Particle-based simulations reveal two positive feedback loops allow relocation and stabilization of the polarity site during yeast mating.

Many cells adjust the direction of polarized growth or migration in response to external directional cues. The yeast Saccharomyces cerevisiae orient their cell fronts (also called polarity sites) up pheromone gradients in the course of mating. However, the initial polarity site is often not oriented towards the eventual mating partner, and cells relocate the polarity site in an indecisive manner before developing a stable orientation. During this reorientation phase, the polarity site displays erratic assembly-disassembly behavior and moves around the cell cortex. The mechanisms underlying this dynamic behavior remain poorly understood. Particle-based simulations of the core polarity circuit revealed that molecular-level fluctuations are unlikely to overcome the strong positive feedback required for polarization and generate relocating polarity sites. Surprisingly, inclusion of a second pathway that promotes polarity site orientation generated relocating polarity sites with properties similar to those observed experimentally. This pathway forms a second positive feedback loop involving the recruitment of receptors to the cell membrane and couples polarity establishment to gradient sensing. This second positive feedback loop also allows cells to stabilize their polarity site once the site is aligned with the pheromone gradient.

Cesium: A public database of evolved oscillatory reaction networks.

New tools and software in systems biology require testing and validation on reaction networks with desired characteristics such as number of reactions or oscillating behaviors. Often, there is only a modest number of published models that are suitable, so researchers must generate reaction networks with the desired characteristics, a process that can be computationally expensive. To reduce these computational costs, we developed a data base of synthetic reaction networks to facilitate reuse. The current database contains thousands of networks generated using directed evolution. The network are of two types: (1) those with oscillations in species concentrations and (2) those for which no oscillation was found using directed evolution. To facilitate access to networks of interest, the database is queryable by the number of species and reactants, the presence or absence of autocatalytic and degradation reactions, and the network behavior. Our analysis of the data revealed some interesting insights, such as the population of oscillating networks possess more autocatalytic reactions compared to random control networks. In the future, this database will be expanded to include other network behaviors.

Spatial models of pattern formation during phagocytosis.

Phagocytosis, the biological process in which cells ingest large particles such as bacteria, is a key component of the innate immune response. Fcγ receptor (FcγR)-mediated phagocytosis is initiated when these receptors are activated after binding immunoglobulin G (IgG). Receptor activation initiates a signaling cascade that leads to the formation of the phagocytic cup and culminates with ingestion of the foreign particle. In the experimental system termed "frustrated phagocytosis", cells attempt to internalize micropatterned disks of IgG. Cells that engage in frustrated phagocytosis form "rosettes" of actin-enriched structures called podosomes around the IgG disk. The mechanism that generates the rosette pattern is unknown. We present data that supports the involvement of Cdc42, a member of the Rho family of GTPases, in pattern formation. Cdc42 acts downstream of receptor activation, upstream of actin polymerization, and is known to play a role in polarity establishment. Reaction-diffusion models for GTPase spatiotemporal dynamics exist. We demonstrate how the addition of negative feedback and minor changes to these models can generate the experimentally observed rosette pattern of podosomes. We show that this pattern formation can occur through two general mechanisms. In the first mechanism, an intermediate species forms a ring of high activity around the IgG disk, which then promotes rosette organization. The second mechanism does not require initial ring formation but relies on spatial gradients of intermediate chemical species that are selectively activated over the IgG patch. Finally, we analyze the models to suggest experiments to test their validity.

Actin nano-architecture of phagocytic podosomes.

Podosomes are actin-enriched adhesion structures important for multiple cellular processes, including migration, bone remodeling, and phagocytosis. Here, we characterize the structure and organization of phagocytic podosomes using interferometric photoactivated localization microscopy, a super-resolution microscopy technique capable of 15-20 nm resolution, together with structured illumination microscopy and localization-based super-resolution microscopy. Phagocytic podosomes are observed during frustrated phagocytosis, a model in which cells attempt to engulf micropatterned IgG antibodies. For circular patterns, this results in regular arrays of podosomes with well-defined geometry. Using persistent homology, we develop a pipeline for semi-automatic identification and measurement of podosome features. These studies reveal an hourglass shape of the podosome actin core, a protruding knob at the bottom of the core, and two actin networks extending from the core. Additionally, the distributions of paxillin, talin, myosin II, α-actinin, cortactin, and microtubules relative to actin are characterized.

