Chaos-hyperchaos transition in three identical quorum-sensing mean-field coupled ring oscillators.

We investigate the dynamics of three identical three-dimensional ring synthetic genetic oscillators (repressilators) located in different cells and indirectly globally coupled by quorum sensing whereby it is meant that a mechanism in which special signal molecules are produced that, after the fast diffusion mixing and partial dilution in the environment, activate the expression of a target gene, which is different from the gene responsible for their production. Even at low coupling strengths, quorum sensing stimulates the formation of a stable limit cycle, known in the literature as a rotating wave (all variables have identical waveforms shifted by one third of the period), which, at higher coupling strengths, converts to complex tori. Further torus evolution is traced up to its destruction to chaos and the appearance of hyperchaos. We hypothesize that hyperchaos is the result of merging the saddle-focus periodic orbit (or limit cycle) corresponding to the rotating wave regime with chaos and present considerations in favor of this conclusion.

Evolution of quasiperiodicity in quorum-sensing coupled identical repressilators.

The dynamics of three three-dimensional repressilators globally coupled by a quorum sensing mechanism was numerically studied. This number (three) of coupled repressilators is sufficient to obtain such a set of self-consistent oscillation frequencies of signal molecules in the mean field that results in the appearance of self-organized quasiperiodicity and its complex evolution over wide areas of model parameters. Numerically analyzing the invariant curves as a function of coupling strength, we observed torus doubling, three torus arising via quasiperiodic Hopf bifurcation, the emergence of resonant cycles, and secondary Neimark-Sacker bifurcation. A gradual increase in the oscillation amplitude leads to chaotizations of the tori and to the birth of weak, but multidimensional chaos.

[The experimental evaluation of the protective effect of the extract of the cyclodextrin-containing phytotherapeutic composition on the development of osteoporosis].

OBJECTIVE: The relevance of the problem considered in the present communication arises to-day from the widespread prevalence of osteoporosis (OP), the rather low effectiveness of the methods currently available for the treatment of this condition, and iatrogenic effects of its medication therapy. The great diversity of phytotherapeutic modalities of traditional medicine are is only poorly supported by the results of the scientific studies results; moreover, most of them are coming from the foreign literature publications. AIM:  The objective of the present study was to evaluate the influence of the phytotherapeutic preparation (Phytocost) having cyclodextrin in its composition on the restoration of the cartilaginous and bony tissues based on the experimental research with the use of the OP experimental model. MATERIAL AND METHODS:  The experimental studies were performed on 5 month-old Balb/c mice used as the prednisolone-induced osteoporosis model. The animals were divided into four study groups according to the daily doses administered to them: 0.005; 0.05; 0.5 and 5.0 mg/mouse during 30 days and 3 control groups: intact, 14 and 30 days after prednisolone administration, naïve mice. RESULTS:  The study has demonstrated the dose-dependent protective effect of cyclodextrin-containing Phytocost. The most pronounced effect in the form of reduction of osteoblast number and the increase in the number of osteocytes was obtained at a Phytocost dose of 0.5 mg/mouse. No undesirable adverse reactions were documented during the study. CONCLUSION:  The domestically produced Phytocost composition differs from its foreign analogues in that it contains a significantly greater number of constituent components because the ultimate goal of the study was to create a medication acting on all currently known mechanisms of OP pathogenesis, whereas our Chinese colleagues proceed from the ancient knowledge gained by traditional medicine that it is sometimes difficult to understand and explain in the light of the modern concepts. All the plants used as raw materials for Phytocost production grow at the territory of the Russian Federation which provides the possibilities for the efficient import substitution of the components necessary for the manufacture of the preparation in question.

FLUORESCENT MICROSCOPY IDENTIFICATION OF THE EXPRESSION OF a2 AND b1 NA +/K+-ATPase, a1S (L-TYPE), ÑÀ2+-CHANNEL, SERCA 1/2/3 CA2+-ATPase SUBUNITS AT FAST AND SLOW MUSCLES IN THE HYPOGRAVITY MODELING EXPERIMENTS IN RATS

The experiments of modeling hypogravity using fluorescent microscopy have shown a decrease of expression of b1 of Na +/K+-ATPase and Ca2+-ATPase subunits and the increase in the insensitivity of synthesis of a1S subunit of the L-type Ca2+-channel of the plasmatic membrane, whereas the synthesis of a2 subunit of Na+/K+-ATPase does not change. In «fast¼ muscle only observed similar for «slow¼ muscle decrease in the expression of b1 subunit without changing other parameters were studied. However, the decrease in fluorescence b1 subunit due to spread of data was not statistically significant. Thus hypogravity adversely affects the functioning primarily skeletal muscles, providing static load.

[The effect of low frequency electrical stimulation on bone tissue regeneration].

