A Model for Direction Sensing in Dictyostelium discoideum: Ras Activity and Symmetry Breaking Driven by a Gβγ-Mediated, Gα2-Ric8 -- Dependent Signal Transduction Network

A bulk-surface mechanobiochemical modelling approach for single cell migration in two-space dimensions

In this work, we present a mechanobiochemical model for two-dimensional cell migration which couples mechanical properties of the cell cytosol with biochemical processes taking place near or on the cell plasma membrane. The modelling approach is based on a recently developed mathematical formalism of evolving bulk-surface partial differential equations of reaction-diffusion type. We solve these equations using finite element methods within a moving-mesh framework derived from the weak formulation of the evolving bulk-surface PDEs. In the present work, the cell cytosol interior (bulk) dynamics are coupled to the cell membrane (surface) dynamics through non-homogeneous Dirichlet boundary conditions. The modelling approach exhibits both directed cell migration in response to chemical cues as well as spontaneous migration in the absence of such cues. As a by-product, the approach shows fundamental characteristics associated with single cell migration such as: (i) cytosolic and membrane polarisation, (ii) actin dependent protrusions, and (iii) continuous shape deformation of the cell during migration. Cell migration is an ubiquitous process in life that is mainly triggered by the dynamics of the actin cytoskeleton and therefore is driven by both mechanical and biochemical processes. It is a multistep process essential for mammalian organisms and is closely linked to a vast diversity of processes; from embryonic development to cancer invasion. Experimental, theoretical and computational studies have been key to elucidate the mechanisms underlying cell migration. On one hand, rapid advances in experimental techniques allow for detailed experimental measurements of cell migration pathways, while, on the other, computational approaches allow for the modelling, analysis and understanding of such observations. The bulk-surface mechanobiochemical modelling approach presented in this work, set premises to study single cell migration through complex non-isotropic environments in two- and three-space dimensions.

Ras suppression potentiates rear actomyosin contractility-driven cell polarization and migration

Ras has been extensively studied as a promoter of cell proliferation, whereas few studies have explored its role in migration. To investigate the direct and immediate effects of Ras activity on cell motility or polarity, we focused on RasGAPs, C2GAPB in Dictyostelium amoebae and RASAL3 in HL-60 neutrophils and macrophages. In both cellular systems, optically recruiting the respective RasGAP to the cell front extinguished pre-existing protrusions and changed migration direction. However, when these respective RasGAPs were recruited uniformly to the membrane, cells polarized and moved more rapidly, whereas targeting to the back exaggerated these effects. These unexpected outcomes of attenuating Ras activity naturally had strong, context-dependent consequences for chemotaxis. The RasGAP-mediated polarization depended critically on myosin II activity and commenced with contraction at the cell rear, followed by sustained mTORC2-dependent actin polymerization at the front. These experimental results were captured by computational simulations in which Ras levels control front- and back-promoting feedback loops. The discovery that inhibiting Ras activity can produce counterintuitive effects on cell migration has important implications for future drug-design strategies targeting oncogenic Ras.

Ras inhibitors gate chemoattractant concentration range for chemotaxis through controlling GPCR-mediated adaptation and cell sensitivity

Chemotaxis plays an essential role in recruitment of leukocytes to sites of inflammation. Eukaryotic cells sense chemoattractant with G protein-coupled receptors (GPCRs) and chemotax toward gradients with an enormous concentration range through adaptation. Cells in adaptation no longer respond to the present stimulus but remain sensitive to stronger stimuli. Thus, adaptation provides a fundamental strategy for eukaryotic cells to chemotax through a gradient. Ras activation is the first step in the chemosensing GPCR signaling pathways that displays a transient activation behavior in both model organism Dictyostelium discoideum and mammalian neutrophils. Recently, it has been revealed that C2GAP1 and CAPRI control the GPCR-mediated adaptation in D. discoideum and human neutrophils, respectively. More importantly, both Ras inhibitors regulate the sensitivity of the cells. These findings suggest an evolutionarily conserved molecular mechanism by which eukaryotic cells gate concentration range of chemoattractants for chemotaxis.

