Stochastic optimal control of single neuron spike trains

Area of Science:

• Computational Neuroscience
• Neuroscience
• Biophysics

Background:

• External control of neuronal spike timing offers insights into sub-threshold dynamics.
• Precise spike time control is crucial for developing advanced brain-machine interfaces and neural prostheses.
• Physiological constraints, such as avoiding tissue damage, must be considered in neural stimulation.

Purpose of the Study:

• To design an optimal electrical stimulation strategy for neurons.
• To achieve a target spike train with precise timing.
• To incorporate physiological constraints, specifically avoiding tissue damage.

Main Methods:

• A stochastic optimal control problem was formulated for a leaky integrate-and-fire (LIF) neuron model with intrinsic or synaptic noise.
• Dynamic programming was used for closed-loop control (with voltage access).
• A maximum principle was applied for open-loop control (with spike time access).

Main Results:

• A stochastic optimal control algorithm was developed for precise spike time generation.
• The algorithm is effective in both supra-threshold and sub-threshold regimes, and under open-loop and closed-loop conditions.
• Accuracy is maintained with arbitrary noise intensity, though it degrades with increasing noise; the method was validated on the Morris-Lecar model.

Conclusions:

• Online feedback control of noisy neurons via input modulation, respecting physiological constraints, is achieved.
• Stochastic optimal control provides a robust method for targeting neural activity, with significant potential for prosthetic applications and understanding in vivo neural control mechanisms.