Towards resolution of a paradox in plant G-protein signaling.

G-proteins are molecular on-off switches that are involved in transmitting a variety of extracellular signals to their intracellular targets. In animal and yeast systems, the switch property is encoded through nucleotides: a GDP-bound state is the "off-state" and the GTP-bound state is the "on-state". The G-protein cycle consists of the switch turning on through nucleotide exchange facilitated by a G-protein coupled receptor and the switch turning off through hydrolysis of GTP back to GDP, facilitated by a protein designated REGULATOR OF G SIGNALING 1 (RGS). In plants, G-protein signaling dramatically differs from that in animals and yeast. Despite stringent conservation of the nucleotide binding and catalytic structures over the 1.6 billion years that separate the evolution of plants and animals, genetic and biochemical data indicate that nucleotide exchange is less critical for this switch to operate in plants. Also, the loss of the single RGS protein in Arabidopsis (Arabidopsis thaliana) confers unexpectedly weaker phenotypes consistent with a diminished role for the G cycle, at least under static conditions. However, under dynamic conditions, genetic ablation of RGS in Arabidopsis results in a strong phenotype. We explore explanations to this conundrum by formulating a mathematical model that takes into account the accruing evidence for the indispensable role of phosphorylation in G-protein signaling in plants and that the G-protein cycle is needed to process dynamic signal inputs. We speculate that the plant G-protein cycle and its attendant components evolved to process dynamic signals through signaling modulation rather than through on-off, switch-like regulation of signaling. This so-called change detection may impart greater fitness for plants due to their sessility in a dynamic light, temperature, and pest environment.

Biosensors based on peptide exposure show single molecule conformations in live cells.

We describe an approach to study the conformation of individual proteins during single particle tracking (SPT) in living cells. "Binder/tag" is based on incorporation of a 7-mer peptide (the tag) into a protein where its solvent exposure is controlled by protein conformation. Only upon exposure can the peptide specifically interact with a reporter protein (the binder). Thus, simple fluorescence localization reflects protein conformation. Through direct excitation of bright dyes, the trajectory and conformation of individual proteins can be followed. Simple protein engineering provides highly specific biosensors suitable for SPT and FRET. We describe tagSrc, tagFyn, tagSyk, tagFAK, and an orthogonal binder/tag pair. SPT showed slowly diffusing islands of activated Src within Src clusters and dynamics of activation in adhesions. Quantitative analysis and stochastic modeling revealed in vivo Src kinetics. The simplicity of binder/tag can provide access to diverse proteins.

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.

Gradient Tracking by Yeast GPCRs in a Microfluidics Chamber.

Cells typically exist in a highly dynamic environment, which cannot easily be recreated in culture dishes or microwell plates. Microfluidic devices can provide precise control of the time, dose, and orientation of a stimulus, while simultaneously capturing quantitative single-cell data. The approach is particularly powerful when combined with the genetically tractable yeast model organism. The GPCR pathway in yeast is structurally conserved and functionally interchangeable with those in humans. We describe the implementation of a microfluidic device to investigate morphological and transcriptional responses of yeast to a gradient or pulse administration of a GPCR ligand, the peptide mating pheromone α-factor.

Bistability in the polarity circuit of yeast.

