In the beginning: the initiation of meiosis

The most-critical point of reproductive development in all sexually reproducing species is the transition from mitotic to meiotic cell cycle. Studies in unicellular fungi have indicated that the decision to enter meiosis must be made before the beginning of the premeiotic S phase. Recent data from the mouse suggest that this timing of meiosis initiation is a universal feature shared also by multicellular eukaryotes. In contrast, the signaling cascade that leads to meiosis initiation shows great diversity among species.     

Systematic Prediction of Scaffold Proteins Reveals New Design Principles in Scaffold-Mediated Signal Transduction

Scaffold proteins play a crucial role in facilitating signal transduction in eukaryotes by bringing together multiple signaling components. In this study, we performed a systematic analysis of scaffold proteins in signal transduction by integrating protein-protein interaction and kinase-substrate relationship networks. We predicted 212 scaffold proteins that are involved in 605 distinct signaling pathways. The computational prediction was validated using a protein microarray-based approach. The predicted scaffold proteins showed several interesting characteristics, as we expected from the functionality of scaffold proteins. We found that the scaffold proteins are likely to interact with each other, which is consistent with previous finding that scaffold proteins tend to form homodimers and heterodimers. Interestingly, a single scaffold protein can be involved in multiple signaling pathways by interacting with other scaffold protein partners. Furthermore, we propose two possible regulatory mechanisms by which the activity of scaffold proteins is coordinated with their associated pathways through phosphorylation process.     

Dynamic studies of scaffold-dependent mating pathway in yeast

The mating pathway in Saccharomyces cerevisiae is one of the best understood signal transduction pathways in eukaryotes. It transmits the mating signal from plasma membrane into the nucleus through the G-protein coupled receptor and the mitogen-activated protein kinase (MAPK) cascade. According to current understanding of the mating pathway, we construct a system of ordinary differential equations to describe the process. Our model is consistent with a wide range of experiments, indicating that it captures some main characteristics of the signal transduction along the pathway. Investigation with the model reveals that the shuttling of the scaffold protein and the dephosphorylation of kinases involved in the MAPK cascade cooperate to regulate the response upon pheromone induction and to help preserve the fidelity of the mating signaling. We explored factors affecting the dose-response curves of this pathway and found that both negative feedback and concentrations of the proteins involved in the MAPK cascade play crucial roles. Contrary to some other MAPK systems where signaling sensitivity is being amplified successively along the cascade, here the mating signal is transmitted through the cascade in an almost linear fashion.     

Oscillatory dynamics arising from competitive inhibition and multisite phosphorylation

There have been a growing number of observations of oscillating protein levels (p53 and NFkB) in eukaryotic signalling pathways. This has resulted in a renewed interest in the mechanism by which such oscillations might occur. Recent computational work has shown that a multisite phosphorylation mechanism such as that found in the MAPK cascade can theoretically exhibit bistability. The bistable behavior was shown to arise from sequestration and saturation mechanisms for the enzymes that catalyse the multisite phosphorylation cycle. These effects generate the positive feedback necessary for bistability. In this paper we describe two kinds of oscillatory dynamics which can occur in a network by which, both use such bistable multisite phosphorylated cycles. In the first example, the fully phosphorylated form of the phosphorylated cycle represses the production of the kinase, which carries out the phosphorylation of the unphosphorylated states of the cycle. The dynamics of this system leads to a relaxation oscillator. In the second example, we consider a cascade of two cycles, in which the fully phosphorylated form of the kinase, in the first cycle, phosphorylates the unphosphorylated forms in the second cycle. A feedback loop, by which the fully phosphorylated form of the second cycle inhibits the kinase step in the first cycle is also present. In this case we obtain a ring oscillator. Both these networks illustrate the versatility of the multisite bistable network.     

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.     

A computational model for the identification of biochemical pathways in the krebs cycle.

