Physical Biology

With the development of microfluidics, it has now become possible to assess the susceptibility of bacteria to antibiotics at the single-cell level instead of relying on population measurements. Such studies are particularly relevant when the growth of bacterial population in the presence of antibiotics is heterogeneous. Here, we build a model to describe such a case, and apply it to experimental measurements on a small population of E. Coli exposed to ciprofloxacin, a drug which is well known for triggering a bistable response.

Bacterial communities grow as dynamic populations that respond to their environments. A clinically relevant example is the inactivation of beta-lactam antibiotics by intracellular beta-lactamase in E. faecalis resistant strains. In these populations, resistant bacteria act as antibiotic sinks, detoxifying the environment and allowing sensitive bacteria to survive treatment through a cooperative interaction. In this work, we study strongly coupled planktonic and biofilm populations of mixed sensitive-resistant E. faecalis bacteria under antibiotic stress using fluorescent microscopy. The presence of resistant bacteria in the system benefits both resistant and sensitive cells, leading to mixed planktonic and biofilm populations at super-inhibitory drug concentrations. We show that a beta-lactam antibiotic with or without the addition of a beta-lactam inhibitor can lead to a population inversion effect, characterized by a non-monotonic relation between initial and final fractions of resistant bacteria. The effect is observed in both the planktonic and biofilm populations and is modulated by the total initial cell density. A well-mixed model with competition mediated by resource sharing and cooperation from global degradation of toxins predicts the experimentally observed behavior. These observations suggest underlying population-level mechanisms that are largely independent of biofilm spatial structure.

T cell receptors (TCRs) are critical for immune surveillance and successful adaptive immune response against foreign antigens. TCRs drive this key arm of the immune system through recognition of peptide epitopes presented on MHC complexes. However, they are limited due to their stochastic nature and generation via genetic recombination. In silico design of functional TCRs that target defined peptide epitopes would be of considerable utility but has up until now been unsuccessful. Here, we develop an artificial intelligence (AI)-powered approach using a hybrid physics-based simulation and generative AI that successfully engineers TCRs against defined epitopes presented by MHC-I. We use this approach to design TCRs against two cancer antigens, a HERC1 neoantigen and an immunogenic neoepitope in mutant EGFR. We engineer multiple TCRs against the HERC1 neoantigen which activate T cells in response to exposure to peptide-MHC I and kill cancer cells more effectively than a patient-derived TCR. In addition, we used generative AI to design functional TCRs that target the EGFR T790M neoantigen, engineering greater specificity against the mutant sequence. We present an AI-based approach to TCR design with broad utility for efforts to engineer TCRs and for the development of new cell therapies. One sentence summaryArtificial intelligence-based approach enables the directed engineering of functional TCRs with enhanced features that target cancer neoantigens.

1Correlations between cellular variables, such as gene-expression levels, provide insights into regulatory mechanisms. We focus here on correlations between mRNA and protein levels and re-examine previously derived analytical predictions. We test this prediction on single-cell E. coli data and see substantial disagreement. We hypothesize that this discrepancy arises from the assumption of constant cell volume and develop a theoretical framework for mRNA-protein correlations in growing and dividing cells. Within this framework, we derive an analytical expression for mRNA- protein correlations and show that explicit incorporation of growth and division substantially alters these correlations. The resulting relation is invariant to upstream transcriptional dynamics, and we validate it using stochastic simulations across multiple gene-regulatory architectures. Finally, we show that the derived predictions are consistent with the E. coli data.

A major challenge in neuroscience is to predict how currents in nanodomains affect voltage and ionic concentrations. Cable and Rall theory provide analytic current-voltage relations by neglecting concentration gradients, and the impact of concentration gradients is usually studied numerically with the Poisson-Nernst-Planck (PNP) model. A precise quantitative understanding of the combined dynamics remains limited because analytic current-voltage-concentration relations are missing. In this work we derive such relations using a novel approach based on cross-diffusion equations. For narrow cylindrical domains, we derive time-dependent and steady-state expressions that explicitly show how currents affect voltage and ionic concentrations. We find that the influx of only one ion can significantly change the concentrations of all the other ions even if no channels for these ions are present. After a current injection we compute a biphasic voltage transient where the small-time asymptotic corresponds to the steady-state solution of the cable equation. We show that the accuracy of cable theory prediction for the voltage depends on how the current is distributed among the various ions. Finally, we develop an iterative method to accurately compute steady-state profiles for voltage and concentrations using first-order results by subdividing a cylinder into small segments.

