Balanced biosynthesis is the hallmark of bacterial cell physiology, where the concentrations of stable proteins remain steady. However, this poses a conceptual challenge to modeling the cell-cycle and cell-size controls in bacteria, as prevailing concentration-based eukaryote models are not directly applicable. In this study, we revisit and significantly extend the initiator-titration model, proposed 30 years ago, and we explain how bacteria precisely and robustly control replication initiation based on the mechanism of protein copy-number sensing. Using a mean-field approach, we first derive an analytical expression of the cell size at initiation based on three biological mechanistic control parameters for an extended initiator-titration model. We also study the stability of our model analytically and show that initiation can become unstable in multifork replication conditions. Using simulations, we further show that the presence of the conversion between active and inactive initiator protein forms significantly represses initiation instability. Importantly, the two-step Poisson process set by the initiator titration step results in significantly improved initiation synchrony with $CV\sim 1/N$ scaling rather than the standard $1/\sqrt{N}$ scaling in the Poisson process, where $N$ is the total number of initiators required for initiation. Our results answer two long-standing questions in replication initiation: (i) Why do bacteria produce almost two orders of magnitude more DnaA, the master initiator proteins, than required for initiation? (ii) Why does DnaA exist in active (DnaA-ATP) and inactive (DnaA-ADP) forms if only the active form is competent for initiation? The mechanism presented in this work provides a satisfying general solution to how the cell can achieve precision control without sensing protein concentrations, with broad implications from evolution to the design of synthetic cells.

Pathogens drive changes in host immune systems that in turn exert pressure for pathogens to evolve. Quantifying and understanding this constant coevolutionary process has clear practical global health implications. Yet its relatively easier accessibility compared to macroevolution makes it a fascinating system to learn about the basic laws of evolution. Focusing on immune-viral evolution, we present an overview of theoretical and experimental approaches that have recently started coming together to build the foundations for a quantitative and predictive coevolutionary theory.

Contact probabilities between loci, separated by arbitrary genomic distance, for a number of cell types have been reported using genome-wide chromosome conformation capture (Hi-C) experiments. How to extract the effective interaction energies between active euchromatin (A) and inactive heterochromatin (B) directly from the experimental data, without an underlying polymer model, is unsolved. Here, we first calculate the pairwise effective interaction energies (A-A, B-B, or A-B) for interphase chromosomes based on Hi-C data by using the concept of statistical potential (SP), which assumes that the interaction energy between two loci is proportional to the logarithm of the frequency with which they interact. Polymer simulations, using the extracted interaction energy values without any parameters, reproduce the segregation between A and B type loci (compartments), and the emergence of topologically associating domains, features that are prominent in the Hi-C data for interphase chromosomes. Remarkably, the values of the SP automatically satisfy the Flory-Huggins phase separation criterion for all the chromosomes, which explains the mechanism of compartment formation in interphase chromosomes. Strikingly, simulations using the SP that accounts for pericentromeric constitutive heterochromatin (C-type) show hierarchical structuring with the high density of C-type loci in the nuclear center, followed by localization of the B-type loci, with euchromatin being confined to the nuclear periphery, which differs from the expected nuclear organization of conventional interphase chromosomes, but is in accord with imaging data. Such an unusual organization of chromosomes is found in the inverted nuclei of photoreceptor rods in nocturnal mammals. The proposed method without free parameters and its applications show that compartment formation in conventional and inverted nuclei is best explained by the inequality between the effective interaction energies, with heterochromatin attraction being the dominant driving force.

The dynamics of cellular pattern formation is crucial for understanding embryonic development and tissue morphogenesis. Recent studies have shown that human dermal fibroblasts cultured on liquid crystal elastomers can exhibit an increase in orientational alignment over time, accompanied by cell proliferation, under the influence of the weak guidance of a molecularly aligned substrate. However, a comprehensive understanding of how this order arises remains largely unknown. This knowledge gap may be attributed, in part, to a scarcity of mechanistic models that can capture the temporal progression of the complex nonequilibrium dynamics during the cellular alignment process. The orientational alignment occurs primarily when cells reach a high density near confluence. Therefore, for accurate modeling, it is crucial to take into account both the cell-cell interaction term and the influence from the substrate, acting as a one-body external potential term. To fill in this gap, we develop a hybrid procedure that utilizes statistical learning approaches to extend the state-of-the-art physics models for quantifying both effects. We develop a more efficient way to perform feature selection that avoids testing all feature combinations through simulation. The maximum likelihood estimator of the model was derived and implemented in computationally scalable algorithms for model calibration and simulation. By including these features, such as the non-Gaussian, anisotropic fluctuations, and limiting alignment interaction only to neighboring cells with the same velocity direction, this model quantitatively reproduce the key system-level parameters—the temporal progression of the velocity orientational order parameters and the variability of velocity vectors—whereas models missing any of the features fail to capture these temporally dependent parameters. The computational tools we develop for automating model construction and calibration can be applied to other systems of active matter.

