A mass action model of a Fibroblast Growth Factor signaling pathway and its simplification

Analytical reduction of combinatorial complexity arising from multiple protein modification sites

Combinatorial complexity is a major obstacle to ordinary differential equation (ODE) modelling of biochemical networks. For example, a protein with 10 sites that can each be unphosphorylated, phosphorylated or bound to adaptor protein requires 3(10) ODEs. This problem is often dealt with by making ad hoc assumptions which have unclear validity and disallow modelling of site-specific dynamics. Such site-specific dynamics, however, are important in many biological systems. We show here that for a common biological situation where adaptors bind modified sites, binding is slow relative to modification/demodification, and binding to one modified site hinders binding to other sites, for a protein with n modification sites and m adaptor proteins the number of ODEs needed to simulate the site-specific dynamics of biologically relevant, lumped bound adaptor states is independent of the number of modification sites and equal to m + 1, giving a significant reduction in system size. These considerations can be relaxed considerably while retaining reasonably accurate descriptions of the true system dynamics. We apply the theory to model, using only 11 ODEs, the dynamics of ligand-induced phosphorylation of nine tyrosines on epidermal growth factor receptor (EGFR) and primary recruitment of six signalling proteins (Grb2, PI3K, PLCγ1, SHP2, RasA1 and Shc1). The model quantitatively accounts for experimentally determined site-specific phosphorylation and dephosphorylation rates, differential affinities of binding proteins for the phosphorylated sites and binding protein expression levels. Analysis suggests that local concentration of site-specific phosphatases such as SHP2 in membrane subdomains by a factor of approximately 10(7) is critical for effective site-specific regulation. We further show how our framework can be extended with minimal effort to consider binding cooperativity between Grb2 and c-Cbl, which is important for receptor trafficking. Our theory has potentially broad application to reduce combinatorial complexity and allow practical simulation of a variety ODE models relevant to systems biology and pharmacology applications to allow exploration of key aspects of complexity that control signal flux.

Normal morphogenesis of epithelial tissues and progression of epithelial tumors

Epithelial cells organize into various tissue architectures that largely maintain their structure throughout the life of an organism. For decades, the morphogenesis of epithelial tissues has fascinated scientists at the interface of cell, developmental, and molecular biology. Systems biology offers ways to combine knowledge from these disciplines by building integrative models that are quantitative and predictive. Can such models be useful for gaining a deeper understanding of epithelial morphogenesis? Here, we take inventory of some recurring themes in epithelial morphogenesis that systems approaches could strive to capture. Predictive understanding of morphogenesis at the systems level would prove especially valuable for diseases such as cancer, where epithelial tissue architecture is profoundly disrupted.

Tuning the mammalian circadian clock: robust synergy of two loops

The circadian clock is accountable for the regulation of internal rhythms in most living organisms. It allows the anticipation of environmental changes during the day and a better adaptation of physiological processes. In mammals the main clock is located in the suprachiasmatic nucleus (SCN) and synchronizes secondary clocks throughout the body. Its molecular constituents form an intracellular network which dictates circadian time and regulates clock-controlled genes. These clock-controlled genes are involved in crucial biological processes including metabolism and cell cycle regulation. Its malfunction can lead to disruption of biological rhythms and cause severe damage to the organism. The detailed mechanisms that govern the circadian system are not yet completely understood. Mathematical models can be of great help to exploit the mechanism of the circadian circuitry. We built a mathematical model for the core clock system using available data on phases and amplitudes of clock components obtained from an extensive literature search. This model was used to answer complex questions for example: how does the degradation rate of Per affect the period of the system and what is the role of the ROR/Bmal/REV-ERB (RBR) loop? Our findings indicate that an increase in the RNA degradation rate of the clock gene Period (Per) can contribute to increase or decrease of the period--a consequence of a non-monotonic effect of Per transcript stability on the circadian period identified by our model. Furthermore, we provide theoretical evidence for a potential role of the RBR loop as an independent oscillator. We carried out overexpression experiments on members of the RBR loop which lead to loss of oscillations consistent with our predictions. These findings challenge the role of the RBR loop as a merely auxiliary loop and might change our view of the clock molecular circuitry and of the function of the nuclear receptors (REV-ERB and ROR) as a putative driving force of molecular oscillations.

