Engineering the synchronization of neuron action potentials using global time-delayed feedback stimulation

We experimentally demonstrate the use of continuous, time-delayed, feedback stimulation for controlling the synchronization of neuron action potentials. Phase-based models were experimentally constructed from a single synaptically isolated cultured hippocampal neuron. These models were used to determine the stimulation parameters necessary to produce the desired synchronization behavior in the action potentials of a pair of neurons coupled through a global time-delayed interaction. Measurements made using a dynamic clamp system confirm the generation of the synchronized states predicted by the experimentally constructed phase model. This model was then utilized to extrapolate the feedback stimulation parameters necessary to disrupt the action potential synchronization of a large population of globally interacting neurons.

Figure 1

Schematic of the patch clamp apparatus setup. For one-cell experiments only one patch clamp apparatus was used and for the two-neuron experiments both patch clamp apparatuses were used.

Figure 2

(a) The membrane potential of a single neuron (top) and the applied stimulation signal (bottom) as functions of time ($K_0=13$ mV, $K_1=350$, $\tau =0.5$ rad$/2\pi$). (b), (c), (d) Period distributions for three separate cells. Middle panel shows the period distribution as the feedback stimulation delay was increased from from 0 to 1 rad$/2\pi$. Left and right panels illustrate the period distribution of the neuron action potentials before and after application of stimulation.

Figure 3

(a) Calculated interaction function data and Fourier fit for three neurons. (b) Calculated response functions for three isolated neurons. (c) Odd part of the interaction function for the experimental system with applied global feedback ($K_0=13$ mV, $K_1=350$, and $\tau =0$ rad$/2\pi$). (d) Odd part of the interaction function for the experimental system with applied global feedback ($K_0=13$ mV, $K_1=350$, and $\tau =0.5$ rad$/2\pi$). In (c) and (d) the open circles are stable states and the gray squares are unstable states.

Figure 4

(a) Membrane potential recording of two neurons. (b) Applied stimulation current ($K_0=13$ mV, $K=400$). (c), (d) Period distribution of neuron action potentials of neurons 1 and 2, respectively. (e) Observed distribution of phase differences between the action potentials of the two neurons.

Figure 5

Eigenvalues calculated for balanced cluster states as a function of feedback stimulation delay. (a) One-, (b) two-, (c) three-, and (d) four-cluster state. Dashed lines indicate region of possible desynchronization. In the three-cluster state ${\lambda }_1={\lambda }_2$, and in the four-cluster state ${\lambda }_1={\lambda }_3$.