The study was performed on 30 male rats of Wistar line (weight 330-360 g, age 3.5 months).In an experimental model of damage to the femur bone in the hip joint studied the effect of low frequency electrical stimulation of the damaged area on the rate of regeneration of bone. The animals were divided into two groups. Control (15 rats) and experienced (15 rats). In the experimental animals underwent stimulation of the injury site for 5 min daily for 7 days, 14 days and 21 days. Stimulation was carried out using a device "Osteon-1" generating a mixed signal of two voltage pulse of varying duty cycle, one of which is modulated to a higher frequency. Signals were not synchronized with respect to each other, unipolar with varying frequencies and amplitudes. The obtained results show the effectiveness of the electrical stimulation currents of low frequency in the restoration of bone tissue after damage. Morphological studies showed that electrical stimulation to accelerate the regeneration of damaged bone at all stages of the study (7, 14, 21 day), causes a more pronounced integration of newly formed bone with the old intact bone and promote the formation of more powerful periosteal calluses in comparison with the control.

[New phytotherapeutic composition for restoring bone and cartilage. Experimental study].

Presents a new import-substituting the composition of the powder mixture 60 medicinal plants and dead bees. In prednisolonbuy models of osteoporosis have shown dose-dependent regenerative effects bone and cartilage of the hip joints of mice. Unwanted side effects when taking composition was observed. It is assumed the possibility of effective application of the composition as a complementary treatment for osteoporosis.

The role of chloride ions in the maintenance of resting membrane potential in rat fast and slow muscles during hypogravity modeling.

Antiorthostatic hindlimb suspension reduces resting membrane potential of rat fast and slow muscles within 7 days. Changes in Na+/K+ pump activity and shifts of the equilibrium potential for chloride ions are the main mechanism of the changes in the resting potential of muscle fibers. The latter is presumably associated with increased intracellular ion current due to activation of the second active Na+, K+, 2Cl- symport. Reduction of the membrane potential is related to muscle denervation. However, membrane depolarization of muscle fibers during antiorthostatic suspension cannot be explained solely by changes in the mechanisms of neurotrophic control from motor neurons.

[A model of primary open-angle glaucoma: manifestations and outcomes].

OBJECTIVE: To determine the expected duration of the disease and the age of the patients with different stages ofprimary open-angle glaucoma complicated by pseudoexfoliation syndrome (PES) and/or patients with pseudoexfoliation glaucoma (PEG). METHODS: The study protocol included data from 120 patients (50 males (41.7%), 70 females (58.3%)); 189 eyes; 102 right eyes; 87 left eyes). The first study group (28 patients, 44 eyes) comprised patients with suspected glaucoma. The second group (53 patients, 84 eyes) consisted ofpatients with early glaucoma. The third group (21 patient, 33 eyes) included patients with advanced glaucoma, the forth group (18 patients, 28 eyes) comprised patients with terminal glaucoma. Mean age of the patients at diagnosis was 61.6 (58.4; 66.9) years and 66.9 (63.4; 72.8) years at the endpoint visit in 2013. In all cases, diagnosis was made in accordance with the differential diagnostics system and confirmed by special diagnostic techniques. The database included data from 3 qualified examinations taking account of the results of tonometry and static automated perimetry. RESULTS: The mean expected age of the patients age at the onset of blindness was 75.1 years. The occurrence of the event was limited to a period of 6.1 years. Mean age at the time of possible glaucoma development was 59.58 (56.14; 64.36) years. The disease itself could develop within 3.24 (-5.38; -1.2) years prior to diagnosis. CONCLUSION: Studies for glaucoma diagnosis should be focused on the age group of 55-60 years. The degree of IOP reduction in patients with advanced glaucoma does not agree with the Russian glaucoma society recommendations which accounts for progression of the disease.

[Influence of modeling of gravitational unloading on the postsynaptic acetylcholine receptor organization and acetylcholinesterase activity in neuromuscular synapses of rat fast and slow muscles].

Using immunofluorescent techniques, we have revealed that, after 35 days of rats hindlimb unloading, neuromuscular synapses of fast and slow muscles show enhanced fluorescence intensity and decreased area of fluorescent staining of acetylcholine receptors; increased fluorescent intensity and area of fluorescent staining for acetylcholinesterase. The ratio of the number of postsynaptic acetylcholine receptors and the amount of acetylcholinesterase changed as well as their spatial position in relation to each other. These rearrangements correspond to electrophysiological data on the reduction of the amplitude of the miniature endplate currents in both muscles. Identified synapses restructuring accompanied by a decrease in the volume of muscle fibers. Hindlimb unloading (simulation of hypogravity) leads to an increase in functional activity of acetylcholinesterase on the background of reduced postsynaptic membrane area occupied by acetylcholine receptors. This leads to a decrease in the amplitude of excitatory postsynaptic potentials thereby reducing the nerve-muscle excitation transmission safety factor.

