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

Traveling-wave chemotaxis of neutrophil-like HL-60 cells

The question of how changes in chemoattractant concentration translate into the chemotactic response of immune cells serves as a paradigm for the quantitative understanding of how cells perceive and process temporal and spatial information. Here, using a microfluidic approach, we analyzed the migration of neutrophil-like HL-60 cells to a traveling wave of the chemoattractants N-formyl-methionyl-leucyl-phenylalanine (fMLP) and leukotriene B4 (LTB4). We found that under a pulsatile wave that travels at a speed of 95 and 170 µm/min, cells move forward in the front of the wave but slow down and randomly orient at the back due to temporal decrease in the attractant concentration. Under a slower wave, cells reorient and migrate at the back of the wave; thus, cell displacement is canceled out or even becomes negative as cells chase the receding wave. Fluorescence resonance energy transfer (FRET)-based analysis indicated that these patterns of movement correlated well with spatiotemporal changes in Cdc42 activity. Furthermore, pharmacological perturbations showed that (re)orientation in front and back of the wave had different susceptibility to Cdc42 and ROCK inhibition. These results suggest that pulsatile attractant waves may recruit or disperse neutrophils, depending on their speed and degree of cell polarization.

Regulatory Effects of Cooperativity and Signal Profile on Adaptive Dynamics in Incoherent Feedforward Loop Networks

Cellular adaptation to external signals is essential for biological functions, and it is an important field of interest in systems biology. This study examines the impact of cooperativity on the adaptation response of the Incoherent Feedforward Loop (IFFL) network motif to various signal profiles. Through comprehensive simulations, we studied how the IFFL motif responds to constant and pulse-type signals under varying levels of cooperativity. The results of our study demonstrate that positive cooperativity generally enhances the system's ability to adapt to different signal profiles. Nevertheless, given specific signal profiles, higher levels of cooperativity may decrease the system's adaptability. On the other hand, the adaptive response breaks down for negative cooperativity. For constant signals, increased positive cooperativity leads to a response with higher amplitude, and it accelerates the response time but delays the return time required to settle back down to the pre-stimulus state. Upon signal cessation, high positive cooperativity not only slows the system's response and return times but, in some cases, can lead to a complete temporary halt in response. For the pulse-like signal, cooperativity increases the maximum amplitude of the oscillatory response. These insights highlight the delicate balance between cooperativity and signal profile in cellular adaptation mechanisms involving the IFFL network motif.

Spatiotemporal orchestration of calcium-cAMP oscillations on AKAP/AC nanodomains is governed by an incoherent feedforward loop

The nanoscale organization of enzymes associated with the dynamics of second messengers is critical for ensuring compartmentation and localization of signaling molecules in cells. Specifically, the spatiotemporal orchestration of cAMP and Ca2+ oscillations is critical for many cellular functions. Previous experimental studies have shown that the formation of nanodomains of A-kinase anchoring protein 79/150 (AKAP150) and adenylyl cyclase 8 (AC8) on the surface of pancreatic MIN6 β cells modulates the phase of Ca2+-cAMP oscillations from out-of-phase to in-phase. In this work, we develop computational models of the Ca2+/cAMP pathway and AKAP/AC nanodomain formation that give rise to the two important predictions: instead of an arbitrary phase difference, the out-of-phase Ca2+/cAMP oscillation reaches Ca2+ trough and cAMP peak simultaneously, which is defined as inversely out-of-phase; the in-phase and inversely out-of-phase oscillations associated with Ca2+-cAMP dynamics on and away from the nanodomains can be explained by an incoherent feedforward loop. Factors such as cellular surface-to-volume ratio, compartment size, and distance between nanodomains do not affect the existence of in-phase or inversely out-of-phase Ca2+/cAMP oscillation, but cellular surface-to-volume ratio and compartment size can affect the time delay for the inversely out-of-phase Ca2+/cAMP oscillation while the distance between two nanodomains does not. Finally, we predict that both the Turing pattern-generated nanodomains and experimentally measured nanodomains demonstrate the existence of in-phase and inversely out-of-phase Ca2+/cAMP oscillation when the AC8 is at a low level, consistent with the behavior of an incoherent feedforward loop. These findings unveil the key circuit motif that governs cAMP and Ca2+ oscillations and advance our understanding of how nanodomains can lead to spatial compartmentation of second messengers.

Eukaryotic Chemotaxis under Periodic Stimulation Shows Temporal Gradient Dependence

When cells of the social amoeba Dictyostelium discoideum are starved of nutrients they start to synthesize and secrete the chemical messenger and chemoattractant cyclic adenosine monophosphate (cAMP). This signal is relayed by other cells, resulting in the establishment of periodic waves. The cells aggregate through chemotaxis toward the center of these waves. We investigated the chemotactic response of individual cells to repeated exposure to waves of cAMP generated by a microfluidic device. For fast-moving waves (short period), the chemotactic ability of the cells was found to increase upon exposure to more waves, suggesting the development of a memory over several cycles. This effect was not significant for slow-moving waves (large period). We show that the experimental results are consistent with a local excitation global inhibition-based model, extended by including a component that rises and decays slowly and that is activated by the temporal gradient of cAMP concentration. The observed enhancement in chemotaxis is relevant to populations in the wild: once sustained, periodic waves of the chemoattractant are established, it is beneficial to cells to improve their chemotactic ability in order to reach the aggregation center sooner.

Genetically encodable biosensors for Ras activity

Genetically encoded Ras biosensors have been instrumental in illuminating the spatiotemporal dynamics of Ras activity since the beginning of the imaging revolution of the early 21st century. In general, these sensors employ Ras sensing units coupled with fluorescent proteins. These biosensors have not only helped elucidate Ras signalling dynamics at the plasma membrane but also revealed novel roles for Ras signalling within subcellular compartments such as the Golgi apparatus. In this review, we discuss the different classes of biosensors used to measure Ras activity and discuss their importance in uncovering new roles for Ras activity in cellular signalling and behavior.

