arXiv subjects

Varun Giri

Publications and source records attributed to Varun Giri.

5 recordsLinked to original sources

arXiv2013

Modeling pre-biotic self-organization: The chemical dynamics of autocatalytic networks

In this thesis we present a mathematical model describing the population dynamics of molecules in an artificial chemistry where large molecules can be produced by successive ligation of pairs of smaller molecules. The chemistry contains a large number of spontaneous reactions of which a small subset could be catalyzed by molecules produced in the chemistry with varying catalytic strengths. We show ACSs, if present in the catalytic network, can focus the resources of the system into a sparse set of molecules. ACSs can produce a bistability in the population dynamics and, in particular, steady states wherein the ACS molecules dominate the population, i.e., have higher concentrations compared to the rest of molecules in the chemistry (background). In this thesis we attempt to address two main questions: First, under what circumstances do molecules belonging to the ACSs dominate over the background, and second, starting from an initial condition that does not contain good catalysts, can a sparse set of large molecules (containing several tens or a few hundred monomers) that are good catalysts arise and be maintained in the system at concentrations significantly above the background? We show that if an ACS catalyzed by large molecules contains within it (or partially overlaps with) a smaller ACS catalyzed by smaller molecules (referred to as a `nested ACS' structure), the catalytic strength required for the large ACS to dominate comes down significantly. We show that when the network contains a cascade of nested ACSs with the catalytic strengths of molecules increasing gradually with their size, a sparse subset of molecules including some very large molecules can come to dominate the system.

nlin.AO↗

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

The origin of large molecules in primordial autocatalytic reaction networks

Large molecules such as proteins and nucleic acids are crucial for life, yet their primordial origin remains a major puzzle. The production of large molecules, as we know it today, requires good catalysts, and the only good catalysts we know that can accomplish this task consist of large molecules. Thus the origin of large molecules is a chicken and egg problem in chemistry. Here we present a mechanism, based on autocatalytic sets (ACSs), that is a possible solution to this problem. We discuss a mathematical model describing the population dynamics of molecules in a stylized but prebiotically plausible chemistry. Large molecules can be produced in this chemistry by the coalescing of smaller ones, with the smallest molecules, the `food set', being buffered. Some of the reactions can be catalyzed by molecules within the chemistry with varying catalytic strengths. Normally the concentrations of large molecules in such a scenario are very small, diminishing exponentially with their size. ACSs, if present in the catalytic network, can focus the resources of the system into a sparse set of molecules. ACSs can produce a bistability in the population dynamics and, in particular, steady states wherein the ACS molecules dominate the population. However to reach these steady states from initial conditions that contain only the food set typically requires very large catalytic strengths, growing exponentially with the size of the catalyst molecule. We present a solution to this problem by studying `nested ACSs', a structure in which a small ACS is connected to a larger one and reinforces it. We show that when the network contains a cascade of nested ACSs with the catalytic strengths of molecules increasing gradually with their size (e.g., as a power law), a sparse subset of molecules including some very large molecules can come to dominate the system.

nlin.AO↗

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↗