PRX Life

Mechanical adaptation underlies mechanical homeostasis by allowing living systems to restore characteristic mechanical variables under sustained perturbations. Across biological scales, turnover-mediated remodeling enables mechanical adaptation by continuously renewing internal structures under load. Despite extensive progress in this field, it remains to be established what closed-loop mathematical structure of mechanics-turnover coupling is sufficient to guarantee homeostasis and how the characteristic adaptation timescale emerges from this coupling. Here, we identify the minimal mathematical structure of closed-loop mechanics-turnover coupling, providing a unifying description of mechanically adaptive remodeling across scales. We derive an analytical expression for the adaptation timescale as a function of the coupling between internal mechanical parameters and turnover kinetics, enabling direct cross-system comparison. To isolate this structure, we formulate a dynamical model linking mechanics and turnover, and establish conditions under which the closed-loop dynamics exhibit integral action. Specifically, our model describes how deviations in the mechanical state modulate the turnover of an internal structural state, and the renewed structure feeds back onto mechanics in a negative-feedback direction, driving recovery toward a reference state. We define systems satisfying this structure as Feedback Adaptive Turnover-mediated Environment-Dependent (FATED) systems. As an experimental example, we formulate mechanical adaptation in terms of mechanically regulated actin turnover. With the generalization of this architecture, we evaluate cross-system consistency by comparing reported adaptation and turnover timescales across representative remodeling systems.

Foraging is a central decision-making behavior performed by all animals, essential to garnishing enough energy for an organism to survive. Similarly, mating is crucial for evolutionary continuity and offspring production. Mate choice is one of the central tenets of sexual selection, driving major evolutionary processes, and can be regarded as a decision-making process between potential mating partners. Often researchers have used coarse-grained models to describe macroscopic phenomenology pertaining to mate choice without detailed quantitative mechanisms of how animals use individual and environmental signals to guide their mating decisions. In this letter, we show that mate choice can be cast as a foraging problem, and we present an analytically tractable optimal foraging-inspired mechanistic theory of decision-making underlying mate choice. We begin from the premise that deciding upon which partner with which to mate is at its core a stochastic decision-making process. Agents adopt a variety of decision strategies, tuned by decision thresholds for leaving or committing to a mate. We find that sensitive leaving thresholds are favored independently of signal availability in the population. By contrast, optimal thresholds for committing to a mate depend upon signal availability in the population, with signal-rich populations generally favoring less eager strategies compared to signal-poor populations.

Embryonic development in multicellular organisms exhibits diverse morphogenetic patterns, which can generally be categorized into fundamental types such as monolayer and multilayer spheres, as well as cell masses. Furthermore, we identify two distinct processes for the formation of spherical structures. These basic patterns are thought to be governed by the microscopic properties of intercellular adhesion. However, the specific mechanisms linking the microscopic factors to the emergence of distinct macroscopic morphogenetic patterns remain poorly understood. In this study, we explore how different morphogenetic patterns arise by employing a computational model that incorporates intercellular adhesion and polarity. Our results demonstrate that all fundamental morphogenetic patterns can be generated through the interplay of two key parameters: the strength of cell polarity and the regulation of polarity via mechanical signals. Furthermore, analytical discussions reveal partial mechanisms underlying the formation of these patterns. These findings highlight the critical role of physical constraints in morphogenesis and suggest potential applications in the design principles for artificial tissues and organoids. Author summaryLiving organisms build their bodies through morphogenesis, during which cells autonomously arrange themselves into functional structures such as sheets, tubes, and spheres. From simple monolayered spheres to complex multilayered tissues organized by adhesion, it remains unclear how such diverse forms arise. Here, we mathematically modeled a population of proliferating cells governed only by two microscopic factors: the strength of polarity-dependent adhesion and the time scale at which polarity is regulated by cell-cell contact. Surprisingly, we found that this minimal model reproduces five basic morphological types observed in living embryos, including monolayer/multilayer structures and two distinct modes of cavity formation: by wrapping around or by inflating from the inside. Systematic simulations revealed that these macroscale outcomes are determined solely by two parameters controlling polarity strength and its regulation, suggesting that simple physical rules underlie diverse developmental architectures. Analysis of the model uncovers phase transitions between the five morphogenetic types and reveals how varying polarity and adhesion can recapitulate features of real embryogenesis. Our work proposes a unified framework that connects microscopic polarity mechanics to diverse developmental morphologies and provides a foundation for future applications in organoid design and tissue engineering.

