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Biology is suffused with rhythmic behaviour, and interacting biological oscillators often synchronize their rhythms with one another. Colonies of some ant species are able to synchronize their activity to fall into coherent bursts, but models of this phenomenon have neglected the potential effects of intrinsic noise and interspecific differences in individual-level behaviour. We investigated the individual and collective activity patterns of two Leptothorax ant species. We show that in one species (Leptothorax sp. W), ants converge onto rhythmic cycles of synchronized collective activity with a period of about 20 min. A second species (Leptothorax crassipilis) exhibits more complex collective dynamics, where dominant collective cycle periods range from 16 min to 2.8 h. Recordings that last 35 h reveal that, in both species, the same colony can exhibit multiple oscillation frequencies. We observe that workers of both species can be stimulated by nest-mates to become active after a refractory resting period, but the durations of refractory periods differ between the species and can be highly variable. We model the emergence of synchronized rhythms using an agent-based model informed by our empirical data. This simple model successfully generates synchronized group oscillations despite the addition of noise to ants' refractory periods. We also find that adding noise reduces the likelihood that the model will spontaneously switch between distinct collective cycle frequencies.

Focal polarization is necessary for finely arranged cell-cell interactions. The yeast mating projection, with its punctate polarisome, is a good model system for this process. We explored the critical role of the polarisome scaffold protein Spa2 during yeast mating with a hypothesis motivated by mathematical modeling and tested by in vivo experiments. Our simulations predicted that two positive feedback loops generate focal polarization, including a novel feedback pathway involving the N-terminal domain of Spa2. We characterized the latter using loss-of-function and gain-of-function mutants. The N-terminal region contains a Spa2 Homology Domain (SHD) which is conserved from yeast to humans, and when mutated largely reproduced the spa2Δ phenotype. Our work together with published data show that the SHD domain recruits Msb3/4 that stimulates Sec4-mediated transport of Bud6 to the polarisome. There, Bud6 activates Bni1-catalyzed actin cable formation, recruiting more Spa2 and completing the positive feedback loop. We demonstrate that disrupting this loop at any point results in morphological defects. Gain-of-function perturbations partially restored focal polarization in a spa2 loss-of-function mutant without restoring localization of upstream components, thus supporting the pathway order. Thus, we have collected data consistent with a novel positive feedback loop that contributes to focal polarization during pheromone-induced polarization in yeast.

Many cellular processes require cell polarization to be maintained as the cell changes shape, grows or moves. Without feedback mechanisms relaying information about cell shape to the polarity molecular machinery, the coordination between cell polarization and morphogenesis, movement or growth would not be possible. Here we theoretically and computationally study the role of a genetically-encoded mechanical feedback (in the Cell Wall Integrity pathway) as a potential coordination mechanism between cell morphogenesis and polarity during budding yeast mating projection growth. We developed a coarse-grained continuum description of the coupled dynamics of cell polarization and morphogenesis as well as 3D stochastic simulations of the molecular polarization machinery in the evolving cell shape. Both theoretical approaches show that in the absence of mechanical feedback (or in the presence of weak feedback), cell polarity cannot be maintained at the projection tip during growth, with the polarization cap wandering off the projection tip, arresting morphogenesis. In contrast, for mechanical feedback strengths above a threshold, cells can robustly maintain cell polarization at the tip and simultaneously sustain mating projection growth. These results indicate that the mechanical feedback encoded in the Cell Wall Integrity pathway can provide important positional information to the molecular machinery in the cell, thereby enabling the coordination of cell polarization and morphogenesis.

We present the validation of the hybrid sSSA-SDPD method for advection-diffusion-reaction problems coupled to discrete biochemical systems, as presented in the publication “A hybrid smoothed dissipative particle dynamics (SDPD) spatial stochastic simulation algorithm (sSSA) for advection-diffusion-reaction problems” (Drawert et al., 2019). We validate 1D diffusion, and 2D diffusion cases against their analytical solutions. We present graphs and tables of data showing the error in the simulation method.

