arXiv subjects

Praful Gagrani

Publications and source records attributed to Praful Gagrani.

11 recordsLinked to original sources

arXiv2026

Topological bounds on the dynamical growth rate of chemical reaction networks

Growth and decay are system-level properties of chemical reaction networks (CRNs) relevant from prebiotic chemistry to cellular metabolism. Their properties are typically analyzed through the kinetics of particular models, which requires specification of the full set of kinetic laws and parameters. In this work, assuming a steady balanced-growth regime, we derive stoichiometry-based constraints on the growth (or shrinkage) rate. The resulting bounds are controlled by a topological quantity, the maximum amplification factor, defined via a von Neumann max-min problem over feasible fluxes as illustrated by numerical tests on random-network ensembles of CRNs. We argue for the relevance of our results in the context of origins of life studies and the design of synthetic chemical reaction networks.

q-bio.MN↗

arXiv2025

Mathematical Analysis for a Class of Stochastic Copolymerization Processes

We study a stochastic model of a copolymerization process that has been extensively investigated in the physics literature. The main questions of interest include: (i) what are the criteria for transience, null recurrence, and positive recurrence in terms of the system parameters; (ii) in the transient regime, what are the limiting fractions of the different monomer types; and (iii) in the transient regime, what is the speed of growth of the polymer? Previous studies in the physics literature have addressed these questions using heuristic methods. Here, we utilize rigorous mathematical arguments to derive the results from the physics literature. Moreover, the techniques developed allow us to generalize to the copolymerization process with finitely many monomer types. We expect that the mathematical methods used and developed in this work will also enable the study of even more complex models in the future.

math.PR↗

arXiv2025

Thermodynamic ranking of pathways in reaction networks

One of the puzzles left open by energetic analyses of irreversible stochastic processes is that boundary conditions that prevent the performance of work or the dissipation of heat make no contribution to an entropy-production budget; yet we see ubiquitously in both engineered and living systems that both transient and persistent energy costs are paid to create and maintain such boundaries. We wish to know whether there are inherent limits for the costs of such phenomena, and common units in which those can be traded off against more familiar costs measured in terms of heat dissipation. We give this problem a concrete framing in the context of CRNs, for the problem of extracting a topologically restricted pathway from a larger distributed network, through activation of some reactions and selective elimination of others. We define a thermodynamic cost function for pathways derived from large-deviation theory of stochastic CRNs, which decomposes into two components: an ongoing maintenance cost to sustain a NESS, and a restriction cost, quantifying the ongoing improbability of neutralizing reactions outside the specified pathway. Applying this formalism to detailed-balanced CRNs in the linear response regime, we make use of their formal equivalence to electrical circuits. We prove that the resistance of a CRN decreases as reactions are added that support the throughput current, and that the maintenance cost, the restriction cost, and the thermodynamic cost of nested pathways are bounded below by those of their hosting network. For small CRNs, we show how catalytic and inhibitory mechanisms can drastically alter pathway costs, enabling unfavorable pathways to become favorable and approach the cost of the hosting pathway. Our results provide insights into the thermodynamic principles governing open CRNs and offer a foundation for understanding the evolution of metabolic networks.

q-bio.MN↗

arXiv2024

Identifying Self-Amplifying Hypergraph Structures through Mathematical Optimization

In this paper, we introduce the concept of self-amplifying structures for hypergraphs, positioning it as a key element for understanding propagation and internal reinforcement in complex systems. To quantify this phenomenon, we define the maximal amplification factor, a metric that captures how effectively a subhypergraph contributes to its own amplification. We then develop an optimization-based methodology to compute this measure. Building on this foundation, we tackle the problem of identifying the subhypergraph maximizing the amplification factor, formulating it as a mixed-integer nonlinear programming (MINLP) problem. To solve it efficiently, we propose an exact iterative algorithm with proven convergence guarantees. In addition, we report the results of extensive computational experiments on realistic synthetic instances, demonstrating both the relevance and effectiveness of the proposed approach. Finally, we present a case study on chemical reaction networks, including the Formose reaction and E. coli core metabolism, where our framework successfully identifies known and novel autocatalytic subnetworks, highlighting its practical relevance to systems chemistry and biology.

