Proceedings of the National Academy of Sciences

Cyanobacteria are leading biomass producers of the ocean whose ecological success relies on their ability to respond to dynamic availability of nutrients like CO2 and nitrogen, which require distinct adaptive mechanisms. To survive nitrogen deprivation, cyanobacteria undergo a reversible transition to a dormant mode. Under low CO2 levels, a CO2 concentrating mechanism (CCM) supports their CO2 fixation. While the CCM and nitrogen assimilation have been shown to share some regulatory pathways, how the CCM impacts the response to nitrogen deprivation remains underexplored. In this study, by using mutants of the coastal cyanobacteria Synechococcus sp. PCC 7002 lacking a CCM component, we show that the high rate of carbon fixation mediated by the CCM tunes the speed of the nitrogen deprivation response in {beta}-cyanobacteria. We first show that CCM mutants are deficient in inducing their typical nitrogen deprivation response under atmospheric CO2. However, at higher CO2 concentrations, the CCM mutants induce the nitrogen deprivation response. By combining Rubisco kinetics modeling with measurement of the response speed to nitrogen in various CO2 concentrations, we show that the speed of the nitrogen deprivation response increases linearly with Rubiscos carboxylation rate. We further reveal that the regulation of nitrogen response by the CCM is also present in the distantly related freshwater cyanobacteria Synechococcus elongatus PCC 7942, suggesting a widespread role of this regulation across {beta}-cyanobacteria. This study demonstrates that CO2 fixation by the cyanobacterial CCM is a key regulator of the nitrogen deprivation response, favoring a rapid response to dynamic environments.

Aging is characterized by progressive functional decline, yet why such decline is observed broadly across living systems remains unclear. While molecular and cellular mechanisms describe how aging progresses, they do not explain why functional decline should arise as a natural consequence of living organization. Here, we show that aging naturally emerges from three general features of life: unavoidable damage, turnover-mediated maintenance, and the energetic constraint of turnover. We develop a hierarchical damage-turnover model in which component-level damage and energetically constrained turnover jointly determine whole-system performance. In the model, damage stochastically converts functional components into non-functional components, whereas turnover restores component performance at a rate coupled to whole-system performance. Analytical and Monte Carlo analyses reveal two regimes: a non-aging regime, in which performance remains finite, and an aging regime, in which performance progressively collapses toward zero. Performance-independent turnover always maintains a positive steady state, whereas performance-dependent turnover generates irreversible decline when reduced performance weakens maintenance capacity. Stochastic fluctuations further promote collapse near the transition boundary, even when deterministic analysis predicts a nonzero steady state. These results indicate that unavoidable damage and energetically constrained turnover are sufficient to generate aging-like decline, providing a minimal theoretical explanation for long-term irreversibility in biological systems.

Cancer progression is increasingly understood as an evolutionary process shaped not only by competition but also by cooperative interactions including those mediated through diffusible "public goods" (PGs). Classical evolutionary game theory predicts that PG-producing (altruistic) subclones cannot invade well-mixed populations of non-producers, creating a paradox given their observed emergence in tumors. Here, we resolve this contradiction by combining stochastic spatial simulations with an analytically tractable Moran model to study the invasion dynamics of PG-producing cells in structured populations. Starting from a single producer cell, we explicitly model stochastic PG secretion, diffusion, binding/unbinding, and cell proliferation across biologically relevant parameter ranges. We demonstrate that spatial structure fundamentally alters invasion dynamics, enabling PG producers to invade and establish even when production incurs a fitness cost. Both numerical and analytical approaches converge on a key unifying parameter, a characteristic length scale{delta} , that captures the combined effects of diffusivity, binding kinetics, and degradation. This length scale determines the spatial extent of PG availability and thus the selective advantage of producers. We identify distinct regimes: when PGs are localized (small{delta} ), producers preferentially benefit and invasion is likely; when PGs are widely dispersed (large{delta} ), benefits are shared and invasion approaches neutrality or is suppressed by costs. Our results highlight that invasion of cooperative traits is governed by spatially mediated resource localization rather than intrinsic fitness alone. This framework provides a mechanistic basis for understanding the emergence of cooperative subclones in tumors and suggests that modulating biophysical transport properties of signaling molecules could influence tumor evolution, metastasis, and therapeutic resistance.

