Physical Biology

Metabolism is built on a foundation of organic chemistry, and employs structures and interactions at many scales. Despite these sources of complexity, metabolism also displays striking and robust regularities in the forms of modularity and hierarchy, which may be described compactly in terms of relatively few principles of composition. These regularities render metabolic architecture comprehensible as a system, and also suggests the order in which layers of that system came into existence. In addition metabolism also serves as a foundational layer in other hierarchies, up to at least the levels of cellular integration including bioenergetics and molecular replication, and trophic ecology. The recapitulation of patterns first seen in metabolism, in these higher levels, motivates us to interpret metabolism as a source of causation or constraint on many forms of organization in the biosphere. Many of the forms of modularity and hierarchy exhibited by metabolism are readily interpreted as stages in the emergence of catalytic control by living systems over organic chemistry, sometimes recapitulating or incorporating geochemical mechanisms.

We identify as modules, either subsets of chemicals and reactions, or subsets of functions, that are re-used in many contexts with a conserved internal structure. At the small molecule substrate level, module boundaries are often associated with the most complex reaction mechanisms, catalyzed by highly conserved enzymes. Cofactors form a biosynthetically and functionally distinctive control layer over the small-molecule substrate. The most complex members among the cofactors are often associated with the reactions at module boundaries in the substrate networks, while simpler cofactors participate in widely generalized reactions. The highly tuned chemical structures of cofactors (sometimes exploiting distinctive properties of the elements of the periodic table) thereby act as 'keys' that incorporate classes of organic reactions within biochemistry.

Module boundaries provide the interfaces where change is concentrated, when we catalogue extant diversity of metabolic phenotypes. The same modules that organize the compositional diversity of metabolism are argued, with many explicit examples, to have governed long-term evolution. Early evolution of core metabolism, and especially of carbon-fixation, appears to have required very few innovations, and to have used few rules of composition of conserved modules, to produce adaptations to simple chemical or energetic differences of environment without diverse solutions and without historical contingency. We demonstrate these features of metabolism at each of several levels of hierarchy, beginning with the small-molecule metabolic substrate and network architecture, continuing with cofactors and key conserved reactions, and culminating in the aggregation of multiple diverse physical and biochemical processes in cells.

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.

More than 60 years of biochemical and biophysical studies have accustomed us to think of proteins as highly purified entities that act in isolation, more or less freely diffusing until they find their cognate partner to bind to. While in vitro experiments that reproduce these conditions largely remain the only way to investigate the intrinsic properties of molecules, this approach ignores an important factor: in their natural milieu , proteins are surrounded by several other molecules of different chemical nature, and this crowded environment can considerably modify their behaviour.

About 40% of the cellular volume on average is occupied by all sorts of molecules. Furthermore, biological macromolecules live and operate in an extremely structured and complex environment within the cell (endoplasmic reticulum, Golgi apparatus, cytoskeletal structures, etc). Hence, to further complicate the picture, the interior of the cell is by no means a simply crowded medium, rather, a most crowded and confining one. In recent times, several approaches have been developed in the attempt to take into account important factors such as the ones mentioned above, at both theoretical and experimental levels, so that this field of research is now emerging as one of the most thriving in molecular and cell biology (see figure 1).

Figure 1. Left: number of articles containing the word 'crowding' as a keyword limited to the biological and chemical science domains (source: ISI Web of Science). The arrow flags the 2003 'EMBO Workshop on Biological Implications of Macromolecular Crowding' (Embo, 2012). Right: number of citations to articles containing the word 'crowding' limited to the same domains (bars) and an exponential regression curve (source: Elsevier Scopus).

To promote the importance of molecular crowding and confinement and provide researchers active in this field an interdisciplinary forum for meeting and exchanging ideas, we recently organized an international conference held in Ascona from 10 to 14 June 2012. In the unique scenario of the Maggiore lake and absorbed in the magic atmosphere of the Centro Stefano Franscini (CSF) at Monte Verità, we enjoyed three-and-a-half days of intense and inspiring activity, where not only many of the most prominent scientists working on macromolecular crowding, but also experts in closely related fields such as colloids and soft matter presented their work. The meeting was intended and has been organized to bring theoreticians and experimentalists together in the attempt to promote an active dialogue. Moreover, we wanted different disciplines to be represented, notably physics and chemistry, besides biology, as cross-fertilization is proving an increasingly fundamental source of inspiration and advancement.

