Andrei Zinovyev Home Page

Andrei Zinovyev

HOME PAGE

Be realistic, demand the impossible!

CV - BOOKS - PUBLICATIONS - PROJECTS - PRESENTATIONS - LINKS - CONTACT INFORMATION - PERSONAL

PhD in Computer Science:
My formal speciality (as written in my Russian state PhD diploma): "Mathematical and software tools for computers, computational complexes and computer networks".
My university diploma was in theoretical physics (cosmology).
Since 2000 I am working in Bioinformatics and Systems Biology.

Current occupation:
Researcher at the Bioinformatics, biostatistics, epidemiology and computational systems biology of cancer unit of Institut Curie, Paris
Coordinator of Computational Systems Biology of Cancer team

was involved in the project Functional Genomics,
past member of Systems Epigenomics Group team

Research interests:

Systems biology in cancer studies
Bioinformatics: sequence analysis
Visualization of multidimensional and complex data
Model and dimension reduction in complex systems

My citations in Google Scholar

See the wordcloud of my publications in PUBMED:

The wordcloud of this page:

Books and selected book chapters:

Computational Systems Biology of Cancer (Amazon link)
by Emmanuel Barillot, Laurence Calzone, Philippe Hupe, Jean-Philippe Vert and Andrei Zinovyev
CRC Press Inc, Chapman & Hall/CRC Mathematical & Computational Biology, 2012. p. 452
"This is the first book specifically focused on computational systems biology of cancer with coherent and proper vision on how to tackle this formidable challenge..." (c) Hiroaki Kitano

The book is accompanied by a web-site containing additional materias

Mathematical modeling of microRNA-mediated mechanisms of translation repression (arXiv)
by Zinovyev A., Morozova N., Gorban A. N., Harel-Belan A.
To appear in MicroRNA cancer regulation: Advanced bioinformatics and systems biology concepts (ed. by Schmitz U., Wolkenhauer O., Vera J.), Springer, 2013.
We describe three simple mathematical models of mRNA translation in the presence of miRNA that can be used as tools in interpreting the experimental data on the dynamics of protein synthesis. The most complex model developed by us includes all known mechanisms of miRNA action.
How cell decides between life and death: mathematical modeling of epigenetic landscapes of cellular fates (PDF)
by Zinovyev A, Calzone L, Tournier L, Fourquet S and Barillot E.
In Patterns formation in Morphogenesis (ed. by Capasso, V.; Gromov, M.; Harel-Bellan, A.; Morozova, N.; Pritchard, L.), Series: Springer Proceedings in Mathematics, Vol. 15. 2012. Springer. 350 p.
We present a mathematical model of cell fate decision between survival, necrosis and apoptosis as a concrete implementation of the Waddington’s methaphor of epigenetic landscape determining cellular phenotype.
Data visualization in political and social sciences (arXiv)
Article in International Encyclopedia of Political Science (eds. Badie, B., Berg-Schlosser, D., Morlino, L. A.), SAGE Publications, 2011.
Short review of principles and applications of data visualization in political and social sciences
Principal Graphs and Manifolds (Alexander Gorban, Andrei Zinovyev) (PDF)
Book chapter in "Handbook of Research on Machine Learning Applications and Trends: Algorithms, Methods and Techniques" (eds. Olivas E.S., Guererro J.D.M., Sober M.M., Benedito J.R.M., Lopes A.J.S.). Information Science Reference, September 4, 2009.
This chapter gives a brief practical introduction into the methods of construction of general principal objects (i.e., objects embedded in the ‘middle’ of the multidimensional data set). As a basis, the unifying framework of mean squared distance approximation of finite datasets is selected. Principal graphs and manifolds are constructed as generalisations of principal components and k-means principal points. For this purpose, the family of expectation/maximisation algorithms with nearest generalisations is presented. Construction of principal graphs with controlled complexity is based on the graph grammar approach

