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.     

Cell population-based model of dermal wound invasion with heterogeneous intracellular signaling properties

A deterministic model of dermal wound invasion, which accounts for the platelet-derived growth factor (PDGF) gradient sensing mechanism in fibroblasts mediated by cell surface receptors and the phosphoinositide 3-kinase (PI3K) signal transduction pathway, was previously described (Biophys J 2006; 90:2297–308). Here, we extend that work and implement a hybrid modeling strategy that treats fibroblasts as discrete entities endowed with heterogeneous properties, namely receptor, PI3K and 3′ phosphoinositide phosphatase expression levels. Analysis of the model suggests that the wound environment fosters the advancement of cells within the population that are better fit to migrate and/or proliferate in response to PDGF stimulation. Thus, cell-to-cell variability results in a significantly higher rate of wound invasion as compared with the deterministic model, in a manner that depends on the way in which individual cell properties are sampled or inherited upon cell division.Key words: wound healing, chemotaxis, gradient sensing, mathematical model, stochastic, signal transduction, phosphoinositide 3-kinase, PDGF     

cAMP regulation of early gene expression in signal transduction mutants of Dictyostelium

We have examined the regulation of three early developmentally regulated genes in Dictyostelium. Two of these genes (D2 and M3) are induced by pulses of cAMP and the other (K5) is repressed. Expression of these genes has been examined in a number of developmental mutants that are specifically blocked in various aspects of the signal transduction/cAMP relay system involved in aggregation and control of early development. The mutant strains include Synag mutants, which are blocked in receptor-mediated activation of adenylate cyclase and do not relay cAMP pulses; FrigidA mutants, which are blocked in receptor-mediated activation of both adenylate cyclase and the putative phosphoinositol bisphosphate (PIP2) turnover pathway and appear to be mutations in the gene encoding one of the G alpha protein subunits; and a StreamerF allele, which lacks cGMP-specific cGMP phosphodiesterase. From the analysis of the developmental expression of these genes under a variety of conditions in these mutant strains, we have drawn a number of conclusions concerning the modes of regulation of these genes. Full induction of D2 and M3 genes requires cAMP interaction with the cell surface receptor and an "oscillation" of the receptor between active and adapted forms. Induction of these genes does not require activation of the signal transduction pathway that leads to adenylate cyclase activation and cAMP relay, but does require activation of other receptor-mediated intracellular signal transduction pathways, possibly that involving PIP2 turnover. Likewise, repression of the K5 gene requires pulses of cAMP. Expression of this gene is insensitive to cAMP pulses in FrigidA mutants, suggesting that a signal transduction pathway is necessary for its repression. Results using the StreamerF mutant suggest that the rise in cGMP in response to cAMP/receptor interactions may not be directly related to control of the pulse-induced genes. In addition, we have examined the effect of caffeine, which M. Brenner and S.D. Thomas (1984, Dev. Biol., 101, 136-146) showed preferentially blocks the cAMP relay system by blocking receptor-mediated activation of adenylate cyclase. We show that in many of the mutants and in an axenic wild-type strain, caffeine causes the induction of pulse-induced gene expression to almost wild-type levels or in some cases to higher than wild-type levels. Our data suggest that caffeine works by activating some step in the signal transduction pathway that must lie downstream from both the receptor and at least one of the G proteins and thus has effects other than simply blocking the receptor-mediated cAMP relay system.     

Analysis of the signal transduction properties of a module of spatial sensing in eukaryotic chemotaxis

The movement of cells in response to a gradient in chemical concentration—known as chemotaxis—is crucial for the proper functioning of uni-and multicellular organisms. How a cell senses the chemical concentration gradient surrounding it, and what signal is transmitted to its motion apparatus is known as gradient sensing. The ability of a cell to sense gradients persists even when the cell is immobilized (i.e., its motion apparatus is deactivated). This suggests that important features of gradient sensing can be studied in isolation, decoupling this phenomenon from the movement of the cell. A mathematical model for gradient sensing in Dictyostelium cells and neutrophils was recently proposed. This consists of an adaptation/spatial sensing module. This spatial sensing module feeds into an amplification module, magnifying the effects of the former. In this paper, we analyze the spatial sensing module in detail and examine its signal transduction properties. We examine the response of this module to several inputs of experimental and biological relevance.     