This issue of Physical Biology (PB) features a selection of the oral contributions presented at the conference, expanded in the form of research or review articles. PB, one of the scientific journals of the Institute of Physics (IOP), is one of the most dynamic and lively forums active at the interface between biology on one side, and physics and mathematics on the other. As its mission is stated by IOP, PB 'focuses on research in which physics-based approaches lead to new insights into biological systems at all scales of space and time, and all levels of complexity'. For these reasons, and also in view of its high reputation and broad readership, PB appears to be the ideal place for disseminating the thriving pieces of research presented at the conference. We are extremely grateful to PB and its kind and efficient editorial staff who helped make this issue a great scientific follow-up to the conference.

The opening lecture of the conference, the first of four day-opening keynote lectures, was given by Allen P Minton from NIH (USA), possibly the most influential among the pioneers in the field. He provided a lucid and well-thought-out overview of the concept of macromolecular crowding through an exhaustive chronological account of the major milestones. It is clear that the concept of excluded volume as a key factor remains central to the concept of molecular crowding. As a consequence, simple descriptive paradigms borrowed essentially from colloid physics may still provide useful tools to understand the subtle effects of crowding and confinement in living matter.

The contiguity between crowding, colloids and soft matter further emerged as an important concept in the course of the conference in several theoretical lectures and a few experimental ones.

Dave Thirumalai, from the University of Maryland (USA), one of the most active theoreticians in the field of theoretical biophysics, outlined scaling theories, concepts from colloid literature and different simulation techniques to describe scenarios for crowding-induced changes in the structure and dynamics of proteins and RNA. In particular, he showed the importance of the shape of crowding particles in affecting folding oligomerization of amyloidogenic peptides.

Johannes Schöneberg, from IMPRS, Mathematics Institute (Germany), illustrated ReaDDy , a newly developed particle-based simulation software tool for reaction–diffusion dynamics, developed in the group of Frank Noe at EMPRS. He showed that ReaDDy makes it possible to bridge the gap between soft matter and molecular dynamics (MD) simulations on the one hand and particle-based stochastic reaction–diffusion simulations on the other. We asked Johannes to organize a tutorial session to lead interested participants into the package and 'get their hands wet' under the guidance of the developers. The tutorial session was indeed successful and the broad possibilities offered by the simulation toolkit appeared to be clear to the participants.

Paolo De Los Rios, from the Ecole Polytechnique Fédérale de Lausanne (EPFL, Switzerland), examined the complexity of the effects caused by crowding conditions from the point of view of statistical physics. Starting from a modification of the well-known Smoluchowski approach to calculate the encounter rate of diffusion-limited reactions, he showed how more realistic situations accounting for crowding effects could be treated equally well on the same theoretical grounds. This talk marked an important point in the conference as it reinforced the idea that simple models of theoretical physics still have the power to provide inspiring results in spite of the intrinsic simplifications of such theoretical approaches. Along the same lines, Nicolas Dorsaz, from the University of Cambridge (UK), proposed an extension of the Smoluchowski framework that incorporates repulsive and attracting interactions between the reactants. This approach was illustrated by reaction rates obtained from event-driven Brownian dynamics and dynamical Monte Carlo simulations.

Another striking example of the physical subtleties associated with modelling crowding effects was provided by Jeffrey Skolnick, from the Georgia Institute of Technology (USA). He examined the role of hydrodynamic interactions in the self-organization of biological assemblies in the presence of crowding. His results strongly suggest that hydrodynamic interactions greatly affect the kinetics of self-assembly reactions, so that including them in the picture appears crucial for understanding the dynamics of biological systems in vivo .

Margareth Cheung, from the University of Houston (USA), emphasized that how the crowded environment inside a cell affects the structural conformation of a protein with a spherical shape is a vital question because the geometry of proteins and protein–protein complexes are far from globules in vivo . Her work demonstrates the malleability of 'native' proteins and implies that crowding-induced shape changes may be important for protein function and malfunction in vivo .

Huan-Xiang Zhou, from the Florida State University (USA), focused on atomistic simulations of protein folding and binding under crowding conditions. His lab has developed a post-processing method that allows the atomistic representation of proteins in folding and binding processes under crowding. A comparison with experimental results was also presented.

Other lecturers pointed out that there are still aspects not entirely explored in the effects of both crowding and confinement. As suggested in the talk by Gary Pielak, from the University of North Carolina (USA), the currently used synthetic crowding agents are far from being satisfactory in replicating naturally occurring effects associated with crowded environments. For example, non-specific binding seems to play a subtle role in the cell, as natural macromolecules can induce both stabilization and destabilization when used as crowders. It is indeed possible to fine-tune the effect of proteins, as crowders, on the stability of other proteins.

