Exploring the interplay between learning and gene expression

In this study we present a mathematical model exploring the interaction between neuronal activity and gene regulatory networks in habituation learning. By integrating a leaky integrate-and-fire neuron model with a two-gene GRN described by continuous ordinary differential equations, we simulate how repeated stimuli lead to a diminished neuronal response, a key feature of habituation. Our results identify key gene interactions that are very convenient for this process given our model: an inhibitory gene suppressing the other gene, the latter being suppressed as well by stimuli and starting with an initial concentration equal to or greater than that of the inhibitory gene. Although the model effectively captures habituation, it simplifies aspects like synaptic interactions and stochasticity for tractability. Future work will refine these elements and validate the model with empirical data. Despite its limitations, this model provides a foundational approach to understanding the molecular mechanisms of learning and offers a basis for further research in computational neuroscience.