Non-coding RNAs and complex distributed genetic networks

In eukaryotic cells, the mRNA-protein interplay can be dramatically influenced by non-coding RNAs (ncRNAs). Although this new paradigm is now widely accepted, an understanding of the effect of ncRNAs on complex genetic networks is lacking. To clarify what may happen in this case, we propose a mean-field kinetic model describing the influence of ncRNA on a complex genetic network with a distributed architecture including mutual protein-mediated regulation of many genes transcribed into mRNAs. ncRNA is considered to associate with mRNAs and inhibit their translation and/or facilitate degradation. Our results are indicative of the richness of the kinetics under consideration. The main complex features are found to be bistability and oscillations. One could expect to find kinetic chaos as well. The latter feature has however not been observed in our calculations. In addition, we illustrate the difference in the regulation of distributed networks by mRNA and ncRNA.     

Hierarchical genetic networks and noncoding RNAs

In eukaryotic cells, many genes are transcribed into noncoding RNAs. Such RNAs may associate with mRNAs and inhibit their translation and facilitate degradation. To clarify what may happen in this case, we propose a kinetic model describing the effect of noncoding RNAs on a mRNA-protein network with the hierarchical three-layer architecture. For positive regulation of the layers, our model predicts either bistability with a fairly narrow hysteresis loop or a unique steady state. For negative or mixed regulation, the steady state is found to be unique.     

Interplay of noncoding RNAs,mRNAs, and proteins during the growth of eukaryotic cells

Numerous biological functions of noncoding RNAs (ncRNAs) in eukaryotic cells are based primarily on their ability to pair with target mRNAs and then either to prevent translation or to result in rapid degradation of the mRNA-ncRNA complex. Using a general model describing this scenario, we show that ncRNAs may help to maintain constant mRNA and protein concentrations during the growth of cells. The possibility of observation of this effect on the global scale is briefly discussed.     

ncRNA-mediated bistability in the synthesis of hundreds of distinct mRNAs and proteins

The kinetics of gene expression can be bistable due to the feedback between the mRNA and protein formation. In eukaryotic cells, the interplay between mRNAs and proteins can be influenced by non-coding RNAs. Some of these RNAs, e.g., microRNAs, may target hundreds of distinct mRNAs. The model presented here shows how a non-coding RNA can be used as a mediator in order to involve numerous mRNAs and proteins into a bistable network.     

Switches in gene expression including microRNA and a large number of distinct mRNAs

In eukaryotic cells, the kinetics of gene expression depends on the interplay of messenger RNAs (mRNAs), proteins, and nonprotein coding RNAs, or, more specifically, microRNAs. Some microRNAs may target hundreds of mRNAs. To describe this case, the author proposes a kinetic model implying that the microRNA synthesis is suppressed by the protein produced via the translation of one of the target mRNAs. With physically reasonable model parameters, the model predicts bistability or, in other words, switches in the expression of hundreds of genes. The text was submitted by the author in English.     

Oscillatory dynamics in a simple gene regulatory network mediated by small RNAs

More and more experiments show that small RNAs regulate gene expression by repressing translation of messenger RNAs (mRNAs) or degrading mRNAs. In this paper, we incorporate the small RNAs into a simple gene regulatory network and investigate its dynamical behaviors. In addition, we also derive the theoretical results of globally asymptotic stability and provide the sufficient conditions for the oscillation of the simple gene regulatory network, and further demonstrate that the amplitudes against the change of delay in the gene regulatory network are robust.     

Vertical seismic profiling on the sea shelf

Results of a numerical experiment on vertical seismic profiling of the sea bottom on the shelf are presented. The results are obtained by analyzing the acoustic fields in the shelf area with the use of both hydroacoustic and seismic bottom sources of radiation. The influence of both transmission depth and source type on the efficiency of seismic wave excitation in the bottom is investigated. The formation of the vertical wave hodographs and its dependence on the acoustic parameters and structure of the bottom in the oceanic shelf region is analyzed. A high sensitivity of the vertical wave hodographs to variations in the parameters of the bottom medium is revealed. For the layered bottom model, the possibility of estimating the positions of layer boundaries in depth and the velocities of waves within the layers is demonstrated.     

