Modeling specificity in the yeast MAPK signaling networks

Multiscale models quantifying yeast physiology: towards a whole-cell model

The yeast Saccharomyces cerevisiae is widely used as a cell factory and as an important eukaryal model organism for studying cellular physiology related to human health and disease. Yeast was also the first eukaryal organism for which a genome-scale metabolic model (GEM) was developed. In recent years there has been interest in expanding the modeling framework for yeast by incorporating enzymatic parameters and other heterogeneous cellular networks to obtain a more comprehensive description of cellular physiology. We review the latest developments in multiscale models of yeast, and illustrate how a new generation of multiscale models could significantly enhance the predictive performance and expand the applications of classical GEMs in cell factory design and basic studies of yeast physiology.

Crosstalk between pathways enhances the controllability of signalling networks

The control of complex networks is one of the most challenging problems in the fields of biology and engineering. In this study, the authors explored the controllability and control energy of several signalling networks, which consisted of many interconnected pathways, including networks with a bow-tie architecture. On the basis of the theory of structure controllability, they revealed that biological mechanisms, such as cross-pathway interactions, compartmentalisation and so on make the networks easier to fully control. Furthermore, using numerical simulations for two realistic examples, they demonstrated that the control energy of normal networks with crosstalk is lower than in networks without crosstalk. These results indicate that the biological networks are optimally designed to achieve their normal functions from the viewpoint of the control theory. The authors' work provides a comprehensive understanding of the impact of network structures and properties on controllability.

Identification of the molecular mechanisms for cell-fate selection in budding yeast through mathematical modeling

The specification and maintenance of cell fates is essential to the development of multicellular organisms. However, the precise molecular mechanisms in cell fate selection are, to our knowledge, poorly understood due to the complexity of multiple interconnected pathways. In this study, model-based quantitative analysis is used to explore how to maintain distinguished cell fates between cell-cycle commitment and mating arrest in budding yeast. We develop a full mathematical model of an interlinked regulatory network based on the available experimental data. By theoretically defining the Start transition point, the model is able to reproduce many experimental observations of the dynamical behaviors in wild-type cells as well as in Ste5-8A and Far1-S87A mutants. Furthermore, we demonstrate that a moderate ratio between Cln1/2→Far1 inhibition and Cln1/2→Ste5 inhibition is required to ensure a successful switch between different cell fates. We also show that the different ratios of the mutual Cln1/2 and Far1 inhibition determine the different cell fates. In addition, based on a new, definition of network entropy, we find that the Start point in wild-type cells coincides with the system's point of maximum entropy. This result indicates that Start is a transition point in the network entropy. Therefore, we theoretically explain the Start point from a network dynamics standpoint. Moreover, we analyze the biological bistablity of our model through bifurcation analysis. We find that the Cln1/2 and Cln3 production rates and the nonlinearity of SBF regulation on Cln1/2 production are potential determinants for irreversible entry into a new cell fate. Finally, the quantitative computations further reveal that high specificity and fidelity of the cell-cycle and mating pathways can guarantee specific cell-fate selection. These findings show that quantitative analysis and simulations with a mathematical model are useful tools for understanding the molecular mechanisms in cell-fate decisions.

Response to hyperosmotic stress

An appropriate response and adaptation to hyperosmolarity, i.e., an external osmolarity that is higher than the physiological range, can be a matter of life or death for all cells. It is especially important for free-living organisms such as the yeast Saccharomyces cerevisiae. When exposed to hyperosmotic stress, the yeast initiates a complex adaptive program that includes temporary arrest of cell-cycle progression, adjustment of transcription and translation patterns, and the synthesis and retention of the compatible osmolyte glycerol. These adaptive responses are mostly governed by the high osmolarity glycerol (HOG) pathway, which is composed of membrane-associated osmosensors, an intracellular signaling pathway whose core is the Hog1 MAP kinase (MAPK) cascade, and cytoplasmic and nuclear effector functions. The entire pathway is conserved in diverse fungal species, while the Hog1 MAPK cascade is conserved even in higher eukaryotes including humans. This conservation is illustrated by the fact that the mammalian stress-responsive p38 MAPK can rescue the osmosensitivity of hog1Δ mutations in response to hyperosmotic challenge. As the HOG pathway is one of the best-understood eukaryotic signal transduction pathways, it is useful not only as a model for analysis of osmostress responses, but also as a model for mathematical analysis of signal transduction pathways. In this review, we have summarized the current understanding of both the upstream signaling mechanism and the downstream adaptive responses to hyperosmotic stress in yeast.

