Physical Biology

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.

Quantifying how cooperative, many-body relationships drive allostery in protein networks remains a major challenge. To address this, we develop the Laplacian minor hierarchy, a mathematical framework that characterizes the geometric invariants of a protein network. Lower-order minors yield standard metrics including the partition function and effective distances, whereas higher-order minors define novel topological measures: cooperation indices, each bounded between zero and one, that characterize pathway correlations at increasing levels of complexity, the third-order minor determines whether allosteric pathways are correlated or uncorrelated, and the fourth-order minor quantifies how distinct pathways communicate through intermediary residues. We apply this framework to analyze the evolutionary adaptation of the PSD95pdz3 domain from Class I to Class II ligand specificity via mutations G330T and H372A. The cooperation index demonstrates a distinct evolutionary hierarchy: the G330T mutation establishes distributed pathway couplings that the H372A mutation subsequently exploits, whereas H372A alone produces minimal global changes. Furthermore, the fourth-order analysis identifies His317 as a critical intermediary node bridging the class-switching (330-372) and class-bridging (330-400) allosteric pathways. These results demonstrate that allosteric dependencies emerge only when mutations accumulate in specific combinations, with a hierarchical organization of pathways structured around position 330 and intermediary nodes His317 and Phe400. Rather than predicting allosteric mechanisms, this framework provides a mechanistic explanation for why and how allostery emerges during protein evolution.

Contact mediated cell-cell communication where direct physical contact between adjacent ligand cells and receptor cells trigger signal output is important during growth, development and regeneration of organisms. While the molecular machinery underlying contact mediated cell signaling is well explored, how the local spatial context of cells affect cell-cell contact mediated gene expression is not clear. Here, we present a vertex-based computational model to study spatial and temporal behavior of contact mediated signal output (which we refer to as output) in growing cell collectives. We consider cell-cell contact length dependent output synthesis and output degradation in receptor cells together with cell division to understand how dynamics at the scale of single cells lead to heterogeneous signal output. By tracking single receptor cells over time in growing cell collectives in silico, we show that cell growth and division lead to continuous and dynamic rearrangement of cell-cell contact between receptor and ligand cells which in turn affect the output levels. Our model predicts that the orientation of cell division plays a key role in the heterogeneity of signal output. We elucidate the link between cell mechanical properties that control cell shape, growth, and division, with signal output in receptor cells during contact mediated signaling processes.

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.

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.

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.

The dominant paradigm for temperature robustness in biomolecular circuits is for the parameters to be tuned to have matching temperature dependencies so that their overall effect cancels out. This contrasts with the robustness due to circuit structure, typically operative in circuits where robustness to a single input parameter is desired. The importance of the circuit structure in temperature robustness is generally unclear. We addressed this issue in a benchmark negative feedback circuit using a combination of theoretical modelling and experimental measurements. We found that the response to a temperature perturbation in a model of negative feedback was qualitatively different from the response in a model without feedback. We experimentally measured the response of the negative feedback circuit to a temperature perturbation and found that it was smaller than that of the circuit without feedback, in line with the theoretical finding. We confirmed this theoretical prediction experimentally. The initial response of the negative feedback circuit, paradoxically, was larger than the circuit without feedback. The resolution of this paradox was in accounting for the faster dynamics in the negative feedback circuit. These results show a simple design principle of temperature robustness that can operate in a widespread circuit motif and may also apply to other perturbations which, like temperature, affect multiple parameters simultaneously.

AnnotationMitochondrial heteroplasmy --the coexistence of both wild-type and mutant copies of mitochondrial DNA (mtDNA) within a cell--is a key factor in the pathogenesis of mitochondrial diseases. Classical approaches, which rely solely on the scalar fraction of mutant DNA, fail to fully account for threshold effects, the stochastic nature of heteroplasmy dynamics, and tissue specificity. The aim of the work is to construct a complex stochastic model of heteroplasmy dynamics, which for the first time combines the effects of selection, genetic drift, migration of mitochondrial genomes between tissues and threshold mechanisms of pathology development, for a quantitative assessment of the risk of mitochondrial diseases. In this paper, we propose a complex-phase formalism in which the state of a cells mitochondrial genome is described by a complex number Z = a + ib, where a and b are the absolute numbers of normal and mutant mtDNA copies, respectively. This approach naturally combines information on copy number and heteroplasmy level, and the argument{phi} = arctan (b / a) is interpreted as a phase characterizing the mutant load. Based on this formalism, we developed a stochastic model of tissue dynamics that includes the processes of selection, genetic drift, and intertissue migration of mitochondrial genomes. Using Monte Carlo methods (1000 simulations), we demonstrated that neuronal tissues are characterized by high heteroplasmy variability and a significant probability of reaching a pathological threshold even with a relatively low systemic mutant load. Kaplan-Meier survival analysis demonstrates that the development of pathology is probabilistic and can be described as a time -to-event process . The proposed approach enables quantitative assessment of the individual risk of developing mitochondrial diseases and opens the door to personalized prognosis.

