SUMMARY: The plasma membrane and accompanying cortex serve as major hubs of signal transduction and cytoskeletal activities that collectively regulate cell physiological processes such as migration, polarity, macropinocytosis, phagocytosis, and cytokinesis. Yet, dynamically tracking membrane-cortex associated protein or lipid kinetics from live-cell image series remains challenging, primarily due to the difficulty of accurately extracting and aligning the cell boundary between consecutive frames as the cell continuously deforms and moves. Here, we present Membrane Kymograph Generator, a cross-platform software that accepts multichannel time-lapse live-cell fluorescent imaging datasets and automates boundary tracking, inter-frame alignment, and intensity sampling along the boundary. The software implements a rotational offset minimization algorithm that aligns boundaries across consecutive frames by exhaustively searching for the optimal angular shift that minimizes point-to-point distances, while handling variations in boundary point counts due to cell shape changes. The software outputs kymographs representing spatiotemporal dynamics of membrane-associated proteins or biosensors, allows users to fine-tune visualization parameters through an interactive interface, and provides built-in correlation analysis tools for multi-channel datasets. Furthermore, a native Python API enables programmatic usage for batch processing and further downstream analysis. Validation tests demonstrated that the Membrane Kymograph Generator accurately tracks, visualizes, and quantitates the spatial kinetics of a wide array of membrane proteins and lipid biosensors over extended time periods, in a variety of cell types including Dictyostelium amoeba, human neutrophils, mouse macrophages, and mammalian cancer cells. The GUI-based software is user-friendly, requires no technical expertise, and significantly reduces the manual effort required for kymograph generation and analysis while ensuring high accuracy and reproducibility. AVAILABILITY AND IMPLEMENTATION: Membrane Kymograph Generator is free and open-source, licensed under GNU General Public License 3.0 or later. It can be installed on both x86-64 and AArch64/ARM64 computers running Windows, macOS, or any standard Linux distribution. The software is distributed as standalone installer files and portable executables targeting specific architectures and operating systems, requiring no dependency resolution. The source code, documentation/wiki, installers, portable binaries, and test data are freely available at https://github.com/tatsatb/membrane-kymograph-generator. The software can also be installed via PIP (package ID: membrane-kymograph, https://pypi.org/project/membrane-kymograph) and accessed programmatically via a built-in Python API. The source code is also archived on Zenodo (DOI: 10.5281/zenodo.20318834).

In the social amoeba Dictyostelium, cell motility is regulated through a signal transduction excitable network that interfaces with the cytoskeleton to control actin polymerization patterns. In turn, the cytoskeleton influences the signaling machinery via several feedback loops, but the nature and function of this feedback remain poorly understood. In this study, we use computational models to discern the essential role of complementary positive and negative feedback loops in polarizing cells. We contrast two potential mechanisms for the negative feedback: local inhibition and global inhibition. Our results indicate that both mechanisms can stabilize the leading edge and inhibit actin polymerization in other sites, preventing multipolarity. While some experimental perturbations align more closely with the local inhibition model, statistical analyses reveal its limited polarization potential within a wide excitability range. Conversely, global inhibition more effectively suppresses secondary and tertiary leading-edge formation, making it a more robust polarization mechanism. This raises an intriguing question: if local inhibition better replicates experimental observations but is less effective for polarization than local excitation and global inhibition, could there be a supplementary mechanism enhancing its polarization potential? To address this, we propose a novel mechanism involving the dynamic partitioning of back molecules which enhances communication between the front and back of the cell and can be leveraged by local feedback interactions between the cytoskeleton and signal transduction to improve polarization efficiency.

During the last decade, a consensus has emerged that the stochastic triggering of an excitable system drives pseudopod formation and subsequent migration of amoeboid cells. The presence of chemoattractant stimuli alters the threshold for triggering this activity and can bias the direction of migration. Though noise plays an important role in these behaviors, mathematical models have typically ignored its origin and merely introduced it as an external signal into a series of reaction-diffusion equations. Here we consider a more realistic description based on a reaction-diffusion master equation formalism to implement these networks. In this scheme, noise arises naturally from a stochastic description of the various reaction and diffusion terms. Working on a three-dimensional geometry in which separate compartments are divided into a tetrahedral mesh, we implement a modular description of the system, consisting of G-protein coupled receptor signaling (GPCR), a local excitation-global inhibition mechanism (LEGI), and signal transduction excitable network (STEN). Our models implement detailed biochemical descriptions whenever this information is available, such as in the GPCR and G-protein interactions. In contrast, where the biochemical entities are less certain, such as the LEGI mechanism, we consider various possible schemes and highlight the differences between them. Our simulations show that even when the LEGI mechanism displays perfect adaptation in terms of the mean level of proteins, the variance shows a dose-dependence. This differs between the various models considered, suggesting a possible means for determining experimentally among the various potential networks. Overall, our simulations recreate temporal and spatial patterns observed experimentally in both wild-type and perturbed cells, providing further evidence for the excitable system paradigm. Moreover, because of the overall importance and ubiquity of the modules we consider, including GPCR signaling and adaptation, our results will be of interest beyond the field of directed migration.

