On the dynamical aspects of local translation at the activated synapse.

BACKGROUND: The key role in the dynamic regulation of synaptic protein turnover belongs to the Fragile X Mental Retardation Protein, which regulates the efficiency of dendritic mRNA translation in response to stimulation of metabotropic glutamate receptors at excitatory synapses of the hippocampal pyramidal cells. Its activity is regulated via positive and negative regulatory loops that function in different time ranges, which is an absolute factor for the formation of chaotic regimes that lead to disrupted proteome stability. The indicated condition may cause a number of neuropsychiatric diseases, including autism and epilepsy. The present study is devoted to a theoretical analysis of the local translation system dynamic properties and identification of parameters affecting the chaotic potential of the system. RESULTS: A mathematical model that describes the maintenance of a specific pool of active receptors on the postsynaptic membrane via two mechanisms - de novo synthesis of receptor proteins and restoration of protein function during the recycling process - has been developed. Analysis of the model revealed that an increase in the values of the parameters describing the impact of protein recycling on the maintenance of a pool of active receptors in the membrane, duration of the signal transduction via the mammalian target of rapamycin pathway, influence of receptors on the translation activation, as well as reduction of the rate of synthesis and integration of de novo synthesized proteins into the postsynaptic membrane - contribute to the reduced complexity of the local translation system dynamic state. Formation of these patterns significantly depends on the complexity and non-linearity of the mechanisms of exposure of de novo synthesized receptors to the postsynaptic membrane, the correct evaluation of which is currently problematic. CONCLUSIONS: The model predicts that an increase of "receptor recycling" and reduction of the rate of synthesis and integration of de novo synthesized proteins into the postsynaptic membrane contribute to the reduced complexity of the local translation system dynamic state. Herewith, stable stationary states occur much less frequently than cyclic states. It is possible that cyclical nature of functioning of the local translation system is its "normal" dynamic state.

Chaos and hyperchaos in simple gene network with negative feedback and time delays.

Today there are examples that prove the existence of chaotic dynamics at all levels of organization of living systems, except intracellular, although such a possibility has been theoretically predicted. The lack of experimental evidence of chaos generation at the intracellular level in vivo may indicate that during evolution the cell got rid of chaos. This work allows the hypothesis that one of the possible mechanisms for avoiding chaos in gene networks can be a negative evolutionary selection, which prevents fixation or realization of regulatory circuits, creating too mild, from the biological point of view, conditions for the emergence of chaos. It has been shown that one of such circuits may be a combination of negative autoregulation of expression of transcription factors at the level of their synthesis and degradation. The presence of such a circuit results in formation of multiple branches of chaotic solutions as well as formation of hyperchaos with equal and sufficiently low values of the delayed argument that can be implemented not only in eukaryotic, but in prokaryotic cells.

Chaos and Hyperchaos in a Model of Ribosome Autocatalytic Synthesis.

Any vital activities of the cell are based on the ribosomes, which not only provide the basic machinery for the synthesis of all proteins necessary for cell functioning during growth and division, but for biogenesis itself. From this point of view, ribosomes are self-replicating and autocatalytic structures. In current work we present an elementary model in which the autocatalytic synthesis of ribosomal RNA and proteins, as well as enzymes ensuring their degradation are described with two monotonically increasing functions. For certain parameter values, the model, consisting of one differential equation with delayed argument, demonstrates both stationary and oscillatory dynamics of the ribosomal protein synthesis, which can be chaotic and hyperchaotic dependent on the value of the delayed argument. The biological interpretation of the modeling results and parameter estimation suggest the feasibility of chaotic dynamics in molecular genetic systems of eukaryotes, which depends only on the internal characteristics of functioning of the translation system.

Alternative splicing can lead to chaos.

Alternative splicing is a widespread phenomenon in higher eukaryotes, where it serves as a mechanism to increase the functional diversity of proteins. This phenomenon has been described for different classes of proteins, including transcription regulatory proteins. We demonstrated that in the simplest genetic system model the formation of the alternatively spliced isoforms with opposite functions (activators and repressors) could be a cause of transition to chaotic dynamics. Under the simplest genetic system we understand a system consisting of a single gene encoding the structure of a transcription regulatory protein whose expression is regulated by a feedback mechanism. As demonstrated by numerical analysis of the models, if the synthesized isoforms regulate the expression of their own gene acting through different sites and independently of each other, for the generation of chaotic dynamics it is sufficient that the regulatory proteins have a dimeric structure. If regulatory proteins act through one site, the chaotic dynamics is generated in the system only when the repressor protein is either a tetrameric or a higher-dimensional multimer. In this case the activator can be a dimer. It was also demonstrated that if the transcription factor isoforms exhibit either activating or inhibiting activity and are lower-dimensional multimers (< 4), independently of the regulation type the model demonstrates either cyclic or stationary trajectories.

On the chaos in gene networks.

The methods for constructing "chaotic" nonlinear systems of differential equations modeling gene networks of arbitrary structure and dimensionality with various types of symmetry are considered. It has been shown that an increase in modality of the functions describing the control of gene expression efficiency allows for a decrease in the dimensionality of these systems with retention of their chaotic dynamics. Three-dimensional "chaotic" cyclic systems are considered. Symmetrical and asymmetrical attractors with "narrow" chaos having a Moebius-like structure have been detected in such systems. As has been demonstrated, a complete symmetry of the systems with respect to permutation of variables does not prevent the emergence of their chaotic dynamics.

Model of the reception of hedgehog morphogen concentration gradient: comparison with an extended range of experimental data.

The model for reception of the concentration gradient of the Hedgehog morphogen has been developed. The mechanism of co-operation of the proteins Patched, Smoothened, and Hedgehog is theoretically analyzed in terms of different versions of interactions within this group of proteins. The parametric stability of the modeled system is considered.