Physical Biology

Single-particle tracking (SPT) is a tool of growing importance which enables biologists to better understand the dynamics of protein interactions at the single-molecule level and in vivo. However, the stochastic nature of the motion of single molecules, the wide variety of types of motion that they can experience and complex transition kinetics between the different states of motion are challenging factors that complicate the interpretation of SPT data. This article presents and benchmarks the tool ExaTrack. Like previous tools, it can handle particles moving in one or multiple states of motion with transitions between states. Its unique feature is that it can simultaneously handle a wide range of complex types of motion such as diffusive motion, directed motion and confined motion while also managing a variety of transition kinetics such as memoryless first-order transitions or more complex time-dependent state transitions. This manuscript focuses on the benchmarking of ExaTrack on simulated data.

Exploring the emergence of spatio-temporal patterns due to nonlinearities in gene expression is a relatively new development. In this work, we explore the effect of resource constraint on gene regulatory motif from both equilibrium and spatio-temporal standpoint, taking into consideration the degradation class of resource, protease. We have demonstrated that protease-tagged degradation can cause an emergent bistability to form in the system in a steady-state scenario. Instead of a graded linear response in protein synthesis, two Saddle-node bifurcations caused by protease competition provide a switch-like response with hysteresis, where two drastically differing protein concentrations can coexist. We next turn our attention to spatio-temporal analysis: we extend our study for a two-dimensional sheet of cells with diffusible protein molecules and report the stationary patterns.To investigate the reasons behind these non-homogeneous stationary patterns, we investigate the traveling wave solution and observe that a stationary pattern is formed by the traveling wave solution. Considering that proteases play a major role in the regulation and expression of genes in a variety of diseased scenarios, the repercussions of this spatial patterning caused by protease competition can be extensive in gene regulatory systems.

The actin cytoskeleton is an inherently disordered active system. the actomyosin cortex and reconstituted actomyosin systems are globally disordered, yet undergo transitions between distinct disordered states as parameters like motor and crosslinker concentration and filament length and rigidity change. In cells these changes are related to genetic mutations or differences in cell state and dictate fundamental biological processes. However, we dont have well established methods to detect and classify differences in disordered polymer networks. Image-based morphology techniques provide a non-invasive, high-throughput method of extracting information about a system. In this work we simulate biopolymer networks under varying conditions and develop and use morphological descriptors to construct trajectories in morphospace. Using statistical analysis we find that morphological descriptors are able to distinguish between different trajectories of the system, including differences not apparent to the eye. However, no single descriptor alone is able to capture all the differences in the simulated trajectories. Nematic order parameters typically perform the worst for our simulations while curvature and texture descriptors can collectively distinguish between dynamic trajectories. This work helps develop quantification of cytoskeleton dynamics for classification and data-driven modeling.

Cell-cell adhesion is a key regulator of cancer invasion. In this work, we extend a pre-existing individual based cancer invasion model by introducing a stochastic representation of N-cadherin-mediated adhesion, where the lifetime of a cell-cell bond depends on the pulling force acting on the bond. Using experimental data, we derive expressions for the mean and standard deviation of N-cadherin bond lifetimes and fit them to Gamma distributions, enabling their treatment as force-dependent random variables. These distributions are then used to modify the diffusion coefficient of mesenchymal cancer cells. The model predicts reduced random motility with increasing adhesion and incorporates a dynamic transition between catch- and slip-bond behaviour. Along with this model for cell motility, we propose a preliminary physical framework, that can be used to model pattern formation as a result of the new adhesion mechanic.

