Stochastic kinetic model of two component system signalling reveals all-or-none, graded and mixed mode stochastic switching responses

Clusterin in the eye: An old dog with new tricks at the ocular surface

The multifunctional protein clusterin (CLU) was first described in 1983 as a secreted glycoprotein present in ram rete testis fluid that enhanced aggregation ('clustering') of a variety of cells in vitro. It was also independently discovered in a number of other systems. By the early 1990s, CLU was known under many names and its expression had been demonstrated throughout the body, including in the eye. Its homeostatic activities in proteostasis, cytoprotection, and anti-inflammation have been well documented, however its roles in health and disease are still not well understood. CLU is prominent at fluid-tissue interfaces, and in 1996 it was demonstrated to be the most highly expressed transcript in the human cornea, the protein product being localized to the apical layers of the mucosal epithelia of the cornea and conjunctiva. CLU protein is also present in human tears. Using a preclinical mouse model for desiccating stress that mimics human dry eye disease, the authors recently demonstrated that CLU prevents and ameliorates ocular surface barrier disruption by a remarkable sealing mechanism dependent on attainment of a critical all-or-none concentration in the tears. When the CLU level drops below the critical all-or-none threshold, the barrier becomes vulnerable to desiccating stress. CLU binds selectively to the ocular surface subjected to desiccating stress in vivo, and in vitro to LGALS3 (galectin-3), a key barrier component. Positioned in this way, CLU not only physically seals the ocular surface barrier, but it also protects the barrier cells and prevents further damage to barrier structure. CLU depletion from the ocular surface epithelia is seen in a variety of inflammatory conditions in humans and mice that lead to squamous metaplasia and a keratinized epithelium. This suggests that CLU might have a specific role in maintaining mucosal epithelial differentiation, an idea that can now be tested using the mouse model for desiccating stress. Most excitingly, the new findings suggest that CLU could serve as a novel biotherapeutic for dry eye disease.

Deciphering Parameter Sensitivity in the BvgAS Signal Transduction

To understand the switching of different phenotypic phases of Bordetella pertussis, we propose an optimized mathematical framework for signal transduction through BvgAS two-component system. The response of the network output to the sensory input has been demonstrated in steady state. An analysis in terms of local sensitivity amplification characterizes the nature of the molecular switch. The sensitivity analysis of the model parameters within the framework of various correlation coefficients helps to decipher the contribution of the modular structure in signal propagation. Once classified, the model parameters are tuned to generate the behavior of some novel strains using simulated annealing, a stochastic optimization technique.

Stochastic simulation of prokaryotic two-component signalling indicates stochasticity-induced active-state locking and growth-rate dependent bistability

Signal transduction by prokaryotes almost exclusively relies on two-component systems for sensing and responding to (extracellular) signals. Here, we use stochastic models of two-component systems to better understand the impact of stochasticity on the fidelity and robustness of signal transmission, the outcome of autoregulatory gene expression and the influence of cell growth and division. We report that two-component systems are remarkably robust against copy number fluctuations of the signalling proteins they are composed of, which enhances signal transmission fidelity. Furthermore, we find that due to stochasticity these systems can get locked in an active state for extended time periods when (initially high) signal levels drop to zero. This behaviour can contribute to a bet-hedging adaptation strategy, aiding survival in fluctuating environments. Additionally, autoregulatory gene expression can cause two-component systems to become bistable at realistic parameter values. As a result, two sub-populations of cells can co-exist-active and inactive cells, which contributes to fitness in unpredictable environments. Bistability proved robust with respect to cell growth and division, and is tunable by the growth rate. In conclusion, our results indicate how single cells can cope with the inevitable stochasticity occurring in the activity of their two-component systems. They are robust to disadvantageous fluctuations that scramble signal transduction and they exploit beneficial stochasticity that generates fitness-enhancing heterogeneity across an isogenic population of cells.

Clusterin Seals the Ocular Surface Barrier in Mouse Dry Eye

Dry eye is a common disorder caused by inadequate hydration of the ocular surface that results in disruption of barrier function. The homeostatic protein clusterin (CLU) is prominent at fluid-tissue interfaces throughout the body. CLU levels are reduced at the ocular surface in human inflammatory disorders that manifest as severe dry eye, as well as in a preclinical mouse model for desiccating stress that mimics dry eye. Using this mouse model, we show here that CLU prevents and ameliorates ocular surface barrier disruption by a remarkable sealing mechanism dependent on attainment of a critical all-or-none concentration. When the CLU level drops below the critical all-or-none threshold, the barrier becomes vulnerable to desiccating stress. CLU binds selectively to the ocular surface subjected to desiccating stress in vivo, and in vitro to the galectin LGALS3, a key barrier component. Positioned in this way, CLU not only physically seals the ocular surface barrier, but it also protects the barrier cells and prevents further damage to barrier structure. These findings define a fundamentally new mechanism for ocular surface protection and suggest CLU as a biotherapeutic for dry eye.