Evolutionary Stability of Small Molecular Regulatory Networks That Exhibit Near-Perfect Adaptation

Large-scale protein regulatory networks, such as signal transduction systems, contain small-scale modules ('motifs') that carry out specific dynamical functions. Systematic characterization of the properties of small network motifs is therefore of great interest to molecular systems biologists. We simulate a generic model of three-node motifs in search of near-perfect adaptation, the property that a system responds transiently to a change in an environmental signal and then returns near-perfectly to its pre-signal state (even in the continued presence of the signal). Using an evolutionary algorithm, we search the parameter space of these generic motifs for network topologies that score well on a pre-defined measure of near-perfect adaptation. We find many high-scoring parameter sets across a variety of three-node topologies. Of all possibilities, the highest scoring topologies contain incoherent feed-forward loops (IFFLs), and these topologies are evolutionarily stable in the sense that, under 'macro-mutations' that alter the topology of a network, the IFFL motif is consistently maintained. Topologies that rely on negative feedback loops with buffering (NFLBs) are also high-scoring; however, they are not evolutionarily stable in the sense that, under macro-mutations, they tend to evolve an IFFL motif and may-or may not-lose the NFLB motif.

Propagation dynamics of electrotactic motility in large epithelial cell sheets

Directional migration initiated at the wound edge leads epithelia to migrate in wound healing. How such coherent migration is achieved is not well understood. Here, we used electric fields to induce robust migration of sheets of human keratinocytes and developed an in silico model to characterize initiation and propagation of epithelial collective migration. Electric fields initiate an increase in migration directionality and speed at the leading edge. The increases propagate across the epithelial sheets, resulting in directional migration of cell sheets as coherent units. Both the experimental and in silico models demonstrated vector-like integration of the electric and default directional cues at free edge in space and time. The resultant collective migration is consistent in experiments and modeling, both qualitatively and quantitatively. The keratinocyte model thus faithfully reflects key features of epithelial migration as a coherent tissue in vivo, e.g. that leading cells lead, and that epithelium maintains cell-cell junction.

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.

Dynamics and Sensitivity of Signaling Pathways

Purpose of Review

Signaling pathways serve to communicate information about extracellular conditions into the cell, to both the nucleus and cytoplasmic processes to control cell responses. Genetic mutations in signaling network components are frequently associated with cancer and can result in cells acquiring an ability to divide and grow uncontrollably. Because signaling pathways play such a significant role in cancer initiation and advancement, their constituent proteins are attractive therapeutic targets. In this review, we discuss how signaling pathway modeling can assist with identifying effective drugs for treating diseases, such as cancer. An achievement that would facilitate the use of such models is their ability to identify controlling biochemical parameters in signaling pathways, such as molecular abundances and chemical reaction rates, because this would help determine effective points of attack by therapeutics.

Recent Findings

We summarize the current state of understanding the sensitivity of phosphorylation cycles with and without sequestration. We also describe some basic properties of regulatory motifs including feedback and feedforward regulation.

Summary

Although much recent work has focused on understanding the dynamics and particularly the sensitivity of signaling networks in eukaryotic systems, there is still an urgent need to build more scalable models of signaling networks that can appropriately represent their complexity across different cell types and tumors.

Short-term bioelectric stimulation of collective cell migration in tissues reprograms long-term supracellular dynamics

The ability to program collective cell migration can allow us to control critical multicellular processes in development, regenerative medicine, and invasive disease. However, while various technologies exist to make individual cells migrate, translating these tools to control myriad, collectively interacting cells within a single tissue poses many challenges. For instance, do cells within the same tissue interpret a global migration 'command' differently based on where they are in the tissue? Similarly, since no stimulus is permanent, what are the long-term effects of transient commands on collective cell dynamics? We investigate these questions by bioelectrically programming large epithelial tissues to globally migrate 'rightward' via electrotaxis. Tissues clearly developed distinct rear, middle, side, and front responses to a single global migration stimulus. Furthermore, at no point poststimulation did tissues return to their prestimulation behavior, instead equilibrating to a 3rd, new migratory state. These unique dynamics suggested that programmed migration resets tissue mechanical state, which was confirmed by transient chemical disruption of cell-cell junctions, analysis of strain wave propagation patterns, and quantification of cellular crowd dynamics. Overall, this work demonstrates how externally driving the collective migration of a tissue can reprogram baseline cell-cell interactions and collective dynamics, even well beyond the end of the global migratory cue, and emphasizes the importance of considering the supracellular context of tissues and other collectives when attempting to program crowd behaviors.

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.

Microtopographical guidance of macropinocytic signaling patches

Morphologies of amoebae and immune cells are highly deformable and dynamic, which facilitates migration in various terrains, as well as ingestion of extracellular solutes and particles. It remains largely unexplored whether and how the underlying membrane protrusions are triggered and guided by the geometry of the surface in contact. In this study, we show that in Dictyostelium, the precursor of a structure called macropinocytic cup, which has been thought to be a constitutive process for the uptake of extracellular fluid, is triggered by micrometer-scale surface features. Imaging analysis and computational simulations demonstrate how the topographical dependence of the self-organizing dynamics supports efficient guidance and capturing of the membrane protrusion and hence movement of an entire cell along such surface features.

In fast-moving cells such as amoeba and immune cells, dendritic actin filaments are spatiotemporally regulated to shape large-scale plasma membrane protrusions. Despite their importance in migration, as well as in particle and liquid ingestion, how their dynamics are affected by micrometer-scale features of the contact surface is still poorly understood. Here, through quantitative image analysis of Dictyostelium on microfabricated surfaces, we show that there is a distinct mode of topographical guidance directed by the macropinocytic membrane cup. Unlike other topographical guidance known to date that depends on nanometer-scale curvature sensing protein or stress fibers, the macropinocytic membrane cup is driven by the Ras/PI3K/F-actin signaling patch and its dependency on the micrometer-scale topographical features, namely PI3K/F-actin–independent accumulation of Ras-GTP at the convex curved surface, PI3K-dependent patch propagation along the convex edge, and its actomyosin-dependent constriction at the concave edge. Mathematical model simulations demonstrate that the topographically dependent initiation, in combination with the mutually defining patch patterning and the membrane deformation, gives rise to the topographical guidance. Our results suggest that the macropinocytic cup is a self-enclosing structure that can support liquid ingestion by default; however, in the presence of structured surfaces, it is directed to faithfully trace bent and bifurcating ridges for particle ingestion and cell guidance.