[Interaction of surface-active base with fraction of membrane-bound Williams's protons].

In the process of mitochondrial respiratory H(+)-pumps functioning, the fraction membrane-bound protons (R-protons), which have an excess of free energy is formed. According to R.J. Williams this fraction is included as energy source in the reaction of ATP synthesis. Previously, in our laboratory was found the formation of this fraction was found in the mitochondria and on the outer surface of mitoplast. On the mitoslast model we strictly shown that non-equilibrium R-proton fraction is localized on the surface of the inner mitochondrial membrane. In this paper a surface-active compound--anion of 2,4,6-trichloro-3-pentadecylphenol (TCP-C15) is described, which selectively interacts with the R-protons fraction in mitochondria. A detailed description of the specific interaction of the TCP-C15 with R-protons fraction in mitochondria is presented. Moreover, in this work it was found that phosphate transport system reacts with the R-protons fraction in mitochondria and plays the role of the endogenous volume regulation system of this fraction. The results of experiments are discussed in the terms of a local coupling model of the phosphorylation mechanism.

"Quorum sensing" generated multistability and chaos in a synthetic genetic oscillator.

We model the dynamics of the synthetic genetic oscillator Repressilator equipped with quorum sensing. In addition to a circuit of 3 genes repressing each other in a unidirectional manner, the model includes a phase-repulsive type of the coupling module implemented as the production of a small diffusive molecule-autoinducer (AI). We show that the autoinducer (which stimulates the transcription of a target gene) is responsible for the disappearance of the limit cycle (LC) through the infinite period bifurcation and the formation of a stable steady state (SSS) for sufficiently large values of the transcription rate. We found conditions for hysteresis between the limit cycle and the stable steady state. The parameters' region of the hysteresis is determined by the mRNA to protein lifetime ratio and by the level of transcription-stimulating activity of the AI. In addition to hysteresis, increasing AI-dependent stimulation of transcription may lead to the complex dynamic behavior which is characterized by the appearance of several branches on the bifurcation continuation, containing different regular limit cycles, as well as a chaotic regime. The multistability which is manifested as the coexistence between the stable steady state, limit cycles, and chaos seems to be a novel type of the dynamics for the ring oscillator with the added quorum sensing positive feedback.

[Immunocytochemical identification of synaptotagmin 1, syntaxin 1, N-type Ca(2+)-channel and nicotinic cholinoreceptor in motor neuromuscular junctions of earthworm somatic muscle Lumbricus terrestris].

The somatic muscle of earthworm contains myoneural synapses forming clusters of "synaptic buttons". In these "buttons", the proteins syntaxin 1, synaptotagmin 1 and alpha 1B subunit of the Ca(2+)-channel of N-type were identified. We suppose that "synaptic buttons" contain a limited number of active zones due to their small size (1-2 microm) and the pattern of distribution of proteins of exo-endocytotic cycle. The postsynaptic membrane of cholinetgic synapses contains nicotinic acetylcholine receptors capable to bind alpha-bungarotoxin. The area of location of receptors on postsynaptic membrane is strictly limited to the region of synaptic contact.

[Ionic and molecular mechanisms of beta-amyloid-induced depolarization of the mouse skeletal muscle fibres].

Excess production and accumulation of beta-amyloid peptide (betaAP) are central for pathogenesis of Alzheimer's disease. Numerous studies showed that betaAP possessed wide range of toxic effects on neurons, however the mechanism of betaAP influence on another types of excitable cells, for example, skeletal muscle fibres, is unknown. In electrophysiological experiments on the mouse diaphragm, we found for the first time that betaAP (25-35 fragment, 10-6 M) disturbs the processes of the resting membrane potential generation in muscle fibres, leading to depolarization by two mechanisms: 1) inhibition of Na+,K(+)-ATPase, which leads to loss of impact of this pump to the resting membrane potential; 2) increase of membrane cationic permeability due to formation of "amyloid" channels blocked with Zn2+ ions. Our results significantly broaden current understanding of mechanisms of motor disturbances and skeletal muscle pathology in Alzheimer's disease, inclusion body myositis and other betaAP-related disorders.

Dynamics of coupled repressilators: the role of mRNA kinetics and transcription cooperativity.

Oscillatory regulatory networks have been discovered in many cellular pathways. An especially challenging area is studying dynamics of cellular oscillators interacting with one another in a population. Synchronization is only one of and the simplest outcome of such interaction. It is suggested that the outcome depends on the structure of the network. Phase-attractive (synchronizing) and phase-repulsive coupling structures were distinguished for regulatory oscillators. In this paper, we question this separation. We study an example of two interacting repressilators (artificial regulatory oscillators based on cyclic repression). We show that changing the cooperativity of transcription repression (Hill coefficient) and reaction timescales dramatically alter synchronization properties. The network becomes birhythmic-it chooses between the in-phase and antiphase synchronization. Thus, the type of synchronization is not characteristic for the network structure. However, we conclude that the specific scenario of emergence and stabilization of synchronous solutions is much more characteristic.

