Diverse sensitivity thresholds in dynamic signaling responses by social amoebae

Noise in biology

Noise permeates biology on all levels, from the most basic molecular, sub-cellular processes to the dynamics of tissues, organs, organisms and populations. The functional roles of noise in biological processes can vary greatly. Along with standard, entropy-increasing effects of producing random mutations, diversifying phenotypes in isogenic populations, limiting information capacity of signaling relays, it occasionally plays more surprising constructive roles by accelerating the pace of evolution, providing selective advantage in dynamic environments, enhancing intracellular transport of biomolecules and increasing information capacity of signaling pathways. This short review covers the recent progress in understanding mechanisms and effects of fluctuations in biological systems of different scales and the basic approaches to their mathematical modeling.

Adaptive molecular networks controlling chemotactic migration: dynamic inputs and selection of the network architecture

Eukaryotic signalling networks underlying the cell's ability to sense the gradient of chemotactic cues frequently have the dual property of perfect adaptation to spatially homogeneous inputs, and persistent activation by inputs that are spatially graded. This property is also shared by bacterial chemotaxis networks, raising the question of whether these two types of chemotactic processes also have similar organization of the underlying biomolecular processes. Interestingly, perfect adaptation can only be achieved robustly by a handful of mechanisms, and while eukaryotic chemotactic networks appear to rely on one of these-the incoherent feed-forward loop, bacterial chemotaxis depends on another-the negative feedback loop. In this review, we discuss how this conclusion can be reached even if the details of the molecular networks are incompletely understood. Furthermore, we argue that the use of distinct network architectures is not accidental and may be a consequence of the nature of the signalling inputs and the limitations of the sensory properties of different cell types.

Robustness of self-organizing chemoattractant field arising from precise pulse induction of its breakdown enzyme: a single-cell level analysis of PDE expression in Dictyostelium

The oscillation of chemoattractant cyclic AMP (cAMP) in Dictyostelium discoideum is a collective phenomenon that occurs when the basal level of extracellular cAMP exceeds a threshold and invokes cooperative mutual excitation of cAMP synthesis and secretion. For pulses to be relayed from cell to cell repetitively, secreted cAMP must be cleared and brought down to the subthreshold level. One of the main determinants of the oscillatory behavior is thus how much extracellular cAMP is degraded by extracellular phosphodiesterase (PDE). To date, the exact nature of PDE gene regulation remains elusive. Here, we performed live imaging analysis of mRNA transcripts for pdsA--the gene encoding extracellular PDE. Our analysis revealed that pdsA is upregulated during the rising phase of cAMP oscillations. Furthermore, by analyzing isolated cells, we show that expression of pdsA is strictly dependent on the presence of extracellular cAMP. pdsA is induced only at ∼1 nM extracellular cAMP, which is almost identical to the threshold concentration for the cAMP relay response. The observed precise regulation of PDE expression together with degradation of extracellular cAMP by PDE form a dual positive and negative feedback circuit, and model analysis shows that this sets the cAMP level near the threshold concentration for the cAMP relay response for a wide range of adenylyl cyclase activity. The overlap of the thresholds could allow oscillations of chemoattractant cAMP to self-organize at various starving conditions, making its development robust to fluctuations in its environment.

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.

Microfluidic platforms for single-cell protein analysis

Elucidation of the heterogeneity of cells is a challenging task due to the lack of efficient analytical tools to make measurements with single-cell resolution. Microfluidics has emerged as a powerful platform for single-cell analysis with the ability to manipulate small volume and integrate multiple sample preparation steps into one device. In this review, we discuss the differentiating advantages of microfluidic platforms that have been demonstrated for single-cell protein analysis.

A design principle of group-level decision making in cell populations

Populations of cells often switch states as a group to cope with environmental changes such as nutrient availability and cell density. Although the gene circuits that underlie the switches are well understood at the level of single cells, the ways in which such circuits work in concert among many cells to support group-level switches are not fully explored. Experimental studies of microbial quorum sensing show that group-level changes in cellular states occur in either a graded or an all-or-none fashion. Here, we show through numerical simulations and mathematical analysis that these behaviors generally originate from two distinct forms of bistability. The choice of bistability is uniquely determined by a dimensionless parameter that compares the synthesis and the transport of the inducing molecules. The role of the parameter is universal, such that it not only applies to the autoinducing circuits typically found in bacteria but also to the more complex gene circuits involved in transmembrane receptor signaling. Furthermore, in gene circuits with negative feedback, the same dimensionless parameter determines the coherence of group-level transitions from quiescence to a rhythmic state. The set of biochemical parameters in bacterial quorum-sensing circuits appear to be tuned so that the cells can use either type of transition. The design principle identified here serves as the basis for the analysis and control of cellular collective decision making.

