A novel stochastic simulation approach enables exploration of mechanisms for regulating polarity site movement.

Cells polarize their movement or growth toward external directional cues in many different contexts. For example, budding yeast cells grow toward potential mating partners in response to pheromone gradients. Directed growth is controlled by polarity factors that assemble into clusters at the cell membrane. The clusters assemble, disassemble, and move between different regions of the membrane before eventually forming a stable polarity site directed toward the pheromone source. Pathways that regulate clustering have been identified but the molecular mechanisms that regulate cluster mobility are not well understood. To gain insight into the contribution of chemical noise to cluster behavior we simulated clustering using the reaction-diffusion master equation (RDME) framework to account for molecular-level fluctuations. RDME simulations are a computationally efficient approximation, but their results can diverge from the underlying microscopic dynamics. We implemented novel concentration-dependent rate constants that improved the accuracy of RDME-based simulations, allowing us to efficiently investigate how cluster dynamics might be regulated. Molecular noise was effective in relocating clusters when the clusters contained low numbers of limiting polarity factors, and when Cdc42, the central polarity regulator, exhibited short dwell times at the polarity site. Cluster stabilization occurred when abundances or binding rates were altered to either lengthen dwell times or increase the number of polarity molecules in the cluster. We validated key results using full 3D particle-based simulations. Understanding the mechanisms cells use to regulate the dynamics of polarity clusters should provide insights into how cells dynamically track external directional cues.

Particle-based simulations of polarity establishment reveal stochastic promotion of Turing pattern formation.

Polarity establishment, the spontaneous generation of asymmetric molecular distributions, is a crucial component of many cellular functions. Saccharomyces cerevisiae (yeast) undergoes directed growth during budding and mating, and is an ideal model organism for studying polarization. In yeast and many other cell types, the Rho GTPase Cdc42 is the key molecular player in polarity establishment. During yeast polarization, multiple patches of Cdc42 initially form, then resolve into a single front. Because polarization relies on strong positive feedback, it is likely that the amplification of molecular-level fluctuations underlies the generation of multiple nascent patches. In the absence of spatial cues, these fluctuations may be key to driving polarization. Here we used particle-based simulations to investigate the role of stochastic effects in a Turing-type model of yeast polarity establishment. In the model, reactions take place either between two molecules on the membrane, or between a cytosolic and a membrane-bound molecule. Thus, we developed a computational platform that explicitly simulates molecules at and near the cell membrane, and implicitly handles molecules away from the membrane. To evaluate stochastic effects, we compared particle simulations to deterministic reaction-diffusion equation simulations. Defining macroscopic rate constants that are consistent with the microscopic parameters for this system is challenging, because diffusion occurs in two dimensions and particles exchange between the membrane and cytoplasm. We address this problem by empirically estimating macroscopic rate constants from appropriately designed particle-based simulations. Ultimately, we find that stochastic fluctuations speed polarity establishment and permit polarization in parameter regions predicted to be Turing stable. These effects can operate at Cdc42 abundances expected of yeast cells, and promote polarization on timescales consistent with experimental results. To our knowledge, our work represents the first particle-based simulations of a model for yeast polarization that is based on a Turing mechanism.

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

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.

BioPrint meets the AI age: development of artificial intelligence-based ADMET models for the drug-discovery platform SAFIRE.

Background: To prioritize compounds with a higher likelihood of success, artificial intelligence models can be used to predict absorption, distribution, metabolism, excretion and toxicity (ADMET) properties of molecules quickly and efficiently. Methods: Models were trained with BioPrint database proprietary data along with public datasets to predict various ADMET end points for the SAFIRE platform. Results: SAFIRE models performed at or above 75% accuracy and 0.4 Matthew's correlation coefficient with validation sets. Training with both proprietary and public data improved model performance and expanded the chemical space on which the models were trained. The platform features scoring functionality to guide user decision-making. Conclusion: High-quality datasets along with chemical space considerations yielded ADMET models performing favorably with utility in the drug discovery process.

A model for migratory B cell oscillations from receptor down-regulation induced by external chemokine fields.