Principal Manifolds for Data Visualization and Dimension Reduction (Alexander Gorban, Balázs Kégl, Donald Wunch, Andrei Zinovyev (eds.)) (Amazon link, whole book text)
Lecture Notes in Computational Science and Engineering, Vol. 58 Springer, November 2007, 340 pages
In 1901, Karl Pearson invented Principal Component Analysis (PCA). Since then, PCA serves as a prototype for many other tools of data analysis, visualization and dimension reduction: Independent Component Analysis (ICA), Multidimensional Scaling (MDS), Nonlinear PCA (NLPCA), Self Organizing Maps (SOM), etc. The book starts with the quote of the classical Pearson definition of PCA and includes reviews of various methods: NLPCA, ICA, MDS, embedding and clustering algorithms, principal manifolds and SOM. New approaches to NLPCA, principal manifolds, branching principal components and topology preserving mappings are described as well. Presentation of algorithms is supplemented by case studies, from engineering to astronomy, but mostly of biological data: analysis of microarray and metabolite data. The volume ends with a tutorial "PCA and K-means decipher genome". The book is meant to be useful for practitioners in applied data analysis in life sciences, engineering, physics and chemistry; it will also be valuable to PhD students and researchers in computer sciences, applied mathematics and statistics.

This book is accompanied by highly recommended site pca.narod.ru (in Russian)

Together with editing, in this book I contributed to writing three chapters:

Elastic Maps and Nets for Approximating Principal Manifolds and Their Application to Microarray Data Visualization (with Alexander Gorban) (PDF)
Principal manifolds are defined as lines or surfaces passing through "the middle" of data distribution. Linear principal manifolds (Principal Components Analysis) are routinely used for dimension reduction, noise filtering and data visualization. Recently, methods for constructing non-linear principal manifolds were proposed, including our elastic maps approach which is based on a physical analogy with elastic membranes. We have developed a general geometric framework for constructing "principal objects" of various dimensions and topologies with the simplest quadratic form of the smoothness penalty which allows very effective parallel implementations. Our approach is implemented in three programming languages (C++, Java and Delphi) with two graphical user interfaces (VidaExpert and ViMiDa applications). In this paper we overview the method of elastic maps and present in detail one of its major applications: the visualization of microarray data in bioinformatics. We show that the method of elastic maps outperforms linear PCA in terms of data approximation, representation of between-point distance structure, preservation of local point neighborhood and representing point classes in low-dimensional spaces.
Beyond The Concept of Manifolds: Principal Trees, Metro Maps, and Elastic Cubic Complexes (with Alexander Gorban and Neil Sumner) (PDF)
Multidimensional data distributions can have complex topologies and variable local dimensions. To approximate complex data, we propose a new type of low-dimensional "principal object": a principal cubic complex. This complex is a generalization of linear and non-linear principal manifolds and includes them as a particular case. To construct such an object, we combine a method of topological grammars with the minimization of an elastic energy defined for its embedment into multidimensional data space. The whole complex is presented as a system of nodes and springs and as a product of one-dimensional continua (represented by graphs), and the grammars describe how these continua transform during the process of optimal complex construction.
The simplest case of a topological grammar ("add a node", "bisect an edge") is equivalent to the construction of "principal trees", an object useful in many practical applications. We demonstrate how it can be applied to the analysis of bacterial genomes and for visualization of cDNA microarray data using the "metro map" representation.
PCA and K-Means Decipher Genome (with Alexander Gorban) (PDF)
In this paper, we aim to give a tutorial for undergraduate students studying statistical methods and/or bioinformatics. The students will learn how data visualization can help in genomic sequence analysis. Students start with a fragment of genetic text of a bacterial genome and analyze its structure. By means of principal component analysis they "discover" that the information in the genome is encoded by non-overlapping triplets. Next, they learn how to find gene positions. This exercise on PCA and K-Means clustering enables active study of the basic bioinformatics notions. The Appendix contains program listings that go along with this exersice.

Visualization of Multidimensional Data (In Russian) ( PDF )
by Andrei Zinovyev
Krasnoyarsk Technical State University Press, 2000.
Method of multidimensional data visualization: theory, applications and software. This is a literature version of my PhD thesis, written 1 year before the thesis.