While the regulation of bacterial cell size is widely studied across generations, the stochastic nature of cell volume growth remains elusive within a cell cycle. Here, we investigate the fluctuations of cell volume growth and report a deviation from standard white-noise models: the random growth rate exhibits subdiffusive dynamics. Specifically, the mean square displacement of the growth-rate noise scales as {Delta}t with an anomalous exponent {approx} 0.27. This low exponent implies strong negative temporal correlations in growth rate noise on timescales of minutes, which are significantly faster than those of gene expression dynamics. We attribute this phenomenon to the physical mechanics of the cell wall. By modeling the peptidoglycan network as a complex viscoelastic material with power-law-distributed relaxation times, we successfully recapitulate the observed subdiffusive behavior. Our results suggest that the heterogeneous mechanical constraints of the peptidoglycan network, rather than biological regulatory programs,govern the short-timescale fluctuations of bacterial growth.

The dynamic assembly of actin filaments underlies diverse cellular morphologies such as lamellipodia, filopodia, and reticulated networks. However, how filament-scale interactions among actin-binding proteins produce distinct actin architectures remains unclear. We developed a filament-resolved computational model of actin self-organization regulated by the Arp2/3 complex and fascin. Individual F-actin filaments are represented as elastic chains, and their stochastic polymerization, Arp2/3-mediated branching, and fascin-mediated crosslinking and bundling are explicitly modeled. The simulations reproduce three actin architectures observed in minimal reconstitution experiments, including lamellipodia-like branched networks, filopodia-like bundled protrusions, and reticulated meshworks, as a function of Arp2/3 and fascin concentrations. We quantify these regimes using actin density, orientational order, and spikiness, which robustly separate the three morphologies across conditions. To connect filament organization to shape change, we further couple the actin network to membrane deformation using a phase-field formulation. This coupling shows how localized remodeling concentrates load to drive pseudopodial protrusions, whereas highly branched networks distribute stresses and stabilize rounded shapes. The model links molecular interactions to emergent architecture and cell-scale morphodynamics.

We investigate the target search process by proteins locating specific target sites along DNA - a phenomenon fundamental to biological functions such as gene regulation, transcription, replication, recombination, and gene-editing technologies. This process proceeds through a repetitive sequence of stochastic motions: consisting of one-dimensional (1D) sliding along the DNA contour interspersed with detachment and three-dimensional (3D) excursions in the bulk, and then reattachment to a random location on DNA. Recognizing this sequence of random events as analogous to the resetting processes widely studied in statistical physics, we employ a first-passage-renewal framework and derive general expressions for both the mean and fluctuations of the total search time. Our results are completely generic and do not depend on the detailed microscopic dynamics of either the 1D or 3D phases. Quite interestingly, we find that intermittent detachment can not only accelerate the mean search but can also regulate fluctuations around it. Our analysis reveals a universal fluctuation inequality that links the variability and mean of the sliding time to the mean excursion time, thereby identifying the fundamental conditions under which target search process becomes efficient. Notably, we find that broad distributions of sliding times emerge as a universal characteristic for optimal search efficiency--a feature emanating from the slow dynamics along the DNA. Using the facilitated diffusion mechanism as a representative example, we validate the generality of our results. These findings provide a unified theoretical framework connecting stochastic search, resetting dynamics, and biological efficiency, while also highlighting the crucial role of DNA structure such as its contour length in modulating search performance.

