Cells respond to countless external cues using a limited repertoire of interconnected pathways that are activated by G-protein-coupled receptors and receptor tyrosine kinases. Recent discoveries changed our perception of the signal specificity and showed that distinct spatio-temporal activation profiles of the same effectors result in diverse physiological responses. Computational models have emerged as a novel tool to provide insights into the temporal dynamics and spatial patterns of signalling responses. Mechanistic models of the epidermal-growth-factor-receptor network have created in silico replicas of signalling dynamics and generated experimentally testable hypotheses. Universal motifs of signalling networks are protein-modification cycles that are catalysed by opposing enzymes, such as a kinase and a phosphatase, or a guanine nucleotide exchange factor and a GTPase-activating protein. Modelling reveals how cycles and cascades process and integrate signals, and which feedback architecture enables robustness, linear or ultrasensitive responses, bistability and oscillations. Complex dynamics arise from simple basic motifs. Two or more phosphorylation sites potentially lead to bistability. A simple one-site modification cycle can turn into a bistable switch by four different destabilizing mechanisms; an extra stabilizing feedback loop can render this bistable switch into a relaxation oscillator by 32 distinct designs. Cells have developed mechanisms for precise sensing of their positional information. Intracellular gradients of protein activities arise from the spatial separation of opposing reactions in protein-modification cycles. These gradients provide positional cues for mitosis, motility and migration. In signalling pathways, including mitogen-activating protein kinase (MAPK) cascades, the membrane confinement of a kinase and the cytosolic localization of phosphatases can result in precipitous gradients of phosphorylated signal-transducers that spread solely by diffusion. Endocytotic trafficking of phosphorylated kinases and travelling waves of protein phosphorylation can propagate phosphorylation signals from the plasma membrane to the nucleus, especially in large cells, such as Xenopus eggs. Rapid survival signals in neurons might be transmitted by waves of protein phosphorylation that emerge from kinase/phosphatase cascades, such as the mitogen-activated protein kinase, the phosphatidylinositol–3 kinase-AKT/protein kinase B and GTPase cascades.

Mitogen-activated protein kinase (MAPK) cascades can operate as bistable switches residing in either of two different stable states. MAPK cascades are often embedded in positive feedback loops, which are considered to be a prerequisite for bistable behavior. Here we demonstrate that in the absence of any imposed feedback regulation, bistability and hysteresis can arise solely from a distributive kinetic mechanism of the two-site MAPK phosphorylation and dephosphorylation. Importantly, the reported kinetic properties of the kinase (MEK) and phosphatase (MKP3) of extracellular signal–regulated kinase (ERK) fulfill the essential requirements for generating a bistable switch at a single MAPK cascade level. Likewise, a cycle where multisite phosphorylations are performed by different kinases, but dephosphorylation reactions are catalyzed by the same phosphatase, can also exhibit bistability and hysteresis. Hence, bistability induced by multisite covalent modification may be a widespread mechanism of the control of protein activity.

Functional organization of signal transduction into protein phosphorylation cascades, such as the mitogen‐activated protein kinase (MAPK) cascades, greatly enhances the sensitivity of cellular targets to external stimuli. The sensitivity increases multiplicatively with the number of cascade levels, so that a tiny change in a stimulus results in a large change in the response, the phenomenon referred to as ultrasensitivity. In a variety of cell types, the MAPK cascades are imbedded in long feedback loops, positive or negative, depending on whether the terminal kinase stimulates or inhibits the activation of the initial level. Here we demonstrate that a negative feedback loop combined with intrinsic ultrasensitivity of the MAPK cascade can bring about sustained oscillations in MAPK phosphorylation. Based on recent kinetic data on the MAPK cascades, we predict that the period of oscillations can range from minutes to hours. The phosphorylation level can vary between the base level and almost 100% of the total protein. The oscillations of the phosphorylation cascades and slow protein diffusion in the cytoplasm can lead to intracellular waves of phospho‐proteins.

During the past decade, our knowledge of molecular mechanisms involved in growth factor signaling has proliferated almost explosively. However, the kinetics and control of information transfer through signaling networks remain poorly understood. This paper combines experimental kinetic analysis and computational modeling of the short term pattern of cellular responses to epidermal growth factor (EGF) in isolated hepatocytes. The experimental data show transient tyrosine phosphorylation of the EGF receptor (EGFR) and transient or sustained response patterns in multiple signaling proteins targeted by EGFR. Transient responses exhibit pronounced maxima, reached within 15–30 s of EGF stimulation and followed by a decline to relatively low (quasi-steady-state) levels. In contrast to earlier suggestions, we demonstrate that the experimentally observed transients can be accounted for without requiring receptor-mediated activation of specific tyrosine phosphatases, following EGF stimulation. The kinetic model predicts how the cellular response is controlled by the relative levels and activity states of signaling proteins and under what conditions activation patterns are transient or sustained. EGFR signaling patterns appear to be robust with respect to variations in many elemental rate constants within the range of experimentally measured values. On the other hand, we specify which changes in the kinetic scheme, rate constants, and total amounts of molecular factors involved are incompatible with the experimentally observed kinetics of signal transfer. Quantitation of signaling network responses to growth factors allows us to assess how cells process information controlling their growth and differentiation.

In the present paper, we describe multiple levels of cross-talk between the PI3K (phosphoinositide 3-kinase)/Akt and Ras/MAPK (mitogen-activated protein kinase) signalling pathways. Experimental data and computer simulations demonstrate that cross-talk is context-dependent and that both pathways can activate or inhibit each other. Positive influence of the PI3K pathway on the MAPK pathway is most effective at sufficiently low doses of growth factors, whereas negative influence of the MAPK pathway on the PI3K pathway is mostly pronounced at high doses of growth factors. Pathway cross-talk endows a cell with emerging capabilities for processing and decoding signals from multiple receptors activated by different combinations of extracellular cues.