Ras inhibitor CAPRI enables neutrophil-like cells to chemotax through a higher-concentration range of gradients

Neutrophils sense and migrate through an enormous range of chemoattractant gradients through adaptation. Here, we reveal that in human neutrophils, calcium-promoted Ras inactivator (CAPRI) locally controls the GPCR-stimulated Ras adaptation. Human neutrophils lacking CAPRI (capri^kd ) exhibit chemoattractant-induced, nonadaptive Ras activation; significantly increased phosphorylation of AKT, GSK-3α/3β, and cofilin; and excessive actin polymerization. capri^kd cells display defective chemotaxis in response to high-concentration gradients but exhibit improved chemotaxis in low- or subsensitive-concentration gradients of various chemoattractants, as a result of their enhanced sensitivity. Taken together, our data reveal that CAPRI controls GPCR activation-mediated Ras adaptation and lowers the sensitivity of human neutrophils so that they are able to chemotax through a higher-concentration range of chemoattractant gradients.

Using Live-Cell Imaging and Synthetic Biology to Probe Directed Migration in Dictyostelium

For decades, the social amoeba Dictyostelium discoideum has been an invaluable tool for dissecting the biology of eukaryotic cells. Its short growth cycle and genetic tractability make it ideal for a variety of biochemical, cell biological, and biophysical assays. Dictyostelium have been widely used as a model of eukaryotic cell motility because the signaling and mechanical networks which they use to steer and produce forward motion are highly conserved. Because these migration networks consist of hundreds of interconnected proteins, perturbing individual molecules can have subtle effects or alter cell morphology and signaling in major unpredictable ways. Therefore, to fully understand this network, we must be able to quantitatively assess the consequences of abrupt modifications. This ability will allow us better control cell migration, which is critical for development and disease, in vivo. Here, we review recent advances in imaging, synthetic biology, and computational analysis which enable researchers to tune the activity of individual molecules in single living cells and precisely measure the effects on cellular motility and signaling. We also provide practical advice and resources to assist in applying these approaches in Dictyostelium.

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.

Sensitivity minimization, biological homeostasis and information theory

All organisms must be able to adapt to changes in the environment. To this end, they have developed sophisticated regulatory mechanisms to ensure homeostasis. Control engineers, who must design similar regulatory systems, have developed a number of general principles that govern feedback regulation. These lead to constraints which impose trade-offs that arise when developing controllers to minimize the effect of external disturbances on systems. Here, we review some of these trade-offs, particularly Bode's integral formula. We also highlight its connection to information theory, by showing that the constraints in sensitivity minimization can be cast as limitations on the information transmission through a system, and these have their root in causality. Finally, we look at how these constraints arise in two biological systems: glycolytic oscillations and the energy cost of perfect adaptation in a bacterial chemotactic pathway.

Cellular memory in eukaryotic chemotaxis depends on the background chemoattractant concentration

Cells of the social amoeba Dictyostelium discoideum migrate to a source of periodic traveling waves of chemoattractant as part of a self-organized aggregation process. An important part of this process is cellular memory, which enables cells to respond to the front of the wave and ignore the downward gradient in the back of the wave. During this aggregation, the background concentration of the chemoattractant gradually rises. In our microfluidic experiments, we exogenously applied periodic waves of chemoattractant with various background levels. We find that increasing background does not make detection of the wave more difficult, as would be naively expected. Instead, we see that the chemotactic efficiency significantly increases for intermediate values of the background concentration but decreases to almost zero for large values in a switch-like manner. These results are consistent with a computational model that contains a bistable memory module, along with a nonadaptive component. Within this model, an intermediate background level helps preserve directed migration by keeping the memory activated, but when the background level is higher, the directional stimulus from the wave is no longer sufficient to activate the bistable memory, suppressing directed migration. These results suggest that raising levels of chemoattractant background may facilitate the self-organized aggregation in Dictyostelium colonies.

Experimental evidence for constraints in amplitude-timescale co-variation of a biomolecular pulse generating circuit design

Understanding constraints on the functional properties of biomolecular circuit dynamics, such as the possible variations of amplitude and timescale of a pulse, is an important part of biomolecular circuit design. While the amplitude-timescale co-variations of the pulse in an incoherent feedforward loop have been investigated computationally using mathematical models, experimental support for any such constraints is relatively unclear. Here, the authors address this using experimental measurement of an existing pulse generating incoherent feedforward loop circuit realisation in the context of a standard mathematical model. They characterise the trends of co-variation in the pulse amplitude and rise time computationally by randomly exploring the parameter space. They experimentally measured the co-variation by varying inducers and found that larger amplitude pulses have a slower rise time. They discuss the gap between the experimental measurements and predictions of the standard model, highlighting model additions and other biological factors that might bridge the gap.

A mechanism for hunchback promoters to readout morphogenetic positional information in less than a minute

Cell fate decisions in the fly embryo are rapid: hunchback genes decide in minutes whether nuclei follow the anterior/posterior developmental blueprint by reading out positional information in the Bicoid morphogen. This developmental system is a prototype of regulatory decision processes that combine speed and accuracy. Traditional arguments based on fixed-time sampling of Bicoid concentration indicate that an accurate readout is impossible within the experimental times. This raises the general issue of how speed-accuracy tradeoffs are achieved. Here, we compare fixed-time to on-the-fly decisions, based on comparing the likelihoods of anterior/posterior locations. We found that these more efficient schemes complete reliable cell fate decisions within the short embryological timescales. We discuss the influence of promoter architectures on decision times and error rates, present concrete examples that rapidly readout the morphogen, and predictions for new experiments. Lastly, we suggest a simple mechanism for RNA production and degradation that approximates the log-likelihood function.

