Research in biosciences

I work on quantitative biological problems typically involving modeling and bioanalyses. The themes include regulation within intra-cellular networks, exploitation of genetic recombination and modeling of crossover formation in meiosis.

Publications in reverse chronological order:

• A Vidal, F Gauthier, ... O.C. Martin and M. Falque, SeSAM: software for automatic construction of order-robust linkage maps, BMC bioinformatics 23 (1), 1-12 (2022). The SeSAM software allows automatic genetic map construction using seriation and placement approaches, to produce (1) a high-robustness framework map which includes as many markers as possible while keeping the order robustness beyond a given statistical threshold, and (2) a high-density total map including the framework plus almost all polymorphic markers

• Y Yadav, A Subbaroyan, OC Martin and A Samal, Relative importance of composition structures and biologically meaningful logics in bipartite Boolean models of gene regulation, Scientific Reports 12 (1), 1-16 (2022). Multiple transcription factors may simultaneously contribute to gene regulation by forming heteromeric complexes, thus giving rise to so-called composition structures. Since bipartite Boolean models are relatively recent, an empirical investigation of their biological plausibility is lacking. Here, we estimate the prevalence of composition structures arising in several public datasets.

• A Subbaroyan, OC Martin and A Samal, A preference for link operator functions can drive Boolean biological networks towards critical dynamics, Journal of Biosciences 47 (1), 1-11 (2022). We theoretically enumerate link operator functions (LOFs) and show that, among all BFs and even within the biologically consistent effective and unate functions, the LOFs form a tiny subset. We then find that the AND-NOT LOFs are particularly abundant in reconstructed biological Boolean networks.

• Y.M. Hsu, M. Falque and O.C. Martin, Quantitative modelling of fine-scale variations in the Arabidopsis thaliana crossover landscape, Plant Quantitative Biology, 3, e3 (2022). Meiotic crossovers occur preferentially in open chromatin, typically near gene promoters and to a lesser extent at the end of genes. Here, in the case of Arabidopsis thaliana, we unveil further trends arising when one considers contextual information, namely summarized epigenetic status, size of underlying genomic regions and degree of divergence between homologs. By integrating such contextual factors, we produce a quantitative and predictive model of the recombination landscape that reproduces much of the experimental variation.

• Ajay Subbaroyan, Olivier C. Martin and Areejit Samal, Minimum complexity drives regulatory logic in Boolean models of living systems, PNAS Nexus, 1,1, pgac017 (2022). We study the preponderance of particular types of Boolean functions in gene regulatory networks. We first compile a reference dataset of 2687 functions extracted from published models. This dataset shows strong enrichments in read-once functions (RoFs) and in nested canalyzing functions (NCFs). These enrichments can be justified by selection for minimum complexity, either Boolean complexity based on string lengths in formal logic which is yet unexplored in the biological context, or average sensitivity which corresponds to maximizing robustness to noise.

• A. Vidal, F. Gauthier, ..., E. Tourrette, O.C. Martin and M. Falque, MAGuS: automatic construction of high-density linkage maps, submitted. MAGuS performs fully-automated optimized construction of high-density genetic maps, and includes a toolkit of interactive functions including simulation of segregation data, format conversions, graphical assessment of data and map quality, and computation of consensus maps.

• E. Tourrette, M. Falque and O.C. Martin, Enhancing backcross programs through increased recombination, Genetics Selection Evolution 53(1), 1 (2021). In breeding programs aiming to introgress genomic loci while maintaining the rest of the genome in an elite state, recombination is essential. Here we investigate whether recently developed methods for increasing recombination will improve such backcross breeding programs. Our conclusion is that they will but only if the targets are in cold regions.