Another aspect that became clear is that new, more powerful methods need to be developed to study the effect of crowding, but even more to compare crowding and confinement. Indeed, it appeared clear from the lecture by Pierandrea Temussi, from the University of Naples (Italy), that a reliable comparison of the effects of crowding and confinement on the stability of proteins can only be based on the measurement of the whole stability curve of the same protein.

Controversial aspects do not pertain only to the influence of crowding on protein stability, but also to aggregation phenomena in natural fluids.

Domenico Sanfelice, from NIMR (London, UK), reported an interesting case of the apparent influence of crowding on aggregation. Hen egg white, a possible natural medium to study macromolecules in crowded conditions can dramatically increase the aggregation kinetics of proteins with an inbuilt tendency to associate. By carefully dissecting the phenomenology, it was shown that only part of this effect is due to crowding, while another factor playing an important role is the interaction with proteins from the milieu . In other words, high-molecular-weight glycoproteins can act as efficient molecular seeds for aggregation.

A special topic of great relevance in the conference appeared to be the direct study of crowding in living systems. Alan Verkman, from the University of California, San Francisco (USA), one of the world's leading scientific personalities in the field of experimental investigation of crowding and confinement, was invited to give the second plenary lecture devoted to the experimental study of crowding effects in vivo . In his keynote lecture, Dr Verkman led us on a wide and compelling tour, exploring the main experimental approaches to study molecular crowding in and around cells. After a thorough examination of methods such as fluorescence recovery after photo-bleaching, fluorescence correlation spectroscopy, photo-activation localization microscopy and stochastic reconstruction microscopy, he concluded that the general consensus emerging from experimental studies is that the notion of universally anomalous diffusion in and around cells as a consequence of molecular crowding may not be correct, and that the slowing of diffusion in cells is less marked than has been widely assumed and can be simply described through a five- to sixfold reduction of the normal diffusion coefficient. A Soranno, from the University of Zürich (Switzerland), described how, by employing FRET measurements, it is possible to quantify the effect of molecular crowding on the dimensions of the highly charged, intrinsically disordered protein human prothymosin alpha. For a large variety of polymeric crowders (PEG, PVP, Ficoll, Dextran, PVA, PAA), a collapse of the polypeptide chain is observed with increasing polymer size and polymer concentration. The largest extent of collapse is observed for polymer radii comparable to the dimensions of the protein, in agreement with theoretical considerations. For his contribution, A Soranno was awarded the CSF Award for the best contributed talk.

In his most inspiring talk, Clifford Brangwynne, from Princeton University (USA), drew attention to very important objects, namely Ribonucleoprotein (RNP) bodies. These are non-membrane-bound macromolecular assemblies that form from the dynamic interactions of RNA and proteins. The assembly of RNP bodies may sensitively depend on the biophysical features of the surrounding cytoplasm, including the degree of crowding, transport coefficients and mechanical properties. This dependency may have important implications for the RNA processing reactions involved in fundamental biological processes such as developmental cell growth. Remarkably, Brangwynne showed how RNPs behave in the cell as liquid droplets, pointing to a possible entirely new means that the cell could use to control and fine-tune its internal processes, in fact, more than that, a completely unexplored, new state of organization of living matter, and a functional one.

Giuseppe Zaccai, from Institut Laue Langevin, Grenoble (France), showed that protein dynamics is more sensitive than structure to environmental factors such as crowding, solvent, temperature or pressure. Furthermore, he convincingly explained how neutron scattering provides unique experimental data to underpin MD calculations in this context. Following up on environment-induced modulations of protein functional dynamics, Ruth Nussinov, from Tel Aviv University (Israel), addressed the important problem of whether cellular signals can travel long distances in a crowded environment. She proposed a model based on the evolution of at least three properties: a modular functional organization of the cellular network, sequences in some key regions of proteins, such as linkers or loops, and compact interactions between proteins, possibly favoured by a crowded environment.

The workshop ended on a keynote lecture by Jean-Marie Lehn, from the Université de Strasbourg (France). Lehn, 1987 Nobel Laureate in chemistry, offered a 'supramolecular view' of the field of molecular interactions. Supramolecular chemistry explores the design of systems undergoing self-organization , i.e. systems capable of generating well-defined functional supramolecular architectures by self-assembling from their components, thus behaving as programmed chemical systems . Chemistry may therefore be considered an information science , the science of informed matter. Supramolecular chemistry is intrinsically a dynamic chemistry in view of the ability of the interactions connecting the molecular components of a supramolecular entity and the resulting ability of supramolecular species to exchange their constituents. The same holds for molecular chemistry when the molecular entity contains covalent bonds that may form and break reversibly, so as to allow a continuous change in constitution by the reorganization and exchange of building blocks. These features define a constitutional dynamic chemistry (CDC) on both the molecular and supramolecular levels. CDC takes advantage of dynamic constitutional diversity to allow variation and selection in response to either internal or external factors to achieve adaptation . The merging of the features—information and programmability, dynamics and reversibility, constitution and structural diversity—points towards the emergence of adaptive and evolutive chemistry .