It was long believed early mammals were nocturnal to avoid interactions with day-active dinosaurs. However, recent evidence indicates many dinosaurs were likely nocturnal, suggesting more complex coevolutionary dynamics prevailed. We simulated coevolution of sleep in a general predator/prey system, using a physiological model. We discovered temporal niche pursuit cycles across evolutionary timescales: prey repeatedly escaping into a novel temporal niche, with predators subsequently invading that niche. We characterized multiple oscillatory patterns for pursuit, involving distinct genetic and phenotypic mechanisms. A low-dimensional model recapitulated the dynamics of the physiological model. These findings reveal rich dynamical processes underlying selection of temporal niche.

Biological phase changes provoked by stress, such as vitrification or gel-sol transitions, enable many organisms, including extremotolerant tardigrades, to enter quiescent states and survive extreme environmental conditions. Protein-driven phase transitions are hypothesized to produce large-scale changes in intracellular viscosity, allowing tardigrades to survive extreme stresses such as desiccation. We report that the tardigrade Hypsibius exemplaris undergoes both large-scale and local increases in intracellular viscosity following exposure to anoxic and hyperosmotic stress. Such dramatic shifts in cellular viscosity would be expected to enhance cellular resilience to physical force. Indeed, we found that tardigrades can survive, behave normally, and reproduce after exposure to the highest simulated hypergravity (HG) achievable in an ultracentrifuge (one million times Earths gravity). In contrast, Caenorhabditis elegans, a similarly sized animal, does not survive these extreme forces owing to loss of cellular integrity. Remarkably, tardigrades frozen during exposure to extreme hypergravitational force show minimal disruption of fine cellular ultrastructure and little evidence of stratification of cellular components whose density varies by nearly a factor of two. Further, exposure to anoxia, hyperosmotic stress, and HG all result in a large increase in reactive oxygen species (ROS), which is required for survival under these extreme environments. Inhibition of NADPH oxidase (NOX) suppresses survival both to HG and hyperosmotic stress. Our findings suggest that intracellular viscosity changes in response to multiple extreme stresses may underlie the resilience of these animals to extraordinary physical stress, and that survival in or recovery from these states relies on ROS signaling via NADPH oxidase. Significance StatementTardigrades are renowned for surviving conditions that are lethal to nearly all other life forms. We reveal two mechanisms that support this resilience: intracellular viscosity changes and NADPH oxidase-mediated ROS signaling. Through direct assessment of the effects of altered cellular material properties, found that tardigrades are resilient to forces up to one million times Earths gravity, establishing them as the most hypergravity-resistant animal currently known.

Cytochrome bc1 is one of the key enzymes of biological energy-conserving systems. In its catalytic Q cycle, the central reaction is the oxidation of quinol (QH2), upon which electrons are directed to two separate cofactor chains. The molecular mechanism of this reaction remains elusive. The canonical model, assuming a sequence of reactions dictated by the equilibrium redox midpoint potentials of cofactors (the 2Fe2S cluster and heme bL), has recently been challenged by a new model of EB derived from quantum mechanical (QM) calculations - EMET (EMergent Electron Transfer) (https://doi.org/10.1021/acsomega.5c13233). These two models predict fundamentally different microstates of the enzyme in which semiquinone (SQ) is formed in the catalytic site (Q o) and also predict different lowest-energy configurations. Here, we test these predictions using EPR spectroscopy on highly concentrated preparations of isolated bacterial cytochrome bc1. We detect SQ spin-coupled to the reduced 2Fe2S cluster (2Fe2Sred), whose population markedly exceeds that of reduced heme bL and forms exclusively in sites containing oxidized heme. We also identify that the lowest-energy configuration corresponds to the state with reduced heme bH (adjacent to heme bL), oxidized heme bL and SQ-2Fe2Sred. These two features are precluded by the canonical model but are consistent with EMET. We conclude that EMET, unlike the canonical EB model, satisfactorily describes the occurrence of stochastic, spin-selective processes that result in electron stoichiometry among hemes b, the 2Fe2S cluster, and SQ at Qo that are observed spectroscopically.