Articles in Wikipedia to which I have contributed

Selected papers and their abstracts:

Synthetic lethality between gene defects affecting a single non-essential molecular pathway with reversible steps (with Inna Kuperstein, Emmanuel Barillot and Wolf-Dietrich Heyer) (Link)
PLoS Comput Biol, April 2013
Recent genome-wide analyses in yeast identified a significant number of within-pathway negative genetic interactions. The molecular mechanisms leading to within-pathway SL are not fully understood. Here, we propose a novel mechanism leading to within-pathway SL involving two genes functioning in a single non-essential pathway. This type of SL termed within-reversible-pathway SL involves reversible pathway steps, catalyzed by different enzymes in the forward and backward directions, and kinetic trapping of a potentially toxic intermediate. Experimental data with recombinational DNA repair genes validate the concept. Mathematical modeling recapitulates the possibility of kinetic trapping and revealed the potential contributions of synthetic, dosage-lethal interactions in such a genetic system as well as the possibility of within-pathway positive masking interactions. Analysis of yeast gene interaction and pathway data suggests broad applicability of this novel concept.
Kinetic signatures of microRNA modes of action (with Nadya Morozova, Nora Nonne, Linda-Louise Pritchard, Alexander N. Gorban, Annick Harel-Bellan) (PDF)
RNA, September 2012
We have created a mathematical model that combines nine known mechanisms of miRNA action and estimated the model parameters from the literature. Based on the mathematical modeling, we have developed a computational tool for discriminating among different possible individual mechanisms of miRNA action based on translation kinetics data that can be experimentally measured (kinetic signatures).
Mathematical Modelling of Cell-Fate Decision in Response to Death Receptor Engagement (with Laurence Calzone, Laurent Tournier, Simon Fourquet, Denis Thieffry, Boris Zhivotovsky, Emmanuel Barillot) (Link)
PLoS Computational Biology, March 2010
Cytokines such as TNF and FASL can trigger death or survival depending on cell lines and cellular conditions. The mechanistic details of how a cell chooses among these cell fates are still unclear. The understanding of these processes is important since they are altered in many diseases, including cancer and AIDS. Using a discrete modelling formalism, we present a mathematical model of cell fate decision recapitulating and integrating the most consistent facts extracted from the literature. This model provides a generic high-level view of the interplays between NF?B pro-survival pathway, RIP1-dependent necrosis, and the apoptosis pathway in response to death receptor-mediated signals. Wild type simulations demonstrate robust segregation of cellular responses to receptor engagement. Model simulations recapitulate documented phenotypes of protein knockdowns and enable the prediction of the effects of novel knockdowns. In silico experiments simulate the outcomes following ligand removal at different stages, and suggest experimental approaches to further validate and specialise the model for particular cell types. We also propose a reduced conceptual model implementing the logic of the decision process. This analysis gives specific predictions regarding cross-talks between the three pathways, as well as the transient role of RIP1 protein in necrosis, and confirms the phenotypes of novel perturbations. Our wild type and mutant simulations provide novel insights to restore apoptosis in defective cells. The model analysis expands our understanding of how cell fate decision is made. Moreover, our current model can be used to assess contradictory or controversial data from the literature. Ultimately, it constitutes a valuable reasoning tool to delineate novel experiments.
Principal manifolds and graphs in practice: from molecular biology to dynamical systems (with Alexander Gorban) (PDF)
International Journal of Neural Systems, March 2010
We present several applications of non-linear data modeling, using principal manifolds and principal graphs constructed using the metaphor of elasticity (elastic principal graph approach). These approaches are generalizations of the Kohonen’s self-organizing maps, a class of artificial neural networks. On several examples we show advantages of using non-linear objects for data approximation in comparison to the linear ones. We propose four numerical criteria for comparing linear and non-linear mappings of datasets into the spaces of lower dimension. The examples are taken from comparative political science, from analysis of high-throughput data in molecular biology, from analysis of dynamical systems.
Dynamical modeling of microRNA action on the protein translation process (with Nadya Morozova, Nora Nonne, Emmanuel Barillot, Annick Harel-Bellan and Alexander Gorban) (Link)
BMC Systems Biology, January 2010