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.

Hierarchical and Dynamic Regulation of Defense-Responsive Specialized Metabolism by WRKY and MYB Transcription Factors

The plant kingdom produces hundreds of thousands of specialized bioactive metabolites, some with pharmaceutical and biotechnological importance. Their biosynthesis and function have been studied for decades, but comparatively less is known about how transcription factors with overlapping functions and contrasting regulatory activities coordinately control the dynamics and output of plant specialized metabolism. Here, we performed temporal studies on pathogen-infected intact host plants with perturbed transcription factors. We identified WRKY33 as the condition-dependent master regulator and MYB51 as the dual functional regulator in a hierarchical gene network likely responsible for the gene expression dynamics and metabolic fluxes in the camalexin and 4-hydroxy-indole-3-carbonylnitrile (4OH-ICN) pathways. This network may have also facilitated the regulatory capture of the newly evolved 4OH-ICN pathway in Arabidopsis thaliana by the more-conserved transcription factor MYB51. It has long been held that the plasticity of plant specialized metabolism and the canalization of development should be differently regulated; our findings imply a common hierarchical regulatory architecture orchestrated by transcription factors for specialized metabolism and development, making it an attractive target for metabolic engineering.

Feedforward Control of Plant Nitrate Transporter NRT1.1 Biphasic Adaptive Activity

Defective nitrate signaling in plants causes disorder in nitrogen metabolism, and it negatively affects nitrate transport systems, which toggle between high- and low-affinity modes in variable soil nitrate conditions. Recent discovery of a plasma membrane nitrate transceptor protein NRT1.1-a transporter cum sensor-provides a clue on this toggling mechanism. However, the general mechanistic description still remains poorly understood. Here, we illustrate adaptive responses and regulation of NRT1.1-mediated nitrate signaling in a wide range of extracellular nitrate concentrations. The results show that the homodimeric structure of NRT1.1 and its dimeric switch play an important role in eliciting specific cytosolic calcium waves sensed by the calcineurin-B-like calcium sensor CBL9, which activates the kinase CIPK23, in low nitrate concentration that is, however, impeded in high nitrate concentration. Nitrate binding at the high-affinity unit initiates NRT1.1 dimer decoupling and priming of the Thr101 site for phosphorylation by CIPK23. This phosphorylation stabilizes the NRT1.1 monomeric state, acting as a high-affinity nitrate transceptor. However, nitrate binding in both monomers, retaining the unmodified NRT1.1 state through dimerization, attenuates CIPK23 activity and thereby maintains the low-affinity mode of nitrate signaling and transport. This phosphorylation-led modulation of NRT1.1 activity shows bistable behavior controlled by an incoherent feedforward loop, which integrates nitrate-induced positive and negative regulatory effects on CIPK23. These results, therefore, advance our molecular understanding of adaptation in fluctuating nutrient availability and are a way forward for improving plant nitrogen use efficiency.

Network Topologies That Can Achieve Dual Function of Adaptation and Noise Attenuation

Many signaling systems execute adaptation under circumstances that require noise attenuation. Here, we identify an intrinsic trade-off existing between sensitivity and noise attenuation in the three-node networks. We demonstrate that although fine-tuning timescales in three-node adaptive networks can partially mediate this trade-off in this context, it prolongs adaptation time and imposes unrealistic parameter constraints. By contrast, four-node networks can effectively decouple adaptation and noise attenuation to achieve dual function without a trade-off, provided that these functions are executed sequentially. We illustrate ideas in seven biological examples, including Dictyostelium discoideum chemotaxis and the p53 signaling network and find that adaptive networks are often associated with a noise attenuation module. Our approach may be applicable to finding network design principles for other dual and multiple functions.

Minimal Network Topologies for Signal Processing during Collective Cell Chemotaxis

Cell-cell communication plays an important role in collective cell migration. However, it remains unclear how cells in a group cooperatively process external signals to determine the group's direction of motion. Although the topology of signaling pathways is vitally important in single-cell chemotaxis, the signaling topology for collective chemotaxis has not been systematically studied. Here, we combine mathematical analysis and simulations to find minimal network topologies for multicellular signal processing in collective chemotaxis. We focus on border cell cluster chemotaxis in the Drosophila egg chamber, in which responses to several experimental perturbations of the signaling network are known. Our minimal signaling network includes only four elements: a chemoattractant, the protein Rac (indicating cell activation), cell protrusion, and a hypothesized global factor responsible for cell-cell interaction. Experimental data on cell protrusion statistics allows us to systematically narrow the number of possible topologies from more than 40,000,000 to only six minimal topologies with six interactions between the four elements. This analysis does not require a specific functional form of the interactions, and only qualitative features are needed; it is thus robust to many modeling choices. Simulations of a stochastic biochemical model of border cell chemotaxis show that the qualitative selection procedure accurately determines which topologies are consistent with the experiment. We fit our model for all six proposed topologies; each produces results that are consistent with all experimentally available data. Finally, we suggest experiments to further discriminate possible pathway topologies.

Non-normality can facilitate pulsing in biomolecular circuits

Non-normality can underlie pulse dynamics in many engineering contexts. However, its role in pulses generated in biomolecular contexts is generally unclear. Here, the authors address this issue using the mathematical tools of linear algebra and systems theory on simple computational models of biomolecular circuits. They find that non-normality is present in standard models of feedforward loops. They used a generalised framework and pseudospectrum analysis to identify non-normality in larger biomolecular circuit models, finding that it correlates well with pulsing dynamics. Finally, they illustrate how these methods can be used to provide analytical support to numerical screens for pulsing dynamics as well as provide guidelines for design.