Morphology matters in immune cell chemotaxis: membrane asymmetry affects amplification

A key mediator of eukaryotic chemotaxis is the asymmetric accumulation of phosphatidylinositol-3,4,5-triphosphate (PIP3) on the cell membrane. Recent work has focused on understanding how a shallow external gradient of chemoattractant leads to an amplified internal gradient of PIP3. In this paper we dissect what fraction of this amplification is derived biochemically by the signal transduction network and how much arises entirely from the effects of cell morphology. Here we identify and formalize the role of morphology in signal detection and demonstrate its effects through simulation and experiments. Our key result is that an asymmetric distribution of membrane accounts for approximately one-half of the measured amplification from ligand concentration to PIP3 production. We also show that the underlying biochemical network behaves as a linear amplifier in the micropipette assay.     

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.     

Three-dimensional stochastic off-lattice model of binding chemistry in crowded environments

Molecular crowding is one of the characteristic features of the intracellular environment, defined by a dense mixture of varying kinds of proteins and other molecules. Interaction with these molecules significantly alters the rates and equilibria of chemical reactions in the crowded environment. Numerous fundamental activities of a living cell are strongly influenced by the crowding effect, such as protein folding, protein assembly and disassembly, enzyme activity, and signal transduction. Quantitatively predicting how crowding will affect any particular process is, however, a very challenging problem because many physical and chemical parameters act synergistically in ways that defy easy analysis. To build a more realistic model for this problem, we extend a prior stochastic off-lattice model from two-dimensional (2D) to three-dimensional (3D) space and examine how the 3D results compare to those found in 2D. We show that both models exhibit qualitatively similar crowding effects and similar parameter dependence, particularly with respect to a set of parameters previously shown to act linearly on total reaction equilibrium. There are quantitative differences between 2D and 3D models, although with a generally gradual nonlinear interpolation as a system is extended from 2D to 3D. However, the additional freedom of movement allowed to particles as thickness of the simulation box increases can produce significant quantitative change as a system moves from 2D to 3D. Simulation results over broader parameter ranges further show that the impact of molecular crowding is highly dependent on the specific reaction system examined.     

Antigen receptor-induced signal transduction imbalances associated with the negative selection of immature B cells

Signals transduced through the B cell Ag receptor (BCR) drive B cell development. However, BCR-induced responses are developmentally regulated; immature B cells are tolerized following antigenic exposure while mature B cells are triggered to proliferate and differentiate. This differential responsiveness allows for the negative selection of self-reactive immature B cells while simultaneously allowing for clonal expansion of mature B cells in response to foreign Ags. Intrinsic differences in BCR-induced signal transduction at various stages of development may account for this functional dichotomy. We had previously demonstrated that the BCR-induced proliferation of mature B cells is accompanied by an increase in intracellular calcium levels and polyphosphoinositide bis phosphate (PIP2) hydrolysis. In contrast, immature B cells that undergo BCR-induced apoptosis increase intracellular calcium in the relative absence of PIP2 hydrolysis. Since PIP2 hydrolysis leads to the generation of diacylglycerol, a cofactor for protein kinase C (PKC) activation, these data suggested that an "imbalance" in BCR-induced signal transduction resulting from a relative inability to activate PKC may play a role in the susceptibility of immature B cells to BCR-induced apoptosis. In support of this hypothesis, we demonstrate that PKC activation can rescue immature B cells from BCR-induced apoptosis. Furthermore, the susceptibility of immature B cells to BCR-induced apoptosis is recapitulated in mature B cells that are either PKC depleted or are stimulated in the presence of PKC inhibitors, suggesting that an uncoupling of PKC activation from BCR-induced signaling is responsible for the apoptotic response of immature B 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.     

Pulsatile signaling in intercellular communication. Periodic stimuli are more efficient than random or chaotic signals in a model based on receptor desensitization.

The efficiency of various patterns of pulsatile stimulation is determined in a model in which a receptor becomes desensitized in the presence of its stimulatory ligand. The effect of stochastic or chaotic changes in the duration and/or interval between successive pulses in a series of square-wave stimuli is investigated. Before addressing the effect of random variations in the pulsatile signal, we first extend the results of a previous analysis (Li, Y.X., and A. Goldbeter. 1989. Biophys. J. 55:125-145) by demonstrating the existence of an optimal periodic signal that maximizes target cell responsiveness whatever the magnitude of stimulation. As to the effect of stochastic or chaotic variations in the pulsatile stimulus, three kinds of random distributions are used, namely, a Gaussian and a white-noise distribution, and a chaotic time series generated by the logistic map. All these random distributions are symmetrically centered around the reference value of the duration or interval that characterizes the optimal periodic stimulus yielding maximal responsiveness in target cells. Stochastically or chaotically varying pulses are less effective than the periodic signal that corresponds to the optimal pattern of pulsatile stimulation. The response of the receptor system is most sensitive to changes in the time interval that separates successive stimuli. Similar conclusions hold when stochastic or chaotic signals are compared to a reference periodic stimulus differing from the optimal one, although the effect of random variations is then reduced. The decreased efficiency of stochastic pulses accounts for the observed superiority of periodic versus stochastic pulses of cyclic AMP (cAMP) in Dictyostelium amoebae. The results are also discussed with respect to the efficiency of periodic versus stochastic or chaotic patterns of hormone secretion.     