Role of functionality in two-component signal transduction: a stochastic study

We present a stochastic formalism for signal transduction processes in a bacterial two-component system. Using elementary mass action kinetics, the proposed model takes care of signal transduction in terms of a phosphotransfer mechanism between the cognate partners of a two-component system, viz., the sensor kinase and the response regulator. Based on the difference in functionality of the sensor kinase, the noisy phosphotransfer mechanism has been studied for monofunctional and bifunctional two-component systems using the formalism of the linear noise approximation. Steady-state analysis of both models quantifies different physically realizable quantities, e.g., the variance, the Fano factor (variance/mean), and mutual information. The resultant data reveal that both systems reliably transfer information of extracellular environment under low external stimulus and in a high-kinase-and-phosphatase regime. We extend our analysis further by studying the role of the two-component system in downstream gene regulation.

The architecture of a prototypical bacterial signaling circuit enables a single point mutation to confer novel network properties

Even a single mutation can cause a marked change in a protein's properties. When the mutant protein functions within a network, complex phenotypes may emerge that are not intrinsic properties of the protein itself. Network architectures that enable such dramatic changes in function from a few mutations remain relatively uncharacterized. We describe a remarkable example of this versatility in the well-studied PhoQ/PhoP bacterial signaling network, which has an architecture found in many two-component systems. We found that a single point mutation that abolishes the phosphatase activity of the sensor kinase PhoQ results in a striking change in phenotype. The mutant responds to stimulus in a bistable manner, as opposed to the wild-type, which has a graded response. Mutant cells in on and off states have different morphologies, and their state is inherited over many generations. Interestingly, external conditions that repress signaling in the wild-type drive the mutant to the on state. Mathematical modeling and experiments suggest that the bistability depends on positive autoregulation of the two key proteins in the circuit, PhoP and PhoQ. The qualitatively different characteristics of the mutant come at a substantial fitness cost. Relative to the off state, the on state has a lower fitness in stationary phase cultures in rich medium (LB). However, due to the high inheritance of the on state, a population of on cells can be epigenetically trapped in a low-fitness state. Our results demonstrate the remarkable versatility of the prototypical two-component signaling architecture and highlight the tradeoffs in the particular case of the PhoQ/PhoP system.

A mutation can cause significant changes to a protein's function. Since proteins often act together in genetic circuits to control various cellular processes, mutant proteins can lead to unexpected consequences for system-level behavior. In this study, we describe a remarkable example of this phenomenon in a mutant of a well-studied bacterial circuit. PhoQ and PhoP are the primary regulatory proteins in a circuit that responds to low magnesium. The wild-type (unmutated) network responds to environmental signals in an analog or graded manner. In contrast, the mutant responds to signals in an OFF-or-ON or digital fashion. Moreover, the distribution of OFF and ON cells is strongly influenced by how cells were cultured in the past. These remarkable changes can be traced to features of the wiring diagram of the PhoQ/PhoP circuit. Since these features are shared among a broad class of bacterial signaling circuits, we suggest that other circuits may show similar remarkable properties when mutated.

A link between dimerization and autophosphorylation of the response regulator PhoB

Response regulator proteins within two-component signal transduction systems are activated by phosphorylation and can catalyze their own covalent phosphorylation using small molecule phosphodonors. To date, comprehensive kinetic characterization of response regulator autophosphorylation is limited to CheY, which follows a simple model of phosphodonor binding followed by phosphorylation. We characterized autophosphorylation of the response regulator PhoB, known to dimerize upon phosphorylation. In contrast to CheY, PhoB time traces exhibited an initial lag phase and gave apparent pseudo-first order rate constants that increased with protein concentration. Furthermore, plots of the apparent autophosphorylation rate constant versus phosphodonor concentration were sigmoidal, as were PhoB binding isotherms for the phosphoryl group analog BeF3(-). Successful mathematical modeling of the kinetic data necessitated inclusion of the formation of a PhoB heterodimer (one phosphorylated and one unphosphorylated monomer) with an enhanced rate of phosphorylation. Specifically, dimerization constants for the PhoB heterodimer and homodimer (two phosphorylated monomers) were similar, but the rate constant for heterodimer phosphorylation was ~10-fold higher than for the monomer. In a test of the model, disruption of the known PhoB(N) dimerization interface by mutation led to markedly slower and noncooperative autophosphorylation kinetics. Furthermore, phosphotransfer from the sensor kinase PhoR was enhanced by dimer formation. Phosphorylation-mediated dimerization allows many response regulators to bind to tandem DNA-binding sites and regulate transcription. Our data challenge the notion that response regulator dimers primarily form between two phosphorylated monomers and raise the possibility that response regulator heterodimers containing one phosphoryl group may participate in gene regulation.

