Chaos and Hyperchaos in a Model of Ribosome Autocatalytic Synthesis

The molecular view of mechanical stress of brain cells, local translation, and neurodegenerative diseases

The assumption that chronic mechanical stress in brain cells stemming from intracranial hypertension, arterial hypertension, or mechanical injury is a risk factor for neurodegenerative diseases was put forward in the 1990s and has since been supported. However, the molecular mechanisms that underlie the way from cell exposure to mechanical stress to disturbances in synaptic plasticity followed by changes in behavior, cognition, and memory are still poorly understood. Here we review (1) the current knowledge of molecular mechanisms regulating local translation and the actin cytoskeleton state at an activated synapse, where they play a key role in the formation of various sorts of synaptic plasticity and long-term memory, and (2) possible pathways of mechanical stress intervention. The roles of the mTOR (mammalian target of rapamycin) signaling pathway; the RNA-binding FMRP protein; the CYFIP1 protein, interacting with FMRP; the family of small GTPases; and the WAVE regulatory complex in the regulation of translation initiation and actin cytoskeleton rearrangements in dendritic spines of the activated synapse are discussed. Evidence is provided that chronic mechanical stress may result in aberrant activation of mTOR signaling and the WAVE regulatory complex via the YAP/TAZ system, the key sensor of mechanical signals, and influence the associated pathways regulating the formation of F actin filaments and the dendritic spine structure. These consequences may be a risk factor for various neurological conditions, including autistic spectrum disorders and epileptic encephalopathy. In further consideration of the role of the local translation system in the development of neuropsychic and neurodegenerative diseases, an original hypothesis was put forward that one of the possible causes of synaptopathies is impaired proteome stability associated with mTOR hyperactivity and formation of complex dynamic modes of de novo protein synthesis in response to synapse-stimulating factors, including chronic mechanical stress.

Evolution and extinction can occur rapidly: a modeling approach

Fossil record of Earth describing the last 500 million years is characterized by evolution discontinuity as well as recurring global extinctions of some species and their replacement by new types, the causes of which are still debate. We developed a model of evolutionary self-development of a large ecosystem. This model of biota evolution based on the universal laws of living systems functioning: reproduction, dependence of reproduction efficiency and mortality on biota density, mutational variability in the process of reproduction and selection of the most adapted individuals. We have shown that global extinctions and phases of rapid growth and biodiversity stasis can be a reflection of the emergence of bistability in a self-organizing system, which is the Earth’s biota. Bistability was found to be characteristic only for ecosystems with predominant sexual reproduction. The reason for the transition from one state to another is the selection of the most adapted individuals. That is, we explain the characteristics of the Earth’s fossil record during the last 500 million years by the internal laws of Earth’s ecosystem functioning, which appeared at a certain stage of evolution as a result of the emergence of life forms with an increased adaptive diversification associated with sexual dimorphism.

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.

Limit cycles in models of circular gene networks regulated by negative feedback loops

BACKGROUND

The regulatory feedback loops that present in structural and functional organization of molecular-genetic systems and the phenomenon of the regulatory signal delay, a time period between the moment of signal reception and its implementation, provide natural conditions for complicated dynamic regimes in these systems. The delay phenomenon at the intracellular level is a consequence of the matrix principle of data transmission, implemented through the rather complex processes of transcription and translation.However, the rules of the influence of system structure on system dynamics are not clearly understood. Knowledge of these rules is particularly important for construction of synthetic gene networks with predetermined properties.

RESULTS

We study dynamical properties of models of simplest circular gene networks regulated by negative feedback mechanisms. We have shown existence and stability of oscillating trajectories (cycles) in these models. Two algorithms of construction and localization of these cycles have been proposed. For one of these models, we have solved an inverse problem of parameters identification.

CONCLUSIONS

The modeling results demonstrate that non-stationary dynamics in the models of circular gene networks with negative feedback loops is achieved by a high degree of non-linearity of the mechanism of the autorepressor influence on its own expression, by the presence of regulatory signal delay, the value of which must exceed a certain critical value, and transcription/translation should be initiated from a sufficiently strong promoter/Shine-Dalgarno site. We believe that the identified patterns are key elements of the oscillating construction design.

