Physical Review Research

A survey of the literature reveals notable discrepancies among the purported exact results for the spectra of stochastic gene expression models. For self-repressing gene circuits, previous studies ([Phys. Rev. Lett. 99, 108103 (2007)], [Phys. Rev. E 83,062902 (2011)], [J. Chem. Phys. 160, 074105 (2024)], and [bioRxiv 2025.02.05.635946 (2025)]) have provided different exact solutions for the eigenvalues of the generator matrix. In this work, we propose a unified Hilbert space framework for the spectral theory of stochastic gene expression. Based on this framework, we analytically derive the spectra for models of constitutive, bursty, and autoregulated gene expression. The eigenvalues and eigenvectors obtained are then used to construct an exact spectral representation of the time-dependent distribution of gene product numbers. The spectral gap between the zero eigenvalue and the first nonzero eigenvalue, which reflects the relaxation rate of the system towards its steady state, is then compared with the prediction of the deterministic model, and we find that deterministic modeling fails to capture the relaxation rate when autoregulation is strong. In particular, our results demonstrate that for infinite-dimensional operators such as in stochastic gene expression models, many conclusions in linear algebra do not apply, and one must rely on the modern theory of functional analysis.

Allostery is an intrinsic dynamic phenomenon that underlies functional long-distance interactions in proteins, which we study here by stochastic calculus approach to elastic network models (ENMs). We show that once you drop the usually accepted high friction limit and include hydrodynamic interactions in ENMs, a simple measure that uses the pairwise difference in the time-delayed correlations of residue fluctuations provides insight about functional sites and their dynamical behaviour in allosteric communication. We present this with three exemplary cases Aspartate Carbamoyl transferase, Insulin Receptor and DNA-dependent Protein Kinase. We show that proteins possess characteristic pathways operating at different time-delay windows with slow to faster motions underlying the protein function. As these pathways help communication between key residues of functionality, they can also be used to identify their locations without any prior knowledge other than the protein crystal structure.

In this letter we address the potential confusion related to our recent demonstration that multiple macroecological laws describe short- and long-term dynamics of microbial communities. Specifically, we clarify that these laws, similarly to many other relationships observed in nature, are characterized not just by the existence of scaling, but also by certain characteristic values of the scaling exponents. By performing proper statistical analysis, we demonstrate that the relationships sensitive to temporal bacterial dynamics are not reproduced in the shuffled data. We also discuss that there is no clear evidence in the data that macroecological relationships in microbiota are primarily driven by external or environmental factors. Proper statistical analyses of the data suggest that the dynamics of gut microbiota, even on a constant diet, contains rich temporal structure. Therefore, it is likely that complex and non-linear internal dynamics may be primarily responsible for the observed macroecological laws in microbiota and other ecological communities.

While biomolecular condensates are often liquid-like, many experiments found that condensates also exhibit solid-like behaviors, making them indissoluble in conditions liquid condensates dissolve. Despite the biological significance of indissoluble condensates to cellular fitness, the mechanisms underlying the indissolubility of solid-like condensates are still unclear. In this work, we study the effects of elasticity on the dissolution of biomolecular condensates. We demonstrate that the bulk stress inside condensates may prevent the condensates from dissolution and obtain a new mechanical equilibrium condition of elastic condensates. Moreover, we theoretically predict a phase diagram of indissolubility for biomolecular condensates and identify a minimum bulk modulus for the condensates to be indissoluble. To verify our theories, we simulate the two-fluid model in which the slow component corresponding to biomolecules generates elastic stress. Our theoretical predictions are nicely confirmed and independent of microscopic details. Our works show that elasticity makes biomolecular condensates less prone to dissolution.

