Stochastic signal processing and transduction in chemotactic response of eukaryotic cells

Single-molecule imaging analysis of chemotactic response in eukaryotic cells has revealed a stochastic nature in the input signals and the signal transduction processes. This leads to a fundamental question about the signaling processes: how does the signaling system operate under stochastic fluctuations or noise? Here, we report a stochastic model of chemotactic signaling in which noise and signal propagation along the transmembrane signaling pathway by chemoattractant receptors can be analyzed quantitatively. The results obtained from this analysis reveal that the second-messenger-production reactions by the receptors generate noisy signals that contain intrinsic noise inherently generated at this reaction and extrinsic noise propagated from the ligand-receptor binding. Such intrinsic and extrinsic noise limits the directional sensing ability of chemotactic cells, which may explain the dependence of chemotactic accuracy on chemical gradients that has been observed experimentally. Our analysis also reveals regulatory mechanisms for signal improvement in the stochastically operating signaling system by analyzing how the SNR of chemotactic signals can be improved on or deteriorated by the stochastic properties of receptors and second-messenger molecules. Theoretical consideration of noisy signal transduction by chemotactic signaling systems can further be applied to signaling systems in general.     

Stochastic signal inputs for chemotactic response in Dictyostelium cells revealed by single molecule imaging techniques

Chemotactic cells can exhibit extreme sensitivity to chemical gradients. Theoretical estimations of the signal inputs required for chemotaxis suggest that the response can be achieved under the strong influence of stochastic input noise generated by the receptors during the transmembrane signaling. This arises a fundamental question regarding the mechanisms for directional sensing: how do cells obtain reliable information regarding gradient direction by using stochastically operating receptors and the downstream molecules? To address this question, we have developed single molecule imaging techniques to visualize signaling molecules responsible for chemotaxis in living Dictyostelium cells, allowing us to monitor the stochastic signaling processes directly. Single molecule imaging of a chemoattractant bound to a receptor demonstrates that signal inputs fluctuate with time and space. Downstream signaling molecules, such as PTEN and a PH domain-containing protein that are constituent parts of chemotactic signaling system, can also be followed at single molecule level in living cells, illuminating the stochastic nature of chemotactic signaling processes. In this report, we start with a brief introduction of chemotactic response of the eukaryotic cells, followed by an explanation for single molecule imaging techniques, and finally discuss these applications to chemotactic signaling system of Dictyostelium cells.     

Responding to chemical gradients: bacterial chemotaxis

Chemotaxis allows bacteria to follow gradients of nutrients and other environmental stimuli. The bacterium Escherichia coli performs chemotaxis via a run-and-tumble strategy in which sensitive temporal comparisons lead to a biased random walk, with longer runs in the preferred gradient direction. The chemotaxis network of E. coli has developed over the years into one of the most thoroughly studied model systems for signal transduction and behavior, yielding general insights into such properties of cellular networks as signal amplification, signal integration, and robustness. Despite its relative simplicity, the operation of the E. coli chemotaxis network is highly refined and evolutionarily optimized at many levels. For example, recent studies revealed that the network adjusts its signaling properties dependent on the extracellular environment, apparently to optimize chemotaxis under particular conditions. The network can even utilize potentially detrimental stochastic fluctuations in protein levels and reaction rates to maximize the chemotactic performance of the population.     

Stochastic control of spontaneous signal generation for gradient sensing in chemotaxis

Chemotaxis is characterized by spontaneous cellular behavior. This spontaneity results, in part, from the stochasticity of intracellular reactions. Spontaneous and random migration of chemotactic cells is regulated by spontaneously generated signals, namely transient local increases in the level of phosphoinositol-3,4,5-triphosphate (PIP3 pulses). In this study, we attempted to elucidate the mechanisms that generate these PIP3 pulses and how the pulses contribute to gradient sensing during chemotaxis. To this end, we constructed a simple biophysical model of intracellular signal transduction consisting of an inositol phospholipid signaling pathway and small GTPases. Our theoretical analysis revealed that an excitable system can emerge from the non-linear dynamics of the model, and that stochastic reactions allow the system to spontaneously become excited, which was corresponded to the PIP3 pulses. Based on these results, we framed a hypothesis of the gradient sensing; a chemical gradient spatially modifies a potential barrier for excitation and then PIP3 pulses are preferentially generated on the side of the cell exposed to the higher chemical concentration. We then validated our hypothesis using stochastic simulations of the signal transduction.     