Langevin equation,Fokker-Planck equation and cell migration

Cell migration can be characterized by two independent variables: the speed,v, and the migration angle, ϕ. Each variable can be described by a stochastic differential equation—a Langevin equation. The migration behaviour of an ensemble of cells can be predicted due to the stochastic processes involved in the signal transduction/response system of each cell. Distribution functions, correlation functions, etc. are determined by using the corresponding Fokker-Planck equation. The model assumptions are verified by experimental results. The theoretical predictions are mainly compared with the galvanotactic response of human granulocytes. The coefficient characterizing the mean effect of the signal transduction/response system of the cell is experimentally determined to 0.08 mm/V sec (galvanotaxis) or 0.7 mm/sec (chemotaxis) and the characteristic time characterizing stochastic effects in the signal transduction/response system is experimentally determined as 30 sec. The temporal directed response induced by electric field pulses is investigated: the experimental cells react slower but are more sensitive than predicted by theory.     

Coupled Stochastic Spatial and Non-Spatial Simulations of ErbB1 Signaling Pathways Demonstrate the Importance of Spatial Organization in Signal Transduction

Background

The ErbB family of receptors activates intracellular signaling pathways that control cellular proliferation, growth, differentiation and apoptosis. Given these central roles, it is not surprising that overexpression of the ErbB receptors is often associated with carcinogenesis. Therefore, extensive laboratory studies have been devoted to understanding the signaling events associated with ErbB activation.

Methodology/Principal Findings

Systems biology has contributed significantly to our current understanding of ErbB signaling networks. However, although computational models have grown in complexity over the years, little work has been done to consider the spatial-temporal dynamics of receptor interactions and to evaluate how spatial organization of membrane receptors influences signaling transduction. Herein, we explore the impact of spatial organization of the epidermal growth factor receptor (ErbB1/EGFR) on the initiation of downstream signaling. We describe the development of an algorithm that couples a spatial stochastic model of membrane receptors with a nonspatial stochastic model of the reactions and interactions in the cytosol. This novel algorithm provides a computationally efficient method to evaluate the effects of spatial heterogeneity on the coupling of receptors to cytosolic signaling partners.

Conclusions/Significance

Mathematical models of signal transduction rarely consider the contributions of spatial organization due to high computational costs. A hybrid stochastic approach simplifies analyses of the spatio-temporal aspects of cell signaling and, as an example, demonstrates that receptor clustering contributes significantly to the efficiency of signal propagation from ligand-engaged growth factor receptors.     

Stochasticity of Intranuclear Biochemical Reaction Processes Controls the Final Decision of Cell Fate Associated with DNA Damage

A massive integrative mathematical model of DNA double-strand break (DSB) generation, DSB repair system, p53 signaling network, and apoptosis induction pathway was constructed to explore the dominant factors of unknown criteria of cell fate decision. In the proposed model, intranuclear reactions were modeled as stochastic processes and cytoplasmic reactions as deterministic processes, and both reaction sets were simulated simultaneously. The simulated results at the single-cell level showed that the model generated several sustained oscillations (pulses) of p53, Mdm2, ATM, and Wip1, and cell-to-cell variability in the number of p53 pulses depended on IR intensity. In cell populations, the model generated damped p53 oscillations, and IR intensity affected the amplitude of the first p53 oscillation. Cells were then subjected to the same IR dose exhibiting apoptosis induction variability. These simulated results are in quantitative agreement with major biological findings observed in human breast cancer epithelial MCF7, NIH3T3, and fibrosarcoma cells, demonstrating that the proposed model was concededly biologically appropriate. Statistical analysis of the simulated results shows that the generation of multiple p53 pulses is a prerequisite for apoptosis induction. Furthermore, cells exhibited considerable individual variability in p53 dynamics, which correlated with intrinsic apoptosis induction. The simulated results based on the proposed model demonstrated that the stochasticity of intranuclear biochemical reaction processes controls the final decision of cell fate associated with DNA damage. Applying stochastic simulation to an exploration of intranuclear biochemical reaction processes is indispensable in enhancing the understanding of the dynamic characteristics of biological multi-layered systems of higher organisms.     

skittles,a Drosophila phosphatidylinositol 4-phosphate 5-kinase,is required for cell viability,germline development and bristle morphology,but not for neurotransmitter release.