Caffeine inhibits PI3K and mTORC2 in Dictyostelium and differentially affects multiple other cAMP chemoattractant signaling effectors

Caffeine is commonly used in Dictyostelium to inhibit the synthesis of the chemoattractant cAMP and, therefore, its secretion and the autocrine stimulation of cells, in order to prevent its interference with the study of chemoattractant-induced responses. However, the mechanism through which caffeine inhibits cAMP synthesis in Dictyostelium has not been characterized. Here, we report the effects of caffeine on the cAMP chemoattractant signaling network. We found that caffeine inhibits phosphatidylinositol 3-kinase (PI3K) and mechanistic target of rapamycin complex 2 (mTORC2). Both PI3K and mTORC2 are essential for the chemoattractant-stimulated cAMP production, thereby providing a mechanism for the caffeine-mediated inhibition of cAMP synthesis. Our results also reveal that caffeine treatment of cells leads to an increase in cAMP-induced RasG and Rap1 activation, and inhibition of the PKA, cGMP, MyoII, and ERK1 responses. Finally, we observed that caffeine has opposite effects on F-actin and ERK2 depending on the assay and Dictyostelium strain used, respectively. Altogether, our findings reveal that caffeine considerably affects the cAMP-induced chemotactic signaling pathways in Dictyostelium, most likely acting through multiple targets that include PI3K and mTORC2.

Multiple sources of signal amplification within the B-cell Ras/MAPK pathway

The Ras-Map kinase (MAPK) cascade underlies functional decisions in a wide range of cell types and organisms. In B-cells, positive feedback-driven Ras activation is the proposed source of the digital (all or none) MAPK responses following antigen stimulation. However, an inability to measure endogenous Ras activity in living cells has hampered our ability to test this model directly. Here we leverage biosensors of endogenous Ras and ERK activity to revisit this question. We find that B-cell receptor (BCR) ligation drives switch-like Ras activation and that lower BCR signaling output is required for the maintenance versus the initiation of Ras activation. Surprisingly, digital ERK responses persist in the absence of positive feedback-mediated Ras activation, and digital ERK is observed at a threshold level of Ras activation. These data suggest an independent analogue-to-digital switch downstream of Ras activation and reveal that multiple sources of signal amplification exist within the Ras-ERK module of the BCR pathway.

A microfluidic platform with pneumatically switchable single-cell traps for selective intracellular signals probing

To investigate rapid suspension cell signaling, a microfluidic platform was urgently needed for flexibly manipulation of single cells and simultaneous generation of controllable chemical signals to stimulate single cells. In this paper, a microfluidic biosensor was developed to monitor intracellular calcium signal, integrated with single-cell trapping, chemical stimulation and releasing. Selective entrapment and discharge of individual cell were achieved by controlling the deformable membrane with pneumatic traps. The activation of intracellular calcium signal was qualitatively and quantitatively investigated by high-controllable chemical single-cell stimulation based on flexible hydrodynamic gating. And performing chemical stimulation and control assay in the same channel would improve the experimental robustness and effectiveness. Further investigation of the cellular responses to ATP pulses of varying concentrations and durations indicated that 20 μM ATP pulses with duration as short as 200 ms resulted in the same level of Ca²⁺ response induced by sustained stimulations. Washing with buffer for 30 s was sufficient for single cell to recover from receptor desensitization caused by ATP stimulation. In addition, the responses of cells to ATP stimulation were heterogeneous. The developed microfluidic method opens up a new avenue for intracellular signaling studies and drug screening.

Exploration and stabilization of Ras1 mating zone: A mechanism with positive and negative feedbacks

In mating fission yeast cells, sensing and response to extracellular pheromone concentrations occurs through an exploratory Cdc42 patch that stochastically samples the cell cortex before stabilizing towards a mating partner. Active Ras1 (Ras1-GTP), an upstream regulator of Cdc42, and Gap1, the GTPase-activating protein for Ras1, localize at the patch. We developed a reaction-diffusion model of Ras1 patch appearance and disappearance with a positive feedback by a Guanine nucleotide Exchange Factor (GEF) and Gap1 inhibition. The model is based on new estimates of Ras1-GDP, Ras1-GTP and Gap1 diffusion coefficients and rates of cytoplasmic exchange studied by FRAP. The model reproduces exploratory patch behavior and lack of Ras1 patch in cells lacking Gap1. Transition to a stable patch can occur by change of Gap1 rates constants or local increase of the positive feedback rate constants. The model predicts that the patch size and number of patches depend on the strength of positive and negative feedbacks. Measurements of Ras1 patch size and number in cells overexpressing the Ras1 GEF or Gap1 are consistent with the model.

Unicellular fission yeasts mate by fusing with partners of the opposite mating type. Each pair member grows towards its selected partner that signals its presence through secreted pheromone. The process of partner selection occurs through an exploratory patch (containing activated signaling protein Cdc42 and upstream regulator Ras1) that assembles and disassembles on the cell cortex, stabilizing in regions of higher opposite pheromone concentration. We present a computational model of the molecular mechanisms driving the dynamical pattern of patch exploration and stabilization. The model is based on reaction and diffusion along the curved cell membrane, with diffusion coefficients measured experimentally. In the model, a positive Ras1 activation feedback loop generates a patch containing most of the activating protein (Ras1 GEF). The fast diffusing inhibitor Gap1 that is recruited locally from the cytoplasm spreads on the cell membrane, limiting patch size and causing its decay. Spontaneous reinitiation of Ras1 activation elsewhere on the cortex provides a mechanism for exploration. Transition of the system’s behavior to that of a single stable patch is possible upon simulated pheromone sensing. The computational model provides predictions for the number of patches and patch size dependence on parameters that we tested experimentally.

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.

Collective gradient sensing and chemotaxis: modeling and recent developments

Cells measure a vast variety of signals, from their environment's stiffness to chemical concentrations and gradients; physical principles strongly limit how accurately they can do this. However, when many cells work together, they can cooperate to exceed the accuracy of any single cell. In this topical review, I will discuss the experimental evidence showing that cells collectively sense gradients of many signal types, and the models and physical principles involved. I also propose new routes by which experiments and theory can expand our understanding of these problems.

