Physical Review E

We show that the p53-Mdm2 gene interaction can be understood as a form of antithetic feedback, but with mixed feedback loops. In particular, we show that this viewpoint sheds light on the emergence and robustness properties of p53's oscillatory behaviour, as observed experimentally.

We investigate the dynamics of the spread of the infection due to a phage- during the range expansion of an E coli colony. We find a rich panoply of spatio-temporal dynamics at large colony-level length scales, arising due to the interplay of mechanical forces, growth and viral infection dynamics at smaller cellular length scales. Strikingly, the phages "surf" the front of the growing bacterial colony by hitchhiking on E coli that are advected due to the growth of bacteria in the colony, resulting in an anisotropic spread of the phages. We identify microscopic processes - of the phage release during lysis (occurring on short millisecond timescales at length scales close to that of a single bacterium) and local nematic alignment of the rod-like E coli bacteria (occurring on timescales comparable to the bacterial growth rate and the length scales of a few bacterial cells) - that enhance the advective effects driving the hitchhiking behavior. Combining our experiments with a mathematical model, we explain the multiple spatio-temporal dynamical regimes - from the coexistence of uninfected bacteria, resistant (lysogenic) cells and phages, to fixed points where the entire population turns resistant or remains uninfected. Our work broaches a new frontier in the investigation of eco-evolutionary processes arising from the mechanical and ecological forces due to the interactions between viruses and their hosts.

Behavioral variability reflects differences in internal and external parameters and provides a substrate for natural selection. However, uncovering its structure is challenging because behavior evolves nonlinearly across multiple timescales. Our goal is to reconstruct phenotypic variation from finite behavioral observations without prescribing the scales at which individuals should be compared. To achieve this, we introduce a multiscale dissimilarity that compares dynamics across all statistically resolvable resolutions by constructing reduced transfer operators at progressively finer scales and weighting their differences by finite-sampling uncertainty. This dissimilarity defines a geometry of dynamical phenotypes, which we reconstruct using diffusion maps. We show that the resulting phenotypic coordinates locally follow the parameter directions to which dynamics are most sensitive. We validate our approach in a stochastic model and apply it to bacterial and larval zebrafish behavior. In bacteria, we identify run speed as a major component of inter-individual variability, associated with the chemotaxis protein CheB. In zebrafish, we find that prior prey experience reshapes behavioral dynamics and phenotypic variability, with paramecia experience concentrating fish in a prey-capture-associated region of phenotypic space. Together, these results provide a framework for identifying internal and environmental variables that structure dynamical phenotypes across scales.

Regular environmental cycles such as day and night or the lunar cycle are ubiquitous and drive many biological processes. Many organisms have evolved endogenous time-keeping mechanisms to anticipate these cycles to accurately time their behavior or synchronize physiological processes. The evolution of such synchronization to environmental cycles and their variability is not very well understood. As an example, we use the marine insect Clunio (Diptera, Chironomidae), which synchronize adult emergence and reproduction with the lunar cycle, and show different emergence patterns across populations. We use a model constructed with replicator-mutator dynamics to provide a novel outlook at the evolution of these emergence patterns. In particular, we investigate the effect of two traits of individual phenotypic variability of emergence, the spread and shape, on population-wide emergence patterns. We find that the semilunar and lunar emergence patterns are alternatively stable and occur when the phenotypic distribution has a narrow and is roughly flat. Arrhythmic emergence occurs when the phenotypic distribution is wide and nearly flat. The semi-lunar pattern can only be observed when the parameter of rhythmicity is changed. With our model, we introduce the concepts of frequency-dependent selection and individual phenotypic variability into the theory of chronobiology, which gives us insights into the evolution of rhythmicity in these organisms.

Recurrent cortical circuits are hypothesized to perform Bayesian posterior sampling through their stochastic dynamics. Yet identifying which sampling algorithm a circuit intrinsically implements, as opposed to mapping manually designing algorithms onto circuits, requires rigorous theoretical analysis of the biological circuit dynamics, and remains a fundamental open challenge because of the analytical intractability of nonlinear recurrent dynamics. Here, we tackle this challenge through comprehensive theoretical analysis of analytically tractable nonlinear recurrent circuit dynamics used in neuroscience research-- the continuous attractor network (CAN). Surprisingly, we find that the circuit, without any non-Gaussian components in its connectivity or internal variability, intrinsically emerges heavy-tailed subspaces dynamics described as scale-mixture Langevin posterior sampling. The mechanism emerges from the circuits own nonlinear dynamics: divisive normalization renders the overall population activation Gamma-distributed which multiplicatively modulates the time constant of the Langevin sampling in the stimulus feature subspace. Eventually, this scale-mixture structure produces a heavy-tailed (Student-t) sampling step size distribution, significantly accelerating the sampling speed. Moreover, the scale-mixture Langevin sampling approaches a Levy-like regime in the weak input limit. Our results analytically identify an intrinsic circuit algorithm embedded in subspaces of nonlinear recurrent dynamics, and establish a minimal circuit mechanism for endogenous heavy-tail statistics without any explicit non-Gaussian components.

