Deterministic mathematical models of the cAMP pathway in Saccharomyces cerevisiae

<p>Abstract</p> <p>Background</p> <p>Cyclic adenosine monophosphate (cAMP) has a key signaling role in all eukaryotic organisms. In <it>Saccharomyces cerevisiae</it>, 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.</p> <p>Results</p> <p>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 <it>in vivo </it>in response to glucose addition in wild-type as well as representative mutant strains such as <it>pde1Δ, pde2Δ</it>, <it>cyr1Δ</it>, and others. The complete model is made available in SBML format.</p> <p>Conclusion</p> <p>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 <it>S. cerevisiae</it>. Similar models could be also useful for studies in the human pathogen <it>Candida albicans </it>as well as other less well-characterized fungal species.</p

Structurally robust biological networks

Background: The molecular circuitry of living organisms performs remarkably robust regulatory tasks, despite the often intrinsic variability of its components. A large body of research has in fact highlighted that robustness is often a structural property of biological systems. However, there are few systematic methods to mathematically model and describe structural robustness. With a few exceptions, numerical studies are often the preferred approach to this type of investigation. Results: In this paper, we propose a framework to analyze robust stability of equilibria in biological networks. We employ Lyapunov and invariant sets theory, focusing on the structure of ordinary differential equation models. Without resorting to extensive numerical simulations, often necessary to explore the behavior of a model in its parameter space, we provide rigorous proofs of robust stability of known bio-molecular networks. Our results are in line with existing literature. Conclusions: The impact of our results is twofold: on the one hand, we highlight that classical and simple control theory methods are extremely useful to characterize the behavior of biological networks analytically. On the other hand, we are able to demonstrate that some biological networks are robust thanks to their structure and some qualitative properties of the interactions, regardless of the specific values of their parameters

Modeling mutant phenotypes and oscillatory dynamics in the Saccharomyces cerevisiae cAMP-PKA pathway

Background The cyclic AMP-Protein Kinase A (cAMP-PKA) pathway is an evolutionarily conserved signal transduction mechanism that regulates cellular growth and differentiation in animals and fungi. We present a mathematical model that recapitulates the short-term and long-term dynamics of this pathway in the budding yeast, Saccharomyces cerevisiae. Our model is aimed at recapitulating the dynamics of cAMP signaling for wild-type cells as well as single (pde1Δ and pde2Δ) and double (pde1Δpde2Δ) phosphodiesterase mutants. Results Our model focuses on PKA-mediated negative feedback on the activity of phosphodiesterases and the Ras branch of the cAMP-PKA pathway. We show that both of these types of negative feedback are required to reproduce the wild-type signaling behavior that occurs on both short and long time scales, as well as the the observed responses of phosphodiesterase mutants. A novel feature of our model is that, for a wide range of parameters, it predicts that intracellular cAMP concentrations should exhibit decaying oscillatory dynamics in their approach to steady state following glucose stimulation. Experimental measurements of cAMP levels in two genetic backgrounds of S. cerevisiae confirmed the presence of decaying cAMP oscillations as predicted by the model. Conclusions Our model of the cAMP-PKA pathway provides new insights into how yeast respond to alterations in their nutrient environment. Because the model has both predictive and explanatory power it will serve as a foundation for future mathematical and experimental studies of this important signaling network

Arvbarhet og biologisk systemdynamikk

The concept of heritability is rooted in the observation that relatives resemble one another more than expected by chance. Narrow-sense heritability is defined as the proportion of phenotypic variance that is attributable to additive genetic variation (i.e. where an allele substitution has the same effect irrespective of the rest of the genotype), while broad-sense heritability denotes the proportion of phenotypic variance caused by genetic variation including non-additive effects. Both concepts have been highly instrumental in evolutionary biology, production biology and biomedical research for several decades. However, this successful instrumental use should not be equated with deep understanding of how underlying biology shapes narrow- and broad-sense heritability. Nor does it guarantee that these statistical definitions and associated methodology are optimally suited to deal with the recent floods of biological data. Seeking a deeper understanding of the relationship between narrow- and broad-sense heritability in terms of biological mechanisms, I simulated genetic variation in dynamic models of biological systems. A striking result was that the ratio between narrow-sense and broad-sense heritability depended strongly on the type of regulatory architecture involved. Applying the same approach to an ensemble of gene regulatory network models, I showed that monotonicity features of genotype-to-phenotype maps reveal deep connections between molecular regulatory architecture and heritability aspects; connections that do not materialize from the classical distinction between additive, dominant and epistatic gene actions. Lastly, I addressed why genome-wide association studies (GWAS) have failed to identify much of the genetic variation underlying highly heritable traits. By linking computational physiology to GWAS, one can do GWAS on lower-level phenotypes that are mathematically related to each other through a dynamic model. This allows much more precise identification of the causal genetic variation, coupled with understanding of its function.Begrepet arvbarhet gjenspeiler det faktum at slektninger jevnt over ligner mer på hverandre enn på andre individer. Arvbarhet i smal forstand defineres som andelen av fenotypisk varians som kan tilskrives additive effekter av genetisk variasjon (altså der en allel-substitusjon har samme effekt uavhengig av resten av genotypen), mens arvbarhet i vid forstand betegner den samlede andelen som skyldes både additive og ikke-additive effekter. Begge begrepene har vist seg nyttige i evolusjonsbiologi, produksjonsbiologi og biomedisinsk forskning over flere tiår. Denne nytten som verktøy er imidlertid ikke ensbetydende med dyp innsikt i hvordan de to typene av arvbarhet formes av underliggende biologi. Det er heller ikke selvsagt at disse statistisk baserte definisjonene og metodene vil være de beste til å møte dagens flom av nye biologiske data. I mitt doktorgradsarbeid har jeg belyst hvordan forholdet mellom arvbarhet i smal og vid forstand henger sammen med biologiske mekanismer, gjennom å simulere genetisk variasjon i dynamiske modeller av fysiologiske systemer. Et slående resultat var at den regulatoriske arkitekturen til systemet har mye å si for forholdstallet mellom arvbarhet i smal og vid forstand. På lignende vis studerte jeg arvbarhet i et knippe modeller av genregulatoriske nettverk med ulike grader av monotonitet i den matematiske sammenhengen mellom genotype og fenotype. Dette avdekket dype bånd mellom arvbarhetsmønstre og molekylær regulatorisk arkitektur; sammenhenger som ikke er åpenbare ut fra det klassiske skillet mellom additive, dominante og epistatiske gen-effekter. Til sist tok jeg for meg svakheter ved dagens statistiske metoder for å forklare hvordan variasjon i sterkt arvbare trekk styres av genetiske forskjeller mellom individer. Såkalte hel-genom-assosiasjons-studier (genome-wide association studies, GWAS) påviser ofte en mengde relevante loci med genetisk variasjon, men disse forklarer likevel bare en liten del av den observerte arvbarheten i overordnede trekk som f.eks. kroppshøyde eller sjukdomsforekomst. En mer lovende tilnærming er å koble matematisk fysiologi til GWAS. Jeg viser at man ved å gjøre GWAS på lavnivå-fenotyper som er matematisk forbundet gjennom en dynamisk modell, kan identifisere den årsaksbestemmende genetiske variasjonen langt mer presist og samtidig øke forståelsen av dennes funksjon