math.OC↗

arXiv2024

The evolution of complexity and the transition to biochemical life

While modern physics and biology satisfactorily explain the passage from the Big Bang to the formation of Earth and the first cells to present-day life, respectively, the origins of biochemical life still remain an open question. Since life, as we know it, requires extremely long genetic polymers, any answer to the question must explain how an evolving system of polymers of ever-increasing length could come about on a planet that otherwise consisted only of small molecular building blocks. In this work, we show that, under realistic constraints, an abstract polymer model can exhibit dynamics such that attractors in the polymer population space with a higher average polymer length are also more probable. We generalize from the model and formalize the notions of complexity and evolution for chemical reaction networks with multiple attractors. The complexity of a species is defined as the minimum number of reactions needed to produce it from a set of building blocks, which in turn is used to define a measure of complexity for an attractor. A transition between attractors is considered to be a progressive evolution if the attractor with the higher probability also has a higher complexity. In an environment where only monomers are readily available, the attractor with a higher average polymer length is more complex. Thus, our abstract polymer model can exhibit progressive evolution for a range of thermodynamically plausible rate constants. We also formalize criteria for open-ended and historically-contingent evolution and explain the role of autocatalysis in obtaining them. Our work provides a basis for searching for prebiotically plausible scenarios in which long polymers can emerge and yield populations with even longer polymers.

q-bio.PE↗

arXiv2024

An Open-Ended Approach to Understanding Local, Emergent Conservation Laws in Biological Evolution

While fields like Artificial Life have made huge strides in quantifying the mechanisms that distinguish living systems from non-living ones, particular mechanisms remain difficult to reproduce in silico. Known as open-endedness, we've been successful in finding mechanisms that generate new states, but have been less successful in finding mechanisms that generate new rules. Here, we weigh whether or not analyzing the effects of internal and external system constraints on a system's dynamics would be a fruitful avenue to understanding open-endedness. We discuss the connection between physical constraints and the ways that the system can physically reach possible states while those constraints are present. It seems that the physical constraints that define biological objects (and dynamics) are maintained by dynamics that occur from within the system. This is in opposition to current modeling approaches where system constraints are maintained externally. We suggest that constraints can be characterized as variables whose values are either completely conserved, quasi-conserved, or conditionally conserved. Regardless of whether or not a constrained variable is a part of the biological object or present in the object's environment, we discuss how the accessible system states under that constraint can lead to local, emergent conservation laws (rules), with examples. Finally, we discuss the possible benefits of formally understanding how system constraints that emerge from within a system lead to system dynamics that can be characterized as new, emergent rules -- particularly for artificial intelligence, hybrid life, embodiment, astrobiology, and more. Understanding how new, local rules might emerge from within the system is crucial for understanding how open-ended systems continually discover new update rules, in addition to continually discovering new states.

physics.bio-ph↗

arXiv2023

Polyhedral geometry and combinatorics of an autocatalytic ecosystem

Developing a mathematical understanding of autocatalysis in reaction networks has both theoretical and practical implications. We review definitions of autocatalytic networks and prove some properties for minimal autocatalytic subnetworks (MASs). We show that it is possible to classify MASs in equivalence classes, and develop mathematical results about their behavior. We also provide linear-programming algorithms to exhaustively enumerate them and a scheme to visualize their polyhedral geometry and combinatorics. We then define cluster chemical reaction networks, a framework for coarse-graining real chemical reactions with positive integer conservation laws. We find that the size of the list of minimal autocatalytic subnetworks in a maximally connected cluster chemical reaction network with one conservation law grows exponentially in the number of species. We end our discussion with open questions concerning an ecosystem of autocatalytic subnetworks and multidisciplinary opportunities for future investigation.

q-bio.MN↗

arXiv2022

Action Functional Gradient Descent algorithm for estimating escape paths in Stochastic Chemical Reaction Networks

We first derive the Hamilton-Jacobi theory underlying continuous-time Markov processes, and then use the construction to develop a variational algorithm for estimating escape (least improbable or first passage) paths for a generic stochastic chemical reaction network that exhibits multiple fixed points. The design of our algorithm is such that it is independent of the underlying dimensionality of the system, the discretization control parameters are updated towards the continuum limit, and there is an easy-to-calculate measure for the correctness of its solution. We consider several applications of the algorithm and verify them against computationally expensive means such as the shooting method and stochastic simulation. While we employ theoretical techniques from mathematical physics, numerical optimization and chemical reaction network theory, we hope that our work finds practical applications with an inter-disciplinary audience including chemists, biologists, optimal control theorists and game theorists.

