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.

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.

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.

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.

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.

Microbes exhibit complex dynamic behavior as the result of a large number of biochemical processes, spatial and temporal interactions, environmental variations, and evolutionary pressure. Although significant progress has been achieved in understanding microbial ecological dynamics, multiple open questions remain, including the microscopic mechanisms of growth and the roles of nutrients and stochasticity. In this work, we present a minimal theoretical approach to clarify the link between consumption of resources by microbes and their growth. A stochastic model that accounts for a single microbial species consuming a single type of resource while growing via cell division is studied analytically and via Monte Carlo computer simulations. We identify three distinct dynamical regimes of microbial growth determined by the relative magnitudes of resource uptake and division rates and initial conditions. We also show that stochasticity influences the dynamic behavior when the amounts of microbes or resources are low. The model recovers Monod growth kinetics and provides a mechanistic interpretation of the Monod constant and maximal growth rate. The theoretical framework presented captures a wide spectrum of dynamic behaviors in microbial systems, providing a clearer microscopic picture to explain their underlying complex mechanisms.

Reaction diffusion (RD) systems play a fundamental role in numerous biochemical and biophysical processes. Here, we present a novel analytical framework for solving RD equations by applying the Wentzel Kramers Brillouin Jeffreys (WKBJ) formalism to Ca nanodomains generated by individual membrane channels, a widely used paradigm for intracellular Ca signaling. Previous models have primarily focused on stationary Ca nanodomains while neglecting diffusion and saturation of intracellular Ca buffers and sensors. In contrast, we derive analytical solutions without these simplifying assumptions. Our analysis demonstrates that sustained Ca influx generates continuously expanding distributions of free Ca, whereas Ca bound buffers and sensors propagate as traveling waves. These predictions are supported experimentally by measurements of one-dimensional fluorescence profiles produced by single-channel activity and two-dimensional profiles generated by whole cell Ca currents. The analytical framework developed here readily extends Michaelis Menten type kinetics to reaction diffusion systems and may therefore be broadly applicable to biochemical and biophysical processes in which diffusion cannot be neglected.

What drove nucleic acids (NA) to associate with proteins (PR) at the Origins of Life? We reason from polymer physics and the Central Dogma (CD) that the fitness value of cooperating through a division of labor - NA for replication fidelity and PR for functional fitness - is much higher than for either polymer alone. Our model shows a Pareto Front, where NA and PR can bootstrap each other to achieve autocatalytic cooperativity towards biology.

The ability to tune protein function through the binding of modulatory ligands enables the development of therapeutics that steer a biological system away from dysfunctional states underlying disease. Understanding the dynamic mechanisms by which allosteric ligands alter protein function remains an important open question. Dynamical network models allow us to quantify information flow between protein functional sites. However, existing network models use time-symmetric metrics for computing information from correlated residue motions extracted from molecular dynamics (MD) simulations, failing to fully capture directional information flow between sites. Here, we developed a Python library, TEntroPy, and analysis workflow using transfer entropy to generate a directional protein network from equilibrium MD trajectories. Applying this workflow to proteins with known allosteric ligands, we identified residues in both allosteric and orthosteric (primary) binding sites acting as broadcasters and receivers of information. We then computed optimal paths of directional information flow between binding sites. The presence of temporal asymmetry in residue coupling identified from simulations of the unbound (apo) state suggests that directional information flow is encoded in the intrinsic dynamics of the protein. To test this, we perturbed key binding-site residues and demonstrated that our TE-weighted network captures perturbation-induced changes in dynamics along communication routes between binding sites. Identifying residue pairs with high temporal asymmetry provides an additional tool for understanding the dynamic mechanisms of allosteric communication.

