Research in biosciences

My earliest work was motivated by biological analogies; at present I am focusing on quantitative biological problems associated with recombination and selection on the one hand and modeling of networks on the other.

Publications in reverse chronological order:

• A. Henry, F. Moneger, A. Samal and O.C. Martin, Network function shapes network structure: the case of the Arabidopsis flower organ specification genetic network, Mol. BioSyst., 2013, DOI: 10.1039/C3MB25562J, 2013. In the "network function shapes network structure scenario", we examine how the gene expression patterns of Arabidopsis flower organogenesis shape edge usage and network motifs.

• M. Zagorski, A. Krzywicki and O.C. Martin, Edge usage, motifs and regulatory logic for cell cycling genetic networks, Phys. Rev. E 87, 012727, 2013. The cell cycle is a tightly controlled process, yet its underlying genetic network shows marked differences across species. Which of the associated structural features follow solely from the ability to impose the appropriate gene expression patterns? We tackle this question in silico, focusing on three cell cycle profiles coming from baker's yeast, fission yeast and mammals.

• M.W. Ganal et al., A Large Maize (Zea mays L.) SNP Genotyping Array: Development and Germplasm Genotyping, and Genetic Mapping to Compare with the B73 Reference Genome, PLoS ONE 6(12): e28334 (2011). We report the establishment of a large maize SNP array and its use for diversity analysis and high density linkage mapping. Two intermated maize recombinant inbred line populations – IBM (B73×Mo17) and LHRF (F2×F252) – were genotyped from which two high density linkage maps with 20,913 and 14,524 markers respectively were generated. These maps were compared to the current B73 assembly, revealing some non-syntenic markers as well as exceptions to colinearity.

• Z. Burda, A. Krzywicki, O.C. Martin and M. Zagorski, Motifs emerge from function in model gene regulatory networks, PNAS 108 (42) 17263-17268, 2011. Gene regulatory networks arise in all living cells, allowing the control of gene expression patterns. The study of their topology has revealed that certain subgraphs of interactions or "motifs" appear at anomalously high frequencies. We show here that this phenomenon may emerge because of the functions carried out by these networks.

• L. Giraut, M. Falque, J. Drouaut, L. Pereira, O.C. Martin and C. Mezard, Genome-wide crossover distribution in Arabidopsis thaliana meiosis reveals sex specific patterns along chromosomes, PLoS Genetics 7(11): e1002354, 2011. We report a detailed, genome-wide characterization of the rate and localization of COs in Arabidopsis thaliana, in male and female meiosis and also perform an analysis of interference.

• O.C. Martin and F. Hospital Distribution of parental genome blocks in recombinant inbred lines, Genetics 189:645-654, 2011.

• A. Samal, A. Wagner and O.C. Martin Environmental versatility promotes modularity in genome-scale metabolic networks, BMC Systems Biology 5:135 2011.

• A. Samal and O.C. Martin Randomizing genome-scale metabolic networks, PLoS One 6(7): e22295 2011.

• C. Espinosa-Soto, O.C. Martin and A. Wagner Phenotypic robustness can increase phenotypic variability after nongenetic perturbations in gene regulatory circuits, J. Evol. Bio. 24(6), 1284 2011.

• F. Gauthier, O.C. Martin and M. Falque CODA (CrossOver Distribution Analyzer): quantitative characterization of crossover position patterns along chromosomes, BMC Bioinformatics 2011, 12:27 2011.

• C. Espinosa-Soto, O.C. Martin and A. Wagner Phenotypic plasticity can facilitate adaptive evolution in gene regulatory circuits, BMC Evolutionary Biology 11:5 2011.

• P. Sulc, A. Wagner and O.C. Martin Quantifying Slow Evolutionary Dynamics in RNA Fitness Landscapes, Journal of Bioinformatics and Computational Biology, Vol. 8, No. 6, 2010. We re-examine the evolutionary dynamics of RNA secondary structures under directional selection towards an optimum RNA structure. We find that the punctuated equilibria lead to a very slow approach to the optimum, following on average an inverse power of the evolutionary time. In addition, our study of the trajectories shows that the out-of-equilibrium effects due to the evolutionary process are very weak. In particular, the distribution of genotypes is close to that arising during equilibrium stabilizing selection. As a consequence, the evolutionary dynamics leave almost no measurable out-of-equilibrium trace, only the transition genotypes (close to the border between different periods of stasis) have atypical mutational properties.

• Z. Burda, A. Krzywicki, O.C. Martin and M. Zagorski, Distribution of essential interactions in model gene regulatory networks under mutation-selection balance, Phys. Rev. E 82, 011908 (2010). Gene regulatory networks typically have low in-degrees and broad distributions for the out-degree. What mechanisms might be responsible for these properties? Starting with an accepted framework of the binding of transcription factors to DNA, we consider a simple model of gene regulatory dynamics. There, we show that selection for a target expression pattern leads to the emergence of minimum connectivities compatible with the selective constraint. "Functionality" is concentrated on a sparse number of interactions as measured for instance by their essentiality. Furthermore, we find that mutations of the transcription factors drive the networks to have broad out-degrees. Finally, these classes of models are evolvable, i.e. significantly different genotypes can emerge gradually under mutation-selection balance.

