Physical Biology

Despite the current wealth of high-throughput data, our understanding of signal transduction is still incomplete. Mathematical modeling can be a tool to gain an insight into such processes. Detailed biochemical modeling provides deep understanding, but does not scale well above relatively a few proteins. In contrast, logic modeling can be used where the biochemical knowledge of the system is sparse and, because it is parameter free (or, at most, uses relatively a few parameters), it scales well to large networks that can be derived by manual curation or retrieved from public databases. Here, we present an overview of logic modeling formalisms in the context of training logic models to data, and specifically the different approaches to modeling qualitative to quantitative data (state) and dynamics (time) of signal transduction. We use a toy model of signal transduction to illustrate how different logic formalisms (Boolean, fuzzy logic and differential equations) treat state and time. Different formalisms allow for different features of the data to be captured, at the cost of extra requirements in terms of computational power and data quality and quantity. Through this demonstration, the assumptions behind each formalism are discussed, as well as their advantages and disadvantages and possible future developments.

Bistability underlies cellular memory and maintains alternative differentiation states. Bistability can emerge only if its parameter range is either physically realizable or can be enlarged to become realizable. We derived a general rule and showed that the bistable range of a reaction parameter is maximized by a pair of other parameters in any gene regulatory network provided they satisfy a general condition. The resulting analytical expressions revealed whether or not such reaction pairs are present in prototypical positive feedback loops. They are absent from the feedback loop enclosed by protein dimers but present in both the toggle-switch and the feedback circuit inhibited by sequestration. Sequestration can generate bistability even at narrow feedback expression range at which cooperative binding fails to do so, provided inhibition is set to an optimal value. These results help to design bistable circuits and cellular reprogramming and reveal whether bistability is possible in gene networks in the range of realistic parameter values.

Concepts rooted in physics are becoming increasingly important in biology as we transition to an era in which quantitative descriptions of all processes from molecular to cellular level are needed. In this perspective I discuss two unexpected findings of universal behavior, uncommon in biology, in the self-assembly of proteins and RNA. These findings, which are surprising, reveal that physics ideas applied to biological problems, ranging from folding to gene expression to cellular movement and communication between cells, might lead to discovery of universal principles operating in adoptable living systems.

This paper explores the potential for simplicity to reveal new biological understanding. Borrowing selectively from physics thinking, and contrasting with Crick's reductionist philosophy, the author argues that greater emphasis on simplicity is necessary to advance biology and its applications.

Bacterial biofilms are communities of bacteria that exist as aggregates that can adhere to surfaces or be free-standing. This complex, social mode of cellular organization is fundamental to the physiology of microbes and often exhibits surprising behavior. Bacterial biofilms are more than the sum of their parts: single-cell behavior has a complex relation to collective community behavior, in a manner perhaps cognate to the complex relation between atomic physics and condensed matter physics. Biofilm microbiology is a relatively young field by biology standards, but it has already attracted intense attention from physicists. Sometimes, this attention takes the form of seeing biofilms as inspiration for new physics. In this roadmap, we highlight the work of those who have taken the opposite strategy: we highlight the work of physicists and physical scientists who use physics to engage fundamental concepts in bacterial biofilm microbiology, including adhesion, sensing, motility, signaling, memory, energy flow, community formation and cooperativity. These contributions are juxtaposed with microbiologists who have made recent important discoveries on bacterial biofilms using state-of-the-art physical methods. The contributions to this roadmap exemplify how well physics and biology can be combined to achieve a new synthesis, rather than just a division of labor.

Despite their cultural differences, physics and biology are destined to interact with each other more in the future. The reason is that modern physics is fundamentally about codification of emergent law, and life is the greatest of all emergent phenomena.

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.

Eukaryotic cells face the challenging task of transporting a variety of particles through the complex intracellular milieu in order to deliver, distribute, and mix the many components that support cell function. In this review, we explore the biological objectives and physical mechanisms of intracellular transport. Our focus is on cytoplasmic and intra-organelle transport at the whole-cell scale. We outline several key biological functions that depend on physically transporting components across the cell, including the delivery of secreted proteins, support of cell growth and repair, propagation of intracellular signals, establishment of organelle contacts, and spatial organization of metabolic gradients. We then review the three primary physical modes of transport in eukaryotic cells: diffusive motion, motor-driven transport, and advection by cytoplasmic flow. For each mechanism, we identify the main factors that determine speed and directionality. We also highlight the efficiency of each transport mode in fulfilling various key objectives of transport, such as particle mixing, directed delivery, and rapid target search. Taken together, the interplay of diffusion, molecular motors, and flows supports the intracellular transport needs that underlie a broad variety of biological phenomena.

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.

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.

