The central regulatory circuit in the gene network controlling the morphogenesis of Drosophila mechanoreceptors: an in silico analysis.

Identification of the mechanisms underlying the genetic control of spatial structure formation is among the relevant tasks of developmental biology. Both experimental and theoretical approaches and methods are used for this purpose, including gene network methodology, as well as mathematical and computer modeling. Reconstruction and analysis of the gene networks that provide the formation of traits allow us to integrate the existing experimental data and to identify the key links and intra-network connections that ensure the function of networks. Mathematical and computer modeling is used to obtain the dynamic characteristics of the studied systems and to predict their state and behavior. An example of the spatial morphological structure is the Drosophila bristle pattern with a strictly defined arrangement of its components - mechanoreceptors (external sensory organs) - on the head and body. The mechanoreceptor develops from a single sensory organ parental cell (SOPC), which is isolated from the ectoderm cells of the imaginal disk. It is distinguished from its surroundings by the highest content of proneural proteins (ASC), the products of the achaete-scute proneural gene complex (AS-C). The SOPC status is determined by the gene network we previously reconstructed and the AS-C is the key component of this network. AS-C activity is controlled by its subnetwork - the central regulatory circuit (CRC) comprising seven genes: AS-C, hairy, senseless (sens), charlatan (chn), scratch (scrt), phyllopod (phyl), and extramacrochaete (emc), as well as their respective proteins. In addition, the CRC includes the accessory proteins Daughterless (DA), Groucho (GRO), Ubiquitin (UB), and Seven-in-absentia (SINA). The paper describes the results of computer modeling of different CRC operation modes. As is shown, a cell is determined as an SOPC when the ASC content increases approximately 2.5-fold relative to the level in the surrounding cells. The hierarchy of the effects of mutations in the CRC genes on the dynamics of ASC protein accumulation is clarified. AS-C as the main CRC component is the most significant. The mutations that decrease the ASC content by more than 40 % lead to the prohibition of SOPC segregation.

Stratifications and foliations in phase portraits of gene network models.

Periodic processes of gene network functioning are described with good precision by periodic trajectories (limit cycles) of multidimensional systems of kinetic-type differential equations. In the literature, such systems are often called dynamical, they are composed according to schemes of positive and negative feedback between components of these networks. The variables in these equations describe concentrations of these components as functions of time. In the preparation of numerical experiments with such mathematical models, it is useful to start with studies of qualitative behavior of ensembles of trajectories of the corresponding dynamical systems, in particular, to estimate the highest likelihood domain of the initial data, to solve inverse problems of parameter identification, to list the equilibrium points and their characteristics, to localize cycles in the phase portraits, to construct stratification of the phase portraits to subdomains with different qualities of trajectory behavior, etc. Such an à priori geometric analysis of the dynamical systems is quite analogous to the basic section "Investigation of functions and plot of their graphs" of Calculus, where the methods of qualitative studies of shapes of curves determined by equations are exposed. In the present paper, we construct ensembles of trajectories in phase portraits of some dynamical systems. These ensembles are 2-dimensional surfaces invariant with respect to shifts along the trajectories. This is analogous to classical construction in analytic mechanics, i. e. the level surfaces of motion integrals (energy, kinetic moment, etc.). Such surfaces compose foliations in phase portraits of dynamical systems of Hamiltonian mechanics. In contrast with this classical mechanical case, the foliations considered in this paper have singularities: all their leaves have a non-empty intersection, they contain limit cycles on their boundaries. Description of the phase portraits of these systems at the level of their stratifications, and that of ensembles of trajectories allows one to construct more realistic gene network models on the basis of methods of statistical physics and the theory of stochastic differential equations.

[Gene Network Controlling the Morphogenesis of D. melanogaster Macrochaetes: An Expanded Model of the Central Regulatory Circuit].

The drosophila macrochaetes act as mechanoreceptors, the sensory organs of the peripheral nervous system. Each mechanoreceptor consists of four specialized cells, namely, the shaft, socket, neuron, and sheath. All these cells develop from a single cell referred to as the sensory organ precursor (SOP) cell. The SOP cell segregates from the surrounding cells of imaginal disc, thereby launching multistage sensory organ development. A characteristic feature of the SOP cell is the highest content of the proneural proteins Achaete and Scute (ASC) as compared with the surrounding cells. The pattern of changes in the content of proneural proteins in the SOP cell is determined by a gene network with the achaete-scute (AS-C) gene complex as its key component. The activity of this complex is controlled by the central regulatory circuit (CRC), containing the genes hairy, senseless (sens), charlatan (chn), scratch (scrt), daughterless (da), extramacrochaete (emc), and groucho (gro), encoding the transcription factors involved in the system of feedforwards and feedbacks and implementing the activation­repression of CRC components, as well as the gene phyllopod (phyl), an adaptor protein that controls the degradation of ASC proteins. A mathematical model describing the CRC functioning in the SOP cell as a regulator of the content of ASC proneural proteins is proposed.