We develop a general geometrical framework for growth processes in which the growth rate depends exponentially on the number of active growth-supporting components. The framework separates the fraction of active components from the size of the accessible component space, allowing qualitatively different growth laws to arise from the same underlying construction. Bacterial population growth provides an example of a fixed-size component space controlled primarily by activation and deactivation, whereas examples such as human population growth or speciation provide an expanding component space in which interactions between individuals promote further growth. This motivates a Replicative geometrical law, dX/dt= X exp({beta} X^{gamma}), whose exponent characterizes the scaling of the effective growth-supporting component space and is tested against historical human-population regimes and eukaryotic lineage-through-time data. For innovation indicators such as patents and arXiv manuscript submissions, where an existing item need not itself reproduce, the same construction motivates a Direct Geometrical production law without the prefactor X. The framework therefore provides a common description of fixed and expanding component spaces while distinguishing Replicative from Direct Geometrical growth.

Collective migration is often attributed to complex cell-cell communication, yet coordinated multicellular dynamics can also emerge in organisms lacking social interactions. Continuum descriptions successfully capture such behaviors but generally rely on phenomenological transport coefficients whose microscopic origin remains elusive. Here we show that these coefficients emerge from cell-cell collisions and can be independently determined from experiments. We investigate the aerotactic dispersal of confined colonies of the solitary amoeba Acanthamoeba castellanii, in which oxygen consumption continuously reshapes the local environment to generate self-organized guidance cues. Combining quantitative videomicroscopy, oxygen mapping with phosphorescent sensing films, and oxygen-controlled microfluidics, we directly measure both the oxygen landscape and the aerotactic response governing colony expansion. We then develop a Patlak-Keller-Segel (PKS) -type drift-diffusion model whose transport coefficients are entirely determined from independent experiments and microscopic-to-macroscopic modeling approach, without adjustable parameters. The model quantitatively reproduces the observed dynamics, including the coexistence of a fast ballistic front and a trailing transient accumulation band. We show that both diffusion and aerotactic transport are modulated by the same collision-controlled mechanism through density-dependent changes in cell persistence. More generally, our results establish transport coefficients as measurable emergent properties bridging microscopic cell dynamics and macroscopic collective behavior, providing a predictive framework for oxygen-guided migration in living active matter.

Emerging research on desynchronization reveals strong relations to memory formation and recollection with much of the evidence originating from studies of the hippocampus, a brain region central to memory processing. However, growing evidence emphasizing the role of desynchronization is accompanied by challenges, most notably the synchronization/desynchronization conundrum. The conundrum arises from an apparent contradiction between learning and Shannon's information theory: spike-timing-dependent plasticity (STDP) acquires information via synchronized populational activity whereas information theory suggests that information channel is encoded through higher variability. Both frameworks are well-founded. Learning is widely accepted as the mathematical abstraction of STDP while Shannon's information theory showcases its power ubiquitously across fields from communication systems to neuroscience. Here, we propose that learning and Shannon's information theory are not necessarily opposing principles. Rather, learning plays a critical role in the process of synchronization and desynchronization. To justify our claim, we conduct computational simulations based on a Hodgkin-Huxley neuronal model coupled with NMDA, AMPA, and GABA synapses with inputs of biologically realistic spiking data. Our results show that enabling STDP significantly influences synchronization and desynchronization dynamics. Specifically, we find that STDP and desynchronization form a regulatory loop, in which STDP regulates the level of synchrony, and synchrony regulates subsequent learning strength. Further study reveals STDP is capable of switching neurons from synchronization to desynchronization. This framework mitigates the synchronization/desynchronization conundrum by clarifying the relationship between desynchronization and learning, and offers a new perspective on how synchrony contributes to memory formation and recollection.

