Macrochaetes (large bristles) are sensor organs of the Drosophila peripheral nervous system with a function of mechanoreceptors. An adult mechanoreceptor comprises four specialized cells: shaft (trichogen), socket (tormogen), neuron, and glial cell (thecogen). All these cells originate from a single cell, the so-called sensor organ precursor (SOP) cell. Separation of the SOP cell from the encompassing cells of the imaginal disc initiates a multistage process of sensory organ development. A characteristic feature of the SOP cell is the highest amount of the proneural proteins AS-C as compared with the encompassing ectodermal cells. The accumulation of proneural proteins and maintenance of their amount in the SOP cell at a necessary level is provided by the gene network with the achaete-scute gene complex (AS-C) as its key component. The activity of this complex is controlled by the central regulatory circuit (CRC). The CRC comprises the genes hairy, senseless (sens), charlatan (chn), scratch (scrt), daughterless (da), extramacrochaete (emc), and groucho (gro), coding for the transcription factors involved in the system of direct links and feedbacks and implementation of activation-repression relationships between the CRC components. The gene phyllopod (phyl), involved in degradation of the AS-C proteins, is also associated with the CRC functioning. In this paper, we propose a mathematical model for the CRC functioning as a regulator of the amount of proneural AS-C proteins in the SOP cell taking into account their degradation. The modeling has demonstrated that a change in the amount of proneural proteins in the SOP cell is stepwise rather than strictly monotonic. This prediction can be tested experimentally.
Keywords: Drosophila; achaete–scute complex; equilibrium points; gene networks; mathematical model; nonlinear dynamic systems.