Physical Review X

1Although resources are typically distributed continuously in space, species distributions often organize into discrete clusters. In his seminal paper [36], Turing demonstrated that such clusters can spontaneously arise in population densities, even when populations evolve in environments with continuously varying conditions. This phenomenon is known as Turing instability. In this work, we focus on two models grounded in population dynamics: a one-dimensional model based on the nonlocal Fisher-KPP equation, and a two-dimensional model involving an environmental gradient. We show that phenotypic clusters (sometimes referred to as "species") emerge in these models. We prove that they do not emerge because of Turing instability, but because of stochasticity, and that they disappear when stochasticity is reduced. First, for both models, we start our simulations with initial populations uniformly distributed in the state space. We show that phenotypic clusters quickly emerge and that the distances between them depend on the population size, that is, on the degree of stochasticity. Next, we start from already clearly defined phenotypic clusters. We identify three regimes in the connection between population size, the initial distances between clusters, and the distances between clusters at equilibrium. Last, on the two-dimensional model, we relax the hypothesis of complete clonality by varying the effective recombination rate, explore its effect on phenotypic clustering, and show that phenotypic clustering decays drastically with slight recombination.

Quantum effects in biology are unavoidable at the molecular scale; the unresolved question is whether they can remain functionally relevant across the timescale gap between femtosecond molecular dynamics and microsecond-to-millisecond biological function. Here we formalize this mismatch as an equilibrium-to-functionality gap and use tubulin as a stringent open-system test case. We combine secular Lindblad, Redfield, and hierarchical equations of motion (HEOM) treatments to quantify decoherence, non-perturbative relaxation, and the physical amplification required for functional relevance. Equilibrium dephasing yields a conservative [Formula] fs at 310 K, with a generic protein-bath baseline of {approx} 13 fs. A completed 30 ps HEOM trajectory for the full 1JFF tryptophan network shows distributed non-Markovian relaxation, with terminal purity Pur = 0.210 and stretched-exponential exponent {beta}KWW {approx} 0.44, confirming that Redfield is useful as a short-time perturbative comparator but not quantitatively interchangeable with HEOM in this intermediate-coupling regime. We introduce a coherence-utility criterion [U] = [K]{tau}coh/{tau}func, separating required amplification from empirically bounded gain. A thermodynamic uncertainty relation closure shows that neural-scale cascade amplification would require Pmin [~] 10-7 W, about five orders of magnitude above the local microtubule GTP budget. Frohlich pumping is found to be linewidth-gated rather than generically micron-scale; ordered-water cavity QED and geometric subradiance remain experimentally testable but severely constrained candidates. The result is not a model of consciousness, but a reproducible physical benchmark framework for evaluating biological quantum-coherence claims under explicit open-system, energetic, and experimental constraints. Six falsifiable experimental programmes are prioritized, and the full computational framework is released with a validation ledger, cryptographic audit trail, and living supplementary material. O_FIG O_LINKSMALLFIG WIDTH=200 HEIGHT=107 SRC="FIGDIR/small/724047v1_ufig1.gif" ALT="Figure 1"> View larger version (20K): org.highwire.dtl.DTLVardef@19e4f42org.highwire.dtl.DTLVardef@65a719org.highwire.dtl.DTLVardef@1bd63beorg.highwire.dtl.DTLVardef@df77d8_HPS_FORMAT_FIGEXP M_FIG O_FLOATNOGraphical abstract.C_FLOATNO Equilibrium tubulin coherence lies in the femtosecond regime, while functional neural timescales lie in the millisecond regime. Frohlich pumping, QED-cavity protection, and geometric subradiance remain experimentally discriminable non-equilibrium candidates requiring independently bounded amplification. C_FIG FundingThis research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors. Versioned computational scope of this releaseThis manuscript reports the theoretical framework, calibrated equilibrium baseline, Redfield/HEOM validation ledger, stratified Bayesian evidence synthesis, classical comparators, and falsifiable experimental design. The release-specific reproduction audit, including the current validation-check total and the SHA-256 fingerprints of the binary production artefacts (.npz, .pkl), is documented in LIVING_SI.md and outputs_data/raw_json/structur al/validation_report.json. A completed 30 ps HEOM production trajectory has been validated on constrained hardware; the master dataset contains the full 8-site population trajectory. A summary of those results is provided in [§]2.2.5. All claims made below are restricted to the numerical and theoretical evidence reported in this manuscript and its associated repository artefacts. The public repository ships the calibrated phenomenological baseline for accessibility; the HEOM production artefacts serve as the non-perturbative validation benchmark. All source figure outputs associated with this release are maintained in the public repository under outputs_data/figures_final/.