• B.K. Pandey, G. Huang, ..., O.C. Martin, .., D. Zhang and M.J. Bennett, Plant roots sense soil compaction through restricted ethylene diffusion, Science 371:6526, 276 (2021). Soil compaction represents a major challenge for modern agriculture. Compaction is intuitively thought to reduce root growth by limiting their ability to penetrate harder soils. We report that root growth in compacted soil is instead actively suppressed by the volatile hormone ethylene. In effect, ethylene acts as an early warning signal for roots to avoid compacted soils, revealing approaches to breed crops resilient to soil compaction.

• E. Carrillo-Perdomo, A. Vidal, ..., M. Falque, O.C. Martin, J. Burstin and G. Aubert, Development of new genetic resources for faba bean (Vicia faba L.) breeding through the discovery of gene-based SNP markers and the construction of a high-density consensus map, Scientific Reports 10, 6790 (2020). Three recombinant line populations of faba bean were used to construct a high-density consensus genetic map encompassing 1,728 markers well distributed in six linkage groups. This will make the identification of candidate genes of interest more efficient and will accelerate marker-assisted selection and genomic-assisted breeding in faba bean.

• M. Falque, K. Jebreen, E. Paux, C. Knaak, S. Mezmouk and O.C. Martin, CNVmap: a method and software to detect copy number variants from linkage mapping data, Genetics 214(3), 561-575 (2020). Structural variations such as copy-number variants (CNVs) represent a large part of natural genetic diversity and contribute significantly to trait variation. We propose here an original method to both detect and genetically map CNVs using mapping panels. We validate this approach on simulated and experimental bi-parental mapping panels in two maize populations and one wheat population.

• E. Tourrette, R. Bernardo, M. Falque and O.C. Martin, Assessing by modeling the consequences of increased recombination in recurrent selection of Oryza sativa and Brassica rapa, G3: Genes, Genomes, Genetics 9(12), 4169-4181 (2019) DOI: 10.1534/g3.119.400545. Two methods have been recently demonstrated to produce many-fold increases in meiotic recombination rates for certain crops. Here we use a quantitative genetics framework to model to what extent that increased shuffling of alleles can lead to higher gains in breeding programs.

• P. Termolino, M. Falque, R. Aiese Cigliano, G. Cremona, R. Paparo, A. Ederveen, O.C. Martin, F.M. Consiglio and C. Conicella, Recombination suppression in heterozygotes for a pericentric inversion induces the interchromosomal effect on crossovers in Arabidopsis, The Plant Journal 100, 1163-1175 (2019) DOI:10.1111/tpj.14505. We investigate the effect of a large heterozygous pericentric inversion in chromosome 3 on male and female recombination in Arabidopsis. Crossover suppression on the rearranged chromosome is associated with a significant increase of COs in the other chromosomes, pointing to a homeostasis of the total number of crossovers per cell.

• K. Jebreen, M. Petrizzelli and O.C. Martin, Probabilities of Multilocus Genotypes in SIB Recombinant Inbred Lines, Front. Genet. 10, 833 (2019) DOI:10.3389/fgene.2019.00833. In 1931 Haldane and Waddington provided the probabilities of 3-locus genotypes in sibling-based recombinant inbred lines (RILs). Here we show how to compute such quantities for more loci. Our computer program can treat up to 10 loci and we illustrate its use to improve the quality of imputation of missing data in the context of these kinds of RILs.

• X. Raffoux, M. Bourge, F. Dumas, O.C. Martin and M. Falque, Role of cis, trans, and inbreeding effects on meiotic recombination in Saccharomyces cerevisiae, Genetics (2018), DOI 10.1534/genetics.118.301644 We measure recombination rates in hybrids between SK1 and a total of 26 S. cerevisiae strains from different geographic origins and habitats. Our overall results indicate that recombination rate is increasingly positively correlated with sequence similarity between homologs (i) in DNA double-strand break rich regions within intervals, (ii) in entire intervals, and (iii) at the whole genome scale. Therefore, these correlations cannot be explained by cis-effects only. We estimated that cis and trans effects explained respectively 38% and 17% of the variance of recombination rates.