[Investigation vesicle cycle in nerve formations in somatic muscle of the earthworm Lumbricus terrestris].

Luminous spots with a diameter of 1-2 microm, which are clusters of "synaptic buds", were revealed in the muscular wall of the earthworm using endocytotic fluorescent dyes FM1-43, FM2-10 and FM4-64. Application of the membrane probe Dil that is capable of being subjected to anterograde axonal transport to abdominal ganglia of the nervous chain, and subsequent (in a day) staining of nerve formations by endocytotic dye FM4-64 showed complete imposition of the emission data of the dyes that fluoresce in different parts of the spectrum. Using fluorescent marker DiBAC4(3) showed an increased emission of neural elements with increasing concentration of K+ in the extracellular environment. Application of FM2-10 showed that the higher concentration of K+ in solution, and hence the depolarization of the nerve cells, the faster the upload of the dye, and vice versa, the process slowed down in the absence of K+ in the medium. The seizure and removal of FM2-10 were blocked in calcium-free solutions in the presence of Ca2+ buffers, BABTA or BABTA-AM, but only after a preliminary 40 min incubation. The processes of exo- and endocytosis occurred in the clusters of synaptic "buds" and were preserved in conditions of "rest". This vesicle cycle depends on membrane potential and concentration of K+ and Ca2+, and, it is very likely that the calcium sensor operates on the principle "all or nothing".

Parameter mismatches and oscillation death in coupled oscillators.

We use a set of qualitatively different models of coupled oscillators (genetic, membrane, Ca-metabolism, and chemical oscillators) to study dynamical regimes in the presence of small detuning. In particular, we focus on a distinct oscillation quenching mechanism, the oscillation death phenomenon. Using bifurcation analysis in general, we demonstrate that under strong coupling via slow variable detuning can eliminate standard oscillatory solutions from a large region of the parameter space, establishing the dominance of oscillation death. We argue furthermore that the oscillation death dominance effect provides a reliable dynamical control mechanism in the general case of N coupled oscillators.

Cooperative differentiation through clustering in multicellular populations.

The coordinated development of multicellular organisms is driven by intercellular communication. Differentiation into diverse cell types is usually associated with the existence of distinct attractors of gene regulatory networks, but how these attractors emerge from cell-cell coupling is still an open question. In order to understand and characterize the mechanisms through which coexisting attractors arise in multicellular systems, here we systematically investigate the dynamical behavior of a population of synthetic genetic oscillators coupled by chemical means. Using bifurcation analysis and numerical simulations, we identify various attractors and attempt to deduce from these findings a way to predict the organized collective behavior of growing populations. Our results show that dynamical clustering is a generic property of multicellular systems. We argue that such clustering might provide a basis for functional differentiation and variability in biological systems.

[New derivatives of azobenzene for the directed modification of proteins].

Derivatives of azobenzene which contained a maleimide group in one of the benzene rings (for binding to a protein cysteine residue) and maleimide, hydroxyl, or carboxyl substitutes in another benzene ring were synthesized. The reactivity of these compounds towards a cysteine residue of a protein and their optical properties in a free state and after their attachment to the mutant forms of the SsoII restriction endonuclease were studied.

Resting membrane potential and Na+,K+-ATPase of rat fast and slow muscles during modeling of hypogravity.

Antiorthostatic hindlimb suspension (unloading) decreased the resting membrane potential (RMP) of skeletal muscle fibers in fast extensor digitorum longus (EDL) and slow soleus (SOL) muscle of the rat by about 10% within 7 days and more. Inactivation of the membrane Na+,K+-pump by ouabain brought about similar depolarization as unloading. The increased sodium permeability of the membrane was excluded as the major cause of this depolarization by experiments in which TRIS was substituted for Na+ in the medium. On the other hand, the decrease in the electrogenic participation of the Na+,K+-pump is apparently one of the causes of RMP decrease during hypogravity, in EDL muscle in particular.

Ionic selectivity of chloride ion symport in mechanisms controlling resting potential and osmotic homeostasis in earthworm somatic muscle cells.

Replacement of Cl(-) for Br(-) in bathing solution did not reduce resting potential and had no effect on modulation of transmembrane potential in hyper- and hypoosmotic solutions. Under these conditions, baclofen, an agonist of GABAergic B-type receptors, failed to activate Na(+)/K(+)-pump in earthworm somatic muscle cells. It was hypothesized that the contribution of Cl(-) symport to osmotic homeostasis is not highly selective in respect to replacement of Cl(-) to Br(-) ions, whereas in case of activation of electrogenic ion pumps, this replacement is equivalent to removal of Cl(-) ions from the bathing solution.