Cell-signalling dynamics in time and space

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.

FIG. 1

Universal motifs of cellular signalling networks. A. One-site phosphorylation cycle. The protein M is phosphorylated by a kinase to yield the phosphorylated form M_p, which is dephosphorylated by an opposing phosphatase. B. A cycle of a small GTPase (Ran). A guanine nucleotide exchange factor (GEF) catalyzes the transformation of an inactive guanosine diphosphate (GDP)-bound form (Ran-GDP) into an active guanosine triphosphate (GTP)-bound form (Ran-GTP). A GTPase–activating protein (GAP) is the opposing enzyme that catalyzes the reverse transformation. C. A cascade of cycles. Negative feedback provides robustness to noise, increasing resistance to disturbances inside the feedback loop, but brings about oscillations if it is too strong and the cascade is ultrasensitive,. Positive feedback greatly increases the sensitivity of the target to the signal and may also lead to bistability and relaxation oscillations,,,.

FIG. 2

Feedback designs that can turn a universal signalling cycle into a bistable switch and relaxation oscillator. Simple cycle can turn bistable in four distinct ways; either M_p or M stimulates its own production (positive feedback) by product activation or substrate inhibition of the kinase or phosphatase reactions. Each of the four rows of feedback designs correspond to a different bistable switch, provided that the kinase and phosphatase abundances are assumed constant and only single feedback (within the M cycle) is present. Sixteen relaxation oscillation designs are generated by extra negative feedback brought about by negative or positive regulation of the synthesis or degradation rates of the kinase protein or phosphatase protein by M_p or M. Designs A*-H* are mirror images of designs A-H. Although synthesis and degradation reactions are shown for both the kinase and phosphatase proteins, the protein concentration that is not controlled by feedback from the M cycle is considered constant, resulting in only two differential equations for each diagram. All feedback regulations are described by simple Michaelis-Menten type expressions (BOX 2 and Supplementary Table S3). The remaining sixteen relaxation oscillation designs are shown in Supplementary FIG.S1 and can require some degree of cooperativity within feedback loops.

FIG. 3

Spatial segregation of two opposing enzymes in a protein-modification cycle generates intracellular gradients. Kinases localize to (A) supra-molecular structures (sphere) or (B) the cell membrane, whereas phosphatases are homogeneously distributed in the cytoplasm. The concentration gradients are shown by colour intensity. C. Stationary phosphorylation levels c_p decline with the distance d from the cell membrane toward the centre[Brown, 1999 #61 (see panel B). The steepness of the gradient (reciprocal of the characteristic length) is determined by the parameter α(α² = k_p/D is the ratio of the phosphatase activity k_p and the protein diffusivity D, BOX 3).

FIG. 3

Spatial segregation of two opposing enzymes in a protein-modification cycle generates intracellular gradients. Kinases localize to (A) supra-molecular structures (sphere) or (B) the cell membrane, whereas phosphatases are homogeneously distributed in the cytoplasm. The concentration gradients are shown by colour intensity. C. Stationary phosphorylation levels c_p decline with the distance d from the cell membrane toward the centre[Brown, 1999 #61 (see panel B). The steepness of the gradient (reciprocal of the characteristic length) is determined by the parameter α(α² = k_p/D is the ratio of the phosphatase activity k_p and the protein diffusivity D, BOX 3).

FIG. 3

Spatial segregation of two opposing enzymes in a protein-modification cycle generates intracellular gradients. Kinases localize to (A) supra-molecular structures (sphere) or (B) the cell membrane, whereas phosphatases are homogeneously distributed in the cytoplasm. The concentration gradients are shown by colour intensity. C. Stationary phosphorylation levels c_p decline with the distance d from the cell membrane toward the centre[Brown, 1999 #61 (see panel B). The steepness of the gradient (reciprocal of the characteristic length) is determined by the parameter α(α² = k_p/D is the ratio of the phosphatase activity k_p and the protein diffusivity D, BOX 3).

Figure Box 1. Parts A, B and C

Figure Box 2. Parts A, B and C

Figure Box 4, Part A, Part B

Figure Box 4, Part A, Part B