Cells polarize their growth or movement in many different physiological contexts. A key driver of polarity is the Rho GTPase Cdc42, which when activated becomes clustered or concentrated at polar sites. Multiple models for polarity establishment have been proposed. All of them rely on positive feedback to reinforce regions of high Cdc42 activity. Positive feedback can lead to bistability, a scenario in which cells can exist in either a polarized or unpolarized state under identical external conditions. Determining if the signaling circuit that drives Cdc42 polarity is bistable would provide important information about the mechanism that underlies polarity establishment and insights into the design features required for proper cellular function. We studied polarity establishment during the mating response of yeast. Using microfluidics to precisely control the temporal profile of mating pheromone and live-cell imaging to monitor the polarity process in single living cells, we found that the polarity circuit of yeast shows hysteresis, a characteristic feature of bistable systems. Our analysis also revealed that cells exposed to high pheromone concentrations rapidly lose polarity following a precipitous removal of pheromone. We used a reaction-diffusion model for polarity establishment to demonstrate that delayed negative regulation is sufficient to explain our experimental results. [Media: see text] [Media: see text] [Media: see text] [Media: see text].

Molecular switch architecture determines response properties of signaling pathways.

Many intracellular signaling pathways are composed of molecular switches, proteins that transition between two states-on and off Typically, signaling is initiated when an external stimulus activates its cognate receptor that, in turn, causes downstream switches to transition from off to on using one of the following mechanisms: activation, in which the transition rate from the off state to the on state increases; derepression, in which the transition rate from the on state to the off state decreases; and concerted, in which activation and derepression operate simultaneously. We use mathematical modeling to compare these signaling mechanisms in terms of their dose-response curves, response times, and abilities to process upstream fluctuations. Our analysis elucidates several operating principles for molecular switches. First, activation increases the sensitivity of the pathway, whereas derepression decreases sensitivity. Second, activation generates response times that decrease with signal strength, whereas derepression causes response times to increase with signal strength. These opposing features allow the concerted mechanism to not only show dose-response alignment, but also to decouple the response time from stimulus strength. However, these potentially beneficial properties come at the expense of increased susceptibility to upstream fluctuations. We demonstrate that these operating principles also hold when the models are extended to include additional features, such as receptor removal, kinetic proofreading, and cascades of switches. In total, we show how the architecture of molecular switches govern their response properties. We also discuss the biological implications of our findings.

Exploratory polarization facilitates mating partner selection in Saccharomyces cerevisiae.

Yeast decode pheromone gradients to locate mating partners, providing a model for chemotropism. How yeast polarize toward a single partner in crowded environments is unclear. Initially, cells often polarize in unproductive directions, but then they relocate the polarity site until two partners' polarity sites align, whereupon the cells "commit" to each other by stabilizing polarity to promote fusion. Here we address the role of the early mobile polarity sites. We found that commitment by either partner failed if just one partner was defective in generating, orienting, or stabilizing its mobile polarity sites. Mobile polarity sites were enriched for pheromone receptors and G proteins, and we suggest that such sites engage in an exploratory search of the local pheromone landscape, stabilizing only when they detect elevated pheromone levels. Mobile polarity sites were also enriched for pheromone secretion factors, and simulations suggest that only focal secretion at polarity sites would produce high pheromone concentrations at the partner's polarity site, triggering commitment.

A predictive model of gene expression reveals the role of network motifs in the mating response of yeast.

Cells use signaling pathways to receive and process information about their environment. These nonlinear systems rely on feedback and feedforward regulation to respond appropriately to changing environmental conditions. Mathematical models describing signaling pathways often lack predictive power because they are not trained on data that encompass the diverse time scales on which these regulatory mechanisms operate. We addressed this limitation by measuring transcriptional changes induced by the mating response in Saccharomyces cerevisiae exposed to different dynamic patterns of pheromone. We found that pheromone-induced transcription persisted after pheromone removal and showed long-term adaptation upon sustained pheromone exposure. We developed a model of the regulatory network that captured both characteristics of the mating response. We fit this model to experimental data with an evolutionary algorithm and used the parameterized model to predict scenarios for which it was not trained, including different temporal stimulus profiles and genetic perturbations to pathway components. Our model allowed us to establish the role of four architectural elements of the network in regulating gene expression. These network motifs are incoherent feedforward, positive feedback, negative feedback, and repressor binding. Experimental and computational perturbations to these network motifs established a specific role for each in coordinating the mating response to persistent and dynamic stimulation.

Stochastic Methods for Inferring States of Cell Migration.