The localization (or polarization) of proteins on the membrane during the mating of budding yeast (Saccharomyces cerevisiae) is an important model system for understanding simple pattern formation within cells. While there are many existing mathematical models of polarization, for both budding and mating, there are still many aspects of this process that are not well understood. In this paper we set out to elucidate the effect that the geometry of the cell can have on the dynamics of certain models of polarization. Specifically, we look at several spatial stochastic models of Cdc42 polarization that have been adapted from published models, on a variety of tip-shaped geometries, to replicate the shape change that occurs during the growth of the mating projection. We show here that there is a complex interplay between the dynamics of polarization and the shape of the cell. Our results show that while models of polarization can generate a stable polarization cap, its localization at the tip of mating projections is unstable, with the polarization cap drifting away from the tip of the projection in a geometry dependent manner. We also compare predictions from our computational results to experiments that observe cells with projections of varying lengths, and track the stability of the polarization cap. Lastly, we examine one model of actin polarization and show that it is unlikely, at least for the models studied here, that actin dynamics and vesicle traffic are able to overcome this effect of geometry.

We present StochSS: Stochastic Simulation as a Service, an integrated development environment for modeling and simulation of both deterministic and discrete stochastic biochemical systems in up to three dimensions. An easy to use graphical user interface enables researchers to quickly develop and simulate a biological model on a desktop or laptop, which can then be expanded to incorporate increasing levels of complexity. StochSS features state-of-the-art simulation engines. As the demand for computational power increases, StochSS can seamlessly scale computing resources in the cloud. In addition, StochSS can be deployed as a multi-user software environment where collaborators share computational resources and exchange models via a public model repository. We demonstrate the capabilities and ease of use of StochSS with an example of model development and simulation at increasing levels of complexity.

We seek to elucidate the role of macromolecular crowding in transcription and translation. It is well known that stochasticity in gene expression can lead to differential gene expression and heterogeneity in a cell population. Recent experimental observations by Tan et al. have improved our understanding of the functional role of macromolecular crowding. It can be inferred from their observations that macromolecular crowding can lead to robustness in gene expression, resulting in a more homogeneous cell population. We introduce a spatial stochastic model to provide insight into this process. Our results show that macromolecular crowding reduces noise (as measured by the kurtosis of the mRNA distribution) in a cell population by limiting the diffusion of transcription factors (i.e. removing the unstable intermediate states), and that crowding by large molecules reduces noise more efficiently than crowding by small molecules. Finally, our simulation results provide evidence that the local variation in chromatin density as well as the total volume exclusion of the chromatin in the nucleus can induce a homogenous cell population.

Although cell polarity is an essential feature of living cells, it is far from being well-understood. Using a combination of computational modeling and biological experiments we closely examine an important prototype of cell polarity: the pheromone-induced formation of the yeast polarisome. Focusing on the role of noise and spatial heterogeneity, we develop and investigate two mechanistic spatial models of polarisome formation, one deterministic and the other stochastic, and compare the contrasting predictions of these two models against experimental phenotypes of wild-type and mutant cells. We find that the stochastic model can more robustly reproduce two fundamental characteristics observed in wild-type cells: a highly polarized phenotype via a mechanism that we refer to as spatial stochastic amplification, and the ability of the polarisome to track a moving pheromone input. Moreover, we find that only the stochastic model can simultaneously reproduce these characteristics of the wild-type phenotype and the multi-polarisome phenotype of a deletion mutant of the scaffolding protein Spa2. Significantly, our analysis also demonstrates that higher levels of stochastic noise results in increased robustness of polarization to parameter variation. Furthermore, our work suggests a novel role for a polarisome protein in the stabilization of actin cables. These findings elucidate the intricate role of spatial stochastic effects in cell polarity, giving support to a cellular model where noise and spatial heterogeneity combine to achieve robust biological function.

We have developed a new algorithm which merges discrete stochastic simulation, using the spatial stochastic simulation algorithm (sSSA), with the particle based fluid dynamics simulation framework of smoothed dissipative particle dynamics (SDPD). This hybrid algorithm enables discrete stochastic simulation of spatially resolved chemically reacting systems on a mesh-free dynamic domain with a Lagrangian frame of reference. SDPD combines two popular mesoscopic techniques: smoothed particle hydrodynamics and dissipative particle dynamics (DPD), linking the macroscopic and mesoscopic hydrodynamics effects of these two methods. We have implemented discrete stochastic simulation using the reaction-diffusion master equations (RDME) formalism, and deterministic reaction-diffusion equations based on the SDPD method. We validate the new method by comparing our results to four canonical models, and demonstrate the versatility of our method by simulating a flow containing a chemical gradient past a yeast cell in a microfluidics chamber.