Computational Model Explains High Activity and Rapid Cycling of Rho GTPases within Protein Complexes

Formation of multiprotein complexes on cellular membranes is critically dependent on the cyclic activation of small GTPases. FRAP-based analyses demonstrate that within protein complexes, some small GTPases cycle nearly three orders of magnitude faster than they would spontaneously cycle in vitro. At the same time, experiments report concomitant excess of the activated, GTP-bound form of GTPases over their inactive form. Intuitively, high activity and rapid turnover are contradictory requirements. How the cells manage to maximize both remains poorly understood. Here, using GTPases of the Rab and Rho families as a prototype, we introduce a computational model of the GTPase cycle. We quantitatively investigate several plausible layouts of the cycling control module that consist of GEFs, GAPs, and GTPase effectors. We explain the existing experimental data and predict how the cycling of GTPases is controlled by the regulatory proteins in vivo. Our model explains distinct and separable roles that the activating GEFs and deactivating GAPs play in the GTPase cycling control. While the activity of GTPase is mainly defined by GEF, the turnover rate is a sole function of GAP. Maximization of the GTPase activity and turnover rate places conflicting requirements on the concentration of GAP. Therefore, to achieve a high activity and turnover rate at once, cells must carefully maintain concentrations of GEFs and GAPs within the optimal range. The values of these optimal concentrations indicate that efficient cycling can be achieved only within dense protein complexes typically assembled on the membrane surfaces. We show that the concentration requirement for GEF can be dramatically reduced by a GEF-activating GTPase effector that can also significantly boost the cycling efficiency. Interestingly, we find that the cycling regimes are only weakly dependent on the concentration of GTPase itself

Modelling Cell Polarization Driven by Synthetic Spatially Graded Rac Activation

The small GTPase Rac is known to be an important regulator of cell polarization, cytoskeletal reorganization, and motility of mammalian cells. In recent microfluidic experiments, HeLa cells endowed with appropriate constructs were subjected to gradients of the small molecule rapamycin leading to synthetic membrane recruitment of a Rac activator and direct graded activation of membrane-associated Rac. Rac activation could thus be triggered independent of upstream signaling mechanisms otherwise responsible for transducing activating gradient signals. The response of the cells to such stimulation depended on exceeding a threshold of activated Rac. Here we develop a minimal reaction-diffusion model for the GTPase network alone and for GTPase-phosphoinositide crosstalk that is consistent with experimental observations for the polarization of the cells. The modeling suggests that mutual inhibition is a more likely mode of cell polarization than positive feedback of Rac onto its own activation. We use a new analytical tool, Local Perturbation Analysis, to approximate the partial differential equations by ordinary differential equations for local and global variables. This method helps to analyze the parameter space and behaviour of the proposed models. The models and experiments suggest that (1) spatially uniform stimulation serves to sensitize a cell to applied gradients. (2) Feedback between phosphoinositides and Rho GTPases sensitizes a cell. (3) Cell lengthening/flattening accompanying polarization can increase the sensitivity of a cell and stabilize an otherwise unstable polarization

Paradoxical signaling regulates structural plasticity in dendritic spines

Transient spine enlargement (3-5 min timescale) is an important event associated with the structural plasticity of dendritic spines. Many of the molecular mechanisms associated with transient spine enlargement have been identified experimentally. Here, we use a systems biology approach to construct a mathematical model of biochemical signaling and actin-mediated transient spine expansion in response to calcium-influx due to NMDA receptor activation. We have identified that a key feature of this signaling network is the paradoxical signaling loop. Paradoxical components act bifunctionally in signaling networks and their role is to control both the activation and inhibition of a desired response function (protein activity or spine volume). Using ordinary differential equation (ODE)-based modeling, we show that the dynamics of different regulators of transient spine expansion including CaMKII, RhoA, and Cdc42 and the spine volume can be described using paradoxical signaling loops. Our model is able to capture the experimentally observed dynamics of transient spine volume. Furthermore, we show that actin remodeling events provide a robustness to spine volume dynamics. We also generate experimentally testable predictions about the role of different components and parameters of the network on spine dynamics

