How cells integrate complex stimuli: the effect of feedback from phosphoinositides and cell shape on cell polarization and motility

Dynamics of Cell Ensembles on Adhesive Micropatterns: Bridging the Gap between Single Cell Spreading and Collective Cell Migration

The collective dynamics of multicellular systems arise from the interplay of a few fundamental elements: growth, division and apoptosis of single cells; their mechanical and adhesive interactions with neighboring cells and the extracellular matrix; and the tendency of polarized cells to move. Micropatterned substrates are increasingly used to dissect the relative roles of these fundamental processes and to control the resulting dynamics. Here we show that a unifying computational framework based on the cellular Potts model can describe the experimentally observed cell dynamics over all relevant length scales. For single cells, the model correctly predicts the statistical distribution of the orientation of the cell division axis as well as the final organisation of the two daughters on a large range of micropatterns, including those situations in which a stable configuration is not achieved and rotation ensues. Large ensembles migrating in heterogeneous environments form non-adhesive regions of inward-curved arcs like in epithelial bridge formation. Collective migration leads to swirl formation with variations in cell area as observed experimentally. In each case, we also use our model to predict cell dynamics on patterns that have not been studied before.

Optimizing micropattern geometries for cell shape and migration with genetic algorithms

Adhesive micropatterns have become a standard tool to control cell shape and function in cell culture.

Methods of myofibrillogenesis modeling

Organization in the heart is important on multiple length scales. Myofibrillogenesis processes control the assembly of this multi-scale architecture. Understanding myofibrillogenesis might allow us to better control self-assembly of cardiac tissues. One approach consists of creating phenomenological models and comparing these models to in vitro data from primary myocytes. In this chapter, we present a method for building these models to recapitulate different aspects of myofibrillogenesis. We present a specific example for a cardiomyocyte model, but the same procedure can be used to model fibrillogenesis with other mechanisms such as motility. In sum, the models allow for a better understanding of mechanisms behind self-assembly.

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.

Cdc42 and RhoA reveal different spatio-temporal dynamics upon local stimulation with Semaphorin-3A

Small RhoGTPases, such as Cdc42 and RhoA, are key players in integrating external cues and intracellular signaling pathways that regulate growth cone (GC) motility. Indeed, Cdc42 is involved in actin polymerization and filopodia formation, whereas RhoA induces GC collapse and neurite retraction through actomyosin contraction. In this study we employed Förster Resonance Energy Transfer (FRET) microscopy to study the spatio-temporal dynamics of Cdc42 and RhoA in GCs in response to local Semaphorin-3A (Sema3A) stimulation obtained with lipid vesicles filled with Sema3A and positioned near the selected GC using optical tweezers. We found that Cdc42 and RhoA were activated at the leading edge of NG108-15 neuroblastoma cells during spontaneous cycles of protrusion and retraction, respectively. The release of Sema3A brought to a progressive activation of RhoA within 30 s from the stimulus in the central region of the GC that collapsed and retracted. In contrast, the same stimulation evoked waves of Cdc42 activation propagating away from the stimulated region. A more localized stimulation obtained with Sema3A coated beads placed on the GC, led to Cdc42 active waves that propagated in a retrograde manner with a mean period of 70 s, and followed by GC retraction. Therefore, Sema3A activates both Cdc42 and RhoA with a complex and different spatial-temporal dynamics.

Emergence and Persistence of Collective Cell Migration on Small Circular Micropatterns

The spontaneous formation of vortices is a hallmark of collective cellular activity. Here, we study the onset and persistence of coherent angular motion as a function of the number of cells N confined in circular micropatterns. We find that the persistence of coherent angular motion increases with N but exhibits a pronounced discontinuity accompanied by a geometric rearrangement of cells to a configuration containing a central cell. Computer simulations based on a generalized Potts model reproduce the emergence of vortex states and show in agreement with experiment that their stability depends on the interplay of the spatial arrangement and internal polarization of neighboring cells. Hence, the distinct migrational states in finite size ensembles reveal significant insight into the local interaction rules guiding collective migration.