The interactions of droplets and filaments can lead to mutual deformations and complex combined behavior. Such interactions also occur within the cell, where biomolecular condensates, distinct liquid phases often composed of proteins, have been observed to structure and affect the organization of the cytoskeleton. In particular, biomolecular condensates have been shown to undergo characteristic deformations when cytoskeletal filaments are fully embedded within them. However, a full understanding of the underlying physical mechanisms is still missing. Here, we combine experiments with coarse-grained molecular dynamics simulations and analytical models to uncover the physical mechanisms that define emerging shapes of droplets containing filaments. We find that the surface tension of the liquid phase and the bending energy of the filament(s) suffice to accurately capture emerging shapes if the length of the filament is small compared to the liquid volume. As the volume fraction of filament(s) increases, wetting effects become increasingly important, setting physical constraints within which surface and bending energies compete to define the droplet shapes. We find that mutual deformations of condensate and filament extend accessible shapes beyond classical stability considerations, leading to structuring and entrapment of contained filaments. Shape deformations may further affect ripening dynamics that favor certain geometries. Our findings provide a physical framework for a better understanding of the possible roles of biomolecular condensates in cytoskeletal organization.

Cell-cell junctions (CCJs) are dynamic biopolymeric systems essential for adherence of biological cells organizing into a tissue or organ. In vertebrate organisms, CCJs present in stable epithelial tissues are maintained primarily by cell-to-cell protein bridges made of an adhesion receptor E-cadherin. CCJs are destabilized during Epithelial (E) to mesenchymal (M) transformation (EMT), an essential step in cancer metastasis, where cells switch states and acquire migratory features. An essential trigger for EMT is a cadherin switch process from E-cadherins with N-cadherin, another cadherin isoform. EMT proceeds through several intermediate states referred to as hybrid E/M cells. These states are characterized by mixed levels of E- and N-cadherins at the junctions and exhibit versatile cancerous traits that are more aggressive than cancerous fully mesenchymal cells. As a result, many such states have emerged as key targets in cancer therapy. However, development of a therapeutic design to counter the hybrid E/M cells has been limited by the absence of a comprehensive understanding of the mechanics and dynamics of hybrid E/M states. Here, we develop a physical model of CCJs as a non-equilibrium system composed of a variable ratio of E- and N-cadherins, considered as coarse-grained molecules driven by ATP-powered machinery observed at CCJs. Our model predicts a robust measure of strength of junctions that captures previous experimental observations, and reveals a minimal mechanochemical landscape of hybrid E/M states. We show the emergence of several groups of CCJ states in this landscape with variable adhesion strengths, many of which resemble different hybrid E/M-characteristics observed experimentally. Finally, we identify that a difference in mechanosenstivity of the two cadherin isoforms towards cytoskeletal forces could be why the hybrid E/M states come into existence.

AO_SCPLOWBSTRACTC_SCPLOWTransitions between stable states are a defining feature of nonlinear dynamical systems, yet the factors controlling their probabilities and timescales remain poorly understood in non-conservative settings. In many theoretical frameworks, such control is commonly interpreted in terms of potential depth, a concept that becomes ambiguous outside equilibrium. By analyzing a gene regulatory network associated with breast cancer subtypes, we uncover a geometric framework in which the phase-space distance between stationary states, together with the bifurcation structure organizing multistability, provides a robust and well-defined determinant of transition probabilities, times, and variability. Our results show that the coexistence of stable states is only a necessary condition for transitions, while their accessibility is constrained by geometric features of the underlying state space. Within this framework, we find that the HER2+ regime exhibits dynamical robustness to intrinsic parameter variations, whereas the TNBC regime displays strong sensitivity and amplified variability. These differences emerge naturally from the geometric organization of the bistable region and offer a dynamical explanation for the pronounced heterogeneity observed in TNBC. Together, our results establish a general geometric perspective on transitions in non-conservative regulatory networks, with implications for understanding phenotypic plasticity in complex biological systems.

Complex systems with nonreciprocal interactions are often stratified into layers. Ecosystems are a prime example, where species at one trophic level grow by consuming those at another. Yet the dynamical consequences of such stratified nonreciprocity--where the correlation between growth and consumption differs across trophic levels--remain unexplored. Here, using an ecological model with three trophic levels, we reveal an emergent asymmetry: nonreciprocal interactions between consumers and predators (top and middle level) destabilize ecosystems far more readily than non-reciprocity between consumers and resources (middle and bottom level). We analytically derive the phase diagram for the model and show that its stability boundary is controlled by energy flow across trophic levels. Because energy flows upward--from resources to predators--diversity is progressively lower at higher trophic levels, which we show explains the asymmetry. Lowering energy flow efficiency flips the asymmetry toward resources and remarkably expands the stable region of the phase diagram, suggesting that the famous "10% energy transfer" seen in natural ecosystems might promote stability. More broadly, our findings show that the location of nonreciprocity within a complex network, not merely its magnitude, determines stability.