Causes of global extinctions in the history of life: facts and hypotheses

Paleontologists define global extinctions on Earth as a loss of about three-quarters of plant and animal species over a relatively short period of time. At least five global extinctions are documented in the Phanerozoic fossil record (~500-million-year period): ~65, 200, 260, 380, and 440 million years ago. In addition, there is evidence of global extinctions in earlier periods of life on Earth - during the Late Cambrian (~500 million years ago) and Ediacaran periods (more than 540 million years ago). There is still no common opinion on the causes of their occurrence. The current study is a systematized review of the data on recorded extinctions of complex life forms on Earth from the moment of their occurrence during the Ediacaran period to the modern period. The review discusses possible causes for mass extinctions in the light of the influence of abiogenic factors, planetary or astronomical, and the consequences of their actions. We evaluate the pros and cons of the hypothesis on the presence of periodicity in the extinction of Phanerozoic marine biota. Strong evidence that allows us to hypothesize that additional mechanisms associated with various internal biotic factors are responsible for the emergence of extinctions in the evolution of complex life forms is discussed. Developing the idea of the internal causes of periodicity and discontinuity in evolution, we propose our own original hypothesis, according to which the bistability phenomenon underlies the complex dynamics of the biota development, which is manifested in the form of global extinctions. The bistability phenomenon arises only in ecosystems with predominant sexual reproduction. Our hypothesis suggests that even in the absence of global abiotic catastrophes, extinctions of biota would occur anyway. However, our hypothesis does not exclude the possibility that in different periods of the Earth's history the biota was subjected to powerful external influences that had a significant impact on its further development, which is reflected in the Earth's fossil record.

Individual Copy Number of Ribosomal Genes as a Factor of Mental Retardation and Autism Risk and Severity

Autism is a complex multifactorial developmental disorder characterized by deficits in communication and restricted interests, often followed by mental retardation. Autism spectrum disorders (ASD) are caused by defects in miscellaneous molecular mechanisms, many of which remain unclear. But a considerable part of the known pathways converges on protein synthesis or degradation processes at different stages in the dendrites, laying the foundation for a concept of disturbed “translational homeostasis” or “proteostasis” in autism. The protein synthesis is conducted on ribosomes, cellular organelles consisting from a complex of riboproteins and a ribosomal RNA (rRNA) framework. The rRNA is encoded by ribosomal genes (RG) existing in multiple copies in the genome. The more copies of RG that are contained in the genome, the higher is the peak (maximum possible) ribosome abundance in the cell. A hypothesis is proposed that the RG copy number, through determining the quantity of ribosomes available in the dendrites, modulates the level of local dendritic translation and thus is a factor of risk and severity of a series of neuropsychiatric disorders caused by aberrant dendritic translation. A carrier of very low copy number of ribosomal genes is expected to have a milder form of ASD than a subject with the same epigenetic and genetic background, but a higher ribosomal gene dosage. Various ways of evaluation and testing the hypothesis on clinical material and animal models are suggested.

Persister Cells - a Plausible Outcome of Neutral Coevolutionary Drift

The phenomenon of bacterial persistence - a non-inherited antibiotic tolerance in a minute fraction of the bacterial population, was observed more than 70 years ago. Nowadays, it is suggested that "persister cells" undergo an alternative scenario of the cell cycle; however, pathways involved in its emergence are still not identified. We present a mathematically grounded scenario of such possibility. We have determined that population drift in the space of multiple neutrally coupled mutations, which we called "neutrally coupled co-evolution" (NCCE), leads to increased dynamic complexity of bacterial populations via appearance of cells capable of carrying out a single cell cycle in two or more alternative ways and that universal properties of the coupled transcription-translation system underlie this phenotypic multiplicity. According to our hypothesis, modern persister cells have derived from such cells and regulatory mechanisms that govern the consolidation of this phenomenon represented the trigger. We assume that the described type of neutrally coupled co-evolution could play an important role in the origin of extremophiles, both in bacteria and archaea.

Dynamic landscape of the local translation at activated synapses

The mammalian target of rapamycin (mTOR) signaling pathway is the central regulator of cap-dependent translation at the synapse. Disturbances in mTOR pathway have been associated with several neurological diseases, such as autism and epilepsy. RNA-binding protein FMRP, a negative regulator of translation initiation, is one of the key components of the local translation system. Activation and inactivation of FMRP occurs via phosphorylation by S6 kinase and dephosphorylation by PP2A phosphatase, respectively. S6 kinase and PP2A phosphatase are activated in response to mGluR receptor stimulation through different signaling pathways and at different rates. The dynamic aspects of this system are poorly understood. We developed a mathematical model of FMRP-dependent regulation of postsynaptic density (PSD) protein synthesis in response to mGluR receptor stimulation and conducted in silico experiments to study the regulatory circuit functioning. The modeling results revealed the possibility of generating oscillatory (cyclic and quasi-cyclic), chaotic and even hyperchaotic dynamics of postsynaptic protein synthesis as well as the presence of multiple attractors in a wide range of parameters of the local translation system. The results suggest that autistic disorders associated with mTOR pathway hyperactivation may be due to impaired proteome stability associated with the formation of complex dynamic regimes of PSD protein synthesis in response to stimulation of mGluR receptors on the postsynaptic membrane of excitatory synapses on pyramidal hippocampal cells.