Transcription factors organize into liquid-like condensates to facilitate gene expression, yet the physical mechanisms governing their formation and properties remain poorly understood. We study the size statistics of transcriptional condensates in human HAP1 cells using widefield and super-resolution microscopy tagging the epigenetic reader BRD4. We find that hubs that appear monolithic in widefield resolve into clusters of smaller droplets that resist coarsening. We link this size control to Active Model B+, a non-equilibrium field theory that captures a regime of reverse Ostwald ripening out of thermal equilibrium. In this regime, chemically driven currents cause larger droplets to transfer mass back to smaller ones, stabilizing a state of microphase segregation. The observed exponential size distribution of BRD4 foci quantitatively matches our numerical simulations, suggesting a universal physical picture for the non-equilibrium self-limitation of cellular condensates.

This Perspective formally proposes Particle Biology as a unifying theoretical framework to address the critical bottleneck in current life science research. Current life science research has reached a critical bottleneck. While the field has advanced to the study of 3D genomic spatial configurations and chromosomal organization, it remains largely descriptive and confined to the macromolecular level. This approach lacks a first-principles understanding of the underlying physical forces that drive biological processes. This Perspective formally proposes Particle Biology as a unifying theoretical framework. We establish an axiomatic system positing that life phenomena are fundamentally emergent spatiotemporal patterns of electromagnetic forces among atoms, electrons, and nuclei operating far from thermodynamic equilibrium. By defining biological states through the Biological Hamiltonian and mapping biochemical pathways to multidimensional Potential Energy Surfaces (PES), we bridge the gap between descriptive biology and predictive physics. We categorize core research technologies into three modalities--seeing, computing, and controlling particles--facilitated by advancements in Cryo-EM, AlphaFold 3, and Boron Neutron Capture Therapy (BNCT). Ultimately, the trajectory of molecular biology has evolved from cells to DNA and onto the 3D spatial genome, yet it cannot go deeper within current paradigms. The next logical evolution is to move beyond the macromolecular bottleneck to focus on the electromagnetic interactions between atoms and ions--the true Particle Biology level--to redefine disease and intervention.

During vertebrate development, the flat surface of the gut epithelium undergoes a dramatic transformation into densely packed arrays of finger-like projections called intestinal villi. Recent studies show that the villus formation relies on a tissue dewetting process, in which mesenchymal tissues buckle the overlying epithelial layer into periodic folds. However, the mechanisms driving subsequent elongation of these folds into finger-like villi remain largely unexplored. Here, we propose a simple mechanism for villus elongation that couples tissue dewetting to cell differentiation, which emerged as a repeated outcome of multiple independent simulations of an evolutionary-developmental Cellular Potts Model. In this mechanism, a liquid-like mesenchymal tissue continuously differentiates into a solid-like mesenchymal tissue at the interface between them. This differentiation drives the liquid-like tissue to continuously retract from the solid-like tissue in the opposite direction of the interface through dewetting, ultimately creating a finger-like projection. A merit of our proposed mechanism is that it only requires two tissues with different viscosities, high surface tension, and cell differentiation. We develop a simplified phase-field model to determine exactly how villus morphology depends on these three requirements. Since these requirements are satisfied not only in intestinal villi but also in many other developing tissues, we propose that the same mechanism could also drive the elongation of other tissues.

