# PARAMETER OPTIMIZATION TO FIX MOSSY CELL FI CURVES, Na and K I-V RELATIONSHIPS
# --------------------
# DATA USED FOR FITTING:
# Howard AL, Neu A, Morgan RJ, Echegoyen JC, Soltesz I. Opposing Modifications in Intrinsic Currents and
# Synaptic Inputs in Post-Traumatic Mossy Cells: Evidence for Single-Cell Homeostasis in a Hyperexcitable Network.
# Journal of Neurophysiology. 2007;97(3):2394–2409. doi:10.1152/jn.00509.2006
# --------------------
# NOTE: Parameters for SOMA ONLY are optimized here, to simplify re-implementation in NEURON
# TODO: consider unifying this file with optimize_HCs.py
#imports
import matplotlib
import numpy as np
# nicer font options:
matplotlib.rcParams['mathtext.fontset'] = 'cm'
matplotlib.rcParams['font.family'] = 'STIXGeneral'
matplotlib.rcParams.update({'font.size': 12})
matplotlib.use('Agg') # hopefully this works over ssh
import matplotlib.pyplot as plt
import pandas as pd
from random import Random
from inspyred import ec # evolutionary algorithm
from netpyne import specs, sim # neural network design and simulation
from clamps import IClamp
from IVdata import IVdata
from find_rheobase import ElectrophysiologicalPhenotype
netparams = specs.NetParams()
mc = netparams.importCellParams(
label='MC',
conds={"cellType": "MossyCell", "cellModel": "MossyCell"},
fileName="objects/MC.hoc",
cellName="MossyCell",
cellArgs=[1],
importSynMechs=False
)
# parameters to be optimized
free_params = {
'bk': ['gkbar'], # big conductance, calcium-activated potassium channel
'ichan2': ['gnatbar', 'vshiftma', 'vshiftmb', 'vshiftha', 'vshifthb', 'vshiftnfa', 'vshiftnfb', 'vshiftnsa',
'vshiftnsb',
'gkfbar', 'gksbar', 'gl'], # sodium, potassium parameters
'ka': ['gkabar'], # A-type (fast inactivating) Kv channel
'lca': ['glcabar'], # l-type calcium
'nca': ['gncabar'], # n-type calcium
'sk': ['gskbar'], # small conductance potassium channel
'ih': ['ghyfbar', 'ghysbar'] # HCN channel
}
with open('figures/mossycell/mc.txt', 'w') as f:
f.write(str(mc))
class optimize_mcs(object):
def __init__(self,
cell,
free_params,
pop_size=10,
max_evaluations=60,
num_selected=10,
mutation_rate=0.03,
):
self.cell_dict = {"secs": cell["secs"]}
self.baseline_dict = {"secs": cell["secs"]}
self.free_params = free_params
self.initialParams = []
self.minParamValues = []
self.maxParamValues = []
self.num_inputs = len(sum(self.free_params.values(), []))
self.free_params = free_params
self.pop_size = pop_size
self.max_evaluations = max_evaluations
self.num_selected = num_selected
self.mutation_rate = mutation_rate
self.num_elites = 1
self.flag = str('mossy')
self.n_simcells = 1 # number of simulated cells
self.plot_results()
def retrieve_baseline_params(self):
""" Saves baseline parameters from cell_dict
Returns:
'list'. List of baseline parameter values.
"""
self.baseline = []
for key in self.free_params.keys():
for val in self.free_params[key]:
self.baseline.append(self.baseline_dict['secs']['soma']['mechs'][key][val])
self.num_inputs = len(self.baseline)
return self.baseline
def curr_inj(self, current, delay=0, duration=1000):
iclamp = IClamp(self.cell_dict, delay=delay, duration=duration, T=duration + delay * 2)
res = iclamp(current)
return res
def sim_fi(self):
ep = ElectrophysiologicalPhenotype(self.cell_dict)
self.simfi = ep.compute_fi_curve(ilow=0, ihigh=0.4, n_steps=11, delay=0, duration=1000)
return self.simfi
def sim_iv_na(self):
iv = IVdata(self.cell_dict) # instantiate class
self.simivna = iv.compute_ivdata(vlow=-80, vhigh=40, n_steps=13, delay=10, duration=5)
return self.simivna
def sim_iv_k(self):
iv = IVdata(self.cell_dict) # instantiate class
self.simivk = iv.compute_ivdata(vlow=-90, vhigh=0, n_steps=10, delay=10, duration=5)
return self.simivk
def data_fi(self):
