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

Nonlinear pharmacokinetics of therapeutic proteins resulting from receptor mediated endocytosis

Receptor mediated endocytosis (RME) plays a major role in the disposition of therapeutic protein drugs in the body. It is suspected to be a major source of nonlinear pharmacokinetic behavior observed in clinical pharmacokinetic data. So far, mostly empirical or semi-mechanistic approaches have been used to represent RME. A thorough understanding of the impact of the properties of the drug and of the receptor system on the resulting nonlinear disposition is still missing, as is how to best represent RME in pharmacokinetic models. In this article, we present a detailed mechanistic model of RME that explicitly takes into account receptor binding and trafficking inside the cell and that is used to derive reduced models of RME which retain a mechanistic interpretation. We find that RME can be described by an extended Michaelis–Menten model that accounts for both the distribution and the elimination aspect of RME. If the amount of drug in the receptor system is negligible a standard Michaelis–Menten model is capable of describing the elimination by RME. Notably, a receptor system can efficiently eliminate drug from the extracellular space even if the total number of receptors is small. We find that drug elimination by RME can result in substantial nonlinear pharmacokinetics. The extent of nonlinearity is higher for drug/receptor systems with higher receptor availability at the membrane, or faster internalization and degradation of extracellular drug. Our approach is exemplified for the epidermal growth factor receptor system

An Indirect Cue of Predation Risk Counteracts Female Preference for Conspecifics in a Naturally Hybridizing Fish Xiphophorus birchmanni

Mate choice is context dependent, but the importance of current context to interspecific mating and hybridization is largely unexplored. An important influence on mate choice is predation risk. We investigated how variation in an indirect cue of predation risk, distance to shelter, influences mate choice in the swordtail Xiphophorus birchmanni, a species which sometimes hybridizes with X. malinche in the wild. We conducted mate choice experiments to determine whether females attend to the distance to shelter and whether this cue of predation risk can counteract female preference for conspecifics. Females were sensitive to shelter distance independent of male presence. When conspecific and heterospecific X. malinche males were in equally risky habitats (i.e., equally distant from shelter), females associated primarily with conspecifics, suggesting an innate preference for conspecifics. However, when heterospecific males were in less risky habitat (i.e., closer to shelter) than conspecific males, females no longer exhibited a preference, suggesting that females calibrate their mate choices in response to predation risk. Our findings illustrate the potential for hybridization to arise, not necessarily through reproductive “mistakes”, but as one of many potential outcomes of a context-dependent mate choice strategy

Targeted Drug Delivery by Gemtuzumab Ozogamicin: Mechanism-Based Mathematical Model for Treatment Strategy Improvement and Therapy Individualization

Gemtuzumab ozogamicin (GO) is a chemotherapy-conjugated anti-CD33 monoclonal antibody effective in some patients with acute myeloid leukemia (AML). The optimal treatment schedule and optimal timing of GO administration relative to other agents remains unknown. Conventional pharmacokinetic analysis has been of limited insight for the schedule optimization. We developed a mechanism-based mathematical model and employed it to analyze the time-course of free and GO-bound CD33 molecules on the lekemic blasts in individual AML patients treated with GO. We calculated expected intravascular drug exposure (I-AUC) as a surrogate marker for the response to the drug. A high CD33 production rate and low drug efflux were the most important determinants of high I-AUC, characterizing patients with favorable pharmacokinetic profile and, hence, improved response. I-AUC was insensitive to other studied parameters within biologically relevant ranges, including internalization rate and dissociation constant. Our computations suggested that even moderate blast burden reduction prior to drug administration enables lowering of GO doses without significantly compromising intracellular drug exposure. These findings indicate that GO may optimally be used after cyto-reductive chemotherapy, rather than before, or concomitantly with it, and that GO efficacy can be maintained by dose reduction to 6 mg/m2 and a dosing interval of 7 days. Model predictions are validated by comparison with the results of EORTC-GIMEMA AML19 clinical trial, where two different GO schedules were administered. We suggest that incorporation of our results in clinical practice can serve identification of the subpopulation of elderly patients who can benefit most of the GO treatment and enable return of the currently suspended drug to clinic

Spatio-Temporal Dependence of the Signaling Response in Immune-Receptor Trafficking Networks Regulated by Cell Density: A Theoretical Model