The distribution of fitness effects (DFE) for spontaneous mutations characterizes both an organ-isms evolutionary potential as well as its genomic functions. The DFE of a genome depends on the specific environment in which it is measured, and for microbes a major feature of their environment is the presence of interactions with other species, such as competing for or cross-feeding nutrients. Several recent studies have empirically measured how the DFE of one microbial species changes in the presence of interactions with other species. However, the underlying mechanisms by which this happens, and the statistical patterns they are expected to produce, are unknown. Here we classify two types of statistical changes in the DFE: global changes to the DFE, such as to its mean or variance, and idiosyncratic changes in the fitness of individual mutants, summarized by the correlation of mutant fitness between environments. We first show that both types of effects occur in empirically measured DFEs across a wide range of species and interactions; idiosyncratic effects appear to have a maximum limit and constrain the size of global effects. We then show that a minimal model of an ecological interaction (competition for a single resource) is sufficient to generate both types of effects. Finally, we extend this model to arbitrary quantitative traits to reveal two general mechanisms of how interactions alter the DFE: 1) interactions can globally change fitness by altering the community growth rate, and 2) interactions can idiosyncratically change fitness of individual mutants by altering relative selection on different traits affected by those mutations.

The internal representations of large language models (LLMs) correlate, or "align", with human neural activity during language comprehension. One view holds that this alignment reflects shared sensitivity to statistical patterns in LLMs and humans, while others hold that it reflects, at least in part, the emergence of shared linguistic representations in these systems. Here, we investigate whether hierarchical linguistic composition, a property believed to be fundamental to human language, modulates LLM-brain alignment. To this end, we manipulated syntax, compositional semantics, and associative semantics in English sentences that were presented to both an LLM and human participants during an electroencephalography (EEG) experiment. We matched linguistically manipulated stimuli in predictability, which allows us to tease apart alignment induced by linguistic structure from statistical factors. By comparing LLM-EEG alignment scores that were derived using a linear encoding model across predictability-matched conditions, we evaluate how linguistic manipulations modulate the alignment between human EEG reading data and contextual embeddings extracted word-by-word from the hidden layers of GPT2-XL. Three key patterns emerge: (1) increased alignment for word sequences with syntactic structure, (2) decreased alignment for sentences with compositional semantics, and (3) associative semantics does not modulate alignment. These observed linguistic modulations of LLM-EEG alignment take place above and beyond predictability. Our results indicate that associative semantics is encoded similarly by LLMs and the brain, as are at least some aspects of syntactic structure, while compositional semantics is more uniquely encoded in the human brain.

-Synuclein (Syn) is an intrinsically disordered protein that preferentially binds anionic membranes with lipid packing defects. Cholesterol is an abundant membrane component that regulates packing and organization within membranes, yet its effect on Syn binding remains unclear as prior studies report both cholesterol-mediated enhancement and suppression. Here, we investigated whether these conflicting effects reflect differences in the intrinsic packing state of the phospholipid bilayer. Using a quantitative fluorescence microscopy-based binding assay, we measured Syn binding preferences among reconstituted phosphatidylcholine/phosphatidylserine membranes with varied cholesterol content, lipid tail chemistry, and vesicle curvature. We found that cholesterols effect depended on the underlying packing regime of the membrane. In defect-rich membranes, cholesterol reduced Syn binding, consistent with cholesterol tightening lipid packing and reducing Syn-accessible defects. In membranes with intermediate defect content, cholesterol enhanced binding, whereas tightly packed membranes remained largely insensitive to cholesterol except when high cholesterol content was combined with high membrane curvature. Curvature further shaped these responses, with high curvature compressing cholesterol-dependent differences between membrane compositions. These results show that cholesterol does not universally promote or inhibit Syn binding. Instead, cholesterol regulates Syn-membrane interactions through a packing-regime-dependent mechanism shaped by both lipid tail chemistry and membrane curvature. This framework helps reconcile opposing reports in the literature and highlights membrane physical state as a key determinant of how cholesterol modulates Syn binding. SignificanceSyn is a membrane-binding protein associated with Parkinsons disease, but the role of cholesterol in regulating its membrane interactions has remained unclear. Some studies report that cholesterol enhances Syn association with membranes, whereas others show that cholesterol suppresses it. This work helps explain why both outcomes can occur. We show that cholesterols effect depends on the membranes underlying packing state: cholesterol can reduce, enhance, or have little effect on Syn binding depending on the membrane environment. These findings shift the question from whether cholesterol is generally pro- or anti-binding to how cholesterol reshapes the membrane physical states that control Syn association.