How can simple organisms lacking nervous systems encode and transmit environmental signals to generate complex, adaptive behaviours? Using the unicellular organism Physarum polycephalum as a model, we identify a unifying mechanochemical mechanism that links intracellular calcium oscillations to large-scale behavioural coordination. We first demonstrate experimentally that local perturbation of the actomyosin cortex is sufficient to induce symmetry breaking and directed migration, even in the absence of nutrient cues. Building on evidence linking calcium concentration to actin depolymerization and contractile relaxation, we develop a mechanochemical tubule model in which self-sustained calcium oscillations are coupled to pressure-driven mechanics. We show that environmental cues, encoded through the local modulation of these oscillations, give rise to directed transport and the redistribution of biomass. By extending this framework to a two-dimensional phase-field model, we demonstrate that this mechanism is sufficient to generate a diverse set of slime mould behaviours, including chemotaxis, network formation, and balancing exploration-exploitation trade-offs. In doing so, we provide a single mechanistic framework linking intracellular dynamics to organism-scale behaviour across spatial and temporal scales. Our work shows that these sophisticated behaviours can emerge from the modulation of self-sustained oscillations coupled by diffusion, providing a physically grounded mechanism for information processing in non-neural organisms and offering insight into the evolutionary origins of coordinated behaviour.

The hierarchical organization of multiphase biomolecular condensates into core-shell architectures is a fundamental problem in soft matter and biophysics. While classical explanations rely on hierarchies of interfacial tension ({gamma}) between coexisting liquids, the ultralow tensions of condensates (0.1-1 {micro}N/m) render such hierarchies potentially fragile. We introduce a robust assembly principle based on Polymer-Assisted Condensation (PAC), in which a single polymer species dictates the entire structure. The polymer nucleates a dense core by recruiting a condensation-incompetent protein (P1). A second incompetent protein (P2), which is repelled or otherwise thermodynamically disfavored from entering the polymer-rich core, is nonetheless recruited to the interface by weak attraction to P1, forming a stable shell. This effective repulsion-driven layering operates across a wide parameter space without requiring{gamma} asymmetries and yields a robust structure that is impervious to concentration fluctuations and environmental perturbations. Phase-field modeling and molecular simulations establish this mechanism and capture key features of nucleolar organization. Our work reveals a general physical pathway for encoding spatial order in soft, multicomponent fluids.

Effective pandemic response requires accurate modeling of population compliance with non-pharmaceutical interventions (NPIs), yet most epidemic models treat behavioral change as fixed scenarios rather than an emergent process. Here, we test whether large language model (LLM)-based agents can generate individualized behavioral responses to time-varying NPIs and disease risk. We instantiate demographically representative agents in three U.S. cities (Boston, Denver, San Antonio) and condition them on evolving outbreak conditions and policies during the early COVID-19 pandemic, without fitting to observed mobility data. Across three frontier LLMs and their ensemble, agents generate zero-shot mobility changes across restaurants, retail, and entertainment venues, benchmarked against cellphone-derived foot-traffic records. The simulations recover average mobility trends across cities and venue types but exhibit overly narrow within-city variation. The three LLMs display distinct biases, while an ensemble approach improves robustness and overall performance. These findings establish LLM agents as a promising framework for modeling adherence to NPIs and highlight the need for further fine-tuning and empirical validation before they can support policy analysis.

Take-off is a fast and energy-efficient strategy for bipedal animals, such as birds, to achieve rapid movement; however, how muscle physiology scales to govern this universal behavior remains unresolved. Research in other species physiologies is not readily applicable. As a result, important questions, whether theropod dinosaurs such as Tyrannosaurus rex were capable of jumping, remain unanswered. In this article, we coupled Lagrangian dynamics with Hills muscle equations and developed new experimental methods to quantify joint rotational stiffness and damping, thereby enabling a systematic description of lower-limb mechanics. The approach establishes a novel kinetic framework that links muscle contractile properties to lower-limb performance without invoking control optimization. Animal observations and tabletop mechanisms validate the framework. The mechanics model reveals that the take-off time of about 0.1 s across body masses of 0.003 to 90 kg is achievable, as heavier birds generate proportionally higher reaction forces. Additionally, Tyrannosaurus rex should be capable of jumping, based on the available physiology data. Beyond evolutionary insights, our framework provides a new methodology for analyzing the mechanical properties of biological joints and informing the design of scalable bio-inspired robots.