Cells dynamically remodel their internal structures by modulating the arrangement of actin filaments (AFs). In this process, individual AFs exhibit stochastic behavior without knowing macroscopic higher-order structures they are meant to create or disintegrate. Cellular adaptation to environmental cues is accompanied with this type of self-assembly and disassembly, but the mechanism allowing for the stochastic process-driven remodeling of the cell structure remains incompletely understood. Here we employ percolation theory to explore how AFs interacting only with neighboring ones without recognizing the overall configuration can nonetheless construct stress fibers (SFs) at particular locations. To achieve this, we determine the binding and unbinding probabilities of AFs undergoing cellular tensional homeostasis, a fundamental property maintaining intracellular tension. We showed that the duration required for the assembly of SFs is shortened by the amount of preexisting actin meshwork, while the disassembly occurs independently of the presence of actin meshwork. This asymmetry between the assembly and disassembly, consistently observed in actual cells, is explained by considering the nature of intracellular tension transmission. Thus, our percolation analysis provides insights into the role of coexisting higher-order actin structures in their flexible responses during cellular adaptation.

Efficient absorption of signaling molecules and carbohydrates through receptors on cell surfaces is crucial for various biological processes. While ubiquitous patterns of receptor distributions, including polar localization in rod-shaped cells, have been widely observed experimentally, their underlying evolutionary advantage is unclear. In this work, we study how spatial distributions of receptors on cell surfaces affect the total flux entering the cell. We innovate a method by which one can calculate the fluxes through all receptors using linear equations, which applies to arbitrarily shaped cells. Our theories recover previous results for spherical cells and further show that the flux through each receptor is spatially dependent in non-spherical cells. In particular, the fluxes are the highest near the poles in rod-shaped cells and the highest near the invagination in defective spherical cells. Surprisingly, we prove that the optimal receptor distribution on an arbitrarily shaped cell maximizing the total flux is precisely the charge density distribution on an ideal conductor of the same shape, which agrees with numerical simulations. Our work unveils the evolutionary origin of receptor localizations.

Aperiodic components of neural activity, characterized by endogenous 1/f noise dynamics, are hypothesized to support the emergence of large-scale cortical order and cognitive flexibility. Here, we combine computational modeling and human brain stimulation to elucidate the role of 1/f noise in modulating neural synchrony. Using a coupled oscillator model, we demonstrate that ubiquitous 1/f noise does more effectively enhances phase synchrony than spectrally flat (white) noise. Crucially, we identify a competitive synergy between noise intensity and the 1/f spectral exponent: starting from optimal white noise-induced synchrony, increasing the 1/f exponent while decreasing noise intensity leads to a further enhancement of synchrony, which peaks at a specific parameter regime before diminishing. To experimentally validate these findings, we developed a transcranial 1/f noise stimulation (tFNS) system and applied it to human subjects. Compared to spectrally white noise stimulation, the tFNS more robustly enhanced corticospinal synchrony, consistent with model predictions. These results uncover a functional advantage of scale-free brain noise in driving coordinated neural dynamics, offering a new framework for optimizing non-invasive brain stimulation. More broadly, our findings suggest that the brain may harness stochastic facilitation through adaptive modulation of its aperiodic activity to support ordered macro-dynamics.

During the expansion of a cell collective, such as the development of microbial colonies and tumor progression, the local cell growth increases the local pressure, which in turn suppresses cell growth. How this pressure-growth coupling affects the expansion of a cell collective remains unclear. Here, we answer this question using a continuum model of cell collective. We find that a fast-growing leading front and a slow-growing interior of the cell collective emerge due to the pressure-dependent growth rate. The leading front can exhibit fingering instability and we confirm the predicted instability criteria numerically with the leading front explicitly simulated. Intriguingly, we find that fingering instability is not only a consequence of local cell growth but also enhances the entire populations growth rate as positive feedback. Our work unveils the fitness advantage of fingering formation quantitatively and suggests that the ability to form protrusion can be evolutionarily selected.

Cargo transport within cells is a vital biological process that relies on the intricate interplay between motor proteins, microtubules, and the complex intracellular environment. In this study, we unveil a universal transport mechanism characterized by stick-slip motion, which governs the dynamics of intracellular vesicle transport. By analyzing a comprehensive dataset of vesicle trajectories across various cell types and intracellular environments, we demonstrate that the cargo velocities consistently follow a Gamma distribution, revealing a common statistical pattern amidst the diversity of biological cargoes. Our experimental findings are well-described by a theoretical model that connects the Brownian-correlated kinetic friction between motor-cargo complexes and their surroundings to the observed universal Gamma distribution of cargo velocities. This model elucidates the stick-slip dynamics governing intracellular cargo transport, which are pertinent to various cellular processes such as vesicle budding, organelle transport, and cell migration.