Viral lysis fuels the microbial loop by enhancing organic matter recycling (via the viral shunt) and can redirect organic matter toward export (via the viral shuttle). However, the global impact of viral infection mediated by shunt and shuttle pathways remains unclear. Here, we implemented viral infection and lysis processes in a global ocean ecosystem model, including a single phytoplankton (representing Prochlorococcus), virus (representing cyanophage), and nanozooplankton. Despite low but plausible levels of viral infection, high shunt efficiencies generated enhanced-productivity regions covering up to approximately one-half of the global ocean. For lower viral shunt efficiencies, the enhanced-productivity regions contracted abruptly, accompanied by steady declines in productivity. Viral-mediated increases in primary productivity reduced the extent of tropical oligotrophic regions at high shunt efficiencies, while lower efficiencies expanded oligotrophic areas. These results provide a path forward to developing predictive models of how viral infection and the fate of cellular lysates shape global ocean ecosystems.

Electron transport in mitochondrial complex I is mediated by a chain of redox centers, yet how electrons traverse this network beyond the canonical pathway remains unclear. While prior models treat transport as a sequential process, they do not resolve whether alternative pathways contribute to functional electron flow. Here, we formulate electron transport as a continuous-time quantum walk on a structure-derived redox network and systematically map pathway-level electron flux inferred from quantum-walk dynamics across species. We identify a conserved structural bottleneck at the N5-N6a interface that suppresses direct electron transfer. Strikingly, quantum-walk flux analysis indicates that this bottleneck does not simply limit transport, but can redistribute electron flux into residue-mediated alternative pathways. Across species, these alternative routes support substantial flux and, in several cases, are comparable to or can exceed the canonical direct pathway, indicating a conserved mechanism of pathway-level flux redistribution. This behavior arises from geometric constraints encoded in protein structure and persists under environmental decoherence, demonstrating that architecture governs not only transport efficiency but also the organization of electron flow within the network. Together, our findings suggest a network-level organization of electron transport in complex I, in which a structurally encoded bottleneck reshapes flux through alternative pathways, consistent with a structurally encoded link between protein geometry and quantum transport behavior. We note that the bottleneck-dominated and flux-redistribution observations are not in tension: suppression of the direct N5-N6a step is precisely what redirects amplitude into the parallel residue-mediated routes.

Working memory depends on the flexible representation of stimulus information in neural activity, which changes dynamically depending on task. Stimulus transformations are thought to be efficient in use of neural resources and optimal for task performance. However, these transformations are often opaque, and efficiency may conflict with optimal performance. Here we show that in a working memory task requiring selective recall of one of two stimuli based on a context cue, the prefrontal cortex of two male monkeys prioritized efficiency by overwriting information within a shared neural subspace rather than maintaining distinct subspaces for each stimulus. In neural activity and recurrent neural networks such efficiency incurs a cost, in that efficient representations are more prone to errors. Conversely, stimulation of the cholinergic forebrain which improves behavior altered this default mechanism by encoding distinct contexts in higher dimensions. These findings demonstrate a fundamental tradeoff between efficiency and effectiveness in flexibly updating working memory.

Cooperative interactions often unfold in environments that are shaped by collective behavior, yet how knowledge about such changing environments feeds back into evolutionary dynamics remains poorly understood. While network reciprocity explains how spatial structure enables clusters of cooperators to emerge and grow under certain conditions, it typically ignores how individuals respond to environmental change. Here, we integrate stochastic environmental feedback with network reciprocity to examine how knowledge about environmental state shapes the evolution of cooperation in structured populations. We compare regimes in which individuals either condition their behavior on the current state or remain unaware of it. Under weak selection, we derive a simple condition showing that cooperation is favored when the benefit-to-cost ratio exceeds a modified classic reciprocity threshold accounting for the effect of environmental transitions and state knowledge. Environmental shifts can either promote or hinder cooperation depending on accessibility and fidelity of state knowledge. Counterintuitively, greater knowledge does not universally enhance cooperation: for certain transition rules, state awareness raises the critical threshold for cooperation, a phenomenon we term a "knowledge curse". Our results reveal that, in an ever-changing environment, cooperation in structured populations emerges from a subtle interplay between environmental feedback and information availability.