# Howard et al.
x = [0, 0.040, 0.080, 0.120, 0.160, 0.200, 0.240, 0.280, 0.320, 0.360, 0.400]
y = [0, 1, 4, 8.5, 14, 17, 20, 21.5, 22, 25, 26]
datafi = [x, y]
self.datafi = np.array(datafi)
return self.datafi
def data_iv_na(self):
# Howard et al.
v = np.linspace(-80, 40, 13)
ina = [-0.01, -0.01, -0.01, -0.02, -0.07, -0.2, -0.38, -0.36, -0.3, -0.24, -0.19, -0.14, -0.11]
dataiv = [v, ina]
self.dataiv_na = np.array(dataiv)
return self.dataiv_na
def data_iv_k(self):
# Howard et al.
v = np.linspace(-90, 0, 10)
ik = [54, 72, 18, 72, 226, 469, 929, 1362, 1796, 2265]
iknA = [x / 1000 for x in ik]
dataiv = [v, iknA]
self.dataiv_k = np.array(dataiv)
return self.dataiv_k
def generate_netparams(self, random, args):
"""
Initialize set of random initial parameter values selected from uniform distribution within min-max bounds.
Returns
'list'. initialParams
"""
self.initialParams = [random.uniform(self.minParamValues[i], self.maxParamValues[i]) for i in
range(self.num_inputs)]
return self.initialParams
def evaluate_netparams(self, candidates, args):
"""
Fitness function that evaluates the fitness of candidate parameters by quantifying the difference between
simulated FI and IV curves to the FI and IV curves from data using mean squared error.
Returns
'list'. Fitness values for sets of candidates
"""
self.fitnessCandidates = []
for cand in candidates:
i = 0
for k in free_params.keys():
for v in free_params[k]:
self.cell_dict['secs']['soma']['mechs'][k][v] = cand[i]
i += 1
FI_data = self.data_fi()
FI_sim = self.sim_fi().to_numpy()
Na_data = self.data_iv_na()
Na_sim = self.sim_iv_na().to_numpy()
K_data = self.data_iv_k()
K_sim = self.sim_iv_k().to_numpy()
ficurves = np.sum([((x1 - x2) ** 2) for (x1, x2) in zip(FI_data[1, :], FI_sim[:, 1])]) / len(FI_data[1, :])
na_currs = np.sum([((x1 - x2) ** 2) for (x1, x2) in zip(Na_data[1, :], Na_sim[:, 1])]) / len(Na_data[1, :])
k_currs = np.sum([((x1 - x2) ** 2) for (x1, x2) in zip(K_data[1, :], K_sim[:, 2])]) / len(K_data[1, :])
fitness = (1 / 3 * ficurves) + (1 / 3 * na_currs) + (1 / 3 * k_currs)
self.fitnessCandidates.append(fitness)
return self.fitnessCandidates
def find_bestcandidate(self):
"""
Sets up custom evolutionary computation and returns list of optimized parameters.
Components of EC
gc_ec : instantiate evolutionary computation with random.Random object
selector: method used to select best candidate based on fitness value
variator: method used to determine how mutations (variations) are made to each generation of params
replacer: method used to determine if/how individuals are replaced in pool of candidates after selection
terminator: method used to specify how to terminate evolutionary algorithm
observer: method that allows for supervision of evolutionary computation across all evaluations
evolve: pulls together all components of custom algorithm, iteratively calls evaluate_netparams, returns
parameters that minimize fitness function.
Returns
'list'. bestCand (list of optimized parameters)
"""
# TODO: Potentially write custom variator function to be compatible with np.random.RandomState
# rand = np.random.RandomState(self.setseed)
rand = Random()
rand.seed(self.setseed) # will take cell # as seed (n_simcells = 1, seed = 0. n_simcells = 2, seed = 1, etc).
