Immune cells exhibit stimulation-dependent traveling waves in the cortex, much faster than typical cortical actin waves. These waves reflect rhythmic assembly of both actin machinery and peripheral membrane proteins such as F-BAR domain-containing proteins. Combining theory and experiments, we develop a mechanochemical feedback model involving membrane shape changes and F-BAR proteins that render the cortex an interesting dynamical system. We show that such cortical dynamics manifests itself as ultrafast traveling waves of cortical proteins, in which the curvature sensitivity-driven feedback always constrains protein lateral diffusion in wave propagation. The resulting protein wave propagation mainly reflects the spatial gradient in the timing of local protein recruitment from cytoplasm. We provide evidence that membrane undulations accompany these protein waves and potentiate their propagation. Therefore, membrane shape change and protein curvature sensitivity may have underappreciated roles in setting high-speed cortical signal transduction rhythms.

Recent breakthroughs of cell phenotype reprogramming impose theoretical challenges on unravelling the complexity of large circuits maintaining cell phenotypes coupled at many different epigenetic and gene regulation levels, and quantitatively describing the phenotypic transition dynamics. A popular picture proposed by Waddington views cell differentiation as a ball sliding down a landscape with valleys corresponding to different cell types separated by ridges. Based on theories of dynamical systems, we establish a novel ‘epigenetic state network’ framework that captures the global architecture of cell phenotypes, which allows us to translate the metaphorical low-dimensional Waddington epigenetic landscape concept into a simple-yet-predictive rigorous mathematical framework of cell phenotypic transitions. Specifically, we simplify a high-dimensional epigenetic landscape into a collection of discrete states corresponding to stable cell phenotypes connected by optimal transition pathways among them. We then apply the approach to the phenotypic transition processes among fibroblasts (FBs), pluripotent stem cells (PSCs) and cardiomyocytes (CMs). The epigenetic state network for this case predicts three major transition pathways connecting FBs and CMs. One goes by way of PSCs. The other two pathways involve transdifferentiation either indirectly through cardiac progenitor cells or directly from FB to CM. The predicted pathways and multiple intermediate states are supported by existing microarray data and other experiments. Our approach provides a theoretical framework for studying cell phenotypic transitions. Future studies at single-cell levels can directly test the model predictions.

The innate immune system, acting as the first line of host defense, senses and adapts to foreign challenges through complex intracellular and intercellular signaling networks. Endotoxin tolerance and priming elicited by macrophages are classic examples of the complex adaptation of innate immune cells. Upon repetitive exposures to different doses of bacterial endotoxin (lipopolysaccharide) or other stimulants, macrophages show either suppressed or augmented inflammatory responses compared to a single exposure to the stimulant. Endotoxin tolerance and priming are critically involved in both immune homeostasis and the pathogenesis of diverse inflammatory diseases. However, the underlying molecular mechanisms are not well understood. By means of a computational search through the parameter space of a coarse-grained three-node network with a two-stage Metropolis sampling approach, we enumerated all the network topologies that can generate priming or tolerance. We discovered three major mechanisms for priming (pathway synergy, suppressor deactivation, activator induction) and one for tolerance (inhibitor persistence). These results not only explain existing experimental observations, but also reveal intriguing test scenarios for future experimental studies to clarify mechanisms of endotoxin priming and tolerance.