Protein Kinase A Regulates Hyphal Growth by Relieving the Interaction of MoSfl1 with the Cyc8-Tup1 Co-repressor in Magnaporthe oryzae

The cAMP-dependent protein kinase A (PKA) signal transduction pathway plays an important role in morphogenesis and virulence in plant pathogenic fungi. In the rice blast fungus Magnaporthe oryzae, it regulates surface recognition, appressorium turgor generation, and invasive growth. Two genes in M. oryzae named CPKA and CPK2 encode the catalytic subunits of cAMP-dependent protein kinase A. Previous studies have shown that deletion of CPKA failed to block response to exogenous cAMP, suggesting the involvement of CPK2 in cAMP signaling. To further characterize the function of the catalytic subunits of PKA in infection-related development in M. oryzae, we generated the cpkA cpk2 double mutant. The double mutant had severe growth and conidiation defects. It was non-pathogenic though the intracellular cAMP level and activation of the Pmk1 MAP kinase were increased. Interestingly, the double mutant spontaneously produced fast-growing suppressors after cultivation on oatmeal agar plates over ten days. Twenty fast-growing suppressors were isolated and characterized. Sequencing analysis showed that loss-of-function mutations in MoSFL1 were responsible for the rescue of growth defects of the cpkA cpk2 mutant. MoSfl1 acts as a transcription repressor by interacting with the Cyc8-Tup1 co-repressor. The interaction between MoSfl1 and Cyc8-Tup1 is relieved by phosphorylation of MoSfl1 by PKA, which is important for normal hyphal growth. In the suppressor strains, loss-of-function mutations in MoSfl1 bypassed the requirement of PKA phosphorylation to release its inhibitory binding with the Cyc8-Tup1 co-repressor complex. In this study, we provide new insights into the role of the catalytic subunits of PKA in growth and development and implicate that its negative effect on the transcription repressor MoSfl1 is required for hyphal growth in M. oryzae

Investigation of mechanisms for restricting the activity of cyclic-AMP dependent protein kinase

Cyclic AMP (cAMP) is an ancient second messenger that is essential for many cellular processes including synaptic plasticity and control of heart rate and contractility. Cyclic AMP-dependent protein kinase (PKA) is the major intracellular receptor for cAMP. PKA consists of dimeric regulatory (R) subunits that bind and inhibit catalytic (C) subunits. PKA is activated upon binding of cAMP to the R subunits, which leads to the release of C subunits, and phosphorylation of intracellular protein substrates. An enduring challenge in cAMP research is to understand how PKA activity is directed to specific substrates, as the C subunits exhibit only limited substrate specificity in vitro. Elevations of cAMP are controlled in both space and time in the cell. This is achieved by the co-localization of enzymes for both the synthesis (cyclases) and breakdown (phosphodiesterases) of cAMP. Anchoring proteins are also essential for directing PKA to substrates in their immediate vicinity. However, a mechanism is yet to be established to explain how the activity of the C subunit of PKA is restrained following its dissociation from R subunits. This thesis details three parallel investigations that apply novel approaches with the shared aim of understanding how C subunit restraint is achieved. First, using quantitative immunoblotting in conjunction with purified PKA subunits, I investigated PKA subunit stoichiometry, finding that PKA R subunits typically outnumber C subunits by ~15-fold. Second, I developed a novel approach for monitoring R subunit isoform-specific association with C subunits in cells, with temporal precision. Comparative experiments using this approach and measurements with a fluorescent reporter of PKA activity show that only a small portion of C subunits need be dissociated to achieve high PKA activity. Third, I applied and developed a novel cross-linking coupled to mass spectrometry (XL-MS) protocol for analysis of the structure of PKA complexes. Insights include the likely orientation of PKA complexes that contain type II R (RII) subunits towards the membrane, and identification of a possible conformational change in PKA upon binding an anchoring protein. Together these experiments illuminate several aspects of PKA to show how the activity of this critical signalling enzyme is restrained within cells