Anaphase is a key cell cycle transition that ensures faithful genome inheritance. At anaphase onset, sister chromatids separate abruptly and synchronously upon activation of the protease separase. Major cell cycle transitions often involve positive feedback, which contributes to their abruptness and irreversibility; however, whether such feedback is required for anaphase remains unclear. Here, we analyze sister chromatid separation dynamics in fission yeast using high-resolution live-cell imaging and computational modeling. We find that anaphase synchrony relies on fast degradation of the separase inhibitor securin, but does not require separase-mediated positive feedback. Hence, sister chromatid separation, being inherently irreversible, may be one of the few major cell cycle transitions that can proceed without positive feedback. A stochastic model fitted to the data revealed that separation synchrony is limited by stochasticity resulting from small-number effects. Together, these results support a feedback-independent mechanism for anaphase onset and identify molecular noise as a fundamental constraint on its temporal precision.

Many gram-positive bacteria like Bacillus subtilis and Clostridium species, exhibit a growing chain-mediated sliding motility that is driven entirely by the force of cell growth. Particularly, the bacteria maintain cell-cell linkage after cell division and form long chains of many cells. The cells in a chain are continuously pushed outward by the mechanical force of cell growth. As the cell number in a chain grows, the cells toward the tip of the chain accelerate, and can in principle reach very high speeds. Although this seems to suggest a highly efficient motility mechanism, recent modeling work predicted mechanical stress builds up in the growing chain and the resulting chain breakage beyond a critical chain length, which ultimately sets a mechanical limitation in the maximum speed of the chain-mediated sliding. In this work we developed models to show that under different conditions the chain can either form sharp kinks or smooth buckles under the increasing stress. This can explain differential behaviors observed in different bacterial species. Our model further predicted how kinking and buckling affect the susceptibility of the chain to breakage. Our model provides a theoretical framework for predicting the dynamics and efficiency of growing chain-mediated bacterial sliding, and suggest cell properties that can optimize sliding efficiency.

Mechanistic mathematical modeling has become an essential tool in modern biological research due to its powerful ability to integrate diverse data, generate hypotheses, and guide experimental design. It is particularly valuable for studying complex cellular mechanisms involving numerous interacting components. While the full dynamics of such systems usually elude direct experimental observation, modeling provides a means to integrate fragmented data with reasonable and/or informed assumptions into coherent mechanistic frameworks, simulate system behavior, and identify promising directions for further experimentation. When closely integrated with experiments, modeling can greatly accelerate progress in cell biology. However, the value of modeling is not automatic-it must be earned through careful model construction, critical interpretation of results, and thoughtful design of follow-up experiments. To demystify this process, we review three of our collaborative projects in mitosis, drawing on our experiences as a modeler and an experimentalist. We describe how the projects were initiated, why specific modeling approaches were chosen, how models were developed and refined, how model predictions guided new experiments, and how integrated modeling and experimentation led to deeper mechanistic insights. Finally, we emphasize that at the heart of every successful collaboration lies human connection. Productive cross-disciplinary communication is fundamental to bridging experimental and modeling perspectives and fully realizing the potential of integrative approaches in modern cell biology.

Adjusting motility patterns according to environmental cues is important for bacterial survival. Myxococcus xanthus, a bacterium moving on surfaces by gliding and twitching mechanisms, modulates the reversal frequency of its front-back polarity in response to mechanical cues like substrate stiffness and cell-cell contact. In this study, we propose that M. xanthus’s gliding machinery senses environmental mechanical cues during force generation and modulates cell reversal accordingly. To examine our hypothesis, we expand an existing mathematical model for periodic polarity reversal in M. xanthus, incorporating the experimental data on the intracellular dynamics of the gliding machinery and the interaction between the gliding machinery and a key polarity regulator. The model successfully reproduces the dependence of cell reversal frequency on substrate stiffness observed in M. xanthus gliding. We further propose reversal control networks between the gliding and twitching motility machineries to explain the opposite reversal responses observed in wild type M. xanthus cells that possess both motility mechanisms. These results provide testable predictions for future experimental investigations. In conclusion, our model suggests that the gliding machinery in M. xanthus can function as a mechanosensor, which transduces mechanical cues into a cell reversal signal.

