One-sentence summary: Analysis of the ERK circuitry suggests the most effective targets in the pathway for inhibition, which may aid in drug development Editor's Summary: Biological Circuits Inform Drug Development The mitogen-activated protein kinase (MAPK) pathway involves a three-tiered kinase module, which amplifies the signal. Many cells also have negative feedback loops from the last kinase in the module back to various points upstream in the pathway. Sturm et al. show that the MAPK module with negative feedback loops results in a system like that of a negative feedback amplifier (NFA), which is an engineering design that smoothens the output to changes in input and makes a system robust to change. These NFA-like properties may explain why some cells are sensitive to inhibition of the second kinase in the cascade (they lack the feedback loops); whereas other cells are resistant to inhibition at this point (their feedback loops are intact). These results also have implications for drug development, because inhibitors that target components that are outside the NFA are more effective at inhibiting the pathway. Abstract Three-tiered kinase modules, such as the Raf-MEK-ERK mitogen-activated protein kinase pathway, are widespread in biology suggesting that this structure conveys evolutionary advantageous properties. Here, we show that the three-tiered kinase amplifier module combined with negative feedback recapitulates the design principles of a negative feedback amplifier (NFA), which is used in electronic circuits to convey robustness, output stabilization, and linearization of nonlinear signal amplification. With mathematical modelling and experimental validation, we demonstrated that the ERK pathway has properties of a NFA that (i) converts intrinsic switch-like activation kinetics into graded linear responses; (ii) conveys robustness to changes in rates of reactions within the NFA module; and (iii) stabilizes outputs in response to drug-induced perturbations of the amplifier. These properties determine biological behavior, including activation kinetics and the response to drugs.

Extracellular signal-regulated kinase (ERK) controls fundamental cellular functions, including cell fate decisions 1,2 . In PC12, cells shifting ERK activation from transient to sustained induces neuronal differentiation 3 . As ERK associates with both regulators and effectors 4 , we hypothesized that the mechanisms underlying the switch could be revealed by assessing the dynamic changes in ERK-interacting proteins that specifically occur under differentiation conditions. Using quantitative proteomics, we identified 284 ERK-interacting proteins. Upon induction of differentiation, 60 proteins changed their binding to ERK, including many proteins that were not known to participate in differentiation. We functionally characterized a subset, showing that they regulate the pathway at several levels and by different mechanisms, including signal duration, ERK localization, feedback, crosstalk with the Akt pathway and differential interaction and phosphorylation of transcription factors. Integrating these data with a mathematical model confirmed that ERK dynamics and differentiation are regulated by distributed control mechanisms rather than by a single master switch.

The MAPK (mitogen-activated protein kinase) pathway is one of the most important and intensively studied signalling pathways. It is at the heart of a molecular-signalling network that governs the growth, proliferation, differentiation and survival of many, if not all, cell types. It is de-regulated in various diseases, ranging from cancer to immunological, inflammatory and degenerative syndromes, and thus represents an important drug target. Over recent years, the computational or mathematical modelling of biological systems has become increasingly valuable, and there is now a wide variety of mathematical models of the MAPK pathway which have led to some novel insights and predictions as to how this system functions. In the present review we give an overview of the processes involved in modelling a biological system using the popular approach of ordinary differential equations. Focusing on the MAPK pathway, we introduce the features and functions of the pathway itself before comparing the available models and describing what new biological insights they have led to.

We give a description of a Petri net-based framework for modelling and analysing biochemical pathways, which unifies the qualitative, stochastic and continuous paradigms. Each perspective adds its contribution to the understanding of the system, thus the three approaches do not compete, but complement each other. We illustrate our approach by applying it to an extended model of the three stage cascade, which forms the core of the ERK signal transduction pathway. Consequently our focus is on transient behaviour analysis. We demonstrate how qualitative descriptions are abstractions over stochastic or continuous descriptions, and show that the stochastic and continuous models approximate each other. Although our framework is based on Petri nets, it can be applied more widely to other formalisms which are used to model and analyse biochemical networks. MotivationBiochemical reaction systems have by their very nature three distinctive characteristics.(1) They are inherently bipartite, i.e. they consist of two types of game players, the species and their interactions. (2) They are inherently concurrent, i.e. several interactions can usually happen independently and in parallel. (3) They are inherently stochastic, i.e. the timing behaviour of the interactions is governed by stochastic laws. So it seems to be a natural choice to model and analyse them with a formal method, which shares exactly these distinctive characteristics: stochastic Petri nets.However, due to the computational efforts required to analyse stochastic models, two abstractions are more popular: qualitative models, abstracting away from any time dependencies, and continuous models, commonly used to approximate stochastic behaviour by a deterministic one. We describe an overall framework to unify these three paradigms, providing a family of related models with high analytical power.The advantages of using Petri nets as a kind of umbrella formalism are seen in the following: M. Bernardo, P. Degano, and G. Zavattaro (Eds.): SFM