A Predictive Model for Yeast Cell Polarization in Pheromone Gradients

Redundancy and the role of protein copy numbers in the cell polarization machinery of budding yeast

How can a self-organized cellular function evolve, adapt to perturbations, and acquire new sub-functions? To make progress in answering these basic questions of evolutionary cell biology, we analyze, as a concrete example, the cell polarity machinery of Saccharomyces cerevisiae. This cellular module exhibits an intriguing resilience: it remains operational under genetic perturbations and recovers quickly and reproducibly from the deletion of one of its key components. Using a combination of modeling, conceptual theory, and experiments, we propose that multiple, redundant self-organization mechanisms coexist within the protein network underlying cell polarization and are responsible for the module's resilience and adaptability. Based on our mechanistic understanding of polarity establishment, we hypothesize that scaffold proteins, by introducing new connections in the existing network, can increase the redundancy of mechanisms and thus increase the evolvability of other network components. Moreover, our work gives a perspective on how a complex, redundant cellular module might have evolved from a more rudimental ancestral form.

Describing the movement of molecules in reduced-dimension models

When addressing spatial biological questions using mathematical models, symmetries within the system are often exploited to simplify the problem by reducing its physical dimension. In a reduced-dimension model molecular movement is restricted to the reduced dimension, changing the nature of molecular movement. This change in molecular movement can lead to quantitatively and even qualitatively different results in the full and reduced systems. Within this manuscript we discuss the condition under which restricted molecular movement in reduced-dimension models accurately approximates molecular movement in the full system. For those systems which do not satisfy the condition, we present a general method for approximating unrestricted molecular movement in reduced-dimension models. We will derive a mathematically robust, finite difference method for solving the 2D diffusion equation within a 1D reduced-dimension model. The methods described here can be used to improve the accuracy of many reduced-dimension models while retaining benefits of system simplification.

Flow-assembled chitosan membranes in microfluidics: recent advances and applications

The integration of membranes in microfluidic devices has been extensively exploited for various chemical engineering and bioengineering applications over the past few decades. To augment the applicability of membrane-integrated microfluidic platforms for biomedical and tissue engineering studies, a biologically friendly fabrication process with naturally occurring materials is highly desired. The in situ preparation of membranes involving interfacial reactions between parallel laminar flows in microfluidic networks, known as the flow-assembly technique, is one of the most biocompatible approaches. Membranes of many types with flexible geometries have been successfully assembled inside complex microchannels using this facile and versatile flow-assembly approach. Chitosan is a naturally abundant polysaccharide known for its pronounced biocompatibility, biodegradability, good mechanical stability, ease of modification and processing, and film-forming ability under near-physiological conditions. Chitosan membranes assembled by flows in microfluidics are freestanding, robust, semipermeable, and well-aligned in microstructure, and show high affinity to bioactive reagents and biological components (e.g. biomolecules, nanoparticles, or cells) that provide facile biological functionalization of microdevices. Here, we discuss the recent developments and optimizations in the flow-assembly of chitosan membranes and chitosan-based membranes in microfluidics. Furthermore, we recapitulate the applications of the chitosan membrane-integrated microfluidic platforms dedicated to biology, biochemistry, and drug release fields, and envision the future developments of this important platform with versatile functions.

The Roles of Signaling in Cytoskeletal Changes, Random Movement, Direction-Sensing and Polarization of Eukaryotic Cells

Movement of cells and tissues is essential at various stages during the lifetime of an organism, including morphogenesis in early development, in the immune response to pathogens, and during wound-healing and tissue regeneration. Individual cells are able to move in a variety of microenvironments (MEs) (A glossary of the acronyms used herein is given at the end) by suitably adapting both their shape and how they transmit force to the ME, but how cells translate environmental signals into the forces that shape them and enable them to move is poorly understood. While many of the networks involved in signal detection, transduction and movement have been characterized, how intracellular signals control re-building of the cyctoskeleton to enable movement is not understood. In this review we discuss recent advances in our understanding of signal transduction networks related to direction-sensing and movement, and some of the problems that remain to be solved.