Protein translation is a multistep process which can be represented as a cascade of biochemical reactions (initiation, ribosome assembly, elongation, etc.), the rate of which can be regulated by small non-coding microRNAs through multiple mechanisms. It remains unclear what mechanisms of microRNA action are the most dominant: moreover, many experimental reports deliver controversal messages on what is the concrete mechanism actually observed in the experiment. Nissan and Parker have recently demonstrated that it might be impossible to distinguish alternative biological hypotheses using the steady state data on the rate of protein synthesis. For their analysis they used two simple kinetic models of protein translation. In contrary to the study by Nissan and Parker, we show that dynamical data allow to discriminate some of the mechanisms of microRNA action. We demonstrate this using the same models as developed by Nissan and Parker for the sake of comparison but the methods developed (asymptotology of biochemical networks) can be used for other models. We formulate a hypothesis that the effect of microRNA action is measurable and observable only if it affects the dominant system (generalization of the limiting step notion for complex networks) of the protein translation machinery. The dominant system can vary in different experimental conditions that can partially explain the existing controversy of some of the experimental data. Our analysis of the transient protein translation dynamics shows that it gives enough information to verify or reject a hypothesis about a particular molecular mechanism of microRNA action on protein translation. For multiscale systems only that action of microRNA is distinguishable which affects the parameters of dominant system (critical parameters), or changes the dominant system itself. Dominant systems generalize and further develop the old and very popular idea of limiting step. Algorithms for identifying dominant systems in multiscale kinetic models are straightforward but not trivial and depend only on the ordering of the model parameters but not on their concrete values. Asymptotic approach to kinetic models allows to put in order diverse experimental observations in complex situations when many alternative hypotheses co-exist.
Asymptotology of chemical reaction networks (with Alexander Gorban and Ovidiu Radulescu) (PDF)
Chemical Engineering Science, September 2009
The concept of the limiting step is extended to the asymptotology of multiscale reaction networks. Complete theory for linear networks with well separated reaction rate constants is developed. We present algorithms for explicit approximations of eigenvalues and eigenvectors of kinetic matrix. Accuracy of estimates is proven. Performance of the algorithms is demonstrated on simple examples. Application of algorithms to nonlinear systems is discussed.
Robust simplifications of multiscale biochemical networks (with Ovidiu Radulescu, Alexander Gorban and Alain Lilienbaum) (Link)
BMC Systems Biology, October 2008
We propose a systematic treatment of model reduction of multiscale biochemical networks. First, we consider linear kinetic models, which appear as "pseudo-monomolecular" subsystems of multiscale nonlinear reaction networks. For such linear models, we propose a reduction algorithm which is based on a generalized theory of the limiting step that we have developed in before. Second, for non-linear systems we develop an algorithm based on dominant solutions of quasi-stationarity equations. For oscillating systems, quasi-stationarity and averaging are combined to eliminate time scales much faster and much slower than the period of the oscillations. In all cases, we obtain robust simplifications and also identify the critical parameters of the model. The methods are demonstrated for simple examples and for a more complex model of NF-kB pathway.
A comprehensive modular map of molecular interactions in RB/E2F pathway (with Laurence Calzone, Amelie Gelay, Francois Radvanyi, Emmanuel Barillot) (PDF)
Molecular Systems Biology, March 2008
We present a detailed and curated map of molecular interactions taking place in the regulation of the cell cycle by the retinoblastoma protein (RB/RB1). Deregulations and/or mutations in this pathway are observed in most human cancers. The map was created using Systems Biology Graphical Notation language with the help of CellDesigner 3.5 software and converted into BioPAX 2.0 pathway description format. In the current state the map contains 78 proteins, 176 genes, 99 protein complexes, 208 distinct chemical species and 165 chemical reactions. Overall, the map recapitulates biological facts from approximately 350 publications annotated in the diagram. The network contains more details about RB/E2F interaction network than existing large-scale pathway databases. Structural analysis of the interaction network revealed a modular organization of the network, which was used to elaborate a more summarized, higher-level representation of RB/E2F network. The simplification of complex networks opens the road for creating realistic computational models of this regulatory pathway.
BiNoM: a Cytoscape plugin for manipulating and analyzing biological networks (with Eric Viara, Laurence Calzone, Emmanuel Barillot) (PDF)
Bioinformatics, April 2008
BiNoM (Biological Network Manager) is a new bioinformatics software that significantly facilitates the usage and the analysis of biological networks in standard systems biology formats (SBML, SBGN, BioPAX). BiNoM implements a full-featured BioPAX editor and a method of 'interfaces' for accessing BioPAX content. BiNoM is able to work with huge BioPAX files such as whole pathway databases. In addition, BiNoM allows the analysis of networks created with CellDesigner software and their conversion into BioPAX format. BiNoM comes as a library and as a Cytoscape plugin which adds a rich set of operations to Cytoscape such as path and cycle analysis, clustering sub-networks, decomposition of network into modules, clipboard operations and others. Last version of BiNoM distributed under the LGPL licence together with documentation, source code and API are available at http://bioinfo.curie.fr/projects/binom
