Physical Biology

Small molecule modifiers whence bound, allosterically, will alter the binding of a macromolecule to one- or more-cognate substrates/partners via conformational and non-conformational changes. Although allostery is inferred directly from empirical data, the mathematical basis of these models, constraints deployed and choice of parameter(s) are not clear. Here, we present and characterize a discrete-to-continuous mathematical model for ensemble distributions of a ligand-interacting macromolecular species across milieux-dependent conformational states and examine its role in the genesis and progression of cooperative binding. The premise, of our model, is a set of occupancy matrices (sparse, binary, strictly delocalized) which can be partitioned by a probability-based hyperparameter into mutually exclusive proper subsets of occupancy matrices with identical multinomial probabilities. Since each subset is canonical with a constituent occupancy matrix, it is characterized by a unique multinomial probability. The inner product of combinatorial pairs of all mutually exclusive subsets of occupancy matrices, with an expression for the summed transitional probabilities (finite differences between unique multinomial probabilities), is the differentiable matrix of strictly positive real-valued numbers for the system of ensemble distributions. Whilst the harmonic mean is presented as a generic solution for a system of ensemble distributions, the row-wise definite integral for each column is the finite union of open intervals (contiguous, strictly monotone) which in tandem with a set of interval-specific and bounded transitional probabilities constitutes a piecewise smooth curve (path-connected-, closed- and compact-set). Our discrete-to-continuous model is phenomenological and able to recapitulate the basic tenets of cooperative binding whilst offering insights into the genesis and progression of the same.

This study introduces a statistical mechanical framework for allosteric communication in proteins based on the spanning-tree ensemble of residue contact networks. By representing protein structures as weighted graphs, we identify each spanning tree as a topological microstate. The canonical partition function is evaluated exactly via the determinant of the reduced weighted Kirchhoff (Laplacian) matrix, allowing for the derivation of global thermodynamic functions (including Helmholtz free energy, internal energy, entropy, and heat capacity) without approximation. Allosteric channels between specific residue pairs are defined as sub-ensembles containing unique simple paths. Using the Burton-Pemantle theorem and the Moore-Penrose pseudoinverse of the graph Laplacian, we compute exact path probabilities and channel-specific thermodynamics. This methodology enables a decomposition of channel heat capacity into energetic and topological components and quantifies residue-level allosteric importance through fractional contributions to the channel partition function. The framework was applied to the G12D mutation in KRAS, comparing wild-type (PDB: 6GOD) and mutant (PDB: 6GOF) proteins. Results show that while the mutation minimally affects mean internal energy and entropy, it reduces global heat capacity by 27.3%. This indicates a topological stiffening where the mutant occupies a significantly narrower landscape of spanning-tree configurations. At the channel level, the mutation maintains distributional stability across six functional routes but triggers a substantial internal redistribution of allosteric importance. Specific residues, such as Q61 and F156, shift occupancy by up to 35.5%. These findings suggest that the G12D mutation does not destroy communication pathways but reorganizes internal information traffic to favor a catalytically impaired state. This approach provides a rigorous, parameter-free metric for understanding how point mutations perturb distal protein signaling.

Cell surface receptors are activated by ligand binding and transmit signals into the cell. Epidermal growth factor (EGF) receptor (EGFR) signaling regulates cell growth, differentiation, and survival, and its dysregulation is linked to cancer. Recent experiments show that ligand binding to EGFR is enhanced for receptors in tetraspanin nanodomains on the cell surface. We use kinetic modeling of receptor confinement, ligand binding, and internalization to compare confinement and signaling behavior for EGFR with spatially localized ligand binding to a hypothetical receptor that has uniform ligand binding anywhere on the cell surface. We find that introducing a membrane domain that confines and enhances ligand binding to receptors leads to more consistent confinement across ligand levels, raises necessary ligand levels for steady-state signaling, and flattens and extends the signaling response to sudden ligand concentration increases. This confining domain that enhances ligand binding provides the cell with a distinct regulatory mechanism to tune its signaling response. We also find that the concentration of receptors in signaling states and the fraction of receptors in signaling states respond to ligand at different ligand concentrations, with substantial increase of the concentration of receptors in signaling states occurring at a much lower ligand concentration than a substantial increase of the fraction of surface receptors in signaling states. This quantitative modeling of spatially restricted receptor activation applies to other receptors with similar characteristics and builds towards physical principles of receptor signaling.

