Modelling dynamic abnormalities caused by an SCN1A mutation

The Matlab scripts uploaded here implement a Hodgkin-Huxley type neuronal model with parameterisation derived directly from experimental voltage clamp results. They correspond in part to the preprint of an upcoming publication. The scripts were used to produce the figures in the final manuscript, which is now out:

Peters C⁺, Rosch RE⁺, Hughes E, Ruben PC (2016): Temperature-dependent changes in neuronal dynamics in a patient with an SCN1A mutation and hyperthermia induced seizures. Sci Rep 6, 31879 ⁺ equal contribution

Fitting Boltzmann Equations and Plotting Steady-State Parameters

steady_state_curves

In the first instance, Boltzmann equations were fitted to an existing formulation of the Hodgkin Huxley Model that describes the dynamics at the membrane of a mammalian cortical neuron. The first component of the script steady_state_curves fits the Boltzmann equations. This formulation is taken as the baseline for all further modelling - i.e. the wildtype at 37ºC is modelled as this baseline parameter composition.

Remaining empirical values are represented as absolute (voltage parameters), or relative (slope parameters) deviations from the baseline in the model. The steady states that this produces for the sodium channel gating parameters are plotted in the second half of the steady_state_curves script.

Virtual Voltage Clamp to Assess for Fast Inactivation

cort_fastinactivation.m

This function evaluates model dynamics by performing a 'virtual voltage clamp' experiments for the four parameterisations of the model (i.e. baseline, wild type sodium channels at 40ºC, SCN1A mutation at 37 and 40ºC). This consists of voltage clamp (i.e. specific voltages being enforced on the model), delivering paired voltage pulses with increasing inter-pulse intervals. Changes in sodium conductance are estimated in a reduced Hodgkin Huxley Model implemented in cort_hh_fastinactivation.m. Current peaks resulting from these paired stimuli are estimated and plotted for each of the individual parameterisations of the model in the figure.

Running Models Under Different Conditions

cort_variable_hh_eval

This script calls cort_variable_hh.m and uses Matlab ODE solver to integrate the model and plot the time course. The parameters are derived from a baseline model of cortical dynamics with experimental values implemented in terms of their deviations from those baseline parameters.

Evaluation of Model Bifurcations

cort_bifurcation.m

This routines calls cort_variable_hh.m and to run simulations of the cortical Hodgkin Huxley model across the four different parameterisations (i.e. baseline, wild type sodium channels at 40ºC, SCN1A mutation at 37 and 40ºC). The model is estimated to steady state, and final state values from one simulation are used as initial values for the next simulation. This simulation is performed repeatedly across increasing, and then decreasing values of the input current Parameter I_stim. The steady state values of each model run are then plotted as bifurcation plots, separately for the four parameterisations of the model.