During mitosis, equal partitioning of chromosomes into two daughter cells requires assembly of a bipolar mitotic spindle. Because the spindle poles are each organized by a centrosome in animal cells, centrosome defects can lead to monopolar or multipolar spindles. However, the cell can effectively recover the bipolar spindle by separating the centrosomes in monopolar spindles and clustering them in multipolar spindles. To interrogate how a cell can separate and cluster centrosomes as needed to form a bipolar spindle, we developed a biophysical model, based on experimental data, which uses effective potential energies to describe key mechanical forces driving centrosome movements during spindle assembly. Our model identified general biophysical factors crucial for robust bipolarization of spindles that start as monopolar or multipolar. These factors include appropriate force fluctuation between centrosomes, balance between repulsive and attractive forces between centrosomes, exclusion of the centrosomes from the cell center, proper cell size and geometry, and a limited centrosome number. Consistently, we found experimentally that bipolar centrosome clustering is promoted as mitotic cell aspect ratio and volume decrease in tetraploid cancer cells. Our model provides mechanistic explanations for many more experimental phenomena and a useful theoretical framework for future studies of spindle assembly.

2.4. Concluding remarks The bacterial flagellum was historically viewed as an apparatus that enables motility. New research has expanded that view by identifying a role for the flagella in surface sensing and other related phenomena. As discussed, several challenges exist in determining the molecular mechanisms by which flagella trigger the transition from planktonic to surface-associated states. Advances in genetic engineering, microscopy, and mechanical stimulation techniques will be necessary to address some of those challenges.

Why do some biological systems and communities persist while others fail? Robustness, a system's stability, and resilience, the ability to return to a stable state, are key concepts that span multiple disciplines within and outside the biological sciences. Discovering and applying common rules that govern the robustness and resilience of biological systems is a critical step toward creating solutions for species survival in the face of climate change, as well as the for the ever-increasing need for food, health, and energy for human populations. We propose that network theory provides a framework for universal scalable mathematical models to describe robustness and resilience and the relationship between them, and hypothesize that resilience at lower organization levels contribute to robust systems. Insightful models of biological systems can be generated by quantifying the mechanisms of redundancy, diversity, and connectivity of networks, from biochemical processes to ecosystems. These models provide pathways towards understanding how evolvability can both contribute to and result from robustness and resilience under dynamic conditions. We now have an abundance of data from model and non-model systems and the technological and computational advances for studying complex systems. Several conceptual and policy advances will allow the research community to elucidate the rules of robustness and resilience. Conceptually, a common language and data structure that can be applied across levels of biological organization needs to be developed. Policy advances such as cross-disciplinary funding mechanisms, access to affordable computational capacity, and the integration of network theory and computer science within the standard biological science curriculum will provide the needed research environments. This new understanding of biological systems will allow us to derive ever more useful forecasts of biological behaviors and revolutionize the engineering of biological systems that can survive changing environments or disease, navigate the deepest oceans, or sustain life throughout the solar system.

