Developmental clock and mechanism of de novo polarization of the mouse embryo.

Embryo polarization is critical for mouse development; however, neither the regulatory clock nor the molecular trigger that it activates is known. Here, we show that the embryo polarization clock reflects the onset of zygotic genome activation, and we identify three factors required to trigger polarization. Advancing the timing of transcription factor AP-2 gamma (Tfap2c) and TEA domain transcription factor 4 (Tead4) expression in the presence of activated Ras homolog family member A (RhoA) induces precocious polarization as well as subsequent cell fate specification and morphogenesis. Tfap2c and Tead4 induce expression of actin regulators that control the recruitment of apical proteins on the membrane, whereas RhoA regulates their lateral mobility, allowing the emergence of the apical domain. Thus, Tfap2c, Tead4, and RhoA are regulators for the onset of polarization and cell fate segregation in the mouse

Cell polarisation in a bulk-surface model can be driven by both classic and non-classic Turing instability

The GTPase Cdc42 is the master regulator of eukaryotic cell polarisation. During this process, the active form of Cdc42 is accumulated at a particular site on the cell membrane called the pole. It is believed that the accumulation of the active Cdc42 resulting in a pole is driven by a combination of activation–inactivation reactions and diffusion. It has been proposed using mathematical modelling that this is the result of diffusion-driven instability, originally proposed by Alan Turing. In this study, we developed, analysed and validated a 3D bulk-surface model of the dynamics of Cdc42. We show that the model can undergo both classic and non-classic Turing instability by deriving necessary conditions for which this occurs and conclude that the non-classic case can be viewed as a limit case of the classic case of diffusion-driven instability. Using three-dimensional Spatio-temporal simulation we predicted pole size and time to polarisation, suggesting that cell polarisation is mainly driven by the reaction strength parameter and that the size of the pole is determined by the relative diffusion

Principles that govern competition or co-existence in Rho-GTPase driven polarization

<div><p>Rho-GTPases are master regulators of polarity establishment and cell morphology. Positive feedback enables concentration of Rho-GTPases into clusters at the cell cortex, from where they regulate the cytoskeleton. Different cell types reproducibly generate either one (e.g. the front of a migrating cell) or several clusters (e.g. the multiple dendrites of a neuron), but the mechanistic basis for unipolar or multipolar outcomes is unclear. The design principles of Rho-GTPase circuits are captured by two-component reaction-diffusion models based on conserved aspects of Rho-GTPase biochemistry. Some such models display rapid winner-takes-all competition between clusters, yielding a unipolar outcome. Other models allow prolonged co-existence of clusters. We investigate the behavior of a simple class of models and show that while the timescale of competition varies enormously depending on model parameters, a single factor explains a large majority of this variation. The dominant factor concerns the degree to which the maximal active GTPase concentration in a cluster approaches a “saturation point” determined by model parameters. We suggest that both saturation and the effect of saturation on competition reflect fundamental properties of the Rho-GTPase polarity machinery, regardless of the specific feedback mechanism, which predict whether the system will generate unipolar or multipolar outcomes.</p></div

Patterning of the cell cortex by Rho GTPase Dynamics

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

Regulated Activation of the PAR Polarity Network Ensures a Timely and Specific Response to Spatial Cues

How do cells polarize at the correct time and in response to the correct cues? In the C. elegans zygote, the timing and geometry of polarization rely on a single dominant cue-the sperm centrosome-that matures at the end of meiosis and specifies the nascent posterior. Polarization requires that the conserved PAR proteins, which specify polarity in the zygote, be poised to respond to the centrosome. Yet, how and when PAR proteins achieve this unpolarized, but responsive, state is unknown. We show that oocyte maturation initiates a fertilization-independent PAR activation program. PAR proteins are initially not competent to polarize but gradually acquire this ability following oocyte maturation. Surprisingly, this program allows symmetry breaking even in unfertilized oocytes lacking centrosomes. Thus, if PAR proteins can respond to multiple polarizing cues, how is specificity for the centrosome achieved? Specificity is enforced by Polo-like and Aurora kinases (PLK-1 and AIR-1 in C. elegans), which impose a delay in the activation of the PAR network so that it coincides with maturation of the centrosome cue. This delay suppresses polarization by non-centrosomal cues, which can otherwise trigger premature polarization and multiple or reversed polarity domains. Taken together, these findings identify a regulatory program that enforces proper polarization by synchronizing PAR network activation with cell cycle progression, thereby ensuring that PAR proteins respond specifically to the correct cue. Temporal control of polarity network activity is likely to be a common strategy to ensure robust, dynamic, and specific polarization in response to developmentally deployed cues

Self-organization in heterogeneous biological systems

Self-organization is an ubiquitous and fundamental process that underlies all living systems. In cellular organisms, many vital processes, such as cell division and growth, are spatially and temporally regulated by proteins -- the building blocks of life. To achieve this, proteins self-organize and form spatiotemporal patterns. In general, protein patterns respond to a variety of internal and external stimuli, such as cell shape or inhomogeneities in protein activity. As a result, the dynamics of intracellular pattern formation generally span multiple spatial and temporal scales. This thesis addresses the underlying mechanisms that lead to the formation of heterogeneous patterns. The main themes of this work are organized into three parts, which are summarized below. The first part deals with the general problem of mass-conserving reaction-diffusion dynamics in spatially non-uniform systems. In section 1 of chapter II, we study the dynamics of the E. coli Min protein system -- a paradigmatic model for pattern formation. More specifically, we consider a setup with a fixed spatial heterogeneity in a control parameter, and show that this leads to complex multiscale pattern formation. We develop a coarse-graining approach that enables us to explain and reduce the dynamics to the "hydrodynamic variables'' at large length and time scales. In another project, we consider a system where spatial heterogeneities are not imposed externally, but self-generated by the dynamics via a mechanochemical feedback loop between geometry and reaction-diffusion system (section 2 of chapter II). We show that the resulting dynamics can be explained from the phase-space geometry of the reaction-diffusion system. The second part focuses on how patterns in realistic cell geometries are controlled by shape and biochemical cues. We examine axis selection of PAR polarity patterns in C. elegans, where we show that spatial variations in the bulk-surface ratio and a tendency of the system to minimize the pattern interface yield robust long-axis polarization of PAR protein patterns (section 1 of chapter III). In a second project, we develop a theoretical model that explains the localization of the B. subtilis Min protein system (section 2 of chapter 3). We show that a biochemical cue -- which acts as a template for pattern formation -- guides and stabilizes Min patterns. In the third part, we study the coupling between lipid membranes and curvature-generating proteins. We demonstrate that myosin-VI motor proteins cooperatively bind to saddle-shaped regions of lipid membranes, and thereby induce large-scale membrane remodeling (section 1 of chapter IV). To understand the dynamics, we develop a coarse-grained geometric model and show that the emergence of regular spatial structures can be explained by a "push-pull'' mechanism: protein binding destabilizes the membrane shape at all length scales, and this is counteracted by line tension. Inspired by this system, we then investigate a general model for the dynamics of growing protein-lipid interfaces (section 2 of chapter IV). A key feature of the model is that the protein binding kinetics is explicitly coupled to the morphology of the interface. We show that such a coupling leads to turbulent dynamics and a roughening transition of the interface that is characterized by universal scaling behaviour