Local perturbation analysis: a computational tool for biophysical reaction-diffusion models

Diffusion and interaction of molecular regulators in cells is often modeled using reaction-diffusion partial differential equations. Analysis of such models and exploration of their parameter space is challenging, particularly for systems of high dimensionality. Here, we present a relatively simple and straightforward analysis, the local perturbation analysis, that reveals how parameter variations affect model behavior. This computational tool, which greatly aids exploration of the behavior of a model, exploits a structural feature common to many cellular regulatory systems: regulators are typically either bound to a membrane or freely diffusing in the interior of the cell. Using well-documented, readily available bifurcation software, the local perturbation analysis tracks the approximate early evolution of an arbitrarily large perturbation of a homogeneous steady state. In doing so, it provides a bifurcation diagram that concisely describes various regimes of the model's behavior, reducing the need for exhaustive simulations to explore parameter space. We explain the method and provide detailed step-by-step guides to its use and application.

Dynamics of cell shape and forces on micropatterned substrates predicted by a cellular Potts model

Micropatterned substrates are often used to standardize cell experiments and to quantitatively study the relation between cell shape and function. Moreover, they are increasingly used in combination with traction force microscopy on soft elastic substrates. To predict the dynamics and steady states of cell shape and forces without any a priori knowledge of how the cell will spread on a given micropattern, here we extend earlier formulations of the two-dimensional cellular Potts model. The third dimension is treated as an area reservoir for spreading. To account for local contour reinforcement by peripheral bundles, we augment the cellular Potts model by elements of the tension-elasticity model. We first parameterize our model and show that it accounts for momentum conservation. We then demonstrate that it is in good agreement with experimental data for shape, spreading dynamics, and traction force patterns of cells on micropatterned substrates. We finally predict shapes and forces for micropatterns that have not yet been experimentally studied.

Coordinating cell polarity: heading in the right direction?

A diverse group of researchers working on both plant and animal systems met at a Company of Biologists workshop to discuss 'Coordinating Cell Polarity'. The meeting included considerable free discussion as well as presentations exploring the ways that groups of cells in these various systems achieve coordinated cell polarity. Here, we discuss commonalities, differences and themes that emerged from these sessions that will serve to inform ongoing studies.

Polarity mechanisms such as contact inhibition of locomotion regulate persistent rotational motion of mammalian cells on micropatterns

Pairs of endothelial cells on adhesive micropatterns rotate persistently, but pairs of fibroblasts do not; coherent rotation is present in normal mammary acini and kidney cells but absent in cancerous cells. Why? To answer this question, we develop a computational model of pairs of mammalian cells on adhesive micropatterns using a phase field method and study the conditions under which persistent rotational motion (PRM) emerges. Our model couples the shape of the cell, the cell's internal chemical polarity, and interactions between cells such as volume exclusion and adhesion. We show that PRM can emerge from this minimal model and that the cell-cell interface may be influenced by the nucleus. We study the effect of various cell polarity mechanisms on rotational motion, including contact inhibition of locomotion, neighbor alignment, and velocity alignment, where cells align their polarity to their velocity. These polarity mechanisms strongly regulate PRM: Small differences in polarity mechanisms can create significant differences in collective rotation. We argue that the existence or absence of rotation under confinement may lead to insight into the cell's methods for coordinating collective cell motility.

Mechanical cell-matrix feedback explains pairwise and collective endothelial cell behavior in vitro

In vitro cultures of endothelial cells are a widely used model system of the collective behavior of endothelial cells during vasculogenesis and angiogenesis. When seeded in an extracellular matrix, endothelial cells can form blood vessel-like structures, including vascular networks and sprouts. Endothelial morphogenesis depends on a large number of chemical and mechanical factors, including the compliancy of the extracellular matrix, the available growth factors, the adhesion of cells to the extracellular matrix, cell-cell signaling, etc. Although various computational models have been proposed to explain the role of each of these biochemical and biomechanical effects, the understanding of the mechanisms underlying in vitro angiogenesis is still incomplete. Most explanations focus on predicting the whole vascular network or sprout from the underlying cell behavior, and do not check if the same model also correctly captures the intermediate scale: the pairwise cell-cell interactions or single cell responses to ECM mechanics. Here we show, using a hybrid cellular Potts and finite element computational model, that a single set of biologically plausible rules describing (a) the contractile forces that endothelial cells exert on the ECM, (b) the resulting strains in the extracellular matrix, and (c) the cellular response to the strains, suffices for reproducing the behavior of individual endothelial cells and the interactions of endothelial cell pairs in compliant matrices. With the same set of rules, the model also reproduces network formation from scattered cells, and sprouting from endothelial spheroids. Combining the present mechanical model with aspects of previously proposed mechanical and chemical models may lead to a more complete understanding of in vitro angiogenesis.