cond-mat.stat-mech↗

arXiv2020

An ecological framework for the analysis of prebiotic chemical reaction networks and their dynamical behavior

It is becoming widely accepted that very early in the origin of life, even before the emergence of genetic encoding, reaction networks of diverse small chemicals might have manifested key properties of life, namely self-propagation and adaptive evolution. To explore this possibility, we formalize the dynamics of chemical reaction networks within the framework of chemical ecosystem ecology. To capture the idea that life-like chemical systems are maintained out of equilibrium by fluxes of energy-rich food chemicals, we model chemical ecosystems in well-mixed containers that are subject to constant dilution by a solution with a fixed concentration of food chemicals. Modelling all chemical reactions as fully reversible, we show that seeding an autocatalytic cycle (AC) with tiny amounts of one or more of its member chemicals results in logistic growth of all member chemicals in the cycle. This finding justifies drawing an instructive analogy between an AC and the population of a biological species. We extend this finding to show that pairs of ACs can show competitive, predator-prey, or mutualistic associations just like biological species. Furthermore, when there is stochasticity in the environment, particularly in the seeding of ACs, chemical ecosystems can show complex dynamics that can resemble evolution. The evolutionary character is especially clear when the network architecture results in ecological precedence (survival of the first), which makes the path of succession historically contingent on the order in which cycles are seeded. For all its simplicity, the framework developed here is helpful for visualizing how autocatalysis in prebiotic chemical reaction networks can yield life-like properties. Furthermore, chemical ecosystem ecology could provide a useful foundation for exploring the emergence of adaptive dynamics and the origins of polymer-based genetic systems.

q-bio.PE↗

arXiv2016

Information Content of the Angular Multipoles of Redshift-Space Galaxy Bispectrum

The redshift-space bispectrum (three point statistics) of galaxies depends on the expansion rate, the growth rate, and geometry of the Universe, and hence can be used to measure key cosmological parameters. In a homogeneous Universe the bispectrum is a function of five variables and unlike its two point statistics counterpart -- the power spectrum, which is a function of only two variables -- is difficult to analyse unless the information is somehow reduced. The most commonly considered reduction schemes rely on computing angular integrals over possible orientations of the bispectrum triangle, thus reducing it to sets of function of only three variables describing the triangle shape. We use Fisher information formalism to study the information loss associated with this angular integration. Without any reduction, the bispectrum alone can deliver constraints on the growth rate parameter $f$ that are better by a factor of $2.5$ compared to the power spectrum, for a sample of luminous red galaxies expected from near future galaxy surveys at a redshift of $z\sim0.65$. At lower redshifts the improvement could be up to a factor of $3$. We find that most of the information is in the azimuthal averages of the first three even multipoles. This suggests that the bispectrum of every configuration can be reduced to just three numbers (instead of a 2D function) without significant loss of cosmologically relevant information.

astro-ph.CO↗

arXiv2016

Optimal Weights For Measuring Redshift Space Distortions in Multi-tracer Galaxy Catalogues

Since the volume accessible to galaxy surveys is fundamentally limited, it is extremely important to analyse available data in the most optimal fashion. One way of enhancing the cosmological information extracted from the clustering of galaxies is by weighting the galaxy field. The most widely used weighting schemes assign weights to galaxies based on the average local density in the region (FKP weights) and their bias with respect to the dark matter field (PVP weights). They are designed to minimize the fractional variance of the galaxy power-spectrum. We demonstrate that the currently used bias dependent weighting scheme can be further optimized for specific cosmological parameters. We develop a procedure for computing the optimal weights and test them against mock catalogues for which the values of all fitting parameters, as well as the input power-spectrum are known. We show that by applying these weights to the joint power-spectrum of Emission Line Galaxies and Luminous Red Galaxies from the Dark Energy Spectroscopic Instrument survey, the variance in the measured growth rate parameter can be reduced by as much as 36 per cent.

astro-ph.CO↗