Computational and Mathematical Modelling of the EGF Receptor System

This chapter gives an overview of computational and mathematical modelling of the EGF receptor system. It begins with a survey of motivations for producing such models, then describes the main approaches that are taken to carrying out such modelling, viz. differential equations and individual-based modelling. Finally, a number of projects that applying modelling and simulation techniques to various aspects of the EGF receptor system are described

Modeling Signal Transduction Using P Systems

Cellular signalling pathways are fundamental to the control and regulation of cell behavior. Understanding of biosignalling network functions is crucial to the study of different diseases and to the design of effective therapies. In this paper we present P systems as a feasible computational modeling tool for cellular signalling pathways that takes into consideration the discrete character of the components of the system and the key role played by membranes in their functioning. We illustrate these cellular models simulating the epidermal growth factor receptor (EGFR) signalling cascade and the FAS–induced apoptosis using a deterministic strategy for the evolution of P systems.Ministerio de Educación y Ciencia TIN2005-09345-C04-01Junta de Andalucía TIC 58

Spatial Stochastic Modeling of the ErbB Receptor Family

ErbB transmembrane receptors are a family of 4 receptor tyrosine kinases that interact with one another through homo and heterodimer interactions. When these dimers form, the kinase domains on the receptor tails interact with one another, transphosphorylating one another, initiating a signal cascade. The signaling pathways these receptors participate in are responsible for many different cell functions including apoptosis, growth, and proliferation. The overexpression of these receptors has been linked to various forms of cancer, emphasizing the importance of understanding how these receptors interact with one another to trigger these cascades. Single Particle Tracking experiments have provided more precise and detailed measures of dimer lifetimes and diffusion. A major observation from the experiments is the anomalous diffusion of the receptors. One suggested contributor to this anomalous diffusion is confinement zones on the membrane. In this work, we develop, validate, and implement a spatial stochastic model to study these receptors and uncover how their kinetics and dynamics as well as the membrane landscape come together to impact erbB activation. We start by focusing on erbB1. Single particle tracking experiments show that receptor pairs interact repeatedly over a period of time. One possible explanation for these repeated interactions is to facilitate phosphorylation. An asymmetric phosphorylation model is proposed, where one receptor in the dimer pair is responsible for activating the other receptor, the receiver, which then in turn phosphorylates the original activator. The model shows that the confinement zones on the membrane play a critical role in causing repeated receptor interactions and reveals that receptors dynamically switch between different activation states over time. Our work continues by delving deeper into the membrane landscape. Single particle tracking data is analyzed to investigate the characteristics of the observed anomalous diffusion. The analysis gives an estimate for the size range of the confinement zones and shows that they are a series of domains, not corrals. Taking the single particle tracking analysis one step further, we develop a Domain Reconstruction Algorithm that reconstructs confinement zone shapes and sizes from single particle tracking trajectories. In the final study, we move on to erbB2 and erbB3 interactions. ErbB3, which is traditionally believed to be kinase dead, has recently been shown to have weak kinase activity. Through kinase assay experiments, we show in the presence of erbB2 and heregulin, erbB3 has measurable kinase activity. Using the reconstructed domains from erbB2 and erbB3 data to create a simulation space, and experimental data from the kinase assay and single particle tracking, we extend the erbB1 spatial stochastic model for this study. We show that erbB2 and erbB3 have significantly different interactions with the cellular membrane confinement zones, erbB3 is dependent on erbB2 activation, and erbB3 homodimer stability inhibits erbB3 activation. Extension of the model to investigate mutation behaviors in erbB3 receptors reveals insights into how a gain of function mutation in the erbB3 kinase domain impacts erbB2 and erbB3 interactions. Finally, discovery of a gain of function mutation in the kinase domain of erbB3 is connected to an uptick in erbB3 kinase activity. As a path forward from this work, we suggest using the spatial stochastic model to investigate more possible mutations in erbB3 receptors to give better insight into which mutations would be promising to explore

EGFR oligomerization organizes kinase-active dimers into competent signalling platforms

Epidermal growth factor receptor (EGFR) signalling is activated by ligand-induced receptor dimerization. Notably, ligand binding also induces EGFR oligomerization, but the structures and functions of the oligomers are poorly understood. Here, we use fluorophore localization imaging with photobleaching to probe the structure of EGFR oligomers. We find that at physiological epidermal growth factor (EGF) concentrations, EGFR assembles into oligomers, as indicated by pairwise distances of receptor-bound fluorophore-conjugated EGF ligands. The pairwise ligand distances correspond well with the predictions of our structural model of the oligomers constructed from molecular dynamics simulations. The model suggests that oligomerization is mediated extracellularly by unoccupied ligand-binding sites and that oligomerization organizes kinase-active dimers in ways optimal for auto-phosphorylation in trans between neighbouring dimers. We argue that ligand-induced oligomerization is essential to the regulation of EGFR signalling