• A. Samal, J.F. Mathias Rodrigues, J. Jost, O.C. Martin and A. Wagner Genotype networks in metabolic reaction spaces, BMC Syst. Bio. 4, 30 2010.

• I. Junier, O. Martin, F. Kepes Spatial and Topological Organization of DNA Chains Induced by Gene Co-localization, PLoS Comput Biol 6(2): e1000678, 2010.

• M. Falque, L.K. Anderson, S. Stack and O.C. Martin, Two pathways of meiotic crossovers coexist in maize, The Plant Cell 21(12): 3915-3925 (2009).

• O.C. Martin and A. Wagner, Effects of Recombination on Complex Regulatory Circuits, Genetics 183: 673-684 (2009). Mutation and recombination are the two main forces generating genetic variation. Most of this variation may be deleterious. Because recombination can reorganize entire genes and genetic circuits, it may have much greater consequences than point mutations. We here explore the effects of recombination on models of transcriptional regulation circuits that play important roles in embryonic development. We show that recombination has weaker deleterious effects on the expression phenotypes of these circuits than mutations.

• C. Saintenac, M. Falque, O.C. Martin. E. Paux, C. Feuillet and P. Sourdille, Detailed Recombination Studies Along Chromosome 3B Provide New Insights on Crossover Distribution in Wheat (Triticum aestivum L.) Genetics 181, 393-403 (2009). In wheat (Triticum aestivum L.), the crossover (CO) frequency increases gradually from the centromeres to the telomeres. However, little is known about the factors affecting both the distribution and the intensity of recombination along this gradient. To investigate this, we studied in detail the pattern of CO along chromosome 3B of bread wheat. A dense reference genetic map comprising 102 markers homogeneously distributed along the chromosome was compared to a physical deletion map. Most of the COs (90%) occurred in the distal subtelomeric regions that represent 40% of the chromosome. About 27% of the proximal regions surrounding the centromere showed a very weak CO frequency with only three COs found in the 752 gametes studied. Moreover, we observed a clear decrease of CO frequency on the distal region of the short arm. Finally, the intensity of interference was assessed for the first time in wheat using a Gamma model. The results showed m values of 1.2 for male recombination and 3.5 for female recombination, suggesting positive interference along wheat chromosome 3B.

• T. Jorg, O.C. Martin and A. Wagner, Neutral network sizes of biological RNA molecules can be computed and are not atypically small, BMC Bioinformatics, 9:464 (2008). Neutral networks or sets consist of all genotypes with a given phenotype. The size and structure of these sets has a strong influence on a biological system's evolutionary properties. Here we introduce a generalized Monte Carlo approach that can measure neutral set sizes in larger spaces. The method is general and applicable to many problems where one has to estimate rare objects. We apply our method to the genotype-to-phenotype mapping of RNA molecules, and show that it can reliably measure neutral set sizes for molecules up to 100 bases, a feat far beyond what has been done previously.

• O.C. Martin and A. Wagner, Multifunctionality and robustness tradeoffs in model genetic circuits, Biophysical Journal 94:2927-2937 (2008). Most genetic circuits have more than one function. Does the need to carry out more than one function severely constrain network architecture? We find that robustness tradeoffs between several functions do not exist in model regulatory networks, and that each function can acquire high robustness through gradual Darwinian evolution.

• D.M. de Vienne, T. Giraud and O.C. Martin, A congruence index for testing topological similarity between trees, Bioinformatics 23(23):3119-3124 (2007).

• S. Ciliberti, O.C. Martin and A. Wagner, Innovation and robustness in complex regulatory gene networks, PNAS 104, 13591-13596 (2007). Innovation is the driving force of long term evolution, but robustness provides for short term enhancement of survival. What allows these two contradictory forces to coexist? We show that cryptic genetic variability (canalization), a principle at work in molecular networks but also in other biological systems, allows for high levels of innovation even within robust populations. This organismal principle is investigated quantitatively using a model of regulatory gene networks.

• J. Drouaud, R. Mercier, L. Chelysheva, A. Berard, M. Falque, O. Martin, V. Zanni, D. Brunel, and C. Mezard, Sex-Specific Crossover Distributions and Variations in Interference Level along Arabidopsis thaliana Chromosome 4, PLoS Genet. 3(6): e106 (2007). We determined the crossover distribution along the Arabidopsis thaliana Chromosome 4 (18 Mb) in male and female meiosis, giving lengths of 88 cM and 52 cM, respectively. This difference is remarkably parallel to that between the synaptonemal complex lengths meiocytes by immunolabeling of ZYP1. From these data we performed a detailed analysis of CO interference, and in particular find that the interference level varies significantly along the chromosome in male meiosis and is correlated to physical distance between crossovers.

