Signal response sensitivity in the yeast mitogen-activated protein kinase cascade

A Discrete Dynamical System Approach to Pathway Activation Profiles of Signaling Cascades

In living organisms, cascades of covalent modification cycles are one of the major intracellular signaling mechanisms, allowing to transduce physical or chemical stimuli of the external world into variations of activated biochemical species within the cell. In this paper, we develop a novel method to study the stimulus-response of signaling cascades and overall the concept of pathway activation profile which is, for a given stimulus, the sequence of activated proteins at each tier of the cascade. Our approach is based on a correspondence that we establish between the stationary states of a cascade and pieces of orbits of a 2D discrete dynamical system. The study of its possible phase portraits in function of the biochemical parameters, and in particular of the contraction/expansion properties around the fixed points of this discrete map, as well as their bifurcations, yields a classification of the cascade tiers into three main types, whose biological impact within a signaling network is examined. In particular, our approach enables to discuss quantitatively the notion of cascade amplification/attenuation from this new perspective. The method allows also to study the interplay between forward and "retroactive" signaling, i.e., the upstream influence of an inhibiting drug bound to the last tier of the cascade.

Characterizing inhibited tumor growth in stem-cell-driven non-spatial cancers

Healthy human tissue is highly regulated to maintain homeostasis. Secreted negative feedback factors that inhibit stem cell division and stem cell self-renewal play a fundamental role in establishing this control. The appearance of abnormal cancerous growth requires an escape from these regulatory mechanisms. In a previous study we found that for non-solid tumors if feedback inhibition on stem cell self-renewal is lost, but the feedback on the division rate is still intact, then the tumor dynamics are characterized by a relatively slow sub-exponential growth that we called inhibited growth. Here we characterize the cell dynamics of inhibited cancer growth by modeling feedback inhibition using Hill equations. We find asymptotic approximations for the growth rates of the stem cell and differentiated cell populations in terms of the strength of the inhibitory signal: stem cells grow as a power law t(1/k+1),and the differentiated cells grow as t(1/k), where k is the Hill coefficient in the feedback law regulating cell divisions. It follows that as the tumor grows, undifferentiated cells take up an increasingly large fraction of the population. Implications of these results for specific cancers including CML are discussed. Understanding how the regulatory mechanisms that continue to operate in cancer affect the rate of disease progression can provide important insights relevant to chronic or other slow progressing types of cancer.

On the origin of bistability in the Stage 2 of the Huang-Ferrell model of the MAPK signaling

Mitogen-activated protein kinases (MAPKs) are important signal transducing enzymes, unique to eukaryotes, that are involved in many pathways of cellular regulation. Successive phosphorylation cascades mediated by MAPKs serve as sensitive switches initiating various cellular processes. Apart from this basic feature, the underlying reaction network is capable of displaying other nonlinear phenomena including bistable steady states and hysteresis as well as periodic oscillations. We show that from the mechanistic point of view, bistability is a consequence of interaction between single and double phosphorylation/dephosphorylation pathways in a Stage 2 subsystem of the Huang-Ferrell model. Within this subsystem we uncover the core subnetwork obtained by systematic reduction relying on the methods of stoichiometric network analysis. For the core model we show that there is either one stable steady state or three steady states of which two are stable and point out the role of interplay between the single and double phosphorylation subnetworks in generating bistability.

Intrinsic feedbacks in MAPK signaling cascades lead to bistability and oscillations

Previous studies have demonstrated that double phosphorylation of a protein can lead to bistability if some conditions are fulfilled. It was also shown that the signaling behavior of a covalent modification cycle can be quantitatively and, more importantly, qualitatively modified when this cycle is coupled to a signaling pathway as opposed to being isolated. This property was named retroactivity. These two results are studied together in this paper showing the existence of interesting phenomena--oscillations and bistability--in signaling cascades possessing at least one stage with a double-phosphorylation cycle as in MAPK cascades.