A major transition in the evolution of eukaryotic cells was phagocytosis: the ability of one cell to engulf another. In some cases, the engulfed cell persists, forming an endosymbiosis which is often mutually beneficial. However, it is unclear whether the interaction between the ancestors was also cooperative. There are clear benefits to developing the ability to eat a competitor, but can it ever be beneficial to eat a cooperator? We use a dynamical systems framework to identify the ecological conditions under which phagocytosis can evolve from a system of cooperating microbes.Beginning with a system of two cooperating species, we use invasion analysis to identify the parameter regimes under which a phagocytosing mutant can invade and the subsequent population dynamics. We identify a critical threshold that determines whether an invading predator will coexist with the cooperative community or replace members. Repeatedly invading with different predators, we find that the system saturates when there are three coexisting species, though this community does not have a single optimal composition. However, if we incorporate additional costs, we find there is a single evolutionarily stable community of two cooperators and a pure predator. Ultimately, we show that it is possible for phagocytosis to evolve from a cooperative community and, moreover, coexist with the original cooperating species.

Phase separating biopolymers are often described by the sticker-spacer model, which accounts for non-attractive linkers that connect discrete attractive moieties. "Associative polymer" theories describe these systems as two coexisting fluids of stickers and spacers, respectively. In such theories the stickers and spacers are decoupled in the sense that sticker binding does not affect spacer conformations or vice versa. Informed by coarse-grained simulations, we develop a phenomenological mean-field theory to determine the microscopic coupling between the sticker and spacer degrees of freedom. Accounting for linkers connecting adjacent spacers introduces free energy contributions due to conformational entropy of the spacer and the binding combinatorics of the stickers. These contributions have opposite dependencies on spacer length because longer spacers allow a greater volume to search for binding partners but incur a greater entropy cost upon bond formation. The length dependent terms from these contributions cancel leaving a length-independent elastic term arising from the fact that a small amount of spacer stretching lowers the free energy by increasing the number of possible binding partners. The cancellation of spacer length from the theory justifies the decoupling approximation and supports mean-field treatments of heterogeneous spacers.

Non-exponential residence times give rise to history-dependent or memory effects in epidemic dynamics, yet their mathematical formulations remain fragmented. Here we develop a unified framework for a history-dependent SEIR model with general latent- and infectious-period distributions. We first establish the equivalence between the stage-age and renewal formulations and show that both admit a unified transition-flow representation. We then introduce the concept of a transition-flow multiplier, which provides a direct link between residence-time distributions and transition flows. When the multiplier is a weighted sum of shifted power functions, the model admits an exact representation in terms of Riemann-Liouville or tempered Riemann-Liouville fractional operators, providing a first-principles foundation for fractional epidemic models. Finally, using Euler-Lotka equations and stochastic-order arguments, we characterize how the latent- and infectious-period distributions shape epidemic growth and decay. A longer latent period slows both early growth and late decay, while, at fixed means, greater variability in the latent period accelerates early growth but slows late decay, whereas greater variability in the infectious period slows both.

Cells use ATP-driven chaperones to extract clients from biomolecular condensates selectively, yet no closed-form criterion links molecular parameters to condensate quality control. We derive a minimal non-equilibrium sorting reactor model that reduces the reaction-diffusion dynamics to one algebraic equation. In the idealized low-load limit, a concentration-dependent partition coefficient produces a saddle-node bifurcation between functional clearance and pathological storage. The critical Damk\"ohler number is \(\mathrm{Da}_{0c}=e^{-2}\) and is independent of the feedback strength. Corrections shift the value but preserve the topology. The model predicts a Kramers-type functional lifetime and recovery costs that scale as \(R^3\). Critical slowing down near the bifurcation provides early-warning signatures for FCS and FRAP.

Most animals move intermittently. Of these, animals that fly and swim move in two stages: during active propulsion, when they beat their wings or swing their tails, and right after, when they glide or coast through the air or water. The kinematics of active movements are typically well studied, but the coasting period afterwards is less understood. We used larval zebrafish as a model of intermittent locomotion. Larval zebrafish swim in discrete bouts lasting ~200 ms, coast for short durations and distances, and then are largely stationary for ~800 ms. We find that larval zebrafish do not coast like a passive object. While they coast for distances that are correlated with the prior swim's strength, as expected from physics, they seem to be able to modulate the mechanics of their coasting: the time constant is not a constant, but varies from coast-to-coast. Furthermore, the time constant is correlated with the duration of the interval between swim bouts. This suggests that larval zebrafish can either shorten or extend their coasting duration, and that coasting inhibits the initiation of the next swim. Finally, the time constant changes quickly, while other swimming kinematics (e.g., distance swum) are autocorrelated over the course of at least several seconds. Altogether, this suggests that fish, and perhaps other animals that move intermittently, actively modulate their post-propulsion movement, possibly to gather sensory feedback in the absence of blurry visual feedback associated with fast locomotion.