How much non-coding DNA do eukaryotes require? (with Sebastian Ahnert and Thomas Fink) (PDF)
Journal of Theoretical Biology, March 2008
Despite tremendous advances in the field of genomics, the amount and function of the large non-coding part of the genome in higher organisms remains poorly understood. Here we report an observation, made for 37 fully sequenced eukaryotic genomes, which indicates that eukaryotes require a certain minimum amount of non-coding DNA (ncDNA). This minimum increases quadratically with the amount of DNA located in exons. Based on a simple model of the growth of regulatory networks, we derive a theoretical prediction of the required quantity of ncDNA and find it to be in excellent agreement with the data. The amount of additional ncDNA (in basepairs) which eukaryotes require obeys NDEF = 1/2 (NC/NP) (NC-NP), where NC is the amount of exonic DNA, and NP is a constant of about 10 Mb. This value NDEF corresponds to a few percent of the genome in Homo sapiens and other mammals, and up to half the genome in simpler eukaryotes. Thus, our findings confirm that eukaryotic life depends on a substantial fraction of ncDNA and also make a prediction of the size of this fraction, which matches the data closely.
The Mystery of Two Straight Lines in Bacterial Genome Statistics (with Alexander Gorban) (PDF)
Bulletin of Mathematical Biology, October 2007
Abstract In special coordinates (codon position-specific nucleotide frequencies), bacterial genomes form two straight lines in 9-dimensional space: one line for eubacterial genomes, another for archaeal genomes. All the 348 distinct bacterial genomes available in Genbank in April 2007, belong to these lines with high accuracy. The main challenge now is to explain the observed high accuracy. The new phenomenon of complementary symmetry for codon position-specific nucleotide frequencies is observed. The results of analysis of several codon usage models are presented.We demonstrate that the mean-field approximation, which is also known as context-free, or complete independence model, or Segre variety, can serve as a reasonable approximation to the real codon usage. The first two principal components of codon usage correlate strongly with genomic G+C content and the optimal growth temperature, respectively. The variation of codon usage along the third component is related to the curvature of the mean-field approximation. First three eigenvalues in codon usage PCA explain 59.1%, 7.8% and 4.7% of variation. The eubacterial and archaeal genomes codon usage is clearly distributed along two third order curves with genomic G+C content as a parameter.
Classification of microarray data using gene networks (with Franck Rapaport, Marie Dutreix, Emmanuel Barillot and Jean-Philippe Vert) (Link)
BMC Bioinformatics, Fevrier 2007
Microarrays have become extremely useful for analysing genetic phenomena, but establishing a relation between microarray analysis results (typically a list of genes) and their biological significance is often difficult. Currently, the standard approach is to map a posteriori the results onto gene networks in order to elucidate the functions perturbed at the level of pathways. However, integrating a priori knowledge of the gene networks could help in the statistical analysis of gene expression data and in their biological interpretation. We propose a method to integrate a priori the knowledge of a gene network in the analysis of gene expression data. The approach is based on the spectral decomposition of gene expression profiles with respect to the eigenfunctions of the graph, resulting in an attenuation of the high-frequency components of the expression profiles with respect to the topology of the graph. We show how to derive unsupervised and supervised classification algorithms of expression profiles, resulting in classifiers with biological relevance. We illustrate the method with the analysis of a set of expression profiles from irradiated and non-irradiated yeast strains. Including a priori knowledge of a gene network for the analysis of gene expression data leads to good classification performance and improved interpretability of the results.
Topological grammars for data approximation (with Alexander Gorban and Neil Sumner) (PDF)
Applied Mathematics Letters, April 2007
A method of topological grammars is proposed for multidimensional data approximation. For data with complex topology we define a principal cubic complex of low dimension and given complexity that gives the best approximation for the dataset. This complex is a generalization of linear and non-linear principal manifolds and includes them as particular cases. The problem of optimal principal complex construction is transformed into a series of minimization problems for quadratic functionals. These quadratic functionals have a physically transparent interpretation in terms of elastic energy. For the energy computation, the whole complex is represented as a system of nodes and springs. Topologically, the principal complex is a product of onedimensional continuums (represented by graphs), and the grammars describe how these continuums transform during the process of optimal complex construction. This factorization of the whole process onto one-dimensional transformations using minimization of quadratic energy functionals allows us to construct efficient algorithms.
