This paper introduces a novel connectionist approach to neural network modelling that integrates dynamic gene networks within neurons with a neural network model. Interaction of genes in neurons affects the dynamics of the whole neural network. Through tuning the gene interaction network and the initial gene/protein expression values, different states of the neural network operation can be achieved. A generic computational neurogenetic model is introduced that implements this approach. It is illustrated by means of a simple neurogenetic model of a spiking neural network (SNN). Functioning of the SNN can be evaluated for instance by the field potentials, thus making it possible to attempt modelling the role of genes in different brain states such as epilepsy, schizophrenia, and other states, where EEG data is available to test the model predictions.