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Deterministic mathematical models of the cAMP pathway in Saccharomyces cerevisiae.

Williamson T, Schwartz JM, Kell DB, Stateva L - BMC Syst Biol (2009)

Bottom Line: These results were used to develop the Complete cAMP Model.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.Similar models could be also useful for studies in the human pathogen Candida albicans as well as other less well-characterized fungal species.

View Article: PubMed Central - HTML - PubMed

Affiliation: Faculty of Life Sciences, The University of Manchester, Manchester, M13 9PT, UK. Thomas.Williamson@postgrad.manchester.ac.uk

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.

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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 kcAMPgain = 0.1, kcAMPloss = 2.2 × 105, kPKAdiss = 1 × 105, kRcAMPdiss = 100, kPKAass = 1000.
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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 kcAMPgain = 0.1, kcAMPloss = 2.2 × 105, kPKAdiss = 1 × 105, kRcAMPdiss = 100, kPKAass = 1000.

Mentions: As shown by the blue trace of Figure 2 (panel A) no free catalytic subunit is present when cAMP is set to zero. The model shows changes in the proportion of free catalytic subunits of PKA when cAMP is set to low (Clow) and high (Chigh) levels. However the difference between the two states is not great – 27.7% when cAMP is low compared to 40.6% when cAMP is high. It is therefore important to optimize the model, and for this purpose parameter sensitivity analysis was carried out. As shown in Figure 2 (panel B), the parameter kcAMPgain is the most sensitive to variations in PKA level. The parameters of this model were scanned further to identify those which determined the highest difference between Clow and Chigh. Figure 2 (panel C) shows how the difference between Clow and Chigh depends on the parameters kcAMPgain and kcAMPloss. The peak values of this distribution were used to create an optimised model, named PKA Model B, whose simulation is shown by the red trace of Figure 2 (panel A). In PKA Model B, the level of Clow now stands at ~10% whilst that of Chigh is approximately 90%.


Deterministic mathematical models of the cAMP pathway in Saccharomyces cerevisiae.

Williamson T, Schwartz JM, Kell DB, Stateva L - BMC Syst Biol (2009)

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 kcAMPgain = 0.1, kcAMPloss = 2.2 × 105, kPKAdiss = 1 × 105, kRcAMPdiss = 100, kPKAass = 1000.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2719611&req=5

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 kcAMPgain = 0.1, kcAMPloss = 2.2 × 105, kPKAdiss = 1 × 105, kRcAMPdiss = 100, kPKAass = 1000.
Mentions: As shown by the blue trace of Figure 2 (panel A) no free catalytic subunit is present when cAMP is set to zero. The model shows changes in the proportion of free catalytic subunits of PKA when cAMP is set to low (Clow) and high (Chigh) levels. However the difference between the two states is not great – 27.7% when cAMP is low compared to 40.6% when cAMP is high. It is therefore important to optimize the model, and for this purpose parameter sensitivity analysis was carried out. As shown in Figure 2 (panel B), the parameter kcAMPgain is the most sensitive to variations in PKA level. The parameters of this model were scanned further to identify those which determined the highest difference between Clow and Chigh. Figure 2 (panel C) shows how the difference between Clow and Chigh depends on the parameters kcAMPgain and kcAMPloss. The peak values of this distribution were used to create an optimised model, named PKA Model B, whose simulation is shown by the red trace of Figure 2 (panel A). In PKA Model B, the level of Clow now stands at ~10% whilst that of Chigh is approximately 90%.

Bottom Line: These results were used to develop the Complete cAMP Model.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.Similar models could be also useful for studies in the human pathogen Candida albicans as well as other less well-characterized fungal species.

View Article: PubMed Central - HTML - PubMed

Affiliation: Faculty of Life Sciences, The University of Manchester, Manchester, M13 9PT, UK. Thomas.Williamson@postgrad.manchester.ac.uk

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.

Show MeSH
Related in: MedlinePlus