Cell signaling processes involve receptor trafficking through highly connected networks of interacting components. The binding of surface receptors to their specific ligands is a key factor for the control and triggering of signaling pathways. In most experimental systems, ligand concentration and cell density vary within a wide range of values. Dependence of the signal response on cell density is related with the extracellular volume available per cell. This dependence has previously been studied using non-spatial models which assume that signaling components are well mixed and uniformly distributed in a single compartment. In this paper, a mathematical model that shows the influence exerted by cell density on the spatio-temporal evolution of ligands, cell surface receptors, and intracellular signaling molecules is developed. To this end, partial differential equations were used to model ligand and receptor trafficking dynamics through the different domains of the whole system. This enabled us to analyze several interesting features involved with these systems, namely: a) how the perturbation caused by the signaling response propagates through the system; b) receptor internalization dynamics and how cell density affects the robustness of dose-response curves upon variation of the binding affinity; and c) that enhanced correlations between ligand input and system response are obtained under conditions that result in larger perturbations of the equilibrium . Finally, the results are compared with those obtained by considering that the above components are well mixed in a single compartment

High- and Low-Affinity Epidermal Growth Factor Receptor-Ligand Interactions Activate Distinct Signaling Pathways

Signaling mediated by the Epidermal Growth Factor Receptor (EGFR) is crucial in normal development, and aberrant EGFR signaling has been implicated in a wide variety of cancers. Here we find that the high- and low-affinity interactions between EGFR and its ligands activate different signaling pathways. While high-affinity ligand binding is sufficient for activation of most canonical signaling pathways, low-affinity binding is required for the activation of the Signal transducers and activators of transcription (Stats) and Phospholipase C-gamma 1 (PLCγ1). As the Stat proteins are involved in many cellular responses including proliferation, migration and apoptosis, these results assign a function to low-affinity interactions that has been omitted from computational models of EGFR signaling. The existence of receptors with distinct signaling properties provides a way for EGFR to respond to different concentrations of the same ligand in qualitatively different ways

Structural and functional analysis of cellular networks with CellNetAnalyzer

BACKGROUND: Mathematical modelling of cellular networks is an integral part of Systems Biology and requires appropriate software tools. An important class of methods in Systems Biology deals with structural or topological (parameter-free) analysis of cellular networks. So far, software tools providing such methods for both mass-flow (metabolic) as well as signal-flow (signalling and regulatory) networks are lacking. RESULTS: Herein we introduce CellNetAnalyzer, a toolbox for MATLAB facilitating, in an interactive and visual manner, a comprehensive structural analysis of metabolic, signalling and regulatory networks. The particular strengths of CellNetAnalyzer are methods for functional network analysis, i.e. for characterising functional states, for detecting functional dependencies, for identifying intervention strategies, or for giving qualitative predictions on the effects of perturbations. CellNetAnalyzer extends its predecessor FluxAnalyzer (originally developed for metabolic network and pathway analysis) by a new modelling framework for examining signal-flow networks. Two of the novel methods implemented in CellNetAnalyzer are discussed in more detail regarding algorithmic issues and applications: the computation and analysis (i) of shortest positive and shortest negative paths and circuits in interaction graphs and (ii) of minimal intervention sets in logical networks. CONCLUSION: CellNetAnalyzer provides a single suite to perform structural and qualitative analysis of both mass-flow- and signal-flow-based cellular networks in a user-friendly environment. It provides a large toolbox with various, partially unique, functions and algorithms for functional network analysis.CellNetAnalyzer is freely available for academic use

Negative regulation of ErbB family receptor tyrosine kinases

Receptors of the EGF receptor or ErbB family of growth factor receptor tyrosine kinases are frequently overexpressed in a variety of solid tumours, and the aberrant activation of their tyrosine kinase activities is thought to contribute to tumour growth and progression. Much effort has been put into developing inhibitors of ErbB receptors, and both antibody and small-molecule approaches have exhibited clinical success. Recently, a number of endogenous negative regulatory proteins have been identified that suppress the signalling activity of ErbB receptors in cells. These include intracellular RING finger E3 ubiquitin ligases such as cbl and Nrdp1 that mediate ErbB receptor degradation, and may include a wide variety of secreted and transmembrane proteins that suppress receptor activation by growth factor ligands. It will be of interest to determine the extent to which tumour cells suppress these pathways to promote their progression, and whether restoration of endogenous receptor-negative regulatory pathways may be exploited for therapeutic benefit