Cell states are increasingly conceptualized as attractors of high-dimensional dynamical systems, yet quantitative approaches for integrating phenotypic information into this framework remain limited. Here, we take an image-based approach that combines unsupervised machine learning (ML) with timelapse imaging to extract and characterize the temporal dynamics of morphological features. Using a cell line with endogenously tagged VE-cadherin, we acquired brightfield and fluorescence timelapse images of human induced pluripotent stem cell-derived endothelial cell (hiPSC-EC) monolayers, which adopt distinct phenotypes at two different magnitudes of shear stress in terms of their morphology, behavior, and VE-cadherin organization. To quantify these phenotypic cell states without segmentation, we trained a diffusion autoencoder to predict VE-cadherin signal from brightfield images. We identified interpretable ML-based features representing cell orientation, elongation, and local density. Treating these variables as dimensions of a morphological state space, we estimated a data-driven vector field and found that the two observed phenotypic cell states correspond to stable fixed points of the inferred dynamical system. Mapping measured cell migration coherence onto this space further distinguished the states. Imaging cells across intermediate shear stresses revealed a regime of bistability in which both states coexist, indicating that the shear-stress-dependent transition between endothelial cell states occurs as a bifurcation of the inferred dynamical system. Finally, we applied this method to study an N-terminal truncation of VE-cadherin, finding that mutated cells preserve alignment and coherent migration, but exhibit altered morphology and increased migration speed. This work demonstrates the applicability of a dynamical systems approach to quantitatively characterize morphological aspects of cell state from interpretable ML-based features.

Phages must locate and bind to bacterial surface receptors to initiate infection. Their tail fiber configuration critically influences this process. We develop a stochastic model describing surface search as a renewal process, incorporating attachment, detachment, and target-finding steps. Using both numerical simulations and analytical calculations, we quantify how tail fiber number, attachment-detachment rates, and geometric constraints impact the mean and the distribution of time to successful adsorption. Notably, the search efficiency shows a nonmonotonic dependence on tail fibers number, governed by a trade-off between binding stability and diffusion-mediated mobility. This optimum shifts depending on the effective bacterial density, target radius, and fiber reach. Short fiber reach imposes severe geometric constraints, reducing mobility at high tail fiber counts and leading to performance degradation. Our findings suggest that phage adsorption strategies are shaped by a balance between anchoring and exploration, with evolutionary implications for tail fiber design and infection efficiency.

Compartmental models of infectious disease transmission make assumptions about human behaviors. Specifically, they parameterize interactions across population groups, assumed to have distinct epidemiologically-relevant behavioral patterns, primarily through contact matrices stratified by demographic variables such as age, gender, or socioeconomic status. Although such demographic characteristics are readily measurable, they may inadequately capture the social and psychological forces that govern protective behaviors. Drawing on 20 waves of a national survey conducted throughout the COVID-19 pandemic in the United States, we show that institutional trust - particularly trust in public health agencies, physicians, and hospitals - is a dominant predictor of protective behavior adoption. For mask wearing during periods of strongest pandemic activity, for example, institutional trust explains more behavioral variance across population groups than age, income, education, and partisan affiliation combined. In unadjusted analyses, the difference in protective behavior adoption between individuals with the highest and lowest trust in the CDC was four- to six-fold larger than the corresponding differences by age, income, or educational attainment, and exceeded the difference between Democratic and Republican respondents. This association was institutionally specific (e.g., the relationship attenuates for trust in banks), and behaviorally specific (e.g., trust in the CDC is associated with protective behaviors but not visiting a doctor). The latter suggests that trust modifies voluntary compliance with public health recommendations rather than access to or use of healthcare. We conclude that compartmental models of disease transmission would be substantially improved by incorporating institutional trust as a stratifying variable. We additionally offer a trust-integrated mathematical modeling framework and recommendations for the data infrastructure needed for its implementation.