Codon usage trajectories and 7-cluster structure of 143 complete bacterial genomic sequences (with Alexander Gorban and Tatyana Popova) (PDF)
Physica A, May 2005
Three results are presented. First, we prove the existence of a universal 7-cluster structure in all 143 completely sequenced bacterial genomes available in Genbank in August 2004, and explained its properties. The 7-cluster structure is responsible for the main part of sequence heterogeneity in bacterial genomes. In this sense, our 7 clusters is the basic model of bacterial genome sequence. We demonstrated that there are four basic ''pure'' types of this model, observed in nature: ''parallel triangles'', ''perpendicular triangles'', degenerated case and the flower-like type. Second, we answered the question: how big are the position-specific information and the contribution connected with correlations between nucleotide. The accuracy of the mean-field (context-free) approximation is estimated for bacterial genomes. We show that codon usage of bacterial genomes is a multi-linear function of their genomic G+C-content with high accuracy (more precisely, by two similar functions, one for eubacterial genomes and the other one for archaea). Description of these two codon-usage trajectories is the third result. All 143 cluster animated 3D-scatters are collected in a database and is made available on our web-site: http://www.ihes.fr/~zinovyev/7clusters.
Elastic Principal Graphs and Manifolds and their Practical Applications (with Alexander Gorban) (PDF)
Computing, May 2005
Principal manifolds serve as useful tool for many practical applications. These manifolds are defined as lines or surfaces passing through "the middle" of data distribution. We propose an algorithm for fast construction of grid approximations of principal manifolds with given topology. It is based on analogy of principal manifold and elastic membrane. First advantage of this method is a form of the functional to be minimized which becomes quadratic at the step of the vertices position refinement. This makes the algorithm very effective, especially for parallel implementations. Another advantage is that the same algorithmic kernel is applied to construct principal manifolds of different dimensions and topologies. We demonstrate how flexibility of the approach allows numerous adaptive strategies like principal graph constructing, etc. The algorithm is implemented as a C++ package elmap and as a part of stand-alone data visualization tool VidaExpert, available on the web. We describe the approach and provide several examples of its application with speed performance characteristics.
Codon Bias Signatures, Organization of Microorganisms in Codon Space, and Lifestyle (with Alessandra Carbone and Francois Kepes) (PDF)
Mol.Biol.Evol., March 2005
New and simple numerical criteria based on a codon adaptation index are applied to the complete genomic sequences of 80 Eubacteria and 16 Archaea, to infer weak and strong genome tendencies toward content bias, translational bias, and strand bias. These criteria can be applied to all microbial genomes, even those for which little biological information is known, and a codon bias signature, that is the collection of strong biases displayed by a genome, can be automatically derived. A codon bias space, where genomes are identified by their preferred codons, is proposed as a novel formal framework to interpret genomic relationships. Principal component analysis confirms that although GC content has a dominant effect on codon bias space, thermophilic and mesophilic species can be identified and separated by codon preferences. Two more examples concerning lifestyle are studied with linear discriminant analysis: suitable separating functions characterized by sets of preferred codons are provided to discriminate: translationally biased (hyper)thermophiles from mesophiles, and organisms with different respiratory characteristics, aerobic, anaerobic, facultative aerobic and facultative anaerobic. These results suggest that codon bias space might reflect the geometry of a prokaryotic ''physiology space.'' Evolutionary perspectives are noted, numerical criteria and distances among organisms are validated on known cases, and various results and predictions are discussed both on methodological and biological grounds.
Four basic symmetry types in the universal 7-cluster structure of microbial genomic sequences (with Alexander Gorban and Tatyana Popova) (HTML)
In Silico Biology, March 2005
Coding information is the main source of heterogeneity (non-randomness) in the sequences of microbial genomes. The heterogeneity corresponds to a cluster structure in triplet distributions of relatively short genomic fragments (200-400bp). We found a universal 7-cluster structure in microbial genomic sequences and explained its properties. We show that codon usage of bacterial genomes is a multi-linear function of their genomic G+C-content with high accuracy. Based on the analysis of 143 completely sequenced bacterial genomes available in Genbank in August 2004, we show that there are four "pure" types of the 7-cluster structure observed. All 143 cluster animated 3D-scatters are collected in a database which is made available on our web-site (http://www.ihes.fr/~zinovyev/7clusters). The findings can be readily introduced into software for gene prediction, sequence alignment or microbial genomes classification.
