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During cell division, the spindle generates force to move chromosomes. In mammals, microtubule bundles called kinetochore-fibers (k-fibers) attach to and segregate chromosomes. To do so, k-fibers must be robustly anchored to the dynamic spindle. We previously developed microneedle manipulation to mechanically challenge k-fiber anchorage, and observed spatially distinct response features revealing the presence of heterogeneous anchorage (Suresh et al., 2020). How anchorage is precisely spatially regulated, and what forces are necessary and sufficient to recapitulate the k-fiber’s response to force remain unclear. Here, we develop a coarse-grained k-fiber model and combine with manipulation experiments to infer underlying anchorage using shape analysis. By systematically testing different anchorage schemes, we find that forces solely at k-fiber ends are sufficient to recapitulate unmanipulated k-fiber shapes, but not manipulated ones for which lateral anchorage over a 3 μm length scale near chromosomes is also essential. Such anchorage robustly preserves k-fiber orientation near chromosomes while allowing pivoting around poles. Anchorage over a shorter length scale cannot robustly restrict pivoting near chromosomes, while anchorage throughout the spindle obstructs pivoting at poles. Together, this work reveals how spatially regulated anchorage gives rise to spatially distinct mechanics in the mammalian spindle, which we propose are key for function.

Key enzymatic processes use the nonequilibrium error correction mechanism called kinetic proofreading to enhance their specificity. The applicability of traditional proofreading schemes, however, is limited because they typically require dedicated structural features in the enzyme, such as a nucleotide hydrolysis site or multiple intermediate conformations. Here, we explore an alternative conceptual mechanism that achieves error correction by having substrate binding and subsequent product formation 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 have the typical structural requirements, making it easier to overlook in experiments. We discuss how the length scales of molecular gradients dictate proofreading performance, and quantify the limitations imposed by realistic diffusion and reaction rates. Our work broadens the applicability of kinetic proofreading and sets the stage for studying spatial gradients as a possible route to specificity.

Active matter systems can generate highly ordered structures, avoiding equilibrium through the consumption of energy by individual constituents. How the microscopic parameters that characterize the active agents are translated to the observed mesoscopic properties of the assembly has remained an open question. These active systems are prevalent in living matter; for example, in cells, the cytoskeleton is organized into structures such as the mitotic spindle through the coordinated activity of many motor proteins walking along microtubules. Here, we investigate how the microscopic motor-microtubule interactions affect the coherent structures formed in a reconstituted motor-microtubule system. This question is of deeper evolutionary significance as we suspect motor and microtubule type contribute to the shape and size of resulting structures. We explore key parameters experimentally and theoretically, using a variety of motors with different speeds, processivities, and directionalities. We demonstrate that aster size depends on the motor used to create the aster, and develop a model for the distribution of motors and microtubules in steady-state asters that depends on parameters related to motor speed and processivity. Further, we show that network contraction rates scale linearly with the single-motor speed in quasi-one-dimensional contraction experiments. In all, this theoretical and experimental work helps elucidate how microscopic motor properties are translated to the much larger scale of collective motor-microtubule assemblies.

Predicting how interactions between transcription factors and regulatory DNA sequence dictate rates of transcription and, ultimately, drive developmental outcomes remains an open challenge in physical biology. Using stripe 2 of the even-skipped gene in Drosophila embryos as a case study, we dissect the regulatory forces underpinning a key step along the developmental decision-making cascade: the generation of cytoplasmic mRNA patterns via the control of transcription in individual cells. Using live imaging and computational approaches, we found that the transcriptional burst frequency is modulated across the stripe to control the mRNA production rate. However, we discovered that bursting alone cannot quantitatively recapitulate the formation of the stripe and that control of the window of time over which each nucleus transcribes even-skipped plays a critical role in stripe formation. Theoretical modeling revealed that these regulatory strategies (bursting and the time window) respond in different ways to input transcription factor concentrations, suggesting that the stripe is shaped by the interplay of 2 distinct underlying molecular processes.

Physical biology offers powerful tools for quantitatively dissecting the various aspects of cellular life that one cannot attribute to inanimate matter. Signature examples of living matter include adaptation, self-organization, and division. In this thesis, we explore different interconnected facets of these processes using statistical mechanics, nonequilibrium thermodynamics, and biophysical modeling.One of the key mechanisms underlying physiological and evolutionary adaptation is allosteric regulation. It allows cells to dynamically respond to changes in the state of the environment often expressed through altered levels of different environmental cues. The first thread of our work is dedicated to exploring the combinatorial diversity of responses available to allosteric proteins that are subject to multiligand regulation. We demonstrate that proteins characterized through the MonodWyman-Changeux model of allostery and operating at thermodynamic equilibrium are capable of eliciting a wide range of response behaviors which include the kinds known from the field of digital circuits (e.g., NAND logic response), as well as more sophisticated computations such as ratiometric sensing.Despite the fact that biomolecules at thermodynamic equilibrium are able to orchestrate a variety of fascinating behaviors, the cell is ultimately ‘alive’ because it constantly metabolizes nutrients and generates energy to drive functions that cannot be sustained in the absence of energy consumption. One prominent example of such a function is nonequilibrium error correction present in high-fidelity processes such as protein synthesis, DNA replication, or pathogen recognition. We begin the second thread of our work by providing a conceptual understanding of the prevailing mechanism used in explaining this high-fidelity behavior, namely that of kinetic proofreading. Specifically, we develop an allostery-based mechanochemical model of a kinetic proofreader where chemical driving is replaced with a mechanical engine with tunable knobs which allow modulating the amount of dissipation in a transparent way. We demonstrate how varying levels of error correction can be attained at different regimes of dissipation and offer intuitive interpretations for the conditions required for efficient biological proofreading.We then extend the notion of error correction to equilibrium enzymes not endowed with structural features typically required for proofreading. We show that, under physiological conditions, purely diffusing enzymes can take advantage of the existing nonequilibrium organization of their substrates in space and enhance the fidelity of catalysis. Our proposed mechanism called spatial proofreading offers a novel perspective on spatial structures and compartmentalization in cells as a route to specificity.In the last thread of the thesis, we make a transition from molecular-scale studies to the mesoscopic scale, and explore the principles of self-organization in nonequilibrium structures formed in reconstituted microtubule-motor mixtures. In particular, we develop a theoretical framework that predicts the spatial distribution of kinesin motors in radially symmetric microtubule asters formed under various conditions using optogenetic control. The model manages to accurately recapitulate the experimentally measured motor profiles through effective parameters that are specific for each kind of kinesin motor used. Our theoretical work of rigorously assessing the motor distribution therefore offers an avenue for understanding the link between the microscopic motor properties (e.g., processivity or binding affinity) and the large-scale structures they create.In all, the thesis encompasses a series of case studies with shared themes of allostery and nonequilibrium, highlighting the capacity of living matter to perform remarkable tasks inaccessible to nonliving materials.

