MOLNs: A cloud platform for interactive, reproducible and scalable spatial stochastic computational experiments in systems biology using PyURDME

Computational experiments using spatial stochastic simulations have led to important new biological insights, but they require specialized tools, a complex software stack, as well as large and scalable compute and data analysis resources due to the large computational cost associated with Monte Carlo computational workflows. The complexity of setting up and managing a large-scale distributed computation environment to support productive and reproducible modeling can be prohibitive for practitioners in systems biology. This results in a barrier to the adoption of spatial stochastic simulation tools, effectively limiting the type of biological questions addressed by quantitative modeling. In this paper, we present PyURDME, a new, user-friendly spatial modeling and simulation package, and MOLNs, a cloud computing appliance for distributed simulation of stochastic reaction-diffusion models. MOLNs is based on IPython and provides an interactive programming platform for development of sharable and reproducible distributed parallel computational experiments

Three-dimensional modeling of carbon/epoxy to titanium single-lap joints with variable adhesive recess length

The objective of this paper was to investigate the performance of recessed single-lap joints with dissimilar adherends through the finite element method. The influence of material and geometric nonlinearity of the adhesive as well as the impact of the recess length was examined in terms of maximum principal stresses. The strength of the joint was obtained as the load to initiate the crack propagation. Results suggested that either adding a spew fillet or considering the adhesive plasticity led to reduced peak stresses at the edge of the adhesive layer. The presence of a spew fillet in the single-lap joint with a recess length of 50% of the overlap length reduced the peak stress concentrations in the adhesive layer by 45.2% and subsequently improved the strength of the joint by 36.3%. Mitigation of stress concentration was observed in cases of an adhesive layer with a smaller recess length. The strength of recessed joints with a gap less than 50% of the overlap length decreased slightly. For the recess length as 70% and 90% of the total overlap length, the strength of the joints reduced 36.4% and 66.3%, respectively. This study suggested a recess of less than 50% of the overlap length may be beneficial for the performance of the joints

Combining Biochemical Signaling and Mechanics to Understand Yeast Mating Morphogenesis

How biological systems are able to form and maintain such a wide variety of patterns and structures is one of the central questions in science. In this dissertation we focus on one example of pattern formation and morphogenesis found in yeast cells. Specifically, we present our work related to understanding how yeast cells are able to change their physical structure and form projections during mating. This is an interesting example of a problem that deals with both intracellular protein signaling and cell mechanics. One issue that has become increasingly important to understanding the dynamics of proteins inside of single cells is the inherent randomness or stochasticity of biochemical reactions. As mathematical modeling and computational techniques have become essential tools in systems biology over the last half century, we first mention our software framework for the efficient simulation of spatial stochastic reaction-diffusion problems which can leverage high-performance computing and cloud infrastructure. This work serves as the basis for our investigation into yeast mating morphogenesis. The first step of yeast mating projection growth is the localization (or polarization) of proteins on the cell membrane. This is a well-studied, yet not fully understood, example of pattern formation in biology. In this dissertation we discuss several mathematical models of polarization and their various properties. When a yeast cell forms a mating projection the cell shape naturally changes in time. To deal with this from a mathematical modeling standpoint, we have developed a novel algorithm for the simulation of spatial stochastic dynamics on moving domains. These technical advances have led to new insight into the biology of yeast mating morphogenesis. In particular, we have elucidated the effects that complex geometries can have on current models of polarization. While polarization is certainly necessary for yeast mating morphogenesis, it is not the whole story. Yeast cells have a cell wall that is responsible for defining cell shape and providing mechanical integrity. To further explore mating projection growth, we have developed methods to couple models of polarization with physically based models for the mechanics of the cell wall. This coupling of biochemical signaling and mechanics allows for a more systems level understanding of yeast mating morphogenesis. We conclude by summarizing our findings about the coupling of polarization and mechanics, and discussing which biological links between the two are important from a mathematical modeling perspective

A framework for discrete stochastic simulation on 3D moving boundary domains.

We have developed a method for modeling spatial stochastic biochemical reactions in complex, three-dimensional, and time-dependent domains using the reaction-diffusion master equation formalism. In particular, we look to address the fully coupled problems that arise in systems biology where the shape and mechanical properties of a cell are determined by the state of the biochemistry and vice versa. To validate our method and characterize the error involved, we compare our results for a carefully constructed test problem to those of a microscale implementation. We demonstrate the effectiveness of our method by simulating a model of polarization and shmoo formation during the mating of yeast. The method is generally applicable to problems in systems biology where biochemistry and mechanics are coupled, and spatial stochastic effects are critical

A framework for discrete stochastic simulation on 3D moving boundary domains.

We have developed a method for modeling spatial stochastic biochemical reactions in complex, three-dimensional, and time-dependent domains using the reaction-diffusion master equation formalism. In particular, we look to address the fully coupled problems that arise in systems biology where the shape and mechanical properties of a cell are determined by the state of the biochemistry and vice versa. To validate our method and characterize the error involved, we compare our results for a carefully constructed test problem to those of a microscale implementation. We demonstrate the effectiveness of our method by simulating a model of polarization and shmoo formation during the mating of yeast. The method is generally applicable to problems in systems biology where biochemistry and mechanics are coupled, and spatial stochastic effects are critical

Coordinating cell polarization and morphogenesis through mechanical feedback.

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

Mechanical feedback coordinates cell wall expansion and assembly in yeast mating morphogenesis.

The shaping of individual cells requires a tight coordination of cell mechanics and growth. However, it is unclear how information about the mechanical state of the wall is relayed to the molecular processes building it, thereby enabling the coordination of cell wall expansion and assembly during morphogenesis. Combining theoretical and experimental approaches, we show that a mechanical feedback coordinating cell wall assembly and expansion is essential to sustain mating projection growth in budding yeast (Saccharomyces cerevisiae). Our theoretical results indicate that the mechanical feedback provided by the Cell Wall Integrity pathway, with cell wall stress sensors Wsc1 and Mid2 increasingly activating membrane-localized cell wall synthases Fks1/2 upon faster cell wall expansion, stabilizes mating projection growth without affecting cell shape. Experimental perturbation of the osmotic pressure and cell wall mechanics, as well as compromising the mechanical feedback through genetic deletion of the stress sensors, leads to cellular phenotypes that support the theoretical predictions. Our results indicate that while the existence of mechanical feedback is essential to stabilize mating projection growth, the shape and size of the cell are insensitive to the feedback

Coordinating cell polarization and morphogenesis through mechanical feedback.

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