• D. Collot, T. Nidelet, J. Ramsayer, O.C. Martin, S. M\E9l\E9ard, C. Dillmann, D. Sicard and J. Legrand, Feedback between environment and traits under selection in a seasonal environment: consequences for experimental evolution, Proc. R. Soc. B, 285(1876), 20180284 (2018), DOI 10.1098/rspb.2018.0284. Recurrent batch cultures form a seasonal environment where different phases repeat periodically. We developed a mathematical model to understand which traits of yeasts in such cultures are under selection and what is the role of the environment in eco-evolutionary feedbacks. We showed that two kinds of traits are under selection: life-history traits, related to growth and mortality, and also transition traits, related to the ability to react to environmental changes.

• X. Raffoux, M. Bourge, F. Dumas, O.C. Martin and M. Falque, High-throughput measurement of recombination rates and genetic interference in Saccharomyces cerevisiae, Yeast, 35(6), 431--442 (2018), DOI 10.1002/yea.3315. We develop a high-throughput and low-cost method to measure recombination rates and crossover patterning (including interference) in large populations of the budding yeast Saccharomyces cerevisiae. Recombination and interference were analysed by flow cytometry, which allows time-consuming steps such as tetrad microdissection or spore growth to be avoided.

• S. Grigolon, B. Bravi and O.C. Martin, Responses to auxin signals: an operating principle for dynamical sensitivity yet high resilience, R. Soc. open sci. (2018) 5 172098; DOI: 10.1098/rsos.172098. Plants depend on the signaling of the phytohormone auxin for their development and for responding to environmental perturbations. The associated biomolecular signaling network involves a negative feedback at the level of the Aux/IAA proteins which mediate the influence of auxin (the signal) on the ARF transcription factors (the drivers of the response). To probe the role of this feedback, we consider alternative in silico signaling networks implementing different operating principles. By a comparative analysis, we find that the presence of a negative regulatory feedback loop allows the system to have a far larger sensitivity in its dynamical response to auxin. At the same time, this sensitivity does not prevent the system from being highly resilient. Given this insight, we reconsider previously published models and build a new quantitative and calibrated biomolecular model of auxin signaling. The model is available on the BIOMODELS website under the name FLAIR.

• A. Samal and O.C. Martin, Haldane, Waddington and recombinant inbred lines: extension of their work to any number of genes, Journal of Genetics, DOI:10.1007/s12041-017-0837-0 (2017). We revisit the multi-locus probabilities of homozygous genotypes arising in recombinant inbred lines and treated for 2 and 3 loci by Haldane and Waddington (H&W) in 1931. From historical perspective, it is interesting to note that the father of statistical genetics, R.A. Fisher, also had strong interests in inbreeding, introducing his own approach based on junctions. It is only now with our mathematical break-through allowing the treatment of many loci that the much greater power of the H&W approach transpires over the one proned by Fisher.

• A. Pele, M. Falque, ..., O.C. Martin, M. Rousseau-Gueutin and A-M. Chevre, Amplifying recombination genome-wide and reshaping crossover landscapes in Brassicas, PLOS Genetics, 13(5): e1006794 (2017). Press coverage (in French). During meiosis, the reciprocal exchanges between the homologous chromosomes due to crossovers (COs) ensure their proper segregation as well as the generation of diversity. However, the number of COs is limited and their location is heterogeneous along chromosomes. A major challenge is to overcome these constraints for enhancing the genetic shuffling of alleles. This work demonstrates that it is possible to do so in Brassica hybrids obtained by manual crossings, combining a complete set of homologous chromosomes and a haploid set provided by a related species. By studying large segregating populations, we find that in allotriploid Brassica hybrids, more COs are formed all along the homologous chromosomes, especially in regions usually deprived of COs, compared to diploids. These results offer the opportunity for geneticists and plant breeders to dramatically enhance the generation of new diversity.

