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Areejit Samal

Publications and source records attributed to Areejit Samal.

36 records · Page 2Linked to original sources
arXiv2016

Forman curvature for complex networks

We adapt Forman's discretization of Ricci curvature to the case of undirected networks, both weighted and unweighted, and investigate the measure in a variety of model and real-world networks. We find that most nodes and edges in model and real networks have a negative curvature. Furthermore, the distribution of Forman curvature of nodes and edges is narrow in random and small-world networks, while the distribution is broad in scale-free and real-world networks. In most networks, Forman curvature is found to display significant negative correlation with degree and centrality measures. However, Forman curvature is uncorrelated with clustering coefficient in most networks. Importantly, we find that both model and real networks are vulnerable to targeted deletion of nodes with highly negative Forman curvature. Our results suggest that Forman curvature can be employed to gain novel insights on the organization of complex networks.

q-bio.MN↗
arXiv2015

Relative Stability of Network States in Boolean Network Models of Gene Regulation in Development

Progress in cell type reprogramming has revived the interest in Waddington's concept of the epigenetic landscape. Recently researchers developed the quasi-potential theory to represent the Waddington's landscape. The Quasi-potential U(x), derived from interactions in the gene regulatory network (GRN) of a cell, quantifies the relative stability of network states, which determine the effort required for state transitions in a multi-stable dynamical system. However, quasi-potential landscapes, originally developed for continuous systems, are not suitable for discrete-valued networks which are important tools to study complex systems. In this paper, we provide a framework to quantify the landscape for discrete Boolean networks (BNs). We apply our framework to study pancreas cell differentiation where an ensemble of BN models is considered based on the structure of a minimal GRN for pancreas development. We impose biologically motivated structural constraints (corresponding to specific type of Boolean functions) and dynamical constraints (corresponding to stable attractor states) to limit the space of BN models for pancreas development. In addition, we enforce a novel functional constraint corresponding to the relative ordering of attractor states in BN models to restrict the space of BN models to the biological relevant class. We find that BNs with canalyzing/sign-compatible Boolean functions best capture the dynamics of pancreas cell differentiation. This framework can also determine the genes' influence on cell state transitions, and thus can facilitate the rational design of cell reprogramming protocols.

q-bio.MN↗
arXiv2015

Phenotypic constraints promote latent versatility and carbon efficiency in metabolic networks

System-level properties of metabolic networks may be the direct product of natural selection or arise as a by-product of selection on other properties. Here we study the effect of direct selective pressure for growth or viability in particular environments on two properties of metabolic networks: latent versatility to function in additional environments and carbon usage efficiency. Using a Markov Chain Monte Carlo (MCMC) sampling based on Flux Balance Analysis (FBA), we sample from a known biochemical universe random viable metabolic networks that differ in the number of directly constrained environments. We find that the latent versatility of sampled metabolic networks increases with the number of directly constrained environments and with the size of the networks. We then show that the average carbon wastage of sampled metabolic networks across the constrained environments decreases with the number of directly constrained environments and with the size of the networks. Our work expands the growing body of evidence about nonadaptive origins of key functional properties of biological networks.

q-bio.MN↗
arXiv2015

Statistical physics methods provide the exact solution to a long-standing problem of genetics

Analytic and computational methods developed within statistical physics have found applications in numerous disciplines. In this letter, we use such methods to solve a long-standing problem in statistical genetics. The problem, posed by Haldane and Waddington [J.B.S. Haldane and C.H. Waddington, Genetics 16, 357-374 (1931)], concerns so-called recombinant inbred lines (RILs) produced by repeated inbreeding. Haldane and Waddington derived the probabilities of RILs when considering 2 and 3 genes but the case of 4 or more genes has remained elusive. Our solution uses two probabilistic frameworks relatively unknown outside of physics: Glauber's formula and self-consistent equations of the Schwinger-Dyson type. Surprisingly, this combination of statistical formalisms unveils the exact probabilities of RILs for any number of genes. Extensions of the framework may have applications in population genetics and beyond.

q-bio.PE↗
arXiv2014

Analysis of the hierarchical structure of the B. subtilis transcriptional regulatory network