A long-standing paradigm in B cell immunology is that effective somatic hypermutation and affinity maturation require cycling between the dark zone and light zone of the germinal center. The cyclic re-entry hypothesis was first proposed based on considerations of the efficiency of affinity maturation using an ordinary differential equations model for B cell population dynamics. More recently, two-photon microscopy studies of B cell motility within lymph nodes in situ have revealed the complex migration patterns of B lymphocytes both in the preactivation follicle and post-activation germinal center. There is strong evidence that chemokines secreted by stromal cells and the regulation of cognate G-protein coupled receptors by these chemokines are necessary for the observed spatial cell distributions. For example, the distribution of B cells within the light and dark zones of the germinal center appears to be determined by the reciprocal interaction between the level of the CXCR4 and CXCR5 receptors and the spatial distribution of their respective chemokines CXCL12 and CXCL13. Computer simulations of individual-based models have been used to study the complex biophysical and mechanistic processes at the individual cell level, but such simulations can be challenging to parameterize and analyze. In contrast, ordinary differential equations are more tractable, but traditional compartment model formalizations ignore the spatial chemokine distribution that drives B cell redistribution. Motivated by the desire to understand the motility patterns observed in an individual-based simulation of B cell migration in the lymph node, we propose and analyze the dynamics of an ordinary differential equation model incorporating explicit chemokine spatial distributions. While there is experimental evidence that B cell migration patterns in the germinal center are driven by extrinsically regulated differentiation programs, the model shows, perhaps surprisingly, that feedback from receptor down-regulation induced by external chemokine fields can give rise to spontaneous interzonal and intrazonal oscillations in the absence of any extrinsic regulation. While the extent to which such simple feedback mechanisms contributes to B cell migration patterns in the germinal center is unknown, the model provides an alternative hypothesis for how complex B cell migration patterns might arise from very simple mechanisms.

Effect of the Organization of Rhodopsin on the Association between Transducin and a Photoactivated Receptor.

After photoactivation, rhodopsin (R), a G-protein-coupled receptor, rapidly activates multiple transducin G-proteins (G) in an initial amplification step of phototransduction. G-protein activation requires diffusion-mediated association with an active rhodopsin (R*) at the rod disk membrane. Different organizations of R within the membrane have been revealded by several microscopy studies, including static and freely diffusing situations. However, it is unclear how such different scenarios influence the activation rate of G proteins. Through Monte Carlo simulations, we study the association reaction between a photoactivated rhodopsin and transducin under different reported receptor organizations including (a) R monomers diffusing freely, (b) R forming static dispersed crystalline domains made of rows of dimers, and (c) R arranged in static tracks formed by two adjacent rows of dimers. A key parameter in our simulations is the probability of binding following a collision ( p). For high p, the association rate between R* and G is higher in the freely diffusive system than in the static organizations, but for low collision efficiencies, the static organizations can result in faster association rates than the mobile system. We also observe that with low p, increasing the concentration of R increases the association rate significantly in the dispersed crystals configuration and just slightly in the free diffusive system. In summary, the lateral organization of rhodopsin influences the association rate between R* and G in a manner strongly dependent on the collision efficiency.

Dendritic spine geometry can localize GTPase signaling in neurons.

Dendritic spines are the postsynaptic terminals of most excitatory synapses in the mammalian brain. Learning and memory are associated with long-lasting structural remodeling of dendritic spines through an actin-mediated process regulated by the Rho-family GTPases RhoA, Rac, and Cdc42. These GTPases undergo sustained activation after synaptic stimulation, but whereas Rho activity can spread from the stimulated spine, Cdc42 activity remains localized to the stimulated spine. Because Cdc42 itself diffuses rapidly in and out of the spine, the basis for the retention of Cdc42 activity in the stimulated spine long after synaptic stimulation has ceased is unclear. Here we model the spread of Cdc42 activation at dendritic spines by means of reaction-diffusion equations solved on spine-like geometries. Excitable behavior arising from positive feedback in Cdc42 activation leads to spreading waves of Cdc42 activity. However, because of the very narrow neck of the dendritic spine, wave propagation is halted through a phenomenon we term geometrical wave-pinning. We show that this can account for the localization of Cdc42 activity in the stimulated spine, and, of interest, retention is enhanced by high diffusivity of Cdc42. Our findings are broadly applicable to other instances of signaling in extreme geometries, including filopodia and primary cilia.