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| { | |
| "cells": [ | |
| { | |
| "cell_type": "code", | |
| "execution_count": 1, | |
| "metadata": { | |
| "collapsed": true | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "import numpy as np\n", | |
| "import pandas as pd\n", | |
| "import matplotlib.pyplot as plt\n", | |
| "import seaborn as sns\n", | |
| "import scipy.constants as sc\n", | |
| "from pprint import pprint as pp\n", | |
| "%matplotlib inline" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "#### Constants\n", | |
| "- $\\mu_s$ : mobility of ion s ($\\frac{m^2}{V\\cdot sec}$)\n", | |
| "- $z_s$ : valence of ion s (e.g. +1 for Na, -1 for Cl)\n", | |
| "- $q$ : elementary charge constant $(C)$\n", | |
| "- $k$ : Boltzman Constant ($\\frac{J}{K}$)\n", | |
| "- $F$ : Faraday Constant $(\\frac{C}{mol})$\n", | |
| "- $J_{diff}$ : Diffusion flux $(\\frac{molecules}{cm^2 \\cdot sec})$" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "#### Variables\n", | |
| "- $V_m$ : Voltage across the membrane $(V)$\n", | |
| "- $[S]_{in}$ : Intracellular Concentration $(\\frac{mol}{m^3})$" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "## Equations\n", | |
| "#### Nernst Eq\n", | |
| "$$V_m = \\frac{kT}{q}z_sln\\frac{[S]_{out}}{[S]_{in}} \\equiv \\frac{RT}{F}z_sln\\frac{[S]_{out}}{[S]_{in}}$$\n", | |
| "\n", | |
| "#### Nernst-Planck Eq\n", | |
| "$$I_{total} = -\\mu z_s^2q[S]\\frac{dV}{dx} - zkT \\mu \\frac{d[S]}{dx}$$\n", | |
| "if $I_{total}=0$...\n", | |
| "$$z_sq[S] dV = -kT d[S]$$\n", | |
| "$$\\int_{V_{in}}^{V_{out}}dV = -\\frac{kT}{z_sq} \\int_{[S]_i}^{[S]_o}\\frac{d[S]}{[S]}$$\n", | |
| "\n", | |
| "#### Goldman Equation\n", | |
| "$$V_m = \\frac{RT}{F} ln\\Big(\\frac{\\sum^mP_m[M]_{out} + \\sum^a P_a[A]_{in} }{\\sum^mP_m[M]_{in} + \\sum^a P_a[A]_{out} }\\Big)$$\n", | |
| "\n", | |
| "\n", | |
| "#### Goldman-Hodgkin-Katz Model\n", | |
| "$$\\Phi_s = (P_s z_s F) (\\frac{z_sq}{kT}V_m)\\frac{[S]_{in}-[S]_{out}e^{- \\frac{z_sq}{kT}V_m}}{1-e^{- \\frac{z_sq}{kT}V_m}}$$\n", | |
| "\n", | |
| "$$\\Phi_s = (P_s z_s F) \\xi\\frac{[S]_{in}-[S]_{out}e^{- \\xi}}{1-e^{- \\xi}} \\equiv \n", | |
| "(P_sz_sF[S]_{in})(\\xi) \\frac{1-\\frac{[S]_{out}}{[S]_{in}}e^{-\\xi}}{1-e^{-\\xi}} $$\n", | |
| "\n", | |
| "\n", | |
| "$$\\Phi_m = \\sum^s\\Phi_s = \\Phi_K + \\Phi_{Na} + \\Phi_{Cl}...$$\n", | |
| "\n", | |
| "$$\\Phi_m = \\frac{F\\xi}{1-e^{-\\xi}} \\cdot \\sum^{s} P_sz_s([S]_{in}-[S]_{out}e^{- \\xi})$$" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 2, | |
| "metadata": { | |
| "collapsed": true | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "# Problem 1 Helper functions\n", | |
| "def plot_iv_curve(voltage,current,ax=None):\n", | |
| " if ax is None:\n", | |
| " fig,ax = plt.subplots(1,1)\n", | |
| " \n", | |
| " ax.plot(voltage,current)\n", | |
| " ax.set_ylim(-10,6)\n", | |
| " return ax\n", | |
| "\n", | |
| "def gen_ghk_eq(c_ratio):\n", | |
| " zqkT = 0.035 # V^-1\n", | |
| " PzFCin = 0.75 # mA\n", | |
| " eta = lambda v: zqkT * v\n", | |
| " return lambda v: PzFCin*eta(v)*(1-(c_ratio)*np.exp(-eta(v)))/(1-np.exp(-eta(v)))\n", | |
| "\n", | |
| "def gen_iv_spread(Vs,C_ratios):\n", | |
| " I_eqs = np.array([ gen_ghk_eq(c_rat) for c_rat in C_ratios])\n", | |
| " return [ghk(Vs) for ghk in I_eqs]\n", | |
| "\n", | |
| "# Execution of problem 1\n", | |
| "def problem_1():\n", | |
| " ratios = [0,0.1,0.2,0.5,1,2,5,10,20,50,100,200,500,1000]\n", | |
| " V = np.arange(0,401)-200\n", | |
| " I = gen_iv_spread(V,ratios)\n", | |
| " fix,ax = plt.subplots(1,1)\n", | |
| " for i in I:\n", | |
| " plot_iv_curve(V,i,ax=ax)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 3, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stderr", | |
| "output_type": "stream", | |
| "text": [ | |