Cell-scale curvature plays important roles in controlling cell and tissue behaviors. However, these roles have not been well quantified, and the underlying mechanisms remain elusive. We combine experiments with theory to study systematically the curvature-dependence of cell migration inside PDMS microcylinders. We find that persistence is positively correlated with speed, following the universal speed-persistence coupling relation, i.e., faster cells turn less. Cell migration inside microcylinders is anisotropic and depends on curvature in a biphasic manner. At small curvatures, as curvature increases, the average speed and anisotropy both increase, but surprisingly, the average persistence decreases. Whereas as the curvature increases over some threshold, cells detach from the surface, the average speed and anisotropy both decrease sharply but the average persistence increases. Moreover, interestingly, cells are found to leave paxillins along their trajectories (on curved but not planar surfaces), facilitating the assembly of focal adhesions of following cells. We propose a minimal model for the biphasic curvotaxis based on three mechanisms: the persistent random "noise", the bending penalty of stress fibers, and the cell-surface adhesion. The findings provide a novel and general perspective on directed cell migration in the widely existing curved microenvironment of cells in vivo.

The immune system discriminates between harmful and harmless antigens based on past experiences; however, the underlying mechanism is largely unknown. From the viewpoint of machine learning, the learning system predicts the observation and updates the prediction based on prediction error, a process known as predictive coding. Here, we modeled the population dynamics of T cells by adopting the concept of predictive coding; helper and regulatory T cells predict the antigen amount and excessive immune response, respectively. Their prediction error signals, possibly via cytokines, induce their differentiation to memory T cells. Through numerical simulations, we found that the immune system identifies antigen risks depending on the concentration and input rapidness of the antigen. Further, our model reproduced history-dependent discrimination, as in allergy onset and subsequent therapy. Together, this study provided a novel framework to improve our understanding of how the immune system adaptively learns the risks of diverse antigens.

Transcription occurs in stochastic bursts, i.e., transcription events are temporally clustered. The clustering does not ensue from environmental fluctuations but springs from the intrinsically stochastic behavior of the regulatory process that controls transcription. Based on microscopic observations of transcription at a single gene copy of yeast, we show that the regulatory process is cyclic and irreversible, i.e., the process violates the detailed balance conditions for thermodynamic equilibrium. The theoretical significance of this finding is discussed.

We propose a novel three-compartment heuristic model that recasts gastric cancer metastasis into a framework of non-equilibrium thermodynamics and nonlinear dynamics. The system, encompassing primary, hepatic, and peritoneal tumor populations, exhibits a well-defined route to chaos: as immune surveillance weakens, the dynamics undergo a supercritical Andronov-Hopf bifurcation, giving rise to a limit cycle, followed by a Shilnikov-type saddle-foci bifurcation cascade leading to chaotic attractors. Our central finding is the introduction of a dissipation function, {Psi}, constructed via a sensitivity-weighted, two-factor ansatz that integrates metabolic flux and dynamical influence. This spatially coarse-grained measure captures the systems thermodynamic robustness. The analysis reveals a dynamical phase transition: while tumor aggressiveness peaks in the pre-metastatic limit-cycle regime, {Psi} emerges as the definitive marker of the chaotic, treatment-resistant metastatic state, quantifying a sharp increase in systemic robustness that correlates decisively with advanced clinical stages (TNM III-IV). Consequently, this work provides a predictive framework grounded in the physics of metastasis, demonstrating that {Psi} not only diagnoses but also defines the primary therapeutic target: the underlying thermodynamic robustness of the metastatic system. Thus, effective intervention must shift from merely reducing tumor mass to strategically destabilizing this robust dissipative structure, thereby preventing recurrence. PACS: 05.45.-a; 87.18.-h; 87.19.xj; 05.70.Ln HighlightsO_LIA novel three-compartment heuristic model reveals phase transitions and chaotic dynamics in gastric cancer metastasis. C_LIO_LIThe dissipation function {Psi} emerges as a quantitative thermodynamic metric of systemic robustness in the metastatic regime. C_LIO_LIDecreasing immune surveillance triggers biological phase transitions towards metastatic disease. C_LIO_LIThe framework integrates nonlinear dynamics with TNM staging, identifying the dissipation function {Psi} as a therapeutic target to overcome metastatic recurrence. C_LI Graphical Abstract O_FIG O_LINKSMALLFIG WIDTH=200 HEIGHT=102 SRC="FIGDIR/small/702339v1_ufig1.gif" ALT="Figure 1"> View larger version (24K): org.highwire.dtl.DTLVardef@1a605c7org.highwire.dtl.DTLVardef@c56e83org.highwire.dtl.DTLVardef@1da7fc8org.highwire.dtl.DTLVardef@1fb30ba_HPS_FORMAT_FIGEXP M_FIG C_FIG