Cells lying in a curved environment can respond to the surface curvature by reorienting their shape. However, whether cells respond to the mean curvature and/or the Gaussian curvature remains largely unexplored. Here, inspired by experimental observations of how ovarian theca cells (TCs) orient themselves on substrates with different curvatures, we propose a theoretical framework for active nematic layers on curved surfaces. In this model, we assume that the nematic directors of the cells respond to both the mean curvature and the Gaussian curvature of the underlying substrate surface. Our theory predicts specific cell orientation patterns on hemicylindrical, hourglass- and dome-like substrates, consistent with experimental observations. In addition, by incorporating curvature-induced active traction, our model successfully recapitulates the experimental observation of TC accumulation at convex regions of hemicylindrical substrates as well as saddle-shaped regions of more complex geometries. Overall, our work reveals the unexpected role of cell curvature sensing in driving collective migration and pattern formation on various substrate curvature. SIGNIFICANCESubstrate surface curvature is a critical environmental cue that can influence multicellular organization and functions. Yet how cells collectively align and migrate on complex curved surfaces remains unclear. Here, we proposed a hydrodynamic theory of active nematic layers over curved surfaces for contractile theca cells (TCs), where we assume that the nematic directors of cells can respond to both the mean curvature and the Gaussian curvature of the underlying substrates. Our theory predicts distinct cell orientation patterns on hemicylindrical, hourglass- and dome-like substrates, consistent with experimental observations. Furthermore, by introducing curvature-induced active traction, our model recapitulates experimentally observed accumulation of TCs at the convex regions of hemicylindrical substrates as well as saddle-shaped regions of more complex geometries. Together, our study provides a simple theoretical framework to unify our understanding of curvature sensing across complex topology, providing insights into geometric control of tissue pattern formation.

Sensorimotor decisions require balancing extrinsic rewards against intrinsic action costs. How these signals are integrated during rapid eye-movement choices remains unclear. We show that human saccade selection follows cost-benefit computations consistent with neuroeconomic decision-making. Across two experiments, participants maximized rewards and minimized effort-costs. Reward titration revealed that more effortful saccades required higher monetary rewards to be chosen equally often. While effort-costs affected choices linearly, small reward differences shifted choices more than equally-sized larger ones. Furthermore, effort-cost (but not reward) differences regulated decision engagement: Deliberation was extended only when cost differences were large. Together, costs and rewards play dissociable roles in saccade selection, positioning eye movements as a tractable model system for economic decisionmaking. Significance statementSensorimotor decisions are thought to balance rewards against intrinsic action costs, yet how these signals are integrated during rapid eye movement choices on where to look next has remained unclear. Across two experiments, we show that saccade selection satisfies escalating criteria of economic decision-making: costs and rewards trade off on a common utility scale, contribute to choices through dissociable computations, and scale deliberation with utility differences. Effort-cost differences alone regulate decision engagement. These findings reposition attentional selection as a neuroeconomic process and a tractable model system for economic decision-making.

Diurnal changes in light availability are a defining feature of life on Earth. Photoautotrophic organisms therefore store reduced carbon during the day to sustain energy metabolism at night. In cyanobacteria, glycogen is the primary carbon storage compound and supports both energy homeostasis and stress responses. Although glycogen-deficient Synechocystis strains have been studied previously, how these mutants cope with the loss of the major daytime carbon sink and can sustain themselves during the night remains unclear. Using single-cell microfluidics, transcriptomics, and metabolomics, we show that {Delta}glgC mutants exhibit pronounced light sensitivity. At sub-lethal light intensities, daytime transcriptional responses are dominated by downregulation of photosynthesis-related genes, likely preventing NADPH overaccumulation in the absence of a carbon sink. During the night, mutants display severe energy limitation, characterized by reduced ATP levels, altered redox balance, and depletion of central carbon intermediates. In contrast, fumarate and malate accumulate, indicating enhanced respiratory flux through succinate dehydrogenase. These metabolic constraints lead to extended lag phases and delayed cell divisions after the onset of light, demonstrating that glycogen-deficient cells fail to efficiently reinitiate growth after dawn. Overall, our results as a snapshot of the initial response to diurnal regimes highlight glycogen as a central integrator of diurnal physiology in Synechocystis, coordinating energy metabolism, redox balance, and cell division, with implications for metabolic robustness and the evolutionary constraints shaping (endo)symbiosis. Short summaryGlycogen deficiency disrupts day-night energy and redox homeostasis in Synechocystis, revealing constraints on growth, division, and symbiotic potential.