A Spatio-Temporal Model Reveals Self-Limiting FcɛRI Cross-Linking by Multivalent Antigens

Aggregation of cell surface receptor proteins by multivalent antigens is an essential early step for immune cell signalling. A number of experimental and modelling studies in the past have investigated multivalent ligand-mediated aggregation of IgE receptors (FcɛRI) in the plasma membrane of mast cells. However, understanding of the mechanisms of FcɛRI aggregation remains incomplete. Experimental reports indicate that FcɛRI forms relatively small and finite-sized clusters when stimulated by a multivalent ligand. By contrast, modelling studies have shown that receptor cross-linking by a trivalent ligand may lead to the formation of large receptor superaggregates that may potentially give rise to hyperactive cellular responses. In this work, we have developed a Brownian dynamics-based spatio-temporal model to analyse FcɛRI aggregation by a trivalent antigen. Unlike the existing models, which implemented non-spatial simulation approaches, our model explicitly accounts for the coarse-grained site-specific features of the multivalent species (molecules and complexes). The model incorporates membrane diffusion, steric collisions and sub-nanometre-scale site-specific interaction of the time-evolving species of arbitrary structures. Using the model, we investigated temporal evolution of the species and their diffusivities. Consistent with a recent experimental report, our model predicted sharp decay in species mobility in the plasma membrane in response receptor cross-linking by a multivalent antigen. We show that, due to such decay in the species mobility, post-stimulation receptor aggregation may become self-limiting. Our analysis reveals a potential regulatory mechanism suppressing hyperactivation of immune cells in response to multivalent antigens

Multiscale analysis and simulation of a signalling process with surface diffusion

We present and analyze a model for cell signaling processes in biological tissues. The model includes diffusion and nonlinear reactions on the cell surfaces and both inter- and intracellular signaling. Using techniques from the theory of two-scale convergence as well the unfolding method, we show convergence of the solutions to the model to solutions of a two-scale macroscopic problem. We also present a two-scale bulk-surface finite element method for the approximation of the macroscopic model. We report on some benchmarking results as well as numerical simulations in a biologically relevant regime that illustrate the influence of cell-scale heterogeneities on macroscopic concentrations

In silico simulation of tumor cell proliferation and movement based on biochemical models of mapk cascade

Systems biology allows analytical investigation of intracellular dynamics, analyzing complex processes and taking into account the interactions among the various subsystems. In this study, biochemical models describing the behavior of regulatory molecular networks were created and interfaced with a simulation system able to reproduce motility and proliferation of eukaryotic cell cultures. The primary focus was on MAPK cascades, particularly Erk1/2 activation by growth factors and mitogens such as EGF through tyrosine kinase receptors (RTKs) as Egfr, which represent a fundamental signal transduction and regulatory network affecting many cellular processes, including proliferation, motility, differentiation and survival. Erk1/2 predicted levels were related to reactions representing the progression of the cell cycle and used to modulate cell growth in a cell simulator. The biochemical model was built starting from literature data and a database of estimated protein concentrations representative of different cell types and experimental conditions and may be run for prolonged time frames and in various experimental conditions, including a vast array of cell lines. A software tool developed on purpose is able to run the model and interface with the cell simulator

The Integrin Receptor in Biologically Relevant Bilayers: Insights from Molecular Dynamics Simulations

Integrins are heterodimeric (αβ) cell surface receptors that are potential therapeutic targets for a number of diseases. Despite the existence of structural data for all parts of integrins, the structure of the complete integrin receptor is still not available. We have used available structural data to construct a model of the complete integrin receptor in complex with talin F2–F3 domain. It has been shown that the interactions of integrins with their lipid environment are crucial for their function but details of the integrin/lipid interactions remain elusive. In this study an integrin/talin complex was inserted in biologically relevant bilayers that resemble the cell plasma membrane containing zwitterionic and charged phospholipids, cholesterol and sphingolipids to study the dynamics of the integrin receptor and its effect on bilayer structure and dynamics. The results of this study demonstrate the dynamic nature of the integrin receptor and suggest that the presence of the integrin receptor alters the lipid organization between the two leaflets of the bilayer. In particular, our results suggest elevated density of cholesterol and of phosphatidylserine lipids around the integrin/talin complex and a slowing down of lipids in an annulus of ~30 Å around the protein due to interactions between the lipids and the integrin/talin F2–F3 complex. This may in part regulate the interactions of integrins with other related proteins or integrin clustering thus facilitating signal transduction across cell membranes