The whole workshop could have not taken place without the help of the Centro Stefano Franscini. The CSF is the congress centre of the Swiss Federal Institute of Technology of Zurich (ETH Zurich) and has been situated at Monte Verità since 1989. It is an ideal meeting point for all members of the international scientific community who wish to discuss the state-of-the-art and new challenges of any field of research. The CSF supports 20–25 international conferences every year and, since 2010, up to ten winter doctoral schools¹. The competence and professionalism of the staff were at the same level of beauty and inspiring character as that of Monte Verità.

A meeting of this sort, if successful, leaves the audience with more open questions than settled answers, and this was definitely the case for Crowding 2012. Excluded volume is clearly a fundamental concept that has allowed crowding, a very familiar concept in soft matter, to enter into the domain of biological sciences. However, the complexity of the biological milieu calls for more refined descriptions. What is the role of electrostatic and electrodynamic interactions? What is the role of hydrodynamics interactions? To what extent does the strong spatial inhomogeneity (clustering of molecules, cellular compartmentalization, etc) have to be taken into account? Or, more generally, what are the minimal elements that prove crucial to describe reactions within a cell? How does the diffusion proceed (diffusion, slow diffusion, sub-diffusion) given that the experimental evidences are still controversial?

In conclusion, we knew that allowing scientists with very different backgrounds and ideas to mingle was a hazardous attempt. Despite that, the workshop turned out to be a very successful experiment, which was highly enjoyed both by the participants and the organizers. Discussions sparked regularly among ever-changing groups, comprising senior scientists and students, despite the rather tight schedule, adding to the sense of fulfilment ignited by the outstanding level of the presentations. Given the success of the meeting Crowding 2012, a new event has been organized and will take place on the same themes during fall 2013, this time in the beautiful scenery of the Loire valley in France. The workshop 'Macromolecular crowding effects in cell biology: models and experiments' will be held on the CNRS campus in Orléans, France, on 24–25 October 2013. More information can be found on the workshop website: http://dirac.cnrs-orleans.fr/∼piazza/.

¹Source: www.csf.ethz.ch/

The sites of interaction between a cell and its surrounding microenvironment serve as dynamic signaling hubs that regulate cellular adaptations during developmental processes, immune functions, wound healing, cell migration, cancer invasion and metastasis, as well as in many other disease states. For most cell types, these interactions are established by integrin receptors binding directly to extracellular matrix proteins, such as the numerous collagens or fibronectin. For the cell, these points of contact provide vital cues by sampling environmental conditions, both chemical and physical. The overall regulation of this dynamic interaction involves both extracellular and intracellular components and can be highly variable. In this review, we highlight recent advances and hypotheses about the mechanisms and regulation of cell–ECM interactions, from the molecular to the tissue level, with a particular focus on cell migration. We then explore how cancer cell invasion and metastasis are deeply rooted in altered regulation of this vital interaction.

Programmed cell death is a basic cellular mechanism. Apoptotic-like programmed cell death (called apoptosis in animals) occurs in both unicellular and multicellular eukaryotes, and some apoptotic mechanisms are observed in bacteria. Endosymbiosis between mitochondria and eukaryotic cells took place early in the eukaryotic evolution, and some of the apoptotic-like mechanisms of mitochondria that were retained after this event now serve as parts of the eukaryotic apoptotic machinery. Apoptotic mechanisms have several functions in unicellular organisms: they include kin-selected altruistic suicide that controls population size, sharing common goods, and responding to viral infection. Apoptotic factors also have non-apoptotic functions. Apoptosis is involved in the cellular aging of eukaryotes, including humans. In addition, apoptosis is a key part of the innate tumor-suppression mechanism. Several anticancer drugs induce apoptosis, because apoptotic mechanisms are inactivated during oncogenesis. Because of the ancient history of apoptosis, I hypothesize that there is a deep relationship between mitochondrial metabolism, its role in aerobic versus anaerobic respiration, and the connection between apoptosis and cancer. Whereas normal cells rely primarily on oxidative mitochondrial respiration, most cancer cells use anaerobic metabolism. According to the Warburg hypothesis, the remodeling of the metabolism is one of the processes that leads to cancer. Recent studies indicate that anaerobic, non-mitochondrial respiration is particularly active in embryonic cells, stem cells, and aggressive stem-like cancer cells. Mitochondrial respiration is particularly active during the pathological aging of human cells in neurodegenerative diseases. According to the reversed Warburg hypothesis formulated by Demetrius, pathological aging is induced by mitochondrial respiration. Here, I advance the hypothesis that the stimulation of mitochondrial metabolism leads to pathological aging.