We have applied an algorithmic methodology which provably decomposes any complex network into a complete family of principal subcircuits to study the minimal circuits that describe the Krebs cycle. Every operational behavior that the network is capable of exhibiting can be represented by some combination of these principal subcircuits and this computational decomposition is linearly efficient. We have developed a computational model that can be applied to biochemical reaction systems which accurately renders pathways of such reactions via directed hypergraphs (Petri nets). We have applied the model to the citric acid cycle (Krebs cycle). The Krebs cycle, which oxidizes the acetyl group of acetyl CoA to CO(2) and reduces NAD and FAD to NADH and FADH(2), is a complex interacting set of nine subreaction networks. The Krebs cycle was selected because of its familiarity to the biological community and because it exhibits enough complexity to be interesting in order to introduce this novel analytic approach. This study validates the algorithmic methodology for the identification of significant biochemical signaling subcircuits, based solely upon the mathematical model and not upon prior biological knowledge. The utility of the algebraic-combinatorial model for identifying the complete set of biochemical subcircuits as a data set is demonstrated for this important metabolic process.     

Dynamics of the cell cycle: checkpoints, sizers, and timers

We have developed a generic mathematical model of a cell cycle signaling network in higher eukaryotes that can be used to simulate both the G1/S and G2/M transitions. In our model, the positive feedback facilitated by CDC25 and wee1 causes bistability in cyclin-dependent kinase activity, whereas the negative feedback facilitated by SKP2 or anaphase-promoting-complex turns this bistable behavior into limit cycle behavior. The cell cycle checkpoint is a Hopf bifurcation point. These behaviors are coordinated by growth and division to maintain normal cell cycle and size homeostasis. This model successfully reproduces sizer, timer, and the restriction point features of the eukaryotic cell cycle, in addition to other experimental findings.     

Split decisions: coordinating cytokinesis in yeast

Cytokinesis in eukaryotes involves the regulated assembly and contraction of a ring comprising filamentous (F)-actin and myosin II. Assembly of the contractile ring occurs through the accumulation of cortical cues at the specified division plane, followed by recruitment of F-actin, myosin II and accessory proteins involved in generating the mature ring. Ring contraction is temporally regulated to occur only after chromosome segregation and, in yeast, it is controlled by a conserved signaling cascade that becomes active only after Cdk1-Cyclin-B inactivation. In this article (which is part of the Cytokinesis series), we discuss recent studies that have begun to clarify both the spatial and the temporal order of ring assembly and that have illuminated the signals that trigger ring contraction in yeast. These studies add to the growing knowledge of the processes that control eukaryotic cell division.     

Nonparametric simulation of signal transduction networks with semi-synchronized update

Simulating signal transduction in cellular signaling networks provides predictions of network dynamics by quantifying the changes in concentration and activity-level of the individual proteins. Since numerical values of kinetic parameters might be difficult to obtain, it is imperative to develop non-parametric approaches that combine the connectivity of a network with the response of individual proteins to signals which travel through the network. The activity levels of signaling proteins computed through existing non-parametric modeling tools do not show significant correlations with the observed values in experimental results. In this work we developed a non-parametric computational framework to describe the profile of the evolving process and the time course of the proportion of active form of molecules in the signal transduction networks. The model is also capable of incorporating perturbations. The model was validated on four signaling networks showing that it can effectively uncover the activity levels and trends of response during signal transduction process.     

Computational identification of four spliceosomal snRNAs from the deep-branching eukaryote Giardia intestinalis

RNAs processing other RNAs is very general in eukaryotes, but is not clear to what extent it is ancestral to eukaryotes. Here we focus on pre-mRNA splicing, one of the most important RNA-processing mechanisms in eukaryotes. In most eukaryotes splicing is predominantly catalysed by the major spliceosome complex, which consists of five uridine-rich small nuclear RNAs (U-snRNAs) and over 200 proteins in humans. Three major spliceosomal introns have been found experimentally in Giardia; one Giardia U-snRNA (U5) and a number of spliceosomal proteins have also been identified. However, because of the low sequence similarity between the Giardia ncRNAs and those of other eukaryotes, the other U-snRNAs of Giardia had not been found. Using two computational methods, candidates for Giardia U1, U2, U4 and U6 snRNAs were identified in this study and shown by RT-PCR to be expressed. We found that identifying a U2 candidate helped identify U6 and U4 based on interactions between them. Secondary structural modelling of the Giardia U-snRNA candidates revealed typical features of eukaryotic U-snRNAs. We demonstrate a successful approach to combine computational and experimental methods to identify expected ncRNAs in a highly divergent protist genome. Our findings reinforce the conclusion that spliceosomal small-nuclear RNAs existed in the last common ancestor of eukaryotes.     