Since the earliest microscopic observations, the geometric organisation of cells has captured biologists interest. Recent work by Gorgi et al. showed that bacterial colony organisation, including biofilms, can be explained across diverse species by radial expansion from fixed initial seeding sites and contact-inhibited growth, with little need for species-specific mechanisms. Here, we extend this geometric framework by incorporating seeding time as an additional driver of colony organisation. Using simulations and analytical models for expected colony size, we show that staggered seeding yields order of magnitude increases in the expected size of early seeded founder colonies. At realistic biofilm growth rates, a 2-day lag between founder and subsequent colony seeding produces an approximately 10-fold increase in expected founder size, while a 1-week lag produces a 25-fold increase. These findings provide a simple geometric basis for biological priority effects, illustrating temporal advantage alone can generate substantial spatial dominance, with implications for cardiovascular devices where host and bacterial cells compete in a race for the surface.

Predicting and understanding behaviour is a primary objective of many disciplines, especially human behaviour, as it is the cause of many of the worlds most pressing problems. Although it is a fundamental concept in multiple disciplines, there is no agreed operational definition of what it is. Neither is there a generally agreed theoretical framework for predicting it. Here we propose a data-driven approach, using the "Conductome" -- the complete set of factors that both predict and explain a behaviour -- to operationalise a discipline-neutral definition of behaviour that is based on an ensemble of stimulus/response measurements of a system, showing that it must be determined through a process of statistical inference. As the prediction of behaviour can be characterised as a classification problem, we argue that Bayesian classifiers offer a promising framework in which explainable prediction models that can approximate the Conductome can be developed. We show the efficacy of the framework using a dataset of 1075 persons, with over 3000 features, constructing a model for predicting sedentariness, a behaviour that is a known risk factor for obesity and metabolic disease. We analyse the effect size, coverage, statistical significance and potential causality of a subset of 396 features associated with 58 variables.of different types.

Based on our experimental observation of activation state oscillations of different frequencies used to communicate information by the master human stress response regulator protein p38 MAPK 1, we develop a simple graphical approach for understanding and predicting the behavior of complex biological networks acting upon signals carrying information as different frequency waves of chemicals. This approach uses the same techniques used for analyzing and understanding information transmission using waves of electrical currents and fields used in electrical alternating current (AC) circuits. We show how biological components can be organized to behave as standard components found in electronic telecommunications circuits. Finally, we demonstrate how such components can be organized into complex biological signaling cascades whose behavior can be qualitatively and quantitatively understood, and whose output resembles that experimentally observed in p38.

A fundamental biological process of transcription occurs in the cell nucleus, which is a complex medium that also contains multiple heterogeneous structures known as biomolecular condensates. Interestingly, some of these condensates contain mRNA molecules in addition to proteins, suggesting an important cellular role in transcription that is not yet well understood. In this work, we develop a minimal theoretical framework for quantitative investigation of the role of reversible mRNA condensation in transcription. Our discrete-state stochastic approach accounts for the most relevant processes, allowing us to explicitly evaluate the properties of the system and clarify the effects of condensation. Analytical calculations supported by computer simulations suggest that reversible mRNA condensation influences the transcription processes by maintaining a constant level of free mRNA in the nucleoplasm while lowering the degree of stochastic noise and increasing the robustness against external perturbations. Physicochemical arguments are presented to explain these observations. The proposed theoretical framework elucidates important microscopic aspects of transcription, providing a convenient quantitative tool for investigating complex biological phenomena.

Understanding noise propagation in gene regulatory circuits requires accounting for both model and resource constraints. In this work, we investigated the role of model order in influencing stochastic behaviour by deriving and analytically comparing reduced protein-only models with higher-order models that include mRNA and molecular complexes, and found that protein-based models can exhibit higher noise levels in the gene expression. Through frequency-response analysis, we explained that the higher-order models provide additional noise-filtering effects. We also analyzed a one-dimensional constrained model and showed that the Fano factor decreases as the strength of resource constraint increases. Finally, we considered larger circuit motifs, such as toggle switches and incoherent feed-forward loops, and found that resource limitations can minimise stochastic switching in a bistable circuit, whereas in an incoherent feed-forward loop, resource constraints can make the adaptation faster. Our results highlight that both mechanistic detail and shared resource constraints play a central role in determining fluctuation levels in biomolecular circuits.