Species at the highest trophic levels are generally the least resilient to perturbations, yet the factors that determine their persistence remain poorly understood. We ask how the intrinsic self-regulation of a basal host governs the persistence of the trophic levels above it. To address this question, we use a minimal discrete-time model of a host-parasitoid-hyperparasitoid system motivated by the biology of trigonalid wasps, obligate hyperparasitoids that complete development only when their caterpillar host is also attacked by a primary parasitoid. We compare two forms of host self-regulation in the absence of natural enemies: scramble (Ricker) fecundity, appropriate when the parasitoid is the host's principal enemy and which recovers the classical model of Beddington and Hammond as a special case; and contest (Beverton-Holt) fecundity, appropriate when the host is held in check by many additional enemies. Using numerical continuation, Lyapunov exponents, and direct computation of the model's trajectories, we find that the form of host regulation is decisive for persistence at the top trophic level. Under scramble host dynamics, coexistence is extremely fragile with respect to both parameter values and initial conditions. Under contest host dynamics, coexistence is robust across broad parameter ranges and loses stability only gradually, through a supercritical Neimark--Sacker bifurcation and a subsequent torus-doubling route to chaos. Therefore, in at least some trophic networks, the resilience of the highest levels can be determined at the base of the network.

Nanopore sensors have transformed single-molecule analysis, enabling real-time detection of biomolecules with unprecedented resolution. Understanding and modelling noise in nanopore sensing is essential to unlocking their full analytical potential. Although mechanistic models of nanopore noise exist, a rigorous statistical framework that characterises noise structure across diverse experimental conditions is still lacking. Here, we present a comprehensive empirical analysis of nanopore noise using twelve diverse experimental conditions acquired with different nanopores, analytes, and electronic recording systems. By employing multiple, mutually reinforcing statistical methods, we establish that nanopore noise is well described by a composite fractional model comprising multiple fractional Gaussian noise and fractional Brownian motion components. This finding is supported by confirmation of Gaussianity, rigorous interpretation of second-order exponents, multifractal analysis, and evidence that transient deviations are attributable to deterministic or experimental artefacts rather than alternative stochastic mechanisms. We further resolve quasi-deterministic structures, such as baseline trends and structural breaks, and demonstrate their separability from the underlying stochastic profile. Collectively, these results provide the first formal statistical validation of a composite fractional model for nanopore noise and establish a principled basis for noise reconstruction, realistic simulation, and statistically grounded algorithm design for nanopore sensing applications. This study provides the foundation for the creation of high-fidelity performance evaluation datasets for signal processing, and the controlled generation and augmentation of data for machine learning while maintaining statistical fidelity to experimental conditions.

We propose a minimal mathematical framework to describe the go-or-grow dynamics of tumor cells comprising two phenotypically distinct populations. One population is migratory and undergoes constant diffusion, while the other proliferates in an oxygen-dependent manner. The local oxygen concentration governs transitions between these phenotypes. We then ask whether the time scale of cyclic hypoxia, where oxygen is spatially homogeneous but fluctuates between normoxic and hypoxic levels over time, alters the dynamics of the reduced generalist model in the fast phenotype-switching regime compared with the full go-or-grow model. We observe that the reduced generalist phenotype model fails to capture the go-or-grow dynamics under rapid oxygen fluctuations. Our results predict that the tumor growth rate increases in the generalist-phenotype model under rapid oxygen fluctuations compared with tumors of the proposed go-or-grow model. We then explore whether oxygen consumption, which leads to spatial heterogeneity in oxygen concentration, plays a role in distinguishing the dynamics of the reduced model from the proposed go-or-grow model. We demonstrate that the tumor in the proposed go-or-grow model exhibits a higher growth rate than the tumor in the reduced generalist-phenotype model under a slow oxygen consumption rate.