On the calculation of signal transduction ability of signaling transduction pathways in intracellular communication: systematic approach

MOTIVATION

The major function of signal transduction pathways in cells is to sense signals from the environment and process the information through signaling molecules in order to regulate the activity of transcription factors. On the molecular level, the information transmitted by a small number of signal molecules is amplified in the internal signaling pathway through enzyme catalysis, molecular modification and via the activation or inhibition of interactions. However, the dynamic system behavior of a signaling pathway can be complex and, despite knowledge of the pathway components and interactions, it is still a challenge to interpret the pathways behavior. Therefore, a systematic method is proposed in this study to quantify the signal transduction ability.

RESULTS

Based on the non-linear signal transduction system, signal transduction ability can be investigated by solving a Hamilton-Jacobi inequality (HJI)-constrained optimization problem. To avoid difficulties associated with solving a complex HJI-constrained optimization problem for signal transduction ability, the Takagi-Sugeno fuzzy model is introduced to approximate the non-linear signal transduction system by interpolating several local linear systems so that the HJI-constrained optimization problem can be replaced by a linear matrix inequality (LMI)-constrained optimization problem. The LMI problem can then be efficiently solved for measuring signal transduction ability. Finally, the signal transduction ability of two important signal transduction pathways was measured by the proposed method and confirmed using experimental data, which is useful for biotechnological and therapeutic application and drug design.

Optimal ratio of scaffold complex to free Fus3 to maximise the accumulation of phosphorylated Fus3 in yeast pheromone signalling pathway

In this study, the author considers the design rule of the intracellular signalling pathway. In yeast pheromone signalling pathway, scaffold Ste5 tethers the components of signalling pathway, Ste11, Ste7 and Fus3. Even though scaffold complex is independently produced before stimuli, excessively expressed Fus3 as compared with scaffold exists in cytoplasm as free kinase. How the ratio of scaffold complex to the free Fus3 is determined is not clear yet. First, the contribution of free Fus3 to signal transduction is theoretically shown by using a simplified model of pheromone signalling pathway. Next, the optimum expression levels of Ste5, Ste11, Ste7 and Fus3 are systematically explored by using the detailed model and genetic algorithm under the constraint that the total expression level of these four genes is limited. Excessive expression of Fus3 is advantageous for the efficient signalling without stall of the signal transduction. The result suggests that the component of signalling pathway is optimally expressed to maximise the accumulation of phosphorylated Fus3 at a fixed time point under the constraint that the total gene expression is limited. The proposed model provides further insight into the signalling network from the point of view of not only its function but also its optimality.

How can yeast cells decide between three activated MAP kinase pathways? A model approach

In yeast (Saccharomyces cerevisiae), the regulation of three MAP kinase pathways responding to pheromones (Fus3 pathway), carbon/nitrogen starvation (Kss1 pathway), and high osmolarity/osmotic stress (Hog1 pathway) is the subject of intensive research. We were interested in the question how yeast cells would respond when more than one of the MAP kinase pathways are activated simultaneously. Here, we give a brief overview over the regulatory mechanisms of the yeast MAP kinase pathways and investigate a kinetic model based on presently known molecular interactions and feedbacks within and between the three mitogen-activated protein kinases (MAPK) pathways. When two pathways are activated simultaneously with the osmotic stress response as one of them, the model predicts that the osmotic stress response (Hog1 pathway) is turned on first. The same is true when all three pathways are activated at the same time. When testing simultaneous stimulations by low nitrogen and pheromones through the Kss1 and Fus3 pathways, respectively, the low nitrogen response dominates over the pheromone response. Due to its autocatalytic activation mechanism, the pheromone response (Fus3 pathway) shows typical sigmoid response kinetics and excitability. In the presence of a small but sufficient amount of activated Fus3, a stimulation by pheromones will lead to a rapid self-amplification of the pheromone response. This 'excitability' appears to be a feature of the pheromone pathway that has specific biological significance.

Modelling and experimental analysis of hormonal crosstalk in Arabidopsis

An important question in plant biology is how genes influence the crosstalk between hormones to regulate growth. We have developed the first hormonal crosstalk network in Arabidopsis by iteratively combining modelling with experimental analysis.

We have revealed that the POLARIS gene interacts with the ethylene receptor and regulates both auxin transport and biosynthesis.