Fluorescence recovery after photobleaching (FRAP) is widely used to characterize diffusion in cells, but quantitative interpretation of the data in small prokaryotes requires explicitly accounting for cell geometry. While this has been successfully achieved for spherical and rod-shaped bacteria, analytical approaches developed in these cases are not directly applicable to cells with more complex morphologies. Here, we explore the application of FRAP to helical bacteria using simulations. We show that half-compartment FRAP experiments, where one-half of the cell is photobleached, provide a robust means of characterizing fast protein diffusion. To help with the practical implementation of this technique, we established the relationship between the diffusion coefficient and characteristic fluorescence recovery time as a function of cell length and helical parameters, and for two different ways of estimating the recovery time. As a first application, we report measurements of the diffusion coefficient of the fluorescent protein, mNeonGreen, in the helical bacterium Paramagnetospirillum magneticum AMB-1. We find it to be D = 4.9 {+/-} 2.2 {micro}m2 s-1 in isosmotic conditions, not significantly different from the value measured in Escherichia coli. Although developed for helical bacteria, including spirilla, spirochetes, and vibrios, our framework can readily be extended to cells or compartments with other geometries.

Understanding how structures arise in microbial communities remains an outstanding challenge in bacterial ecology. When replicating within dense and confined environments, bacterial populations may collectively self-organize as a result of mechanical interactions. Model dual-populations of bacteria, colonizing open-ended microchannels, were found to either quickly fixate to a single population or segregate into long-lived, coexisting populations. This latter quasi-stability results from the alignment of bacteria into lanes, forcing cells to grow toward the open ends of the channel, with inter-lane invasion events driving the boundary between populations. Here we apply agent-based (AB) simulations to explore the boundary dynamics between dual-bacterial populations of varying morphology and division rate. We find that the simulated boundary dynamics are well described by a simple drift-diffusion model, which enables us to estimate the mean time to fixation within competitive scenarios where the fixation time is difficult to access by AB simulations. Coccus cells display a competitive advantage over bacillus cells as they can more effectively invade and ultimately fixate, while coexisting populations of bacillus cells are effectively stable. And while faster-dividing cells should have a selective advantage, their morphologydetermines if this advantage drives fixation or acts as a defensive strategy to maintain their population. These findings highlight the critical role that cell morphology and mechanics play in shaping bacterial communities. Author summaryBacteria are often found in multi-species communities, many of which are critical to human health, the environment, and industry. Within these communities, a competition for resources shapes the overall population structure and resulting ecology. Model systems can provide a test bed for understanding the interaction networks of these more complex communities. Here we show how mechanical forces between cells and their environment can be critical to the stability (or instability) of a bacterial community. Using simulations of dual species competition within two-dimensional microchannels, along with mathematical modeling, we find that cell morphology can be a determining factor in the stability of a multi-species community.

One of the most critical steps in human reproduction is the selection of the dominant follicle when a single follicle is chosen from a large group of follicles to ovulate. Although this process involves complex hormonal regulation, the complete microscopic picture of unique selectivity remains unclear. We propose a novel stochastic mechanism for dominant follicle selection that incorporates the actions of the most relevant hormones, follicle-stimulating hormone (FSH) and estradiol. Our theoretical picture suggests the following sequence of events. As soon as the FSH concentration reaches the critical threshold, one of the available follicles is randomly selected, which immediately stimulates the production of estradiol, which, via a negative feedback mechanism, suppresses further FSH production, lowering its concentration below the critical threshold. This suppression limits the time window for the possible second follicle selection event, allowing only a single follicle to be selected. Based on this picture, a minimal quantitative theoretical model of dominant follicle selection is developed and analyzed using analytical calculations and computer simulations. Theoretical analysis shows how the interplay between different parameters that govern follicle selection leads to high selectivity. Our theoretical approach can explain some key known observations, providing a quantitative tool for analyzing biological reproduction phenomena.

