Stability of the genetic code and optimal parameters of amino acids

The standard genetic code is known to be much more efficient in minimizing adverse effects of misreading errors and one-point mutations in comparison with a random code having the same structure, i.e. the same number of codons coding for each particular amino acid. We study the inverse problem, how the code structure affects the optimal physico-chemical parameters of amino acids ensuring the highest stability of the genetic code. It is shown that the choice of two or more amino acids with given properties determines unambiguously all the others. In this sense the code structure determines strictly the optimal parameters of amino acids. In the code with the structure of the standard genetic code the resulting values for hydrophobicity obtained in the scheme leave one out and in the scheme with fixed maximum and minimum parameters correlate significantly with the natural scale. This indicates the co-evolution of the genetic code and physico-chemical properties of amino acids.Comment: 9 pages, 3 figure

Genome packaging within icosahedral capsids and large-scale segmentation in viral genomic sequences

The assembly and maturation of viruses with icosahedral capsids must be coordinated with icosahedral symmetry. The icosahedral symmetry imposes also the restrictions on the cooperative specific interactions between genomic RNA/DNA and coat proteins that should be reflected in quasi-regular segmentation of viral genomic sequences. Combining discrete direct and double Fourier transforms, we studied the quasi-regular large-scale segmentation in genomic sequences of different ssRNA, ssDNA, and dsDNA viruses. The particular representatives included satellite tobacco mosaic virus and the strains of satellite tobacco necrosis virus, STNV-C, STNV-1, STNV-2, Escherichia phages MS2, phiX174, alpha3, and HK97, and Simian virus 40. In all their genomes, we found the significant quasi-regular segmentation of genomic sequences related to the virion assembly and the genome packaging within icosahedral capsid. We also found good correspondence between our results and available cryo-electron microscopy data on capsid structures and genome packaging in these viruses. Fourier analysis of genomic sequences provides the additional insight into mechanisms of hierarchical genome packaging and may be used for verification of the concepts of 3-fold or 5-fold intermediates in virion assembly. The results of sequence analysis should be taken into account at the choice of models and data interpretation. They also may be helpful for the development of antiviral drugs.Comment: 55 pages, 14 figure

Statistics of genome architecture

The main statistical distributions applicable to the analysis of genome architecture and genome tracks are briefly discussed and critically assessed. Although the observed features in distributions of element lengths can be equally well fitted by the different statistical approximations, the interpretation of observed regularities may strongly depend on the chosen scheme. We discuss the possible evolution scenarios and describe the main characteristics obtained with different distributions. The expression for the assessment of levels in hierarchical chromatin folding is derived and the quantitative measure of genome architecture inhomogeneity is suggested. This theory provides the ground for the regular statistical study of genome architecture and genome tracks.Comment: 25 pages, 8 figures, 1 tabl

Three-dimensional Modeling of the Matter Flow Structure in Semidetached Binary Systems

Results of numerical simulations of matter flows in a semidetached binary system similar to the low-mass X-ray binary X1822--371 are presented. Three-dimensional modeling of the mass transfer gas dynamics makes it possible to investigate gas streams in the system and to study the influence of a common envelope. The presence of the common envelope leads to the absence of shock interaction between the stream of matter flowing from the inner Lagrange point and the gas in the accretion disk. The stream is deflected by the gas in the common envelope and approaches the disk tangentially, so that it does not cause any shock perturbation ("hot spot") on the disk. At the same time, the interaction of the stream with the common envelope leads to the formation of an extended shock wave along the edge of the stream. The observational manifestation of this shock is estimated to be equivalent to that of a hot spot in the disk. The calculated accretion disk parameters are presented.Comment: 9 pages, LaTeX, 6 EPS figures, using AAS2PP4 style (included

Driven-disk model for binaries with precessing donor star. Three-dimensional simulations

We present the results of three-dimensional numerical simulations of mass transfer in semi-detached binary with a donor star whose rotation vector precesses around the orbital rotation axis of the binary in the observer's coordinate frame. The calculations support our previous model of flow without a `hot spot'. Characteristic features of the flow in this model, such as the formation of an circumbinary envelope, the absence of a `hot spot' at the edge of the accretion disk, and the formation of a shock wave along the edge of the stream, are also present in the solution for a binary with precessing donor star. The parameters of accretion disk and of the structure of the near-disk regions recur with the precessional period of the rotation axis of donor star.Comment: LaTeX, 10 page

Synthetic Doppler maps of gaseous flows in semidetached binaries based on the results of 3D gas dynamical simulations

