Incoherent feedforward control governs adaptation of activated ras in a eukaryotic chemotaxis pathway

Gradient sensing during chemotaxis

Eukaryotic cells have the ability to sense chemoattractant gradients and to migrate toward the sources of attractants. The chemical gradient-guided cell movement is referred to as chemotaxis. Chemoattractants are detected by members of G-protein-coupled receptors (GPCRs) that link to heterotrimeric G-proteins. The GPCR/G-protein sensing machinery is able to translate external chemoattractants fields into intercellular cues, which direct reorganization of the actin cytoskeleton that drives cell movement. Here, I review our current understanding of the formation of chemoattractant gradients in vivo, the GPCR-mediated gradient sensing, and the sophisticated signaling network that guides the function of the actin cytoskeleton.

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.

Excitable behavior in amoeboid chemotaxis

Chemotaxis, the directed motion of cells in response to chemical gradients, is a fundamental process. Eukaryotic cells detect spatial differences in chemoattractant receptor occupancy with high precision and use these differences to bias the location of actin-rich protrusions to guide their movement. Research into chemotaxis has benefitted greatly from a systems biology approach that combines novel experimental and computational tools to pose and test hypotheses. Recently, one such hypothesis has been postulated proposing that chemotaxis in eukaryotic cells is mediated by locally biasing the activity of an underlying excitable system. The excitable system hypothesis can account for a number of cellular behaviors related to chemotaxis, including the stochastic nature of the movement of unstimulated cells, the directional bias imposed by chemoattractant gradients, and the observed spatial and temporal distribution of signaling and cytoskeleton proteins.

Systems biology: the role of engineering in the reverse engineering of biological signaling

One of the principle tasks of systems biology has been the reverse engineering of signaling networks. Because of the striking similarities to engineering systems, a number of analysis and design tools from engineering disciplines have been used in this process. This review looks at several examples including the analysis of homeostasis using control theory, the attenuation of noise using signal processing, statistical inference and the use of information theory to understand both binary decision systems and the response of eukaryotic chemotactic cells.

Chemoattractant stimulation of TORC2 is regulated by receptor/G protein-targeted inhibitory mechanisms that function upstream and independently of an essential GEF/Ras activation pathway in Dictyostelium

Protein kinase TORC2 is regulated by Ras response to distinct stimulatory ligands. Cells insensitive to one chemoattractant for TORC2 activation remain fully responsive to other ligands. Receptor-specific inhibitory circuits in Dictyostelium are found upstream and independent of GEF/Ras and downstream, feedback, or feedforward responses.

Global stimulation of Dictyostelium with different chemoattractants elicits multiple transient signaling responses, including synthesis of cAMP and cGMP, actin polymerization, activation of kinases ERK2, TORC2, and phosphatidylinositide 3-kinase, and Ras-GTP accumulation. Mechanisms that down-regulate these responses are poorly understood. Here we examine transient activation of TORC2 in response to chemically distinct chemoattractants, cAMP and folate, and suggest that TORC2 is regulated by adaptive, desensitizing responses to stimulatory ligands that are independent of downstream, feedback, or feedforward circuits. Cells with acquired insensitivity to either folate or cAMP remain fully responsive to TORC2 activation if stimulated with the other ligand. Thus TORC2 responses to cAMP or folate are not cross-inhibitory. Using a series of signaling mutants, we show that folate and cAMP activate TORC2 through an identical GEF/Ras pathway but separate receptors and G protein couplings. Because the common GEF/Ras pathway also remains fully responsive to one chemoattractant after desensitization to the other, GEF/Ras must act downstream and independent of adaptation to persistent ligand stimulation. When initial chemoattractant concentrations are immediately diluted, cells rapidly regain full responsiveness. We suggest that ligand adaptation functions in upstream inhibitory pathways that involve chemoattractant-specific receptor/G protein complexes and regulate multiple response pathways.