Gene drives are genetic elements that can rapidly spread through populations, offering potential solutions for controlling disease vectors and pests. In some scenarios, it is necessary to utilize drives that can be confined to only target populations. The success of these threshold-dependent gene drives, which require a minimum local frequency to establish, depends critically on the spatial strategy used for introduction. Here, we use a reaction-diffusion model to systematically identify optimal release patterns that maximize the per-capita efficiency for four distinct gene drive designs as well as use of Wolbachia bacteria, which spread similarly to frequency-dependent gene drives. We find that the most efficient release strategy is highly dynamic, transitioning from a broad "everywhere" release for short timeframes to a "multiple-ring" pattern for intermediate times, and finally to a focused "center" release for longer timeframes. These timeframes depend on the specific type of drive, with more powerful variants transitioning more quickly to center releases. Our results demonstrate that these optimized, variable release strategies can be substantially more effective than simple uniform releases. This study provides a quantitative framework for designing effective gene drive implementations, highlighting that a carefully planned spatial strategy is essential for maximizing impact, making optimal use of available resources.

A methodology for computationally unstructuring proteins is described and the results of its application to a variety of proteins analyzed and discussed. Some proteins prove more susceptible than others, and fold topology plays a part in this. Alpha helical structure is found to be generally somewhat robust, and, perhaps unsurprisingly, unstructuring often begins at exposed chain termini. Phosphofructokinase-1 and phosphofructokinase-2, which have similar sizes but different fold topologies, are found to differ markedly in their unstructuring behaviour.

Understanding how cells migrate through confined environments is crucial for elucidating fundamental biological processes, including cancer invasion, immune surveillance, and tissue morphogenesis. The nucleus, as the largest and stiffest cellular organelle, often limits cellular deformability, making it a key factor in migration through narrow pores or highly constrained spaces. In this work, we introduce a geometric surface partial differential equation (GS-PDE) model in which the cell plasma membrane and nuclear envelope are described as evolving energetic closed surfaces governed by force-balance equations. We replicate the results of a biophysical experiment, where a microfluidic device is used to impose compressive stresses on cells by driving them through narrow microchannels under a controlled pressure gradient. The model is validated by reproducing cell entry into the microchannels. A parametric sensitivity analysis highlights the dominant influence of specific parameters, whose accurate estimation is essential for faithfully capturing the experimental setup. We found that surface tension and confinement geometry emerge as key determinants of translocation efficiency. Although tailored to this specific setup for validation purposes, the framework is sufficiently general to be applied to a broad range of cell mechanics scenarios, providing a robust and flexible tool for investigating the interplay between cell mechanics and confinement. It also offers a solid foundation for future extensions integrating more complex biochemical processes such as active confined migration.

A morphospace is an abstract space of theoretically possible biological traits, shapes, or property values. It is interesting to explore which parts of a morphospace life occupies, as compared to those parts which could be occupied, but are not. Comparing random and natural non-coding (nc) RNA secondary structures is an established approach to studying morphospace occupation for RNA structures. Most earlier studies have focused on the minimum free energy (MFE) structure, while relatively few have looked at the Boltzmann distribution, describing the ensemble of energetically suboptimal RNA folds. These suboptimal structures may have important roles and functions, and hence should be examined carefully. Here we compare random and natural ncRNA in terms of their Boltzmann distributions, finding that natural RNA tend to have very similar profiles to random RNA, with the main difference being that natural RNA are slightly more energetically stable, except for very short sequences (20 to 30 nucleotides) which tend to be slightly less stable. We infer that natural ncRNA occupy similar parts of the morphospace that random RNA do, indicating that the biophysics of the genotype-phenotype map largely determines the ensemble properties of ncRNA.

