Using multi-objective evolutionary algorithms to predict the parameters that determine membrane resonance in a biophysical model of bursting neurons

Many neurons exhibit membrane potential resonance (MPR), a peak in the membrane impedance amplitude (|Z|) in response to oscillatory inputs at nonzero frequency (fmax) [1]. MPR arises from nonlinearity and timescales of voltage-gated currents and may set frequency of network oscillations. Pacemaker PD neurons of the crab pyloric network show MPR whose fmax is correlated with the network frequency (~ 1Hz) [2]. In contrast, the LP follower neuron shows a higher fmax of ~ 1.4 Hz. The impedance profile of biological PD and LP neurons and the model neuron was measured using a logarithmic ZAP function (fmin=0.1 Hz, fmax=4 Hz) in voltage clamp (Vlow=-60mV and Vhigh=-30mV). The fmaxin biological PD neurons increases if either Vlow or Vhigh are increased [3], whereas the LP neuron fmax is only sensitive to Vhigh. Additionally MPR in the PD neurons is sensitive to blockers of ICa and Ih. We hypothesize that: (1) many combinations of parameters can produce MPR in PD and LP neurons; (2) The MPR mechanism in LP is distinct from PD. Experimentally, ICais difficult to measureand therefore a top-down approach is adopted to elucidate the contributions of ICaand Ih to MPR in PD and LP. Because resonance depends on the kinetics of ICaand Ih, a brute-force sampling of the parameter space is computationally unfeasible and, therefore, we search for model parameters using a genetic algorithm. The biological data were used to constrain the range of leak, ICa and Ih parameters in a single-compartment model. The genetic algorithm, NSGA-II [4] was used to optimize the MPR profile and produce a population of optimal models. A sensitivity analysis of MPR attributes on model parameters was done in these models. The distributions of optimal parameters were tightly constrained for gleak, V½_Ca_act, V½_Ca_inact and τ_Ca_inact. Additionally, strong correlations were observed between τ_Ca_act and τ_Ca_inact (negative), between V½_Ca_act and V½_Ca_inact and between gCaand V½_Ca_act (negative). In models with low Ih, fmax correlated strongly with the frequency which ICa peaked, which is controlled by τ_Ca_act and τ_Ca_inact. The parameter sensitivities also support the sensitivity to ICatime constants, demonstrating potential targets for neuromodulation. The MOEA was also used to optimize the fmaxshifts with Vlow and Vhigh to produce two model groups with properties that correspond to the differences between PD and LP. These results suggest that fmaxshift is due to different activation rates of Ih and therefore these two neurons may generate MPR through different mechanisms; a result which we aim to test experimentally. Many neurons display emergent properties in response to oscillatory inputs, such as amplified responses in certain frequency bands. These properties may be important in shaping coherent network activity. The underlying nonlinearities and time scales that shape specific features of impedance profiles can be used to link sub-threshold dynamics to supra-threshold voltage responses. We have used an MOEA to understand the multiple underlying ionic mechanisms that generate resonance and explained how PD, and not LP, fmaxcan be adjusted according to different input amplitudes.