Optical control demonstrates switch-like PIP3 dynamics underlying the initiation of immune cell migration

There is a dearth of approaches to experimentally direct cell migration by continuously varying signal input to a single cell, evoking all possible migratory responses and quantitatively monitoring the cellular and molecular response dynamics. Here we used a visual blue opsin to recruit the endogenous G-protein network that mediates immune cell migration. Specific optical inputs to this optical trigger of signaling helped steer migration in all possible directions with precision. Spectrally selective imaging was used to monitor cell-wide phosphatidylinositol (3,4,5)-triphosphate (PIP3), cytoskeletal, and cellular dynamics. A switch-like PIP3 increase at the cell front and a decrease at the back were identified, underlying the decisive migratory response. Migration was initiated at the rapidly increasing switch stage of PIP3 dynamics. This result explains how a migratory cell filters background fluctuations in the intensity of an extracellular signal but responds by initiating directionally sensitive migration to a persistent signal gradient across the cell. A two-compartment computational model incorporating a localized activator that is antagonistic to a diffusible inhibitor was able to simulate the switch-like PIP3 response. It was also able simulate the slow dissipation of PIP3 on signal termination. The ability to independently apply similar signaling inputs to single cells detected two cell populations with distinct thresholds for migration initiation. Overall the optical approach here can be applied to understand G-protein-coupled receptor network control of other cell behaviors.

The utility of paradoxical components in biological circuits

A recurring theme in biological circuits is the existence of components that are antagonistically bifunctional, in the sense that they simultaneously have two opposing effects on the same target or biological process. Examples include bifunctional enzymes that carry out two opposing reactions such as phosphorylating and dephosphorylating the same target, regulators that activate and also repress a gene in circuits called incoherent feedforward loops, and cytokines that signal immune cells to both proliferate and die. Such components are termed "paradoxical", and in this review we discuss how they can provide useful features to cell circuits that are otherwise difficult to achieve. In particular, we summarize how paradoxical components can provide robustness, generate temporal pulses, and provide fold-change detection, in which circuits respond to relative rather than absolute changes in signals.

A characterization of scale invariant responses in enzymatic networks

An ubiquitous property of biological sensory systems is adaptation: a step increase in stimulus triggers an initial change in a biochemical or physiological response, followed by a more gradual relaxation toward a basal, pre-stimulus level. Adaptation helps maintain essential variables within acceptable bounds and allows organisms to readjust themselves to an optimum and non-saturating sensitivity range when faced with a prolonged change in their environment. Recently, it was shown theoretically and experimentally that many adapting systems, both at the organism and single-cell level, enjoy a remarkable additional feature: scale invariance, meaning that the initial, transient behavior remains (approximately) the same even when the background signal level is scaled. In this work, we set out to investigate under what conditions a broadly used model of biochemical enzymatic networks will exhibit scale-invariant behavior. An exhaustive computational study led us to discover a new property of surprising simplicity and generality, uniform linearizations with fast output (ULFO), whose validity we show is both necessary and sufficient for scale invariance of three-node enzymatic networks (and sufficient for any number of nodes). Based on this study, we go on to develop a mathematical explanation of how ULFO results in scale invariance. Our work provides a surprisingly consistent, simple, and general framework for understanding this phenomenon, and results in concrete experimental predictions.

Sensory systems often adapt, meaning that certain measured variables return to their basal levels after a transient response to a stimulus. An additional property that many adapting systems enjoy is that of scale invariance: the transient response remains the same when a stimulus is scaled. This work presents a mathematical study of biochemical enzymatic networks that exhibit scale-invariant behavior.

Linear conversion of pressure into concentration, rapid switching of concentration, and generation of linear ramps of concentration in a microfluidic device

Mixing of liquids to produce solutions with different concentrations is one of the basic functionalities of microfluidic devices. Generation of specific temporal patterns of concentration in microfluidic devices is an important technique to study responses of cells and model organisms to variations in the chemical composition of their environment. Here, we present a simple microfluidic network that linearly converts pressure at an inlet into concentration of a soluble reagent in an observation region and also enables independent concurrent linear control of concentrations of two reagents. The microfluidic device has an integrated mixer channel with chaotic three-dimensional flow that facilitates rapid switching of concentrations in a continuous range. A simple pneumatic setup generating linear ramps of pressure is used to produce smooth linear ramps and triangular waves of concentration with different slopes. The use of chaotic vs. laminar mixers is discussed in the context of microfluidic devices providing rapid switching and generating temporal waves of concentration.

Chemoattractant signaling in dictyostelium: adaptation and amplification

The social amoebae Dictyostelium discoideum has long proved a powerful model organism for studying how cells sense and interpret chemoattractant gradients. Because of the rich behavior observed in its response to chemoattractants, as well as the complex nature of the signaling pathways involved, this research has attracted and benefited from the use of theoretical models. Recent quantitative experiments provide support for a popular model: the local excitation, global inhibition mechanism of gradient sensing. Here, I discuss these findings and suggest some important open problems.