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.

Whether the nom de guerre is Mathematical Oncology, Computational or Systems Biology, Theoretical Biology, Evolutionary Oncology, Bioinformatics, or simply Basic Science, there is no denying that mathematics continues to play an increasingly prominent role in cancer research. Mathematical Oncology—defined here simply as the use of mathematics in cancer research—complements and overlaps with a number of other fields that rely on mathematics as a core methodology. As a result, Mathematical Oncology has a broad scope, ranging from theoretical studies to clinical trials designed with mathematical models. This Roadmap differentiates Mathematical Oncology from related fields and demonstrates specific areas of focus within this unique field of research. The dominant theme of this Roadmap is the personalization of medicine through mathematics, modelling, and simulation. This is achieved through the use of patient-specific clinical data to: develop individualized screening strategies to detect cancer earlier; make predictions of response to therapy; design adaptive, patient-specific treatment plans to overcome therapy resistance; and establish domain-specific standards to share model predictions and to make models and simulations reproducible. The cover art for this Roadmap was chosen as an apt metaphor for the beautiful, strange, and evolving relationship between mathematics and cancer.

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.

Diversity indices are useful single-number metrics for characterizing a complex distribution of a set of attributes across a population of interest. The utility of these different metrics or sets of metrics depends on the context and application, and whether a predictive mechanistic model exists. In this topical review, we first summarize the relevant mathematical principles underlying heterogeneity in a large population, before outlining the various definitions of 'diversity' and providing examples of scientific topics in which its quantification plays an important role. We then review how diversity has been a ubiquitous concept across multiple fields, including ecology, immunology, cellular barcoding experiments, and socioeconomic studies. Since many of these applications involve sampling of populations, we also review how diversity in small samples is related to the diversity in the entire population. Features that arise in each of these applications are highlighted.

Complex biological systems offer a variety of interesting phenomena at the different physical scales. With increasing abstraction, details of the microscopic scales can often be extrapolated to average or typical macroscopic properties. However, emergent properties and cross-scale interactions can impede naïve abstractions and necessitate comprehensive investigations of these complex systems.

In this review paper, we focus on microbial communities, and first, summarize a general hierarchy of relevant scales and description levels to understand these complex systems: (1) genetic networks, (2) single cells, (3) populations, and (4) emergent multi-cellular properties. Second, we employ two illustrating examples, microbial competition and biofilm formation, to elucidate how cross-scale interactions and emergent properties enrich the observed multi-cellular behavior in these systems.

Finally, we conclude with pointing out the necessity of multi-scale investigations to understand complex biological systems and discuss recent investigations.

Uncontrolled growth of tumor cells in confined spaces leads to the accumulation of compressive stress within the tumor. Although the effects of tension within 3D extracellular matrices (ECMs) on tumor growth and invasion are well established, the role of compression in tumor mechanics and invasion is largely unexplored. In this study, we modified a Transwell assay such that it provides constant compressive loads to spheroids embedded within a collagen matrix. We used microscopic imaging to follow the single cell dynamics of the cells within the spheroids, as well as invasion into the 3D ECMs. Our experimental results showed that malignant breast tumor (MDA-MB-231) and non-tumorigenic epithelial (MCF10A) spheroids responded differently to a constant compression. Cells within the malignant spheroids became more motile within the spheroids and invaded more into the ECM under compression; whereas cells within non-tumorigenic MCF10A spheroids became less motile within the spheroids and did not display apparent detachment from the spheroids under compression. These findings suggest that compression may play differential roles in healthy and pathogenic epithelial tissues and highlight the importance of tumor mechanics and invasion.

