Three generic bistable scenarios of the interplay of voltage pulses and gene expression in neurons.

The long-term changes of the neuron function are often related to the interplay of the membrane voltage pulses and gene expression. In the present work, this phenomenon is modeled by combining the standard stochastic integrate-and-fire neuron model with generic kinetic models describing gene expression. The three scenarios under consideration include, respectively, the voltage-related regulation of (i) gene transcription into mRNA, (ii) gene transcription into miRNA, and (iii) proteasome formation. Typical transient and steady-state kinetics are shown. The latter kinetics exhibit a unique steady state, bistability, or oscillations. The conditions of realization of these regimes are investigated numerically. The transient and oscillatory kinetics are predicted on the time scale of about one hour or longer. The implications of these results for interpretation of synaptic plasticity and learning and long-term memory are briefly discussed.