MAPK cascade possesses decoupled controllability of signal amplification and duration

The three important characteristics of the output signal of mitogen activated protein kinase (MAPK) cascade are time delay between stimulus and response, amplitude gain, and duration of the output signal. In this study, we performed a sensitivity analysis on the computational model of epidermal growth factor receptor (EGFR) activated MAPK cascade developed by Schoeberl and co-workers (1) to identify the sensitive steps of the pathway affecting these characteristics. We show that the signaling network is sensitive in a decoupled manner, which provides the ability to control its output amplitude and duration one at a time. Signal duration is found sensitive only to the phosphatase reactions at the MEK level. In contrast, signal amplitude is found most sensitive to the phosphatase reactions at the ERK level. Time delay is found to be a robust characteristic of the system.     

Graded mitogen-activated protein kinase activity precedes switch-like c-Fos induction in mammalian cells

The mitogen-activated protein kinase (MAPK) pathway is an evolutionarily conserved signaling module that controls important cell fate decisions in a variety of physiological contexts. During Xenopus oocyte maturation, the MAPK cascade converts an increasing progesterone stimulus into a switch-like, all-or-nothing response. While the importance of such switch-like behavior is widely discussed in the literature, it is not known whether the MAPK pathway in mammalian cells exhibits a switch-like or graded response. For this study, we used flow cytometry and immunofluorescence to generate single-cell measurements of MAPK signaling in Swiss 3T3 fibroblasts. In contrast to the case in Xenopus oocytes, we found that ERK activation in individual mammalian cells is not ultrasensitive and shows a graded response to changes in agonist concentration. Thus, the conserved MAPK signaling module exhibits different systems-level properties in different cellular contexts. Furthermore, the graded ERK response was converted into a more switch-like behavior at the level of immediate-early gene induction and cell cycle progression. Thus, while MAPK signaling is involved in all-or-nothing cell fate decisions for both Xenopus oocyte maturation and mammalian fibroblast proliferation, the underlying mechanisms responsible for the switch-like nature of the cellular responses are different in these two systems, with the mechanism appearing to lie downstream of the kinase cascade in mammalian fibroblasts.     

Control of the eukaryotic cell cycle by MAP kinase signaling pathways.

In an often rapidly changing environment, cells must adapt by monitoring and reacting quickly to extracellular stimuli detected by membrane-bound receptors and proteins. Reversible phosphorylation of intracellular regulatory proteins has emerged as a crucial mechanism effecting the transmission and modulation of such signals and is determined by the relative activities of protein kinases and phosphatases within the cell. These are often arranged into complex signaling networks that may function independently or be subject to cross-regulation. Recently, genetic and biochemical analyses have identified the universally conserved mitogen-activated protein (MAP) kinase cascade as one of the most ubiquitous signal transduction systems. This pathway is activated after a variety of cellular stimuli and regulates numerous physiological processes, particularly the cell division cycle. Progression through the cell cycle is critically dependent on the presence of environmental growth factors and stress stimuli, and failure to correctly integrate such signals into the cell cycle machinery can lead to the accumulation of genetic damage and genomic instability characteristic of cancer cells. Here we focus on the MAP kinase cascade and discuss the molecular mechanisms by which these extensively studied signaling pathways influence cell growth and proliferation.     

The potential for signal integration and processing in interacting MAP kinase cascades