In a recent PNAS publication, Kirby and Zilman studied kinetic proofreading for receptor signaling and argued that having more proofreading steps does not generally improve ligand discrimination when stochastic effects are taken into account. In their analysis, however, the authors made an implicit assumption about a fixed discrimination time, which is not always warranted. We show that when the discrimination time is allowed to vary in order to maintain a fixed level of signaling activity, the proofreading performance can, in fact, uniformly improve with the number of steps. We therefore call for a comprehensive study of the interplay between discrimination time, discrimination accuracy, and signaling activity, where the two seemingly contradictory results will be slices of the trade-off surface along different axes.

Kinetic proofreading is an error correction mechanism present in the processes of the central dogma and beyond, and typically requires the free energy of nucleotide hydrolysis for its operation. Though the molecular players of many biological proofreading schemes are known, our understanding of how energy consumption is managed to promote fidelity remains incomplete. In our work, we introduce an alternative conceptual scheme called 'the piston model of proofreading' where enzyme activation through hydrolysis is replaced with allosteric activation achieved through mechanical work performed by a piston on regulatory ligands. Inspired by Feynman's ratchet and pawl mechanism, we consider a mechanical engine designed to drive the piston actions powered by a lowering weight, whose function is analogous to that of ATP synthase in cells. Thanks to its mechanical design, the piston model allows us to tune the 'knobs' of the driving engine and probe the graded changes and trade-offs between speed, fidelity and energy dissipation. It provides an intuitive explanation of the conditions necessary for optimal proofreading and reveals the unexpected capability of allosteric molecules to beat the Hopfield limit of fidelity by leveraging the diversity of states available to them. The framework that we built for the piston model can also serve as a basis for additional studies of driven biochemical systems.

In a recent PNAS publication, Kirby and Zilman argued that when stochasticity is taken into account, having more steps in kinetic proofreading generally does not improve the discrimination of different receptor-binding ligands based on the counts of signaling molecules produced. However, their conclusion is based on a major technical error that, once corrected, contradicts their main conclusion. Also, throughout their analysis, the authors made the implicit assumption that discrimination time is fixed. We argue below that, for a fuller understanding, kinetic proofreading for ligand discrimination should be studied in the context of speed-accuracy tradeoffs.Competing Interest StatementThe authors have declared no competing interest.

In biochemical systems the Michaelis-Menten (MM) scheme is one of the best-known models of the enzyme- catalyzed kinetics. In the academic literature the MM approximation has been thoroughly studied in the context of differential equation models. At the level of the cell, however, molecular fluctuations have many important consequences, and thus, a stochastic investigation of the MM scheme is often necessary. In their work Barik et al. [Biophysical Journal, 95, 3563-3574, (2008)] presented a stochastic approximation of the MM scheme. They suggested a substitution of the propensity function in the reduced master equation with the total quasi-steady- state approximation (tQSSA) rate. The justification of the substitution, however, was provided for a special case only and did not cover the whole parameter domain of the tQSSA. In this manuscript we present a derivation of the stochastic tQSSA that is valid for the entire tQSSA parameter domain.

During cell division, the spindle generates force to move chromosomes. In mammals, microtubule bundles called kinetochore-fibers (k-fibers) attach to and segregate chromosomes. To do so, k-fibers must be robustly anchored to the dynamic spindle. We previously developed microneedle manipulation to mechanically challenge k-fiber anchorage, and observed spatially distinct response features revealing the presence of heterogeneous anchorage (Suresh et al. 2020). How anchorage is precisely spatially regulated, and what forces are necessary and sufficient to recapitulate the k-fiber's response to force remain unclear. Here, we develop a coarse-grained k-fiber model and combine with manipulation experiments to infer underlying anchorage using shape analysis. By systematically testing different anchorage schemes, we find that forces solely at k-fiber ends are sufficient to recapitulate unmanipulated k-fiber shapes, but not manipulated ones for which lateral anchorage over a 3 μm length scale near chromosomes is also essential. Such anchorage robustly preserves k-fiber orientation near chromosomes while allowing pivoting around poles. Anchorage over a shorter length scale cannot robustly restrict pivoting near chromosomes, while anchorage throughout the spindle obstructs pivoting at poles. Together, this work reveals how spatially regulated anchorage gives rise to spatially distinct mechanics in the mammalian spindle, which we propose are key for function. Competing Interest Statement The authors have declared no competing interest.