Plasticity in the macromolecular-scale causal networks of cell migration

Heterogeneous and dynamic single cell migration behaviours arise from a complex multi-scale signalling network comprising both molecular components and macromolecular modules, among which cell-matrix adhesions and F-actin directly mediate migration. To date, the global wiring architecture characterizing this network remains poorly defined. It is also unclear whether such a wiring pattern may be stable and generalizable to different conditions, or plastic and context dependent. Here, synchronous imaging-based quantification of migration system organization, represented by 87 morphological and dynamic macromolecular module features, and migration system behaviour, i.e., migration speed, facilitated Granger causality analysis. We thereby leveraged natural cellular heterogeneity to begin mapping the directionally specific causal wiring between organizational and behavioural features of the cell migration system. This represents an important advance on commonly used correlative analyses that do not resolve causal directionality. We identified organizational features such as adhesion stability and adhesion F-actin content that, as anticipated, causally influenced cell migration speed. Strikingly, we also found that cell speed can exert causal influence over organizational features, including cell shape and adhesion complex location, thus revealing causality in directions contradictory to previous expectations. Importantly, by comparing unperturbed and signalling-modulated cells, we provide proof-of-principle that causal interaction patterns are in fact plastic and context dependent, rather than stable and generalizable.

Bidirectional coupling between integrin-mediated signaling and actomyosin mechanics explains matrix-dependent intermittency of leading-edge motility

A physicochemical model is used to describe the coupling of adhesion, cytoskeletal, and signaling dynamics during cell migration. Analysis of stochastic simulations predicts relationships between measurable quantities that reflect partitioning of stress between F-actin–bound adhesions, which act as a molecular clutch, and retrograde F-actin flow.

Animal cell migration is a complex process characterized by the coupling of adhesion, cytoskeletal, and signaling dynamics. Here we model local protrusion of the cell edge as a function of the load-bearing properties of integrin-based adhesions, actin polymerization fostered by adhesion-mediated signaling, and mechanosensitive activation of RhoA that promotes myosin II–generated stress on the lamellipodial F-actin network. Analysis of stochastic model simulations illustrates how these pleiotropic functions of nascent adhesions may be integrated to govern temporal persistence and frequency of protrusions. The simulations give mechanistic insight into the documented effects of extracellular matrix density and myosin abundance, and they show characteristic, nonnormal distributions of protrusion duration times that are similar to those extracted from live-cell imaging experiments. Analysis of the model further predicts relationships between measurable quantities that reflect the partitioning of stress between tension on F-actin–bound adhesions, which act as a molecular clutch, and dissipation by retrograde F-actin flow.

Periodic migration in a physical model of cells on micropatterns

We extend a model for the morphology and dynamics of a crawling eukaryotic cell to describe cells on micropatterned substrates. This model couples cell morphology, adhesion, and cytoskeletal flow in response to active stresses induced by actin and myosin. We propose that protrusive stresses are only generated where the cell adheres, leading to the cell's effective confinement to the pattern. Consistent with experimental results, simulated cells exhibit a broad range of behaviors, including steady motion, turning, bipedal motion, and periodic migration, in which the cell crawls persistently in one direction before reversing periodically. We show that periodic motion emerges naturally from the coupling of cell polarization to cell shape by reducing the model to a simplified one-dimensional form that can be understood analytically.

From simple to detailed models for cell polarization

Many mathematical models have been proposed for the process of cell polarization. Some of these are 'functional models' that capture a class of dynamical behaviour, whereas others are derived from features of signalling molecules. Some mechanistic models are detailed, and therefore complex, whereas others are simplified. Each type contributes to our understanding of cell polarization. However, the huge variety at different levels of detail makes comparisons challenging. Here, we provide examples of both elementary and more detailed models for polarization. We also display how a recent mathematical method, local perturbation analysis, can provide an appropriate tool for such comparisons. This technique simplifies and speeds up the model development process by revealing the effect of model extensions, parameter variations and in silico manipulations such as knock-out or over-expression of key molecules. Finally, simulations in both one dimension and two dimensions, and particularly in deforming two-dimensional 'cells', can highlight behaviour not captured by traditional simulation methods.

