William M. Bement

During cytokinesis in amphibian and echinoderm embryos, propagating waves of Rho activity and F-actin assembly – cortical excitability – are amplified and focused at the equatorial cortex by the mitotic spindle. Such cortical waves are proposed to result from fast positive feedback based on Rho and the Rho GEF, Ect2, and delayed negative feedback involving F-actin and the Rho GAP, RGA-3/4. Currently, this model is tenuous, in part because the relationship between F-actin and RGA-3/4 is not well understood. Therefore, we investigated how RGA-3/4 regulates F-actin structure both in vivo and in vitro . Full-length RGA-3/4, when expressed alone in Xenopus oocytes, localizes to and bundles cortical F-actin. In vitro , purified full-length RGA-3/4 protein directly binds to and bundles F-actin. TIRF microscopy revealed that RGA-3/4 binds to F-actin cooperatively and accumulates on the filaments before filament crosslinking events. Structure-function analyses demonstrated both the amino-terminal region and the intrinsically disordered region at the carboxyl-terminal portion of RGA-3/4 are essential for normal F-actin interaction. These results provide the first demonstration that RGA-3/4 is a direct, cooperative F-actin binding and bundling protein. We propose that its special features make RGA-3/4 uniquely suited to provide F-actin-dependent negative feedback during cortical excitability and cytokinesis. Significance statement: Cortical excitability during cytokinesis relies on delayed negative feedback based on F-actin and the Rho GAP, RGA-3/4. However, the molecular basis of the interaction between F-actin and RGA-3/4 is uncharacterized. We show that RGA-3/4 directly and cooperatively binds to and bundles F-actin and identify the regions of RGA-3/4 required for the F-actin interaction. Our work provides a new framework to understand how RGA-3/4 contributes to actin remodeling in cytokinesis and other essential morphogenetic processes.

Cells generate dynamic patterns of Rho GTPase activation to direct the subsequent patterning of Rho GTPase effectors needed to remodel the cell cortex during processes ranging from cell division to cell repair. To understand how such patterns arise, we used live cell imaging, time-resolved Rho GTPase manipulations, and a novel computational tool to study the spatiotemporal dynamics of Rho, Cdc42 and several downstream Cdc42 targets in wounded Xenopus laevis oocytes. We find that the characteristic wound-induced segregation of Rho and Cdc42 activity into concentric zones is followed by polarization of the Cdc42 zone such that Toca-1 progressively concentrates at the back of the Cdc42 zone while Arp2/3, cofilin, cortactin, and the Rho GAP p190RhoGAP progressively concentrate at the front of the Cdc42 zone, where it overlaps the Rho zone. Remarkably, the juxtaposition of Rho activity to Cdc42 is required for the polarization of p190RhoGAP, while p190RhoGAP is responsible for establishing the boundary between the Cdc42 and Rho zones. The results indicate that the characteristic segregation of the Rho and Cdc42 zones, as well as the polarization of the Cdc42 zone, arise from cortical self-organization. Further, these findings reveal a simple mechanism for hierarchical establishment of cortical patterns: recruitment of new proteins to regions of signaling compartment overlap.

Topological Data Analysis (TDA) can be used to detect and characterize holes in an image, such as zero-dimensional holes (connected components) or one-dimensional holes (loops). However, there is currently no widely accepted statistical framework for modeling spatiotemporal dependence in the evolution of topological features, such as holes, within a time series of images. We propose a hypothesis testing framework to identify statistically significant topological features of images in space and time, simultaneously. This addition of time may induce higher-dimensional topological features which can be used to establish temporal connections between the lower-dimensional features at each point in time. The temporal evolution of these lower-dimensional features is then represented on a zigzag persistence diagram, as a topological summary statistic focused on time dynamics. We demonstrate that the method effectively captures the emergence and progression of topological features in a study of a series of images of a wounded cell as it repairs. The proposed method outperforms a current approach in a simulation study that includes features of the wound healing process. Since, the wounded cell images exhibit nonlinear, dynamic, spatial, and temporal structures during single-cell repair, they provide a good application for this method.