Antibiotic responses in bacteria are highly dynamic and heterogeneous, with sudden exposure of bacterial colonies to high drug doses resulting in the coexistence of recovered and arrested cells. The dynamics of the response is determined by regulatory circuits controlling the expression of resistance genes, which are in turn modulated by the drug's action on cell growth and metabolism. Despite advances in understanding gene regulation at the molecular level, we still lack a framework to describe how feedback mechanisms resulting from the interdependence between expression of resistance and cell metabolism can amplify naturally occurring noise and create heterogeneity at the population level. To understand how this interplay affects cell survival upon exposure, we constructed a mathematical model of the dynamics of antibiotic responses that links metabolism and regulation of gene expression, based on the tetracycline resistance tet operon in E. coli. We use this model to interpret measurements of growth and expression of resistance in microfluidic experiments, both in single cells and in biofilms. We also implemented a stochastic model of the drug response, to show that exposure to high drug levels results in large variations of recovery times and heterogeneity at the population level. We show that stochasticity is important to determine how nutrient quality affects cell survival during exposure to high drug concentrations. A quantitative description of how microbes respond to antibiotics in dynamical environments is crucial to understand population-level behaviors such as biofilms and pathogenesis.

Understanding the structural and functional development of human-induced pluripotent stem-cell-derived cardiomyocytes (hiPSC-CMs) is essential to engineering cardiac tissue that enables pharmaceutical testing, modeling diseases, and designing therapies. Here we use a method not commonly applied to biological materials, small angle x-ray scattering, to characterize the structural development of hiPSC-CMs within three-dimensional engineered tissues during their preliminary stages of maturation. An x-ray scattering experimental method enables the reliable characterization of the cardiomyocyte myofilament spacing with maturation time. The myofilament lattice spacing monotonically decreases as the tissue matures from its initial post-seeding state over the span of 10 days. Visualization of the spacing at a grid of positions in the tissue provides an approach to characterizing the maturation and organization of cardiomyocyte myofilaments and has the potential to help elucidate mechanisms of pathophysiology, and disease progression, thereby stimulating new biological hypotheses in stem cell engineering.

Dopaminergic neurons are specialized cells in the substantia nigra, tasked with dopamine secretion. This secretion relies on intracellular calcium signaling coupled to neuronal electrical activity. These neurons are known to display spontaneous calcium oscillations in-vitro and in-vivo, even in synaptic isolation, controlling the basal dopamine levels. Here we outline a kinetic model for the ion exchange across the neuronal plasma membrane. Crucially, we relax the assumption of constant, cytoplasmic sodium and potassium concentration. We show that sodium-potassium dynamics are strongly coupled to calcium dynamics and are essential for the robustness of spontaneous firing frequency. The model predicts several regimes of electrical activity, including tonic and 'burst' oscillations, and predicts the switch between those in response to perturbations. 'Bursting' correlates with increased calcium amplitudes, while maintaining constant average, allowing for a vast change in the calcium signal responsible for dopamine secretion. All the above traits provide the flexibility to create rich action potential dynamics that are crucial for cellular function.

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.

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.

Uncontrolled growth of tumor cells in confined spaces leads to the accumulation of compressive stress within the tumor. Although the effects of tension within 3D extracellular matrices (ECMs) on tumor growth and invasion are well established, the role of compression in tumor mechanics and invasion is largely unexplored. In this study, we modified a Transwell assay such that it provides constant compressive loads to spheroids embedded within a collagen matrix. We used microscopic imaging to follow the single cell dynamics of the cells within the spheroids, as well as invasion into the 3D ECMs. Our experimental results showed that malignant breast tumor (MDA-MB-231) and non-tumorigenic epithelial (MCF10A) spheroids responded differently to a constant compression. Cells within the malignant spheroids became more motile within the spheroids and invaded more into the ECM under compression; whereas cells within non-tumorigenic MCF10A spheroids became less motile within the spheroids and did not display apparent detachment from the spheroids under compression. These findings suggest that compression may play differential roles in healthy and pathogenic epithelial tissues and highlight the importance of tumor mechanics and invasion.

Antibiotic responses in bacteria are highly dynamic and heterogeneous, with sudden exposure of bacterial colonies to high drug doses resulting in the coexistence of recovered and arrested cells. The dynamics of the response is determined by regulatory circuits controlling the expression of resistance genes, which are in turn modulated by the drug's action on cell growth and metabolism. Despite advances in understanding gene regulation at the molecular level, we still lack a framework to describe how feedback mechanisms resulting from the interdependence between expression of resistance and cell metabolism can amplify naturally occurring noise and create heterogeneity at the population level. To understand how this interplay affects cell survival upon exposure, we constructed a mathematical model of the dynamics of antibiotic responses that links metabolism and regulation of gene expression, based on the tetracycline resistance tet operon in E. coli. We use this model to interpret measurements of growth and expression of resistance in microfluidic experiments, both in single cells and in biofilms. We also implemented a stochastic model of the drug response, to show that exposure to high drug levels results in large variations of recovery times and heterogeneity at the population level. We show that stochasticity is important to determine how nutrient quality affects cell survival during exposure to high drug concentrations. A quantitative description of how microbes respond to antibiotics in dynamical environments is crucial to understand population-level behaviors such as biofilms and pathogenesis.

