Signaling through receptors and scaffolds: independent interactions reduce combinatorial complexity

Chemical organisation theory

Complex dynamical reaction networks consisting of many components that interact and produce each other are difficult to understand, especially, when new component types may appear and present component types may vanish completely. Inspired by Fontana and Buss (Bull. Math. Biol., 56, 1-64) we outline a theory to deal with such systems. The theory consists of two parts. The first part introduces the concept of a chemical organisation as a closed and self-maintaining set of components. This concept allows to map a complex (reaction) network to the set of organisations, providing a new view on the system's structure. The second part connects dynamics with the set of organisations, which allows to map a movement of the system in state space to a movement in the set of organisations. The relevancy of our theory is underlined by a theorem that says that given a differential equation describing the chemical dynamics of the network, then every stationary state is an instance of an organisation. For demonstration, the theory is applied to a small model of HIV-immune system interaction by Wodarz and Nowak (Proc. Natl. Acad. USA, 96, 14464-14469) and to a large model of the sugar metabolism of E. Coli by Puchalka and Kierzek (Biophys. J., 86, 1357-1372). In both cases organisations where uncovered, which could be related to functions.

Systems biology--an engineering perspective

The interdisciplinary field of systems biology has evolved rapidly over the last years. Different disciplines have aided the development of both its experimental and theoretical branches. One field, which has played a significant role is engineering science and, in particular chemical engineering. Here, we review and illustrate some of these contributions, ranging from modeling approaches to model analysis with a special focus on technique which have not yet been substantially exploited but can be potentially useful in the analysis of biochemical systems.

Rules for modeling signal-transduction systems

Formalized rules for protein-protein interactions have recently been introduced to represent the binding and enzymatic activities of proteins in cellular signaling. Rules encode an understanding of how a system works in terms of the biomolecules in the system and their possible states and interactions. A set of rules can be as easy to read as a diagrammatic interaction map, but unlike most such maps, rules have precise interpretations. Rules can be processed to automatically generate a mathematical or computational model for a system, which enables explanatory and predictive insights into the system's behavior. Rules are independent units of a model specification that facilitate model revision. Instead of changing a large number of equations or lines of code, as may be required in the case of a conventional mathematical model, a protein interaction can be introduced or modified simply by adding or changing a single rule that represents the interaction of interest. Rules can be defined and visualized by using graphs, so no specialized training in mathematics or computer science is necessary to create models or to take advantage of the representational precision of rules. Rules can be encoded in a machine-readable format to enable electronic storage and exchange of models, as well as basic knowledge about protein-protein interactions. Here, we review the motivation for rule-based modeling; applications of the approach; and issues that arise in model specification, simulation, and testing. We also discuss rule visualization and exchange and the software available for rule-based modeling.

Stochastic dynamics of macromolecular-assembly networks

The formation and regulation of macromolecular complexes provides the backbone of most cellular processes, including gene regulation and signal transduction. The inherent complexity of assembling macromolecular structures makes current computational methods strongly limited for understanding how the physical interactions between cellular components give rise to systemic properties of cells. Here, we present a stochastic approach to study the dynamics of networks formed by macromolecular complexes in terms of the molecular interactions of their components. Exploiting key thermodynamic concepts, this approach makes it possible to both estimate reaction rates and incorporate the resulting assembly dynamics into the stochastic kinetics of cellular networks. As prototype systems, we consider the lac operon and phage lambda induction switches, which rely on the formation of DNA loops by proteins and on the integration of these protein-DNA complexes into intracellular networks. This cross-scale approach offers an effective starting point to move forward from network diagrams, such as those of protein-protein and DNA-protein interaction networks, to the actual dynamics of cellular processes.

