Mathematical Modeling of the Cancer Cell ’ s Control Circuitry: Paving the Way to Individualized Therapeutic Strategies

Protein-protein complexes can undermine ultrasensitivity-dependent biological adaptation

Robust perfect adaptation (RPA) is a ubiquitously observed signalling response across all scales of biological organization. A major class of network architectures that drive RPA in complex networks is the Opposer module-a feedback-regulated network into which specialized integral-computing 'opposer node(s)' are embedded. Although ultrasensitivity-generating chemical reactions have long been considered a possible mechanism for such adaptation-conferring opposer nodes, this hypothesis has relied on simplified Michaelian models, which neglect the presence of protein-protein complexes. Here we develop complex-complete models of interlinked covalent-modification cycles with embedded ultrasensitivity, explicitly capturing all molecular interactions and protein complexes. Strikingly, we demonstrate that the presence of protein-protein complexes thwarts the network's capacity for RPA in any 'free' active protein form, conferring RPA capacity instead on the concentration of a larger protein pool consisting of two distinct forms of a single protein. We further show that the presence of enzyme-substrate complexes, even at comparatively low concentrations, play a crucial and previously unrecognized role in controlling the RPA response-significantly reducing the range of network inputs for which RPA can obtain, and imposing greater parametric requirements on the RPA response. These surprising results raise fundamental new questions as to the biochemical requirements for adaptation-conferring Opposer modules within complex cellular networks.

Design Principles Underlying Robust Adaptation of Complex Biochemical Networks

Biochemical networks are often characterized by tremendous complexity-both in terms of the sheer number of interacting molecules ("nodes") and in terms of the varied and incompletely understood interactions among these molecules ("interconnections" or "edges"). Strikingly, the vast and intricate networks of interacting proteins that exist within each living cell have the capacity to perform remarkably robustly, and reproducibly, despite significant variations in concentrations of the interacting components from one cell to the next and despite mutability over time of biochemical parameters. Here we consider the ubiquitously observed and fundamentally important signalling response known as robust perfect adaptation (RPA). We have recently shown that all RPA-capable networks, even the most complex ones, must satisfy an extremely rigid set of design principles, and are modular, being decomposable into just two types of network building-blocks-opposer modules and balancer modules. Here we present an overview of the design principles that characterize all RPA-capable network topologies through a detailed examination of a collection of simple examples. We also introduce a diagrammatic method for studying the potential of a network to exhibit RPA, which may be applied without a detailed knowledge of the complex mathematical principles governing RPA.

Ultrasensitivity and bistability in covalent-modification cycles with positive autoregulation

Switch-like behaviours in biochemical networks are of fundamental significance in biological signal processing, and exist as two distinct types: ultra-sensitivity and bistability. Here we propose two new models of a reversible covalent-modification cycle with positive autoregulation (PAR), a motif structure that is thought to be capable of both ultrasensitivity and bistability in different parameter regimes. These new models appeal to a modelling framework that we call complex-complete, which accounts fully for the molecular complexities of the underlying signalling mechanisms. Each of the two new models encodes a specific molecular mechanism for PAR. We demonstrate that the modelling simplifications for PAR models that have been used in previous work, which rely on Michaelian approximations, are unable to accurately recapitulate the qualitative signalling responses supported by our detailed models. Strikingly, we show that complex-complete PAR models are capable of new qualitative responses such as one-way switches and a 'prozone' effect, depending on the specific PAR-encoding mechanism, which are not supported by Michaelian simplifications. Our results highlight the critical importance of accurately representing the molecular details of biochemical signalling mechanisms, and strongly suggest that the Michaelian approximation is inadequate for predictive models of enzyme-mediated chemical reactions with added regulations such as PAR.

The evolving role of nuclear molecular imaging in cancer

BACKGROUND: Novel therapies targeted to specific tumor pathways are entering the clinic. The need for in vivo monitoring of resulting molecular changes, particularly with respect to the tumor microenvironment, is growing. Molecular imaging is evolving to include a variety of imaging methods to enable in vivo monitoring of cellular and molecular processes. OBJECTIVES: This article reviews the emerging role of molecular imaging in the development of improved therapeutic strategies that provide better patient selection for therapeutic personalization (i.e. determine which therapies have the greatest chance of success given the individual patient's disease genetic, and phenotypical profile). METHODS: In order to illustrate the utility of integrating molecular imaging into therapy development strategies, current and emerging applications of nuclear molecular imaging strategies will be compared with conventional strategies. Proposed methods of integrating molecular imaging techniques into cancer therapeutic development and limitations of these techniques will be discussed. RESULTS/CONCLUSION: Molecular imaging provides a variety of new tools to accelerate the development of cancer therapies. The recent drive to develop molecular imaging probes and standardize molecular imaging techniques is creating the scaffolding for the evolving paradigm shift to personalized cancer therapy.

Proteins, drug targets and the mechanisms they control: the simple truth about complex networks

Realizing the promise of molecularly targeted inhibitors for cancer therapy will require a new level of knowledge about how a drug target is wired into the control circuitry of a complex cellular network. Here we review general homeostatic principles of cellular networks that enable the cell to be resilient in the face of molecular perturbations, while at the same time being sensitive to subtle input signals. Insights into such mechanisms may facilitate the development of combination therapies that take advantage of the cellular control circuitry, with the aim of achieving higher efficacy at a lower drug dosage and with a reduced probability of drug-resistance development.