Navigation in complex environments relies on internal spatial representations that guide action. While the brain employs a diverse repertoire of spatial tuning cells--including grid, place, and head-direction cells--a normative theory linking these static neural codes to the dynamic process of navigation remains elusive. In this work, we propose a Unified Laplacian Framework derived from first principles of representational smoothness and efficiency. We first demonstrate that diverse spatial codes emerge naturally as spectral decompositions of the Laplace operator. Crucially, bridging the gap from representation to action, we derive a biologically plausible navigation policy based on the Greens function potential. We show that this potential encodes the environments intrinsic geometry to enable simple, trap-free gradient ascent, achieving improved sample efficiency and generalization in goal-reaching tasks. Furthermore, we demonstrate that these spectral representations can be learned directly from high-dimensional visual inputs, confirming their plausibility in realistic environments. Our results suggest that the "cognitive map" can be viewed as a spectral embedding of the Laplacian, providing a rigorous foundation for spatial cognition in both biological and artificial agents.

Biodiversity is commonly summarized by macroecological mean patterns, most prominently the species-area relationship (SAR) linking habitat area to expected species richness. Yet conservation, policy, and economic decisions increasingly require risk metrics: probabilities of rare but consequential biodiversity shortfalls, including local collapse. Such tail risks are central in finance and insurance but remain difficult to quantify in ecology because the data needed to estimate full richness distributions are rarely available at decision scales. Here we provide a mechanistic route from species-area relationships to biodiversity risk metrics. We show that when regional species abundances are well approximated by Fishers log-series, a minimal immigration-extinction mechanism yields a closed-form stationary distribution for local richness whose structure tightly couples the mean SAR to richness variability and lower-tail probabilities. This coupling implies exact fluctuation-response identities and an explicit integral transform that reconstructs collapse probabilities and other tail risk measures directly from the mean SAR. These results define ecological analogues of financial risk metrics--such as collapse probability and lower-tail quantiles--without requiring direct estimation of the full richness distribution. Using high-resolution ForestGEO tree censuses spanning tropical, subtropical, and temperate forests, we find empirical support for these predictions across spatial scales. Together, our results show how widely measurable species-area relationships can be elevated from descriptive averages to operational tools for biodiversity risk assessment and reliability-based conservation planning.

How combinatorial cell signaling controls cellular decisions in the face of crosstalk is a fundamental problem in biology. A key open question is whether a single snapshot of signaling is sufficient to predict cell fate, especially given substantial evidence that signaling dynamics shape fate decisions. Here, we show that a snapshot of combinatorial signaling accurately predicts cell fate at the single-cell level in a model for human embryonic patterning. To this end, we developed Sig2Fate, a quantitative method integrating iterative immunofluorescence, information theory, and machine learning. Cell fate is encoded by combinatorial yet redundant signaling that reduces to a single angular coordinate in the high-dimensional signaling space, providing a simple interpretation of the signal-to-fate map. This map generalizes across variations in BMP concentration and pharmacological perturbations of ERK, Wnt, and YAP signaling, enabling prediction of drug responses from control data alone when signaling crosstalk is accounted for. Our findings provide a framework for predicting and explaining complex phenotypes from signaling perturbations across biological systems.

Neuronal computation depends on the balance between excitation and inhibition, yet how this balance is implemented across the dendritic tree remains unclear. Classical views predict that inhibition should be most effective near the soma or along the path from excitation to output, but many interneuron subtypes preferentially target remote dendritic compartments. This apparent paradox is sharpened by active dendrites, where local NMDA spikes, calcium plateaus and backpropagating action potentials can make distal branches powerful contributors to somatic firing. Here we develop an analytical framework that extracts general principles of inhibition from biophysically detailed multi-compartment simulations. By reformulating the implicit voltage update of detailed neuron models as a matrix recursion, we derive exact voltage sensitivities to inhibitory synaptic perturbations. This leads to a unified {Phi}-a law: the somatic impact of inhibition factorizes into a global dendritic susceptibility term and a local synaptic perturbation term. Using this law to map inhibitory leverage and identify optimal inhibitory interventions, we show that active dendritic excitation can shift inhibitory hot zones from perisomatic regions toward distal or intermediate compartments. Across neocortical, hippocampal and striatal neuron models, the same response law explains convergent inhibitory strategies despite distinct cellular mechanisms. Our framework turns detailed numerical simulation into analytical theory, providing a general principle for how diverse dendritic inhibition controls active neurons.

