", "@time for t = 1:nt\n", " v = hh_neurons(Ie[t, :])\n", " varr[t, :] = v\n", " gatearr[t, :, :] .= [hh_neurons.m; hh_neurons.h; hh_neurons.n]\n", "end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "結果は次のようになる." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "Figure(PyObject
)" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "PyObject Text(0.5, 24.0, 'Times (ms)')" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fig, axes = subplots(3,1, figsize=(5, 3), height_ratios=[1, 1, 0.5], constrained_layout=true) \n", "axes[1].set_title(\"Postinhibitory rebound\")\n", "axes[1].plot(time, varr[:, 1], color=\"black\"); axes[1].set_ylabel(\"V (mV)\")\n", "\n", "labellist=[\"m\" \"h\" \"n\"] \n", "for i in 1:3\n", " axes[2].plot(time, gatearr[:, i, 1], label=labellist[i])\n", "end; \n", "axes[2].set_ylabel(\"Gating Value\"); axes[2].legend(loc=\"center left\", bbox_to_anchor=(1, 0.5))\n", "axes[3].plot(time, Ie[:, 1], color=\"black\"); \n", "axes[3].set_ylabel(\"Current\\n\"*L\"($\\mu$A/cm$^2$)\"); axes[3].set_xlabel(\"Times (ms)\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "なぜこのようなことが起こるか, というと過分極の状態から静止膜電位へと戻る際にNa$^+$チャネルが活性化 (Na$^+$チャネルの活性化パラメータ$m$が増加し, 不活性化パラメータ$h$が減少)し, 膜電位が脱分極することで再度Na$^+$チャネルが活性化する, というポジティブフィードバック過程(**自己再生的過程**)に突入するためである (もちろん, この過程は通常の活動電位発生のメカニズムである). この際, 発火に必要な閾値が膜電位の低下に応じて下がった, ということもできる.\n", "\n", "なお,PIRに関連する現象として抑制後促通 (Postinhibitory facilitation; PIF)がある.これは抑制入力の後に興奮入力がある一定の時間内で入ると発火が起こるという現象である {cite:p}`Dodla2006-fj`." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 参考文献\n", "```{bibliography}\n", ":filter: docname in docnames\n", "```" ] } ], "metadata": { "kernelspec": { "display_name": "Julia 1.10.2", "language": "julia", "name": "julia-1.10" }, "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "1.10.2" } }, "nbformat": 4, "nbformat_minor": 4 }