The Poisson-Nernst-Planck (PNP) system is an accurate model of electrodiffusion of ionic species. It is commonly used in situations where nanoscale resolution is required, for instance close to ion channels in the membranes of biological cells. The inherent stiffness of the equations has made them challenging to solve and has limited the applicability of the system. In particular, the time step required for stable solutions has typically needed to be very short (nanoseconds), which makes simulations on the time scale of an action potential (milliseconds) difficult. Recently, it has been observed that avoiding operator splitting and instead solving the concentration equations and the electrostatic equation in a coupled manner relaxes the time-step limitation considerably. However, no theoretical explanation of this observation has been provided. Here, we aim to explain why the coupled scheme allows much larger time steps. We illustrate the mechanism by considering special cases that define necessary, but not sufficient, conditions for stability. We also show that these conditions remain relevant for the fully coupled PNP model in 3D.

Vertex models are widely used within the field of developmental biology to study tissue morphogenesis. These models are well-suited for modeling deformation at the cellular level where movement is driven by local forces. However, understanding how these microscopic movements coordinate to yield macroscopic phenomena such as the shapes of entire tissues remains a challenge. Here we study a top-down approach using differentiable programming on a simplified vertex model of a laminar tissue, and investigate whether the attributes of individual cells can be tuned to make the mesh as a whole acquire a predefined shape. We let the mesh evolve according to simple rules defined by the input to each polygon, and evaluate the resulting shape against a target boundary. Additionally, we show how the high degeneracy of the output can be reduced by constraining the polygon distributions: first, by adding simple penalties on tissue-wide attributes; and second, by dividing the tissue into regions, within which we bias the attributes toward characteristic values. Our study shows how a simple vertex model can be combined with differentiable programming to model developing tissues, and provides insight into the way individual cells must coordinate to yield macroscopic phenomena such as pre-programmed shapes.

Cells communicate via extracellular ligands, such as hormones, which bind to plasma membrane receptors and trigger intracellular signaling cascades. G Protein-Coupled Receptors (GPCRs) exemplify this mechanism by initiating signaling both at the cell surface and, from intracellular compartments such as endosomes. The kinetics and spatial localization of these signals are critical determinants of cellular responses, yet receptor trafficking-including internalization, endosomal sorting, and recycling-remains a pivotal but often overlooked component of theoretical GPCR models. In this study, we present a mathematical framework that integrates receptor trafficking and signaling compartmentalization into generic GPCR dynamic models. Using a compartmentalized approach based on systems of ordinary differential equations (Chemical Reaction Networks), we analyze how receptor internalization and recycling modulate ligand-induced responses. Our results show that the balance between plasma membrane and endosomal signaling can significantly enhance or diminish ligand efficacy. Calibrated with high-throughput kinetic data, our model offers a refined tool for ligand pharmacological characterization and advances the understanding of GPCR signaling spatial organization.

Infectious disease time series often show signs of epidemic transitions, such as the peaks and troughs of the time series. In these time series, key system parameters can lead to catastrophic changes in the dynamical system behaviour (often called critical transitions). Modellers have increasingly shown that early warning signals can anticipate these transitions, both critical and non-critical, in infectious disease time series. Existing methods, however, generally focus on univariate time series data, or ignore spatiotemporal patterns that may be present as a disease spreads through a population. Recent ecological literature developments expand existing temporal and spatial methods to consider the covariance matrix of multiple, related time series. However, many of these proposed signals still make an assumption of stationary time series/system equilibrium. Whilst often true in ecological modelling, disease systems are seldom at equilibrium. In this paper, we propose the usage of the eigendecomposition of the non-stationary covariance matrix as a more suitable early warning signal for epidemiological data. We first analyse the expected trends in the eigenvalues and eigenbasis of the covariance matrix on approach to a transition. Next we apply these methods to a spatially-structured susceptible-infectious-recovered model to explore how the eigenbasis may provide extra information to modellers. Finally, we test these methods on SARS-CoV-2 case data during the 2020-2021 pandemic period in England.