Focal adhesions (FAs) are integrin-based transmembrane assemblies that connect a cell to its extracellular matrix (ECM). They are mechanosensors through which cells exert actin cytoskeleton-mediated traction forces to sense the ECM stiffness. Interestingly, FAs themselves are dynamic structures that adapt their growth in response to mechanical force. It is unclear how the cell manages the plasticity of the FA structure and the associated traction force to accurately sense ECM stiffness. Strikingly, FA traction forces oscillate in time and space, and govern the cell mechanosensing of ECM stiffness. However, precisely how and why the FA traction oscillates is unknown. We developed a model of FA growth that integrates the contributions of the branched actin network and stress fibers (SFs). Using the model in combination with experimental tests, we show that the retrograde flux of the branched actin network promotes the proximal growth of the FA and contributes to a traction peak near the FA’s distal tip. The resulting traction gradient within the growing FA favors SF formation near the FA’s proximal end. The SF-mediated actomyosin contractility further stabilizes the FA and generates a second traction peak near the center of the FA. Formin-mediated SF elongation negatively feeds back with actomyosin contractility, resulting in central traction peak oscillation. This underpins the observed FA traction oscillation and, importantly, broadens the ECM stiffness range over which FAs can accurately adapt to traction force generation. Actin cytoskeleton-mediated FA growth and maturation thus culminate with FA traction oscillation to drive efficient FA mechanosensing.

The bacterial flagellar motor plays a crucial role in both bacterial locomotion and chemotaxis. Recent experiments reveal that the switching dynamics of the motor depend on the rotation speed of the motor, and thus the motor torque, non-monotonically. Here we present a unified mathematical model which treats motor torque generation based on experimental torque-speed curves and the torque-dependent switching based on the conformational spread model. The model successfully reproduces the observed switching rate as a function of the rotation speed, and provides a generic physical explanation independent of most details. A stator affects the switching dynamics through two mechanisms: accelerating the conformational flipping rate of individual rotor-switching units, which contributes most when the stator works at a high torque and thus a low speed; and influencing a larger number of rotor-switching units within unit time, whose contribution is the greatest when the motor rotates at a high speed. Consequently, the switching rate shows a maximum at intermediate speed, where the above two mechanisms find an optimal output. The load-switching relation may serve as a mechanism for sensing the physical environment, similar to the chemotaxis mechanism for sensing the chemical environment. It may also coordinate the switch dynamics of motors within the same cell.

The microtubule assembly process has been extensively studied, but the underlying molecular mechanism remains poorly understood. The structure of an artificially generated sheet polymer that alternates two types of lateral contacts and that directly converts into microtubules, has been proposed to correspond to the intermediate sheet structure observed during microtubule assembly. We have studied the self-assembly process of GMPCPP tubulins into sheet and microtubule structures using thermodynamic analysis and stochastic simulations. With the novel assumptions that tubulins can laterally interact in two different forms, and allosterically affect neighboring lateral interactions, we can explain existing experimental observations. At low temperature, the allosteric effect results in the observed sheet structure with alternating lateral interactions as the thermodynamically most stable form. At normal microtubule assembly temperature, our work indicates that a class of sheet structures resembling those observed at low temperature is transiently trapped as an intermediate during the assembly process. This work may shed light on the tubulin molecular interactions, and the role of sheet formation during microtubule assembly.

The dynamic assembly and disassembly of microtubules and the mechanical properties of these polymers are essential for many key cellular processes. Mathematical and computational modeling, especially coupled mechanochemical modeling, has contributed significantly to our understanding of microtubule dynamics. However, critical discrepancies exist between experimental observations and modeling results that need to be resolved before further progress toward a complete model can be made. Open sheet structures ranging in length from several hundred nanometers to one micron have often been observed at the growing ends of microtubules in in vitro studies. Existing modeling studies predict these sheet structures to be short and rare intermediates of microtubule disassembly rather than important components of the assembly process. Atomic force microscopy (AFM) studies also reveal interesting step-like gaps of the force-indentation curve that cannot yet be explained by existing theoretical models. We have carried out computational studies to compare the mechanical properties of two alternative models: a more conventional model where tubulin dimers are added directly into a microtubule lattice, and one that considers an additional type of tubulin lateral interaction proposed to exist in intermediate sheet structures during the microtubule assembly process. The first model involves a single type of lateral interactions between tubulin subunits, whereas the latter considers a second type that can convert to the canonical lateral contact during microtubule closure into a cylinder. Our analysis shows that only the second model can reproduce the AFM results over a broad parameter range. We propose additional studies using different sizes of AFM tips that would allow to unambiguously distinguish the relative validity of the two models.

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