Although the genetic circuits underlying state switching at the single-cell level are well understood, how such circuits work in concert among many cells to support the population-level switching of cellular behaviors is not fully explored. Experiments using microbial signaling systems show that group-level changes in cellular state occur in either a graded or an all-or-none fashion. We show that the type of group-level decision making used by populations is uniquely determined by a single dimensionless parameter that compares the quorum-signaling molecules accumulated within the cells with those secreted by the population. Bacterial quorum-sensing circuits appear to be tuned so that the cells can convert between the two types of decision-making in response to slight biochemical variations. Furthermore, the role of the parameter is universal such that it not only applies to the autoinducing circuits typically found in bacteria but also to the more complex gene circuits involved in transmembrane receptor signaling and negative feedback. The design principle that we describe thus serves as the basis for the analysis and control of collective cellular decision making in general.

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.

Collective behavior of Dictyostelium discoideum monitored by impedance analysis

Dictyostelium discoideum cells respond to periodic signals of extracellular cAMP by collective changes of cell-cell and cell-substrate contacts. This was confirmed by dielectric analysis employing electric cell-substrate impedance sensing (ECIS) and impedance measurements involving cell-filled micro channels in conjunction with optical microscopy providing a comprehensive picture of chemotaxis under conditions of starvation.

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.

Dictyostelium Ric8 is a nonreceptor guanine exchange factor for heterotrimeric G proteins and is important for development and chemotaxis

Heterotrimeric G proteins couple external signals to the activation of intracellular signal transduction pathways. Agonist-stimulated guanine nucleotide exchange activity of G-protein-coupled receptors results in the exchange of G-protein-bound GDP to GTP and the dissociation and activation of the complex into Gα-GTP and a Gβγ dimer. In Dictyostelium, a basal chemotaxis pathway consisting of heterotrimeric and monomeric G proteins is sufficient for chemotaxis. Symmetry breaking and amplification of chemoattractant sensing occurs between heterotrimeric G protein signaling and Ras activation. In a pull-down screen coupled to mass spectrometry, with Gα proteins as bait, we have identified resistant to inhibitors of cholinesterase 8 (Ric8) as a nonreceptor guanine nucleotide exchange factor for Gα-protein. Ric8 is not essential for the initial activation of heterotrimeric G proteins or Ras by uniform chemoattractant; however, it amplifies Gα signaling, which is essential for Ras-mediated symmetry breaking during chemotaxis and development.

Actin cytoskeleton of chemotactic amoebae operates close to the onset of oscillations

The rapid reorganization of the actin cytoskeleton in response to external stimuli is an essential property of many motile eukaryotic cells. Here, we report evidence that the actin machinery of chemotactic Dictyostelium cells operates close to an oscillatory instability. When averaging the actin response of many cells to a short pulse of the chemoattractant cAMP, we observed a transient accumulation of cortical actin reminiscent of a damped oscillation. At the single-cell level, however, the response dynamics ranged from short, strongly damped responses to slowly decaying, weakly damped oscillations. Furthermore, in a small subpopulation, we observed self-sustained oscillations in the cortical F-actin concentration. To substantiate that an oscillatory mechanism governs the actin dynamics in these cells, we systematically exposed a large number of cells to periodic pulse trains of different frequencies. Our results indicate a resonance peak at a stimulation period of around 20 s. We propose a delayed feedback model that explains our experimental findings based on a time-delay in the regulatory network of the actin system. To test the model, we performed stimulation experiments with cells that express GFP-tagged fusion proteins of Coronin and actin-interacting protein 1, as well as knockout mutants that lack Coronin and actin-interacting protein 1. These actin-binding proteins enhance the disassembly of actin filaments and thus allow us to estimate the delay time in the regulatory feedback loop. Based on this independent estimate, our model predicts an intrinsic period of 20 s, which agrees with the resonance observed in our periodic stimulation experiments.