A systems approach to investigate GPCR-mediated Ras signaling network in chemoattractant sensing

A GPCR-mediated signaling network enables a chemotactic cell to generate adaptative Ras signaling in response to a large range of concentrations of a chemoattractant. To explore potential regulatory mechanisms of GPCR-controlled Ras signaling in chemosensing, we applied a software package, Simmune, to construct detailed spatiotemporal models simulating responses of the cAR1-mediated Ras signaling network. We first determined the dynamics of G-protein activation and Ras signaling in Dictyostelium cells in response to cAMP stimulations using live-cell imaging and then constructed computation models by incorporating potential mechanisms. Using simulations, we validated the dynamics of signaling events and predicted the dynamic profiles of those events in the cAR1-mediated Ras signaling networks with defective Ras inhibitory mechanisms, such as without RasGAP, with RasGAP overexpression, or with RasGAP hyperactivation. We describe a method of using Simmune to construct spatiotemporal models of a signaling network and run computational simulations without writing mathematical equations. This approach will help biologists to develop and analyze computational models that parallel live-cell experiments.

How Phagocytes Acquired the Capability of Hunting and Removing Pathogens From a Human Body: Lessons Learned From Chemotaxis and Phagocytosis of Dictyostelium discoideum (Review)

How phagocytes find invading microorganisms and eliminate pathogenic ones from human bodies is a fundamental question in the study of infectious diseases. About 2.5 billion years ago, eukaryotic unicellular organisms-protozoans-appeared and started to interact with various bacteria. Less than 1 billion years ago, multicellular animals-metazoans-appeared and acquired the ability to distinguish self from non-self and to remove harmful organisms from their bodies. Since then, animals have developed innate immunity in which specialized white-blood cells phagocytes- patrol the body to kill pathogenic bacteria. The social amoebae Dictyostelium discoideum are prototypical phagocytes that chase various bacteria via chemotaxis and consume them as food via phagocytosis. Studies of this genetically amendable organism have revealed evolutionarily conserved mechanisms underlying chemotaxis and phagocytosis and shed light on studies of phagocytes in mammals. In this review, we briefly summarize important studies that contribute to our current understanding of how phagocytes effectively find and kill pathogens via chemotaxis and phagocytosis.

Three-dimensional stochastic simulation of chemoattractant-mediated excitability in cells

During the last decade, a consensus has emerged that the stochastic triggering of an excitable system drives pseudopod formation and subsequent migration of amoeboid cells. The presence of chemoattractant stimuli alters the threshold for triggering this activity and can bias the direction of migration. Though noise plays an important role in these behaviors, mathematical models have typically ignored its origin and merely introduced it as an external signal into a series of reaction-diffusion equations. Here we consider a more realistic description based on a reaction-diffusion master equation formalism to implement these networks. In this scheme, noise arises naturally from a stochastic description of the various reaction and diffusion terms. Working on a three-dimensional geometry in which separate compartments are divided into a tetrahedral mesh, we implement a modular description of the system, consisting of G-protein coupled receptor signaling (GPCR), a local excitation-global inhibition mechanism (LEGI), and signal transduction excitable network (STEN). Our models implement detailed biochemical descriptions whenever this information is available, such as in the GPCR and G-protein interactions. In contrast, where the biochemical entities are less certain, such as the LEGI mechanism, we consider various possible schemes and highlight the differences between them. Our simulations show that even when the LEGI mechanism displays perfect adaptation in terms of the mean level of proteins, the variance shows a dose-dependence. This differs between the various models considered, suggesting a possible means for determining experimentally among the various potential networks. Overall, our simulations recreate temporal and spatial patterns observed experimentally in both wild-type and perturbed cells, providing further evidence for the excitable system paradigm. Moreover, because of the overall importance and ubiquity of the modules we consider, including GPCR signaling and adaptation, our results will be of interest beyond the field of directed migration.