Juicy stories on female reproductive tissue development: coordinating the hormone flows

In the past 20-30 years, developmental biologists have made tremendous progress in identifying genes required for the specification of individual cell types of an organ and in describing how they interact in genetic networks. In comparison, very little is known about the mechanisms that regulate tissue polarity and overall organ patterning. Gynoecia and fruits from members of the Brassicaceae family of flowering plants provide excellent model systems to study organ patterning and tissue specification because they become partitioned into distinct domains whose formation is determined by polarity establishment both at a cellular and whole tissue level. Interactions among key regulators of Arabidopsis gynoecium and fruit development have revealed a network of upstream transcription factor activities required for such tissue differentiation. Regulation of the plant hormone auxin is emerging as both an immediate downstream output and input of these activities, and here we aim to provide an overview of the current knowledge regarding the link between auxin and female reproductive development in plants. In this review, we will also demonstrate how available data can be exploited in a mathematical modeling approach to reveal and understand the feedback regulatory circuits that underpin the polarity establishment, necessary to guide auxin flows.

Cell and tissue deformation measurements: texture correlation with third-order approximation of displacement gradients

Cells remarkably are capable of large deformations during motility and when subjected to mechanical force. Measurement of mechanical deformation (i.e. displacements, strain) is critical to understand functional changes in cells and biological tissues following disease, and to elucidate basic relationships between applied force and cellular biosynthesis. Microscopy-based imaging modalities provide the ability to noninvasively visualize small cell or tissue structures and track their motion over time, often using two-dimensional (2D) digital image (texture) correlation algorithms. For the measurement of complex and nonlinear motion in cells and tissues, implementation of texture correlation algorithms with high order approximations of displacement mapping terms are needed to minimize error. Here, we extend a texture correlation algorithm with up to third-order approximation of displacement mapping terms for the measurement of cell and tissue deformation. We additionally investigate relationships between measurement error and image texture, defined by subset entropy. Displacement measurement error is significantly reduced when the order of displacement mapping terms in the texture correlation algorithm matches or exceeds the order of the deformation observed. Displacement measurement error is also inversely proportional to subset entropy, with well-defined cell and tissue structures leading to high entropy and low error. For cell and tissue studies where complex or nonlinear displacements are expected, texture correlation algorithms with high order terms are required to best characterize the observed deformation.

Interaction of motility, directional sensing, and polarity modules recreates the behaviors of chemotaxing cells

Chemotaxis involves the coordinated action of separable but interrelated processes: motility, gradient sensing, and polarization. We have hypothesized that these are mediated by separate modules that account for these processes individually and that, when combined, recreate most of the behaviors of chemotactic cells. Here, we describe a mathematical model where the modules are implemented in terms of reaction-diffusion equations. Migration and the accompanying changes in cellular morphology are demonstrated in simulations using a mechanical model of the cell cortex implemented in the level set framework. The central module is an excitable network that accounts for random migration. The response to combinations of uniform stimuli and gradients is mediated by a local excitation, global inhibition module that biases the direction in which excitability is directed. A polarization module linked to the excitable network through the cytoskeleton allows unstimulated cells to move persistently and, for cells in gradients, to gradually acquire distinct sensitivity between front and back. Finally, by varying the strengths of various feedback loops in the model we obtain cellular behaviors that mirror those of genetically altered cell lines.

Chemotaxis is the movement of cells in response to spatial gradients of chemical cues. While single-celled organisms rely on sensing and responding to chemical gradients to search for nutrients, chemotaxis is also an essential component of the mammalian immune system. However, chemotaxis can also be deleterious, since chemotactic tumor cells can lead to metastasis. Due to its importance, understanding the process by which cells sense and respond to chemical gradients has attracted considerable interest. Moreover, because of the complexity of chemotactic signaling, which includes multiple feedback loops and redundant pathways, this has been a research area in which computational models have had a significant impact in understanding experimental findings. Here, we propose a modular description of the signaling network that regulates chemotaxis. The modules describe different processes that are observed in chemotactic cells. In addition to accounting for these behaviors individually, we show that the overall system recreates many features of the directed motion of migrating cells. The signaling described by our modules is implemented as a series of equations, whereas movement and the accompanying cellular deformations are simulated using a mechanical model of the cell and implemented using level set methods, a method that allows simulations of cells as they change morphology.