• S.R. Hosseini, O.C. Martin and A Wagner, Phenotypic innovation through recombination in genome-scale metabolic networks, Proc. R. Soc. B 283 (1839), 20161536 (2016). We show that recombination is much more likely to create novel metabolic abilities than random changes in chemical reactions of a metabolic network. We also find that phenotypic innovation is more likely when recombination occurs between parents that are genetically closely related, phenotypically highly diverse, and viable on few rather than many carbon sources.

• A. Henry and O.C. Martin, Short relaxation times but long transient times in both simple and complex reaction networks, J. R. Soc. Interface 13, 20160388 (2016). By mathematical analysis of simple reaction networks, we pin-point the reason why the standard relaxation time does not provide relevant information on the potentially long transient times of typical infinitesimal perturbations.

• O.C. Martin, A. Krzywicki and M. Zagorski, Drivers of structural features in gene regulatory networks: From biophysical constraints to biological function, Phys. Life Rev. (2016). The logic of a regulatory program can sometimes be guessed at by examining the network of influences amongst its components. Studies of gene regulatory networks have unveiled structural features ranging from broad distributions of out-degrees to recurrent "motifs", that is small subgraphs having a specific pattern of interactions. We review here different approaches to understanding what factors drive such structuring and show how selection for phenotypes, i.e., the function of a regulatory network, can shape the structure of the network.

• M. Mori, T. Hwa, O.C. Martin, A. De Martino and E. Marinari, Constrained Allocation Flux Balance Analysis, PLOS Comput Biol 12(6): e1004913 (2016). We introduce a computational genome-scale framework which provides a quantitative approach to balancing the trade-off between growth and its associated biosynthetic costs at genome-scale, without the burden of tuning many inaccessible parameters.

• G.K. Sidhu, C. Fang, M.A. Olson, M. Falque, O.C. Martin, and W.P. Pawlowski, Recombination patterns in maize reveal limits to crossover homeostasis, PNAS (2015) 1514265112. During meiosis, chromosomes exchange segments in a process of crossing-over. The crossover number is tightly regulated so that at least one crossover (but not many more) is formed per chromosome. The process of crossover homeostasis is thought to play a major role in this regulation by ensuring a stable crossover number even if the number of DNA breaks that initiate crossover formation varies. However, we found that, in maize, the crossover number changes with the number of DNA breaks, suggesting that different species exhibit different crossover control mechanisms. Plant breeders rely on recombination to create new combinations of alleles. Our data suggest that increasing recombination rates in plants may be accomplished by increasing the number of DNA breaks.

• A. Samal, O.C. Martin, Statistical physics methods provide the exact solution to a long-standing problem of genetics, Phys. Rev. Lett. 114, 238101 (2015). (Supplemental Material and C source code.) Highlighted as a "Editors' choice", received press coverage in Physics Today and was in the news of several institutions (ICTP, Italy, and INRA, both for the Versailles-Grignon center and nationally). In a landmark 1931 paper, Haldane and Waddington formulated the statistical genetics problem of finding the probabilities of all different genetic outcomes when repeatedly inbreeding a plant. Those authors gave a mathematical solution when restricting the situation to just two or three genes at a time. Extending Haldane and Waddington's results to 4 or more genes has seemed unsurmountable since that seminal paper of over 80 years ago. Yet, in this work, we provide the generalization of the formulas to any number of genes. The key to our solution is the exploitation of framework equations developed by Nobel physicists Roy Glauber and Julian Schwinger. Surprisingly, the associated formulas involve only the standard four operations (addition, subtraction, multiplication and division) and can be produced automatically. These multi-variate probabilities can be included in genetic analyses while extensions of our framework may provide mathematical solutions to other interdisciplinary problems involving many variables.

• S. Grigolon, P. Sollich, O.C. Martin, Modelling the emergence of polarity patterns for the intercellular transport of auxin in plants , J. R. Soc. Interface (2015) 12 20141223. The hormone auxin is actively transported throughout plants via protein machineries including the dedicated transporter known as PIN. The associated transport is ordered with nearby cells driving auxin flux in similar directions. Here, we provide a model of both the auxin transport and of the dynamics of cellular polarization based on flux sensing. Our main findings are: (i) spontaneous intracellular PIN polarization arises if PIN recycling dynamics are sufficiently nonlinear, (ii) there is no need for an auxin concentration gradient and (iii) ordered multi-cellular patterns of PIN polarization are favoured by molecular noise.