Though the term noise usually carries negative connotations, it can also contribute positively to the characteristic dynamics of a system. In biological systems, where noise arises from the stochastic interactions between molecules, its study is usually confined to genetic regulatory systems in which copy numbers are small and fluctuations large. However, noise can have important roles when the number of signaling molecules is large. The extension of pseudopods and the subsequent motion of amoeboid cells arises from the noise-induced trigger of an excitable system. Chemoattractant signals bias this triggering thereby directing cell motion. To date, this paradigm has not been tested by mathematical models that account accurately for the noise that arises in the corresponding reactions. In this study, we employ a reaction-diffusion master equation approach to investigate the effects of noise. Using a modular approach and a three-dimensional cell model with specific subdomains attributed to the cell membrane and cortex, we explore the spatiotemporal dynamics of the system. Our simulations recreate many experimentally-observed cell behaviors thereby supporting the biased-excitable network hypothesis.

Mathematical modeling of chemotaxis guided amoeboid cell swimming

Cells and microorganisms adopt various strategies to migrate in response to different environmental stimuli. To date, many modeling research has focused on the crawling-basedDictyostelium discoideum(Dd) cells migration induced by chemotaxis, yet recent experimental results reveal that even without adhesion or contact to a substrate, Dd cells can still swim to follow chemoattractant signals. In this paper, we develop a modeling framework to investigate the chemotaxis induced amoeboid cell swimming dynamics. A minimal swimming system consists of one deformable Dd amoeboid cell and a dilute suspension of bacteria, and the bacteria produce chemoattractant signals that attract the Dd cell. We use themathematical amoeba modelto generate Dd cell deformation and solve the resulting low Reynolds number flows, and use a moving mesh based finite volume method to solve the reaction-diffusion-convection equation. Using the computational model, we show that chemotaxis guides a swimming Dd cell to follow and catch bacteria, while on the other hand, bacterial rheotaxis may help the bacteria to escape from the predator Dd cell.

Multiscale phenomena and patterns in biological systems: special issue in honour of Hans Othmer

This special issue on "Multiscale phenomena and patterns in biological systems" is an homage to the seminal contributions of Hans Othmer. He has remained at the forefront of multiscale modelling and pattern formation in biology for over half a century, developing models for molecular signalling networks, the mechanics of cellular movements, the interactions between multiple cells and their contributions to tissue patterning and dynamics. The contributions in this special issue follow Hans' legacy in using advanced mathematics to understand complex biological processes.

Spatial gradient sensing and chemotaxis via excitability in Dictyostelium discoideum

The social amoeba Dictyostelium discoideum performs chemotaxis under starvation conditions, aggregating towards clusters of cells following waves of the signaling molecule cAMP. Cells sense extracellular cAMP and produce internal caches of cAMP to be released, relaying the signal. These events lead to traveling waves of cAMP washing over the population of cells. While much research has been performed to understand the functioning of the chemotaxis network in D. discoideum, limited work has been done to link the operation of the signal relay network with the chemotaxis network to provide a holistic view of the system. We take inspiration from D. discoideum and propose a model that directly links the relaying of a chemical message to the directional sensing of that signal. Utilizing an excitable dynamical systems model that has been previously validated experimentally, we show that it is possible to have both signal amplification and perfect adaptation in a single module. We show that noise plays a vital role in chemotaxing to static gradients, where stochastic tunneling of transient bursts biases the system towards accurate gradient sensing. Moreover, this model also automatically matches its internal time scale of adaptation to the naturally occurring periodicity of the traveling chemical waves generated in the population. Numerical simulations were performed to study the qualitative phenomenology of the system and explore how the system responds to diverse dynamic spatiotemporal stimuli. Finally, we address dynamical instabilities that impede chemotactic ability in a continuum version of the model.