Scaffolding protein Grb2-associated binder 1 sustains epidermal growth factor-induced mitogenic and survival signaling by multiple positive feedback loops

Grb2-associated binder 1 (GAB1) is a scaffold protein involved in numerous interactions that propagate signaling by growth factor and cytokine receptors. Here we explore in silico and validate in vivo the role of GAB1 in the control of mitogenic (Ras/MAPK) and survival (phosphatidylinositol 3-kinase (PI3K)/Akt) signaling stimulated by epidermal growth factor (EGF). We built a comprehensive mechanistic model that allows for reliable predictions of temporal patterns of cellular responses to EGF under diverse perturbations, including different EGF doses, GAB1 suppression, expression of mutant proteins, and pharmacological inhibitors. We show that the temporal dynamics of GAB1 tyrosine phosphorylation is significantly controlled by positive GAB1-PI3K feedback and negative MAPK-GAB1 feedback. Our experimental and computational results demonstrate that the essential function of GAB1 is to enhance PI3K/Akt activation and extend the duration of Ras/MAPK signaling. By amplifying positive interactions between survival and mitogenic pathways, GAB1 plays the critical role in cell proliferation and tumorigenesis.

Cell-signalling dynamics in time and space

The specificity of cellular responses to receptor stimulation is encoded by the spatial and temporal dynamics of downstream signalling networks. Temporal dynamics are coupled to spatial gradients of signalling activities, which guide pivotal intracellular processes and tightly regulate signal propagation across a cell. Computational models provide insights into the complex relationships between the stimuli and the cellular responses, and reveal the mechanisms that are responsible for signal amplification, noise reduction and generation of discontinuous bistable dynamics or oscillations.

Gradients in the self-organization of the mitotic spindle

Recent evidence points at a role of protein interaction gradients around chromatin in mitotic spindle morphogenesis in large eukaryotic cells. Here, we explain how gradients can arise over distances of tens of microns around supramolecular structures from mixtures of soluble molecules. We discuss how coupled sets of such reaction diffusion processes generate the spatial information that determines the local dynamics of microtubules required to form a bipolar spindle. We argue that such reaction diffusion processes are involved in the self-organization of supramolecular structures in the cell.

Trading the micro-world of combinatorial complexity for the macro-world of protein interaction domains

Membrane receptors and proteins involved in signal transduction display numerous binding domains and operate as molecular scaffolds generating a variety of parallel reactions and protein complexes. The resulting combinatorial explosion of the number of feasible chemical species and, hence, different states of a network greatly impedes mechanistic modeling of signaling systems. Here we present novel general principles and identify kinetic requirements that allow us to replace a mechanistic picture of all possible micro-states and transitions by a macro-description of states of separate binding sites of network proteins. This domain-oriented approach dramatically reduces computational models of cellular signaling networks by dissecting mechanistic trajectories into the dynamics of macro- and meso-variables. We specify the conditions when the temporal dynamics of micro-states can be exactly or approximately expressed in terms of the product of the relative concentrations of separate domains. We prove that our macro-modeling approach equally applies to signaling systems with low population levels, analyzed by stochastic rather than deterministic equations. Thus, our results greatly facilitate quantitative analysis and computational modeling of multi-protein signaling networks.

A domain-oriented approach to the reduction of combinatorial complexity in signal transduction networks

BACKGROUND

Receptors and scaffold proteins possess a number of distinct domains and bind multiple partners. A common problem in modeling signaling systems arises from a combinatorial explosion of different states generated by feasible molecular species. The number of possible species grows exponentially with the number of different docking sites and can easily reach several millions. Models accounting for this combinatorial variety become impractical for many applications.

RESULTS

Our results show that under realistic assumptions on domain interactions, the dynamics of signaling pathways can be exactly described by reduced, hierarchically structured models. The method presented here provides a rigorous way to model a large class of signaling networks using macro-states (macroscopic quantities such as the levels of occupancy of the binding domains) instead of micro-states (concentrations of individual species). The method is described using generic multidomain proteins and is applied to the molecule LAT.

CONCLUSION

The presented method is a systematic and powerful tool to derive reduced model structures describing the dynamics of multiprotein complex formation accurately.