A model for intracellular actin waves explored by nonlinear local perturbation analysis

Waves and dynamic patterns in chemical and physical systems have long interested experimentalists and theoreticians alike. Here we investigate a recent example within the context of cell biology, where waves of actin (a major component of the cytoskeleton) and its regulators (nucleation promoting factors, NPFs) are observed experimentally. We describe and analyze a minimal reaction diffusion model depicting the feedback between signalling proteins and filamentous actin (F-actin). Using numerical simulation, we show that this model displays a rich variety of patterning regimes. A relatively recent nonlinear stability method, the Local Perturbation Analysis (LPA), is used to map the parameter space of this model and explain the genesis of patterns in various linear and nonlinear patterning regimes. We compare our model for actin waves to others in the literature, and focus on transitions between static polarization, transient waves, periodic wave trains, and reflecting waves. We show, using LPA, that the spatially distributed model gives rise to dynamics that are absent in the kinetics alone. Finally, we show that the width and speed of the waves depend counter-intuitively on parameters such as rates of NPF activation, negative feedback, and the F-actin time scale.

An intracellular partitioning-based framework for tissue cell polarity in plants and animals

Tissue cell polarity plays a major role in plant and animal development. We propose that a fundamental building block for tissue cell polarity is the process of intracellular partitioning, which can establish individual cell polarity in the absence of asymmetric cues. Coordination of polarities may then arise through cell-cell coupling, which can operate directly, through membrane-spanning complexes, or indirectly, through diffusible molecules. Polarity is anchored to tissues through organisers located at boundaries. We show how this intracellular partitioning-based framework can be applied to both plant and animal systems, allowing different processes to be placed in a common evolutionary and mechanistic context.

Geometrical constraints and physical crowding direct collective migration of fibroblasts

Migrating cells constantly interact with their immediate microenvironment and neighbors. Although studies on single cell migration offer us insights into the molecular and biochemical signaling pathways, they cannot predict the influence of cell crowding and geometrical cues. Using microfabrication techniques, we examine the influence of cell density and geometrical constraints on migrating fibroblasts. Fibroblasts were allowed to migrate on fibronectin strips of different widths. Under such conditions, cells experience various physical guidance cues including boundary effect, confinement and contact inhibition from neighboring cells. Fibroblasts migrating along the edge of the fibronectin pattern exhibit spindle-like morphology, reminiscent of migrating cells within confined space and high cell density are associated with increased alignment and higher speed in migrating fibroblasts.

Multidimensional control of cell structural robustness

Ample adaptive and functional opportunities of a living cell are determined by the complexity of its structural organisation. However, such complexity gives rise to a problem of maintenance of the coherence of inner processes in macroscopic interims and in macroscopic volumes which is necessary to support the structural robustness of a cell. The solution to this problem lies in multidimensional control of the adaptive and functional changes of a cell as well as its self-renewing processes in the context of environmental conditions. Six mechanisms (principles) form the basis of this multidimensional control: regulatory circuits with feedback loops, redundant inner diversity within a cell, multilevel distributed network organisation of a cell, molecular selection within a cell, continuous informational flows and functioning with a reserve of power. In the review we provide detailed analysis of these mechanisms, discuss their specific functions and the role of the superposition of these mechanisms in the maintenance of cell structural robustness in a wide range of environmental conditions.

Envisioning migration: mathematics in both experimental analysis and modeling of cell behavior

The complex nature of cell migration highlights the power and challenges of applying mathematics to biological studies. Mathematics may be used to create model equations that recapitulate migration, which can predict phenomena not easily uncovered by experiments or intuition alone. Alternatively, mathematics may be applied to interpreting complex data sets with better resolution--potentially empowering scientists to discern subtle patterns amid the noise and heterogeneity typical of migrating cells. Iteration between these two methods is necessary in order to reveal connections within the cell migration signaling network, as well as to understand the behavior that arises from those connections. Here, we review recent quantitative analysis and mathematical modeling approaches to the cell migration problem.

A comparison of computational models for eukaryotic cell shape and motility

Eukaryotic cell motility involves complex interactions of signalling molecules, cytoskeleton, cell membrane, and mechanics interacting in space and time. Collectively, these components are used by the cell to interpret and respond to external stimuli, leading to polarization, protrusion, adhesion formation, and myosin-facilitated retraction. When these processes are choreographed correctly, shape change and motility results. A wealth of experimental data have identified numerous molecular constituents involved in these processes, but the complexity of their interactions and spatial organization make this a challenging problem to understand. This has motivated theoretical and computational approaches with simplified caricatures of cell structure and behaviour, each aiming to gain better understanding of certain kinds of cells and/or repertoire of behaviour. Reaction–diffusion (RD) equations as well as equations of viscoelastic flows have been used to describe the motility machinery. In this review, we describe some of the recent computational models for cell motility, concentrating on simulations of cell shape changes (mainly in two but also three dimensions). The problem is challenging not only due to the difficulty of abstracting and simplifying biological complexity but also because computing RD or fluid flow equations in deforming regions, known as a “free-boundary” problem, is an extremely challenging problem in applied mathematics. Here we describe the distinct approaches, comparing their strengths and weaknesses, and the kinds of biological questions that they have been able to address.