# SET UP MIN/MAX BOUNDS FOR PARAMETERS ------------------
# TODO: find cleaner way of dealing with these lists, allow for easier modification
#self.minParamValues = [0.4 * param for param in self.baseline] # 0.5 best for IF, Na
#self.maxParamValues = [3.0 * param for param in self.baseline] # 3.0 best for IF, Na
soma_minbounds = [(0.0165 * 0.1), (0.05 * 0.8), (43 * 0.8), (22 * 0.8), (125 * 0.8), (15 * 0.8),
(18.0 * 0.1), (43.0 * 0.1), (30.0 * 0.1), (55.0 * 0.1), (0.03 * 0.8), (0.01 * 0.2),
(1.1e-05 * 0.1),
(1e-05 * 0.1), (0.0006 * 0.1), (8e-05 * 0.1), (0.016 * 0.1),
(5e-06 * 0.1), (5e-06 * 0.1)
]
soma_maxbounds = [(0.0165 * 2.0), (0.05 * 1.2), (43 * 1.2), (22 * 1.5), (125 * 1.5), (15 * 1.5),
(18.0 * 2.0), (43.0 * 2.0), (30.0 * 2.0), (55.0 * 2.0), (0.03 * 1.5), (0.01 * 1.8),
(1.1e-05 * 2.0),
(1e-05 * 2.0), (0.0006 * 2.0), (8e-05 * 2.0), (0.016 * 2.0),
(5e-06 * 2.0), (5e-06 * 2.0)
]
self.minParamValues = soma_minbounds
self.maxParamValues = soma_maxbounds
# SET UP EVOLUTIONARY COMPUTATION ----------------------
self.gc_ec = ec.EvolutionaryComputation(rand)
self.gc_ec.selector = ec.selectors.truncation_selection # purely deterministic
self.gc_ec.variator = [ec.variators.uniform_crossover, ec.variators.gaussian_mutation]
self.gc_ec.replacer = ec.replacers.generational_replacement
self.gc_ec.terminator = ec.terminators.evaluation_termination # terminates after max number of evals is met
self.gc_ec.observer = ec.observers.plot_observer # save to file, use observers.file_observer
self.final_pop = self.gc_ec.evolve(generator=self.generate_netparams, # f'n for initializing params
evaluator=self.evaluate_netparams, # f'n for evaluating fitness values
pop_size=self.pop_size, # number of parameter sets per evaluation
maximize=False, # best fitness corresponds to minimum value
bounder=ec.Bounder( # set min/max param bounds
self.minParamValues,
self.maxParamValues
),
max_evaluations=self.max_evaluations,
num_selected=self.num_selected,
mutation_rate=self.mutation_rate,
num_inputs=self.num_inputs,
num_elites=self.num_elites
)
self.final_pop.sort(reverse=True) # sort final population so best fitness is first in list
self.bestCand = self.final_pop[0].candidate # bestCand <-- individual @ start of list
plt.savefig('figures/mossycell/observer_%s.pdf' % self.flag) # save fitness vs. iterations graph
plt.close()
return self.bestCand
def build_optimizedcell(self):
""" Replaces baseline parameters with parameters from best candidate, then uses current injection experiment
to build 'optimized' cell.
Returns
'dict'. Results of current clamp from optimized cell.
"""
j = 0
for key in self.free_params.keys():
for val in self.free_params[key]:
self.cell_dict['secs']['soma']['mechs'][key][val] = self.bestCand[j]
j = j + 1
finalclamp = self.curr_inj(0.33)
# self.ep_opt = ElectrophysiologicalPhenotype(self.cell_dict)
return finalclamp
def store_curves(self):
""" Generates set of n optimized neurons (n_simcells), stores baseline and optimized parameters,
IF and IV curves.
Returns
'tuple' of two DataFrames, (sim_fi_store, sim_iv_store)
"""
# initialize empty DataFrames, populate with baseline parameters
baselineparams = self.retrieve_baseline_params()
self.param_store = pd.DataFrame({"param": sum(free_params.values(), []), "baseline": baselineparams})
self.sim_fi_store = pd.DataFrame([])
self.sim_ivna_store = pd.DataFrame([])
self.sim_ivk_store = pd.DataFrame([])
# generate set of n_simcells, populate DataFrames above with FI, IV, params
for cell_n in range(0, self.n_simcells):
self.setseed = cell_n # set new seed for evol'n computation
newparams = self.find_bestcandidate() # find optimized parameters
newparamdf = pd.DataFrame({"Cell_%s" % cell_n: newparams}) # store those params with a label
self.param_store = pd.concat([self.param_store, newparamdf], axis=1) # append params to DF
self.build_optimizedcell() # build the optimized cell
newcellfi = self.sim_fi() # generate simulated FI curve