Based on a Jumpstart-Reintegrating Biology Vision Paper, developed during Town Hall meetings funded by The National Science Foundation in 2019-2020. Synopsis Why do some biological systems and communities persist while others fail? Robustness, a system’s stability, and resilience, the ability to return to a stable state, are key concepts that span multiple disciplines within and outside the biological sciences. Discovering and applying common rules that govern the robustness and resilience of biological systems is a critical step toward creating solutions for species survival in the face of climate change, as well as the for the ever-increasing need for food, health, and energy for human populations. We propose that network theory provides a framework for universal scalable mathematical models to describe robustness and resilience and the relationship between them, and hypothesize that resilience at lower organization levels contribute to robust systems. Insightful models of biological systems can be generated by quantifying the mechanisms of redundancy, diversity, and connectivity of networks, from biochemical processes to ecosystems. These models provide pathways towards understanding how evolvability can both contribute to and result from robustness and resilience under dynamic conditions. We now have an abundance of data from model and non-model systems and the technological and computational advances for studying complex systems. Several conceptual and policy advances will allow the research community to elucidate the rules of robustness and resilience. Conceptually, a common language and data structure that can be applied across levels of biological organization needs to be developed. Policy advances such as cross-disciplinary funding mechanisms, access to affordable computational capacity, and the integration of network theory and computer science within the standard biological science curriculum will provide the needed research environments. This new understanding of biological systems will allow us to derive ever more useful forecasts of biological behaviors and revolutionize the engineering of biological systems that can survive changing environments or disease, navigate the deepest oceans, or sustain life throughout the solar system.

Contrasting most known bacterial motility mechanisms, a bacterial sliding motility discovered in at least two gram-positive bacterial families does not depend on designated motors. Instead, the cells maintain end-to-end connections following cell divisions to form long chains and exploit cell growth and division to push the cells forward. To investigate the dynamics of this motility mechanism, we constructed a mechanical model that depicts the interplay of the forces acting on and between the cells comprising the chain. Due to the exponential growth of individual cells, the tips of the chains can, in principle, accelerate to speeds faster than any known single-cell motility mechanism can achieve. However, analysis of the mechanical model shows that the exponential acceleration comes at the cost of an exponential buildup in mechanical stress in the chain, making overly long chains prone to breakage. Additionally, the mechanical model reveals that the dynamics of the chain expansion hinges on a single non-dimensional parameter. Perturbation analysis of the mechanical model further predicts the critical stress leading to chain breakage and its dependence on the non-dimensional parameter. Finally, we developed a simplistic population-expansion model that uses the predicted breaking behavior to estimate the physical limit of chain-mediated population expansion. Predictions from the models provide critical insights into how this motility depends on key physical properties of the cell and the substrate. Overall, our models present a generically applicable theoretical framework for cell-chain-mediated bacterial sliding motility and provide guidance for future experimental studies on such motility.

Circadian rhythms in a wide range of organisms are mediated by molecular mechanisms based on transcription-translation feedback. In this paper, we use bifurcation theory to explore mathematical models of genetic oscillators, based on Kim & Forger's interpretation of the circadian clock in mammals. At the core of their models is a negative feedback loop whereby PER proteins (PER1 and PER2) bind to and inhibit their transcriptional activator, BMAL1. For oscillations to occur, the dissociation constant of the PER:BMAL1 complex, [Formula: see text], must be ≤ 0.04 nM, which is orders of magnitude smaller than a reasonable expectation of 1-10 nM for this protein complex. We relax this constraint by two modifications to Kim & Forger's 'single negative feedback' (SNF) model: first, by introducing a multistep reaction chain for posttranscriptional modifications of Per mRNA and posttranslational phosphorylations of PER, and second, by replacing the first-order rate law for degradation of PER in the nucleus by a Michaelis-Menten rate law. These modifications increase the maximum allowable [Formula: see text] to ~2 nM. In a third modification, we consider an alternative rate law for gene transcription to resolve an unrealistically large rate of Per2 transcription at very low concentrations of BMAL1. Additionally, we studied extensions of the SNF model to include a second negative feedback loop (involving REV-ERB) and a supplementary positive feedback loop (involving ROR). Contrary to Kim & Forger's observations of these extended models, we find that, with our modifications, the supplementary positive feedback loop makes the oscillations more robust than observed in the models with one or two negative feedback loops. However, all three models are similarly robust when accounting for circadian rhythms (~24 h period) with [Formula: see text] ≥ 1 nM. Our results provide testable predictions for future experimental studies.