The relationship between genotypic and phenotypic variation is determined by the complex interaction of genetic and environmental factors. While statistical methods capable of detecting such interactions exist, an axiomatic mathematical framework that seamlessly describes the combined effects of genetic modifications and environmental exposures on a common scale is lacking. In this report, buffering concepts are used to construct a measurement system that enables the geometric representation of both gene-by-gene and gene-by-environment interactions on the extended complex plane (i.e., as projections on the Riemann sphere). In this manner, any such interaction, or combination thereof, can be precisely defined and quantified as the deviation from the neutral value calculated through the applicable complex transformation. When thus conceptualized, the framework's parameterization defines the "state space" of a given measurable phenotype along both the real and imaginary dimensions, thus establishing an unambiguous and broadly applicable method for determining the phenotypic value expected upon combinatorial changes in genetic and/or environmental variables. Remarkably, by applying these methods, it is possible to quantify the effects of any gene-by-environment interaction using the equation, AGxE=Im([z]obs*zexp)/2, where zobs and zexp are complex numbers representing the observed and expected phenotypes of a given genotype expressed in terms of the buffering parameters, and b.

Integrins are adhesion proteins that diffuse along the cell membrane, bind to ligands, and cluster with each other in the early stage of cell adhesion. Integrin clustering and its specific spatial distribution play important roles in subsequent biological processes; however, the mechanisms that give rise to their characteristic spatial distribution remain poorly understood. To address this issue, we developed a cell adhesion model that incorporates cell membrane deformation and integrin dynamics. A hybrid continuous/discrete model was applied to represent membrane deformation, whereas Brownian dynamics combined with a transition state model was used to describe integrin dynamics and binding kinetics. Comparison of numerical simulations of cell adhesion to a substrate with experimental observations at the early stage of adhesion successfully reproduced the characteristic spatial distribution of integrin clusters, in which high-density clusters formed at the periphery of the region adhering to the substrate. These results suggest that the cellular-scale distribution of integrin clusters can be reproduced using only minimal elements, such as adhesion-driven membrane deformation and integrin-ligand binding. In addition, we found that the strength of integrin-ligand binding regulates the degree of clustering by changing the size of the part of the membrane that is deformed, thereby mechanically supporting the mechanical involvement of the actin cytoskeleton in integrin clustering. Furthermore, the formation and spatial distribution of integrin clusters were shown to be determined not only by the static mechanical equilibrium of membrane deformation and physical adsorption, but also by membrane spreading/deformation and the dynamic behavior of integrins. This suggests that the size and spatial distribution of integrin clusters may be controllable by modulating the speed of membrane spreading.

The development and physiology of neurons rely on their microtubule organization, which is characterized by plus-end-out oriented microtubules in the axon and a mix of plus-end-out and plus-end-in oriented microtubules in dendrites. This orientational pattern is established early in neuronal development and is tightly linked to axon-dendrite differentiation. Even though multiple potentially relevant mechanisms have been proposed, fundamental questions remain: How does the microtubule organization in neurons emerge, and how does a neuron develop a single axon and multiple dendrites? Here, we address these questions at two distinct, complementary levels: at a higher level by proposing a conceptual framework, in which we classify mechanisms into three categories based on how they contribute to the microtubule organization: orientational bias, parallel amplification, and polarization; at a lower level we build a biophysical model that incorporates multiple mechanisms of microtubule dynamics in a neuron, from which, using analytical calculations and simulations, we derive insights into the emergence of microtubule organization in developing neurons. We show that geometrical effects alone can confer a bias in microtubule orientation. Parallel amplification then enhances the resulting polarity. Coupling multiple neurites to a common cell body that serves as a shared reservoir of resources allows for a polarization mechanism that ensures that the microtubule organization of one neurite becomes axonal while all others are dendritic. This framework unifies diverse molecular observations and yields experimentally testable predictions about microtubule self-organization in early neuronal development. Author summaryNeurons communicate through long protrusions called neurites, which are of two types: dendrites, which receive signals, and axons, which send signals. Their development relies primarily on microtubules, which are polar filaments with two distinct ends, known as the plus and minus ends. Microtubules self-organize into functional architectures that are significantly different between axons and dendrites. In axons, all microtubules point their plus end away from the cell body, whereas in dendrites, they point either towards the cell body or have mixed orientations depending on the species. This orientation guides intracellular transport by motors and is closely linked to whether a neurite develops into an axon or a dendrite. Despite decades of research identifying individual mechanisms, the bigger picture behind the emergence of microtubule orientation in neurons remains unclear. Here, we construct a conceptual framework and a biophysical model to identify the principles underlying the emergence of microtubule orientation in developing neurons. Our conceptual framework provides a high-level perspective on how individual mechanisms influence microtubule organization in neurites. In our concrete biophysical model, we study a selection of mechanisms to gain specific, quantitative insight into the organizational process. We propose a minimal model of a neuron that exhibits neuronal polarization, giving rise to a single axon-like neurite and multiple dendrite-like ones, consistent with experimental observations. This in silico neuron helps to explain how neurons break symmetry during development and provides a systematic way to generate and test new hypotheses about neuronal polarity.

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.

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.