Our modelling analysis has reproduced all known mutants. With new experimental data, it has provided new insights into how the POLARIS gene regulates auxin concentration for root development in Arabidopsis, by controlling the relative contribution of auxin transport and biosynthesis and by integrating auxin, ethylene and cytokinin signalling.

Modelling and experimental analysis have revealed that a bell-shaped dose–response relationship between endogenous auxin and root length is established via POLARIS.

Hormone signalling systems coordinate plant growth and development through a range of complex interactions. The activities of plant hormones, such as auxin, ethylene and cytokinin, depend on cellular context and exhibit interactions that can be either synergistic or antagonistic. An important question regarding the understanding of those interactions is how genes act on the crosstalk between hormones to regulate plant growth.

Previously, we identified the POLARIS (PLS) gene of Arabidopsis, which transcribes a short mRNA encoding a 36-amino acid peptide that is required for correct root growth and vascular development (Casson et al, 2002). Experimental evidence shows that there is a link between PLS, ethylene signalling, auxin homeostasis and microtubule cytoskeleton dynamics (Chilley et al, 2006). Specifically, mutation of PLS results in an enhanced ethylene-response phenotype, defective auxin transport and homeostasis, and altered sensitivity to microtubule inhibitors. These defects, along with the short-root phenotype, are suppressed by genetic and pharmacological inhibition of ethylene action. The expression of PLS is itself repressed by ethylene and induced by auxin. It was also shown that pls mutant roots are hyper-responsive to exogenous cytokinins and show increased expression of the cytokinin inducible gene ARR5/IBC6 compared with the wild type (Casson et al, 2002). Therefore, PLS may also be required for correct auxin–cytokinin homeostasis to modulate root growth.

In this study, we model PLS gene function and crosstalk between auxin, ethylene and cytokinin in Arabidopsis.

Experimental evidence suggests that PLS acts on or close to the ethylene receptor ETR1, and a mathematical model describing possible PLS–ethylene pathway interactions is developed, and used to make quantitative predictions about PLS–hormone interactions. Modelling correctly predicts experimental results for the effect of the pls gene mutation on endogenous cytokinin concentration. Modelling also reveals a role for PLS in auxin biosynthesis in addition to a role in auxin transport (Figures 1 and 4).

The model reproduces available mutants, and with new experimental data provides new insights into how PLS regulates auxin concentration, by controlling the relative contribution of auxin transport and biosynthesis and by integrating auxin, ethylene and cytokinin signalling. Modelling further reveals that a bell-shaped dose–response relationship between endogenous auxin and root length is established via PLS.

In summary, we developed the first hormonal crosstalk model in Arabidopsis and revealed a hormonal crosstalk circuit through PLS and the downstream of ethylene signalling. Our study provides a platform to further integrate hormonal crosstalk in space and time in Arabidopsis.

An important question in plant biology is how genes influence the crosstalk between hormones to regulate growth. In this study, we model POLARIS (PLS) gene function and crosstalk between auxin, ethylene and cytokinin in Arabidopsis. Experimental evidence suggests that PLS acts on or close to the ethylene receptor ETR1, and a mathematical model describing possible PLS–ethylene pathway interactions is developed, and used to make quantitative predictions about PLS–hormone interactions. Modelling correctly predicts experimental results for the effect of the pls gene mutation on endogenous cytokinin concentration. Modelling also reveals a role for PLS in auxin biosynthesis in addition to a role in auxin transport. The model reproduces available mutants, and with new experimental data provides new insights into how PLS regulates auxin concentration, by controlling the relative contribution of auxin transport and biosynthesis and by integrating auxin, ethylene and cytokinin signalling. Modelling further reveals that a bell-shaped dose–response relationship between endogenous auxin and root length is established via PLS. This combined modelling and experimental analysis provides new insights into the integration of hormonal signals in plants.

Ultrasensitive responses and specificity in cell signaling

Background

Interconnected cell signaling pathways are able to efficiently and accurately transmit a multitude of different signals, despite an inherent potential for undesirable levels of cross-talk. To ensure that an appropriate response is produced, biological systems have evolved network-level mechanisms that insulate pathways from crosstalk and prevent 'leaking' or 'spillover' between pathways. Many signaling pathways have been shown to respond in an ultrasensitive (switch-like) fashion to graded input, and this behavior may influence specificity. The relationship of ultrasensitivity to signaling specificity has not been extensively explored.

