Physical Biology

Trigger waves are positive feedback-mediated traveling waves that propagate without slowing down or diminishing in amplitude, enabling biochemical coordination over distances where diffusion alone would be insufficient. Apoptosis can spread as trigger waves of caspase activity, as demonstrated in Xenopus eggs and egg extracts. We measured apoptotic wave speeds in extracts at two cell cycle states and found that waves propagated more slowly in M-phase arrested cytostatic factor (CSF) extracts than in interphase extracts (21 versus 27 m min-1). Luther's equation, v=2{surd}D{kappa}, predicts wave speed from the diffusion coefficient D and the positive-feedback doubling rate {kappa}. However, D and {kappa} were comparable between the two extracts and could not explain the speed difference. This discrepancy highlighted a key limitation of the classical equation: it does not account for an activation threshold in trigger wave initiation, and in fact the threshold required to trigger apoptosis was found to differ between cell cycle states. We therefore extended Luther's equation to include such a threshold, obtaining v{propto}{surd}(AD/Uc ), where A is the reaction rate and Uc is the activation threshold. Perturbing apoptotic sensitivity confirmed the predicted threshold-speed relationship. These findings establish the activation threshold as a key determinant of trigger wave speed and provide a broadly applicable scaling law for predicting the spread of switch-like biochemical signals.

Quantitative characterization of cell proliferation is central to preclinical drug discovery. Here, we evaluated Random Forest (RF) regression for predicting confluence-based cell growth trends using data from human cancer cell lines and benchmarked its performance against the widely used logistic and Gompertz models. The RF model achieved higher predictive accuracy within the evaluated dataset, particularly at higher initial seeding densities. We further extended the RF framework to predict growth curves across seeding densities. Collectively, these findings highlight the potential of data-driven modeling to complement conventional mathematical approaches and support more informed cell-culture design.

Oncogenic mutations are known to occur at non-random rates and specific hotspots, yet the structural and thermodynamic factors underlying these hotspots remain poorly understood. This study presents molecular dynamics simulations of 22 cancer hotspots across 10 oncogene families, simulated as histone-DNA complexes. Across 18 of 22 mutations, thermodynamic effects were predominantly localized to within 6 [A] of the DNA-histone interface (mean capture 104%), with van der Waals interactions driving the effect at the thermodynamic extremes, indicating that oncogenic mutations alter nucleosome binding through precise local contact changes rather than global structural rearrangements. Further, analysis revealed a gene-family correlated pattern in thermodynamic stability. RAS family mutations showed a consistent trend toward nucleosome stabilization (mean {Delta}{Delta}G = -4.82 kcal mol-1), while kinase domain mutations trended toward destabilization (mean {Delta}{Delta}G = +40.12 kcal mol-1), a difference reaching statistical significance in this exploratory analysis (Mann-Whitney U, p = 0.008). This interface-specific mechanism, combined with the gene-family-correlated thermodynamic pattern, provides a biophysical framework for understanding nucleosome-level contributions to cancer hotspot mutation biology.

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.

Social genetic effects can substantially influence phenotypes in animals and plants and the study of them is of interest. Group housing in animals for example, in pigs provide an ideal framework for studying interactions among individuals. In animals, the genetic of social effects has been studied by simplifying the underlying interactions for example, by assuming that all the individuals in the group contribute equally to the social environment. This homogeneous behaviour is not observed in real conditions. Here, we address this issue showing that identification of interacting individuals is feasible in pig behaviour during growth, and we propose a model that leads to more accurate modelling of social genetics. Our approach infers the strength of interaction via time interval between visits of animals to automatic feeders. This measure of strength was then used in a reaction norm model to evaluate the genetic determinism of social effects. We also build a framework to transform variance components estimated for a trait continuously measured, such as feed intake per visit, into variance of total or aggregated trait e.g. during the growth period. Including social effects improves the fitting of the models. Visit-based social interaction was highest at short time intervals, decreasing rapidly and becoming negligible after 80 seconds. Variance components for the aggregated trait the total feed intake support the contribution of the social interactions. Our approach allows more precise understanding of social effects through individual feeding events and a measure of interaction strength, and further translates these into in an aggregated phenotype of interest.

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.

Multi-cellular pattern formation is a key process in organism development, regeneration, and disease. Such multi-cellular patterns include, for instance, cell density and gene expression patterns. Here, we develop a cell-track-based method that quantifies how much individual cellular processes contribute to the emergence of large-scale patterns. These cellular processes include changes in cellular expression levels, cell motion, cell divisions, and apoptosis. We validate our method using synthetic data, before demonstrating it on two sets of experimental data. Our method is purely geometric and does not require any mechanistic assumptions about the underlying pattern-forming processes, making it very generic and robust. It thus enables unbiased, data-driven study of the mechanisms driving pattern formation across a broad class of systems.

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.