The transcriptional regulation of gene expression is orchestrated by complex networks of interacting genes. Increasing evidence indicates that these transcriptional regulatory networks (TRNs) in bacteria have an inherently hierarchical architecture, although the design principles and the specific advantages offered by this type of organization have not yet been fully elucidated. In this study, we focussed on the hierarchical structure of the TRN of the gram-positive bacterium Bacillus subtilis and performed a comparative analysis with the TRN of the gram-negative bacterium Escherichia coli. Using a graph-theoretic approach, we organized the transcription factors (TFs) and sigma-factors in the TRNs of B. subtilis and E. coli into three hierarchical levels (Top, Middle and Bottom) and studied several structural and functional properties across them. In addition to many similarities, we found also specific differences, explaining the majority of them with variations in the distribution of sigma-factors across the hierarchical levels in the two organisms. We then investigated the control of target metabolic genes by transcriptional regulators to characterize the differential regulation of three distinct metabolic subsystems (catabolism, anabolism and central energy metabolism). These results suggest that the hierarchical architecture that we observed in B. subtilis represents an effective organization of its TRN to achieve flexibility in the response to diverse stimuli.

q-bio.MN↗
arXiv2012

Flux-based classification of reactions reveals a functional bow-tie organization of complex metabolic networks

Unraveling the structure of complex biological networks and relating it to their functional role is an important task in systems biology. Here we attempt to characterize the functional organization of the large-scale metabolic networks of three microorganisms. We apply flux balance analysis to study the optimal growth states of these organisms in different environments. By investigating the differential usage of reactions across flux patterns for different environments, we observe a striking bimodal distribution in the activity of reactions. Motivated by this, we propose a simple algorithm to decompose the metabolic network into three sub-networks. It turns out that our reaction classifier which is blind to the biochemical role of pathways leads to three functionally relevant sub-networks that correspond to input, output and intermediate parts of the metabolic network with distinct structural characteristics. Our decomposition method unveils a functional bow-tie organization of metabolic networks that is different from the bow-tie structure determined by graph-theoretic methods that do not incorporate functionality.

q-bio.MN↗
arXiv2011

Environmental versatility promotes modularity in genome-scale metabolic networks

The ubiquity of modules in biological networks may result from an evolutionary benefit of a modular organization. For instance, modularity may increase the rate of adaptive evolution, because modules can be easily combined into new arrangements that may benefit their carrier. Conversely, modularity may emerge as a by-product of some trait. We here ask whether this last scenario may play a role in genome-scale metabolic networks that need to sustain life in one or more chemical environments. For such networks, we define a network module as a maximal set of reactions that are fully coupled, i.e., whose fluxes can only vary in fixed proportions. This definition overcomes limitations of purely graph based analyses of metabolism by exploiting the functional links between reactions. We call a metabolic network viable in a given chemical environment if it can synthesize all of an organism's biomass compounds from nutrients in this environment. An organism's metabolism is highly versatile if it can sustain life in many different chemical environments. We here ask whether versatility affects the modularity of metabolic networks.

q-bio.MN↗
arXiv2011

Randomizing genome-scale metabolic networks

Networks coming from protein-protein interactions, transcriptional regulation, signaling, or metabolism may appear to have "unusual" properties. To quantify this, it is appropriate to randomize the network and test the hypothesis that the network is not statistically different from expected in a motivated ensemble. However, when dealing with metabolic networks, the randomization of the network using edge exchange generates fictitious reactions that are biochemically meaningless. Here we provide several natural ensembles of randomized metabolic networks. A first constraint is to use valid biochemical reactions. Further constraints correspond to imposing appropriate functional constraints. We explain how to perform these randomizations with the help of Markov Chain Monte Carlo (MCMC) and show that they allow one to approach the properties of biological metabolic networks. The implication of the present work is that the observed global structural properties of real metabolic networks are likely to be the consequence of simple biochemical and functional constraints.

q-bio.MN↗
arXiv2010

Flows in complex biochemical networks: Role of low degree nodes

Metabolic networks have two properties that are generally regarded as unrelated: One, they have metabolic reactions whose single knockout is lethal for the organism, and two, they have correlated sets of reactions forming functional modules. In this review we argue that both essentiality and modularity seem to arise as a consequence of the same structural property: the existence of low degree metabolites. This observation allows a prediction of (a) essential metabolic reactions which are potential drug targets in pathogenic microorganisms and (b) regulatory modules within biological networks, from purely structural information about the metabolic network.