Biofilm formation--the establishment of cellular communities within a self-secreted polymer matrix--is a behavior exhibited by almost all species of bacteria. Bacterial biofilms are well described as viscoelastic materials, with properties that grant physical advantages, such as elastic resilience and viscous adaptability. Additionally, many biofilm-forming species produce a subpopulation of highly resilient spores. In the model biofilm- and spore-forming species Bacillus subtilis, sporulation and matrix production are regulated by a common gene pathway, provoking the question of how sporulation influences biofilm viscoelastic properties. Investigating this point will facilitate the management of both salutary and deleterious biofilms, especially through manipulating their establishment and dispersion. Here, we investigate the interplay of sporulation and viscoelastic properties using rheological measurements of B. subtilis biofilms with varied matrix and spore production. We find that, to a significantly greater extent than matrix production, biofilm physical development is strongly altered by activation of sporulation through the spo0A regulation pathway. Spore-deficient strains initially establish physically robust biofilms with linear viscoelastic properties and recovery behavior distinct from spore-producing biofilms. However, spore-deficient biofilms fail to maintain their physical properties over time. In contrast, spore-producing wild-type and matrix-mutant biofilms exhibit more stable physical properties. Our results demonstrate that cell-level gene regulation is associated with macroscopic mechanical transitions in cellular communities, with sporulation granting not only a cellular-level survival advantage, but also greater community-level physical stability.

Centrosome positioning is governed by mechanical interactions between the actin and microtubule cytoskeletons, yet the contribution of different actin architectures and their attachment to the cell membrane remains unclear. We use numerical simulations to study a centrosomal array of microtubules interacting with cortical, bulk, and centrosome-associated actin networks, including passive cross-linkers, motor proteins, and ERM-mediated coupling of actin to the cell membrane. We find that bulk and centrosome-associated actin alone are insufficient for robust centrosome centering, whereas sufficiently dense cortical actin promotes centering through steric interactions with growing microtubules. ERM-mediated attachment of cortical actin to the cell membrane enhances this effect, allowing stable centering at lower actin densities. In a two-centrosome system, microtubule interactions generate a spindle-like structure, while the organization of actin and its membrane attachment through ERM regulate centrosome separation. Antagonistic microtubule motors further limit centrosome separation and establish a finite spindle length. These results demonstrate that ERM-mediated coupling of actin to the cell membrane provides an important mechanical link between the actin cortex and microtubule-driven centrosome positioning, influencing both centrosome centering and spindle geometry.

Astrocytes actively regulate synaptic transmission and neuronal excitability, yet their role in orchestrating macroscopic cortical network regimes and slow-wave oscillations remains an active area of reasearch. This study investigates how bidirectional neuron astrocyte interactions shape emergent population dynamics using a computational network model of excitatory and inhibitory neurons coupled to an astrocyte. The results identify astrocytic feedback topology, rather than astrocytic coupling strength alone, as a key determinant of emergent cortical network dynamics. By systematically dissecting pathway-specific connectivity, it has been shown that the neuronal population driving astrocytic activation and the neuronal population receiving gliotransmission jointly determine whether the network occupies asynchronous irregular (AI), synchronous irregular (SI), synchronous regular(SR), asynchronous regular(AR) or quiescent regimes.Directing gliotransmission selectively onto excitatory neurons consistently promotes population synchrony regardless of the population influencing astrocytic dynamics, whereas selective modulation of inhibitory interneurons induces network quiescence via strong suppression. Under dual-target gliotransmission, network synchrony is dictated by the population driving astrocytic dynamics: excitatory-only drive promotes synchrony, while combined or inhibitory-specific drive preserves asynchronous states. Furthermore, the model reveals that astrocytic signaling kinetics provide an additional temporal control mechanism that regulates the frequency and persistence of self sustained up states.

It is important to determine whether native state dynamics drive the misfolding and oligomerization of the prion protein, which are important events in prion disease, and how they are modulated by conformational conversion. Native (N) mouse prion protein (moPrP) is known to form small (OS) and large (OL) oligomers rich in {beta}-sheet, and in this study, photoinduced electron transfer-fluorescence correlation spectroscopy (PET-FCS) has been used to characterize intramolecular dynamics within individual monomeric units in both isolated OS and OL, as well as the diffusion properties of the oligomers. It is estimated that OS and OL comprise of about 15 and 55 monomeric units, respectively. Microsecond dynamics at each of the two regions that are the 1-3 and 2-3 interfaces of native protein are distinct in N, OS and OL, although they occur on very similar timescales. Analysis of the evolution of the distribution of diffusion times, determined using the maximum entropy method, indicates heterogeneity in the oligomerization reaction. Analysis of the change in the fluctuations which occur in two different timescales in the native state ensemble shows that they are damped more at the erstwhile 1-3 interface than the erstwhile 2-3 interface. The difference in the extent of damping at the erstwhile 1-3 and 2-3 interfaces can be explained on the basis of the structural changes known to occur across each region. The changes in dynamics occur concurrently in both regions, indicating that the structural changes accompanying conformational conversion also occur simultaneously during the oligomerization of moPrP.