There is a vast literature on the voltage gating of ion channels, with a fairly large fraction concerned with potassium channels, especially of the KV1 family, including Shaker. Experimental evidence derived from protein structure has been interpreted to give gating mechanisms that largely disregard water. We propose that the K+ ion, in order to pass through the gating region and enter the cavity pore, must be largely dehydrated. Competitive interactions of each single hydration shell water at the gate, with counterions, protein, or other water molecules, can remove one water at a time. There are several such interactions for the ion hydration shell; for the ion to pass through the gating region, there must be enough such interactions to leave the ion with at most two hydrating water molecules, in which case the gate is open. Protein conformational changes are secondary, small, and mostly unimportant. The hypothesis has a second part: protons, previously shown to be candidate carriers of the gating current (Kariev and Green, JPC B, 2019, Membranes, 2022, 2024) are capable of reaching the gate; adding four protons to the gate prevents dehydration, leaving the ion with at least three hydrating water molecules, enough to block passage. Quantum calculations presented here support the dehydration part of the hypothesis; they also mostly support the second part, concerning the protons, but further work will be required to fully confirm this. The hypothesis explains the experimental finding that the P475D mutant is essentially constitutively open, while the P475S mutant, with a wider gate opening, is closed at all relevant potentials; the computations presented here show the mechanism for this in detail, further confirming the first part of the hypothesis, and largely but not completely confirming the second part, concerning protons, while showing where further work is needed. This mechanism can also qualitatively account for flicker noise and fluctuations, and their consequences.

Background. Sentinel lymph node biopsy (SLNB) is an essential component of axillary staging in breast cancer. Fluorescence-guided mapping with indocyanine green (ICG) enables real-time visualization of lymphatic drainage; however, the parameters of fluorescence-signal recording require standardization. Objective. To assess the technical feasibility and clinical applicability of SLNB with ICG under near-infrared (NIR) imaging guidance in patients with breast cancer. Materials and Methods. This prospective single-center study included 30 patients who underwent ICG-guided SLNB between 2023 and 2025. In 24 patients, ICG mapping was combined with technetium-99m radioisotope navigation; in 6 patients, ICG guidance alone was used. The protocol comprised periareolar ICG injection, standardized imaging conditions, and fluorescence-index recording. Results. The protocol was completed in all 30 patients. Fluorescent visualization of the lymphatic pathway and/or the sentinel lymph node (SLN) was achieved in every case, and no ICG-related adverse reactions were recorded. The mean fluorescence index was 213.0 +/- 24.7, the median was 206.0 [192.5-237.2], and the min-max was 180-255. Conclusion. SLNB with ICG under NIR imaging guidance demonstrated technical feasibility in a prospective single-center cohort. Quantitative fluorescence-index recording may serve as a component of standardizing intraoperative fluorescence guidance. Keywords: breast cancer; sentinel lymph node biopsy; indocyanine green; near-infrared imaging; fluorescence lymphography; fluorescence index; axillary staging.

We perform a large-scale computational characterization of the map of protein primary to secondary structure using an AVR3a class protein effector domain from the plant pathogen P. palmivora as a case study. We formulate a modified site-scanning approach for exploring the neutral component of secondary structure phenotypes based on predictions from the machine-learning algorithm Porter 5 and apply it to the AVR3a phenotype. We predict a set of sensitive sites within the effector domain that are generally located at or near the boundaries of structured regions, with restrictions on the possible amino acid residues at these sites dictated by the secondary structure type that they participate in within the WT. We characterize a set of mutated phenotypes derived through the exploration of the neutral component of the WT effector domain, selecting them so that they span a range including both very rarely and very commonly seen secondary structures, and that they include both secondary structures nearly identical to the WT and ones far removed from it. We find that all these diverse phenotypes have an estimated robustness of the same order as that of the WT, and that the robustness scales logarithmically phenotype frequency, as seen in other genotype-to-phenotype maps. Furthermore, we observe that the dependence of the estimated phenotype frequency on the Kolmogorov complexity indicates simplicity bias in the protein secondary structure map.