How bacteria sense local chemical gradients and decide to move has been a fascinating area of recent study. Chemotaxis of bacterial populations has been traditionally modeled using either individual-based models describing the motion of a single bacterium as a velocity jump process, or macroscopic PDE models that describe the evolution of the bacterial density. In these models, the hydrodynamic interaction between the bacteria is usually ignored. However, hydrodynamic interaction has been shown to induce collective bacterial motion and self-organization resulting in larger mesoscale structures. In this paper, the role of hydrodynamic interactions in bacterial chemotaxis is investigated by extending a hybrid computational model that incorporates hydrodynamic interactions and adding components from a classical velocity jump model. It is shown that by including hydrodynamic interactions, a suspension with a low initial volume fraction can exhibit locally high concentrations in bacterial aggregates. Also, it is shown that hydrodynamic interactions enhance the merging of the small aggregates into larger ones and lead to qualitatively different aggregate behavior than possible with pure chemotaxis models. Namely, differences in the shape, number, and dynamics of these emergent clusters.

Recent advances in live cell imaging of F-actin structures, combined with pulse-chase imaging and computational modeling have suggested that actin is transported along the axon via biased polymerization of metastable actin fibers (actin trails). This mechanism is distinct from motor driven polymer transport, such as for neurofilaments and can be best described as molecular hitchhiking, where G-actin molecules are intermittently incorporated into actin fibers which grow preferentially in the anterograde direction. In this paper, we discuss how various axonal and actin trail parameters like axon diameter, trail nucleation rates, basal G-actin concentration, and trail length influence the transport rate. These predictions can help guide future experiments to verify this novel protein transport mechanism. We introduce a simplified, analytically solvable model of actin transport which relates these parameters to experimentally measurable quantities. We also discuss why a simple diffusion-based transport mechanism cannot explain bulk actin transport in the axon.

Lactic acid bacteria (LAB) are frequently used in food fermentation and are invaluable for the taste and nutritional value of the fermentation end-product. To gain a better understanding of underlying biochemical and microbiological mechanisms and cell-to-cell variability in LABs, single-molecule techniques such as single-particle tracking photo-activation localization microscopy (sptPALM) hold great promises but are not yet employed due to the lack of detailed protocols and suitable assays.

Here, we qualitatively test various fluorescent proteins including variants that are photoactivatable and therefore suitable for sptPALM measurements in Lactococcus lactis, a key LAB for the dairy industry. In particular, we fused PAmCherry2 to dCas9 allowing the successful tracking of single dCas9 proteins, whilst the dCas9 chimeras bound to specific guide RNAs retained their gene silencing ability in vivo. The diffusional information of the dCas9 without any targets showed different mechanistic states of dCas9: freely diffusing, bound to DNA, or transiently interacting with DNA. The capability of performing sptPALM with dCas9 in L. lactis can lead to a better, general understanding of CRISPR-Cas systems as well as paving the way for CRISPR-Cas based interrogations of cellular functions in LABs.

Motile biological cells in tissue often display the phenomenon of durotaxis, i.e. they tend to move towards stiffer parts of substrate tissue. The mechanism for this behavior is not completely understood. We consider simplified models for durotaxis based on the classic persistent random walker scheme. We show that even a one-dimensional model of this type sheds interesting light on the classes of behavior cells might exhibit. Our results strongly indicate that cells must be able to sense the gradient of stiffness in order to show the effects observed in experiment. This is in contrast to the claims in recent publications that it is sufficient for cells to be more persistent in their motion on stiff substrates to show durotaxis: i.e. it would be enough to sense the value of the stiffness. We show that these cases give rise to extremely inefficient transport towards stiff regions. Gradient sensing is almost certainly the selected behavior.

By means of replica exchange molecular dynamics simulations we investigate how the length of a silk-like, alternating diblock oligopeptide influences its secondary and quaternary structure. We carry out simulations for two protein sizes consisting of three and five blocks, and study the stability of a single protein, a dimer, a trimer and a tetramer. Initial configurations of our simulations are β-roll and β-sheet structures. We find that for the triblock the secondary and quaternary structures upto and including the tetramer are unstable: the proteins melt into random coil structures and the aggregates disassemble either completely or partially. We attribute this to the competition between conformational entropy of the proteins and the formation of hydrogen bonds and hydrophobic interactions between proteins. This is confirmed by our simulations on the pentablock proteins, where we find that, as the number of monomers in the aggregate increases, individual monomers form more hydrogen bonds whereas their solvent accessible surface area decreases. For the pentablock β-sheet protein, the monomer and the dimer melt as well, although for the β-roll protein only the monomer melts. For both trimers and tetramers remain stable. Apparently, for these the entropy loss of forming β-rolls and β-sheets is compensated for in the free-energy gain due to the hydrogen-bonding and hydrophobic interactions. We also find that the middle monomers in the trimers and tetramers are conformationally much more stable than the ones on the top and the bottom. Interestingly, the latter are more stable on the tetramer than on the trimer, suggesting that as the number of monomers increases protein-protein interactions cooperatively stabilize the assembly. According to our simulations, the β-roll and β-sheet aggregates must be approximately equally stable.

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.