How genetically identical cells spontaneously break symmetry to assume divergent fates is a fundamental problem in developmental biology. While modern genomics has mapped the vast molecular repertoire involved in gene regulation, understanding the mechanism of cell state transitions that drive differentiation remains a formidable challenge. To address this, we use a reaction-kinetic framework to analyze recurring motifs of two and three competing master regulators. While typically such circuits are studied numerically, we show that assuming symmetry in nodes and interactions provides exact analytical description of the bifurcations governing cell fate transitions. We find that the possible cell fates across all considered topologies are dictated by a single dimensionless quantity, {beta}--the ratio of protein degradation to production rates. In the binary Toggle Switch (TS), decreasing {beta} destabilizes the symmetric (stem cell) state, giving rise to two asymmetric (differentiated) fates via a supercritical pitchfork bifurcation. In the three-component Toggle Triad (TT), low values of {beta} yield three asymmetric fates through subcritical pitchfork bifurcation, creating an intermediate range of {beta} where both symmetric and asymmetric fates are simultaneously stable. For the Self-Activating Toggle Switch (SATS), we identify a new parameter for the self-activation threshold ({theta}) and show that decreasing{theta} progressively stabilizes the uncommitted state, leading to a regime of tristability. Building on these temporal bifurcations, we next address the feasibility of spatial structure formation: can these multistable fates stably coexist within a spatial domain? Through a minimal model of cell-cell communication via free diffusion, we extend these motifs into reaction-diffusion systems, which reveals a direct role of network topology on spatial organization. We prove that any heterogeneous pattern in two-node circuits is inherently transient and unstable. In contrast, the three-node repressive network supports the stable spatial coexistence of differentiated phenotypes through pure diffusion, a phenomenon we analyze by studying heteroclinic interface solutions as building blocks. By reducing complex regulatory dynamics to tractable models with physically meaningful parameters, we establish a minimal framework which relates topology to cell fate. Finally, the effects of temporal multistability on pattern formation provide an excellent studying ground for morphogenesis, synthetic biology, and the overarching problem of spatiotemporal self-organization.

The nuclear lamina, composed of supramolecular structures of lamin proteins, is a two-dimensional protein meshwork that preserves the structural integrity, elasticity, and morphology of the nucleus. Lamins--A/C-type and B-type--assemble into dynamic, individual but interacting networks with distinct structural properties. Lamina meshwork assembly can be disrupted by lamin mutations in diseases known as laminopathies. Despite extensive experimental insights, the biophysical mechanisms that alter the lamina meshwork topology in health and disease remain relatively poorly understood. In this study, we develop a coarse-grained molecular dynamics (MD) model of lamina self-assembly, where lamin dimers are modeled as semiflexible polymers confined within an elastic nuclear shell. By systematically interrogating inter-lamin and lamin-shell association affinities, our simulations reproduce a plethora of experimentally observed lamina architectures, from lattice-like to fibrous meshwork topologies. This elucidates how the interplay between inter-lamin and lamin-nuclear envelope interactions can shape the nuclear lamina. Importantly, inter-lamin interactions can cause a heterogeneous distribution of lamins on the surface and result in large, lamin-free surface domains at sufficiently low lamin-shell affinities. Furthermore, paracrystalline lamin sheets form with increasing propensity for parallel lamin alignment, in addition to the canonical, sticky terminal groups. Overall, our integrative MD and network analysis provide the first explicit polymer physics model of the lamina and demonstrate how lamin interactions may affect the mesoscale architecture of the lamina in disease.