An established normative approach for understanding the algorithmic basis of neural computation is to derive online algorithms from principled computational objectives and evaluate their compatibility with anatomical and physiological observations. Similarity matching objectives have served as successful starting points for deriving online algorithms that map onto neural networks (NNs) with point neurons and Hebbian/anti-Hebbian plasticity. These NN models account for many anatomical and physiological observations; however, the objectives have limited computational power, and the derived NNs do not explain multicompartmental neuronal structures and non-Hebbian forms of plasticity that are prevalent throughout the brain. In this article, we unify and generalize recent extensions of the similarity matching approach to address more complex objectives, including a large class of unsupervised and self-supervised learning tasks that can be formulated as symmetric generalized eigenvalue problems or non-negative matrix factorization problems. Interestingly, the online algorithms derived from these objectives naturally map onto NNs with multicompartmental neurons and local, non-Hebbian learning rules. Therefore, this unified extension of the similarity matching approach provides a normative framework that facilitates understanding multicompartmental neuronal structures and non-Hebbian plasticity found throughout the brain.

Initiating replication synchronously at multiple origins of replication allows the bacterium Escherichia coli to divide even faster than the time it takes to replicate the entire chromosome in nutrient-rich environments. What mechanisms give rise to synchronous replication initiation remain, however, poorly understood. Via mathematical modeling, we identify four distinct synchronization regimes depending on two quantities: the duration of the so-called licensing period during which the initiation potential in the cell remains high after the first origin has fired and the duration of the blocking period during which already initiated origins remain blocked. For synchronous replication initiation, the licensing period must be long enough such that all origins can be initiated, but shorter than the blocking period to prevent reinitiation of origins that have already fired. Our model reveals that the delay between the firing of the first and the last origin scales with the coefficient of variation (CV) of the initiation volume. Matching these to the values measured experimentally shows that the firing rate must rise with the cell volume with an effective Hill coefficient that is at least 20; the probability that all origins fire before the blocking period is over is then at least 92%. Our analysis thus predicts that the low CV of the initiation volume is a consequence of synchronous replication initiation. Finally, we show that the previously presented molecular model for the regulation of replication initiation in E. coli can give rise to synchronous replication initiation for biologically realistic parameters.

Biological condensates are assemblies of proteins and nucleic acids that form membraneless compartments in cells and play essential roles in cellular functions. In many cases they exhibit the physical properties of liquid droplets that coexist in a surrounding fluid. Recently, quantitative studies on the material properties of biological condensates have become available, revealing complex material properties. In vitro experiments have shown that protein condensates exhibit time dependent material properties, similar to aging in glasses. To understand this phenomenon from a theoretical perspective, we develop a rheological model based on the physical picture of protein diffusion and stochastic binding inside condensates. The complex nature of protein interactions is captured by a distribution of binding energies, incorporated in a trap model originally developed to study glass transitions. Our model can describe diffusion of constituent particles, as well as the material response to time-dependent forces, and it recapitulates the age dependent relaxation time of Maxwell glass observed experimentally both in active and passive rheology. We derive fluctuation-response relations of our model in which the relaxation function does not obey time translation invariance. Our study sheds light on the complex material properties of biological condensates and provides a theoretical framework for understanding their aging behavior.

To better understand the conditions prevailing when acquiring complex, compositional memories, we introduce, in a previously studied Potts model of long-range cortical interactions, a differentiation between a frontal and a posterior subnetwork. “Frontal” units, representing patches of anterior cortex, are endowed with a higher number $S$ of local attractor states, in keeping with the larger number of local synaptic contacts of neurons there, than in some posterior, e.g., occipital, cortices. A thermodynamic analysis and computer simulations confirm that disorder leads to glassy properties and slow dynamics but, surprisingly, the frontal network, which would be slower if isolated, becomes faster than the posterior network when interacting with it. From an abstract, drastically simplified model we take some steps towards approaching a neurally plausible one, and find that the speed inversion effect is basically preserved. We argue that this effect may facilitate learning, through the acquisition of new dynamical attractors.

Rapid epithelial tissue flows are essential to building and shaping developing embryos. However, the mechanical properties of embryonic epithelial tissues and the factors that control these properties are not well understood. Actomyosin generates contractile tensions and contributes to the mechanical properties of cells and cytoskeletal networks in vitro, but it remains unclear how the levels and patterns of actomyosin activity contribute to embryonic epithelial tissue mechanics in vivo. To dissect the roles of cell-generated tensions in the mechanics of flowing epithelial tissues, we use optogenetic tools to manipulate actomyosin contractility with spatiotemporal precision in the Drosophila germband epithelium, which rapidly flows during body axis elongation. We find that manipulating actomyosin-dependent tensions by either optogenetic activation or deactivation of actomyosin alters the solid-fluid mechanical properties of the germband epithelium, leading to changes in cell rearrangements and tissue-level flows. Optogenetically activating actomyosin leads to increases in the overall level but decreases in the anisotropy of tension in the tissue, whereas optogenetically deactivating actomyosin leads to decreases in both the level and anisotropy of tension compared to in wild-type embryos. We find that optogenetically activating actomyosin results in more solidlike (less fluidlike) tissue properties, which is associated with reduced cell rearrangements and tissue flow compared to in wild-type embryos. Optogenetically deactivating actomyosin also results in more solidlike properties than in wild-type embryos but less solidlike properties compared to optogenetically activating actomyosin. Together, these findings indicate that increasing the overall tension level is associated with more solidlike properties in tissues that are relatively isotropic, whereas high-tension anisotropy fluidizes the tissue. Our results reveal that epithelial tissue flows in developing embryos involve the coordinated actomyosin-dependent regulation of the mechanical properties of tissues and the tensions driving them to flow in order to achieve rapid tissue remodeling.