newcellivna = self.sim_iv_na() # generate simulated IV curves
newcellivk = self.sim_iv_k() # generate simulated IV curves
self.sim_fi_store = pd.concat([newcellfi, self.sim_fi_store]) # append FI curve to DF
self.sim_ivna_store = pd.concat([newcellivna, self.sim_ivna_store]) # append IV curve to DF
self.sim_ivk_store = pd.concat([newcellivk, self.sim_ivk_store]) # append IV curve to DF
# save dataframes to .csv
self.sim_fi_store.to_csv('data/parameters/simFIs_%s.csv' % self.flag)
self.sim_ivna_store.to_csv('data/parameters/simIVsNa_%s.csv' % self.flag)
self.sim_ivk_store.to_csv('data/parameters/simIVsK_%s.csv' % self.flag)
self.param_store.to_csv('data/parameters/parameters_%s.csv' % self.flag)
return self.sim_fi_store, self.sim_ivna_store, self.sim_ivk_store
def compute_avg_curves(self):
""" Computes average simulated FI and IV curves and SEM
Returns
'tuple' of two DataFrames, (avg_FI, avg_IV)
"""
sim_stores = self.store_curves()
sim_fi_store = sim_stores[0]
sim_ivna_store = sim_stores[1]
sim_ivk_store = sim_stores[2]
# average simulated FI curve:
avgfi = sim_fi_store.groupby(['I']).agg({'F': ['mean']}).values
semfi = sim_fi_store.groupby(['I']).agg({'F': ['std']}).values / np.sqrt(self.n_simcells)
self.avg_FI = np.c_[np.linspace(0, 0.4, 11), avgfi, semfi]
iv_na = sim_ivna_store.groupby(['V']).agg({'Na': ['mean']}).values
iv_k = sim_ivk_store.groupby(['V']).agg({'K': ['mean']}).values
stdv_na = sim_ivna_store.groupby(['V']).agg({'Na': ['std']}).values / np.sqrt(self.n_simcells)
stdv_k = sim_ivk_store.groupby(['V']).agg({'K': ['std']}).values / np.sqrt(self.n_simcells)
self.avg_IV_Na = np.c_[np.linspace(-80, 40, 13), iv_na, stdv_na]
self.avg_IV_K = np.c_[np.linspace(-90, 0, 10), iv_k, stdv_k]
return self.avg_FI, self.avg_IV_Na, self.avg_IV_K
def plot_results(self):
""" Plots average simulated IV and FI curves from optimized neurons against avg curves from data. Saves
figure to 'figures/mossycell'. Automatically called when optimizeparams is instantiated.
"""
# Generate and collect all data for plotting
baselinecellfi = self.sim_fi().to_numpy()
baselinecellivna = self.sim_iv_na().to_numpy()
baselinecellivk = self.sim_iv_k().to_numpy()
exp_fi = self.data_fi()
exp_ivna = self.data_iv_na()
exp_ivk = self.data_iv_k()
simcurves = self.compute_avg_curves()
avg_fi = simcurves[0]
avg_ivna = simcurves[1]
avg_ivk = simcurves[2]
fig1, (ax1, ax2, ax3) = plt.subplots(3, 1)
# FI curves
ax1.plot(baselinecellfi[:, 0], baselinecellfi[:, 1], color='0.7', linestyle='dashed', label='Baseline')
ax1.plot(exp_fi[0, :], exp_fi[1, :], color='0.5', label='Data')
ax1.errorbar(avg_fi[:, 0], avg_fi[:, 1], yerr=avg_fi[:, 2], color='0.0', label='Optimized')
ax1.legend(loc='center left', bbox_to_anchor=(1, 0.5))
ax1.set_xlabel("Current (nA)")
ax1.set_ylabel("Frequency (Hz)")
# IV curve: Na
ax2.plot(baselinecellivna[:, 0], baselinecellivna[:, 1], color='0.7', linestyle='dashed', label='Baseline Na')
ax2.plot(exp_ivna[0, :], exp_ivna[1, :], color='0.5', label='Data Na')
ax2.plot(avg_ivna[:, 0], avg_ivna[:, 1], color='0.0', label='Optimized Na')
ax2.axhline(0, lw=0.25, color='0.0') # x = 0
ax2.axvline(0, lw=0.25, color='0.0') # y = 0
ax2.legend(loc='center left', bbox_to_anchor=(1, 0.5))
ax2.set_xlabel("Voltage (mV)")
ax2.set_ylabel("Current (nA)")
ax3.plot(baselinecellivk[:, 0], baselinecellivk[:, 2], color='0.7', linestyle='dashed', label='Baseline K')
ax3.plot(exp_ivk[0, :], exp_ivk[1, :], color='0.5', label='Data K')
ax3.plot(avg_ivk[:, 0], avg_ivk[:, 1], color='0.0', label='Optimized K')
ax3.axhline(0, lw=0.25, color='0.0') # x = 0
ax3.axvline(0, lw=0.25, color='0.0') # y = 0
ax3.legend(loc='center left', bbox_to_anchor=(1, 0.5))
ax3.set_xlabel("Voltage (mV)")
ax3.set_ylabel("Current (nA)")
fig1.tight_layout()
fig1.savefig('figures/mossycell/optimizationresults_%s.pdf' % self.flag, bbox_inches="tight")
OptimizeMCs = optimize_mcs(mc, free_params)