Simulation of radiative heating of snow and ice coating

Numerical simulation of thermal state was performed for semitransparent medium; the thermal state is formed under impact of incident radiation and convective heat transfer to the ambient medium. The model takes into account the heat transfer to the semi-infinite opaque substrate below the layer of semitransparent material. Computation was performed for governing parameters typical of snow and ice coating during winter period. Solving the radiative part of problem uses the modified average flux method. This method takes into account the dependence of optical properties on the wavelength of incident radiation, scattering, and reflective properties of the layer boundaries.     

A deep learning method for solving third-order nonlinear evolution equations

It has still been difficult to solve nonlinear evolution equations analytically. In this paper, we present a deep learning method for recovering the intrinsic nonlinear dynamics from spatiotemporal data directly. Specifically, the model uses a deep neural network constrained with given governing equations to try to learn all optimal parameters. In particular, numerical experiments on several third-order nonlinear evolution equations, including the Korteweg–de Vries (KdV) equation, modified KdV equation, KdV–Burgers equation and Sharma–Tasso–Olver equation, demonstrate that the presented method is able to uncover the solitons and their interaction behaviors fairly well.     

Boundary layer and scaling properties in turbulent thermal convection

Summary We describe an experiment which has been designed to measure both spatial and temporal features of turbulent thermal convection in a fluid layer heated from below. Specifically we have studied the dependence of the heat flowvs. the Rayleigh number, the thermal boundary layer profile, the temperature probability distribution function, the frequency and wave number power spectra. All the results have been compared with recent theories. The relevant scales of the problem, the Bolgiano and dissipative lengths, are also computed as a function of control parameters.     

CP violating asymmetry in stop decay into bottom and chargino

In the MSSM with complex parameters, loop corrections to the decay of a stop into a bottom quark and a chargino can lead to a CP violating decay rate asymmetry. We calculate this asymmetry at full one-loop level and perform a detailed numerical study, analyzing the dependence on the parameters and complex phases involved. If the stop can decay into a gluino, the self-energy and the vertex correction dominate due to the strong coupling. It is shown that the vertex contribution is always suppressed. We therefore give a simple approximate formula for the asymmetry. We account for the constraints on the parameters coming from several experimental limits. Asymmetries up to 25 percent are obtained. We also comment on the feasibility of measuring this asymmetry at the LHC.     

Dynamics and Mechanism of A Quorum Sensing Network Regulated by Small RNAs in Vibrio Harveyi

Bacterial quorum sensing (QS) has attracted much interests and it is an important process of cell communication. Recently, Bassler et al. studied the phenomena of QS regulated by small RNAs and the experimental data showed that small RNAs played important role in the QS of Vibrio harveyi and it can permit the fine-tuningof gene regulation and maintenance of homeostasis. According to Michaelis-Menten kinetics and mass action law in this paper, we construct a mathematical model to investigate the mechanism induced QS by coexist of small RNA and signal molecular (AI) and show that there are periodic oscillation when the time delay and Hill coefficient exceed a critical value and the periodic oscillation produces the change of concentration and induces QS. These results are fit to the experimental results. In the meanwhile, we also get some theoretical value of Hopf Bifurcation on time deday. In addition, we also find this network is robust against noise.     

Method and results of estimating acoustic characteristics of bottom-sediment upper layers in the shelf region using seismic exploration instruments

The potential of seismic exploration instruments for estimating the surface layers of soil in the towing zone of an extended multielement array is investigated. In contrast to the well-known method of common depth point, in which the main estimated parameters are the transit times of waves reflected from deep layers of the sea bottom, two-dimensional spectral analysis is used to measure the longitudinal wavenumbers of the modes forming an infrasonic field in the water layer. The measured longitudinal wavenumbers of modes serve initial data for estimating the acoustic characteristics of the upper layers of bottom sediments directly in the towing zone of pulse emitter and extended multielement array. It is concluded that the use of data on the parameters of upper soil layers in seismic exploration should increase the accuracy of contouring oil and gas condensate fields.