Weak magnetic fields affect many biological processes across the tree of life, though the precise molecular sensors and pathways involved in such magnetoresponses remain mostly uncharacterized. Fluorescence is a useful tool for investigating magnetic field effects in flavoproteins, as their chromophores fluorescence intensity can be shown to depend on the spin states of electronic radical pairs. Here, we describe a four-state ordinary differential equation model to understand what parameter sets result in fluorescence contrast between spin states in photocycles with singlet and triplet radical pairs. We conclude that only certain sets of parameters result in the fluorescence intensity being a good proxy measurement for singlet yield. In particular, we observe that the illumination intensity required to obtain fluorescence contrast depends on the rate of the slow spin-independent radical termination reactions that recover ground-state oxidized fluorophores. Moreover, to observe a magnetic field effect in fluorescence intensity when an external magnetic field modulates the singlet yield, the illumination intensity must be strong enough such that photoexcitation is not the rate-limiting step. This understanding suggests that flavoproteins that do not exhibit magnetic field effects in their fluorescence emission under certain experimental setups may still be sensitive to weak magnetic fields in terms of function, as magnetosensitivity in fluorescence depends strongly on illumination conditions.

Biomolecular condensates are widespread cellular self-assembled structures with essential functions. There are suggestions of condensates formed by different proteins being near criticality. However, systematic investigation of the criticality of condensates is absent, and critical exponents defining their universality class have not been found. Here, using long-time simulations, we show that condensates exhibit typical critical phenomena, including scale-free spatiotemporal correlations, critical slowing down, divergence of correlation length and dynamic scaling. From these scaling behaviors, a set of critical exponents is determined. Based on dynamic critical exponent, diverse condensates can be divided into two distinct universality classes, arising from differences in their molecular components and interaction types.

Single-molecule tracking measures the stochastic motion of individual biomolecules in the cellular environment. Statistical analysis of trajectory ensembles is required to gain insight into the biophysical nature of mobility states and molecular interactions that they reflect. Mobility states can be parameterized by a generalized diffusion coefficient and anomalous exponent. Experimental constraints such as finite track length and localization precision limit how accurately these parameters can be determined. We compare the performance of analysis methods to recover the input parameters from ensembles of simulated single molecule tracks from different states spanning the range of anomalous diffusive behaviors observed in the cell nucleus. We further develop a framework to quantify error rates in the assignment of mobility states to individual molecules based on recall rates and precision. Our analysis shows that single-track analysis methods are superior to bulk methods in their ability to recover parametric descriptors from mixed populations. The most complete description is obtained by combining outputs from different tools. Our work provides a guide to assess the accuracy of analyses and obtain the most accurate parametric description of experimental single particle tracking data. Statement of significanceExperimental single particle tracking data provides rich insight into molecular interactions directly in living cells. But data analysis depends critically on choosing the correct diffusion model and appropriate tools to extract accurate information. Importantly, it is usually not obvious from the output of a method whether the results are accurate or not. In this work, we use ensembles of tracks simulated with fractional Brownian motion methods to characterize the impact of track length and localization precision on analysis outcomes. We elaborate on specific strengths and weaknesses of commonly used and newly developed analysis tools to provide a template for thorough assessment and quantification of error rates in experimental data analysis.

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.

Cells adjust their internal circuits in response to changes in their environment. Hence, exposing cells to changing conditions provides a way to probe the intrinsic dynamics of cellular internal circuits. Metabolic networks are examples of such circuits since metabolic fluxes dynamically adjust when environmental conditions are transiently altered. Most existing theoretical frameworks focus on cellular metabolic steady states and do not consider the dynamics of changes in metabolic fluxes. In this work, we applied transfer function analysis from control theory to analyze the changes of NADH oxidative fluxes in the mitochondria and cytoplasm in mouse oocytes in response to dynamical perturbations of oxygen depletion and recovery. We observed an overshoot of NADH oxidative flux in the cytoplasm upon oxygen recovery which is absent in the mitochondrial NADH oxidative flux. Metabolic perturbation experiments and transfer function analysis indicate that this cytoplasmic NADH overshoot results from the coupling of the mitochondrial and cytoplasmic NADH cycles. The degree of overshoot is determined by competing timescales associated with the exchange rates of lactate and pyruvate with the media and their interconversion rates catalyzed by lactate dehydrogenase. Applying control theory to the data enables the inference of the exchange and conversion rates of pyruvate and lactate, allowing predictions of the contribution of lactate to mitochondrial respiration. Our work indicates that the oocytes maintain a homeostatic respiration rate across nutrient conditions by modulating the contribution of lactate to mitochondrial respiration.