Cell migration refers to the ability of cells to translocate across a substrate or through a matrix. To achieve net movement requires spatiotemporal regulation of the actin cytoskeleton. Computational approaches are necessary to identify and quantify the regulatory mechanisms that generate directed cell movement. To address this need, we developed computational tools, based on stochastic modeling, to analyze time series data for the position of randomly migrating cells. Our approach allows parameters that characterize cell movement to be efficiently estimated from cell track data. We applied our methods to analyze the random migration of Mouse Embryonic Fibroblasts (MEFS) and HeLa cells. Our analysis revealed that MEFs exist in two distinct states of migration characterized by differences in cell speed and persistence, whereas HeLa cells only exhibit a single state. Further analysis revealed that the Rho-family GTPase RhoG plays a role in determining the properties of the two migratory states of MEFs. An important feature of our computational approach is that it provides a method for predicting the current migration state of an individual cell from time series data. Finally, we applied our computational methods to HeLa cells expressing a Rac1 biosensor. The Rac1 biosensor is known to perturb movement when expressed at overly high concentrations; at these expression levels the HeLa cells showed two migratory states, which correlated with differences in the spatial distribution of active Rac1.

Recurrent mismatch binding by MutS mobile clamps on DNA localizes repair complexes nearby.

DNA mismatch repair (MMR), the guardian of the genome, commences when MutS identifies a mismatch and recruits MutL to nick the error-containing strand, allowing excision and DNA resynthesis. Dominant MMR models posit that after mismatch recognition, ATP converts MutS to a hydrolysis-independent, diffusive mobile clamp that no longer recognizes the mismatch. Little is known about the postrecognition MutS mobile clamp and its interactions with MutL. Two disparate frameworks have been proposed: One in which MutS-MutL complexes remain mobile on the DNA, and one in which MutL stops MutS movement. Here we use single-molecule FRET to follow the postrecognition states of MutS and the impact of MutL on its properties. In contrast to current thinking, we find that after the initial mobile clamp formation event, MutS undergoes frequent cycles of mismatch rebinding and mobile clamp reformation without releasing DNA. Notably, ATP hydrolysis is required to alter the conformation of MutS such that it can recognize the mismatch again instead of bypassing it; thus, ATP hydrolysis licenses the MutS mobile clamp to rebind the mismatch. Moreover, interaction with MutL can both trap MutS at the mismatch en route to mobile clamp formation and stop movement of the mobile clamp on DNA. MutS's frequent rebinding of the mismatch, which increases its residence time in the vicinity of the mismatch, coupled with MutL's ability to trap MutS, should increase the probability that MutS-MutL MMR initiation complexes localize near the mismatch.

Deep learning enables structured illumination microscopy with low light levels and enhanced speed.

Structured illumination microscopy (SIM) surpasses the optical diffraction limit and offers a two-fold enhancement in resolution over diffraction limited microscopy. However, it requires both intense illumination and multiple acquisitions to produce a single high-resolution image. Using deep learning to augment SIM, we obtain a five-fold reduction in the number of raw images required for super-resolution SIM, and generate images under extreme low light conditions (at least 100× fewer photons). We validate the performance of deep neural networks on different cellular structures and achieve multi-color, live-cell super-resolution imaging with greatly reduced photobleaching.

Mechanistic models of PLC/PKC signaling implicate phosphatidic acid as a key amplifier of chemotactic gradient sensing.

Chemotaxis of fibroblasts and other mesenchymal cells is critical for embryonic development and wound healing. Fibroblast chemotaxis directed by a gradient of platelet-derived growth factor (PDGF) requires signaling through the phospholipase C (PLC)/protein kinase C (PKC) pathway. Diacylglycerol (DAG), the lipid product of PLC that activates conventional PKCs, is focally enriched at the up-gradient leading edge of fibroblasts responding to a shallow gradient of PDGF, signifying polarization. To explain the underlying mechanisms, we formulated reaction-diffusion models including as many as three putative feedback loops based on known biochemistry. These include the previously analyzed mechanism of substrate-buffering by myristoylated alanine-rich C kinase substrate (MARCKS) and two newly considered feedback loops involving the lipid, phosphatidic acid (PA). DAG kinases and phospholipase D, the enzymes that produce PA, are identified as key regulators in the models. Paradoxically, increasing DAG kinase activity can enhance the robustness of DAG/active PKC polarization with respect to chemoattractant concentration while decreasing their whole-cell levels. Finally, in simulations of wound invasion, efficient collective migration is achieved with thresholds for chemotaxis matching those of polarization in the reaction-diffusion models. This multi-scale modeling framework offers testable predictions to guide further study of signal transduction and cell behavior that affect mesenchymal chemotaxis.