Synthetic spatially graded Rac activation drives cell polarization and movement

Migrating cells possess intracellular gradients of active Rho GTPases, which serve as central hubs in transducing signals from extracellular receptors to cytoskeletal and adhesive machinery. However, it is unknown whether shallow exogenously induced intracellular gradients of Rho GTPases are sufficient to drive cell polarity and motility. Here, we use microfluidic control to generate gradients of a small molecule and thereby directly induce linear gradients of active, endogenous Rac without activation of chemotactic receptors. Gradients as low as 15% were sufficient not only to trigger cell migration up the chemical gradient but to induce both cell polarization and repolarization. Cellular response times were inversely proportional to the steepness of Rac inducer gradient in agreement with a mathematical model, suggesting a function for chemoattractant gradient amplification upstream of Rac. Increases in activated Rac levels beyond a well-defined threshold augmented polarization and decreased sensitivity to the imposed gradient. The threshold was governed by initial cell polarity and PI3K activity, supporting a role for both in defining responsiveness to Rac activation. Our results reveal that Rac can serve as a starting point in defining cell polarity. Furthermore, our methodology may serve as a template to investigate processes regulated by intracellular signaling gradients.

Chemotactic migration of T cells towards dendritic cells promotes the detection of rare antigens

In many immunological processes chemoattraction is thought to play a role in guiding cells to their sites of action. However, based on in vivo two-photon microscopy experiments in the absence of cognate antigen, T cell migration in lymph nodes (LNs) has been roughly described as a random walk. Although it has been shown that dendritic cells (DCs) carrying cognate antigen in some circumstances attract T cells chemotactically, it is currently still unclear whether chemoattraction of T cells towards DCs helps or hampers scanning. Chemoattraction towards DCs could on the one hand help T cells to rapidly find DCs. On the other hand, it could be deleterious if DCs become shielded by a multitude of attracted yet non-specific T cells. Results from a recent simulation study suggested that the deleterious effect dominates. We re-addressed the question whether T cell chemoattraction towards DCs is expected to promote or hamper the detection of rare antigens using the Cellular Potts Model, a formalism that allows for dynamic, flexible cellular shapes and cell migration. Our simulations show that chemoattraction of T cells enhances the DC scanning efficiency, leading to an increased probability that rare antigen-specific T cells find DCs carrying cognate antigen. Desensitization of T cells after contact with a DC further improves the scanning efficiency, yielding an almost threefold enhancement compared to random migration. Moreover, the chemotaxis-driven migration still roughly appears as a random walk, hence fine-tuned analysis of cell tracks will be required to detect chemotaxis within microscopy data.

Modelling cell polarization driven by synthetic spatially graded Rac activation

The small GTPase Rac is known to be an important regulator of cell polarization, cytoskeletal reorganization, and motility of mammalian cells. In recent microfluidic experiments, HeLa cells endowed with appropriate constructs were subjected to gradients of the small molecule rapamycin leading to synthetic membrane recruitment of a Rac activator and direct graded activation of membrane-associated Rac. Rac activation could thus be triggered independent of upstream signaling mechanisms otherwise responsible for transducing activating gradient signals. The response of the cells to such stimulation depended on exceeding a threshold of activated Rac. Here we develop a minimal reaction-diffusion model for the GTPase network alone and for GTPase-phosphoinositide crosstalk that is consistent with experimental observations for the polarization of the cells. The modeling suggests that mutual inhibition is a more likely mode of cell polarization than positive feedback of Rac onto its own activation. We use a new analytical tool, Local Perturbation Analysis, to approximate the partial differential equations by ordinary differential equations for local and global variables. This method helps to analyze the parameter space and behaviour of the proposed models. The models and experiments suggest that (1) spatially uniform stimulation serves to sensitize a cell to applied gradients. (2) Feedback between phosphoinositides and Rho GTPases sensitizes a cell. (3) Cell lengthening/flattening accompanying polarization can increase the sensitivity of a cell and stabilize an otherwise unstable polarization.