q-bio.MN↗
arXiv2010

STDP-driven networks and the \emph{C. elegans} neuronal network

We study the dynamics of the structure of a formal neural network wherein the strengths of the synapses are governed by spike-timing-dependent plasticity (STDP). For properly chosen input signals, there exists a steady state with a residual network. We compare the motif profile of such a network with that of a real neural network of \emph{C. elegans} and identify robust qualitative similarities. In particular, our extensive numerical simulations show that this STDP-driven resulting network is robust under variations of the model parameters.

q-bio.NC↗
arXiv2010

Genotype networks in metabolic reaction spaces

Background: A metabolic genotype comprises all chemical reactions an organism can catalyze via enzymes encoded in its genome. A genotype is viable in a given environment if it is capable of producing all biomass components the organism needs to survive and reproduce. Previous work has focused on the properties of individual genotypes while little is known about how genome-scale metabolic networks with a given function can vary in their reaction content. Results: We here characterize spaces of such genotypes. Specifically, we study metabolic genotypes whose phenotype is viability in minimal chemical environments that differ in their sole carbon sources. We show that regardless of the number of reactions in a metabolic genotype, the genotypes of a given phenotype typically form vast, connected, and unstructured sets -- genotype networks -- that nearly span the whole of genotype space. The robustness of metabolic phenotypes to random reaction removal in such spaces has a narrow distribution with a high mean. Different carbon sources differ in the number of metabolic genotypes in their genotype network; this number decreases as a genotype is required to be viable on increasing numbers of carbon sources, but much less than if metabolic reactions were used independently across different chemical environments. Conclusions: Our work shows that phenotype-preserving genotype networks have generic organizational properties and that these properties are insensitive to the number of reactions in metabolic genotypes.

q-bio.MN↗
arXiv2009

Conservation of high-flux backbone in alternate optimal and near-optimal flux distributions of metabolic networks

Constraint-based flux balance analysis (FBA) has proven successful in predicting the flux distribution of metabolic networks in diverse environmental conditions. FBA finds one of the alternate optimal solutions that maximizes the biomass production rate. Almaas et al have shown that the flux distribution follows a power law, and it is possible to associate with most metabolites two reactions which maximally produce and consume a give metabolite, respectively. This observation led to the concept of high-flux backbone (HFB) in metabolic networks. In previous work, the HFB has been computed using a particular optima obtained using FBA. In this paper, we investigate the conservation of HFB of a particular solution for a given medium across different alternate optima and near-optima in metabolic networks of E. coli and S. cerevisiae. Using flux variability analysis (FVA), we propose a method to determine reactions that are guaranteed to be in HFB regardless of alternate solutions. We find that the HFB of a particular optima is largely conserved across alternate optima in E. coli, while it is only moderately conserved in S. cerevisiae. However, the HFB of a particular near-optima shows a large variation across alternate near-optima in both organisms. We show that the conserved set of reactions in HFB across alternate near-optima has a large overlap with essential reactions and reactions which are both uniquely consuming (UC) and uniquely producing (UP). Our findings suggest that the structure of the metabolic network admits a high degree of redundancy and plasticity in near-optimal flow patterns enhancing system robustness for a given environmental condition.

q-bio.MN↗
arXiv2009

Preferential attachment renders an evolving network of populations robust against crashes

We study a model for the evolution of chemical species under a combination of population dynamics on a short time scale and a selection mechanism on a longer time scale. Least fit nodes are replaced by new nodes whose links are attached to the nodes of the given network via preferential attachment. In contrast to a random attachment of newly incoming nodes that was used in previous work, this preferential attachment mechanism accelerates the generation of a so-called autocatalytic set after a start from a random geometry and the growth of this structure until it saturates in a stationary phase in which the whole system is an autocatalytic set. Moreover, the system in the stationary phase becomes much more stable against crashes in the population size as compared to random attachment. We explain in detail in terms of graph theoretical notions which structure of the resulting network is responsible for this stability. Essentially it is a very dense core with many loops and less nodes playing the role of a keystone that prevents the system against crashes almost completely.

nlin.AO↗
arXiv2008

Study of the structure and dynamics of complex biological networks

In this thesis, we have studied the large scale structure and system level dynamics of certain biological networks using tools from graph theory, computational biology and dynamical systems. We study the structure and dynamics of large scale metabolic networks inside three organisms, Escherichia coli, Saccharomyces cerevisiae and Staphylococcus aureus. We also study the dynamics of the large scale genetic network controlling E. coli metabolism. We have tried to explain the observed system level dynamical properties of these networks in terms of their underlying structure. Our studies of the system level dynamics of these large scale biological networks provide a different perspective on their functioning compared to that obtained from purely structural studies. Our study also leads to some new insights on features such as robustness, fragility and modularity of these large scale biological networks. We also shed light on how different networks inside the cell such as metabolic networks and genetic networks are interrelated to each other.