We present synthetic Doppler maps of gaseous flows in semidetached binaries based on the results of 3D gas dynamical simulations. Using of gas dynamical calculations alongside with Doppler tomography technique permits to identify main features of the flow on the Doppler maps without solution of ill-posed inverse problem. Comparison of synthetic tomograms with observations makes possible both to refine the gas dynamical model and to interpret the observational data.Comment: To be published in Proceedings of International Workshop "Hot Points in Astrophysics", Dubna, Russia, August 22-26, 200

The Influence of Parameters on the Flow Structure in Semidetached Binary Systems: 3D Numerical Simulation

The basic parameters determining the flow pattern for a nonviscous, non-heat-conducting gas in a semidetached binary system without a magnetic field are identified. Three-dimensional gas-dynamical modeling of the mass transfer enables investigation of the influence of these parameters on the structure of gas flows. The parameter on which the flow pattern depends most strongly is the adiabatic index $\gamma$. The effect of other parameters is small, and only leads to unimportant quantitative changes in the solutions obtained. The main properties of flows typical of semidetached binaries without magnetic fields are summarized.Comment: 16 pages, LaTeX, 8 EPS figures, using AAS2PP4 style, accepted by Astron. Report

Detection of large-scale noisy multi-periodic patterns with discrete double Fourier transform

In many processes, the variations in underlying characteristics can be approximated by noisy multi-periodic patterns. If large-scale patterns are superimposed by a noise with long-range correlations, the detection of multi-periodic patterns becomes especially challenging. To solve this problem, we developed a discrete double Fourier transform (DDFT). DDFT is based on the equidistance property of harmonics generated by multi-periodic patterns in the discrete Fourier transform (DFT) spectra. As the large-scale patterns generate long enough equidistant series, they can be detected by the iteration of the primary DFT. DDFT is defined as Fourier transform of intensity spectral harmonics or of their functions. It comprises widely used cepstrum transform as a particular case. We present also the relevant analytical criteria for the assessment of statistical significance of peak harmonics in DDFT spectra in the presence of noise. DDFT technique was tested by extensive numerical simulations. The practical applications of DDFT technique are illustrated by the analysis of variations in solar wind speed related to solar rotation and by the study of large-scale multi-periodic patterns in DNA sequences. The latter application can be considered as generic example for the general spectral analysis of symbolic sequences. The results are compared with those obtained by the cepstrum transform. The mutual combination of DFT and DDFT provides an efficient technique to search for noisy large-scale multi-periodic patterns.Comment: 45 pages, 15 figure

Large-scale chromosome folding versus genomic DNA sequences: A discrete double Fourier transform technique

Using state-of-the-art techniques combining imaging methods and high-throughput genomic mapping tools leaded to the significant progress in detailing chromosome architecture of various organisms. However, a gap still remains between the rapidly growing structural data on the chromosome folding and the large-scale genome organization. Could a part of information on the chromosome folding be obtained directly from underlying genomic DNA sequences abundantly stored in the databanks? To answer this question, we developed an original discrete double Fourier transform (DDFT). DDFT serves for the detection of large-scale genome regularities associated with domains/units at the different levels of hierarchical chromosome folding. The method is versatile and can be applied to both genomic DNA sequences and corresponding physico-chemical parameters such as base-pairing free energy. The latter characteristic is closely related to the replication and transcription and can also be used for the assessment of temperature or supercoiling effects on the chromosome folding. We tested the method on the genome of Escherichia coli K-12 and found good correspondence with the annotated domains/units established experimentally. As a brief illustration of further abilities of DDFT, the study of large-scale genome organization for bacteriophage PHIX174 and bacterium Caulobacter crescentus was also added. The combined experimental, modeling, and bioinformatic DDFT analysis should yield more complete knowledge on the chromosome architecture and genome organization.Comment: 37 pages, 9 figure

Three-dimensional modeling of mass transfer in close binary systems with non-synchronous rotation

We present the results of three-dimensional numerical simulations of mass transfer in semi-detached binary systems in which the mass-losing star is rotating. The cases of aligned and misaligned non-synchronous rotation of the donor star are considered; the resulting flow patterns are compared to the synchronous case. The main properties of the flow, such as the formation of an circumbinary envelope, the absence of a "hot spot" on the edge of the accretion disk, and the formation of a shock wave along the flow edge, are qualitatively similar to those obtained earlier. For the case of misaligned, non-synchronous rotation, the behavior of the disk and surrounding matter in established flow regime reflects changes in the boundary conditions at the surface of the donor star; in other words, a "driven disk" model is realized in the calculations.Comment: LaTeX, 22 pages, accepted for publication in Astronomy Report