Understanding the structural and functional development of human-induced pluripotent stem-cell-derived cardiomyocytes (hiPSC-CMs) is essential to engineering cardiac tissue that enables pharmaceutical testing, modeling diseases, and designing therapies. Here we use a method not commonly applied to biological materials, small angle x-ray scattering, to characterize the structural development of hiPSC-CMs within three-dimensional engineered tissues during their preliminary stages of maturation. An x-ray scattering experimental method enables the reliable characterization of the cardiomyocyte myofilament spacing with maturation time. The myofilament lattice spacing monotonically decreases as the tissue matures from its initial post-seeding state over the span of 10 days. Visualization of the spacing at a grid of positions in the tissue provides an approach to characterizing the maturation and organization of cardiomyocyte myofilaments and has the potential to help elucidate mechanisms of pathophysiology, and disease progression, thereby stimulating new biological hypotheses in stem cell engineering.

Dopaminergic neurons are specialized cells in the substantia nigra, tasked with dopamine secretion. This secretion relies on intracellular calcium signaling coupled to neuronal electrical activity. These neurons are known to display spontaneous calcium oscillations in-vitro and in-vivo, even in synaptic isolation, controlling the basal dopamine levels. Here we outline a kinetic model for the ion exchange across the neuronal plasma membrane. Crucially, we relax the assumption of constant, cytoplasmic sodium and potassium concentration. We show that sodium-potassium dynamics are strongly coupled to calcium dynamics and are essential for the robustness of spontaneous firing frequency. The model predicts several regimes of electrical activity, including tonic and 'burst' oscillations, and predicts the switch between those in response to perturbations. 'Bursting' correlates with increased calcium amplitudes, while maintaining constant average, allowing for a vast change in the calcium signal responsible for dopamine secretion. All the above traits provide the flexibility to create rich action potential dynamics that are crucial for cellular function.

A fundamental question in complex systems is how to relate interactions between individual components ('microscopic description') to the global properties of the system ('macroscopic description'). Furthermore, it is unclear whether such a macroscopic description exists and if such a description can capture large-scale properties. Here, we address the validity of a macroscopic description of a complex biological system using the collective motion of desert locusts as a canonical example. One of the world's most devastating insect plagues begins when flightless juvenile locusts form 'marching bands'. These bands display remarkable coordinated motion, moving through semiarid habitats in search of food. We investigated how well macroscopic physical models can describe the flow of locusts within a band. For this, we filmed locusts within marching bands during an outbreak in Kenya and automatically tracked all individuals passing through the camera frame. We first analyzed the spatial topology of nearest neighbors and found individuals to be isotropically distributed. Despite this apparent randomness, a local order was observed in regions of high density in the radial distribution function, akin to an ordered fluid. Furthermore, reconstructing individual locust trajectories revealed a highly aligned movement, consistent with the one-dimensional version of the Toner-Tu equations, a generalization of the Navier–Stokes equations for fluids, used to describe the equivalent macroscopic fluid properties of active particles. Using this effective Toner–Tu equation, which relates the gradient of the pressure to the acceleration, we show that the effective 'pressure' of locusts increases as a linear function of density in segments with the highest polarization (for which the one-dimensional approximation is most appropriate). Our study thus demonstrates an effective hydrodynamic description of flow dynamics in plague locust swarms.

Proteins populate a manifold in the high-dimensional sequence space whose geometrical structure guides their natural evolution. Leveraging recently-developed structure prediction tools based on transformer models, we first examine the protein sequence landscape as defined by an effective energy that is a proxy of sequence foldability. This landscape shares characteristics with optimization challenges encountered in machine learning and constraint satisfaction problems. Our analysis reveals that natural proteins predominantly reside in wide, flat minima within this energy landscape. To investigate further, we employ statistical mechanics algorithms specifically designed to explore regions with high local entropy in relatively flat landscapes. Our findings indicate that these specialized algorithms can identify valleys with higher entropy compared to those found using traditional methods such as Monte Carlo Markov Chains. In a proof-of-concept case, we find that these highly entropic minima exhibit significant similarities to natural sequences, especially in critical key sites and local entropy. Additionally, evaluations through Molecular Dynamics suggests that the stability of these sequences closely resembles that of natural proteins. Our tool combines advancements in machine learning and statistical physics, providing new insights into the exploration of sequence landscapes where wide, flat minima coexist alongside a majority of narrower minima.