Arterial thrombosis is initiated when mechanical forces in flowing blood exceed the activation thresholds of platelets and von Willebrand factor (vWF). Despite extensive experimental characterization of shear-induced platelet aggregation, a unified theoretical framework that maps hemodynamic forcing onto clot nucleation is lacking. Here we present Force-Gated Thrombosis (FGT), a non-equilibrium mechanical theory that treats thrombus formation as a continuous phase transition driven by an effective mechanical forcing {Sigma} ={sigma} + |{nabla}{sigma}| + {beta}{varepsilon}, which combines local wall shear stress{sigma} , shear gradient |{nabla}{sigma}|, and extensional strain rate{varepsilon} . We introduce a dimensionless Thrombosis Number {Theta} = ({Sigma}/{Sigma}c)(P/P0)m(C/C0)n, which incorporates platelet concentration P and coagulation factor concentration C, and governs the transition between stable flow ({Theta} < 1) and active clot growth ({Theta} > 1). The thrombus density is represented by a scalar order parameter{varphi} whose dynamics follow a Ginzburg- Landau free energy functional. For a simplified stenosed artery we derive an analytic closed-form thrombosis onset criterion and a critical flow rate [Formula], where{delta} is stenosis severity. Linear stability analysis shows that perturbations grow at rate{omega} (k) = {Lambda}({Theta}) - D{varphi}k2, becoming unstable when {Theta} > 1. Near threshold the clot volume fraction scales as{varphi} [~] ({Theta} - 1)1/2, a mean-field critical exponent consistent with Ginzburg- Landau theory. Systematic comparison with fifteen published experimental and computational datasets spanning shear rates from 100 to 15,000 s-1 confirms that FGT correctly predicts the existence, location, and approximate severity of pathological thrombus formation across diverse vascular geometries. The theory provides a quantitative bridge between single-molecule mechanobiology and macroscale clinical thrombosis, and yields experimentally testable predictions distinguishing FGT from purely biochemical models.

Neural oscillations are thought to play a central role in encoding and transmitting cognitive information across large-scale brain networks, yet the relative contributions of phase synchrony and amplitude co-modulations to distributed coding remain unclear. A key obstacle is the absence of tools that can simultaneously quantify task-relevant information in the frequency domain and disentangle its phase and amplitude components across pairwise and higher-order interactions. Here, we introduce a spectral partial information decomposition framework (named NeOPID) for quantifying information about cognitive variables in power and phase contributions, and to quantify redundant and synergistic information in brain relations, from pairwise to higher-order interactions. We validated the approach on Kuramoto and Stuart-Landau oscillator networks, including a whole-brain model constrained by macaque anatomical connectivity. NeOPID accurately recovers ground-truth encoding schemes and reveals that phase relations and amplitude co-modulations act as complementary coding channels with both redundant and synergistic components. NeOPID further extends this decomposition to higher-order functional interactions enabling the characterization of how cognitive information is collectively distributed across multiple oscillatory edges via redundant and synergistic encoding. To illustrate biological applicability, we applied NeOPID to local field potentials (LFPs) recorded from the macaque fronto-parietal network during a working memory task. In this dataset, NeOPID identified beta-band amplitude co-modulations as the primary carrier of stimulus information, and revealed that higher-order phase interactions exhibit both redundant and synergistic structure during the memory delay. These results establish NeOPID as a principled tool for dissecting the informational architecture about cognitive processes of oscillatory brain networks.