Kinase family proteins constitute the second largest protein class targeted in drug development efforts, most prominently to treat cancer, but also several other diseases associated with kinase dysfunction. In this work we focus on type II kinase inhibitors which bind to the "classical" inactive conformation of the protein kinase catalytic domain where the DFG motif has a "DFG-out" orientation and the activation loop is folded. Many Tyrosine kinases (TKs) exhibit strong binding affinity with a wide spectrum of type II inhibitors while serine/threonine kinases (STKs) often bind more weakly. Recent work suggests this difference is largely due to differences in the folded to extended conformational equilibrium of the activation loop between TKs vs. STKs. The binding affinity of a type II inhibitor to its kinase target can be decomposed into a sum of two contributions: (1) the free energy cost to reorganize the protein from the active to inactive state, and (2) the binding affinity of the type II inhibitor to the inactive kinase conformation. In previous work we used a Potts statistical energy potential based on sequence co-variation to thread sequences over ensembles of active and inactive kinase structures. The threading function was used to estimate the free energy cost to reorganize kinases from the active to classical inactive conformation, and we showed that this estimator is consistent with the results of molecular dynamics free energy simulations for a small set of STKs and TKs. In the current study, we analyze the results of a large-scale study of the binding affinities of 50 type II inhibitors to 348 kinases, of which the results for 16 of the 50 type II inhibitors were reported in an earlier study (the "Davis dataset"); the binding data for the remaining 34 type II inhibitors to the panel of 348 kinases were recently obtained (the "Schrodinger dataset"). We use the Potts statistical energy model to investigate the contribution of protein reorganization to the selectivity of the large kinase panel against the set of 50 type II inhibitors, and find that protein reorganization makes a significant contribution to the selectivity. The AUC of the receiver-operator characteristic curve is [~]0.8. We report the results of an internal "blind test", that shows how Potts threading energies can provide more accurate estimates of kinase selectivity than corresponding predictions using experimental results of small sample size. We discuss why two STK phylogenetic kinase families, STE and CMGC, appear to contain many outliers, and how to improve the ability to predict kinase selectivity with a more complete analysis of the kinase conformational landscape. We compare the performance of Potts threading for predicting binding properties of the large set of (50) Type II inhibitors to 348 kinases, with those of a sequence-based purely machine learning model, DeepDTAGen, a publicly available machine learning model that was trained on the complete Davis dataset, including both Type I and Type II kinase inhibitors. We observe that DeepDTAGen performs well on binding predictions for the 16 type II inhibitors in the Davis dataset, but performs poorly on binding predictions for the 34 type II inhibitors against 348 kinases in the Schrodinger dataset.

Cells must maintain stable protein levels despite the inherently stochastic nature of gene expression, as excessive fluctuations can disrupt cellular function and impair the reliability of decision-making. Regulatory mechanisms, such as negative feedback, buffer protein fluctuations. Yet, it remains unclear how fluctuations are affected by delays that depend on a molecules specific state. Here, we develop a stochastic model in which proteins are produced in bursts as inactive molecules and pass through a series of intermediate steps before becoming active. The duration of such activation delays depends on the current level of active protein, creating a state-dependent feedback loop. Our model provides explicit analytical expressions relating the delay structure and feedback strength to the variability of active protein levels, quantified using the Fano factor, and shows that state-dependent delays can reduce fluctuations below the baseline expected from simple bursty production. Stochastic simulations confirm these predictions, and incorporating negative feedback in burst production further decreases variability while keeping system behavior predictable. These results reveal how temporal and state-dependent regulation stabilizes protein expression, offering guidance for understanding natural cellular control and designing robust synthetic gene circuits.

Understanding how cells migrate in response to external cues has important implications for biology, medicine, and bioengineering. Chemical, mechanical, and electrical signals are the primary drivers of directed cell migration, and each has been extensively studied over the past decades. Among them, chemical cues were the first to be investigated and remain the most widely studied due to their undeniable role in in vivo guidance. Mechanical signals--particularly substrate stiffness gradients--have gained prominence for their ubiquity across cell types and their potential to direct migration. More recently, growing evidence suggests that electrotaxis offers a highly precise and programmable means to guide cell movement. Despite this, these cues are often studied in isolation, whereas in vivo they typically coexist and interact. Using wellestablished biophysical models, we investigate how mechanical and electrical signals cooperate and how they can be engineered to compete for control over cell migration. We demonstrate that an electric field can override and even reverse durotaxis, with outcomes that depend strongly on the specific cell type. To address this large variability in controlling cell migration, we propose particular steps toward further exploration. To support such future research, we provide a freely available platform for predicting electro-mechanical interactions in cell migration, based on a given cells sensing and signaling characteristics, which could tailor the mechanical and electrical signals that arise naturally during organ development, cancer invasion, or tissue regeneration.