Endothelial cell capture of heparin-binding growth factors under flow

Circulation is an important delivery method for both natural and synthetic molecules, but microenvironment interactions, regulated by endothelial cells and critical to the molecule's fate, are difficult to interpret using traditional approaches. In this work, we analyzed and predicted growth factor capture under flow using computer modeling and a three-dimensional experimental approach that includes pertinent circulation characteristics such as pulsatile flow, competing binding interactions, and limited bioavailability. An understanding of the controlling features of this process was desired. The experimental module consisted of a bioreactor with synthetic endothelial-lined hollow fibers under flow. The physical design of the system was incorporated into the model parameters. The heparin-binding growth factor fibroblast growth factor-2 (FGF-2) was used for both the experiments and simulations. Our computational model was composed of three parts: (1) media flow equations, (2) mass transport equations and (3) cell surface reaction equations. The model is based on the flow and reactions within a single hollow fiber and was scaled linearly by the total number of fibers for comparison with experimental results. Our model predicted, and experiments confirmed, that removal of heparan sulfate (HS) from the system would result in a dramatic loss of binding by heparin-binding proteins, but not by proteins that do not bind heparin. The model further predicted a significant loss of bound protein at flow rates only slightly higher than average capillary flow rates, corroborated experimentally, suggesting that the probability of capture in a single pass at high flow rates is extremely low. Several other key parameters were investigated with the coupling between receptors and proteoglycans shown to have a critical impact on successful capture. The combined system offers opportunities to examine circulation capture in a straightforward quantitative manner that should prove advantageous for biologicals or drug delivery investigations.

Computational modeling of the EGFR network elucidates control mechanisms regulating signal dynamics

Background

The epidermal growth factor receptor (EGFR) signaling pathway plays a key role in regulation of cellular growth and development. While highly studied, it is still not fully understood how the signal is orchestrated. One of the reasons for the complexity of this pathway is the extensive network of inter-connected components involved in the signaling. In the aim of identifying critical mechanisms controlling signal transduction we have performed extensive analysis of an executable model of the EGFR pathway using the stochastic pi-calculus as a modeling language.

Results

Our analysis, done through simulation of various perturbations, suggests that the EGFR pathway contains regions of functional redundancy in the upstream parts; in the event of low EGF stimulus or partial system failure, this redundancy helps to maintain functional robustness. Downstream parts, like the parts controlling Ras and ERK, have fewer redundancies, and more than 50% inhibition of specific reactions in those parts greatly attenuates signal response. In addition, we suggest an abstract model that captures the main control mechanisms in the pathway. Simulation of this abstract model suggests that without redundancies in the upstream modules, signal transduction through the entire pathway could be attenuated. In terms of specific control mechanisms, we have identified positive feedback loops whose role is to prolong the active state of key components (e.g., MEK-PP, Ras-GTP), and negative feedback loops that help promote signal adaptation and stabilization.

Conclusions

The insights gained from simulating this executable model facilitate the formulation of specific hypotheses regarding the control mechanisms of the EGFR signaling, and further substantiate the benefit to construct abstract executable models of large complex biological networks.

Biological pathways as communicating computer systems

Time and cost are the enemies of cell biology. The number of experiments required to rigorously dissect and comprehend a pathway of even modest complexity is daunting. Methods are needed to formulate biological pathways in a machine-analysable fashion, which would automate the process of considering all possible experiments in a complex pathway and identify those that command attention. In this Essay, we describe a method that is based on the exploitation of computational tools that were originally developed to analyse reactive communicating computer systems such as mobile phones and web browsers. In this approach, the biological process is articulated as an executable computer program that can be interrogated using methods that were developed to analyse complex software systems. Using case studies of the FGF, MAPK and Delta/Notch pathways, we show that the application of this technology can yield interesting insights into the behaviour of signalling pathways, which have subsequently been corroborated by experimental data.