Theory predicts that strong species interactions drive ecological instability, but strong interactions are common in ecosystems while strong instability appears rare. This discrepancy motivates enduring interest in ecological mechanisms that limit or counteract instability. Dormancy - reversible metabolic suppression - may be one. Dormancy is a ubiquitous life history trait found in organisms ranging from bacteria to trees. Dormant individuals form "seed banks" that are temporarily disengaged from demographic processes and species interactions, creating a memory of past ecological dynamics. Seed banks can stabilize predator-prey interactions, but whether, when, and how they affect the stability of larger ecological networks is uncertain. We show that dormancy stabilizes oscillatory dynamics in a minimal mathematical model and illustrate how dormancy converts high oscillation frequency into strong restoring force. We find that dormancy can have qualitative stabilizing effects in structured food webs that undergo Hopf bifurcations and exhibit oscillatory instability, but not in unstructured networks or those dominated by competitive or mutualistic interactions. This classification remains accurate when only a subset of species go dormant and drive stabilization. Our results clarify when dormancy can promote stability, indicating that dormancy may be an important but overlooked stabilizing factor in food webs.

Marine microalgae form major parts of phytoplankton and are highly relevant for global CO2 fixation. Although microalgae have lived together with bacteria in the oceans for billions of years, these ecosystem-relevant interactions remain largely uncharacterized. Here, we have studied biotic interactions between two marine bacteria and a marine microalga. We show that an N2-fixing Vibrio provides ammonium for Chlamydomonas sp. and a Marinobacterium. Both microorganisms cannot survive in an ammonium-free environment. In exchange, the microalga promotes the growth of both bacteria, via secretion of heat-resistant metabolites in case of Marinobacterium. Reciprocally, the Marinobacterium releases heat-resistant metabolites that stimulate algal growth and increase its photosynthetic pigments, Photosystem II quantum yield, and starch accumulation. Electron microscopy reveals a strengthened starch sheath around the algal pyrenoid and indicates a modified periplasmic space for metabolic exchange. Our data highlight a tight synergy of a marine microbial trio promoting each others growth and algal fitness.

Voice disorders affect nearly 20 million Americans and cost more than $13 billion annually. Vocal fold (VF) fibrosis, a major cause of chronic dysphonia, disrupts normal vocal fold vibration by replacing the flexible extracellular matrix with stiff fibrotic tissue. Although TGF-{beta} drives fibrosis, it also activates intrinsic negative feedback mechanisms, including SMAD7 induction and SMAD3 downregulation, to restrain excessive signaling. Broad inhibition of TGF-{beta} or canonical SMAD signaling may disrupt these protective feedback loops and impair normal tissue homeostasis. An ideal anti-fibrotic strategy should differentially target the pro-fibrotic output of TGF-{beta}. Here, we show YAP/TAZ inhibition selectively suppresses pro-fibrotic TGF-{beta} signaling in VF fibroblasts. Pharmacologic inhibition of YAP/TAZ blocked TGF-{beta}-induced fibroblast activation and fibrotic gene expression, while only modestly affecting canonical SMAD feedback responses. Integrated RNA-seq and ChIP-seq analyses demonstrated YAP/TAZ primarily regulate non-canonical TGF-{beta} signaling and pro-fibrotic transcriptional programs. In a rat model of VF fibrosis, YAP/TAZ inhibition reduced nuclear YAP/TAZ localization and attenuated scar formation. Together, these findings identify YAP/TAZ inhibition as a promising therapeutic strategy for VF fibrosis and other fibrotic diseases.

F1-ATPase, the catalytic domain of ATP synthase, is pivotal for mechanochemical energy conversion in mitochondria. Aiming at a minimal yet quantitative and thermodynamically consistent model for its rotary catalysis mechanism, here we developed a chemo-mechanical Markov model incorporating essential conformational and chemical degrees of freedom. By systematically evaluating over 14,000 model variants via Bayesian inference and cross-validation, we find that a fully functional minimal model requires four functionally distinct {beta}-subunit conformations. Our model reconciles the decade-long bi-site versus tri-site controversy, showing that both pathways contribute depending on ATP concentration. Furthermore, our model suggests a Brownian-ratchet-like mechanism that explains the observation that one ATP hydrolysis event can trigger larger than 120{degrees} rotations, thereby explaining seemingly over 100% efficiency. Beyond this prototypic example of a complex biomolecular machine, our approach should enable one to study other enzymatic mechanisms that implement close coupling between conformational motions, substrate binding, and chemical reactions.