Stochastic modeling of human papillomavirusearly promoter gene regulation.

High risk forms of human papillomaviruses (HPVs) promote cancerous lesions and are implicated in almost all cervical cancer. Of particular relevance to cancer progression is regulation of the early promoter that controls gene expression in the initial phases of infection and can eventually lead to pre-cancer progression. Our goal was to develop a stochastic model to investigate the control mechanisms that regulate gene expression from the HPV early promoter. Our model integrates modules that account for transcriptional, post-transcriptional, translational and post-translational regulation of E1 and E2 early genes to form a functioning gene regulatory network. Each module consists of a set of biochemical steps whose stochastic evolution is governed by a chemical Master Equation and can be simulated using the Gillespie algorithm. To investigate the role of noise in gene expression, we compared our stochastic simulations with solutions to ordinary differential equations for the mean behavior of the system that are valid under the conditions of large molecular abundances and quasi-equilibrium for fast reactions. The model produced results consistent with known HPV biology. Our simulation results suggest that stochasticity plays a pivotal role in determining the dynamics of HPV gene expression. In particular, the combination of positive and negative feedback regulation generates stochastic bursts of gene expression. Analysis of the model reveals that regulation at the promoter affects burst amplitude and frequency, whereas splicing is more specialized to regulate burst frequency. Our results also suggest that splicing enhancers are a significant source of stochasticity in pre-mRNA abundance and that the number of viruses infecting the host cell represents a third important source of stochasticity in gene expression.

Ratiometric GPCR signaling enables directional sensing in yeast.

Accurate detection of extracellular chemical gradients is essential for many cellular behaviors. Gradient sensing is challenging for small cells, which can experience little difference in ligand concentrations on the up-gradient and down-gradient sides of the cell. Nevertheless, the tiny cells of the yeast Saccharomyces cerevisiae reliably decode gradients of extracellular pheromones to find their mates. By imaging the behavior of polarity factors and pheromone receptors, we quantified the accuracy of initial polarization during mating encounters. We found that cells bias the orientation of initial polarity up-gradient, even though they have unevenly distributed receptors. Uneven receptor density means that the gradient of ligand-bound receptors does not accurately reflect the external pheromone gradient. Nevertheless, yeast cells appear to avoid being misled by responding to the fraction of occupied receptors rather than simply the concentration of ligand-bound receptors. Such ratiometric sensing also serves to amplify the gradient of active G protein. However, this process is quite error-prone, and initial errors are corrected during a subsequent indecisive phase in which polarity clusters exhibit erratic mobile behavior.

Software for lattice light-sheet imaging of FRET biosensors, illustrated with a new Rap1 biosensor.

Lattice light-sheet microscopy (LLSM) is valuable for its combination of reduced photobleaching and outstanding spatiotemporal resolution in 3D. Using LLSM to image biosensors in living cells could provide unprecedented visualization of rapid, localized changes in protein conformation or posttranslational modification. However, computational manipulations required for biosensor imaging with LLSM are challenging for many software packages. The calculations require processing large amounts of data even for simple changes such as reorientation of cell renderings or testing the effects of user-selectable settings, and lattice imaging poses unique challenges in thresholding and ratio imaging. We describe here a new software package, named ImageTank, that is specifically designed for practical imaging of biosensors using LLSM. To demonstrate its capabilities, we use a new biosensor to study the rapid 3D dynamics of the small GTPase Rap1 in vesicles and cell protrusions.