| "/opt/conda/envs/py27/lib/python2.7/site-packages/ipykernel_launcher.py:14: RuntimeWarning: invalid value encountered in divide\n", | |
| " \n", | |
| "/opt/conda/envs/py27/lib/python2.7/site-packages/matplotlib/font_manager.py:1297: UserWarning: findfont: Font family [u'sans-serif'] not found. Falling back to DejaVu Sans\n", | |
| " (prop.get_family(), self.defaultFamily[fontext]))\n" | |
| ] | |
| }, | |
| { | |
| "data": { | |
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eVIzFnGJt+xBlznEEJDQ6K9bSa+gR2tg+GSWWi2PVabmtppirSh1oNWcL974T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\n", | |
| "text/plain": [ | |
| "<matplotlib.figure.Figure at 0x7f6684117050>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "# Problem 1 output graphs\n", | |
| "problem_1()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 4, | |
| "metadata": { | |
| "collapsed": true | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "# Problem 2 utilities\n", | |
| "\n", | |
| "# Object for managing ion parameters of a model\n", | |
| "class Ion():\n", | |
| " def __init__(self,name,**kwargs):\n", | |
| " # If user only supplies an ion name, use these default values \n", | |
| " ion_defaults = dict(\n", | |
| " na=dict(perm=5,Cout=145.0,Cin=15.0,z=1),\n", | |
| " k=dict(perm=100,Cout=4.5,Cin=120.0,z=1),\n", | |
| " cl=dict(perm=10, Cout=116.0, Cin=20.0,z=-1)\n", | |
| " )\n", | |
| " \n", | |
| " # Helper function for showing sign of valence\n", | |
| " int2sym = lambda x: x<1 and '-' or '+'\n", | |
| " \n", | |
| " # Check args, prepopulate defaults\n", | |
| " if len(kwargs) is 0:\n", | |
| " kwargs = ion_defaults[name.lower()]\n", | |
| " \n", | |
| " # Process parameters\n", | |
| " self.name = name\n", | |
| " self.P = kwargs['perm']\n", | |
| " self.Cout = kwargs['Cout']\n", | |
| " self.Cin = kwargs['Cin']\n", | |
| " self.z = kwargs['z']\n", | |
| " self.z_sym = int2sym(self.z)\n", | |
| " \n", | |
| " # Custom string representation for the ion object\n", | |
| " # e.g. Ion(Na_perm=10, [Na]_out=200, [Na]_in= 50)\n", | |
| " def __repr__(self):\n", | |
| " return \"Ion({0}_perm={1}, [{0}]_out={2}, [{0}]_in={3})\".format(self.name,self.P,self.Cout,self.Cin)\n", | |
| "\n", | |
| "\n", | |
| "class GHK():\n", | |
| " def _scaled_result(self,r,u,scale):\n", | |
| " return (r*scale[u],u)\n", | |
| " \n", | |
| " def _filterbyz(self,seq,val):\n", | |
| " for el in seq:\n", | |
| " if el.z==val: yield el\n", | |
| " \n", | |
| " def C2K(self,t):\n", | |
| " return sc.convert_temperature(t,old_scale='C',new_scale='K')\n", | |
| " \n", | |
| " def _I_ion(self,ion,Tc):\n", | |
| " Tk = self.C2K(Tc)\n", | |
| " eta = lambda v: (ion.z*self.F*v)/(self.R*Tk)\n", | |
| " num = lambda v: 1-((ion.Cout/ion.Cin)*np.exp(-eta(v)))\n", | |
| " denom = lambda v: 1 - np.exp(eta(v))\n", | |
| " \n", | |
| " return lambda v: ion.P*ion.z*self.F*ion.Cin*eta(v)*num(v)/denom(v)\n", | |
| " \n", | |
| " def __init__(self,*args):\n", | |
| " self.ions = args\n", | |
| " self.pos_ions = list(self._filterbyz(self.ions,1))\n", | |
| " self.neg_ions = list(self._filterbyz(self.ions,-1))\n", | |
| " self.F_constant = sc.physical_constants['Faraday constant']\n", | |
| " self.R_constant = sc.physical_constants['molar gas constant']\n", | |
| " self.F = self.F_constant[0]\n", | |
| " self.R = self.R_constant[0]\n", | |
| " self.q = sc.elementary_charge\n", | |
| " self.k = sc.Boltzmann\n", | |
| " self.v_scale = {'mV':1000,'V':1,'kV':0.001}\n", | |
| " \n", | |
| " def resting_membrane_potential(self,Tc=20,unit='V'):\n", | |
| " # Convert Temp to Kelvin\n", | |
| " Tk = self.C2K(Tc)\n", | |
| "\n", | |
| " # Implement Goldman Equation\n", | |
| " num = sum([i.P*i.Cout for i in self.pos_ions]) + sum([i.P*i.Cin for i in self.neg_ions])\n", | |