Quantifying task difficulty remains an open theoretical problem in neuroscience and artificial intelligence. While difficulty is often treated as a scalar property of stimuli or optimization landscapes, neural computation unfolds as a transient reconfiguration of high-dimensional dynamical systems. Here we propose a dynamical manifold theory of difficulty based on heterogeneous, modular FitzHugh-Nagumo networks subjected to structured task demand. Task difficulty is modeled as a conflict-driven control parameter that perturbs competing neural submodules. We define four dynamical metrics: (i) transition action (energetic cost), (ii) peak dispersion entropy, (iii) coherence recovery deficit, and (iv) mean-field trajectory curvature. Across systematic sweeps of task demand, we demonstrate that difficulty does not collapse to a single axis but instead emerges as a multidimensional manifold. Energetic cost and dispersion entropy form a dominant axis, while geometric curvature and integration recovery exhibit partial independence and nontrivial correlations. These results suggest that cognitive difficulty corresponds to structured reorganization in neural state space rather than mere increases in activation amplitude. The proposed framework provides a biophysically interpretable foundation for linking neural dynamics, cognitive effort, and difficulty estimation in artificial systems.

Primary body-axis development is a highly conserved process that proceeds through somitogenesis and subsequent subdivision into dermatome, myotome, and sclerotome. Defects in somitic-clock genes such as Hes7 lead to vertebral-segmentation defects in mice and fish. Here we show that in the axolotl, although Hes7 is necessary for proper embryonic vertebral segmentation, it is-- surprisingly--dispensable during tail regeneration. We investigated the mechanism of vertebral segmentation during regeneration which initially occurs through extension of a cartilage rod ventral to the spinal cord. We find that the regenerating cartilage rod undergoes a periodic wrinkling that provides a template for vertebral segmentation. Via direct mechanical measurements and biophysical perturbations, we show that a model of compression-induced buckling instability can predict vertebral segmentation. The cartilage rod and other somitic derivatives (muscle, cartilage, tendon, fibroblasts) arise from tendon-like, Lfng+ multi-potent mesenchymal progenitors, which display a gene regulatory state distinct from somitic progenitors. In summary, we uncover a mechanism of vertebral segmentation during axolotl tail regeneration that is distinct from the somite-based developmental mechanism.

The spatiotemporal progression of tau aggregates in neurodegenerative diseases like Alzheimers follows the brains structural connectome, yet a profound gap exists between the slow macroscopic spread observed over years and the rapid protein kinetics occurring over hours. Current graph-diffusion models fail to reconcile this timescale disparity or incorporate the cellular mechanisms driving transmission. Here, we advance the Network Transport Model (NTM) to bridge these scales by integrating directional active transport along microtubules, continuous toxic tau production, and exosome-mediated trans-neuronal release and uptake. This framework constitutes one of the most mechanistically complete and biologically detailed models of tau spread on the whole brain to date, representing a significant innovation in how multiscale proteinopathies are simulated. To overcome the computational complexity of the underlying partial differential equations, we developed a quasi-static approximation that separates fast axonal transport from slow network-wide exchange. Simulations on the whole-brain mouse connectome demonstrate that this framework emergently replicates empirical tau propagation patterns without the need for case-specific empirical fitting. Our results identify trans-neuronal release and uptake rates as the primary mechanistic "bottleneck" on macroscopic spread, providing a biologically grounded explanation for the diseases slow progression. Furthermore, we find that high aggregation rates can paradoxically sequester tau within neurons, limiting global transmission, while transport polarity (anterograde vs. retrograde) fundamentally dictates spatial patterning. By linking molecular mechanics to system-wide pathology, this model provides a predictive "in-silico" framework to evaluate how cellular-targeted interventions might alter the trajectory of tauopathic dementias.

Chromosome segregation is a tightly-regulated process that normally occurs with high fidelity. Errors in chromosome segregation are associated with aging, cancer, and infertility. Initially erroneously attached chromosomes are corrected over the course of mitosis, with the spindle assembly checkpoint preventing entry into anaphase until this error correction is complete. Despite extensive work on the molecular basis of error correction and the spindle assembly checkpoint, it is still unclear how disruption of these processes contribute to chromosome segregation errors. Here, we develop and experimentally test a coarse-grained model of error correction in the presence of a faulty spindle assembly checkpoint. We use the resulting model to disentangle the impact of various small molecule and genetic perturbations on both error correction and the spindle assembly checkpoint, and to compare chromosomally stable hTERT-RPE-1 cells and chromosomally unstable U2-OS cells. We find that the probability of error-free chromosome segregation is determined by the ratio of the checkpoint failure rate to the error correction rate, and validate a simple heuristic for understanding the source of chromosome segregation errors: perturbations which cause errors by disrupting the spindle assembly checkpoint decrease anaphase times, while those that disrupt error correction increase anaphase times. Taken together, this work provides a quantitative framework for understanding how error correction and the spindle assembly checkpoint contribute to mitotic timing and fidelity.