• L.K. Anderson, L.D. Lohmiller, X. Tang, D.B. Hammond, L. Javernick, L. Shearer, S. Basu-Roy, O.C. Martin, M. Falque, Combined fluorescent and electron microscopic imaging unveils the specific properties of two classes of meiotic crossovers , PNAS (2014) 111 (37) 13415-13420. Highlighted in the INRA news. By identifying COs from each class simultaneously on tomato meiotic chromosomes, we reveal that the two CO classes have different distributions, with class II COs enriched in short arms and heterochromatin. Although class II CO distributions are consistent with no interference, interference between the two pathways was detected, with suppression of close class I and class II COs.

• M. Tagliaro Jahns, D. Verzon, A. Chambon, L. Pereira, M. Falque, O.C. Martin, L. Chelysheva, M. Grelon, Crossover Localisation Is Regulated by the Neddylation Posttranslational Regulatory Pathway, PLOS Biology (2014) 12(8):e1001930. Post-translational protein modification by neddylation is involved in regulating the position but not the number of crossovers during meiosis in the model plant Arabidopsis.

• A. Barve, S-R. Hosseini, O.C. Martin and A. Wagner, Historical contingency and the gradual evolution of metabolic properties in central carbon and genome-scale metabolisms, BMC Systems Biology (2014) 8:48. Using a Flux Balance Analysis framework, we show that metabolism is highly evolvable, in the sense that its properties can be fine-tuned by successively altering individual reactions. Historical contingency does not strongly restrict the origin of novel metabolic phenotypes.

• L. Suay, D. Zhang, ..., A.-M. Chevre, Crossover rate between homologous chromosomes and interference are regulated by the addition of specific unpaired chromosomes in Brassica, New Phytologist (2014) 201 (2), 645-656. The homologous recombination rate between A genomes in AAC hybrids of Brassica napus is affected by the presence of the C chromosomes. By comparing the the genetic map lengths of different hybrids, we show for the first time that the presence of one chromosome, C9, increases significantly the recombination rate and reduces crossover interference.

• E. Bauer, M. Falque, ..., O.C. Martin and C.-C. Schoen, Intraspecific variation of recombination rate in maize, Genome Biology, 14:R103 (2013). Recombination landscapes in crosses between 22 European maize inbred lines are determined from high-density genotyping of double-haploid populations. We show that there are significant differences and that these cannot be attributed only to the presence of the dent and flint groups in these lines. We also analyze crossoer interference, revealing a negative association between recombination rate and interference strength.

• S. Basu Roy, F. Gauthier, L. Giraut, C. Mezard, M. Falque and O.C. Martin, Hot Regions of Non-Interfering Crossovers Coexist with a Non-Uniformly Interfering Pathway in Arabidopsis thaliana, Genetics 113.155549 (2013). Using 1500 male and female meioses in Arabidopsis thaliana, we find that the interfering pathway has markedly higher interference strength nu in female than male meiosis and also that male meiosis has a higher proportion p of non-interfering crossovers. Furthermore, we test for intra-chromosomal variations of nu and p. Our conclusion is that there are clear differences between left and right arms as well as between central and peripheral regions. Finally, statistical tests unveil a genome-wide picture of small scale heterogeneities, pointing to the existence of hot regions in the genome where COs form preferentially without interference.

• A. Samal and O.C. Martin Shining fresh light on the evolution of photosynthesis, eLife 2:e01403 (2013). There are two types of photosynthesis, C3 and the evolutionarily more recent one, C4. There is much interest in trying to transfer some C4 features such as high photosynthetic efficiency and drought resistance into important C3 crop plants such as rice. The present article is an insight into the computational study of Williams, Johnston, Covshoff and Hibberd who explore how C4 plants evolved many different times from C3 ancestors. Such multiple paths may provide strategies for genetically engineering crop plants.