Mass-conserved reaction-diffusion systems are used as mathematical models for various phenomena such as cell polarity. Numerical simulations of this system present transient dynamics in which multiple stripe patterns converge to spatially monotonic patterns. Previous studies indicated that the transient dynamics are driven by a mass conservation law and by variations in the amount of substance contained in each pattern, which we refer to as "pattern flux". However, it is challenging to mathematically investigate these pattern dynamics. In this study, we introduce a reaction-diffusion compartment model to investigate the pattern dynamics in view of the conservation law and the pattern flux. This model is defined on multiple intervals (compartments), and diffusive couplings are imposed on each boundary of the compartments. Corresponding to the transient dynamics in the original system, we consider the dynamics around stripe patterns in the compartment model. We derive ordinary differential equations describing the pattern dynamics of the compartment model and analyze the existence and stability of equilibria for the reduced ODE with respect to the boundary parameters. For a specific parameter setting, we obtained results consistent with previous studies. Moreover, we present that the stripe patterns in the compartment model are potentially stabilized by changing the parameter, which is not observed in the original system. We expect that the methodology developed in this paper is extendable to various directions, such as membrane-induced pattern control.

The error catastrophe refers to the proliferation of non-functional molecules in conditions where molecular replication has low accuracy, which is likely to correspond to conditions present at the Origin of Life. This error catastrophe can be avoided thanks to transient compartmentalization, provided that the compartments are sufficiently tight to prevent molecular leakage. Typically, transient compartmentalization models assume that the content of the compartments is completely pooled periodically, resulting in the complete loss of the compositional memory of the compartment. Furthermore, previous models that include the possibility of ecological interactions between molecular parasites and replicators within compartments generally do not study the effect of transient compartmentalization on their coevolution. To address both issues, we develop a framework that accounts for the coevolution of molecular replicators and parasites, along with specific compartmentalization dynamics that are transient yet partial, allowing compositional memory to accumulate from one round of compartmentalization to the next. We benchmark our model with a serial dilution experiment that displays complex oscillatory dynamics among four well-characterized RNA replicators. We also perform experiments to quantify the level of mixing in compartments when stronger stirring tends to homogenize their composition. We then model stirring-induced mixing and show how stirring alters the dynamics of compartmentalized replicators. We conclude that compositional memory arising from transient compartmentalization plays a major role in the dynamics of early molecular systems.

Protein-DNA complexes are involved in vital cellular functions like gene regulation, replication, transcription, packaging, rearrangement, and damage repair. In this work, streamlined geometric formalism for computing the absolute binding free energy was used to obtain chemical accurate in silico estimation of binding free energy of three Protein-DNA complexes. Additionally, molecular interactions between Protein and DNA involved hydrogen bonds, electrostatic, van der Waals, and hydrophobic interactions. Using this formalism, researcher can obtain the absolute binding free energy for a Protein-DNA complex with remarkable accuracy and modest computational cost.