Protein Pattern Formation

Protein pattern formation is essential for the spatial organization of many intracellular processes like cell division, flagellum positioning, and chemotaxis. A prominent example of intracellular patterns are the oscillatory pole-to-pole oscillations of Min proteins in \textit{E. coli} whose biological function is to ensure precise cell division. Cell polarization, a prerequisite for processes such as stem cell differentiation and cell polarity in yeast, is also mediated by a diffusion-reaction process. More generally, these functional modules of cells serve as model systems for self-organization, one of the core principles of life. Under which conditions spatio-temporal patterns emerge, and how these patterns are regulated by biochemical and geometrical factors are major aspects of current research. Here we review recent theoretical and experimental advances in the field of intracellular pattern formation, focusing on general design principles and fundamental physical mechanisms.Comment: 17 pages, 14 figures, review articl

RhoA GTPase inhibition organizes contraction during epithelial morphogenesis

During morphogenesis, contraction of the actomyosin cytoskeleton within individual cells drives cell shape changes that fold tissues. Coordination of cytoskeletal contractility is mediated by regulating RhoA GTPase activity. Guanine nucleotide exchange factors (GEFs) activate and GTPase-activating proteins (GAPs) inhibit RhoA activity. Most studies of tissue folding, including apical constriction, have focused on how RhoA is activated by GEFs to promote cell contractility, with little investigation as to how GAPs may be important. Here, we identify a critical role for a RhoA GAP, Cumberland GAP (C-GAP), which coordinates with a RhoA GEF, RhoGEF2, to organize spatiotemporal contractility during Drosophila melanogaster apical constriction. C-GAP spatially restricts RhoA pathway activity to a central position in the apical cortex. RhoGEF2 pulses precede myosin, and C-GAP is required for pulsation, suggesting that contractile pulses result from RhoA activity cycling. Finally, C-GAP expression level influences the transition from reversible to irreversible cell shape change, which defines the onset of tissue shape change. Our data demonstrate that RhoA activity cycling and modulating the ratio of RhoGEF2 to C-GAP are required for tissue folding.American Cancer Society (125792-RSG-14-039-01-CSM

Flux Analysis in Process Models via Causality

We present an approach for flux analysis in process algebra models of biological systems. We perceive flux as the flow of resources in stochastic simulations. We resort to an established correspondence between event structures, a broadly recognised model of concurrency, and state transitions of process models, seen as Petri nets. We show that we can this way extract the causal resource dependencies in simulations between individual state transitions as partial orders of events. We propose transformations on the partial orders that provide means for further analysis, and introduce a software tool, which implements these ideas. By means of an example of a published model of the Rho GTP-binding proteins, we argue that this approach can provide the substitute for flux analysis techniques on ordinary differential equation models within the stochastic setting of process algebras

THE ROLE OF THE MECHANICAL ENVIRONMENT ON CD117+ ENDOTHELIAL CELL ANGIOGENESIS

Angiogenesis is a complex process coordinating cell migration, proliferation, and lumen formation. Changes to the microenvironment regulate angiogenesis through mechanotransduction and cytokine signals. In pulmonary hypertension, something in the process becomes abnormal, resulting in changes to the microenvironment and the formation of a glomerulus of dysfunctional capillaries, called a plexiform lesion. Endothelial cells, expressing CD117 (CD117+ EC clones) increase in the plexiform lesions of pulmonary hypertension, independent of pro-angiogenic VEGF signaling. We hypothesize that the mechanical environment and the macromolecular composition of the extracellular matrix, both, contribute to the aberrant angiogenesis. When we changed the mechanical environment, we changed the angiogenic potential and cellular phenotype of CD117+ Endothelial cell clones. Turbulent flow, pathologic substrate stiffness, and pathologic stretch increased Endothelial-to-mesenchymal markers, such as acta2, cnn1, snail, and slug in CD117+ EC clones while CD117- ECs showed minimal change. We perturbed the mechanical environment of CD117+ EC clones and identified changes in Bone Morphogenic Protein-2, an often overlooked pro-angiogenic cytokine. We coupled changes in the mechanical environment to Rho GTPase intracellular signaling, to predict how changes to the mechanotransduction would affect angiogenesis through a computational model. In our model of angiogenesis, we found vessel synchronicity to depend on both which cell undergoes mitosis, and also at which phase of GTPase cycling the cell undergoes mitosis. We believe changes to the GTPase cycling may be the mechanism linking mechanotransduction to the abnormal vessels found in pulmonary hypertension. We are the first group to look at the role of the ECM composition, independent of stiffness. Our results show diseased ECM composition alone leads to phenotypic changes indicative of PH progression. In conclusion, these results provide a possible cytokine implicated in the mechanotransduction of PH, established a computational model of angiogenesis which provides a mechanotransduction mechanism of disease progression, and established that the ECM composition alone is capable of phenotypic changes leading to disease progression