The cellular response to environmental stimuli requires biochemical information processing through which sensory inputs and cellular status are integrated and translated into appropriate responses by way of interacting networks of enzymes. One such network, the mitogen-activated protein (MAP) kinase cascade is a highly conserved signal transduction module that propagates signals from cell surface receptors to various cytosolic and nuclear targets by way of a phosphorylation cascade. We have investigated the potential for signal processing within a network of interacting feed-forward kinase cascades typified by the MAP kinase cascade. A genetic algorithm was used to search for sets of kinetic parameters demonstrating representative key input-output patterns of interest. We discuss two of the networks identified in our study, one implementing the exclusive-or function (XOR) and another implementing what we refer to as an in-band detector (IBD) or two-sided threshold. These examples confirm the potential for logic and amplitude-dependent signal processing in interacting MAP kinase cascades demonstrating limited cross-talk. Specifically, the XOR function allows the network to respond to either one, but not both signals simultaneously, while the IBD permits the network to respond exclusively to signals within a given range of strength, and to suppress signals below as well as above this range. The solution to the XOR problem is interesting in that it requires only two interacting pathways, crosstalk at only one layer, and no feedback or explicit inhibition. These types of responses are not only biologically relevant but constitute signal processing modules that can be combined to create other logical functions and that, in contrast to amplification, cannot be achieved with a single cascade or with two non-interacting cascades. Our computational results revealed surprising similarities between experimental data describing the JNK/MKK4/MKK7 pathway and the solution for the IBD that evolved from the genetic algorithm. The evolved IBD not only exhibited the required non-monotonic signal strength-response, but also demonstrated transient and sustained responses that properly reflected the input signal strength, dependence on both of the MAPKKs for signaling, phosphorylation site preferences by each of the MAPKKs, and both activation and inhibition resulting from the overexpression of one of the MAPKKs.     

Systems‐level interactions between insulin–EGF networks amplify mitogenic signaling

Crosstalk mechanisms have not been studied as thoroughly as individual signaling pathways. We exploit experimental and computational approaches to reveal how a concordant interplay between the insulin and epidermal growth factor (EGF) signaling networks can potentiate mitogenic signaling. In HEK293 cells, insulin is a poor activator of the Ras/ERK (extracellular signal‐regulated kinase) cascade, yet it enhances ERK activation by low EGF doses. We find that major crosstalk mechanisms that amplify ERK signaling are localized upstream of Ras and at the Ras/Raf level. Computational modeling unveils how critical network nodes, the adaptor proteins GAB1 and insulin receptor substrate (IRS), Src kinase, and phosphatase SHP2, convert insulin‐induced increase in the phosphatidylinositol‐3,4,5‐triphosphate (PIP₃) concentration into enhanced Ras/ERK activity. The model predicts and experiments confirm that insulin‐induced amplification of mitogenic signaling is abolished by disrupting PIP₃‐mediated positive feedback via GAB1 and IRS. We demonstrate that GAB1 behaves as a non‐linear amplifier of mitogenic responses and insulin endows EGF signaling with robustness to GAB1 suppression. Our results show the feasibility of using computational models to identify key target combinations and predict complex cellular responses to a mixture of external cues.     

Specification, annotation, visualization and simulation of a large rule-based model for ERBB receptor signaling

ABSTRACT: BACKGROUND: Mathematical/computational models are needed to understand cell signaling networks, which are complex. Signaling proteins contain multiple functional components and multiple sites of post-translational modification. The multiplicity of components and sites of modification ensures that interactions among signaling proteins have the potential to generate myriad protein complexes and post-translational modification states. As a result, the number of chemical species that can be populated in a cell signaling network, and hence the number of equations in an ordinary differential equation model required to capture the dynamics of these species, is prohibitively large. To overcome this problem, the rule-based modeling approach has been developed for representing interactions within signaling networks efficiently and compactly through coarse-graining of the chemical kinetics of molecular interactions. RESULTS: Here, we provide a demonstration that the rule-based modeling approach can be used to specify and simulate a large model for ERBB receptor signaling that accounts for site-specific details of protein-protein interactions. The model is considered large because it corresponds to a reaction network containing more reactions than can be practically enumerated. The model encompasses activation of ERK and Akt, and it can be simulated using a network-free simulator, such as NFsim, to generate time courses of phosphorylation for 55 individual serine, threonine, and tyrosine residues. The model is annotated and visualized in the form of an extended contact map. CONCLUSIONS: With the development of software that implements novel computational methods for calculating the dynamics of large-scale rule-based representations of cellular signaling networks, it is now possible to build and analyze models that include a significant fraction of the protein interactions that comprise a signaling network, with incorporation of the site-specific details of the interactions. Modeling at this level of detail is important for understanding cellular signaling.