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 ( f max ) [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 f max is correlated with the network frequency (~ 1Hz) [2]. In contrast, the LP follower neuron shows a higher f max of ~ 1.4 Hz. The impedance profile of biological PD and LP neurons and the model neuron was measured using a logarithmic ZAP function ( f min =0.1 Hz, f max =4 Hz) in voltage clamp ( V low =-60mV and V high =-30mV). The f max in biological PD neurons increases if either V low or V high are increased [3], whereas the LP neuron f max is only sensitive to V high . Additionally MPR in the PD neurons is sensitive to blockers of I Ca and I h . 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.

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 (f max ) [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 f max is correlated with the network frequency (~1Hz) [2]. In contrast, the LP follower neuron shows a higher f max of 1.4 Hz. The impedance profile of biological PD and LP neurons and the model neuron was measured using a logarithmic ZAP function (f min =0.1 Hz, f max =4 Hz) in voltage clamp (V low =-60mV and V high =-30mV). The f max in biological PD neurons increases if either V low or V high are increased [3], whereas the LP neuron f max is only sensitive to V high . Additionally MPR in the PD neurons is sensitive to blockers of I Ca and I h . 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, I Ca is difficult to measureand therefore a top-down approach is adopted to elucidate the contributions of I Ca and I h to MPR in PD and LP. Because resonance depends on the kinetics of I Ca and I h , a bruteforce 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, I Ca and I h 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 g leak , V ½_Ca_act , V ½_Ca_inact and τ _Ca_inact . Additionally, strong correlations were observed between τ _Ca_act and τ _Ca_inact (negative), between V ½_Ca_act and V ½_Ca_inact and between g Ca and V ½_Ca_act (negative). In models with low I h , f max correlated strongly with the frequency which I Ca peaked, which is controlled by τ _Ca_act and τ _Ca_inact . The parameter sensitivities also support the sensitivity to I Ca time constants, demonstrating potential targets for neuromodulation.
The MOEA was also used to optimize the f max shifts with V low and V high to produce two model groups with properties that correspond to the differences between PD and LP. These results suggest that f max shift is due to different activation rates of I h 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, f max can be adjusted according to different input amplitudes.