Results

We studied the behavior of simple mathematical models of signaling networks composed of two interconnected pathways that share an intermediate component, asking if the two pathways in the network could exhibit both output specificity (preferentially activate their own output) and input fidelity (preferentially respond to their own input). Previous results with weakly-activated pathways indicated that neither mutual specificity nor mutual fidelity were obtainable in the absence of an insulating mechanism, such as cross-pathway inhibition, combinatorial signaling or scaffolding/compartmentalization. Here we found that mutual specificity is obtainable for hyperbolic or ultrasensitive pathways, even in the absence of an insulating mechanism. However, mutual fidelity is impossible at steady-state, even if pathways are hyperbolic or ultrasensitive. Nevertheless, ultrasensitivity does provide advantages in attaining specificity and fidelity to networks that contain an insulating mechanism. For networks featuring cross-pathway inhibition or combinatorial signaling, ultrasensitive activation can increase specificity in a limited way, and can only be utilized by one of the two pathways. In contrast, for networks featuring scaffolding/compartmentalization, ultrasensitive activation of both pathways can dramatically improve network specificity.

Conclusions

There are constraints to obtaining performance objectives associated with signaling specificity; such constraints may have influenced the evolution of signal transduction networks. Notably, input fidelity (preferential response to an authentic input) is a more difficult objective to achieve than output specificity (preferential targeting to an authentic output). Indeed, mutual fidelity is impossible in the absence of an insulating mechanism, even if pathways are ultrasensitive. Ultrasensitivity does, however, significantly enhance the performance of several insulating mechanisms. In particular, the ultrasensitive activation of both pathways can provide substantial improvement to networks containing scaffolding/compartmentalization.

Signal response sensitivity in the yeast mitogen-activated protein kinase cascade

The yeast pheromone response pathway is a canonical three-step mitogen activated protein kinase (MAPK) cascade which requires a scaffold protein for proper signal transduction. Recent experimental studies into the role the scaffold plays in modulating the character of the transduced signal, show that the presence of the scaffold increases the biphasic nature of the signal response. This runs contrary to prior theoretical investigations into how scaffolds function. We describe a mathematical model of the yeast MAPK cascade specifically designed to capture the experimental conditions and results of these empirical studies. We demonstrate how the system can exhibit either graded or ultrasensitive (biphasic) response dynamics based on the binding kinetics of enzymes to the scaffold. At the basis of our theory is an analytical result that weak interactions make the response biphasic while tight interactions lead to a graded response. We then show via an analysis of the kinetic binding rate constants how the results of experimental manipulations, modeled as changes to certain of these binding constants, lead to predictions of pathway output consistent with experimental observations. We demonstrate how the results of these experimental manipulations are consistent within the framework of our theoretical treatment of this scaffold-dependent MAPK cascades, and how future efforts in this style of systems biology can be used to interpret the results of other signal transduction observations.

Understanding inhibition of viral proteins on type I IFN signaling pathways with modeling and optimization

The interferon system provides a powerful and universal intracellular defense mechanism against viruses. As one part of their survival strategies, many viruses have evolved mechanisms to counteract the host type I interferon (IFN-alpha/beta) responses. In this study, we attempt to investigate virus- and double-strand RNA (dsRNA)-triggered type I IFN signaling pathways and understand the inhibition of IFN-alpha/beta induction by viral proteins using mathematical modeling and quantitative analysis. Based on available literature and our experimental data, we develop a mathematical model of virus- and dsRNA-triggered signaling pathways leading to type I IFN gene expression during the primary response, and use the genetic algorithm to optimize all rate constants in the model. The consistency between numerical simulation results and biological experimental data demonstrates that our model is reasonable. Further, we use the model to predict the following phenomena: (1) the dose-dependent inhibition by classical swine fever virus (CSFV) N(pro) or E(rns) protein is observed at a low dose and can reach a saturation above a certain dose, not an increase; (2) E(rns) and N(pro) have no synergic inhibitory effects on IFN-beta induction; (3) the different characters in an important transcription factor, phosphorylated IRF3 (IRF3p), are exhibited because N(pro) or E(rns) counteracted dsRNA- and virus-triggered IFN-beta induction by targeting the different molecules in the signaling pathways and (4) N(pro) inhibits the IFN-beta expression not only by interacting with IFR3 but also by affecting its complex with MITA. Our approaches help to gain insight into system properties and rational therapy design, as well as to generate hypotheses for further research.