Predicting protein-protein interactions is a fundamental problem in molecular biology. Experimental approaches for identifying protein-protein interactions are time-consuming and labor-intensive, motivating the development of efficient computational alternatives, including machine learning-based methods. However, conventional machine learning methods often rely on manually engineered features that require substantial domain expertise. In this study, we propose a two-stage framework to address these limitations. In the first stage, a one-dimensional convolutional neural network autoencoder is used to automatically learn latent representations from protein sequences. The quality of these features is evaluated through reconstruction error, reflecting how accurately the model reconstructs the original sequence. In the second stage, these learned features are combined with amino acid frequency-based features to form a hybrid feature set for predicting protein-protein interactions. A systematic comparison is performed between models trained on frequency features alone and those using a hybrid representation. The comparison showed that incorporating one-dimensional convolutional neural network-derived latent features improved the models performance of predicting protein-protein interactions. The dataset was split into training, validation, and test sets. Nested cross-validation was employed, with inner loops for hyperparameter tuning and outer loops for model selection. The random forest classifier achieved the best performance, with a mean receiver operating characteristic-area under curve of 0.91 and a test F1-score of 0.87. These results highlight the effectiveness of integrating deep feature learning with ensemble methods for predicting protein-protein interactions and build upon previous work focused on this fundamental problem. Author SummaryProtein-protein interactions are fundamental in all biological processes. However, predicting these interactions is a key problem in molecular biology. Computational approaches have been tested to address this problem. We applied a mix of machine learning and deep learning to gain insight into the qualities of proteins that engage in interaction. First, we trained a deep learning model, which automatically learned the primary sequence and characters related thereto, reducing bias in the actual prediction process. We combined these features, or latent representations, with amino acid frequency features of protein sequences, and called the two together "hybrid features." Then we performed a systematic comparison of amino acid frequency features-only with hybrid features, among four different machine learning classifiers. Our results suggest that the random forest classifier performed best among all four classifiers at predicting interactions between proteins. We propose that this approach could be used to improve efficiency in testing protein-protein interactions at the bench and may have applications to other biologically relevant molecular interactions.

The increasing number of computational methods designed to predict the effects of genetic perturbations on cellular gene expression profiles has led to a need for rigorous evaluation metrics. Recent benchmarking studies rely on correlation or cosine similarity of differential expression relative to a shared population of control cells. We show that these metrics are systematically inflated by statistical bias induced by reusing the same control population to define both quantities being compared. As a result, even non-informative methods can appear to perform well, particularly in datasets with limited numbers of control cells. Reanalysis of published datasets using a simple control-splitting procedure that removes this bias leads to a substantial reduction in performance previously attributed to biological signal.

This work focuses on the global and partial identification problem for fractional differential equations. We provide a general numerical procedure based on global and local optimization algorithms with two refinements for biological systems that ensure solution positivity and homogeneous parameter units. The method is applied to a new fractional model of Dengue outbreak called the Fractional Homogeneous Nishiura (FHN) model, calibrated using data of newly infected people in Cape Verde. We show that our identification method yields a better fit between data and model solutions than previous approaches and that our FHN model captures the dynamics of Dengue more closely than existing systems.

Cell migration is fundamental to various biological processes, including morphogenesis, wound healing, and cancer metastasis. Durotaxis--directed migration of cells in response to spatial variations in stiffness--has been extensively studied using engineered substrates with prescribed stiffness. However, recent work has increasingly shifted toward understanding cell migration in fibrous matrices that can be actively remodeled by the actomyosin contractility, as commonly observed in tumor and epithelial cells. Despite these advances, a theoretical framework explaining how cells structurally remodel their surrounding matrix to promote their own durotaxis, and which cellular forces govern this behavior, remains elusive. To address this gap, we developed a biomechanical model in which polarized cells contract and migrate over a fibrous matrix. Using this model, we first confirmed that cells on an externally strained matrix preferentially migrate along the direction of applied strain. Then, we investigated how cells autonomously remodel the matrix to create stiffness patterns favorable for durotaxis. In the presence of intercellular adhesion, cells acted collectively to stiffen the matrix, after which a small subset of cells escaped the main population and migrated outward. This behavior is reminiscent of intravasation during cancer metastasis, where cohesive cell clusters generate local matrix remodeling that facilitates the departure of more motile subpopulations. These results illustrate how matrix stiffening driven by cell cohesion and contractility regulates durotactic behavior and provide mechanistic insight into collective invasion processes relevant to cancer metastasis.