Mitotic and pheromone-specific intrinsic polarization cues interfere with gradient sensing in Saccharomyces cerevisiae

Polarity decisions are central to many processes, including mitosis and chemotropism. In Saccharomyces cerevisiae, budding and mating projection (MP) formation use an overlapping system of cortical landmarks that converges on the small G protein Cdc42. However, pheromone-gradient sensing must override the Rsr1-dependent internal polarity cues used for budding. Using this model system, we asked what happens when intrinsic and extrinsic spatial cues are not aligned. Is there competition, or collaboration? By live-cell microscopy and microfluidics techniques, we uncovered three previously overlooked features of this signaling system. First, the cytokinesis-associated polarization patch serves as a polarity landmark independently of all known cues. Second, the Rax1-Rax2 complex functions as a pheromone-promoted polarity cue in the distal pole of the cells. Third, internal cues remain active during pheromone-gradient tracking and can interfere with this process, biasing the location of MPs. Yeast defective in internal-cue utilization align significantly better than wild type with artificially generated pheromone gradients.

Chemotropism among populations of yeast cells with spatiotemporal resolution in a biofabricated microfluidic platform

Chemotropism is an essential response of organisms to external chemical gradients that direct the growth of cells toward the gradient source. Chemotropic responses between single cells have been studied using in vitro gradients of synthetically derived signaling molecules and helped to develop a better understanding of chemotropism in multiple organisms. However, dynamic changes including spatial changes to the gradient as well as fluctuations in levels of cell generated signaling molecules can result in the redirection of chemotropic responses, which can be difficult to model with synthetic peptides and single cells. An experimental system that brings together populations of cells to monitor the population-scale chemotropic responses yet retain single cell spatiotemporal resolution would be useful to further inform on models of chemotropism. Here, we describe a microfluidic platform that can measure the chemotropic response between populations of mating yeast A- and α-cells with spatiotemporal programmability and sensitivity by positioning cell populations side by side in calcium alginate hydrogels along semipermeable membranes with micrometer spatial control. The mating phenotypes of the yeast populations were clearly observed over hours. Three distinct responses were observed depending on the distance between the A- and α-cell populations: the cells either continued to divide, arrest, and develop a stereotypical polarized projection termed a "shmoo" toward the cells of opposite mating type or formed shmoos in random directions. The results from our studies of yeast mating suggest that the biofabricated microfluidic platform can be adopted to study population-scale, spatial-sensitive cell-cell signaling behaviors that would be challenging using conventional approaches.

Molecular mechanisms of chemotropism and cell fusion in unicellular fungi

In all eukaryotic phyla, cell fusion is important for many aspects of life, from sexual reproduction to tissue formation. Fungal cells fuse during mating to form the zygote, and during vegetative growth to connect mycelia. Prior to fusion, cells first detect gradients of pheromonal chemoattractants that are released by their partner and polarize growth in their direction. Upon pairing, cells digest their cell wall at the site of contact and merge their plasma membrane. In this Review, I discuss recent work on the chemotropic response of the yeast models Saccharomyces cerevisiae and Schizosaccharomyces pombe, which has led to a novel model of gradient sensing: the cell builds a motile cortical polarized patch, which acts as site of communication where pheromones are released and sensed. Initial patch dynamics serve to correct its position and align it with the gradient from the partner cell. Furthermore, I highlight the transition from cell wall expansion during growth to cell wall digestion, which is imposed by physical and signaling changes owing to hyperpolarization that is induced by cell proximity. To conclude, I discuss mechanisms of membrane fusion, whose characterization remains a major challenge for the future.

Self-organization principles of intracellular pattern formation

Dynamic patterning of specific proteins is essential for the spatio-temporal regulation of many important intracellular processes in prokaryotes, eukaryotes and multicellular organisms. The emergence of patterns generated by interactions of diffusing proteins is a paradigmatic example for self-organization. In this article, we review quantitative models for intracellular Min protein patterns in Escherichia coli, Cdc42 polarization in Saccharomyces cerevisiae and the bipolar PAR protein patterns found in Caenorhabditis elegans. By analysing the molecular processes driving these systems we derive a theoretical perspective on general principles underlying self-organized pattern formation. We argue that intracellular pattern formation is not captured by concepts such as ‘activators’, ‘inhibitors’ or ‘substrate depletion’. Instead, intracellular pattern formation is based on the redistribution of proteins by cytosolic diffusion, and the cycling of proteins between distinct conformational states. Therefore, mass-conserving reaction–diffusion equations provide the most appropriate framework to study intracellular pattern formation. We conclude that directed transport, e.g. cytosolic diffusion along an actively maintained cytosolic gradient, is the key process underlying pattern formation. Thus the basic principle of self-organization is the establishment and maintenance of directed transport by intracellular protein dynamics.