How scaffolds shape MAPK signaling: what we know and opportunities for systems approaches

Scaffolding proteins add a new layer of complexity to the dynamics of cell signaling. Above their basic function to bring several components of a signaling pathway together, recent experimental research has found that scaffolds influence signaling in a much more complex way: scaffolds can exert some catalytic function, influence signaling by allosteric mechanisms, are feedback-regulated, localize signaling activity to distinct regions of the cell or increase pathway fidelity. Here we review experimental and theoretical approaches that address the function of two MAPK scaffolds, Ste5, a scaffold of the yeast mating pathway and KSR1/2, a scaffold of the classical mammalian MAPK signaling pathway. For the yeast scaffold Ste5, detailed mechanistic models have been valuable for the understanding of its function. For scaffolds in mammalian signaling, however, models have been rather generic and sketchy. For example, these models predicted narrow optimal scaffold concentrations, but when revisiting these models by assuming typical concentrations, rather a range of scaffold levels optimally supports signaling. Thus, more realistic models are needed to understand the role of scaffolds in mammalian signal transduction, which opens a big opportunity for systems biology.

Effects of multiple enzyme-substrate interactions in basic units of cellular signal processing

Covalent modification cycles are a ubiquitous feature of cellular signalling networks. In these systems, the interaction of an active enzyme with the unmodified form of its substrate is essential for signalling to occur. However, this interaction is not necessarily the only enzyme-substrate interaction possible. In this paper, we analyse the behaviour of a basic model of signalling in which additional, non-essential enzyme-substrate interactions are possible. These interactions include those between the inactive form of an enzyme and its substrate, and between the active form of an enzyme and its product. We find that these additional interactions can result in increased sensitivity and biphasic responses, respectively. The dynamics of the responses are also significantly altered by the presence of additional interactions. Finally, we evaluate the consequences of these interactions in two variations of our basic model, involving double modification of substrate and scaffold-mediated signalling, respectively. We conclude that the molecular details of protein-protein interactions are important in determining the signalling properties of enzymatic signalling pathways.

Protein scaffolds can enhance the bistability of multisite phosphorylation systems

The phosphorylation of a substrate at multiple sites is a common protein modification that can give rise to important structural and electrostatic changes. Scaffold proteins can enhance protein phosphorylation by facilitating an interaction between a protein kinase enzyme and its target substrate. In this work we consider a simple mathematical model of a scaffold protein and show that under specific conditions, the presence of the scaffold can substantially raise the likelihood that the resulting system will exhibit bistable behavior. This phenomenon is especially pronounced when the enzymatic reactions have sufficiently large K(M), compared to the concentration of the target substrate. We also find for a closely related model that bistable systems tend to have a specific kinetic conformation. Using deficiency theory and other methods, we provide a number of necessary conditions for bistability, such as the presence of multiple phosphorylation sites and the dependence of the scaffold binding/unbinding rates on the number of phosphorylated sites.

Scaffold-mediated nucleation of protein signaling complexes: elementary principles

Proteins with multiple binding sites play important roles in cell signaling systems by nucleating protein complexes in which, for example, enzymes and substrates are co-localized. Proteins that specialize in this function are called by a variety names, including adapter, linker and scaffold. Scaffold-mediated nucleation of protein complexes can be either constitutive or induced. Induced nucleation is commonly mediated by a docking site on a scaffold that is activated by phosphorylation. Here, by considering minimalist mathematical models, which recapitulate scaffold effects seen in more mechanistically detailed models, we obtain analytical and numerical results that provide insights into scaffold function. These results elucidate how recruitment of a pair of ligands to a scaffold depends on the concentrations of the ligands, on the binding constants for ligand-scaffold interactions, on binding cooperativity, and on the milieu of the scaffold, as ligand recruitment is affected by competitive ligands and decoy receptors. For the case of a bivalent scaffold, we obtain an expression for the unique scaffold concentration that maximally recruits a pair of monovalent ligands. Through simulations, we demonstrate that a bivalent scaffold can nucleate distinct sets of ligands to equivalent extents when the scaffold is present at different concentrations. Thus, the function of a scaffold can potentially change qualitatively with a change in copy number. We also demonstrate how a scaffold can change the catalytic efficiency of an enzyme and the sensitivity of the rate of reaction to substrate concentration. The results presented here should be useful for understanding scaffold function and for engineering scaffolds to have desired properties.