Interception of moving objects is a universal pattern of animal behavior with many industrial applications. Inspired by the behavior of the characid fish Brycon guatemalensis, which catches fruits falling onto the surface of a river, we study one-shot (i.e., open-loop) interceptions using both stochastic optimal control theory and reinforcement learning. In the first instance, an agent actuates a control (wait time before launch and heading angle) to meet its target, given a noisy estimate of the target initial state. In a minimal setting, where launch velocity and actuated control are constants, we show that the optimal wait time is attenuated by noise in both the target measurement and control actuation, as well as agent energy conservation. We then derive an upper bound for the heading angle variance which scales as the ratio of the non-vanishing optimal interception error to the initial planar separation. Complementing our control framework, our deep reinforcement learning approach shows that the neural network representing the fish first learns the value function for the interception, then learns how to aim, and finally learns the optimal wait time. Beyond the specific problem at hand, our results may also have applications to problems with little time for feedback or corrections such as perching, landing, and docking.

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.

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.

Game theory in biology started as an attempt to model animal contests by making assumptions about the fitness costs individuals pay in aggressive interactions. Among the different approaches, a notable one is to construct mechanistic models, using assumptions about behaviours and cognitive processes. Reinforcement learning is an important cognitive process, and we use it here to model pairwise and coalitional contests. We study situations where territorial neighbours become so-called dear enemies. A defending individual can get help from a neighbour through a defender-neighbour coalition against a challenger attempting territory takeover. In our model, coalition members have an advantage in contests in terms of costs of aggression, with the challenger being exposed to aggression from both members and each member only receiving part of the aggression from the challenger. We find that notable costs of border conflicts between neighbours, together with substantial advantages for coalitions, favour intervention. Neighbours intervene when they can help weaker defenders, in this way avoiding costs of border renegotiation with a new and potentially stronger territory owner. We also introduce different forms of perceived costs into the model, which we show correspond to the range from pure mutual assessment to partial self-assessment.

The mechanisms by which organisms extract relevant information from complex sensory signals and use it for decision-making constitute a fundamental issue in biological and cognitive sciences. In social animal societies, individual decision-making is profoundly shaped by information provided by conspecifics. Collective patch-foraging experiments in the laboratory provide a controlled setting in which social information use can be quantified. Here, we consider a go/no-go task in which groups choose between two patches differing in food reward probability. We use agent-based simulations, underpinned by an augmented collective drift-diffusion model, to investigate alternative mechanisms for representing and integrating social information. We consider two representations, continuous (counting representation) and discrete (pulsatile representation), and two integration mechanisms, biasing the decision threshold (threshold modulation) and modifying the accumulated belief (belief modulation), yielding four distinct social models, in addition to a non-interacting model. We first characterize the collective dynamics generated by these models across cognitive parameters and experimental conditions. The temporal dynamics of group accuracy provide informative signatures of the underlying mechanisms. We then assess model selection and parameter identifiability using Bayesian inference and Wasserstein distance minimization, applied to group-accuracy and departure-time distributions. Bayesian inference using distributions of group accuracy provides the most reliable identification across the conditions considered. Importantly, model selection and parameter identifiability are associated with different aspects of collective behavior: model selection is closely linked to the presence of oscillations in the temporal dynamics, whereas parameter identifiability is more closely related to the global accuracy value. Thus, the information available for distinguishing the underlying cognitive mechanisms is not necessarily the same as that required to recover their parameters. Our results further show that identification depends not only on model structure but also on the experimental conditions. Overall, this study provides practical guidelines for identifying socio-cognitive mechanisms in collective foraging experiments.

Simulations have emerged as a pillar in biophysics to understand behavior at the molecular scale, in particular for proteins such as intrinsically disordered proteins. These often show transient folding with long-lived states that are challenging to efficiently sample using conventional simulations. Here, we show that Hamiltonian replica-exchange at the level of hydrogen bonds can be used to systematically explore the conformational landscape of proteins. Investigating the IM30 protein, a partially alpha helical protein, under the PLUM coarse-grain force-field, we show that this approach straightforwardly allows characterization of local helix stability, which would be otherwise hard to obtain. For instance, we show that some regions of the conserved coiled-coil structure are less stable than others. By combining the different replicas with principal component analysis, we are able to dissect the conformational landscape of the IM30 protein. Taken together, this indicates that enhanced sampling remains an important part of simulations, allowing insights that cannot be easily obtained in traditional simulations.

Somatic mutations in sequenced tumors are often detected with imperfect sensitivity. They can be missed because tumor heterogeneity results in some mutations being absent in a sample at hand or present at very low frequencies which, combined with technical limitations like insufficient sequencing depth, reduces their detectability. It becomes apparent with multi-regional sequencing that some mutations confined to specific areas can be overlooked in single-region analyses. Adjusting for such sensitivity becomes critical when mutation frequencies between groups of subjects are compared, such as responders and non-responders to a given therapy. Otherwise, the estimate of the mutation prevalence, or of the difference in prevalences between the groups, can be biased, leading to inflated type I error. Here, we propose a weighted approach to adjust for imperfect sensitivity of the mutation detection and compared it to the unweighted approach. We assume that a surrogate of mutation sensitivity is observed only among patients with called mutation, and we derive its unconditional mean. Such adjustment leads to less biased estimates of mutational frequencies and better control of the type 1 error.