Transcriptional condensates operate far from equilibrium, where continuous RNA synthesis and degradation dynamically reshape condensate composition. To investigate how RNA synthesis regulates condensate properties at sub-molecular resolution, we introduce REACT-RNA, a chemically specific coarse-grained molecular dynamics framework that explicitly couples RNA polymerisation, degradation, and nucleotide fluxes to sequence-dependent protein-RNA phase behaviour. Using FUS and MED1 as model systems, we show that RNA growth remodels condensate phase behaviour by altering RNA length distributions and intermolecular connectivity. Sustained RNA polymerisation drives re-entrant condensate dissolution, even of aged gel-like condensates, whereas RNA degradation stabilises long-lived non-equilibrium condensates containing excess RNA and negative charge beyond that tolerated at equilibrium. Our results suggest that RNA synthesis, degradation, and nucleotide fluxes drive transcriptional condensates out of thermodynamic equilibrium while condensates in turn promote reactive molecular configurations that favour RNA production, enabling transient accumulation of excess RNA and negative charge beyond equilibrium electroneutrality constraints during bursts of transcription.

Biomolecular function is often controlled by structural and dynamical adaptations to binding events. Although molecular dynamics (MD) simulations can capture these events at atomic resolution, separating functional signatures from stochastic noise remains challenging. Traditional methods often struggle to isolate mechanistically relevant differences across independent replicas. Here, we introduce an explainable deep learning approach that learns state-specific dynamic signatures directly from MD trajectories. By coupling a dynamic protein graph representation with group-aware contrastive learning across independent replicas, the model detects the signatures, filtering out trajectory-specific correlations. An explainable AI framework then maps the identified differences on individual residues. We demonstrate this approach by identifying "binding-ready" conformations in a T4-Lysozyme mutant, recovering the allosteric determinants of peptide recognition in the PDZ3 domain, and isolating a ligand-independent activation signature for the A2A receptor. Our GISTnet-MD method generalizes across unseen data during comparative MD analysis, translating raw trajectory differences into residue-level determinants of protein function.

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.

Pharmacokinetic analysis has spent half a century compressing drug concentration-time curves into scalar summaries--AUC, Cmax, clearance--discarding the shape information that encodes mechanistic fingerprints of the underlying physiology. We introduce Topological Pharmacokinetics (TPK), a framework that reads the shape of pharmacokinetic trajectories directly from data without prior commitment to a compartmental model. TPK uses delay embedding to reconstruct the pharmacokinetic attractor from the concentration-time curve, and persistent homology to extract its topological invariants--connected components and loops--as a Pharmacokinetic Topological Invariant (PTI) vector. We validate TPK across three levels: linear systems (negative control), nonlinear saturable elimination (detection of the N_PTP +1 rule and a nonlinear diagnostic triad), and endogenous circadian rhythms (contrastive detection of rhythmic interference via Dev specificity and Decouple Collapse). The PTI vector provides a model-agnostic shape fingerprint that, in simulation, demonstrates the diagnostic potential of shape-based analysis; validation on experimental data is required to assess whether this potential generalizes to real pharmacokinetic data. All findings are demonstrated as proof of concept on simulated data; validation on experimentally measured concentration-time curves is the essential next step.

AO_SCPLOWBSTRACTC_SCPLOWNeural integrators convert brief inputs into persistent firing and underlie functions such as working memory, evidence accumulation, and gaze holding. Classical integrator models typically rely on finely tuned recurrent connectivity. Here we identify a biologically plausible route by which randomly connected noisy spiking networks can approximate integration over a finite region of parameter space. Mean-field theory (MFT) reveals surprisingly simple dynamics in such networks, governed by the mean recurrent weight and mean feedforward weight, and shows that linear integration critically depends on noise. We further show that this regime can be reached through a local, reward-modulated two-trace plasticity rule. Comparing the model with new experimental results from a delay-switching tactile decision-making task, we find that it reproduces key features of adaptive ramp-to-threshold cortical dynamics during timing-related learning. The same framework further connects to oculomotor persistence and evidence accumulation, providing a mechanistic realization of single-boundary drift-diffusion dynamics.