Bursting.ipynb

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      "'''\n",
      "In the following, m, h, and n are gating variables controlling the activation or inactivation of certain channels.\n",
      "M is approximated as starting instantaneously, so we never need a dm/dt equation-we can just use m_inf in place of m.\n",
      "Below are three strings containing different models, different in only the following way: \n",
      "one has both I_NaPh and I_NaP, one has the first only, and one has the second only. \n",
      "I've tested all three and found that only the equation with I_NaPh works properly. The only current issue for the code\n",
      "is that the voltages are too small. Otherwise, the shape of the curve seems correct.\n",
      "'''\n",
      "%reset\n",
      "import time\n",
      "t0 = time.clock()\n",
      "from brian import *\n",
      "from brian.library.ionic_currents import *\n",
      "%matplotlib inline\n",
      "'''\n",
      "from brian.experimental import codegen2 as cg2\n",
      "set_global_preferences(gcc_options='-march=native')\n",
      "set_global_preferences(useweave = True)\n",
      "set_global_preferences(usecodegen = True)\n",
      "set_global_preferences(usecodegenweave=True)\n",
      "set_global_preferences(usenewpropagate=True)\n",
      "set_global_preferences(magic_useframes=False)\n",
      "'''\n",
      "\n",
      "\n",
      "eqs = '''\n",
      "dv/dt = (ge+gi-(v+49*mV))/(20*ms) : volt\n",
      "dge/dt = -ge/(5*ms) : volt\n",
      "dgi/dt = -gi/(10*ms) : volt\n",
      "'''\n",
      "'''\n",
      "code, vars, params = cg2.make_c_integrator(eqs, method=cg2.euler, dt=0.1*ms)\n",
      "print code\n",
      "print vars\n",
      "print params\n",
      "return\n",
      "'''\n",
      "\n",
      "\n",
      "\n",
      "print \"duration (import brian): \", time.clock()-t0\n",
      "\n",
      "#defaultclock.reinit()\n",
      "reinit_default_clock()\n",
      "#number of seconds to run simulation (include units)\n",
      "runtime = 5*second\n",
      "\n",
      "\n",
      "# temperature dependence, borrowed from Cochlear neuron model of Rothman & Manis in Brian Examples @\n",
      "# http://www.briansimulator.org/docs/examples-frompapers_Rothman_Manis_2003.html\n",
      "# I've used q10 term in gateing variable eqns of eqs_noNaP.\n",
      "celsius = 36.\n",
      "q10 = 1.0#3.**((celsius-22)/10.)#commented out bc q10 is related to temperature change not absolute temp.\n",
      "\n",
      "#The nominal params for leak current are gL=2.8 nS and EL=-65 mV.\n",
      "EL = -57.0*mvolt\n",
      "EK = -85.0*mvolt\n",
      "ENa = 50.0*mvolt\n",
      "C = 21 * pF\n",
      "gL = 2.8*nsiemens\n",
      "gK = 11.2*nsiemens\n",
      "gNa = 28*nsiemens\n",
      "gNaP = 2.8*nsiemens\n",
      "\n",
      "#---Model 1 of butera99a\n",
      "#---time constants are consistent for all currents in Model 1 of butera99a\n",
      "tauMaxH = 10000*ms\n",
      "tauMaxN = 10*ms\n",
      "\n",
      "#constants for K and Na\n",
      "thetaN = -29*mvolt\n",
      "thetaM = -34*mvolt\n",
      "sigmaN = -4*mvolt\n",
      "sigmaM = -5*mvolt\n",
      "\n",
      "#constants for NaP and Nap-h\n",
      "thetaH = -48*mvolt\n",
      "sigmaH = 6*mvolt\n",
      "thetaM_nap = -40*mvolt\n",
      "sigmaM_nap = -6*mvolt\n",
      "\n",
      "#eqns for Na and K\n",
      "mInf = lambda v: (1+exp((v-thetaM)/sigmaM))**-1\n",
      "nInf = lambda v: (1+exp((v-thetaN)/sigmaN))**-1\n",
      "tauN = lambda v: tauMaxN/cosh((v-thetaN)/(2*sigmaN))\n",
      "\n",
      "#eqns for NaP and NaP-h\n",
      "hInf = lambda v: (1+exp((v-thetaH)/sigmaH))**-1\n",
      "mInf_nap = lambda v: (1+exp((v-thetaM_nap)/sigmaM_nap))**-1\n",
      "tauH = lambda v: tauMaxH/cosh((v-thetaH)/(2*sigmaH))\n",
      "\n",
      "#no nap - this one seems to be correct\n",
      "eqs_noNaP = '''\n",
      "dV/dt = -((gNa*(1-n)*(V-ENa)*mInf(V)**3)+ (gNaP*(V-ENa)*h*mInf_nap(V)) + \\\n",
      "(gK*(V-EK)*n**4) + gL*(V-EL))/C:mvolt\n",
      "#\n",
      "#Sodium and Potassium Activation\n",
      "#mInf_1 = mInf(V):1\n",
      "#n_inf = nInf(V):1\n",
      "#tau_n=tauN(V):ms\n",
      "dn/dt =  q10*(nInf(V) - n)/tauN(V):1\n",
      "#\n",
      "#sodium inactivation (nap or naph)\n",
      "#mInf_2 = mInf_nap(V):1\n",
      "#h_inf = hInf(V):1\n",
      "#tau_h=tauH(V):ms\n",
      "dh/dt = q10*(hInf(V) - h)/tauH(V):1\n",
      "I:amp\n",
      "'''\n",
      "\n",
      "t1 = time.clock()\n",
      "\n",
      "eqs = Equations(eqs_noNaP)\n",
      "t2 = time.clock()\n",
      "print \"duration (make equation)= \",(t2 - t1)\n",
      "\n",
      "'''\n",
      "print \"units: \",eqs._units\n",
      "'''\n",
      "neurons=NeuronGroup(1, eqs, method = \"RK\", clock = defaultclock, freeze=True)\n",
      "#neurons=NeuronGroup(1, eqs, clock = defaultclock, freeze=True)\n",
      "#default updater is nonlinear w/ 4 state variables\n",
      "t3 = time.clock()\n",
      "print \"duration (make group)= \",(t3 - t2)\n",
      "\n",
      "neurons.V = EL\n",
      "neurons.h = hInf(EL)\n",
      "neurons.n = nInf(EL)\n",
      "M = StateMonitor(neurons, 'V', record=True)\n",
      "\n",
      "run(runtime)\n",
      "t4 = time.clock()\n",
      "print \"duration (run sim)= \",(t4-t3)\n",
      "print \"time \", time.strftime(\"%H:%M:%S\")\n",
      "\n",
      "p=plot(M.times, M[0]/mV)\n",
      "xlabel('Time (ms)')\n",
      "ylabel('Membrane potential (mV)')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "name": "stdout",
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Once deleted, variables cannot be recovered. Proceed (y/[n])? y\n"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "duration (import brian):  0.00391\n",
        "0.999499798893\n",
        "0.998000696278\n",
        "0.999347034662\n"
       ]
      }
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     "prompt_number": 3
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