Positive feedback and temperature mediated molecular switch controls differential gene regulation in Bordetella pertussis

Based on the phosphorelay kinetics operative within BvgAS two component system we propose a mathematical framework for signal transduction and gene regulation of phenotypic phases in Bordetella pertussis. The proposed model identifies a novel mechanism of transcriptional interference between two promoters present in the bvg locus. To understand the system behavior under elevated temperature, the developed model has been studied in two different ways. First, a quasi-steady state analysis has been carried out for the two component system, comprising of sensor BvgS and response regulator BvgA. The quasi-steady state analysis reveals temperature induced sharp molecular switch, leading to amplification in the output of BvgA. Accumulation of a large pool of BvgA thus results into differential regulation of the downstream genes, including the gene encoding toxin. Numerical integration of the full network kinetics is then carried out to explore time dependent behavior of different system components, that qualitatively capture the essential features of experimental results performed in vivo. Furthermore, the developed model has been utilized to study mutants that are impaired in their ability to phosphorylate the transcription factor, BvgA, of the signaling network.

Equation-free analysis of two-component system signalling model reveals the emergence of co-existing phenotypes in the absence of multistationarity

Phenotypic differences of genetically identical cells under the same environmental conditions have been attributed to the inherent stochasticity of biochemical processes. Various mechanisms have been suggested, including the existence of alternative steady states in regulatory networks that are reached by means of stochastic fluctuations, long transient excursions from a stable state to an unstable excited state, and the switching on and off of a reaction network according to the availability of a constituent chemical species. Here we analyse a detailed stochastic kinetic model of two-component system signalling in bacteria, and show that alternative phenotypes emerge in the absence of these features. We perform a bifurcation analysis of deterministic reaction rate equations derived from the model, and find that they cannot reproduce the whole range of qualitative responses to external signals demonstrated by direct stochastic simulations. In particular, the mixed mode, where stochastic switching and a graded response are seen simultaneously, is absent. However, probabilistic and equation-free analyses of the stochastic model that calculate stationary states for the mean of an ensemble of stochastic trajectories reveal that slow transcription of either response regulator or histidine kinase leads to the coexistence of an approximate basal solution and a graded response that combine to produce the mixed mode, thus establishing its essential stochastic nature. The same techniques also show that stochasticity results in the observation of an all-or-none bistable response over a much wider range of external signals than would be expected on deterministic grounds. Thus we demonstrate the application of numerical equation-free methods to a detailed biochemical reaction network model, and show that it can provide new insight into the role of stochasticity in the emergence of phenotypic diversity.

It is a surprising fact that genetically identical bacteria, living in identical conditions, can develop in completely different ways: for example, one subpopulation might grow very fast and another very slowly. These different phenotypes are thought to be one reason why bacteria that cause disease can survive antibiotic treatment or become persistent. This diversity of behaviour is usually attributed to the existence of multiple stable phenotypic states, or to the coexistence of one stable state with another unstable excited state, or finally to the possibility of the whole biochemical system that controls the phenotype being switched on and off. In this paper we describe a different scenario that leads to phenotypic diversity in two-component system signalling, a very common mechanism that bacteria use to sense external signals and control their response to changes in their environment. We use probability theory and equation-free computational analysis to calculate the average number of molecules of each chemical species present in the two-component system and hence show that sporadic production of either of two key chemical components required for signalling can delay the response to the external signal in some bacterial cells and so lead to the emergence of two distinct cell populations.

