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Results for “Hodgkin–Huxley”

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4 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Bypassing Fast Time Scales of the Hodgkin-Huxley Neuron Model via a Thresholded Hard Reset

We propose a modification to the Hodgkin-Huxley model to reduce the numerical stiffness of the equations by introducing an explicit voltage threshold. When this threshold is crossed, the voltage and the gating variables are reset to constant values. It is found that, for all of the current stimuli considered, the proposed model accurately reproduces the behavior of the baseline Hodgkin-Huxley model while bypassing the fast dynamics of spiking. Specifically, the model accurately reproduces the spike times and, between spikes, the time courses of the membrane potential and gating variables.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Multimodal parameter spaces of a complex multi-channel neuron model

One of the most common types of models that helps us to understand neuron behavior is based on the Hodgkin–Huxley ion channel formulation (HH model). A major challenge with inferring parameters in HH models is non-uniqueness: many different sets of ion channel parameter values produce similar outputs for the same input stimulus. Such phenomena result in an objective function that exhibits multiple modes (i.e., multiple local minima). This non-uniqueness of local optimality poses challenges for parameter estimation with many algorithmic optimization techniques. HH models additionally have severe non-linearities resulting in further challenges for inferring parameters in an algorithmic fashion. To address these challenges with a tractable method in high-dimensional parameter spaces, we propose using a particular Markov chain Monte Carlo (MCMC) algorithm, which has the advantage of inferring parameters in a Bayesian framework. The Bayesian approach is designed to be suitable for multimodal solutions to inverse problems. We introduce and demonstrate the method using a three-channel HH model. We then focus on the inference of nine parameters in an eight-channel HH model, which we analyze in detail. We explore how the MCMC algorithm can uncover complex relationships between inferred parameters using five injected current levels. The MCMC method provides as a result a nine-dimensional posterior distribution, which we analyze visually with solution maps or landscapes of the possible parameter sets. The visualized solution maps show new complex structures of the multimodal posteriors, and they allow for selection of locally and globally optimal value sets, and they visually expose parameter sensitivities and regions of higher model robustness. We envision these solution maps as enabling experimentalists to improve the design of future experiments, increase scientific productivity and improve on model structure and ideation when the MCMC algorithm is applied to experimental data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Learning emergent partial differential equations in a learned emergent space

We propose an approach to learn effective evolution equations for large systems of interacting agents. This is demonstrated on two examples, a well-studied system of coupled normal form oscillators and a biologically motivated example of coupled Hodgkin-Huxley-like neurons. For such types of systems there is no obvious space coordinate in which to learn effective evolution laws in the form of partial differential equations. In our approach, we accomplish this by learning embedding coordinates from the time series data of the system using manifold learning as a first step. In these emergent coordinates, we then show how one can learn effective partial differential equations, using neural networks, that do not only reproduce the dynamics of the oscillator ensemble, but also capture the collective bifurcations when system parameters vary. The proposed approach thus integrates the automatic, data-driven extraction of emergent space coordinates parametrizing the agent dynamics, with machine-learning assisted identification of an emergent PDE description of the dynamics in this parametrization.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

A Unidirectional Two-Compartment Neuron Circuit with On-chip STDP learning

Most neuromorphic chips implement the single-compartment point neuron model where synapse circuits connect directly to a leaky integrate and fire (LIF) soma circuit. However, when using a biologically plausible soma circuit (e.g., Hodgkin-Huxley neuron model), an interface circuitry, such as a current conveyor circuit, is needed to transmit synaptic current to the soma circuit. This is especially true for ultra-low power neuron circuits, where membrane capacitance is on the order of 20 fF. This need for an interface circuit arises because the parasitic capacitance and leakage current caused by fabrication mismatch and second-order effects of the output transistors in the synapse circuits can disturb the spiking dynamics of the soma circuit if connected without an interface. Using an interface circuit to isolate the soma’s membrane capacitor from synapses resolves this issue. We propose to use a unidirectional resistor (a transconductance circuit) to connect the synapse and soma circuits instead of conventional current conveyor circuits. Using a biologically plausible spike pattern detection model, we show that the on-chip spike-timing-dependent plasticity (STDP) learning performance of the proposed unidirectional two-compartment neuron circuit is similar to a single-compartment circuit (with a current conveyor as an interface) and additionally, it is more power-efficient and biologically plausible. The chip is fabricated in the Taiwan Semiconductor Manufacturing Company (TSMC) 250 nm technology node and comprises a single neuron circuit.

Gautam, Ashish [ORNL]↗