Interplay of packing and flip-flop in local bilayer deformation. How phosphatidylglycerol could rescue mitochondrial function in a cardiolipin-deficient yeast mutant

In a previous work, we have shown that a spatially localized transmembrane pH gradient, produced by acid micro-injection near the external side of cardiolipin-containing giant unilamellar vesicles, leads to the formation of tubules that retract after the dissipation of this gradient. These tubules have morphologies similar to mitochondrial cristae. The tubulation effect is due to direct phospholipid packing modification in the outer leaflet that is promoted by protonation of cardiolipin headgroups. Here we compare the case of cardiolipin-containing giant unilamellar vesicles with that of phosphatidylglycerol-containing giant unilamellar vesicles. Local acidification also promotes formation of tubules in the latter. However, compared to cardiolipin-containing giant unilamellar vesicles the tubules are longer, exhibit a visible pearling and have a much longer lifetime after acid micro-injection is stopped. We attribute these differences to an additional mechanism that increases monolayer surface imbalance, namely inward PG flip-flop promoted by the local transmembrane pH-gradient. Simulations using a fully non-linear membrane model as well as geometrical calculations are in agreement with this hypothesis. Interestingly, among yeast mutants deficient in cardiolipin biosynthesis, only the crd1-null mutant, which accumulates phosphatidylglycerol, displays significant mitochondrial activity. Our work provides a possible explanation of such a property and further emphasizes the salient role of specific lipids in mitochondrial function.Comment: 28 pages, 10 figure

Universal features of cell polarization processes

Cell polarization plays a central role in the development of complex organisms. It has been recently shown that cell polarization may follow from the proximity to a phase separation instability in a bistable network of chemical reactions. An example which has been thoroughly studied is the formation of signaling domains during eukaryotic chemotaxis. In this case, the process of domain growth may be described by the use of a constrained time-dependent Landau-Ginzburg equation, admitting scale-invariant solutions {\textit{\`a la}} Lifshitz and Slyozov. The constraint results here from a mechanism of fast cycling of molecules between a cytosolic, inactive state and a membrane-bound, active state, which dynamically tunes the chemical potential for membrane binding to a value corresponding to the coexistence of different phases on the cell membrane. We provide here a universal description of this process both in the presence and absence of a gradient in the external activation field. Universal power laws are derived for the time needed for the cell to polarize in a chemotactic gradient, and for the value of the smallest detectable gradient. We also describe a concrete realization of our scheme based on the analysis of available biochemical and biophysical data.Comment: Submitted to Journal of Statistical Mechanics -Theory and Experiment

Mechanisms of cellular symmetry breaking in S. cerevisiae

Cell polarization is vital to diverse biological processes, from maintenance of stem cell identity to chemotaxis of neutrophils. The small GTPase Cdc42 has long been known to be a primary regulator of polarity, but the mechanistic details of how Cdc42 may shift from an isotropic to a polarized distribution, balancing diffusion with targeting in a dynamic system, are not well understood. Here we investigate this question using the budding yeast S. cerevisiae as a model system. Yeast polarize via two distinct but coupled mechanisms. Actin-dependent polarization comprises a positive feedback loop wherein Cdc42-dependent nucleation of polarized actin cables leads to a transport of Cdc42 to the polarized site. A standing question in this model was how Cdc42 could maintain concentration in the cap in the presence of membrane flux due to docking and excision of vesicles. Careful imaging revealed a spatiotemporal heterogeneity of Cdc42 distribution at the cap, with peaks corresponding to regions of high exocytosis, low endocytosis, and low diffusion of Cdc42 within the membrane. Mathematical simulation revealed that these microdomains were sufficient to support polarization via the actin pathway in the presence of membrane flux, with concentration of Cdc42 onto vesicles having a lesser impact. We next sought to gain mechanistic insight into actin-independent polarization, which requires both the guanine nucleotide dissociation inhibitor (GDI) Rdi1, which extracts Cdc42 from the peripheral membrane into a rapidly diffusing cytosolic complex, and the adaptor molecule Bem1, which binds both active Cdc42GTP and its guanine nucleotide exchange factor (GEF) or activator Cdc24. It was thought that Bem1 mediated symmetry breaking through a positive feedback loop wherein Bem1 recruited Cdc24 to sites of Cdc42GTP, upon which Cdc24 would catalyze the activation of additional Cdc42. To critically test the proposed feedback loop, we examined the capacity of cells to undergo actin-independent polarization when specific steps in the loop were disrupted. We found that although binding of Bem1 with the GEF was required, binding of Bem1 with Cdc42 was not required and, strikingly, nor was localization of Bem1 to the polar cap. Using a Cdc42 activation biosensor, we found that Bem1 binding boosts Cdc24 GEF activity. Importantly, expression of a constitutively active GEF partially rescued actin-independent polarization in the Bem1-Cdc24 binding mutant. Wondering if polarization could occur via an Rdi1-dependent mechanism of extraction and targeted deposition in the presence of uniformly activated Cdc42, we turned to mathematical modeling. We found that polarization could indeed occur within a defined range of Rdi1/Cdc42 ratios, which we verified experimentally