Buruli ulcer (BU) is a neglected tropical skin disease caused by infection with Mycobacterium ulcerans. The mode of its transmission into the skin has not been fully clarified, but it is believed to involve mechanical transfer, perhaps by insect bites. M. ulcerans secretes a toxin called mycolactone which causes necrosis of the skin and formation of large skin lesions. Understanding the development of these skin lesions over time is crucial to understand the pathogenesis of BU. We formulate a mathematical model to describe the space-time dynamics of M. ulcerans bacteria, mycolactone and skin cell densities as well as fibrin deposition. We investigate the relative contributions to ulcer formation of direct cytotoxicity of mycolactone and ischaemia following the loss of coagulation control. Our results are consistent with existing biological evidence that higher mycolactone concentrations accelerate cell death. Furthermore, the model indicates that the rate of wound expansion is primarily controlled by the diffusion and net birth rate of bacteria, which sets the overall scaling for the speed of wound expansion, along with two dimensionless constants that define the shape of the trajectory of wound edge position against time, namely the ratio of the mycolactone diffusion coefficient to the bacterial diffusion coefficient, and the ratio of the mycolactone degradation rate to the bacterial net birth rate. When mycolactone diffuses significantly faster than bacteria spread or when mycolactone degrades more slowly than bacteria reproduce, the initial development of the wound is faster. In contrast, the long-term wound expansion speed appears to be relatively unchanged across a wide range of the dimensionless parameters.

Protein function is determined not only by the static structure of molecules, but also by coordinated conformational fluctuations that occur across various spatial and temporal scales. Molecular dynamics simulations, elastic network models, principal component analysis, and related approaches offer useful descriptions of protein motion. However, representing heterogeneous trajectories in a compact, informative manner that is applicable to proteins with different sequences, structures, and historical evolution is not trivial. Here we present the Topology Invariant Dynamic Graph Network (TIDGN), a deep representation learning approach that encodes protein conformational dynamics into a shared latent representation, termed the protein motion signature (Zp). TIDGN encodes each trajectory as a time-dependent residue-level graph and builds structural connectivity, dynamic cross-correlation, low-dimensional motion features, sequence context, and temporal aggregation into the design. Instead of learning a protein-specific collective variable, the approach learns a representation that retains functionally informative patterns of coordinated motion applicable to different proteins. We evaluate the framework using 1,250 molecular-dynamics trajectories representing 1,120 distinct proteins that range in size from 50-600 residues, 142 CATH/SCOP families, 88 structural folds, and six broad functional classes. The set of trajectories spans durations of 100 ns to 10 (mu)s, sampled at 100 ps intervals, representing approximately 12.5 million conformational frames in total. In the context of a sequence-disjoint evaluation using a 30% sequence-identity threshold, the approach achieves a mean AUROC of 0.8838 (margin of error:) 0.0107 compared to 0.8174 for a dynamic graph neural-network baseline, 0.7257 for a dynamic descriptor, 0.7227 for a PCA descriptor, 0.6592 for a sequence baseline, and 0.6587 for a static-structure baseline. As the biological distance between training and evaluation proteins increases, transfer performance decreases, with AUROC values of 0.92 for random splitting, 0.85 for sequence-disjoint evaluation, 0.78 for family-disjoint evaluation, and 0.71 for fold-disjoint evaluation. Component ablations suggest that graph structure, dynamic cross-correlation, low-dimensional motion features, sequence information, and the combination of these factors contribute to predictive performance. Residue-level attribution, when applied to adenylate kinase, highlights regions that are associated with known conformational rearrangements that involve the LID and NMP domains, offering a biologically interpretable hypothesis about the dynamic information that is encoded by the model. Taken together, these results suggest that it is possible to learn transferable representations of protein dynamics that retain functionally informative patterns of coordinated motion beyond considerations of sequence identity and static structure. Moreover, although the learned representation is transferable, it is not universally invariant to the biological distance between training and evaluation proteins. The resulting approach offers a computational basis for connecting molecular motion, functional prediction, and mechanistically informative representation learning.

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.

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.

Moment-closure methods provide a widely used approach for approximating low-order statistics of stochastic biochemical reaction networks, but the resulting closed equations may exhibit physically meaningless dynamics. Here, we systematically investigate the stability of second-order moment-closure approximations for a bursty gene expression model with nonlinear protein degradation. We consider the Gaussian, log-normal, and negative-binomial closures. By analyzing the resulting dynamical systems, we show that the Gaussian closure fails the proposed stability criterion for all parameter values, whereas both the log-normal and negative-binomial closures possess a unique physically accessible fixed point and are stable if and only if kB(1 + 2B) [≥] 1, where B is the mean burst size and k is the dimensionless protein synthesis rate. Moreover, this condition is automatically satisfied when the steady-state mean protein copy number is at least one, suggesting that it is mild in biologically relevant regimes. Numerical comparisons over a broad parameter range further show that the negative-binomial closure is the most accurate, while the Gaussian closure is the least accurate. We further develop higher-order negative-binomial moment-closure schemes and demonstrate that increasing the closure order substantially improves predictive accuracy. These results highlight the importance of considering dynamical stability, in addition to numerical accuracy, when assessing moment-closure approximations.