This work presents the development of a novel approach to model the dynamics of cancer cells in microcirculation. We investigate the role the membrane elasticity, and cancer cell shape on deformation dynamics under the shear and pressure forces in a micro-channel. The proposed numerical model is based on a hybrid continuum-particle approach. The cancer cell model includes the cell membrane, nucleus, cytoplasm and the cytoskeleton. The Dissipative Particle Dynamics method was employed to simulate the mechanical components. The blood plasma is modeled as a Newtonian incompressible fluid. A Fluid-Structure Interaction coupling, leveraging the Immersed Boundary Method is developed to simulate the cells response to flow dynamics. We quantify how subtle variations in these biophysical properties alter deformation indices such as sphericity and aspect ratio, and stress distributions on the membrane of the cancer cell. Our findings align well with existing computational and experimental studies. Results reveal that increased membrane stiffness reduces overall deformation as well as the total distance traveled. Similarly, cell geometry strongly influences flow-structure interactions: near-spherical morphologies exhibit stable deformation with minimal sensitivity to shear variations, whereas elongated geometries show pronounced orientation and stretching effects. Collectively, these findings highlight the critical importance of cell-specific heterogeneity in governing cell dynamics in microvascular flows. Furthermore, the intracellular and extracellular dynamics response of the cancer cell are intrinsically linked to their shape, in which certain morphologies displayed strong resistance to the fluid-induced forces and the ability to migrate in various directions. The insights obtained provide a mechanistic framework for understanding circulating tumor cell transport in shear-dominated environments during metastasis. Our work may inform the design of biomimetic microfluidic systems and therapeutic strategies targeting cancer cell detection and cancer prognosis.

Protein condensates that form via phase separation typically become more viscous over time and can harden in a process referred to as "molecular aging". Several mechanisms have been identified for this phenomenon. Of these, the ones involving enhanced {beta}-sheet or -strand interactions are of pathological relevance since they have been associated with neurodegeneration. Although there is much understanding of biopolymer phase behavior, an inclusive thermodynamic framework that unifies phase separation and {beta}-sheet-based aging is lacking. We present a time-dependent, multi-component extension of associating polymer theory that describes phase separation and aging of an intrinsically disordered protein (IDP) capable of associating through local, reversible folding. The model shows how the Second Law of Thermodynamics applies throughout, whether phase separation precedes and encourages aging or, vice versa, whether the increase in "stickiness" during aging drives phase separation. Our calculations show how the time-dependence of the average valency of associating sites determines the aging kinetics and the development of viscoelastic properties of a biocondensate. The agreement between our calculations and the change in dynamics of condensates of perfect repeat analogues of nucleoporin-98 not only validates the theory but also identifies these Nup98 variants as model systems for studying aging.

Methods to visualize and quantify the molecular responses of cells to local forces exerted at adhesions are crucial to elucidate how physical forces control cellular behavior. Of the many proteins involved in focal adhesions, vinculin plays a key role in mediating force-sensitive processes. Here, we combined optical tweezers and Forster resonance energy transfer (FRET) microscopy to measure the intensity and FRET efficiency of the vinculin tension sensor, VinTS, in response to a force. Fibroblasts expressing VinTS formed adhesions on fibronectin-coated, 3m-diameter, polystyrene beads. As the beads were displaced by the cell, we applied an optical trap to counteract this movement and increase the traction force required by the cell to maintain the bead displacement. The optical trap stiffness varied from zero (no laser) up to 0.26 pN/nm. In this range, the median bead displacement after 5 min was ~200nm in all trapping conditions inducing counteracting forces in the 10-100pN range. To maintain this displacement, vinculin recruitment increased (up to 35% in relative intensity at high stiffness) while tension increased but more moderately (1-2% decrease in absolute FRET efficiency). For higher trap stiffness, the main response was an increase in vinculin recruitment, while the tension did not increase significantly. The increase in vinculin intensity was correlated with the decrease in FRET efficiency at 0.26 pN/nm but not at lower stiffness. Thus, the presence of the high stiffness optical trap over 5 min appears to induce a positive correlation between vinculin recruitment and vinculin tension. In a few instances, vinculin puncta migrated a few microns away from the bead exceeding the bead movement speed while experiencing an increase in both vinculin intensity and tension. Taken together, the results suggest that combining an optical trap with vinculin tension measurements uncovers novel vinculin dynamics in the presence of a force.