Physical Biology

This study explores the relationship between residue fluctuations and molecular communication in proteins, emphasizing the role of these dynamics in allosteric regulation. We employ computational tools including the Gaussian network model, mutual information, and interaction information, to analyze how stochastic interactions among residues contribute to functional interactions while also introducing noise. Our approach is based on the postulate that residues experience continuous stochastic bombardment from impulses generated by their neighbors, forming a complex network characterized by small-world scaling topology. By mapping these interactions through the Kirchhoff matrix framework, we demonstrate how conserved correlations enhance signaling pathways and provide stability against noise-like fluctuations. Notably, we highlight the importance of selecting relevant eigenvalues to optimize the signal-to-noise ratio in our analyses, a topic that has yet to be thoroughly investigated in the context of residue fluctuations. This work underscores the significance of viewing proteins as adaptive information processing systems, and emphasizes the fundamental mechanisms of biological information processing. The basic idea of this paper is the following: given two interacting residues on an allosteric path, what are the contributions of the remaining residues on this interaction. This naturally leads to the concept of synergy, redundancy and noise in proteins, which we analyze in detail for three proteins CheY, tyrosine phosphatase and β-lactoglobulin.

Tracking and motion analyses of semi-flexible biopolymer networks from time-lapse microscopy images are important tools that enable quantitative measurements to unravel the dynamic and mechanical properties of biopolymers in living tissues, crucial for understanding their organization and function. Biopolymer networks are challenging to track due to continuous stochastic transitions, such as merges and splits, which cause local neighborhood rearrangements over short time and length scales. To address this, we propose the Spatio Temporal Information on Pixel Subsets algorithm to track these events by creating pixel subsets that link trajectories across frames. Using this method, we analyzed actin-enriched protrusions, or 'microridges,' which form dynamic labyrinthine patterns on squamous cell epithelial surfaces, mimicking 'active Turing-patterns.' Our results reveal two distinct actomyosin-based rhythmic dynamics in neighboring cells: a common pulsatile mechanism between 2 and 6.25 min period governing both fusion and fission events contributing to pattern maintenance, and cell area pulses predominantly exhibiting 10 min period.

The electric potential across the inner mitochondrial membrane must be maintained within certain bounds for the proper functioning of the cell. A feedback control mechanism for the homeostasis of this membrane potential is proposed whereby an increase in the electric field decreases the rate-limiting steps of the electron transport chain (ETC). An increase in trans-membrane electric field limits the rate of proton pumping to the inter-membrane gap by slowing the ETC reactions and by intrinsically induced electroporation that depolarizes the inner membrane. The proposed feedback mechanism is akin to a Le Chatelier's-type principle of trans-membrane potential feedback control.

Ion channels are protein structures that facilitate the selective passage of ions across the membrane cells of living organisms. They are known for their high conductance and high selectivity. The precise mechanism between these two seemingly contradicting features is not yet firmly established. One possible candidate is the quantum coherence. In this work we study the quantum model of the soft knock-on conduction using the Lindblad equation taking into account the non-hermiticity of the model. We show that the model exhibits a regime in which high conductance coexists with high coherence. Our findings second the role of quantum effects in the transport properties of the ion channels.

Natural variations in gene expression, called noise, are fundamental to biological systems. The expression noise can be beneficial or detrimental to cellular functions. While the impact of noise on individual genes is well-established, our understanding of how noise behaves when multiple genes are co-expressed by shared regulatory elements within transcription networks remains elusive. This lack of understanding extends to how the architecture and regulatory features of these networks influence noise. To address this gap, we study the multi-output feed-forward loop motif. The motif is prevalent in bacteria and yeast and influences co-expression of multiple genes by shared transcription factors (TFs). Focusing on a two-output variant of the motif, the present study explores the interplay between its architecture, co-expression (symmetric and asymmetric) patterns of the two genes, and the associated noise dynamics. We employ a stochastic modeling approach to investigate how the binding affinities of the TFs influence symmetric and asymmetric expression patterns and the resulting noise dynamics in the co-expressed genes. This knowledge could guide the development of strategies for manipulating gene expression patterns through targeted modulation of TF binding affinities.

