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Kabir Husain

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Biological Physics cond-mat.stat-mech Populations and Evolution cond-mat.soft Molecular Networks Quantitative Methods

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preprint2026arXiv

Conditioning as a route to stereotyped behavior in growing populations

Biological systems perform complex multi-step processes in a reproducible way despite underlying stochasticity. The standard explanation is micromanagement by molecular machinery that recognizes and corrects specific errors. Here we study conditioning, a qualitatively different strategy in which attempts failing a coarse criterion are destroyed and do not leave a physical record. The surviving, i.e., conditioned, ensemble is narrower and therefore more ordered. We model conditioning through stochastic resets in a ''socks-before-shoes'' model of a growing population, where $n$ actions must be completed in any order to replicate and any replication attempt not finished by a threshold time is discarded. We find that resets impose hierarchical temporal ordering of the $n$ actions without microscopic control over which action happens when. When disorder carries a sufficient time penalty, this ordering is free: the fastest-growing population is automatically the most ordered, with no direct selection for order required. Save points, at which verified progress is preserved across resets, allow conditioning to scale to complex multi-step processes. Conditioning provides a minimal route to reliable behavior, requiring only a clock rather than molecular machinery that recognizes specific errors. For the right class of processes, it pays for itself.

preprint2022arXiv

Robust Molecular Computation by Active Mechanics

The living cell expends energetic and material resources to reliably process information from its environment. To do so, it utilises unreliable molecular circuitry that is subject to thermal and other fluctuations. Here, we argue that active, physical processes can provide error correcting mechanisms for information processing. We analyse a model in which fluctuating receptor activation induces contractile stresses that recruit further receptors, dynamically controlling resource usage and accuracy. We show that this active scheme can outperform passive, static clusters (as formed, for instance, by protein crosslinking). We consider simple binary environments, informative decision trees, and chemical computations; in each case, active stresses serve to contextually build signalling platforms that dynamically suppress error and allows for robust cellular computation.

preprint2020arXiv

Proofreading through spatial gradients

Key enzymatic processes in biology use the nonequilibrium error correction mechanism called kinetic proofreading to enhance their specificity. Kinetic proofreading typically requires several dedicated structural features in the enzyme, such as a nucleotide hydrolysis site and multiple enzyme-substrate conformations that delay product formation. Such requirements limit the applicability and the adaptability of traditional proofreading schemes. Here, we explore an alternative conceptual mechanism of error correction that achieves delays between substrate binding and subsequent product formation by having these events occur at distinct physical locations. The time taken by the enzyme-substrate complex to diffuse from one location to another is leveraged to discard wrong substrates. This mechanism does not require dedicated structural elements on the enzyme, making it easier to overlook in experiments but also making proofreading tunable on the fly. We discuss how tuning the length scales of enzyme or substrate concentration gradients changes the fidelity, speed and energy dissipation, and quantify the performance limitations imposed by realistic diffusion and reaction rates in the cell. Our work broadens the applicability of kinetic proofreading, and sets the stage for the study of spatial gradients as a possible route to specificity.

preprint2019arXiv

Tuning environmental timescales to evolve and maintain generalists

Natural environments can present diverse challenges, but some genotypes remain fit across many environments. Such `generalists' can be hard to evolve, out-competed by specialists fitter in any particular environment. Here, inspired by the search for broadly-neutralising antibodies during B-cell affinity maturation, we demonstrate that environmental changes on an intermediate timescale can reliably evolve generalists, even when faster or slower environmental changes are unable to do so. We find that changing environments on timescales comparable to evolutionary transients in a population enhances the rate of evolving generalists from specialists, without enhancing the reverse process. The yield of generalists is further increased in more complex dynamic environments, such as a `chirp' of increasing frequency. Our work offers design principles for how non-equilibrium fitness `seascapes' can dynamically funnel populations to genotypes unobtainable in static environments.

preprint2016arXiv

Efficiency of a Stochastic Search with Punctual and Costly Restarts

The mean completion time of a stochastic process may be rendered finite and minimised by a judiciously chosen restart protocol, which may either be stochastic or deterministic. Here we study analytically an arbitrary stochastic search subject to an arbitrary restart protocol, each characterised by a distribution of waiting times. By a direct enumeration of paths we construct the joint distribution of completion time and restart number, in a form amenable to analytical evaluation or quadrature; thereby we optimise the search over both time and potentially costly restart events. Analysing the effect of a punctual, i.e. almost deterministic, restart, we demonstrate that the optimal completion time always increases proportionately with the variance of the restart distribution; the constant of proportionality depends only on the search process. We go on to establish simple bounds on the optimal restart time. Our results are relevant to the analysis and rational design of efficient and optimal restart protocols.