Exponential Signaling Gain at the Receptor Level Enhances Signal-to-Noise Ratio in Bacterial Chemotaxis

Cellular signaling systems show astonishing precision in their response to external stimuli despite strong fluctuations in the molecular components that determine pathway activity. To control the effects of noise on signaling most efficiently, living cells employ compensatory mechanisms that reach from simple negative feedback loops to robustly designed signaling architectures. Here, we report on a novel control mechanism that allows living cells to keep precision in their signaling characteristics – stationary pathway output, response amplitude, and relaxation time – in the presence of strong intracellular perturbations. The concept relies on the surprising fact that for systems showing perfect adaptation an exponential signal amplification at the receptor level suffices to eliminate slowly varying multiplicative noise. To show this mechanism at work in living systems, we quantified the response dynamics of the E. coli chemotaxis network after genetically perturbing the information flux between upstream and downstream signaling components. We give strong evidence that this signaling system results in dynamic invariance of the activated response regulator against multiplicative intracellular noise. We further demonstrate that for environmental conditions, for which precision in chemosensing is crucial, the invariant response behavior results in highest chemotactic efficiency. Our results resolve several puzzling features of the chemotaxis pathway that are widely conserved across prokaryotes but so far could not be attributed any functional role.     

Live visualization and quantification of pathway signaling with dual fluorescent and bioluminescent reporters

Despite their fundamental importance, the dynamics of signaling pathways in living cells remain challenging to study, due to a lack of non-invasive tools for temporal assessment of signal transduction in desired cell models. Here we report a dual-reporter strategy that enables researchers to monitor signal transduction in mammalian cells in real-time, both temporally and quantitatively. This is achieved by co-expressing green fluorescent protein and firefly luciferase in response to signaling stimuli. To display the versatility of this approach, we constructed and assessed eight unique signaling pathway reporters. We further validated the system by establishing stable NF-κB pathway reporter cell lines. Using these stable cell lines, we monitored the activity of NF-κB-mediated inflammatory pathway in real-time, both visually and quantitatively. Live visualization has the power to reveal individual cell responses and is compatible with single cell analysis, In addition, we provide evidence that this system is readily amenable to a high-throughput format. Together, our findings demonstrate the potential of the dual reporter system, which significantly improves the capacity to study signal transduction pathways in mammalian cells.     

The Relation of Signal Transduction to the Sensitivity and Dynamic Range of Bacterial Chemotaxis

Complex networks of interacting molecular components of living cells are responsible for many important processes, such as signal processing and transduction. An important challenge is to understand how the individual properties of these molecular interactions and biochemical transformations determine the system-level properties of biological functions. Here, we address the issue of the accuracy of signal transduction performed by a bacterial chemotaxis system. The chemotaxis sensitivity of bacteria to a chemoattractant gradient has been measured experimentally from bacterial aggregation in a chemoattractant-containing capillary. The observed precision of the chemotaxis depended on environmental conditions such as the concentration and molecular makeup of the chemoattractant. In a quantitative model, we derived the chemotactic response function, which is essential to describing the signal transduction process involved in bacterial chemotaxis. In the presence of a gradient, an analytical solution is derived that reveals connections between the chemotaxis sensitivity and the characteristics of the signaling system, such as reaction rates. These biochemical parameters are integrated into two system-level parameters: one characterizes the efficiency of gradient sensing, and the other is related to the dynamic range of chemotaxis. Thus, our approach explains how a particular signal transduction property affects the system-level performance of bacterial chemotaxis. We further show that the two parameters can be derived from published experimental data from a capillary assay, which successfully characterizes the performance of bacterial chemotaxis.     

Noise enhanced hormonal signal transduction through intracellular calcium oscillations.

In a wide range of non-linear dynamical systems, noise may enhance the detection of weak deterministic input signals. Here, we demonstrate this phenomenon for transmembrane signaling in a hormonal model system of intracellular Ca(2+) oscillations. Adding Gaussian noise to a subthreshold extracellular pulsatile stimulus increased the sensitivity in the dose-response relation of the Ca(2+) oscillations compared to the same noise signal added as a constant mean level. These findings may have important physiological consequences for the operation of hormonal and other physiological signal transduction systems close to the threshold level.     

Optimal noise filtering in the chemotactic response of Escherichia coli

Information-carrying signals in the real world are often obscured by noise. A challenge for any system is to filter the signal from the corrupting noise. This task is particularly acute for the signal transduction network that mediates bacterial chemotaxis, because the signals are subtle, the noise arising from stochastic fluctuations is substantial, and the system is effectively acting as a differentiator which amplifies noise. Here, we investigated the filtering properties of this biological system. Through simulation, we first show that the cutoff frequency has a dramatic effect on the chemotactic efficiency of the cell. Then, using a mathematical model to describe the signal, noise, and system, we formulated and solved an optimal filtering problem to determine the cutoff frequency that bests separates the low-frequency signal from the high-frequency noise. There was good agreement between the theory, simulations, and published experimental data. Finally, we propose that an elegant implementation of the optimal filter in combination with a differentiator can be achieved via an integral control system. This paper furnishes a simple quantitative framework for interpreting many of the key notions about bacterial chemotaxis, and, more generally, it highlights the constraints on biological systems imposed by noise.     