• Sumedha, O.C. Martin and A. Wagner, New structural variation in evolutionary searches of RNA neutral networks, BioSystems 90, 475--485 (2007). An RNA neutral network is a computationally accessible realization of a genotype to phenotype map. Evolutionary innovation is facilitated by the connectivity of such networks. We show that both biological and random structures share a high rate of innovation. Furthermore, genotypes of high robustness have a long lasting suppressive effect on the rate of innovation in their neighborhood.

• M. Falque, R. Mercier, C. Mezard, D. de Vienne, and O.C. Martin, Patterns of recombination and MLH1 foci density along mouse chromosomes: modeling effects of interference and obligate chiasma, Genetics 176(3), 1453-67 (2007). We consider a new model to incorporate the known biological feature of "obligate chiasma" whereby in most organisms each bivalent almost always has at least one crossover. Our model provides a better fit to experimental data as compared to the standard chi-square model. It also predicts an enhancement of the recombination rate near the extremities.

• Sumedha, O.C. Martin and L. Peliti, Selection and population size effects in evolutionary dynamics, J. Stat. Mech. P05011 (2007). We study evolutionary dynamics subject to selective pressures, focusing on the spread and the neutrality of the population in the steady state. In the presence of drift these observables depend mainly on M mu, M being the population size and mu the mutation rate, while corrections to this scaling go as 1/M. Such corrections can be quite large in the presence of selection if there are barriers in the fitness landscape. Finally, we show that by reducing the strength of the drift the M mu scaling can be modified to a mu-independent scaling; then the genotypic diversity increases from O(\log M) to O(M).

• S. Ciliberti, O.C. Martin and A. Wagner, Robustness Can Evolve Gradually in Complex Regulatory Gene Networks with Varying Topology, PLoS Computational Biology 3(2), e15 (2007). For a model of transcriptional regulation networks, we explore millions of different network topologies to understand circuit robustness and its Darwinian evolution. All networks that attain a given gene expression state can be organized into a (meta)graph that can be easily traversed by gradual changes of circuit topology. This connectedness and evolvability of robust networks may be a general organizational principle of all biological systems.

• C. Wolfrom, O. Martin, M. Laurent, J. Deschatrette, Sinusoidal swinging dynamics of the telomere repair and cell growth activation functions of telomerase in rat liver cancer cells, FEBS Letters, v581(1), 125--130 (2007). Telomerase is a multimolecular complex of reverse transcriptase, RNA template, and regulatory proteins. It has two known functions: catalysis of the addition of [TTAGGG] repeats to telomeric DNA and the activation of various genes controlling cell proliferation. The possible coordination of these two functions is a key issue in understanding the growth of cancer cells. We report long-term changes to this complex system, as shown by specific data analysis methods. We show that the dynamics of the two functions of telomerase are tightly linked, with a change in predominant function every 13-14 weeks. The conservative behavior of this dynamic system probably accounts for the persistent proliferation of cancer cells.

• O.C. Martin and F. Hospital, Two and three-locus tests for linkage analysis using recombinant inbred lines, Genetics 173, 451-459 (2006). We derive the three-locus genotype frequencies arising in RIL and IRIL and show how to use these for data analysis, e.g. for interference and QTL detection.

• B. Servin, O.C. Martin, M. Mezard and F. Hospital, Toward a theory of marker-assisted gene pyramiding, Genetics 168, 513-523 (2004). We investigate the best way to combine into a single genotype a series of target genes identified in different parents (gene pyramiding). Assuming individuals can be selected and mated according to their genotype, the best procedure corresponds to an optimal succession of crosses over several generations (pedigree). Examples are given for eight target genes, and compared to a reference genotype selection method.

• E. Guerry, O.C. Martin, H. Tricoire, R. Siebert, and L. Valentin, A numerical study of persistence length effects on DNA conformation in sequencing electrophoresis, Electrophoresis 17 (1996) 1420-1424. We perform a numerical study of the effects of persistence length on DNA conformation in gels for sequence electrophoresis. We show that the DNA's persistence length leads to an increase of the chain's orientation along the electric field and to a higher friction force.

• J. Boutet de Monvel and O.C. Martin, Memory capacity in large idiotypic networks, Bulletin of Mathematical Biology, vol 57, No.1, p109-136 (1995). We examine generalizations of the Weisbuch, De Boer, and Perelson immune networks when the connectivity is very large and random. We find that the memory capacity is essentially reduced to nil.

• E. Felten, O. Martin, S. Otto, and J. Hutchinson, Multi-Scale Training of a Large Backpropagation Net, Biol. Cybern. 62, (1990) 503-509. We propose and test a multi-scale technique to improve the learning properties of feed-forward neural networks.

• O. Martin, A. Odlyzko, and S. Wolfram, Algebraic Properties of Cellular Automata, Commun. Math. Phys. 93 (1984) 219-258. We perform an in depth study of the limiting behavior (fixed points and cycles) of cellular automata on a ring.

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