Mitogen-activated protein kinase signaling in plants

Eukaryotic mitogen-activated protein kinase (MAPK) cascades have evolved to transduce environmental and developmental signals into adaptive and programmed responses. MAPK cascades relay and amplify signals via three types of reversibly phosphorylated kinases leading to the phosphorylation of substrate proteins, whose altered activities mediate a wide array of responses, including changes in gene expression. Cascades may share kinase components, but their signaling specificity is maintained by spaciotemporal constraints and dynamic protein-protein interactions and by mechanisms that include crossinhibition, feedback control, and scaffolding. Plant MAPK cascades regulate numerous processes, including stress and hormonal responses, innate immunity, and developmental programs. Genetic analyses have uncovered several predominant MAPK components shared by several of these processes including the Arabidopsis thaliana MAPKs MPK3, 4, and 6 and MAP2Ks MKK1, 2, 4, and 5. Future work needs to focus on identifying substrates of MAPKs, and on understanding how specificity is achieved among MAPK signaling pathways.

Cascading signaling pathways improve the fidelity of a stochastically and deterministically simulated molecular RS latch

Background

While biological systems have often been compared with digital systems, they differ by the strong effect of crosstalk between signals due to diffusivity in the medium, reaction kinetics and geometry. Memory elements have allowed the creation of autonomous digital systems and although biological systems have similar properties of autonomy, equivalent memory mechanisms remain elusive. Any such equivalent memory system, however, must silence the effect of crosstalk to maintain memory fidelity.

Results

Here, we present a system of enzymatic reactions that behaves like an RS latch (a simple memory element in digital systems). Using both a stochastic molecular simulator and ordinary differential equation simulator, we showed that crosstalk between two latches operating in the same spatial localization disrupts the memory fidelity of both latches. Crosstalk was reduced or silenced when simple reaction loops were replaced with multiple step or cascading reactions, showing that cascading signaling pathways are less susceptible to crosstalk.

Conclusion

Thus, the common biological theme of cascading signaling pathways is advantageous for maintaining the fidelity of a memory latch in the presence of crosstalk. The experimental implementation of such a latch system will lead to novel approaches to cell control using synthetic proteins and will contribute to our understanding of why cells behave differently even when given the same stimulus.

Specificity and robustness of the mammalian MAPK-IEG network

The mitogen-activated protein kinase cascade is a conserved signal transduction pathway found in organisms of complexity spanning from yeast to humans. In many mammalian tissue types, this pathway can correctly transduce signals from different extracellular messengers, leading to specific and often mutually exclusive cellular responses. The transduced signal is tuned by a complicated set of positive and negative feedback control mechanisms and fed into a downstream gene expression network. This network, based on the immediate early gene system, has two possible, mutually exclusive outcomes. Using a mathematical model, we study how different stimuli lead to different temporal signal structure. Further, we investigate how each of the feedback controls contributes to the overall specificity of the gene expression output, and hypothesize that the complicated nature of the mammalian mitogen-activated protein kinase pathway results in a system able to robustly identify and transduce the proper signal without investing in two completely separate signal cascades. Finally, we quantify the role of the RKIP protein in shaping the signal, and propose a novel mechanism of its involvement in cancer metastasis.

Putting the pieces together in diabetes research: towards a hierarchical model of whole-body glucose homeostasis

Type 2 diabetes is one of the most widespread and rapidly spreading diseases world-wide and has been subject of extensive research efforts. However, understanding the molecular basis of the disease is increasing piecemeal and a consensus regarding the overall picture of normal metabolic regulation and malfunction in diabetes has not emerged. A systems biology approach, combining mathematical modelling with simultaneous high-throughput measurements, can be of considerable help. On the whole-body level, this has been done in pharmacokinetic and pharmacodynamic models, which recently have started to mature into more physiologically realistic organ-based models. At the other end of the spectrum, detailed models for crucial cellular processes are starting to mature into complete modules that potentially can be fitted into such whole-body organ-based models. The result of such a merge is a multi-level hierarchical model, which is a model type that has been common in technical systems. In this review, we report and exemplify some of the recent progress that has been made to achieve such a hierarchical model, and we argue why it is only through such a model that a complete picture of diabetes mellitus can be obtained.

A simple reaction kinetic model of rapid (G protein dependent) and slow (beta-Arrestin dependent) transmission

In this paper the qualitative dynamic behavior of reaction kinetic models of G protein signaling is examined. A simplified basic G protein signaling structure is defined, which is extended to be able to take the effect of slow transmission, RGS mediated feedback regulation and ERK-phosphatase mediated feedback regulation into account. The resulting model gives rise to an acceptable qualitative approximation of the G protein dependent and independent ERK activation dynamics that is in good agreement with the experimentally observed behavior.