| " denom = sum([i.P*i.Cin for i in self.pos_ions]) + sum([i.P*i.Cout for i in self.neg_ions])\n", | |
| " result = self.R*Tk/self.F*np.log(num/denom)\n", | |
| " \n", | |
| " # Return result as tuple with specified unit\n", | |
| " return self._scaled_result(result,unit,self.v_scale)\n", | |
| "\n", | |
| "k_ion = Ion('K',perm=1,Cin=400,Cout=10,z=1)\n", | |
| "na_ion = Ion('Na',perm=0.03,Cin=50,Cout=460,z=1)\n", | |
| "cl_ion = Ion('Cl',perm=0.1,Cin=40,Cout=540,z=-1)\n", | |
| "def problem_2(k,na,cl):\n", | |
| " ghk = GHK(k,na,cl)\n", | |
| " Vm = ghk.resting_membrane_potential(Tc=20,unit='mV')\n", | |
| " print('Resting Potential: %0.2f %s'%Vm)\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 5, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stdout", | |
| "output_type": "stream", | |
| "text": [ | |
| "Resting Potential: -70.64 mV\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "k_ion = Ion('K',perm=1,Cin=400,Cout=10,z=1)\n", | |
| "na_ion = Ion('Na',perm=0.03,Cin=50,Cout=460,z=1)\n", | |
| "cl_ion = Ion('Cl',perm=0.1,Cin=40,Cout=540,z=-1)\n", | |
| "\n", | |
| "problem_2(k_ion, na_ion,cl_ion)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 8, | |
| "metadata": { | |
| "collapsed": true | |
| }, | |
| "outputs": [], | |
| "source": [ | |
| "def problem_3(c_r=10):\n", | |
| " V = np.arange(0,401)-200\n", | |
| " C_ratios = np.arange(0,1001,10)\n", | |
| " I = gen_iv_spread(V,C_ratios)\n", | |
| " table = []\n", | |
| " for i,v in enumerate(V):\n", | |
| " for j,c in enumerate(C_ratios):\n", | |
| " table.append(dict(voltage=v,C_ratio=c,current=I[j][i]))\n", | |
| "\n", | |
| " table_df = pd.DataFrame.from_records(table)\n", | |
| " p_table = table_df.pivot(\"C_ratio\",'voltage','current')\n", | |
| " ax = sns.heatmap(p_table,xticklabels=50,yticklabels=20,cmap='jet',center=-2500)\n", | |
| " ax.invert_yaxis()\n", | |
| " choice = np.squeeze(np.argwhere(C_ratios==c_r)).tolist()\n", | |
| " ax = plot_iv_curve(V,I[choice])\n", | |
| " ax.set_ylim(-60,10)" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 9, | |
| "metadata": {}, | |
| "outputs": [ | |
| { | |
| "name": "stderr", | |
| "output_type": "stream", | |
| "text": [ | |
| "/opt/conda/envs/py27/lib/python2.7/site-packages/ipykernel_launcher.py:14: RuntimeWarning: invalid value encountered in divide\n", | |
| " \n" | |
| ] | |
| }, | |
| { | |
| "data": { | |
| "image/png": 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zByyr6mMiTdcVthEfoap5YrZ/KriLjFnE7veMnjIrrp6Ud/kS93xEzb6/LiJn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\nfjhwGbAbcDXwKlVdLhu334r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| |
| "text/plain": [ | |
| "<matplotlib.figure.Figure at 0x7f663a5eb7d0>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| }, | |
| { | |
| "data": { | |
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Z09bh4uHndlJe08IFZxdwxVemB3uRIiIRza+St9Z+u5959wL3+vP6Q9HR1c1v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\n", | |
| "text/plain": [ | |
| "<matplotlib.figure.Figure at 0x7f6684117a50>" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "problem_3(c_r=10)\n", | |
| "plt.show()" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": { | |
| "collapsed": true | |
| }, | |
| "outputs": [], | |
| "source": [] | |
| } | |
| ], | |
| "metadata": { | |
| "kernelspec": { | |
| "display_name": "Python 2", | |
| "language": "python", | |
| "name": "python2" | |
| }, | |
| "language_info": { | |
| "codemirror_mode": { | |
| "name": "ipython", | |
| "version": 2 | |
| }, | |
| "file_extension": ".py", | |
| "mimetype": "text/x-python", | |
| "name": "python", | |
| "nbconvert_exporter": "python", | |
| "pygments_lexer": "ipython2", | |
| "version": "2.7.13" | |
| } | |
| }, | |
| "nbformat": 4, | |
| "nbformat_minor": 2 | |
| } |
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