Spatial proofreading is a mechanism that can enhance molecular discrimination by exploiting nonequilibrium diffusive transport between spatially separated source and readout regions. Here, we introduce a thermodynamically consistent reaction-diffusion model in which a gradient of active substrates is generated self-consistently by a reversible kinase-phosphatase switch coupled to nucleotide chemostats. The resulting chemical-potential gradient explicitly controls the nonequilibrium driving and allows the discrimination potential to be related to microscopic chemical rates and diffusive transport. A simple one-dimensional analysis shows that the ability of an enzyme to discriminate between wrong and right substrates is governed by a subtle balance between substrate-gradient confinement, controlled by phosphatase activity, the diffusive crossing time across the source-readout domain, and selective complex dissociation. We then extend the model to two-dimensional domains, showing that source, i.e. kinase, localization modulates spatial specificity by shaping the effective diffusive paths to the readout boundary. Finally, stochastic simulations reveal that molecular fluctuations generate intermittent wrong-readout events, which can be characterized through an event-weighted measure of specificity. Interestingly, we find that fluctuations promote frequent transitions to long-residence states in which discrimination is better than predicted by the deterministic estimate. Overall, our work highlights the importance of thermodynamically consistent descriptions of spatial proofreading and clarifies how energy input, transport, and spatial organization jointly shape biochemical discrimination.

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.

1.Partial Rank Correlation Coefficient (PRCC), usually performed following Latin Hyper-cube Sampling (LHS), is a global sensitivity analysis that quantifies the monotonic relationship between model parameters and the desired output. To carry out this analysis, a range of acceptable parameter values must be known or estimated. However, within a biological context, approximating these values may be difficult. Parameter values and ranges can be taken from different organisms or systems or be estimated to produce qualitative phenomena in the model. Using a mathematical model of the epithelial mesenchymal transition (EMT) as a test case, this work examines how the parameter ranges chosen prior to analysis can influence LHS-PRCC results and shape subsequent analysis interpretations. Previous LHS-PRCC analysis of this model restricted parameters to {+/-}10% of their original value, which limits the scope and interpretability of parameter influence. Such a small range assumes, in the biological sense, that parameters are well-measured with little variability. Here, this work extends the previous analysis and explores several parameter ranges ({+/-}25%, {+/-}50% of the original value). This work also tests whether, within the {+/-}10%, {+/-}25% and {+/-}50% parameter ranges, the bistable switch present in the original model are maintained. Ultimately, this work showcases how a choice made prior to analysis, such as the accepted parameter ranges for biological rates and values in complex dynamical systems can influence sensitivity analysis results and interpretability. Additionally, these choices can have hidden consequences, such as the loss of phenomenological behavior. Thus, explicit prior knowledge about the appropriate parameter values is needed before using analysis to guide future experiments and model development.

Early studies of synaptic transmission by Bernard Katz and colleagues suggested that neurotransmitter release at graded-potential synapses occurs through statistically independent (i.e. Poissonian) quanta [1, 2]. Subsequent experimental work supported this framework [3]. However, these measurements were performed in vitro on relatively simple synapses and under non-physiological conditions, often converting spiking neurons into graded-potential neurons through the use of channel blockers. Relying on the conventional assumption that vesicle exocytosis follows a Poisson process, measurements of the contrast power transfer spectrum and noise power spectral density of large monopolar cells (LMCs) in the blowfly C. vicina imply a sustained vesicle release rate exceeding 105 vesicles per second per LMC. Given the physical dimensions of photoreceptors and synaptic vesicles, such a release rate appears physiologically implausible. If vesicle release is more temporally structured, low-frequency noise could be suppressed, substantially reducing the vesicle release rate required to account for experimental observations. The reduction of noise at low frequencies is especially advantageous given inputs such as photoreceptor signals which are already low-pass filtered. Visual activity generates substantial extracellular potentials within the lamina cartridge [4]. We propose that these extracellular potentials regulate vesicle release by modulating the voltage sensors that trigger exocytosis. We provide experimental evidence for the connection between currents driving the LMC and the extracellular potentials during visual activity, and demonstrate, using simple models, how effective "Poisson" rates are maximized due to vesicle regularization.

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.

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.