Noise propagation in two-step series MAPK cascade

Series MAPK enzymatic cascades, ubiquitously found in signaling networks, act as signal amplifiers and play a key role in processing information during signal transduction in cells. In activated cascades, cell-to-cell variability or noise is bound to occur and thereby strongly affects the cellular response. Commonly used linearization method (LM) applied to Langevin type stochastic model of the MAPK cascade fails to accurately predict intrinsic noise propagation in the cascade. We prove this by using extensive stochastic simulations for various ranges of biochemical parameters. This failure is due to the fact that the LM ignores the nonlinear effects on the noise. However, LM provides a good estimate of the extrinsic noise propagation. We show that the correct estimate of intrinsic noise propagation in signaling networks that contain at least one enzymatic step can be obtained only through stochastic simulations. Noise propagation in the cascade depends on the underlying biochemical parameters which are often unavailable. Based on a combination of global sensitivity analysis (GSA) and stochastic simulations, we developed a systematic methodology to characterize noise propagation in the cascade. GSA predicts that noise propagation in MAPK cascade is sensitive to the total number of upstream enzyme molecules and the total number of molecules of the two substrates involved in the cascade. We argue that the general systematic approach proposed and demonstrated on MAPK cascade must accompany noise propagation studies in biological networks.     

Sphingosine-1-phosphate inhibits PDGF-induced chemotaxis of human arterial smooth muscle cells: spatial and temporal modulation of PDGF chemotactic signal transduction

Activation of the PDGF receptor on human arterial smooth muscle cells (SMC) induces migration and proliferation via separable signal transduction pathways. Sphingosine-1-phosphate (Sph-1-P) can be formed following PDGF receptor activation and therefore may be implicated in PDGF-receptor signal transduction. Here we show that Sph-1-P does not significantly affect PDGF-induced DNA synthesis, proliferation, or activation of mitogenic signal transduction pathways, such as the mitogen-activated protein (MAP) kinase cascade and PI 3-kinase, in human arterial SMC. On the other hand, Sph-1-P strongly mimics PDGF receptor-induced chemotactic signal transduction favoring actin filament disassembly. Although Sph-1-P mimics PDGF, exogenously added Sph-1-P induces more prolonged and quantitatively greater PIP2 hydrolysis compared to PDGF-BB, a markedly stronger calcium mobilization and a subsequent increase in cyclic AMP levels and activation of cAMP-dependent protein kinase. This excessive and prolonged signaling favors actin filament disassembly by Sph-1-P, and results in inhibition of actin nucleation, actin filament assembly and formation of focal adhesion sites. Sph-1-P-induced interference with the dynamics of PDGF-stimulated actin filament disassembly and assembly results in a marked inhibition of cell spreading, of extension of the leading lamellae toward PDGF, and of chemotaxis toward PDGF. The results suggest that spatial and temporal changes in phosphatidylinositol turnover, calcium mobilization and actin filament disassembly may be critical to PDGF-induced chemotaxis and suggest a possible role for endogenous Sph-1-P in the regulation of PDGF receptor chemotactic signal transduction.     

Active regulation of receptor ratios controls integration of quorum‐sensing signals in Vibrio harveyi

Quorum sensing is a chemical signaling mechanism used by bacteria to communicate and orchestrate group behaviors. Multiple feedback loops exist in the quorum‐sensing circuit of the model bacterium Vibrio harveyi. Using fluorescence microscopy of individual cells, we assayed the activity of the quorum‐sensing circuit, with a focus on defining the functions of the feedback loops. We quantitatively investigated the signaling input–output relation both in cells with all feedback loops present as well as in mutants with specific feedback loops disrupted. We found that one of the feedback loops regulates receptor ratios to control the integration of multiple signals. Together, the feedback loops affect the input–output dynamic range of signal transmission and the noise in the output. We conclude that V. harveyi employs multiple feedback loops to simultaneously control quorum‐sensing signal integration and to ensure signal transmission fidelity.     

Modeling Dynamics of Cell-to-Cell Variability in TRAIL-Induced Apoptosis Explains Fractional Killing and Predicts Reversible Resistance