The phosphatidylinositol pathway is implicated in the regulation of numerous cellular functions and responses to extracellular signals. An important branching point in the pathway is the phosphorylation of phosphatidylinositol 4-phosphate by the phosphatidylinositol 4-phosphate 5-kinase (PIP5K) to generate the second messenger phosphatidylinositol 4,5-bis-phosphate (PIP2). PIP5K and PIP2 have been implicated in signal transduction, cytoskeletal regulation, DNA synthesis, and vesicular trafficking. We have cloned and generated mutations in a Drosophila PIP5K type I (skittles). Our analysis indicates that skittles is required for cell viability, germline development, and the proper structural development of sensory bristles. Surprisingly, we found no evidence for PIP5KI involvement in neural secretion.     

Studies of Signal Transduction of Salicylic Acid in Cucumber Cells

For the first time, the signal transduction pathway of salicylic acid (SA) was investigated by using 3H-labelling, thin-layer chromatography and anion exchange column chromatography. It was found that SA stimulated the activity of membrane bound phospholipase C (PLC), accelerated the bm&down of phosphatidylinositol-4-monophosphate (PIP) and phosphatidylinositol-4,5-bisphos- phate (PIP2) and increased the levels of inositol-1,4-bisphosphate (IP2), inositol-1, 4,5-trisphos- phate (IP3) and diacylglycerol (DAG). These indicated that signal transduction of SA was probably accomplished through the mediation of phosphatidylinositide signal transduction system in cucumber ( Cucumis sativa L. ).     

The synergistic effect of serotonin and epinephrine on the human platelet at the level of signal transduction

Simultaneous addition to platelets of submaximal amounts of excitatory agonists acts synergistically in provoking secretory and aggregatory responses. By measuring changes in intracellular free Ca2+ concentration, inositol phospholipid metabolism and protein phosphorylation, we verified whether synergism could be evidenced at the level of signal transduction. Challenging platelets with epinephrine only induced minor changes on the measured parameters. However, when added together with serotonin, epinephrine amplified mobilisation of intracellular Ca2+, PA formation, PIP formation, protein kinase C and myosin light chain kinase activity as compared to the alterations induced by serotonin alone. It is concluded that synergistic effects on simultaneous addition of serotonin and epinephrine might originate at the level of signal transduction.     

Putative role of inositol phospholipid metabolism in neurons

Inositol phospholipids play a crucial role in the intracellular signal transduction in most cell types. Activation of an enzyme called phospholipase C or PIP2-phosphodiesterase (PIP2-PDE) leads to the production of two second messenger molecules, diacylglycerol (DG) and inositol 1,4,5-triphosphate (IP3). DG activates a kinase called protein kinase C, whereas IP3 mediates the release of Ca2+ from intracellular storage sites. The measurement of IP3 and its degradation products, inositol diphosphate (IP2) and inositol monophosphate (IP1) provides a way of assessing the extent to which this complex system has been activated. In the central nervous system (CNS) most of the studies on the neurotransmitter stimulated formation of inositol phosphates (IPs) have been performed on brain slices, a mixture of mainly neurons and glial cells. The recent development of pure neuronal cultures provides a means of determining which of these responses were of neuronal origin. The purpose of this review is to summarize the results obtained in neurons in primary culture together with a brief appraisal of the possible function of this second messenger system in neurons.     

Quantitative imaging of single live cells reveals spatiotemporal dynamics of multistep signaling events of chemoattractant gradient sensing in Dictyostelium

Activation of G-protein-coupled chemoattractant receptors triggers dissociation of Galpha and Gbetagamma subunits. These subunits induce intracellular responses that can be highly polarized when a cell experiences a gradient of chemoattractant. Exactly how a cell achieves this amplified signal polarization is still not well understood. Here, we quantitatively measure temporal and spatial changes of receptor occupancy, G-protein activation by FRET imaging, and PIP3 levels by monitoring the dynamics of PH(Crac)-GFP translocation in single living cells in response to different chemoattractant fields. Our results provided the first direct evidence that G-proteins are activated to different extents on the cell surface in response to asymmetrical stimulations. A stronger, uniformly applied stimulation triggers not only a stronger G-protein activation but also a faster adaptation of downstream responses. When naive cells (which have not experienced chemoattractant) were abruptly exposed to stable cAMP gradients, G-proteins were persistently activated throughout the entire cell surface, whereas the response of PH(Crac)-GFP translocation surprisingly consisted of two phases, an initial transient and asymmetrical translocation around the cell membrane, followed by a second phase producing a highly polarized distribution of PH(Crac)-GFP. We propose a revised model of gradient sensing, suggesting an important role for locally controlled components that inhibit PI3Kinase activity.