Constructive Methods of Invariant Manifolds for Kinetic Problems (with Alexander Gorban and Iliya Karlin) (PDF)
Physics Reports, March 2004
The conception of the slow invariant manifold is recognized as the central idea underpinning a transition from micro to macro and model reduction in kinetic theories. We present the Constructive Methods of Invariant Manifolds for model reduction in physical and chemical kinetics, developed during last two decades. The physical problem of reduced description is studied in a most general form as a problem of constructing the slow invariant manifold. The invariance conditions are formulated as the differential equation for a manifold immersed in the phase space (the invariance equation). The equation of motion for immersed manifolds is obtained ( the film extension of the dynamics). Invariant manifolds are fixed points for this equation, and slow invariant manifolds are Lyapunov stable fixed points, thus slowness is presented as stability.
A collection of methods to derive analytically and to compute numerically the slow invariant manifolds is presented. Among them, iteration methods based on incomplete linearization, relaxation method and the method of invariant grids are developed. The systematic use of thermodynamics structures and of the quasi--chemical representation allow to construct approximations which are in concordance with physical restrictions.
The following examples of applications are presented: Nonperturbative deviation of physically consistent hydrodynamics from the Boltzmann equation and from the reversible dynamics, for Knudsen numbers $Kn\sim 1$; construction of the moment equations for nonequilibrium media and their dynamical correction (instead of extension of list of variables) to gain more accuracy in description of highly nonequilibrium flows; determination of molecules dimension (as diameters of equivalent hard spheres) from experimental viscosity data; model reduction in chemical kinetics; derivation and numerical implementation of constitutive equations for polymeric fluids; the limits of macroscopic description for polymer molecules, etc.
Invariant grids for reaction kinetics (with Alexander Gorban and Iliya Karlin) (PDF)
Physica A, June 2003
In this paper, we review the construction of low-dimensional manifolds of reduced description for equations of chemical kinetics from the standpoint of the method of invariant manifold (MIM). MIM is based on a formulation of the condition of invariance as an equation, and its solution by Newton iterations. A grid-based version of MIM is developed. Generalizations to open systems are suggested. The set of methods covered makes it possible to effectively reduce description in chemical kinetics.
The most essential new element of this paper is the systematic consideration of a discrete analogue of the slow (stable) positively invariant manifolds for dissipative systems, invariant grids. We will describe the Newton method and the relaxation method for the invariant grids construction. The problem of the grid correction is fully decomposed into the problems of the grid's nodes correction. The edges between the nodes appears only in the calculation of the tangent spaces. This fact determines high computational efficiency of the invariant grids method.
Codon Adaptation Index as a measure of dominating codon bias (with Alessandra Carbone and Francois Kepes) (PDF)
Bioinformatics, January 2003
We propose a simple algorithm to detect dominating synonymous codon usage bias in genomes. The algorithm is based on a precise mathematical formulation of the problem that lead us to use the Codon Adaptation Index (CAI) as a "universal" measure of codon bias. This measure has been previously employed in the specific context of translational bias. With the set of coding sequences as a sole source of biological information, the algorithm provides a reference set of genes which is highly representative of the bias. This set can be used to compute the Codon Adaptation Index of genes of prokaryotic and eukaryotic organisms, including those whose functional annotation is not yet available. An important application concerns the detection of a reference set characterizing translational bias which is known to correlate to expression levels; in this case, the algorithm becomes a key tool to predict gene expression levels, to guide regulatory circuit reconstruction, and to compare species. The algorithm detects also leading-lagging strands bias, GC-content bias, GC3 bias, and horizontal gene transfer. The approach is validated on 12 slow-growing and fast-growing bacteria, Saccharomyces cerevisiae, Caenorhabditis elegans and Drosophila melanogaster. Supplementary materials (PDF)
Visualization of Data by Method of Elastic Maps and Its Applications in Genomics, Economics and Sociology (with Alexander N. Gorban) (PS , PDF)
Institut des Hautes Etudes Scientifiques Preprint, July 2001
Technology of data visualization and data modeling is suggested. The basic of the technology is original idea of elastic net and methods of its construction and application. A short review of relevant methods has been made. The methods proposed are illustrated by applying them to the real biological, economical, sociological datasets and to some model data distributions.