Hybrid Modeling of Cell Signaling and Transcriptional Reprogramming and Its Application in C. elegans Development

Modeling of signal driven transcriptional reprogramming is critical for understanding of organism development, human disease, and cell biology. Many current modeling techniques discount key features of the biological sub-systems when modeling multiscale, organism-level processes. We present a mechanistic hybrid model, GESSA, which integrates a novel pooled probabilistic Boolean network model of cell signaling and a stochastic simulation of transcription and translation responding to a diffusion model of extracellular signals. We apply the model to simulate the well studied cell fate decision process of the vulval precursor cells (VPCs) in C. elegans, using experimentally derived rate constants wherever possible and shared parameters to avoid overfitting. We demonstrate that GESSA recovers (1) the effects of varying scaffold protein concentration on signal strength, (2) amplification of signals in expression, (3) the relative external ligand concentration in a known geometry, and (4) feedback in biochemical networks. We demonstrate that setting model parameters based on wild-type and LIN-12 loss-of-function mutants in C. elegans leads to correct prediction of a wide variety of mutants including partial penetrance of phenotypes. Moreover, the model is relatively insensitive to parameters, retaining the wild-type phenotype for a wide range of cell signaling rate parameters.

Protein phosphorylation in bacterial signal transduction

BACKGROUND

Protein phosphorylation has emerged as one of the major post translational modifications in bacteria, involved in regulating a myriad of physiological processes. In a complex and dynamic system such as the bacterial cell, connectivity of its components accounts for a number of emergent properties. This article is part of a Special Issue entitled: Systems Biology of Microorganisms.

SCOPE OF REVIEW

This review focuses on the implications of bacterial protein phosphorylation in cell signaling and regulation and highlights the connections and cross talk between various signaling pathways: bacterial two-component systems and serine/threonine kinases, but also the interference between phosphorylation and other post-translational modifications (methylation and acetylation).

MAJOR CONCLUSIONS

Recent technical developments in high accuracy mass spectrometry have profoundly transformed proteomics, and today exhaustive site-specific phosphoproteomes are available for a number of bacterial species. Nevertheless, prediction of phosphorylation sites remains the main guide for many researchers, so we discuss the characteristics, limits and advantages of available phosphorylation predictors.

GENERAL SIGNIFICANCE

The advent of quantitative phosphoproteomics has brought the field on the doorstep of systems biology, but a number of challenges remain before the bacterial phosphorylation networks can be efficiently modeled and their physiological role understood. This article is part of a Special Issue entitled: Systems Biology of Microorganisms.

Binary and graded evolution in time in a simple model of gene induction

We solve analytically the model of gene expression induction which consists of three steps: gene activation, gene products synthesis, and product degradation. The solution is given as a time-dependent probability distribution for gene products. Following the distribution in time from the inactive state of the gene to the stationary state we observe binary or graded response depending solely on the ratio r of the gene activation rate to the rate of the gene product degradation. If r << 1 the response is binary and the continuous transition from binary to graded response occurs between r=0.1 and r=1. Therefore, if binary response is observed during relaxation to steady state, then the activation rate constant must be smaller than the degradation rate constant.

The interplay of multiple feedback loops with post-translational kinetics results in bistability of mycobacterial stress response

Bacterial persistence is the phenomenon in which a genetically identical fraction of a bacterial population can survive exposure to stress by reduction or cessation of growth. Persistence in mycobacteria has been recently linked to a stress-response network, consisting of the MprA/MprB two-component system and alternative sigma factor sigma(E). This network contains multiple positive transcriptional feedback loops which may give rise to bistability, making it a good candidate for controlling the mycobacterial persistence switch. To analyze the possibility of bistability, we develop a method that involves decoupling of the network into transcriptional and post-translational interaction modules. As a result we reduce the dimensionality of the dynamical system and independently analyze input-output relations in the two modules to formulate a necessary condition for bistability in terms of their logarithmic gains. We show that neither the positive autoregulation in the MprA/MprB network nor the sigma(E)-mediated transcriptional feedback is sufficient to induce bistability in a biochemically realistic parameter range. Nonetheless, inclusion of the post-translational regulation of sigma(E) by RseA increases the effective cooperativity of the system, resulting in bistability that is robust to parameter variation. We predict that overexpression or deletion of RseA, the key element controlling the ultrasensitive response, can eliminate bistability.

Global regulation by the seven-component Pi signaling system

This review concerns how Escherichia coli detects environmental inorganic orthophosphate (P(i)) to regulate genes of the phosphate (Pho) regulon by the PhoR/PhoB two-component system (TCS). P(i) control by the PhoR/PhoB TCS is a paradigm of a bacterial signal transduction pathway in which occupancy of a cell surface receptor(s) controls gene expression in the cytoplasm. The P(i) signaling pathway requires seven proteins, all of which probably interact in a membrane-associated signaling complex. Our latest studies show that P(i) signaling involves three distinct processes, which appear to correspond to different states of the sensory histidine kinase PhoR: an inhibition state, an activation state, and a deactivation state. We describe a revised model for P(i) signal transduction of the E. coli Pho regulon.