Cancer stem cells (CSCs) exhibit increased resistance to radiotherapy, contributing to tumor recurrence and progression. While CSCs are known for their intrinsic resistance, the role of their spatial organization remains poorly understood. We extend a computational model of tumorsphere growth to investigate how the spatial distribution of CSCs influences radiation response. The model explicitly tracks cell lineages and spatial positions, revealing a preferential accumulation of CSCs in the spheroid interior. Because radiosensitivity increases with oxygen availability, and oxygen levels are lowest in the tumor core, this spatial organization confers a protective advantage to the CSC population. We find that this effect is negligible in small, well-oxygenated tumorspheres but becomes pronounced as growth leads to the emergence of hypoxic regions. To isolate the role of spatial structure, we compare these results with control simulations in which CSC positions are randomly reassigned. In these synthetic configurations, CSC survival under irradiation is markedly reduced, demonstrating that spatial localization is a key determinant of radioresistance. This effect persists even after the onset of central necrosis, suggesting that the "spatial niche" of CSCs is a critical target for improving therapeutic outcomes. Author SummaryCancer stem cells are known to survive radiotherapy better than other cancer cells, often leading to tumor recurrence. While this resistance is usually attributed to intrinsic biological differences between cells, in this study we show that their physical location within the tumor plays a critical and previously underestimated role. We developed a three-dimensional computer model that simulates the growth of a tumorsphere from a single cancer stem cell. Because oxygen levels influence how sensitive cells are to radiation, our model tracks the position of each cell and calculates the oxygen distribution. We found that cancer stem cells naturally accumulate in the poorly oxygenated spheroid core, where radiation is less effective. To confirm that this location directly causes their survival advantage, we performed a "digital experiment": We artificially redistributed the same cells randomly throughout the tumorsphere before applying simulated radiation. In this random configuration, cancer stem cell survival dropped significantly. Our results show that radioresistance is not only an intrinsic cell property, but also a consequence of the spatial structure of the tumor. This finding suggests that future therapies could be improved by targeting not only the stem cells themselves, but also the protective hypoxic niches where they reside.

Aptamers are single stranded DNA or RNA molecules selected for their high affinity and specificity to bind target molecules, similar to antibodies. They are commonly selected through the SELEX process, which involves the iterative exposure of a random sequence library to a target and retaining the sequences showing good binding properties. To improve Lyme disease detection, we propose designing aptamers that specifically bind to the CspZ protein on the surface of Borrelia burgdorferi, the bacterium responsible for the disease. Starting with a SELEX process consisting of thirteen rounds, from which selected in vitro sequence candidates have emerged, we aim to propose a holistic process that selects in silico new sequence candidates that are further validated experimentally. Our approach relies on 1) using Machine Learning (ML) techniques, specifically a Restricted Boltzmann Machine (RBM), to digitally replicate the last round of the SELEX process, 2) integrating insights from text analysis methods, such as word2vec and n-grams, into the RBM model trained on the final-round SELEX dataset to represent and compare newly generated sequences with in vitro candidates, 3) selecting in silico sequences with strong potential to bind to CspZ protein, 4) experimentally validating the selected in silico sequences of step 3. Our holistic approach combines biological insights with statistical models to improve the efficiency and outcome of the SELEX process. We enhance the RBM model, designed to replicate the distribution of the final SELEX round, by integrating geometric representations of sequences, which is especially advantageous when dealing with limited datasets relative to the vast sequence space. In addition, it provides in silico sequence candidates with strong binding properties.

Mechanical properties of epithelial tissues play essential roles in morphogenesis and physiological function. In this study, we analytically derived the in-plane bulk modulus, shear modulus, and Poissons ratio of a three-dimensional cell vertex model of epithelial monolayers. We showed that the model can robustly reproduce a near-zero in-plane Poissons ratio, a mechanical feature reported in cultured epithelial tissues. Numerical simulations further confirmed that the theoretically predicted Poissons ratio accurately describes the response of the model under finite, biologically relevant strains. In addition, the model exhibits not only morphological bistability between squamous-like and columnar-like states, but also mechanical bistability characterized by distinct elastic responses. Together, these results provide a minimal three-dimensional framework that links cell-scale mechanical interactions and epithelial morphology to tissue-scale elastic properties.