On-going projects with my active participation:

	ACSN - Atlas of Cancer Signalling Networks
	NaviCell - Web tool for exploring large maps of molecular interactions
	Servier-Curie Alliance - Finding new therapeutical targets in basal-like breast cancer
	ASSET (EU-FP7) - Analysing and Stryking the Sensitivities of Embryonal Tumours, EU FP7.
	SYBEWING (INCA) - Systems Biology of Ewing sarcoma
	BiNoM - Biological Network Manager: Cytoscape plug-in for manipulating and analysis of biological networks

Past projects:

	CALAMAR (ANR) - Compositional modelling and Analysis of LArge MoleculAr Regulatory networks - application to the control of human cell proliferation.
	APO-SYS (EU-FP7) - Apoptosis Systems Biology Applied to Cancer and AIDS (first European cancer systems biology project)
	ANR SITCON - Modeling Signal Transduction Induced By A Chimeric Oncogene EWS/FLI1 in Ewing sarcoma
	RB - Regulation of cell cycle by Retinoblastoma protein: Systems Biology approach
	ISC-PIF MATBRAC - Mathematical theory of biological robustness with experimental applications in cancer systems biology
	NFKB - Model reduction for the study of Nfkb pathway dynamics (with Ovidiu Radulescu)
	MIG - Method of Invariant Grids for chemical kinetics equations
	FP6 CA ESBIC-D - European Systems Biology Initiative combating complex diseases
	ACE - Annotation of Complex Rnhancers (in progress), multilayered approach to study gene regulation
	ACI IMPBIO KernelChip - Integration of gene expression data and gene regulatory networks for the study of cancers
	ViMiDa - Java-applet for VIsualization of MIcroarray DAta
	ViDaExpert - Multidimensional Data Visualization Tool
	ELMAP - Method of elastic maps for fast and effective construction of complex principal manifolds
	CAIJAVA - Comparison of different genomes, based on codon bias and automatic calculation of CAIs
	PLUG&BLAST - Bioinformatics platform, oriented to the cluster-based parallel computations
	SEVEN CLUSTERS - Exploration of the large-scale structure of triplet distributions in whole genomes
	FOREST HAHN - Forest model which shows that one can have twice bigger wood harvest arranging trees in a proper way

Conference and tutorials co-organizing

Coping with Complexity: Model Reduction and Data Analysis Research Workshop, Ambleside, Lake District, UK, August 31 – September 4, 2009

APO-SYS workshop on genome and transcriptome microarray data analysis, biological network analysis and pathway charting. Paris, Institut Curie, 28 April 2008.

PRINCIPAL MANIFOLDS - 2006, Leicester, UK, August, 2006

GEOMETRY OF GENOME, Leicester, UK, September,2005

Presentations:

	Modeling cell life and cell death in cancer (PDF)
	How much non-coding DNA do eukaryotes require? (PDF)
	Hierarchical cluster structures and symmetries in genomic sequences (PPT)
	Invariant manifolds for reaction kinetics (PPT)
	Non-linear Principal Manifolds - elastic maps approach (animated PPT)
	CAI and the most biased genes (HTML, PPT)
	Seven clusters in genomic triplet distributions (HTML, PPT)
	ACE&RACE: annotation of complex/combinatorial expressions (PPT)
	Doubling wood harvest with tree group planting (PPT)

Friendly and highly recommended links:

pca.narod.ru - site in russian on Nonlinear Principal Manifolds with extensive collection of seminal papers, books and theses, including the original paper of Pearson (1901)
ddarwin.narod.ru - site devoted to the exceptional and insightfull book on evolution 'Demon of Darwin' by Alexander Gorban and Rem Khlebopros (1988) (in Russian)
thermotree.narod.ru - site in russian devoted to thermodinamics in kinetics and related fields (including "mathematician-chemist" conflict typology!)

Web pages of my colleages, friends and co-authors:

Alexander Gorban, my 'scientific father'
Alessandra Carbone
Sebastian Ahnert
Thomas Fink
Jean-Philippe Vert
Ovidiu Radulescu
Valentina Boeva
Arndt Benecke
Laurence Calzone

Contact information :

Institut Curie, Service Bioinformatique, 26 rue d'Ulm, F75248, Paris, France
Tel.: (33)1-56-24-69-89
Email: andrei.zinovyev@curie.fr

CV - BOOKS - PUBLICATIONS - PROJECTS - PRESENTATIONS - LINKS - CONTACT INFORMATION - PERSONAL