Biomolecular condensates are domains within cells with distinct compositions, held together by intermolecular cohesion. They are implicated in a variety of cellular processes, and in vitro studies have revealed the molecular driving forces that underly their condensation. However, in vitro condensates do not capture essential features of cellular condensates. In particular, enrichment of proteins, quantified by partition coefficients, is often exaggerated in these simplified systems. We show that the addition of free amino acids and other small molecules to model condensates can bring their partition coefficients within physiological range. In this limit, where there is low biochemical contrast between condensates and their surroundings, we observe striking changes to condensate behavior. Such low-contrast condensates exhibit large fluctuations in shape and composition and show enhanced sensitivity to changes in their environment. These behaviors reflect dramatic shifts to their material properties, including interfacial tension, rheology, and chemical susceptibilities. We note remarkable similarities in these effects across seemingly unrelated two-phase fluid systems. To explain these trends, we reformulate classic models of critical phenomena in terms of partition coefficients. This framework simplifies application of theory to experiments with near-critical fluids and suggests new experimental approaches for assessing condensate physiology in live cells.

Evolutionary therapies regulate heterogeneous populations by altering selective pressures through treatment sequences in cancer and infections. This letter develops an invariant-set framework for treatment-induced containment based on positive triangular invariant sets. For periodically switched systems, sufficient conditions are derived for the existence of such invariant regions. Robustness with respect to mutation is established by showing that the invariant simplex persists under small perturbations of the subsystem matrices. In the two-phenotype case, the analysis yields an explicit mutation threshold that separates regimes in which therapy cycling maintains containment from regimes in which mutation can enable evolutionary escape. Simulations illustrate the geometry of the invariant sets and the role of mutation and dwell time in containment robustness.

How developmental timings are regulated is a fundamental open question. Two widely considered mechanisms are the clock, in which an internal timer determines when each stage occurs, and the domino, in which the completion of each stage triggers the next. It is often unclear how to establish either mechanism. Here, we construct a quantitative framework that uses the correlation structure of developmental timings to test the clock and domino mechanisms. We apply this framework to human pre-implantation development by using ~1 million images of 2946 embryos acquired during IVF treatment, establishing mathematical models of developmental rate. We find that a domino mechanism governs the cleavage timings, while a pronuclei fade-triggered clock mechanism governs the morula and blastocyst timings. These results are consistent with the cell cycle oscillator governing the cleavage timings and the accumulation of embryonic gene products or the degradation of maternally deposited factors governing the morula and blastocyst timings. We next investigate the physiological regulators of developmental timing by analyzing how the timings are statistically associated with the clinical pregnancy outcome. While embryos that result in a clinical pregnancy tend to exhibit shorter cleavage timings, this association is primarily driven by patient-specific properties. In contrast, embryo-specific properties independently influence the pregnancy outcome and the cleavage timings, so that factors directly determining implantation potential, such as aneuploidy, can only weakly impact the cleavage timings. Taken together, this work provides a robust framework for decoding developmental timing mechanisms, with significant implications for fundamental biology and clinical practice.

Osmotic pressure is a fundamental physical determinant of cellular homeostasis, and its perturbation is recognized as a critical factor in cancer progression and therapy. However, whether cancer cells and normal cells respond to osmotic pressure changes differently remains unclear. Here, we subjected cancer and normal cells to osmotic shocks and compared their volume and traction force changes. Under hypotonic conditions, cancer cells recovered their volume and forces much more slowly than normal cells, although both cell types responded similarly to hypertonic shock. We found that actin-based cortical tension controlled the recovery speed; whereas myosin-mediated contractility tuned the volume change extent. Substrate stiffness also influenced the recovery process by altering cytoskeletal constraint. A theoretical model integrating adhesion energy, ion and water transport, and surface tension was developed. The results matched the experimental observations. Our work uncovered the distinct mechanobiological behaviors of cancer cells upon hypotonic shock, providing a mechanical framework for understanding cancer mechanisms that may inform the development of cancer therapeutics.