Cell migration plays a central role in numerous physiological and pathological processes and emerges from the coordinated interplay between intracellular force generation, adhesion dynamics, and mechanical interactions with the environment. A minimal, mechanistically grounded understanding of these processes is required to disentangle the respective contributions of cell-intrinsic and environmental cues. Here, a two-dimensional in silico cell motility model is introduced to describe mesenchymal migration driven by intracellular traction forces generated within actin-rich protrusions anchored to a substrate. The model explicitly accounts for adhesion nucleation, maturation, force buildup and rupture, and relies on a small set of physically interpretable parameters. A systematic mechanical analysis identifies parameter regimes that permit effective cell translocation and delineates conditions leading to stalled or mobile cells. Within motile regimes, the model reproduces a broad spectrum of cell morphologies and migratory behaviours. In particular, cell trajectories exhibit the statistical features of a persistent random walk, with a crossover from ballistic to diffusive motion that arises solely from adhesion dynamics and force balance, without imposing polarization or directional bias. Cell morphology is shown to strongly regulate migration speed, persistence, and pausing behaviour. Altogether, this model provides a minimal reference framework for cell migration on non-deformable substrates and establishes a baseline for future studies of mechanically driven guidance. By construction, it is well suited for extension to deformable fibrous substrates, where cell-induced matrix remodeling and stiffness feedback are expected to bias migration and regulate cell encounters relevant to tissue morphogenesis and anastomosis.

Cancer progression following treatment failure is an evolutionary process in which therapy acts as a selection pressure driving Darwinian selection on heritable variation to favor resistant clones. This ability to generate variation, i.e., the cancers evolvability, is a key determinant of how rapidly tumors adapt to therapy. Here, we present an evolutionary game-theoretic model to evaluate how evolvability shapes resistance dynamics under two treatment modalities: targeted therapy and chemotherapy. We first compare cancer populations with fixed evolvabilities: low or high. Targeted therapy imposes a steep selection gradient, enabling rapid resistance evolution, while chemotherapy exerts a flatter gradient but drives tumors toward more extreme resistance strategies. We show that targeted therapy works better in low-evolvability cancers, whereas chemotherapy better controls high-evolvability populations. We then extend the model to incorporate facultative evolvability in which cancer cells dynamically adjust their evolvability in response to therapy-induced stress in which cells fine-tune the trade-off between acquiring higher resistance and limiting the costs of resistance and evolvability. The latter strategy sustains a higher tumor burden than fixed-evolvability populations. To address the challenges of facultative evolvability for therapy efficacy, we develop and simulate an evolutionary double bind using sequential cycles of chemotherapy and targeted therapy. With an appropriate sequence and timing, this strategy can drive cancer cells with facultative evolvability to extinction. Our results highlight the importance of evolvability in shaping treatment response and underscore the need to incorporate evolutionary principles into therapy design.

As the duration of space flights increases, so does the need to optimize off-planet microbial growth. Microbes can both be unintentionally brought into space and cause human disease or be intentionally harnessed for on-site bioengineering functions. However, optimizing microbial growth is challenging due to an insufficient understanding of how microbial communities are affected by the extraterrestrial environment. To address this gap, we have modified a previously developed model for cell growth in microgravity. By improving the functional form used for cell growth as well as the code usability, we enable further research into how microbial communities are influenced by gravity. Applying this model to isolate individual effects of gravity on cell growth indicates that a lack of gravity-driven flow decreases cell growth in microgravity, while the absence of sedimentation increases cell growth in microgravity. These opposite effects likely contribute to the system-dependent effects of microgravity observed experimentally.

Protein tyrosine phosphatase receptor J (PTPRJ) restrains cell proliferation and migration by dephosphorylating receptor tyrosine kinases (RTKs) including the epidermal growth factor receptor (EGFR). PTPRJ is a purported tumor suppressor, and alterations to its expression and/or function are associated with colorectal, breast, lung, and other cancers. While there is interest in controlling PTPRJ-regulated phenotypes, efforts are limited by the complexity of PTPRJ-mediated signaling. PTPRJ dephosphorylates multiple RTKs, and the degree to which PTPRJ control of signaling and phenotypes depends on local cellular RTK activation profiles is unknown. To probe the context dependence of PTPRJ signaling regulation, we collected signaling measurements across 16 pathway nodes at two time points in a panel of HSC3 carcinoma cells engineered with different PTPRJ expression profiles. Cells were treated with three different RTK ligands, and paired phenotype measurements (viability, wound healing, xCELLigence cell index) were made. Partial least squares regression models were developed to predict relationships between PTPRJ-regulated signaling pathways and cell phenotypes. The model effectively separated contributions to variance arising from the PTPRJ expression background and growth factor context. In testing model predictions, we demonstrated that PTPRJ suppressed MET-induced cell cell proliferation via regulation of a HER3/AKT signaling axis that stabilized PTPRJ expression through an unanticipated feedback mechanism. We also found that PTPRJ regulated HSC3 cell migration via JNK signaling that was preferentially activated by MET. Our results identify new regulatory nodes through which PTPRJ influences cancer cell phenotypes and demonstrates that these processes preferentially occur in the context of distinct RTK activation states.