Fungi expand in space and time to form complex multicellular communities. The mechanisms by which they do so can vary dramatically and determine the life-history and dispersal traits of expanding populations. These traits influence deterministic and stochastic components of evolution, resulting in complex eco-evolutionary dynamics during colony expansion. We perform experiments on budding yeast strains genetically engineered to display rough-surface and smooth-surface phenotypes in colony-like structures called 'mats'. Previously, it was shown that the rough-surface strain has a competitive advantage over the smooth-surface strain when grown on semi-solid media. We experimentally observe the emergence and expansion of segments with a distinct smooth-surface phenotype during rough-surface mat development. We propose a trade-off between dispersal and local carrying capacity to explain the relative fitness of these two phenotypes. Using a modified stepping-stone model, we demonstrate that this trade-off gives the high-dispersing, rough-surface phenotype a competitive advantage from standing variation, but that it inhibits this phenotype's ability to invade a resident smooth-surface population via mutation. However, the trade-off improves the ability of the smooth-surface phenotype to invade in rough-surface mats, replicating the frequent emergence of smooth-surface segments in experiments. Together, these computational and experimental findings advance our understanding of the complex eco-evolutionary dynamics of fungal mat expansion.

Neuronal populations in the cerebral cortex engage in probabilistic coding, effectively encoding the state of the surrounding environment with high accuracy and extraordinary energy efficiency. A new approach models the inherently probabilistic nature of cortical neuron signaling outcomes as a thermodynamic process of non-deterministic computation. A mean field approach is used, with the trial Hamiltonian maximizing available free energy and minimizing the net quantity of entropy, compared with a reference Hamiltonian. Thermodynamic quantities are always conserved during the computation; free energy must be expended to produce information, and free energy is released during information compression, as correlations are identified between the encoding system and its surrounding environment. Due to the relationship between the Gibbs free energy equation and the Nernst equation, any increase in free energy is paired with a local decrease in membrane potential. As a result, this process of thermodynamic computation adjusts the likelihood of each neuron firing an action potential. This model shows that non-deterministic signaling outcomes can be achieved by noisy cortical neurons, through an energy-efficient computational process that involves optimally redistributing a Hamiltonian over some time evolution. Calculations demonstrate that the energy efficiency of the human brain is consistent with this model of non-deterministic computation, with net entropy production far too low to retain the assumptions of a classical system.

The tubular network-forming slime mold Physarum polycephalum is able to maintain long-scale contraction patterns driven by an actomyosin cortex. The resulting shuttle streaming in the network is crucial for the organism to respond to external stimuli and reorganize its body mass giving rise to complex behaviors. However, the chemical basis of the self-organized flow pattern is not fully understood. Here, we present ratiometric measurements of free intracellular calcium in simple morphologies of Physarum networks. The spatiotemporal patterns of the free calcium concentration reveal a nearly anti-correlated relation to the tube radius, suggesting that calcium is indeed a key regulator of the actomyosin activity. We compare the experimentally observed phase relation between the radius and the calcium concentration to the predictions of a theoretical model including calcium as an inhibitor. Numerical simulations of the model suggest that calcium indeed inhibits the contractions in Physarum, although a quantitative difference to the experimentally measured phase relation remains. Unraveling the mechanism underlying the contraction patterns is a key step in gaining further insight into the principles of Physarum's complex behavior.

The technique presented here identifies tethered mould designs, optimised for growing cultured tissue with very highly-aligned cells. It is based on a microscopic biophysical model for polarised cellular hydrogels. There is an unmet need for tools to assist mould and scaffold designs for the growth of cultured tissues with bespoke cell organisations, that can be used in applications such as regenerative medicine, drug screening and cultured meat. High-throughput biophysical calculations were made for a wide variety of computer-generated moulds, with cell-matrix interactions and tissue-scale forces simulated using a contractile network dipole orientation model. Elongated moulds with central broadening and one of the following tethering strategies are found to lead to highly-aligned cells: (1) tethers placed within the bilateral protrusions resulting from an indentation on the short edge, to guide alignment (2) tethers placed within a single vertex to shrink the available space for misalignment. As such, proof-of-concept has been shown for mould and tethered scaffold design based on a recently developed biophysical model. The approach is applicable to a broad range of cell types that align in tissues and is extensible for 3D scaffolds.