Actin-Based Feedback Circuits in Cell Migration and Endocytosis

In this thesis, we study the switch and pulse functions of actin during two important cellular processes, cell migration and endocytosis. Actin is an abundant protein that can polymerize to form a dendritic network. The actin network can exert force to push or bend the cell membrane. During cell migration, the actin network behaves like a switch, assembling mostly at one end or at the other end. The end with the majority of the actin network is the leading edge, following which the cell can persistently move in the same direction. The other end, with the minority of the actin network, is the trailing edge, which is dragged by the cell as it moves forward. When subjected to large fluctuations or external stimuli, the leading edge and the trailing edge can interchange and change the direction of motion, like a motion switch. Our model of the actin network in a cell reveals that mechanical force is crucial for forming the motion switch. We find a transition from single state symmetric behavior to switch behavior, when tuning parameters such as the force. The model is studied by both stochastic simulations, and a set of rate equations that are consistent with the simulations. Endocytosis is a process by which cells engulf extracellular substances and recycle the cell membrane. In yeast cells, the actin network is transiently needed to overcome the pressure difference across the cell membrane caused by turgor pressure. The actin network behaves like a pulse, which assembles and then disassembles within about 30 seconds. Using a stochastic model, we reproduce the pulse behaviors of the actin network and one of its regulatory proteins, Las17. The model matches green fluorescence protein (GFP) experiments for wild-type cells. The model also predicts some phenotypes that modify or diminish the pulse behavior. The phenotypes are verified with both experiments performed at Washington University and with other groups\u27 experiments. We find that several feedback mechanisms are critical for the pulse behavior of the actin network, including the autocatalytic assembly of F-actin, the negative feedback of F-actin on Las17, and the autocatalytic self-assembly of Las17. These feedback mechanisms are also studied by a simple ordinary differential equation (ODE) model. Finally, we develop a partial differential equation (PDE) model that is more realistic than the ODE model and more computationally efficient than the stochastic model. We use the PDE model to explore the rich spectrum of behaviors of the actin network beyond pulses, such as oscillations and permanent patches. The predictions of the PDE model are of high interest for suggesting future experiments that can test the model

Spontaneous Cdc42 polarization independent of GDI-mediated extraction and actin-based trafficking.

The small Rho-family GTPase Cdc42 is critical for cell polarization and polarizes spontaneously in absence of upstream spatial cues. Spontaneous polarization is thought to require dynamic Cdc42 recycling through Guanine nucleotide Dissociation Inhibitor (GDI)-mediated membrane extraction and vesicle trafficking. Here, we describe a functional fluorescent Cdc42 allele in fission yeast, which demonstrates Cdc42 dynamics and polarization independent of these pathways. Furthermore, an engineered Cdc42 allele targeted to the membrane independently of these recycling pathways by an amphipathic helix is viable and polarizes spontaneously to multiple sites in fission and budding yeasts. We show that Cdc42 is highly mobile at the membrane and accumulates at sites of activity, where it displays slower mobility. By contrast, a near-immobile transmembrane domain-containing Cdc42 allele supports viability and polarized activity, but does not accumulate at sites of activity. We propose that Cdc42 activation, enhanced by positive feedback, leads to its local accumulation by capture of fast-diffusing inactive molecules

Doctor of Philosophy

dissertationWe formulate and analyze three spatio-temporal models for cell polarization in budding yeast, fission yeast, and the neuronal growth cone, respectively. We focus on the roles of diffusion and active transport of cytosolic molecules along cytoskeletal filaments on the establishment of a polarized distribution of membrane-bound molecules. Our first model couples the diffusion equation on a finite interval to a pair of delay differential equations at the boundaries. The model is used to study the oscillatory dynamics of the signaling molecule Cdc42 in fission yeast. We explore the effect of diffusion by performing a bifurcation analysis and find that the critical time delay for the onset of oscillations increases as the diffusion coefficient decreases. We then extend the model to a growing domain and show that there is a transition from asymmetric to symmetric oscillations as the cell grows. This is consistent with the experimental findings of “new-end-takeoff†in fission yeast. In our second model, we study the active transport of signaling molecules along a two-dimensional microtubule (MT) network in the neuronal growth cone. We consider a Rac1-stathmin-MT pathway and use a modified Dogteromâ€"Leibler model for the microtubule growth. In the presence of a nonuniform Rac1 concentration, we derive the resulting nonuniform length distribution of MTs and couple it to the active transport model. We calculate the polarized distribution of signaling molecules at the membrane using perturbation analysis and numerical simulation. We find the distribution is sensitive to the explicit Rac1 distribution and the stahmin-MT pathway. Our third model is a stochastic active transport model for vesicles containing signaling molecules in a filament network. We first derive the corresponding advection-diffusion model by a quasi-steady-state analysis. We find the diffusion is anisotropic and depends on the local density of filaments. The stability of the homogeneous steady state is sensitive to the geometry of filaments. For a parallelMTnetwork, the homogeneous steady state is linearly stable. For a network with filaments nucleated from the membrane (actin cytoskeleton), the homogeneous steady state is linearly unstable and a polarized distribution can occur