This article is part of the theme issue ‘Self-organization in cell biology’.

eGFRD in all dimensions

Biochemical reactions often occur at low copy numbers but at once in crowded and diverse environments. Space and stochasticity therefore play an essential role in biochemical networks. Spatial-stochastic simulations have become a prominent tool for understanding how stochasticity at the microscopic level influences the macroscopic behavior of such systems. While particle-based models guarantee the level of detail necessary to accurately describe the microscopic dynamics at very low copy numbers, the algorithms used to simulate them typically imply trade-offs between computational efficiency and biochemical accuracy. eGFRD (enhanced Green's Function Reaction Dynamics) is an exact algorithm that evades such trade-offs by partitioning the N-particle system into M ≤ N analytically tractable one- and two-particle systems; the analytical solutions (Green's functions) then are used to implement an event-driven particle-based scheme that allows particles to make large jumps in time and space while retaining access to their state variables at arbitrary simulation times. Here we present "eGFRD2," a new eGFRD version that implements the principle of eGFRD in all dimensions, thus enabling efficient particle-based simulation of biochemical reaction-diffusion processes in the 3D cytoplasm, on 2D planes representing membranes, and on 1D elongated cylinders representative of, e.g., cytoskeletal tracks or DNA; in 1D, it also incorporates convective motion used to model active transport. We find that, for low particle densities, eGFRD2 is up to 6 orders of magnitude faster than conventional Brownian dynamics. We exemplify the capabilities of eGFRD2 by simulating an idealized model of Pom1 gradient formation, which involves 3D diffusion, active transport on microtubules, and autophosphorylation on the membrane, confirming recent experimental and theoretical results on this system to hold under genuinely stochastic conditions.

Multicompartment cell-based modeling of confined migration: regulation by cell intrinsic and extrinsic factors

Though cell and nuclear deformability are expected to influence efficiency of confined migration, their individual and collective influence on migration efficiency remains incompletely understood. In addition to cell intrinsic properties, the relevance of cell extrinsic factors on confined migration, if any, has not been adequately explored. Here we address these questions using a statistical mechanics-based stochastic modeling approach where cell/nuclear dimensions and their deformability are explicitly taken into consideration. In addition to demonstrating the importance of cell softness in sustaining confined migration, our results suggest that dynamic tuning of cell and nuclear properties at different stages of migration is essential for maximizing migration efficiency. Our simulations also implicate confinement shape and confinement history as two important cell extrinsic regulators of cell invasiveness. Together, our findings illustrate the strength of a multicompartment model in dissecting the contributions of multiple factors that collectively influence confined cell migration.

Bridging intracellular scales by mechanistic computational models

The impact of intracellular spatial organization beyond classical compartments on processes such as cell signaling is increasingly recognized. A quantitative, mechanistic understanding of cellular systems therefore needs to account for different scales in at least three coordinates: time, molecular abundances, and space. Mechanistic mathematical models may span all these scales, but corresponding multi-scale models need to resolve mechanistic details on small scales while maintaining computational tractability for larger ones. This typically results in models that combine different levels of description: from a microscopic representation of chemical reactions up to continuum dynamics in space and time. We highlight recent progress in bridging these model classes and outline current challenges in multi-scale models such as active transport and dynamic geometries.

Local sampling paints a global picture: Local concentration measurements sense direction in complex chemical gradients

Detecting and interpreting extracellular spatial signals is essential for cellular orientation within complex environments, such as during directed cell migration or growth in multicellular development. Although the molecular understanding of how cells read spatial signals like chemical gradients is still lacking, recent work has revealed that stochastic processes at different temporal and spatial scales are at the core of this gradient sensing process in a wide range of eukaryotes. Fast biochemical reactions like those underlying GTPase activity dynamics form a functional module together with slower cell morphological changes driven by membrane remodelling. This biochemical-morphological module explores the environment by stochastic local concentration sampling to determine the source of the gradient signal, enabling efficient signal detection and interpretation before polarised growth or migration towards the gradient source is initiated. Here we review recent data describing local sampling and propose a model of local fast and slow feedback counteracted by gradient-dependent substrate limitation to be at the core of gradient sensing by local sampling.