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.

Rapid exposure of macrophages to drugs resolves four classes of effects on the leading edge sensory pseudopod: Non-perturbing, adaptive, disruptive, and activating

Leukocyte migration is controlled by a membrane-based chemosensory pathway on the leading edge pseudopod that guides cell movement up attractant gradients during the innate immune and inflammatory responses. This study employed single cell and population imaging to investigate drug-induced perturbations of leading edge pseudopod morphology in cultured, polarized RAW macrophages. The drugs tested included representative therapeutics (acetylsalicylic acid, diclofenac, ibuprofen, acetaminophen) as well as control drugs (PDGF, Gö6976, wortmannin). Notably, slow addition of any of the four therapeutics to cultured macrophages, mimicking the slowly increasing plasma concentration reported for standard oral dosage in patients, yielded no detectable change in pseudopod morphology. This finding is consistent with the well established clinical safety of these drugs. However, rapid drug addition to cultured macrophages revealed four distinct classes of effects on the leading edge pseudopod: (i) non-perturbing drug exposures yielded no detectable change in pseudopod morphology (acetylsalicylic acid, diclofenac); (ii) adaptive exposures yielded temporary collapse of the extended pseudopod and its signature PI(3,4,5)P3 lipid signal followed by slow recovery of extended pseudopod morphology (ibuprofen, acetaminophen); (iii) disruptive exposures yielded long-term pseudopod collapse (Gö6976, wortmannin); and (iv) activating exposures yielded pseudopod expansion (PDGF). The novel observation of adaptive exposures leads us to hypothesize that rapid addition of an adaptive drug overwhelms an intrinsic or extrinsic adaptation system yielding temporary collapse followed by adaptive recovery, while slow addition enables gradual adaptation to counteract the drug perturbation in real time. Overall, the results illustrate an approach that may help identify therapeutic drugs that temporarily inhibit the leading edge pseudopod during extreme inflammation events, and toxic drugs that yield long term inhibition of the pseudopod with negative consequences for innate immunity. Future studies are needed to elucidate the mechanisms of drug-induced pseudopod collapse, as well as the mechanisms of adaptation and recovery following some inhibitory drug exposures.

The Use of Diffusion Calculations and Monte Carlo Simulations to Understand the Behavior of Cells in Dictyostelium Communities

Microbial communities are the simplest possible model of multicellular tissues, allowing studies of cell-cell interactions to be done with as few extraneous factors as possible. For instance, the eukaryotic microbe Dictyostelium discoideum proliferates as single cells, and when starved, the cells aggregate together and form structures of ~20,000 cells. The cells use a variety of signals to direct their movement, inform each other of their local cell density and whether they are starving, and organize themselves into groups of ~20,000 cells. Mathematical models and computational approaches have been a key check on, and guide of, the experimental work. In this minireview, I will discuss diffusion calculations and Monte Carlo simulations that were used for Dictyostelium studies that offer general paradigms for several aspects of cell-cell communication. For instance, computational work showed that diffusible secreted cell-density sensing (quorum) factors can diffuse away so quickly from a single cell that the local concentration will not build up to incorrectly cause the cell to sense that it is in the presence of a high density of other cells secreting that signal. In another example, computation correctly predicted a mechanism that allows a group of cells to break up into subgroups. These are thus some examples of the power and necessity of computational work in biology.