Sperm swimming is crucial to fertilize the egg, in nature and in assisted reproductive technologies. Modeling the sperm dynamics involves elasticity, hydrodynamics, internal active forces, and out-of-equilibrium noise. Here we give experimental evidence in favor of the relevance of energy dissipation for sperm beating fluctuations. For each motile cell, we reconstruct the time evolution of the two main tail's spatial modes, which together trace a noisy limit cycle characterized by a maximum level of precision $p_{\text{max}}$. Our results indicate $p_{\text{max}}\sim {10}^2{\text{s}}^{-1}$, remarkably close to the estimated precision of a dynein molecular motor actuating the flagellum, which is bounded by its energy dissipation rate according to the thermodynamic uncertainty relation. Further experiments under oxygen deprivation show that $p_{\text{max}}$ decays with energy consumption, as it occurs for a single molecular motor. Both observations are explained by conjecturing a high level of coordination among the conformational changes of dynein motors. This conjecture is supported by a theoretical model for the beating of an ideal flagellum actuated by a collection of motors, including a motor-motor nearest-neighbor coupling of strength $K$: When $K$ is small the precision of a large flagellum is much higher than the single motor one. On the contrary, when $K$ is large the two become comparable. Based upon our strong-motor-coupling conjecture, old and new data coming from different kinds of flagella can be collapsed together on a simple master curve.

Flagellates are key components of aquatic microbial food webs. Their flagella propel the cell through the water and/or generate a feeding current from which bacterial prey is harvested, but the activity of the flagella also disturbs the ambient water, thereby attracting the flagellate's flow-sensing predators. Here we use computational fluid dynamics to explore the optimality and fluid dynamics of the diverse arrangements, beat patterns, and external morphologies of flagella found among free-living flagellates in light of the fundamental propulsion–foraging–predation-risk trade-off. We examine 5-$\mu \mathrm{m}$-sized representative model organisms with different resource acquisition modes: autotrophs relying on photosynthesis and uptake of nutrient molecules, phagotrophs that feed on bacteria, and mixotrophs that employ both strategies. For all types, the transport of inorganic molecules is diffusion dominated, and the flagellum in autotrophic species therefore mainly serves propulsion purposes. Flagellates with a single, naked flagellum found among nonforaging swarmer stages have a waveform (less than one wave) that is optimized for swimming and stealth but inefficient for feeding. Flagellates with a hairy flagellum typically have many waves, which optimizes swimming and stealth but is suboptimal for foraging, leading to a design trade-off. However, when compared with naked flagella, the presence of hairs allows a very efficient feeding current, making these primarily phagotrophic flagellates the most efficient and dominant bacterivores in the ocean. Autotrophic biflagellates have wave patterns optimized for both propulsion and foraging but conflicting weakly with stealth. Finally, the mixotrophic haptophytes are optimized for foraging, conflicting with both stealth and propulsion. This is largely due to the long, slender filament (haptonema) that improves prey collection but at the cost of stealth and propulsion. We use dimensional analysis to rationalize our findings. We conclude that phagotrophic flagellates must trade off stealth and propulsion for foraging efficiency, while in autotrophic flagellates stealth is traded off for propulsion and foraging efficiency.

Living tissues are characterized by an intrinsically mechanochemical interplay of active physical forces and complex biochemical signaling pathways. Either feature alone can give rise to complex emergent phenomena, for example, mechanically driven glassy dynamics and rigidity transitions, or chemically driven reaction-diffusion instabilities. An important question is how to quantitatively assess the contribution of these different cues to the large-scale dynamics of biological materials. We address this in Madin-Darby canine kidney (MDCK) monolayers, considering both mechanochemical feedback between extracellular signal-regulated kinase (ERK) signaling activity and cellular density as well as a mechanically active tissue rheology via a self-propelled vertex model. We show that the relative strength of active migration forces to mechanochemical couplings controls a transition from a uniform active glass to periodic spatiotemporal waves. We parametrize the model from published experimental data sets on MDCK monolayers and use it to make new predictions on the correlation functions of cellular dynamics and the dynamics of topological defects associated with the oscillatory phase of cells. Interestingly, MDCK monolayers are best described by an intermediary parameter region in which both mechanochemical couplings and noisy active propulsion have a strong influence on the dynamics. Finally, we study how tissue rheology and ERK waves produce feedback on one another and uncover a mechanism via which tissue fluidity can be controlled by mechanochemical waves at both the local and global levels.