Chemotaxis involves the coordinated action of separable but interrelated processes: motility, gradient sensing, and polarization. We have hypothesized that these are mediated by separate modules that account for these processes individually and that, when combined, recreate most of the behaviors of chemotactic cells. Here, we describe a mathematical model where the modules are implemented in terms of reaction-diffusion equations. Migration and the accompanying changes in cellular morphology are demonstrated in simulations using a mechanical model of the cell cortex implemented in the level set framework. The central module is an excitable network that accounts for random migration. The response to combinations of uniform stimuli and gradients is mediated by a local excitation, global inhibition module that biases the direction in which excitability is directed. A polarization module linked to the excitable network through the cytoskeleton allows unstimulated cells to move persistently and, for cells in gradients, to gradually acquire distinct sensitivity between front and back. Finally, by varying the strengths of various feedback loops in the model we obtain cellular behaviors that mirror those of genetically altered cell lines.

Cytokinesis occurs through the coordinated action of several biochemically-mediated stresses acting on the cytoskeleton. Here, we develop a computational model of cellular mechanics, and using a large number of experimentally measured biophysical parameters, we simulate cell division under a number of different scenarios. We demonstrate that traction-mediated protrusive forces or contractile forces due to myosin II are sufficient to initiate furrow ingression. Furthermore, we show that passive forces due to the cell's cortical tension and surface curvature allow the furrow to complete ingression. We compare quantitatively the furrow thinning trajectories obtained from simulation with those observed experimentally in both wild-type and myosin II null Dictyostelium cells. Our simulations highlight the relative contributions of different biomechanical subsystems to cell shape progression during cell division.

The ability for a living organism to sense and respond to its external environment is crucial to its survival. Understanding mechanosensation, the mechanism by which organisms react in response to mechanical stimuli, presents many interesting and challenging problems for both experimental and computational biologists. A major difficulty in studying mechanosensors is their inherent multiscale nature. The systems involved in mechanosesnsing can span eight orders of magnitude in length scale and up to 10 orders of magnitude in time scale. Trying to ascertain information across these length and time scales simultaneously is challenging. This problem has led to the need to approach these types of problems using an integrative approach, combining both computational and experimental biology. This review classifies the major types of mechanosensors and explains methods that have been employed in understanding their behavior, both using modeling and experimental techniques. Multiscale modeling methods combined with experimental techniques in an integrative approach are suggested as ways of undertaking the study of such systems.

Many cellular systems rely on the ability to interpret spatial heterogeneities in chemoattractant concentration to direct cell migration. The accuracy of this process is limited by stochastic fluctuations in the concentration of the external signal and in the internal signaling components. Here we use information theory to determine the optimal scheme to detect the location of an external chemoattractant source in the presence of noise. We compute the minimum amount of mutual information needed between the chemoattractant gradient and the internal signal to achieve a prespecified chemotactic accuracy. We show that more accurate chemotaxis requires greater mutual information. We also demonstrate that a priori information can improve chemotaxis efficiency. We compare the optimal signaling schemes with existing experimental measurements and models of eukaryotic gradient sensing. Remarkably, there is good quantitative agreement between the optimal response when no a priori assumption is made about the location of the existing source, and the observed experimental response of unpolarized Dictyostelium discoideum cells. In contrast, the measured response of polarized D. discoideum cells matches closely the optimal scheme, assuming prior knowledge of the external gradient-for example, through prolonged chemotaxis in a given direction. Our results demonstrate that different observed classes of responses in cells (polarized and unpolarized) are optimal under varying information assumptions.

Information-carrying signals in the real world are often obscured by noise. A challenge for any system is to filter the signal from the corrupting noise. This task is particularly acute for the signal transduction network that mediates bacterial chemotaxis, because the signals are subtle, the noise arising from stochastic fluctuations is substantial, and the system is effectively acting as a differentiator which amplifies noise. Here, we investigated the filtering properties of this biological system. Through simulation, we first show that the cutoff frequency has a dramatic effect on the chemotactic efficiency of the cell. Then, using a mathematical model to describe the signal, noise, and system, we formulated and solved an optimal filtering problem to determine the cutoff frequency that bests separates the low-frequency signal from the high-frequency noise. There was good agreement between the theory, simulations, and published experimental data. Finally, we propose that an elegant implementation of the optimal filter in combination with a differentiator can be achieved via an integral control system. This paper furnishes a simple quantitative framework for interpreting many of the key notions about bacterial chemotaxis, and, more generally, it highlights the constraints on biological systems imposed by noise.

BACKGROUND: Robustness of mathematical models of biochemical networks is important for validation purposes and can be used as a means of selecting between different competing models. Tools for quantifying parametric robustness are needed. RESULTS: Two techniques for describing quantitatively the robustness of an oscillatory model were presented and contrasted. Single-parameter bifurcation analysis was used to evaluate the stability robustness of the limit cycle oscillation as well as the frequency and amplitude of oscillations. A tool from control engineering--the structural singular value (SSV)--was used to quantify robust stability of the limit cycle. Using SSV analysis, we find very poor robustness when the model's parameters are allowed to vary. CONCLUSION: The results show the usefulness of incorporating SSV analysis to single parameter sensitivity analysis to quantify robustness.