Isogenic cells sensing identical external signals can take markedly different decisions. Such decisions often correlate with pre-existing cell-to-cell differences in protein levels. When not neglected in signal transduction models, these differences are accounted for in a static manner, by assuming randomly distributed initial protein levels. However, this approach ignores the a priori non-trivial interplay between signal transduction and the source of this cell-to-cell variability: temporal fluctuations of protein levels in individual cells, driven by noisy synthesis and degradation. Thus, modeling protein fluctuations, rather than their consequences on the initial population heterogeneity, would set the quantitative analysis of signal transduction on firmer grounds. Adopting this dynamical view on cell-to-cell differences amounts to recast extrinsic variability into intrinsic noise. Here, we propose a generic approach to merge, in a systematic and principled manner, signal transduction models with stochastic protein turnover models. When applied to an established kinetic model of TRAIL-induced apoptosis, our approach markedly increased model prediction capabilities. One obtains a mechanistic explanation of yet-unexplained observations on fractional killing and non-trivial robust predictions of the temporal evolution of cell resistance to TRAIL in HeLa cells. Our results provide an alternative explanation to survival via induction of survival pathways since no TRAIL-induced regulations are needed and suggest that short-lived anti-apoptotic protein Mcl1 exhibit large and rare fluctuations. More generally, our results highlight the importance of accounting for stochastic protein turnover to quantitatively understand signal transduction over extended durations, and imply that fluctuations of short-lived proteins deserve particular attention.     

An information-theoretic characterization of the optimal gradient sensing response of cells

Many cellular systems rely on the ability to interpret spatial heterogeneities in chemoattractant concentration to direct cell migration. The accuracy of this process is limited by stochastic fluctuations in the concentration of the external signal and in the internal signaling components. Here we use information theory to determine the optimal scheme to detect the location of an external chemoattractant source in the presence of noise. We compute the minimum amount of mutual information needed between the chemoattractant gradient and the internal signal to achieve a prespecified chemotactic accuracy. We show that more accurate chemotaxis requires greater mutual information. We also demonstrate that a priori information can improve chemotaxis efficiency. We compare the optimal signaling schemes with existing experimental measurements and models of eukaryotic gradient sensing. Remarkably, there is good quantitative agreement between the optimal response when no a priori assumption is made about the location of the existing source, and the observed experimental response of unpolarized Dictyostelium discoideum cells. In contrast, the measured response of polarized D. discoideum cells matches closely the optimal scheme, assuming prior knowledge of the external gradient-for example, through prolonged chemotaxis in a given direction. Our results demonstrate that different observed classes of responses in cells (polarized and unpolarized) are optimal under varying information assumptions.     

Directed evolution reveals the mechanism of HitRS signaling transduction in Bacillus anthracis

Two component systems (TCSs) are a primary mechanism of signal sensing and response in bacteria. Systematic characterization of an entire TCS could provide a mechanistic understanding of these important signal transduction systems. Here, genetic selections were employed to dissect the molecular basis of signal transduction by the HitRS system that detects cell envelope stress in the pathogen Bacillus anthracis. Numerous point mutations were isolated within HitRS, 17 of which were in a 50-residue HAMP domain. Mutational analysis revealed the importance of hydrophobic interactions within the HAMP domain and highlighted its essentiality in TCS signaling. In addition, these data defined residues critical for activities intrinsic to HitRS, uncovered specific interactions among individual domains and between the two signaling proteins, and revealed that phosphotransfer is the rate-limiting step for signal transduction. Furthermore, this study establishes the use of unbiased genetic selections to study TCS signaling and provides a comprehensive mechanistic understanding of an entire TCS.     

First-occupancy model for signal transfer in the brain

In rats and rabbits, optic nerve fibers are asymmetrically decussated. Evoked bioelectric signal/noise power ratio as a function of decussation ratio afferent to the lateral geniculate and thence to visual cortex conforms approximately to what one would expect if the visual system functioned as a parallel coherent detector. Brain mechanisms which can quantitatively account for these findings have not been previously proposed. A theoretical model is proposed to explain observed bioelectric input-output relationships in asymmetrically decussated visual systems and to suggest a general mechanism for signal transfer in the mammalian brain. The model is stochastic and is based upon earlier work concerning coherent neuronal activity. A specific quantitative implication of the model is that, on the average, three ganglion cells in the retina will drive each principal cell in the lateral geniculate. This prediction of the model is verified by recent experimental findings.     

Evolution and Design Governing Signal Precision and Amplification in a Bacterial Chemosensory Pathway

Understanding the principles underlying the plasticity of signal transduction networks is fundamental to decipher the functioning of living cells. In Myxococcus xanthus, a particular chemosensory system (Frz) coordinates the activity of two separate motility systems (the A- and S-motility systems), promoting multicellular development. This unusual structure asks how signal is transduced in a branched signal transduction pathway. Using combined evolution-guided and single cell approaches, we successfully uncoupled the regulations and showed that the A-motility regulation system branched-off an existing signaling system that initially only controlled S-motility. Pathway branching emerged in part following a gene duplication event and changes in the circuit structure increasing the signaling efficiency. In the evolved pathway, the Frz histidine kinase generates a steep biphasic response to increasing external stimulations, which is essential for signal partitioning to the motility systems. We further show that this behavior results from the action of two accessory response regulator proteins that act independently to filter and amplify signals from the upstream kinase. Thus, signal amplification loops may underlie the emergence of new connectivity in signal transduction pathways.