Computational modeling of cancer can help unveil dynamics and interactions that are hard to replicate experimentally. Thanks to the advancement in cancer databases and data analysis technologies, these models have become more robust than ever. There are many mathematical models which investigate cancer through different approaches, from sub-cellular to tissue scale, and from treatment to diagnostic points of view. In this study, we lay out a step-by-step methodology for a data-driven mechanistic model of the tumor microenvironment. We discuss data acquisition strategies, data preparation, parameter estimation, and sensitivity analysis techniques. Furthermore, we propose a possible approach to extend mechanistic ordinary differential equation models to PDE models coupled with mechanical growth. The workflow discussed in this article can help understand the complex temporal and spatial interactions between cells and cytokines in the tumor microenvironment and their effect on tumor growth.

Cells communicate with each other to jointly regulate cellular processes during cellular differentiation and tissue morphogenesis. This multiscale coordination arises through the spatiotemporal activity of morphogens to pattern cell signaling and transcriptional factor activity. This coded information controls cell mechanics, proliferation, and differentiation to shape the growth and morphogenesis of organs. While many of the molecular components and physical interactions have been identified in key model developmental systems, there are still many unresolved questions related to the dynamics involved due to challenges in precisely perturbing and quantitatively measuring signaling dynamics. Recently, a broad range of synthetic optogenetic tools have been developed and employed to quantitatively define relationships between signal transduction and downstream cellular responses. These optogenetic tools can control intracellular activities at the single cell or whole tissue scale to direct subsequent biological processes. In this brief review, we highlight a selected set of studies that develop and implement optogenetic tools to unravel quantitative biophysical mechanisms for tissue growth and morphogenesis across a broad range of biological systems through the manipulation of morphogens, signal transduction cascades, and cell mechanics. More generally, we discuss how optogenetic tools have emerged as a powerful platform for probing and controlling multicellular development.

Eukaryotic chromosomes exhibit a hierarchical organization that spans a spectrum of length scales, ranging from sub-regions known as loops, which typically comprise hundreds of base pairs, to much larger chromosome territories that can encompass a few mega base pairs. Chromosome conformation capture experiments that involve high-throughput sequencing methods combined with microscopy techniques have enabled a new understanding of inter- and intra-chromosomal interactions with unprecedented details. This information also provides mechanistic insights on the relationship between genome architecture and gene expression. In this article, we review the recent findings on three-dimensional interactions among chromosomes at the compartment, topologically associating domain, and loop levels and the impact of these interactions on the transcription process. We also discuss current understanding of various biophysical processes involved in multi-layer structural organization of chromosomes. Then, we discuss the relationships between gene expression and genome structure from perturbative genome-wide association studies. Furthermore, for a better understanding of how chromosome architecture and function are linked, we emphasize the role of epigenetic modifications in the regulation of gene expression. Such an understanding of the relationship between genome architecture and gene expression can provide a new perspective on the range of potential future discoveries and therapeutic research.

Mitochondria serve a wide range of functions within cells, most notably via their production of ATP. Although their morphology is commonly described as bean-like, mitochondria often form interconnected networks within cells that exhibit dynamic restructuring through a variety of physical changes. Further, though relationships between form and function in biology are well established, the extant toolkit for understanding mitochondrial morphology is limited. Here, we emphasize new and established methods for quantitatively describing mitochondrial networks, ranging from unweighted graph-theoretic representations to multi-scale approaches from applied topology, in particular persistent homology. We also show fundamental relationships between mitochondrial networks, mathematics, and physics, using ideas of graph planarity and statistical mechanics to better understand the full possible morphological space of mitochondrial network structures. Lastly, we provide suggestions for how examination of mitochondrial network form through the language of mathematics can inform biological understanding, and vice versa.

How cells build and maintain dynamic structures of defined size is currently an important unsolved problem in quantitative cell biology. The flagella of the unicellular green alga Chlamydomonas provide a highly tractable model system to investigate this general question, but while the powerful genetics of this organism have revealed numerous genes required for proper flagellar length, in most cases we do not understand their mechanistic role in length control. Flagellar length can be viewed as the steady state solution of a dynamical system involving assembly and disassembly of axonemal microtubules, with assembly depending on an active transport process known as intraflagellar transport (IFT). The inherent length dependence of IFT gives rise to a family of simple models for length regulation that can account for many previously described phenomena such as the ability of flagella to maintain equal lengths. But these models requires that the cell has a way to measure flagellar length in order to adjust IFT rates accordingly. Several models for length sensing have been modeled theoretically and evaluated experimentally, allowing them to be ruled out. Current data support a model in which the diffusive return of the kinesin motor driving IFT provides a length dependence that ultimately is the basis for length regulation. By combining models of length sensing with a more detailed representation of cargo transport and availability, it is now becoming possible to formulate concrete hypotheses to explain length altering mutants.