Biomolecular condensates are thought to play a pivotal role in cellular organization by regulating biochemical reactants in space and time. Sustained molecular fluxes across condensate boundaries, together with the participation of phase-separating molecules in active chemical reactions such as ATP hydrolysis, call for a nonequilibrium description. Here, we propose a self-consistent framework in which diffusion-drift dynamics and chemical reactions are coupled through a conditional free energy, defined as the excess contribution to the chemical potential. Self-consistency is achieved by deriving this quantity from the same free-energy functional that governs molecular interactions and phase separation. We apply the framework to a minimal client-scaffold system and investigate how active chemical processes and phase separation interact at steady state. In doing so, our approach recovers the fundamental rules previously identified for the emergence of nonequilibrium steady-state fluxes. The model shows that active reactions involving the scaffold molecules can regulate the phase behavior of the condensate. Moreover, nonequilibrium steady-state fluxes are maximal near the boundary between the phase-separated and homogeneous regimes, suggesting that condensates sustaining molecular transport may operate close to their stability threshold. In the same region, client fluxes are also enhanced, revealing an indirect coupling between scaffold activity and client transport. These results provide a baseline for developing more detailed theories of chemically active condensates.

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.

Generative diffusion models have demonstrated an ability to produce novel images sampled from the learned underlying data distribution. These models are able to infer system characteristics for parameter combinations that were not seen during training. We investigate the ability of these models to infer trends in biological data from limited samples. Specifically, we consider the response of system scale behaviors such as cortical flow in a simulated actomyosin system as we tune filament turnover rates. We train a diffusion model on coarse grained actin curvature and density heatmap images, and are able to generate images from conditioning variables not seen during training. These images are predictive of nonlinear trends in the system. We also consider characteristics of the system that allows this level of inference, such as the strong linear relationship between average density and filament turnover in the system, and by exploring minimal underlying dynamics with a motor binding model.

The light absorption of the protein cryptochrome and its chromophore FAD is important for the regulation of circadian rhythms and in some species for sensing magnetic fields. To compute the absorption spectrum of chromophore, typically only a small region is treated quantum-mechanically due the high computational cost of spectroscopic calculations. We present a formalism that allows a quantum-mechanical treatment of not only the chromophore but also the neighbouring amino acids which differ from species to species. This is achieved by using the real-time time-dependent Hartree-Fock method. This method allows extending the quantum domain from typically only a few dozen atoms up to around 1,200 atoms for the largest calculations. The presented framework allows the treatment of neighbouring tryptophan residues or the cofactor molecule MTHF in the same calculation and allows to extract information of which regions absorb light depending on wavelength. The presented results also show that the environment around the chromophore FAD amplifies the light absorption in cryptochrome.

The influence of arbitrary randomness in cell division times on the variability of protein copy numbers within a lineage ensemble has been recently studied, going beyond the contributions of noisy gene expression and partitioning error. However, variability of protein concentrations need separate study, since cell size growth between cell divisions dilute protein concentrations at the same rate as size growth, which also determines mean division times. Here for a model of bursty protein production, we present exact moments (of all orders) of protein concentrations in the cyclo-stationary state, comparing: (i) population and lineage cell ensembles, and (ii) statistics at different cell ages. Two interesting results emerge. While the variance of protein concentration changes with the degree of division time heterogeneity at any cell age, the age-averaged variance is independent of it within lineage ensemble but stays dependent within population ensemble. The skewness within population ensemble is higher in younger cells than within lineage ensemble, and this behavior reverses at older ages. Such a feature vanishes for the age-averaged distribution, with population based skewness always dominating over that of lineage. We also show that mother-daughter correlations in generation times, do not add any significant difference to the results.

Transcription factors form clusters often described as condensates that exhibit emergent biophysical properties. Here we present a software package to simulate transcription factor spatial distributions from molecular diffusion and binding kinetics alone. The software simulates microscopy data and FRAP experiments and recapitulates the clustering behavior of experimentally characterized transcription factors. Our results demonstrate that condensate-like structures can emerge from molecular kinetics principles without invoking higher-order processes like phase separation.

AO_SCPLOWBSTRACTC_SCPLOWCell fate decisions are driven by gene regulatory networks (GRNs). While the mutually inhibitory toggle switch effectively models binary fate decisions, fully connected inhibitory networks with more than two nodes fail to capture multi-fate decisions due to the low prevalence of "single high states", where only a single master regulator is highly expressed. The goal of this study is to find network structures that support all single high states. We find that the only network that attains the highest possible prevalence of all single high states within the set of monotone Boolean (MB) models is completely disconnected. Since biological networks typically require connectivity, we investigate network structures that support equipotency, where all single high states have equal prevalence within MB models. Finally, we characterize the networks that support multistability between all single high states, finding that it is possible only in networks in which each node either has self-activations or is inhibited by every other network node. Our findings provide a theoretical framework for understanding the network design principles that can support simultaneous differentiation into multiple distinct cell types.