Rho GTPases form plasma membrane-associated patterns that control the cytoskeleton during cell division, morphogenesis, migration, and wound repair. Their patterning involves transitions between inactive cytosolic and active membrane-bound states, regulated by guanine nucleotide exchange factors (GEFs), GTPase-activating proteins (GAPs), and guanine nucleotide dissociation inhibitors (GDIs). However, the relationships between these transitions and role of different regulators remain unclear. We developed a novel reconstitution approach to study Rho GTPase patterning with all major GTPase regulators in a biochemically defined system. We show that Rho GTPase dissociation from RhoGDI is rate-limiting for its membrane association. Rho GTPase activation occurs after membrane insertion, which is unaffected by GEF activity. Once activated, Rho GTPases are retained at the membrane through effector interactions, essential for their enrichment at activation sites. Thus, high cytosolic levels of RhoGDI-bound GTPases ensure a constant supply of inactive GTPases for the membrane, where GEF-mediated activation and effector binding stabilize them. These results delineate the route by which Rho GTPase patterns are established and define stage-dependent roles of its regulators.

Living systems are driven far from thermodynamic equilibrium through the continuous consumption of ambient energy. In the cell cortex, this energy is invested in the formation of diverse patterns in chemical and mechanical activities, whose spatial and temporal dynamics determine the cell phenotypes and behaviours. How cells partition internal energy between these activities is unknown. Here we measured the entropy production rate of both chemical and mechanical subsystems of the cell cortex across a variety of patterns as the system is driven further from equilibrium. We do this by manipulating the Rho GTPase pathway, which controls the cortical actin filaments and myosin-II. At lower levels of GTPase-activating protein expression, which produce pulses or choppy Rho and actin filament waves, energy is proportionally partitioned between the two subsystems and is subject to the constraint of Onsager reciprocity. Within the range of reciprocity, the entropy production rate is maximized in choppy waves. As the cortex is driven into labyrinthine or spiral travelling waves, reciprocity is broken, marking an increasingly differential partitioning of energy and an uncoupling of chemical and mechanical activities. We further demonstrate that energy partitioning and reciprocity are determined by the competing timescales between chemical reaction and mechanical relaxation.

Living systems are driven far from thermodynamic equilibrium through the continuous consumption of ambient energy ¹ . In the cell cortex, this energy is invested in the formation of diverse patterns in chemical and mechanical activities, whose unique spatial and temporal dynamics determine cell phenotypes and behaviors ^2-6 . However, how cells partition internal energy between chemical and mechanical work is unknown ^7-9 . Here we measured the entropy production rate (EPR) of both the chemical and mechanical subsystems of the cell cortex across a broad range of periodic patterns as the system is driven further from equilibrium via manipulation of the Rho GTPase pathway, which controls cortical actin filaments (F-actin) and myosin-II. We find that at lower levels of Rho GAP (GTPase activating protein) expression, which produce pulses or “choppy” Rho and F-actin waves, energy is comparably partitioned between the chemical and mechanical subsystems and is subject to the constraint of Onsager reciprocity. Within the range of reciprocity, the EPR is maximized in choppy waves that resemble the waves associated with cell division ^3,10 . However, as the cortex is driven even further from equilibrium into elaborate labyrinthine or spiral traveling wave trains via increased GAP expression, reciprocity is broken, marking an increasingly differential partitioning of energy and an uncoupling of chemical and mechanical activities. We further demonstrate that energy partitioning and reciprocity are determined by the competition between the timescales of chemical reaction and mechanical relaxation. These results indicate that even within coupled cellular subsystems, both the relative proportions of energy partitioned to each subsystem and the ultimate phenotypic outcome vary dramatically as a function of the overall energy investment.

The Rho GTPases — RHOA, RAC1 and CDC42 — are small GTP binding proteins that regulate basic biological processes such as cell locomotion, cell division and morphogenesis by promoting cytoskeleton-based changes in the cell cortex. This regulation results from active (GTP-bound) Rho GTPases stimulating target proteins that, in turn, promote actin assembly and myosin 2-based contraction to organize the cortex. This basic regulatory scheme, well supported by in vitro studies, led to the natural assumption that Rho GTPases function in vivo in an essentially linear matter, with a given process being initiated by GTPase activation and terminated by GTPase inactivation. However, a growing body of evidence based on live cell imaging, modelling and experimental manipulation indicates that Rho GTPase activation and inactivation are often tightly coupled in space and time via signalling circuits and networks based on positive and negative feedback. In this Review, we present and discuss this evidence, and we address one of the fundamental consequences of coupled activation and inactivation: the ability of the Rho GTPases to self-organize, that is, direct their own transition from states of low order to states of high order. We discuss how Rho GTPase self-organization results in the formation of diverse spatiotemporal cortical patterns such as static clusters, oscillatory pulses, travelling wave trains and ring-like waves. Finally, we discuss the advantages of Rho GTPase self-organization and pattern formation for cell function.