Semiflexible polymer networks are ubiquitous in biological systems, including a scaffolding structure within cells called the actin cytoskeleton. The polymers in these networks are often interconnected by transient bonds. For example, actin filaments in the cytoskeleton are physically connected via cross-linkers. The mechanical and kinetic properties of the cross-linkers significantly affect the rheological properties of the actin cytoskeleton. Here, we employed an agent-based model to elucidate how the force-dependent behaviors of the cross-linkers determine the material properties of passive networks without molecular motors and the force generation of active networks with molecular motors. The cross-linkers are assumed to behave as a slip bond whose dissociation rate is proportional to forces or as a catch-slip bond whose dissociation rate is inversely proportional to forces at low force level but proportional to forces at high force level. We found that catch-slip-bond cross-linkers can increase both stress and strain at a yield point by forming force-bearing elements that turn over continuously, which is impossible to achieve without the catch-slip bonds. In addition, we demonstrated that the catch-slip-bond cross-linkers help myosin motors generate greater internal contractile forces by reinforcing the force-bearing parts of the active network.

Recent experimental investigations into Hydra regeneration revealed a remarkable phenomenon: the morphological transformation of a tissue fragment from the incipient spherical configuration to a tube-like structure - the hallmark of a mature Hydra - has the dynamical characteristics of a first-order phase-transition, with calcium field fluctuations within the tissue playing an essential role. This morphological transition was shown to be generated by activation over an energy barrier within an effective potential that underlies morphogenesis. Inspired by this intriguing insight, we propose a novel mechanism where stochastic fluctuations drive the emergence of morphological patterns. Thus, the inherent fluctuations determine the nature of the dynamics and are not incidental noise in the background of the otherwise deterministic dynamics. Instead, they play an important role as a driving force that defines the attributes of the pattern formation dynamics and the nature of the transition itself. Here, we present a simple model that captures the essence of this novel mechanism for morphological pattern formation. Specifically, we consider a one-dimensional tissue arranged as a closed contour embedded in a two-dimensional space, where the local curvature of the contour is coupled to a non-negative scalar field. An effective temperature parameter regulates the strength of the fluctuations in the system. The tissue exhibits fluctuations near a circular shape at sufficiently low coupling strengths, but as the coupling strength exceeds some critical value, the circular state becomes unstable. The nature of the transition to the new state, namely whether it is a first-order-like or a second-order-like transition, depends on the temperature and the effective cutoff on the wavelength of the spatial variations in the system. It is also found that entropic barriers separate the various metastable states of the system.

Dynamical processes on complex networks have a long history of study with increasing applications across many fields. While epidemics in heterogeneous networks have received much attention in terms of how connectivity patterns drive epidemic outbreaks, affect critical thresholds, timescales, final outbreak size and immunization efforts, less attention has been devoted to endemic multi-strain scenarios and questions of selection and coexistence dynamics. Here, we provide an SIS framework for multiple co-circulating strains and co-infection, which can be reduced to a replicator dynamics on a host contact network. Using the analytical tractability of the replicator formalism, we study how network heterogeneity affects multi-strain dynamics, and compare its effects relative to the homogeneous contact distribution, identifying key relevant metrics for comparison. In particular, the pairwise invasion fitness matrix comparison reveals that higher network heterogeneity acts to increase the speed of multi-strain dynamics and typically tends to have stabilizing effects that reduce the number of coexisting strains. While many aspects of the replicator dynamics remain complex to study, especially for high number of strains, the advantage of this model representation lies in the dimensional reduction of a huge system, enabling general, more direct and efficient numerical computations. Furthermore the explicit bottom-up constitution of crucial parameters yields biological and epidemiological insight for critical system transitions across macroscopic gradients and can be used to guide interventions.