Temporal sampling, resetting, and adaptation orchestrate gradient sensing in sperm

Sperm use temporal sampling, resetting of intracellular calcium level, and adaptation of their sensitivity to respond to a wide range of chemoattractant concentrations during their voyage toward the egg.

Sperm, navigating in a chemical gradient, are exposed to a periodic stream of chemoattractant molecules. The periodic stimulation entrains Ca²⁺ oscillations that control looping steering responses. It is not known how sperm sample chemoattractant molecules during periodic stimulation and adjust their sensitivity. We report that sea urchin sperm sampled molecules for 0.2–0.6 s before a Ca²⁺ response was produced. Additional molecules delivered during a Ca²⁺ response reset the cell by causing a pronounced Ca²⁺ drop that terminated the response; this reset was followed by a new Ca²⁺ rise. After stimulation, sperm adapted their sensitivity following the Weber–Fechner law. Taking into account the single-molecule sensitivity, we estimate that sperm can register a minimal gradient of 0.8 fM/µm and be attracted from as far away as 4.7 mm. Many microorganisms sense stimulus gradients along periodic paths to translate a spatial distribution of the stimulus into a temporal pattern of the cell response. Orchestration of temporal sampling, resetting, and adaptation might control gradient sensing in such organisms as well.

Chemotaxis of Dictyostelium discoideum: collective oscillation of cellular contacts

Chemotactic responses of Dictyostelium discoideum cells to periodic self-generated signals of extracellular cAMP comprise a large number of intricate morphological changes on different length scales. Here, we scrutinized chemotaxis of single Dictyostelium discoideum cells under conditions of starvation using a variety of optical, electrical and acoustic methods. Amebas were seeded on gold electrodes displaying impedance oscillations that were simultaneously analyzed by optical video microscopy to relate synchronous changes in cell density, morphology, and distance from the surface to the transient impedance signal. We found that starved amebas periodically reduce their overall distance from the surface producing a larger impedance and higher total fluorescence intensity in total internal reflection fluorescence microscopy. Therefore, we propose that the dominant sources of the observed impedance oscillations observed on electric cell-substrate impedance sensing electrodes are periodic changes of the overall cell-substrate distance of a cell. These synchronous changes of the cell-electrode distance were also observed in the oscillating signal of acoustic resonators covered with amebas. We also found that periodic cell-cell aggregation into transient clusters correlates with changes in the cell-substrate distance and might also contribute to the impedance signal. It turned out that cell-cell contacts as well as cell-substrate contacts form synchronously during chemotaxis of Dictyostelium discoideum cells.

The application of information theory to biochemical signaling systems

Cell signaling can be thought of fundamentally as an information transmission problem in which chemical messengers relay information about the external environment to the decision centers within a cell. Due to the biochemical nature of cellular signal transduction networks, molecular noise will inevitably limit the fidelity of any messages received and processed by a cell's signal transduction networks, leaving it with an imperfect impression of its environment. Fortunately, Shannon's information theory provides a mathematical framework independent of network complexity that can quantify the amount of information that can be transmitted despite biochemical noise. In particular, the channel capacity can be used to measure the maximum number of stimuli a cell can distinguish based upon the noisy responses of its signaling systems. Here, we provide a primer for quantitative biologists that covers fundamental concepts of information theory, highlights several key considerations when experimentally measuring channel capacity, and describes successful examples of the application of information theoretic analysis to biological signaling.

Microfluidic technologies for studying synthetic circuits

Advances in synthetic biology have augmented the available toolkit of biomolecular modules, allowing engineering and manipulation of signaling in a variety of organisms, ranging in complexity from single bacteria and eukaryotic cells to multi-cellular systems. The richness of synthetic circuit outputs can be dramatically enhanced by sophisticated environmental control systems designed to precisely pattern spatial-temporally heterogeneous environmental stimuli controlling these circuits. Moreover, the performance of the synthetic modules and 'blocks' needed to assemble more complicated networks requires more complete characterization as a function of arbitrarily complex environmental inputs. Microfluidic technologies are poised to meet these needs through a variety of innovative designs capitalizing on the unique benefits of manipulating fluids on the micro-scales and nano-scales. This review discusses the utility of microfluidics for the study of synthetic circuits and highlights recent work in the area.

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.