Eukaryotic Cell Dynamics from Crawlers to Swimmers

Movement requires force transmission to the environment, and motile cells are robustly, though not elegantly, designed nanomachines that often can cope with a variety of environmental conditions by altering the mode of force transmission used. As with humans, the available modes range from momentary attachment to a substrate when crawling, to shape deformations when swimming, and at the cellular level this involves sensing the mechanical properties of the environment and altering the mode appropriately. While many types of cells can adapt their mode of movement to their microenvironment (ME), our understanding of how they detect, transduce and process information from the ME to determine the optimal mode is still rudimentary. The shape and integrity of a cell is determined by its cytoskeleton (CSK), and thus the shape changes that may be required to move involve controlled remodeling of the CSK. Motion in vivo is often in response to extracellular signals, which requires the ability to detect such signals and transduce them into the shape changes and force generation needed for movement. Thus the nanomachine is complex, and while much is known about individual components involved in movement, an integrated understanding of motility in even simple cells such as bacteria is not at hand. In this review we discuss recent advances in our understanding of cell motility and some of the problems remaining to be solved.

Reaction fronts of the autocatalytic hydrogenase reaction

We have built a model to describe the hydrogenase catalyzed, autocatalytic, reversible hydrogen oxidation reaction where one of the enzyme forms is the autocatalyst. The model not only reproduces the experimentally observed front properties, but also explains the found hydrogen ion dependence. Furthermore, by linear stability analysis, two different front types are found in good agreement with the experiments.

Non-Gaussianity, population heterogeneity, and transient superdiffusion in the spreading dynamics of amoeboid cells

What is the underlying diffusion process governing the spreading dynamics and search strategies employed by amoeboid cells?

QSP Toolbox: Computational Implementation of Integrated Workflow Components for Deploying Multi-Scale Mechanistic Models

Quantitative systems pharmacology (QSP) modeling has become increasingly important in pharmaceutical research and development, and is a powerful tool to gain mechanistic insights into the complex dynamics of biological systems in response to drug treatment. However, even once a suitable mathematical framework to describe the pathophysiology and mechanisms of interest is established, final model calibration and the exploration of variability can be challenging and time consuming. QSP models are often formulated as multi-scale, multi-compartment nonlinear systems of ordinary differential equations. Commonly accepted modeling strategies, workflows, and tools have promise to greatly improve the efficiency of QSP methods and improve productivity. In this paper, we present the QSP Toolbox, a set of functions, structure array conventions, and class definitions that computationally implement critical elements of QSP workflows including data integration, model calibration, and variability exploration. We present the application of the toolbox to an ordinary differential equations-based model for antibody drug conjugates. As opposed to a single stepwise reference model calibration, the toolbox also facilitates simultaneous parameter optimization and variation across multiple in vitro, in vivo, and clinical assays to more comprehensively generate alternate mechanistic hypotheses that are in quantitative agreement with available data. The toolbox also includes scripts for developing and applying virtual populations to mechanistic exploration of biomarkers and efficacy. We anticipate that the QSP Toolbox will be a useful resource that will facilitate implementation, evaluation, and sharing of new methodologies in a common framework that will greatly benefit the community.

Expanding the scale of molecular biophysics

Here, I argue that some of the secrets of complex biological function rely on assemblies of many heterogeneous proteins that together enable sophisticated sensing and actuating processes. Evolution seems to delight in making these structures and in continually elaborating upon their capabilities. Developing tools that can go beyond the few protein limit, both on the experimental frontier and from a theoretical, conceptual framework, should be an extremely high priority for the next generation of molecular biophysicists.

Progress and perspectives in signal transduction, actin dynamics, and movement at the cell and tissue level: lessons from Dictyostelium

Movement of cells and tissues is a basic biological process that is used in development, wound repair, the immune response to bacterial invasion, tumour formation and metastasis, and the search for food and mates. While some cell movement is random, directed movement stimulated by extracellular signals is our focus here. This involves a sequence of steps in which cells first detect extracellular chemical and/or mechanical signals via membrane receptors that activate signal transduction cascades and produce intracellular signals. These intracellular signals control the motile machinery of the cell and thereby determine the spatial localization of the sites of force generation needed to produce directed motion. Understanding how force generation within cells and mechanical interactions with their surroundings, including other cells, are controlled in space and time to produce cell-level movement is a major challenge, and involves many issues that are amenable to mathematical modelling.