The mitotic checkpoint (also called spindle assembly checkpoint, SAC) is a signaling pathway that safeguards proper chromosome segregation. Correct functioning of the SAC depends on adequate protein concentrations and appropriate stoichiometries between SAC proteins. Yet very little is known about the regulation of SAC gene expression. Here, we show in the fission yeast Schizosaccharomyces pombe that a combination of short mRNA half-lives and long protein half-lives supports stable SAC protein levels. For the SAC genes mad2+ and mad3+ , their short mRNA half-lives are caused, in part, by a high frequency of nonoptimal codons. In contrast, mad1+ mRNA has a short half-life despite a higher frequency of optimal codons, and despite the lack of known RNA-destabilizing motifs. Hence, different SAC genes employ different strategies of expression. We further show that Mad1 homodimers form co-translationally, which may necessitate a certain codon usage pattern. Taken together, we propose that the codon usage of SAC genes is fine-tuned to ensure proper SAC function. Our work shines light on gene expression features that promote spindle assembly checkpoint function and suggests that synonymous mutations may weaken the checkpoint.

Many bacteria move on solid surfaces using gliding motility, without involvement of flagella or pili. Gliding of Myxococcus xanthus is powered by a proton channel homologous to the stators in the bacterial flagellar motor. Instead of being fixed in place and driving the rotation of a circular protein track like the flagellar basal body, the gliding machinery of M. xanthus travels the length of the cell along helical trajectories, while mechanically engaging with the substrate. Such movement entails a different molecular mechanism to generate propulsion on the cell. In this perspective, we will discuss the similarities and differences between the M. xanthus gliding machinery and bacterial flagellar motor, and use biophysical principles to generate hypotheses about the operating mechanism, efficiency, sensitivity to control, and mechanosensing of M. xanthus gliding.

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.

Sensing and responding to mechanical cues in the environment are important for the survival and propagation of bacteria. A ‘social’ bacterium, Myxococcus xanthus , which exhibits periodic cell reversals, modulates its reversal frequency in response to environmental mechanical cues, such as substrate stiffness and cell-cell contact. In M. xanthus populations, the cell-cell contact-dependent reversal control is particularly important for formation of complex multicellular patterns and structures during the cooperative ‘social’ behaviors. Here we hypothesize that the gliding motility machinery of M. xanthus can sense the environmental mechanical cues during force generation and modulate the timing and frequency of cell reversal through signaling the cell’s reversal control pathway. To examine our hypothesis, we extend an existing mathematical model for periodic polarity switching (which mediates periodic cell reversal) in M. xanthus , and incorporate the experimentally suggested (i) intracellular dynamics of the gliding motors and (ii) interactions between the gliding motors and reversal regulators. The model results suggest the proper mode of interaction between the gliding motors and reversal regulators that can generate the observed increase of cell reversal frequency on stiffer substrates. Furthermore, the selected model predicts a cell reversal response to cell-cell contact, which is sufficient for generating the rippling wave, an important multicellular pattern in M. xanthus populations. Our model highlights a potential role of the gliding machinery of M. xanthus as a ‘mechanosensor’ that transduces mechanical cues into a reversal control signal.### Competing Interest StatementThe authors have declared no competing interest.

Many bacteria species are able to expedite colony expansion through motility of the cells. Clostridium perfringens, the primary cause of lethal gas gangrene, exhibit a unique mode of colony expansion on a substrate surface that, surprisingly, does not depend on motility in single cells. Specifically, daughter cells maintain end-to-end connections after cell division, amounting to long chains of cells that continuously grow as individual cells grow and divide. Such cell growth-driven motility would accelerate as cell divisions increase the number of cells in a chain, and the tip of a long chain can potentially reach a very high speed. To investigate the efficacy of such growth-driven motility, we built a mechanical model to simulate the growth of these bacterial chains based on the interplay between cell growth, strength of connections between cells, and drag forces from the environment. Our model shows that stress at the joints between adjacent cells increases exponentially as the cell chain grows, suggesting that longer chains are likely more prone to breakage. We devised a perturbation theory to estimate the characteristic stress associated with mechanical instabilities in joints between two cells. Based on this characteristic breakage force, we were able to estimate the physical limits of the growth rate of a single cell chain and found it to fall short of the observed behavior of wild C. perfringens. This finding suggests that C. perfringens exploits additional mechanism(s) to delay breakage of the cell chain and thereby achieve a higher expansion rate.