Filling GAPs in G protein- coupled receptor (GPCR)-mediated Ras adaptation and chemotaxis

Eukaryotic cells sense and migrate toward chemoattractant gradients using G protein-coupled receptor (GPCR) signaling pathways. The fascinating feature of chemotaxis is that cells migrate through chemoattractant gradients with huge concentration ranges by "adaptation." Adaptive cells no longer respond to the present stimulus but remain sensitive to stronger stimuli, providing the fundamental strategy for chemotaxis through gradients with a broad range of concentrations. Ras activation is the first step in the GPCR-mediated chemosensing signaling pathways that displays adaptation. However, the molecular mechanism of Ras adaptation is not fully understood. Here, we highlight C2GAP1, a GPCR-activated Ras negative regulator, that locally inhibits Ras signaling for adaptation and long-range chemotaxis in D. discoideum.

The cAMP-induced G protein subunits dissociation monitored in live Dictyostelium cells by BRET reveals two activation rates, a positive effect of caffeine and potential role of microtubules

To study the dynamics and mechanisms controlling activation of the heterotrimeric G protein Gα2βγ in Dictyostelium in response to stimulation by the chemoattractant cyclic AMP (cAMP), we monitored the G protein subunit interaction in live cells using bioluminescence resonance energy transfer (BRET). We found that cAMP induces the cAR1-mediated dissociation of the G protein subunits to a similar extent in both undifferentiated and differentiated cells, suggesting that only a small number of cAR1 (as expressed in undifferentiated cells) is necessary to induce the full activation of Gα2βγ. In addition, we found that treating cells with caffeine increases the potency of cAMP-induced Gα2βγ activation; and that disrupting the microtubule network but not F-actin inhibits the cAMP-induced dissociation of Gα2βγ. Thus, microtubules are necessary for efficient cAR1-mediated activation of the heterotrimeric G protein. Finally, kinetics analyses of Gα2βγ subunit dissociation induced by different cAMP concentrations indicate that there are two distinct rates at which the heterotrimeric G protein subunits dissociate when cells are stimulated with cAMP concentrations above 500 nM versus only one rate at lower cAMP concentrations. Quantitative modeling suggests that the kinetics profile of Gα2βγ subunit dissociation results from the presence of both uncoupled and G protein pre-coupled cAR1 that have differential affinities for cAMP and, consequently, induce G protein subunit dissociation through different rates. We suggest that these different signaling kinetic profiles may play an important role in initial chemoattractant gradient sensing.

A computational model for how cells choose temporal or spatial sensing during chemotaxis

Cell size is thought to play an important role in choosing between temporal and spatial sensing in chemotaxis. Large cells are thought to use spatial sensing due to large chemical difference at its ends whereas small cells are incapable of spatial sensing due to rapid homogenization of proteins within the cell. However, small cells have been found to polarize and large cells like sperm cells undergo temporal sensing. Thus, it remains an open question what exactly governs spatial versus temporal sensing. Here, we identify the factors that determines sensing choices through mathematical modeling of chemotactic circuits. Comprehensive computational search of three-node signaling circuits has identified the negative integral feedback (NFB) and incoherent feedforward (IFF) circuits as capable of adaptation, an important property for chemotaxis. Cells are modeled as one-dimensional circular system consisting of diffusible activator, inactivator and output proteins, traveling across a chemical gradient. From our simulations, we find that sensing outcomes are similar for NFB or IFF circuits. Rather than cell size, the relevant parameters are the 1) ratio of cell speed to the product of cell diameter and rate of signaling, 2) diffusivity of the output protein and 3) ratio of the diffusivities of the activator to inactivator protein. Spatial sensing is favored when all three parameters are low. This corresponds to a cell moving slower than the time it takes for signaling to propagate across the cell diameter, has an output protein that is polarizable and has a local-excitation global-inhibition system to amplify the chemical gradient. Temporal sensing is favored otherwise. We also find that temporal sensing is more robust to noise. By performing extensive literature search, we find that our prediction agrees with observation in a wide range of species and cell types ranging from E. coli to human Fibroblast cells and propose that our result is universally applicable.

Unicellular organisms and other single cells often have to migrate towards food sources or away from predators by sensing chemicals present in the environment. There are two ways for a cell to sense these external chemicals: temporal sensing, where the cell senses the external chemical at two different time points after it has moved through a certain distance, or spatial sensing, where the cell senses the external chemical at two different locations on its cellular surface (e.g., the front and rear of the cell) simultaneously. It has been thought that small unicellular organisms employ temporal sensing as their small size prohibits sensing at two different locations on the cellular surface. Using computational modeling, we find that the choice between temporal and spatial sensing is determined by the ratio of cell velocity to the product of cell diameter and rate of signaling, as well as the diffusivities of the signaling proteins. Predictions from our model agree with experimental observations over a wide range of cells, where a fast-moving, small cell performs better comparing the chemoattractant at different times in its trajectory; whereas, a slow-moving, big cell performs better by comparing the chemoattractant concentration at its two ends.

Adaptation of Living Systems

Adaptation refers to the biological phenomenon where living systems change their internal states in response to changes in their environments in order to maintain certain key functions critical for their survival and fitness. Adaptation is one of the most ubiquitous and arguably one of the most fundamental properties of living systems. It occurs throughout all biological scales, from adaptation of populations of species over evolutionary time to adaptation of a single cell to different environmental stresses during its life span. In this article, we review some of the recent progress made in understanding molecular mechanisms of cellular level adaptation. We take the minimalist (or the physicist) approach and study the simplest systems that exhibit generic adaptive behaviors. We focus on understanding the basic biochemical interaction networks in living matter that are responsible for adaptation dynamics. By combining theoretical modeling with quantitative experimentation, we demonstrate universal features in adaptation as well as important differences in different cellular systems, including chemotaxis in bacterium cells (Escherichia coli) and eukaryotic cells (Dictyostelium). Future work in extending the modeling framework to study adaptation in more complex systems such as sensory neurons are discussed.