This study explores the relationship between residue fluctuations and molecular communication in proteins, emphasizing the role of these dynamics in allosteric regulation. We employ computational tools including the Gaussian network model, mutual information, and interaction information, to analyze how stochastic interactions among residues contribute to functional interactions while also introducing noise. Our approach is based on the postulate that residues experience continuous stochastic bombardment from impulses generated by their neighbors, forming a complex network characterized by small-world scaling topology. By mapping these interactions through the Kirchhoff matrix framework, we demonstrate how conserved correlations enhance signaling pathways and provide stability against noise-like fluctuations. Notably, we highlight the importance of selecting relevant eigenvalues to optimize the signal-to-noise ratio in our analyses, a topic that has yet to be thoroughly investigated in the context of residue fluctuations. This work underscores the significance of viewing proteins as adaptive information processing systems, and emphasizes the fundamental mechanisms of biological information processing. The basic idea of this paper is the following: given two interacting residues on an allosteric path, what are the contributions of the remaining residues on this interaction. This naturally leads to the concept of synergy, redundancy and noise in proteins, which we analyze in detail for three proteins CheY, tyrosine phosphatase and β-lactoglobulin.

Tracking and motion analyses of semi-flexible biopolymer networks from time-lapse microscopy images are important tools that enable quantitative measurements to unravel the dynamic and mechanical properties of biopolymers in living tissues, crucial for understanding their organization and function. Biopolymer networks are challenging to track due to continuous stochastic transitions, such as merges and splits, which cause local neighborhood rearrangements over short time and length scales. To address this, we propose the Spatio Temporal Information on Pixel Subsets algorithm to track these events by creating pixel subsets that link trajectories across frames. Using this method, we analyzed actin-enriched protrusions, or 'microridges,' which form dynamic labyrinthine patterns on squamous cell epithelial surfaces, mimicking 'active Turing-patterns.' Our results reveal two distinct actomyosin-based rhythmic dynamics in neighboring cells: a common pulsatile mechanism between 2 and 6.25 min period governing both fusion and fission events contributing to pattern maintenance, and cell area pulses predominantly exhibiting 10 min period.

The electric potential across the inner mitochondrial membrane must be maintained within certain bounds for the proper functioning of the cell. A feedback control mechanism for the homeostasis of this membrane potential is proposed whereby an increase in the electric field decreases the rate-limiting steps of the electron transport chain (ETC). An increase in trans-membrane electric field limits the rate of proton pumping to the inter-membrane gap by slowing the ETC reactions and by intrinsically induced electroporation that depolarizes the inner membrane. The proposed feedback mechanism is akin to a Le Chatelier's-type principle of trans-membrane potential feedback control.

Ion channels are protein structures that facilitate the selective passage of ions across the membrane cells of living organisms. They are known for their high conductance and high selectivity. The precise mechanism between these two seemingly contradicting features is not yet firmly established. One possible candidate is the quantum coherence. In this work we study the quantum model of the soft knock-on conduction using the Lindblad equation taking into account the non-hermiticity of the model. We show that the model exhibits a regime in which high conductance coexists with high coherence. Our findings second the role of quantum effects in the transport properties of the ion channels.

How much information does a cell inherit from its ancestors beyond its genetic sequence? What are the epigenetic mechanisms that allow this? Despite the rise in available epigenetic data, how such information is inherited through the cell cycle is still not fully understood. Often, epigenetic marks can display bistable behaviour and their bistable state is transmitted to daughter cells through the cell cycle, providing the cell with a form of memory. However, loss-of-memory events also take place, where a daughter cell switches epigenetic state (with respect to the mother cell). Here, we develop a framework to compute these epigenetic switching rates, for the case when they are driven by DNA replication, i.e. the frequency of loss-of-memory events due to replication. We consider the dynamics of histone modifications during the cell cycle deterministically, except at DNA replication, where nucleosomes are randomly distributed between the two daughter DNA strands, which is therefore implemented stochastically. This hybrid stochastic-deterministic approach enables an analytic derivation of the replication-driven switching rate. While retaining great simplicity, this framework can explain experimental switching rate data, establishing its biological importance as a framework to quantitatively study epigenetic inheritance.

