Supervised classification for gene network reconstruction.

One of the central problems of functional genomics is revealing gene expression networks - the relationships between genes that reflect observations of how the expression level of each gene affects those of others. Microarray data are currently a major source of information about the interplay of biochemical network participants in living cells. Various mathematical techniques, such as differential equations, Bayesian and Boolean models and several statistical methods, have been applied to expression data in attempts to extract the underlying knowledge. Unsupervised clustering methods are often considered as the necessary first step in visualization and analysis of the expression data. As for supervised classification, the problem mainly addressed so far has been how to find discriminative genes separating various samples or experimental conditions. Numerous methods have been applied to identify genes that help to predict treatment outcome or to confirm a diagnosis, as well as to identify primary elements of gene regulatory circuits. However, less attention has been devoted to using supervised learning to uncover relationships between genes and/or their products. To start filling this gap a machine-learning approach for gene networks reconstruction is described here. This approach is based on building classifiers--functions, which determine the state of a gene's transcription machinery through expression levels of other genes. The method can be applied to various cases where relationships between gene expression levels could be expected.

Basic properties of populations generated in the frame of one-parameter discrete model of genetic diversity.

Previously, when discussing the properties of one parameter discrete model of genetic diversity (M.Yu. Shchelkanov et al, J. Biomol. Struct. Dyn. 15, 887-894 (1998)), we took into account Hamming distance distribution only between precursor and arbitrary descendant sequences. However, really there are sets of sequence populations produced during amplification process. In the presented work we have investigated Hamming distance distributions between sequences from different descendant sets produced in the frame of one parameter discrete model. Two basic descendant generation operators (so called amplifiers) are introduced: 1) the last generation amplifier, L, which produces descendants with precursor elimination; 2) all generations amplifier, G, which produces descendants without precursor elimination. Generalization of one-parameter discrete model for the case when precursor sequences do not coincide are carried out. Using this generalization we investigate the distribution of Hamming distances between L- and G-generated sequences. Basic properties of L and G operators, L/G-choice alternative problem have been discussed. Obtained results have common theoretical significance, but they are more suitable for high level genetic diversity process (for example, HIV diversity).

Stochastic properties of one-parameter discrete model of genetic diversity in the unique random parameter case.

Stochastic properties of previously introduced one parameter discrete model of genetic diversity (M. Yu. Shchelkanov et al, J. Biomol. Struct. Dyn. 15, 887-894 (1998)) are investigated. Two approaches are compared: (A) when the on-step substitution number and/or the number of substitution steps are random variables; (B) referred parameters are replaced by mathematical expectations of the respective variables. It has been demonstrated, that estimations of sequence measure based on the number of replication steps are more under the assumption of case (A) as compared with (B). Thus, real biological situation relating to the case (A) could additionally promote the increasing of distinctions between different taxons (e.g. HIV, etc.). Peculiarities of one-parameter discrete model of genetic diversity during calculation of the distinctions between symbol (e.g. nucleotide) sequence sets are also discussed.

Dependencies of substitution steps number on Hamming distance are identical for one-parameter discrete models of both direct and parallel genetic diversity.

With the help of previously introduced enumeration procedure (M.Yu. Shchelkanov, A.N. Yudin, A.V Antonov, N.S. Starikov, A.A. Vedenov, E.V. Karamov, J. Biomol. Struct. Dyn. 15, 217-229 (1997)) and probability distribution function for the enumeration after some substitution steps (M.Yu. Shchelkanov, L.A. Soinov, V.V. Zalunin, D.A. Gumennyi, A.N. Yudin, A.A. Natan, V.B. Kireev, E.V. Karamov, J. Biomol. Struct. Dyn. 15, N 4, (1998)) we have demonstrated that dependencies of replication acts number on Hamming distance are identical for one-parameter discrete models of both direct and parallel genetic diversity.

One-parameter discrete model of the genetic diversity.

One-parameter discrete model estimating genetic distance between precursor and descendant nucleotide sequences after several steps of substitution acts is developed. This model based on the previously introduced symbol sequences enumeration procedure (M.Y. Shchelkanov, A.N. Yudin, A.V. Antonov, N.S. Starikov, A.A. Vedenov, E.V. Karamov, J. Biomol. Struct. Dyn. 15, 231-241 (1997)) differs from Jukes-Cantor and Kimura models by the absence of the assumptions usual for continuous Markov's processes. Formula obtained with the help of our model are more preferable since they take into account multiple repetition substitution ability and they are correct in the entire admissible range of parameters.

Variability analysis of HIV-1 gp120 V3 region: II. Hierarchy of taxons.

In the previous work (M. Yu. Shchelkanov, A. N. Yudin, A. V. Antonov, N. S. Starikov, A. A. Vedenov, E. V. Karamov, J. Biomol. Struct. Dyn. 15, 217-229 (1997)) we have introduced the amino acid distribution function within HIV-1 taxons and Hamming-transformed Euclidean measures between their characteristics: consensus, subconsensus and sample mean. In this work the referred characteristics are used for hierarchical classification of amino acid sequences of gp120 V3 region belonging to different HIV-1 taxons. A comparative analysis of the results produced by various classification methods is carried out. Multidimensional scaling of distance matrix for the specified characteristics is used to visualize the pattern of HIV-1 variability.