The Dictyostelium GSK3 kinase GlkA coordinates signal relay and chemotaxis in response to growth conditions

GSK3 plays a central role in orchestrating key biological signaling pathways, including cell migration. Here, we identify GlkA as a GSK3 family kinase with functions that overlap with and are distinct from those of GskA. We show that GlkA, as previously shown for GskA, regulates the cell's cytoskeleton through MyoII assembly and control of Ras and Rap1 function, leading to aberrant cell migration. However, there are both qualitative and quantitative differences in the regulation of Ras and Rap1 and their downstream effectors, including PKB, PKBR1, and PI3K, with glkA^- cells exhibiting a more severe chemotaxis phenotype than gskA^- cells. Unexpectedly, the severe glkA^- phenotypes, but not those of gskA^-, are only exhibited when cells are grown attached to a substratum but not in suspension, suggesting that GlkA functions as a key kinase of cell attachment signaling. Using proteomic iTRAQ analysis we show that there are quantitative differences in the pattern of protein expression depending on the growth conditions in wild-type cells. We find that GlkA expression affects the cell's proteome during vegetative growth and development, with many of these changes depending on whether the cells are grown attached to a substratum or in suspension. These changes include key cytoskeletal and signaling proteins known to be essential for proper chemotaxis and signal relay during the aggregation stage of Dictyostelium development.

GPCR-controlled membrane recruitment of negative regulator C2GAP1 locally inhibits Ras signaling for adaptation and long-range chemotaxis

Eukaryotic cells chemotax in a wide range of chemoattractant concentration gradients, and thus need inhibitory processes that terminate cell responses to reach adaptation while maintaining sensitivity to higher-concentration stimuli. However, the molecular mechanisms underlying inhibitory processes are still poorly understood. Here, we reveal a locally controlled inhibitory process in a GPCR-mediated signaling network for chemotaxis in Dictyostelium discoideum We identified a negative regulator of Ras signaling, C2GAP1, which localizes at the leading edge of chemotaxing cells and is activated by and essential for GPCR-mediated Ras signaling. We show that both C2 and GAP domains are required for the membrane targeting of C2GAP1, and that GPCR-triggered Ras activation is necessary to recruit C2GAP1 from the cytosol and retains it on the membrane to locally inhibit Ras signaling. C2GAP1-deficient c2gapA^- cells have altered Ras activation that results in impaired gradient sensing, excessive polymerization of F actin, and subsequent defective chemotaxis. Remarkably, these cellular defects of c2gapA^- cells are chemoattractant concentration dependent. Thus, we have uncovered an inhibitory mechanism required for adaptation and long-range chemotaxis.

Emergent versus Individual-Based Multicellular Chemotaxis

Multicellular chemotaxis can occur via individually chemotaxing cells that are mechanically coupled. Alternatively, it can emerge collectively, from cells chemotaxing differently in a group than they would individually. Here we consider collective movement that emerges from cells on the exterior of the collective responding to chemotactic signals, whereas bulk cells remain uninvolved in sensing and directing the collective. We find that the precision of this type of emergent chemotaxis is higher than that of individual-based chemotaxis for one-dimensional cell chains and two-dimensional cell sheets, but not three-dimensional cell clusters. We describe the physical origins of these results, discuss their biological implications, and show how they can be tested using common experimental measures such as the chemotactic index.

G-Protein Dependent Signal Transduction and Ubiquitination in Dictyostelium

Signal transduction through G-protein-coupled receptors (GPCRs) is central for the regulation of virtually all cellular functions, and it has been widely implicated in human diseases. These receptors activate a common molecular switch that is represented by the heterotrimeric G-protein generating a number of second messengers (cAMP, cGMP, DAG, IP3, Ca²⁺ etc.), leading to a plethora of diverse cellular responses. Spatiotemporal regulation of signals generated by a given GPCR is crucial for proper signalling and is accomplished by a series of biochemical modifications. Over the past few years, it has become evident that many signalling proteins also undergo ubiquitination, a posttranslational modification that typically leads to protein degradation, but also mediates processes such as protein-protein interaction and protein subcellular localization. The social amoeba Dictyostelium discoideum has proven to be an excellent model to investigate signal transduction triggered by GPCR activation, as cAMP signalling via GPCR is a major regulator of chemotaxis, cell differentiation, and multicellular morphogenesis. Ubiquitin ligases have been recently involved in these processes. In the present review, we will summarize the most significant pathways activated upon GPCRs stimulation and discuss the role played by ubiquitination in Dictyostelium cells.

Oscillatory stimuli differentiate adapting circuit topologies

Adapting pathways consist of negative feedback loops (NFLs) or incoherent feedforward loops (IFFLs), which we show can be differentiated using oscillatory stimulation: NFLs but not IFFLs generically show ‘refractory period stabilization’ or ‘period skipping’. Using these signatures and genetic rewiring we identified the circuit dominating cell cycle timing in yeast. In C. elegans AWA neurons we uncovered a Ca2+-NFL, diffcult to find by other means, especially in wild-type, intact animals. (70 words)

Revisiting chemoaffinity theory: Chemotactic implementation of topographic axonal projection

Neural circuits are wired by chemotactic migration of growth cones guided by extracellular guidance cue gradients. How growth cone chemotaxis builds the macroscopic structure of the neural circuit is a fundamental question in neuroscience. I addressed this issue in the case of the ordered axonal projections called topographic maps in the retinotectal system. In the retina and tectum, the erythropoietin-producing hepatocellular (Eph) receptors and their ligands, the ephrins, are expressed in gradients. According to Sperry's chemoaffinity theory, gradients in both the source and target areas enable projecting axons to recognize their proper terminals, but how axons chemotactically decode their destinations is largely unknown. To identify the chemotactic mechanism of topographic mapping, I developed a mathematical model of intracellular signaling in the growth cone that focuses on the growth cone's unique chemotactic property of being attracted or repelled by the same guidance cues in different biological situations. The model presented mechanism by which the retinal growth cone reaches the correct terminal zone in the tectum through alternating chemotactic response between attraction and repulsion around a preferred concentration. The model also provided a unified understanding of the contrasting relationships between receptor expression levels and preferred ligand concentrations in EphA/ephrinA- and EphB/ephrinB-encoded topographic mappings. Thus, this study redefines the chemoaffinity theory in chemotactic terms.