In this paper, we analyze the role of fear in a three-species non-delayed ecological model that examines the interactions among susceptible prey, infectious (diseased) prey, and predators within a food web. The prey population grows in a logistic manner until it achieves a carrying capacity, reflecting common population dynamics in the absence of predators. Diseased prey is assumed to transmit infection to healthful prey by the use of a Holling type II reaction. Predators, alternatively, are modeled to consume their prey using Beddington–DeAngelis and Crowley–Martin response features. This evaluation specializes in ensuring the non-negativity of solutions, practical constraints on population dynamics, and long-term stability of the system. Each biologically possible equilibrium point is tested to understand the environmental stable states. Local stability is assessed through eigenvalue analysis, while global stability of positive equilibria is evaluated by the use of Lyapunov features to determine the overall stability of the model. Furthermore, Hopf bifurcation is explored primarily based on infection rate ɛ. Numerical simulations are carried out to validate the theoretical effects and offer practical insights into the model behaviour under specific conditions.

Throughout the course of the SARS-CoV-2 pandemic, genetic variation has contributed to the spread and persistence of the virus. For example, various mutations have allowed SARS-CoV-2 to escape antibody neutralization or to bind more strongly to the receptors that it uses to enter human cells. Here, we compared two methods that estimate the fitness effects of viral mutations using the abundant sequence data gathered over the course of the pandemic. Both approaches are grounded in population genetics theory but with different assumptions. One approach, tQLE, features an epistatic fitness landscape and assumes that alleles are nearly in linkage equilibrium. Another approach, MPL, assumes a simple, additive fitness landscape, but allows for any level of correlation between alleles. We characterized differences in the distributions of fitness values inferred by each approach and in the ranks of fitness values that they assign to sequences across time. We find that in a large fraction of weeks the two methods are in good agreement as to their top-ranked sequences, i.e. as to which sequences observed that week are most fit. We also find that agreement between the ranking of sequences varies with genetic unimodality in the population in a given week.

Recent experimental studies have shown that physical exercise has the potential to suppress tumor progression. Such suppression has been reported to be mediated by the exercise-induced activation of natural killer (NK) cells through the release of IL-6, a cytokine. Aimed at shedding light on how exercise-induced NK cell activation helps in the suppression of cancer, we developed a coarse-grained mathematical model based on a system of ordinary differential equations describing the interaction between IL-6, NK-cells, and tumor cells. The model is then used to study how exercise duration and exercise intensity affect tumor suppression. Our results show that increasing exercise intensity or increasing exercise duration leads to greater and sustained tumor suppression. Furthermore, multi-bout exercise patterns hold promise for improving cancer treatment strategies by adjusting exercise intensity and frequency. Thus, the proposed mathematical model provides insights into the role of exercise in tumor suppression and can be instrumental in guiding future experimental studies, potentially leading to more effective exercise interventions.

We consider a Markovian model for the kinetics of RNA Polymerase (RNAP) which provides a physical explanation for the phenomenon of cooperative pushing during transcription elongation observed in biochemical experiments on Escherichia coli and yeast RNAP. To study how backtracking of RNAP affects cooperative pushing we incorporate into this model backward (upstream) RNAP moves. With a rigorous mathematical treatment of the model we derive conditions on the mutual static and kinetic interactions between RNAP under which backtracking preserves cooperative pushing. This is achieved by exact computation of several key properties in the steady state of this model, including the distribution of headway between two RNAP along the DNA template and the average RNAP velocity and flux.

Finding the stiffness map of biological tissues is of great importance in evaluating their healthy or pathological conditions. However, due to the heterogeneity and anisotropy of biological fibrous tissues, this task presents challenges and significant uncertainty when characterized only by single-mode loading experiments. In this study, we propose a new theoretical framework to map the stiffness landscape of fibrous tissues, specifically focusing on brain white matter tissue. Initially, a finite element (FE) model of the fibrous tissue was subjected to six loading cases, and their corresponding stress–strain curves were characterized. By employing multiobjective optimization, the material constants of an equivalent anisotropic material model were inversely extracted to best fit all six loading modes simultaneously. Subsequently, large-scale FE simulations were conducted, incorporating various fiber volume fractions and orientations, to train a convolutional neural network capable of predicting the equivalent anisotropic material properties solely based on the fibrous architecture of any given tissue. The proposed method, leveraging brain fiber tractography, was applied to a localized volume of white matter, demonstrating its effectiveness in precisely mapping the anisotropic behavior of fibrous tissue. In the long-term, the proposed method may find applications in traumatic brain injury, brain folding studies, and neurodegenerative diseases, where accurately capturing the material behavior of the tissue is crucial for simulations and experiments.