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Cell-signalling dynamics in time and space

Key Points

  • 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.

Abstract

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.

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Figure 1: Universal motifs of cell-signalling networks.
Figure 2: Feedback designs that can turn a universal signalling cycle into a bistable switch and relaxation oscillator.
Figure 3: Spatial segregation of two opposing enzymes in a protein-modification cycle generates intracellular gradients.

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Acknowledgements

I am grateful to J. Hoek, M. Birtwistle, A. Kiyatkin, N. Markevich, J. Pastorino and M. Tsyganov for stimulating discussions and help with illustrative materials. I apologize that it was not possible to cite all of the many valuable contributions to the field. This work is supported by a National Institutes of Health grant.

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FURTHER INFORMATION

Boris N. Kholodenko's homepage

The International Consortium 'Systems Biology of RTK signalling'

The Systems Biology Markup Language (SBML) page

BioModels Database

BioNetGen

DOQCS

DBsolve

Gepasi

Systems Biology Workbench

Silicon Cell

SigPath

Virtual Cell

XPPAUT

EGF signalling pathway

Signalling pathway mediated by EGF

Glossary

Apoptosis

Active cell death; the process by which cells commit suicide.

Steady state

A dynamic system state that does not change over time. If a system is described by differential equations, a steady state is determined by equating the time derivatives of all variables to zero.

Brownian motion

Random, thermal motion of molecular species.

Travelling wave

A wave that propagates through a medium (a classical example is a solution that travels at constant velocity with fixed shape, but there are more types of waves).

Temporal dynamics

A quantitative description of how a system changes over time.

Deterministic

A dynamic system is deterministic if its trajectory is uniquely determined by the initial state and a given parameter set.

Stochastic

A system that, at a given initial state in the phase space, can go to different states with different probabilities. The same input given to a stochastic system several times will result in different trajectories, whereas for a deterministic system the outcomes will be identical.

Ordinary differential equation

An equation in which differentiation occurs with respect to only a single independent variable. A partial differential equation contains partial derivatives with respect to two or more independent variables.

Guanine nucleotide exchange factor

(GEF). A protein that catalyses the exchange of GDP for GTP for a GTP-binding protein.

GTPase-activating protein

(GAP). A protein that facilitates the GTP hydrolysis by a GTP-binding protein.

Bistability

Coexistence of two stable steady states separated by an unstable steady state.

Relaxation oscillations

Relaxation oscillations usually arise when a slow process causes a bistable dynamic system to switch periodically between steady states.

Dynamic system

A group of interacting components described mathematically by the state variables that are coordinates in an abstract phase space or state space. Dynamic systems can be deterministic or stochastic. A special dynamical rule specifies the immediate changes in the state variables, thereby generating the trajectory in the phase space.

Parameter

A fixed quantity in a mathematical model, as opposed to a variable.

Hysteresis

Different steady states are reached depending on whether a bifurcation parameter increases or decreases (a kind of 'memory'). As a parameter is increased, the system jumps to the alternative state at a particular value of the parameter. However, if the parameter then decreases, the system jumps back to the original state at a lower parameter value.

Multi-stability

Coexistence of more than two stable steady states at given parameter values.

Bifurcation

An abrupt qualitative change in the system's dynamics when one or more parameter pass through critical values, for instance the loss of stability and appearance of sustained oscillations.

Diffusion-limited rate

An upper limit to a reaction rate in the cytoplasm or membrane equal to the encounter rate.

Concentration gradient

A gradual change in the concentration over a specific distance.

Diffusivity

The proportionality constant that is used to describe the diffusion flux as linearly proportional to the negative of the concentration gradient (Fick's law).

Endocytosis

The process in which areas of the plasma membrane invaginate and pinch off to form intracellular vesicles.

Spatio-temporal dynamics

A quantitative description of how a system changes in space and time.

Retrograde transport

Movement of material from the nerve terminal to the soma.

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Kholodenko, B. Cell-signalling dynamics in time and space. Nat Rev Mol Cell Biol 7, 165–176 (2006). https://doi.org/10.1038/nrm1838

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