The mammalian circadian clock is deeply rooted in rhythmic regulation of gene expression. Rhythmic transcriptional control mediated by the circadian transcription factors is thought to be the main driver of mammalian circadian gene expression. However, mounting evidence has demonstrated the importance of rhythmic post-transcriptional controls, and it remains unclear how the transcriptional and post-transcriptional mechanisms collectively control rhythmic gene expression. In mouse liver, hundreds of genes were found to exhibit rhythmicity in poly(A) tail length, and the poly(A) rhythms are strongly correlated with the protein expression rhythms. To understand the role of rhythmic poly(A) regulation in circadian gene expression, we constructed a parsimonious model that depicts rhythmic control imposed upon basic mRNA expression and poly(A) regulation processes, including transcription, deadenylation, polyadenylation, and degradation. The model results reveal the rhythmicity in deadenylation as the strongest contributor to the rhythmicity in poly(A) tail length and the rhythmicity in the abundance of the mRNA subpopulation with long poly(A) tails (a rough proxy for mRNA translatability). In line with this finding, the model further shows that the experimentally observed distinct peak phases in the expression of deadenylases, regardless of other rhythmic controls, can robustly cluster the rhythmic mRNAs by their peak phases in poly(A) tail length and abundance of the long-tailed subpopulation. This provides a potential mechanism to synchronize the phases of target gene expression regulated by the same deadenylases. Our findings highlight the critical role of rhythmic deadenylation in regulating poly(A) rhythms and circadian gene expression.

Mitosis proceeds through a defined series of events that is largely conserved, but the amount of time needed for their completion can vary in different cells and organisms. In many systems, mitotic duration depends on the time required to satisfy and silence the spindle assembly checkpoint (SAC), also known as the mitotic checkpoint. Because SAC silencing involves trafficking SAC molecules among kinetochores, spindle, and cytoplasm, the size and geometry of the spindle relative to cell volume are expected to affect mitotic duration by influencing the timing of SAC silencing. However, the relationship between SAC silencing, cell size, and spindle dimensions is unclear. To investigate this issue, we used four DLD-1 tetraploid (4N) clones characterized by small or large nuclear and cell size. We found that the small 4N clones had longer mitotic durations than the parental DLD-1 cells and that this delay was due to differences in their metaphase duration. Leveraging a previous mathematical model for spatiotemporal regulation of SAC silencing, we show that the difference in metaphase duration, i.e., SAC silencing time, can be explained by the distinct spindle microtubule densities and sizes of the cell, spindle, and spindle poles in the 4N clones. Lastly, we demonstrate that manipulating spindle geometry can alter mitotic and metaphase duration, consistent with a model prediction. Our results suggest that spindle size does not always scale with cell size in mammalian cells and cell size is not sufficient to explain the differences in metaphase duration. Only when a number of spindle architectural features are considered along with cell size can the kinetics of SAC silencing, and hence mitotic duration, in the different clones be explained.

Tetraploidy has long been of interest to both cell and cancer biologists, partly because of its documented role in tumorigenesis. A common model proposes that the extra centrosomes that are typically acquired during tetraploidization are responsible for driving tumorigenesis. However, tetraploid cells evolved in culture have been shown to lack extra centrosomes. This observation raises questions about how tetraploid cells evolve and more specifically about the mechanisms(s) underlying centrosome loss. Here, using a combination of fixed cell analysis, live cell imaging, and mathematical modeling, we show that populations of newly formed tetraploid cells rapidly evolve in vitro to retain a near-tetraploid chromosome number while losing the extra centrosomes gained at the time of tetraploidization. This appears to happen through a process of natural selection in which tetraploid cells that inherit a single centrosome during a bipolar division with asymmetric centrosome clustering are favored for long-term survival.