Single-cell dynamics during cell state transitions (CST) are highly constrained, enabling precise control. However, there are challenges in achieving a system-level understanding or extracting general principles for CST dynamics due to the complexity of gene-gene interactions. Here, we introduce a new perspective to deal with these challenges using Fisher information. We found that, during CST, single cells exhibit pronounced sloppiness: cell states are sensitive only to a few "stiff" parameters while remaining robust to changes in numerous "sloppy" parameters. Critical transitions coincided with changes in stiff parameters. Moreover, stiff parameters typically exhibited minimal fluctuations and low velocities, whereas sloppy parameters allowed greater flexibility. Together, these findings can be summarized by stating that transition paths approximately adhere to a principle of least action. By characterizing the low dimensionality and constraints of CST through sloppiness and action, our work thus introduces a new conceptual and computational framework for analyzing single-cell dynamics. TeaserExcept when transitions occur, single-cell dynamics exhibit sloppiness, adhering approximately to a least action principle.

Hydrodynamic coordination of cilia is ubiquitous in biology. It is commonly modeled using the steady Stokes equations. The flow around ciliated cells, however, exhibits finite time vorticity diffusion, requiring a dynamical description. We present a model of elastic cilia coupled by transient viscous flow in the bulk fluid. Therein, vorticity diffusion impacts cilia coordination qualitatively and quantitatively. In particular, pairs of cilia synchronize in antiphase for long diffusion times. Moreover, metachronal waves occur in cilia chains larger than the viscous penetration depth, whereas global synchronization occurs in Stokes flow.

This study investigates global stability and tipping point prediction in cell fate decision-making systems through non-equilibrium landscape flux theory. We demonstrate that cell fate dynamics are governed by the interplay between potential landscape and curl flux, where the landscape guides systems toward stable states while curl flux mediates transitions between them. Our analysis reveals that non-zero curl flux generates irreversible dominant pathways between multi-stable states. We identify several quantitative measures for transition prediction, including barrier heights, kinetic switching times, entropy production rates, and average flux. We introduce novel non-equilibrium early warning indicators based on time irreversibility of cross-correlations ({Delta}C), average flux, and entropy production rate. These indicators exhibit significant changes near bifurcations, enabling transition prediction before state stability loss, with superior predictive capability compared to traditional critical slowing down theory. The rotational nature of curl flux is shown to destabilize attractor states, providing a dynamical foundation for phase transitions in cell differentiation, reprogramming, and transdifferentiation processes. These findings advance our understanding of non-equilibrium dynamics in cell fate decisions and offer practical implications for stem cell research and regenerative medicine, potentially enabling more precise therapeutic strategies in stem cell applications.

Biomolecular condensates are viscoelastic, and their mechanical properties are intimately related to their biological functions. However, the connection between microscopic networks formed by intermolecular crosslinks and viscoelasticity is still elusive. Here, we model biomolecular condensates as random crosslinked polymer solutions to elucidate how random connectivity fundamentally alters their viscoelasticity. We decompose the entire solution into multiple tree networks and demonstrate that for networks with size n, their spectra of relaxation rates{lambda} exhibit a power-law scaling pn({lambda}) [~]{lambda} -1/3 with a lower cutoff{lambda} min [~] n-3/2. By integrating all networks, we show that for the entire solution, random crosslinks generate an abundance of soft modes involving multiple linear polymers with a flat spectrum of relaxation rates. The soft modes cause anomalous linear frequency scaling of the dynamic modulus, in particular, they significantly boost the low-frequency storage modulus relative to uncrosslinked systems. Our predictions agree quantitatively with the experimental data from distinct biomolecular condensates.