Understanding Robust Adaptation Dynamics of Gene Regulatory Network

Robust adaptation is a critical attribute for gene regulatory network (GRN), understanding the relationship between adaptation and the GRN topology, and corresponding parameters is a challenging issue. The work in this paper includes: first, seven constraint multiobjective optimization algorithms are used to find sufficient solutions to get more reliable statistic rules. Meanwhile, the algorithms are compared to facilitate the future algorithm selection; second, a fuzzy c-mean algorithm is used to analyze solutions and to classify the solutions into different groups; third, the histogram analysis for all satisfactory solutions shows the preferred parameter range, i.e., parameter motif. The contributions of this paper includes: 1) Two new adaptation indices i.e., peak time and settle down time, are proposed for the first time to give more accurate description of the robust adaptation. Our conclusion is that some solutions even with satisfactory sensitivity and precision are not practically of robust adaptation because of too long time needed. 2) The relationship between topology, parameter set, and robust adaptation of GRN is discovered in the sense of both preferred topology and parameter motif. Our conclusion is that the robust adaptation depends more on the GRN topology than the model parameter set in two feasible topologies.

A module for Rac temporal signal integration revealed with optogenetics

Dissecting the logic of individual signaling modules in complex networks can be challenging for cascades that exhibit feedback and redundancy. In this study, Graziano et al. take an optogenetics-based approach to identify and dissect a module that converts sustained PIP₃ production to transient Rac activation in the neutrophil chemotaxis signaling network.

Sensory systems use adaptation to measure changes in signaling inputs rather than absolute levels of signaling inputs. Adaptation enables eukaryotic cells to directionally migrate over a large dynamic range of chemoattractant. Because of complex feedback interactions and redundancy, it has been difficult to define the portion or portions of eukaryotic chemotactic signaling networks that generate adaptation and identify the regulators of this process. In this study, we use a combination of optogenetic intracellular inputs, CRISPR-based knockouts, and pharmacological perturbations to probe the basis of neutrophil adaptation. We find that persistent, optogenetically driven phosphatidylinositol (3,4,5)-trisphosphate (PIP₃) production results in only transient activation of Rac, a hallmark feature of adaptive circuits. We further identify the guanine nucleotide exchange factor P-Rex1 as the primary PIP₃-stimulated Rac activator, whereas actin polymerization and the GTPase-activating protein ArhGAP15 are essential for proper Rac turnoff. This circuit is masked by feedback and redundancy when chemoattractant is used as the input, highlighting the value of probing signaling networks at intermediate nodes to deconvolve complex signaling cascades.

Systematic comparison of the response properties of protein and RNA mediated gene regulatory motifs

We present a framework enabling the dissection of the effects of motif structure (feedback or feedforward), the nature of the controller (RNA or protein), and the regulation mode (transcriptional, post-transcriptional or translational) on the response to a step change in the input. We have used a common model framework for gene expression where both motif structures have an activating input and repressing regulator, with the same set of parameters, to enable a comparison of the responses. We studied the global sensitivity of the system properties, such as steady-state gain, overshoot, peak time, and peak duration, to parameters. We find that, in all motifs, overshoot correlated negatively whereas peak duration varied concavely with peak time. Differences in the other system properties were found to be mainly dependent on the nature of the controller rather than the motif structure. Protein mediated motifs showed a higher degree of adaptation i.e. a tendency to return to baseline levels; in particular, feedforward motifs exhibited perfect adaptation. RNA mediated motifs had a mild regulatory effect; they also exhibited a lower peaking tendency and mean overshoot. Protein mediated feedforward motifs showed higher overshoot and lower peak time compared to the corresponding feedback motifs.

Fold-change detection and scale invariance of cell-cell signaling in social amoeba

Cell-cell signaling is subject to variability in the extracellular volume, cell number, and dilution that potentially increase uncertainty in the absolute concentrations of the extracellular signaling molecules. To direct cell aggregation, the social amoebae Dictyostelium discoideum collectively give rise to oscillations and waves of cyclic adenosine 3',5'-monophosphate (cAMP) under a wide range of cell density. To date, the systems-level mechanism underlying the robustness is unclear. By using quantitative live-cell imaging, here we show that the magnitude of the cAMP relay response of individual cells is determined by fold change in the extracellular cAMP concentrations. The range of cell density and exogenous cAMP concentrations that support oscillations at the population level agrees well with conditions that support a large fold-change-dependent response at the single-cell level. Mathematical analysis suggests that invariance of the oscillations to density transformation is a natural outcome of combining secrete-and-sense systems with a fold-change detection mechanism.

Protein kinase A regulates the Ras, Rap1 and TORC2 pathways in response to the chemoattractant cAMP in Dictyostelium

Efficient directed migration requires tight regulation of chemoattractant signal transduction pathways in both space and time, but the mechanisms involved in such regulation are not well understood. Here, we investigated the role of protein kinase A (PKA) in controlling signaling of the chemoattractant cAMP in Dictyostelium discoideum We found that cells lacking PKA display severe chemotaxis defects, including impaired directional sensing. Although PKA is an important regulator of developmental gene expression, including the cAMP receptor cAR1, our studies using exogenously expressed cAR1 in cells lacking PKA, cells lacking adenylyl cyclase A (ACA) and cells treated with the PKA-selective pharmacological inhibitor H89, suggest that PKA controls chemoattractant signal transduction, in part, through the regulation of RasG, Rap1 and TORC2. As these pathways control the ACA-mediated production of intracellular cAMP, they lie upstream of PKA in this chemoattractant signaling network. Consequently, we propose that the PKA-mediated regulation of the upstream RasG, Rap1 and TORC2 signaling pathways is part of a negative feedback mechanism controlling chemoattractant signal transduction during Dictyostelium chemotaxis.