Deterministic mathematical models of the cAMP pathway in Saccharomyces cerevisiae

Abstract

Background: Cyclic adenosine monophosphate (cAMP) has a key signaling role in all eukaryotic organisms. In Saccharomyces cerevisiae, it is the second messenger in the Ras/PKA pathway which regulates nutrient sensing, stress responses, growth, cell cycle progression, morphogenesis, and cell wall biosynthesis. A stochastic model of the pathway has been reported.

Results: We have created deterministic mathematical models of the PKA module of the pathway, as well as the complete cAMP pathway. First, a simplified conceptual model was created which reproduced the dynamics of changes in cAMP levels in response to glucose addition in wild-type as well as cAMP phosphodiesterase deletion mutants. This model was used to investigate the role of the regulatory Krh proteins that had not been included previously. The Krh-containing conceptual model reproduced very well the experimental evidence supporting the role of Krh as a direct inhibitor of PKA. These results were used to develop the Complete cAMP Model. Upon simulation it illustrated several important features of the yeast cAMP pathway: Pde1p is more important than is Pde2p for controlling the cAMP levels following glucose pulses; the proportion of active PKA is not directly proportional to the cAMP level, allowing PKA to exert negative feedback; negative feedback mechanisms include activating Pde1p and deactivating Ras2 via phosphorylation of Cdc25. The Complete cAMP model is easier to simulate, and although significantly simpler than the existing stochastic one, it recreates cAMP levels and patterns of changes in cAMP levels observed experimentally in vivo in response to glucose addition in wild-type as well as representative mutant strains such as pde1Delta, pde2Delta, cyr1Delta, and others. The complete model is made available in SBML format.

Conclusion: We suggest that the lower number of reactions and parameters makes these models suitable for integrating them with models of metabolism or of the cell cycle in S. cerevisiae. Similar models could be also useful for studies in the human pathogen Candida albicans as well as other less well-characterized fungal species.

Figure 1

Schematic representation of elements of the cAMP pathway in S. cerevisiae.

Figure 2

Deterministic model of the PKA module. (A) Simulation of PKA Model A (blue trace) and PKA Model B (red trace). The cAMP level is 0 initially, and is increased to 270900 molecules per cell (equivalent to 0.015 mM) after 10 seconds, increased to 909000 molecules per cell after 30 seconds, and decreased to 270900 molecules per cell after 60 seconds. (B) Steady state parameter sensitivity analysis carried out on the PKA module. (C) Parameter scan of PKA Model A. The greatest value for PKA difference (79.1%) is achieved when k_cAMPgain = 0.1, k_cAMPloss = 2.2 × 10⁵, k_PKAdiss = 1 × 10⁵, k_RcAMPdiss = 100, k_PKAass = 1000.

Figure 3

Optimisation of the PKA model. The blue trace shows the simulation of PKA Model B, the red trace – PKA Model C, and the green trace – PKA Model D. The cAMP level is 0 initially, and is increased to 270900 molecules per cell (equivalent to 0.015 mM) after 10 seconds, increased to 909000 molecules per cell after 30 seconds, and decreased to 270900 molecules per cell after 60 seconds.

Figure 4

Steady state levels of free C in the PKA models under various cAMP levels. The blue trace shows the simulation of PKA Model B, the red trace – PKA Model C, and the green trace – PKA Model D. Parameters of PKA Model B are the same as in Figure 3. Parameters of PKA Model C are: k_A = 8.72 × 10^-17; k_R = 1000. Parameters of PKA Model D are: k_cat = 10^-13; K_mF = 10⁷; V_maxR = 1000; K_mR = 0.01.

Figure 5

Predictions of Simplified cAMP Model A. (A) Species concentrations before and after a pulse of glucose. (B) Cyclic AMP levels of pde1Δ and pde2Δ mutants: blue trace – wild type; red trace – pde2Δ; green trace – pde1Δ. Glucose is increased to 5 after 5 seconds in both simulations.

Figure 6

Cyclic AMP and PKAa levels in Simplified cAMP Model B mutants when cAMP levels are set to 1 and PKAa set to 0. Model mutant genotypes are: cyr1Δ (green), cyr1Δpde2Δ (blue), cyr1Δpde2Δkrh1/2Δ (red), cyr1Δpde2Δ GPA2^Q300L (cyan).

Figure 7

Schematic representation of the Complete cAMP model, using the SBGN notation.

Figure 8

Result of parameter estimation of the Complete cAMP Model. The blue dotted trace represents cAMP data from [35], and the solid blue trace represents cAMP levels computed by the model.

Figure 9

Predictions of the Complete cAMP Model. (A) cAMP synthesis and hydrolysis rates. Glucose is increased to 5 mM at time 60, and increased to 100 mM at time 240. Blue trace: rate of cAMP synthesis. Red trace: rate of cAMP hydrolysis by Pde1. Green trace: rate of cAMP hydrolysis by Pde2. (B) Levels of species in the Gpa2 module. Blue trace: inactive Gpa2. Green trace: active Gpa2. Red trace: Krh. Cyan trace: complex of activated Gpa2 and Krh. (C) Levels of active (blue trace) and inactive (green trace) PKA. (D) Levels of Ras2a and Cdc25 in response to 5 mM glucose at time 60sec, and 100 mM at 240 sec. Top part: Ras2a (blue trace); bottom part: phosphorylated (green trace) and unphosphorylated (blue trace) Cdc25.