• 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., 9(7), 1726--1735, (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, ..., O.C. Martin and M. Falque, 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). Exploiting renewal processes and enumerations of random walks on hypercubes, we derive statistical properties of the mosaic genomes arising in RILS. Particular attention is given to the distribution of number and of length of Identical by Descent (IBD) blocks for both SSD and SIB RILs.

• A. Samal, A. Wagner and O.C. Martin Environmental versatility promotes modularity in genome-scale metabolic networks, BMC Systems Biology 5:135 (2011). We consider in silico metabolic genotypes capable of growing on various media based on the Flux Balance Analysis mapping from genotype to phenotype. We find that imposing growth capabilities in more and more media leads to enhanced modularity of the underlying metabolic networks.

• A. Samal and O.C. Martin Randomizing genome-scale metabolic networks, PLoS One 6(7): e22295 (2011). To make patent unexpected structures in biological networks, practice is to compare experimental networks to randomized in silico networks for which the edges have been shuffled. However this makes no sense in the case of metabolic networks because it does not conserve atomic species. We show how to use a different randomization algorithm which has the property of using only valid biochemical reactions in all in silico metabolic networks.

• 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). Within a transcriptional regulation model of gene expression, we examine the putative tradeoff between phenotypic robustness and phenotypic diversity under environmental changes. Interestingly, in some circumstances, the tradeoff can become a positive correlation.

• 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). This note provides a software system for analyzing crossover datasets using either one or two pathways of formation of those crossovers, allowing the interfering pathway to be specified either by the Gamma model or by the Beam-film model. The user-friendly interface also provides simulational capabilities.

• 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). Within a model of gene regulation connecting genotypes to phenotypes, we consider the set of all Gene Regulatory Networks (GRNs) having a given phenotypic behavior. In such a framework, we find that a GRN having phenotypic plasticity has a greater chance under mutation of producing new phenotypes.

• 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 punctuated equilibria that 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). We use MCMC to sample in silico the metabolic genotypes capable of growing on given media according to Flux Balance Analysis. The associated set of genotypes belongs to a network which we show spans much of all genotypic space and which essentially forms one giant connected component.

• 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). Chromosome conformations are investigated in silico based on a thermodynamic modeling of a polymer. If transcription factors are multi-valent, they will tend to cluster their targets and thereby induce organized phases in which DNA looping plays a key role.

• 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). Based on electron microscopy imaging of late nodules in pachytene which are markers of crossovers, we perform a two-pathway analysis on the patterns of occurrences of crossovers in maize. The abundance of nearby crossovers allows us to show that the second (non-interfering) pathway is present and provides around 20% of the crossovers for each of the chromosomes. Data analyzed here has kindly been provided by Lorrie Anderson for research purposes only and if you do publish work based on these data cite both this 2009 paper and her original 2003 paper (see instructions at top of this Excel data file).

• 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 covering 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. Furthermore, 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, pointing to 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 quantitatively measure neutral set sizes in huge 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). Our index is computationally efficient and allows for computing p-values for very large trees.

• 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 crossover interference, and in particular find that the interference level varies significantly along the chromosome in male meiosis and is correlated to physical distance.

• 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 population dynamics subject to selective pressures, focusing on spread and neutrality. In the presence of drift, these observables depend mainly on the product 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 manipulating drift, the M mu scaling can be modified to a mu-independent scaling; then the genotypic diversity in the population 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 multi-molecular 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 in cancer cells, as exhibited 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.

• 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 1420-1424 (1996). 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, 503-509 (1990). 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. 93 219-258 (1984). We perform an in depth study of the limiting behavior (fixed points and cycles) of cellular automata on a ring.

UMR G\E9n\E9tique V\E9g\E9tale Olivier MARTIN Home Page