Protein folding is the process by which a polypeptide chain organizes into its three-dimensional structure through a balance of stabilizing and destabilizing interactions encoded by the sequence. A central question in protein biophysics is how thermodynamic factors guide a polypeptide toward its native folded state despite the rugged energy landscape and the competing influence of nonnative interactions. In many biomolecular processes, cooperativity provides a mechanism by which multiple weak interactions act collectively to generate a robust response. In the context of protein folding, such cooperative effects may arise when the formation of one native contact enhances the stability or likelihood of nearby native contacts, thereby promoting collective organization toward the folded state. At the same time, folding is opposed by the much larger number of non-native interactions, whose heterogeneity can introduce frustration and destabilize folding even when the average native bias favors the folded phase. The interplay of these competing effects in determining foldability remains unclear in statistical-mechanical models. Here, we address this problem using a one-dimensional spin-glass model of protein folding with explicit shared-residue cooperative interactions encoded through wedge-based motifs. We show that modest cooperative bias can stabilize folding even where the noncooperative system remains unfolded, whereas non-native energetic fluctuation suppresses folding and shifts the transition to higher cooperative strengths. We further find that partial cooperative coverage is sufficient to lower the folding threshold. Therefore, the model provides a mean-field framework for incorporating cooperative interaction strength into the native one-dimensional model of protein folding and for describing how local cooperativity reshapes the folding transition.

A priori assessment of target proteins' druggability remains an unsolved problem in the field of drug development. The empirical approaches widely used to solve this problem demonstrate low efficiency. In this work, we investigated the factor of hydration of a representative set of 65 evolutionarily and structurally unrelated human enzymes in a water environment. This factor depends only on the structure of the proteins, and not on the physical and chemical properties of any potential ligands. The results show that, unlike the widely used approaches based on calculations of the accessible surface area (ASA), the content of low-entropy water molecules (LEW) in the active sites of human enzymes is systematically higher than that in other areas of their surface, including inactive cavities. Optimal criteria and a step-by-step procedure for identifying protein ligand binding sites are proposed. The proposed approach, based on the calculation of the LEW content in the first hydration layer of potentially interesting target proteins, makes it possible to evaluate their medicinal suitability even before the development of any ligands. The article also presents the results of a comparative analysis of experimental Raman spectroscopy data and the results of molecular dynamics simulations of water hydrogen bonds using three widely used water models (TIP3P, OPC3, and TIP5P) and standard algorithms for calculating hydrogen bond networks.

Mechanotransduction via the actin cytoskeleton is linked to fundamental cellular processes such as morphogenesis, cell division, and motility, requiring the control of tensile forces mediated by the motor protein non-muscle myosin 2 (NM2). Formins such as mDia1 have been shown to elongate actin structures that are under mechanical tension; conversely, mDia1s elongation rates are modulated by the applied force. Despite their relevance at the membrane/cortex interface, reported values for tension in formin-elongated actin filaments stem from theoretical estimates and simulations, but have not been amenable experimentally so far. Thus, we developed a Forster resonance energy transfer (FRET)-based, tension-sensitive probe (mDia1TS) and quantified the measured tension in live U2OS cells using fluorescence lifetime imaging microscopy (FLIM). Through whole-cell ROI analysis we show a short and long lifetime component, reporting an intensity-weighted, averaged lifetime corresponding to [~]3.5 pN. Upon mitogen stimulation of cells using EGF, we show that the tension homeostasis changed significantly, with a measurable increase in tension in the cells periphery and relaxation in its center. Furthermore, the reported average tension relaxed by 2 pN after adding the NM2 inhibitor para-nitroblebbistatin. We utilized siRNA knockdowns of individual NM2 paralogs (NM2-A, NM2-B, or NM2-C) to measure their individual contribution, revealing NM2-A as the main paralog to produce tensile force in this system. Taken together, we demonstrate that mDia1TS is able to directly determine that active mDia1 in cells is under tension, and that subcellular quantification with pN precision is possible. SignificanceDespite the fundamental importance of formins in regulating actin-based processes, reported values for tension in formin-mediated actin structures stem from simulations and theoretical estimates. In this study we developed a FRET-based, tension-sensitive reporter probe for formin mDia1, which we termed mDia1TS. Given the expanding clinical spectrum of DIAPH1/mDia1 mutations, our tool mDia1TS provides a quantitative tool for elucidation of changes in cytoskeletal assemblies.