Spatial turing-type pattern formation in a model of signal transduction involving membrane-based receptors coupled by g proteins

Abstract

In this paper, a model of signaling pathways involving G proteins is investigated. The model incorporates reaction-diffusion mechanisms in which various reactants participate inside and on the extra-cellular surface membrane. The messenger molecules may diffuse over the surface of the cell membrane and signal transduction across the cell membrane is mediated by membrane receptor bound proteins which connect the genetically controlled biochemical intra-cellular reactions to the production of the second messenger, leading to desired functional responses. Dynamic and steady-state properties of the model are then investigated through weakly nonlinear stability analysis. Turing-type patterns are shown to form robustly under different delineating conditions on the system parameters. The theoretical predictions are then discussed in the context of some recently reported experimental evidence.

Keywords: G proteins; Turing pattern; membrane based receptors; signal transduction; weakly nonlinear stability.

Figure 1.

The G protein GTPase cycle (Figure is based on a scheme in the report by A.M. Spiegel (2000)). (1) Synthesis and targeting of components, (2) Receptor activation by signaling molecule, (3) Receptor activation of G protein, (4) G protein subunits-effector interaction and (5) GTPase activity terminates the interaction and returns α subunit to inactivated state.

Figure 2.

Contour plot of s for the critical point II in (3.14) with a₁ = 0.6, a₂ = 0.8, a₃ = 0.5, a₄ = 0.4, a₅ = 0.005, a₆ = 0.001, b₁ = 0.0002, b₂ = 0.55, μ = 0.00262, and $\phi =\frac{\pi }{2}$.

Figure 3.

Contour plot of s for the critical point III in (3.15) with a₁ = 0.1, a₂ = 0.2, a₃ = 0.5, a₄ = 0.4, a₅ = 0.05, a₆ = 0.001, b₁ = 0.001, b₂ = 1.5, μ = 0.0959972, and $\phi =\frac{\pi }{3}$.

Figure 4.

Contour plot of s for the critical point III⁺ in (3.35) with a₁ = 0.1, a₂ = 1.5, a₃ = 0.6, a₄ = 0.9, a₅ = 0.001, a₆ = 0.0001, b₁ = 0.5, b₂ =2, μ = 0.841495.

Figure 5.

Contour plot of s for the critical point III^– in (3.35) with a₁ = 0.5, a₂ = 1.5, a₃ = 0.6, a₄ = 0.5, a₅ = 0.00001, a₆ = 0.01, b₁ = 0.95, b₂ = 3, μ = 1.13812.