q-bio.MN↗
arXiv2007

The regulatory network of E. coli metabolism as a boolean dynamical system exhibits both homeostasis and flexibility of response

Elucidating the architecture and dynamics of large scale genetic regulatory networks of cells is an important goal in systems biology. We study the system level dynamical properties of the genetic network of Escherichia coli that regulates its metabolism, and show how its design leads to biologically useful cellular properties. Our study uses the database (Covert et al., Nature 2004) containing 583 genes and 96 external metabolites which describes not only the network connections but also the boolean rule at each gene node that controls the switching on or off of the gene as a function of its inputs. We have studied how the attractors of the boolean dynamical system constructed from this database depend on the initial condition of the genes and on various environmental conditions corresponding to buffered minimal media. We find that the system exhibits homeostasis in that its attractors, that turn out to be fixed points or low period cycles, are highly insensitive to initial conditions or perturbations of gene configurations for any given fixed environment. At the same time the attractors show a wide variation when external media are varied implying that the system mounts a highly flexible response to changed environmental conditions. The regulatory dynamics acts to enhance the cellular growth rate under changed media. Our study shows that the reconstructed genetic network regulating metabolism in {\it E. coli} is hierarchical, modular, and largely acyclic, with environmental variables controlling the root of the hierarchy. This architecture makes the cell highly robust to perturbations of gene configurations as well as highly responsive to environmental changes. The twin properties of homeostasis and response flexibility are achieved by this dynamical system even though it is not close to the edge of chaos.

q-bio.MN↗
arXiv2005

Low Degree Metabolites Explain Essential Reactions and Enhance Modularity in Biological Networks

Recently there has been a lot of interest in identifying modules at the level of genetic and metabolic networks of organisms, as well as in identifying single genes and reactions that are essential for the organism. A goal of computational and systems biology is to go beyond identification towards an explanation of specific modules and essential genes and reactions in terms of specific structural or evolutionary constraints. In the metabolic networks of E. coli, S. cerevisiae and S. aureus, we identified metabolites with a low degree of connectivity, particularly those that are produced and/or consumed in just a single reaction. Using FBA we also determined reactions essential for growth in these metabolic networks. We find that most reactions identified as essential in these networks turn out to be those involving the production or consumption of low degree metabolites. Applying graph theoretic methods to these metabolic networks, we identified connected clusters of these low degree metabolites. The genes involved in several operons in E. coli are correctly predicted as those of enzymes catalyzing the reactions of these clusters. We independently identified clusters of reactions whose fluxes are perfectly correlated. We find that the composition of the latter `functional clusters' is also largely explained in terms of clusters of low degree metabolites in each of these organisms. Our findings mean that most metabolic reactions that are essential can be tagged by one or more low degree metabolites. Those reactions are essential because they are the only ways of producing or consuming their respective tagged metabolites. Furthermore, reactions whose fluxes are strongly correlated can be thought of as `glued together' by these low degree metabolites.

q-bio.MN↗
arXiv2005

Evidence of a universal power law characterizing the evolution of metabolic networks

Metabolic networks are known to be scale free but the evolutionary origin of this structural property is not clearly understood. One way of studying the dynamical process is to compare the metabolic networks of species that have arisen at different points in evolution and hence are related to each other to varying extents. We have compared the reaction sets of each metabolite across and within 15 groups of species. For a given pair of species and a given metabolite, the number $Δk$ of reactions of the metabolite that appear in the metabolic network of only one species and not the other is a measure of the distance between the two networks. While $Δk$ is small within groups of related species and large across groups, we find its probability distribution to be $\sim (Δk)^{-γ'}$ where $γ'$ is a universal exponent that is the same within and across groups. This exponent equals, upto statistical uncertainties, the exponent $γ$ in the scale free degree distribution $\sim k^{-γ}$. We argue that this, as well as our finding that $Δk$ is approximately linearly correlated with the degree $k$ of the metabolite, is evidence of a `proportionate change' process in evolution. We also discuss some molecular mechanisms that might be responsible for such an evolutionary process.

q-bio.MN↗