Báo cáo khoa học: A modelling approach to quantify dynamic crosstalk between the pheromone and the starvation pathway in baker’s yeast

A modelling approach to quantify dynamic crosstalk between the pheromone and the starvation pathway in baker’s yeast

Tác giả: Jörg Schaber, Bente Kofahl, Axel Kowald, Edda Klipp

Lĩnh vực: Sinh học tế bào, Mô hình hóa hệ thống

Nội dung tài liệu:
Nghiên cứu này trình bày một phương pháp mô hình hóa động lực học để định lượng sự tương tác (crosstalk) giữa hai con đường tín hiệu chính trong tế bào nấm men: con đường tín hiệu pheromone và con đường tín hiệu tăng trưởng sợi. Các tác giả đã xây dựng một mô hình toán học động lực học, tích hợp kiến thức hiện có về cách hai con đường này liên kết và tương tác với nhau. Nghiên cứu này giới thiệu hai thước đo mới về tương tác động lực học: độ đặc hiệu nội tại (intrinsic specificity) và độ đặc hiệu ngoại lai (extrinsic specificity). Các thước đo này xem xét tín hiệu tổng hợp từ nhiều tác nhân kích thích đồng thời, giúp cung cấp cái nhìn sâu sắc hơn về cách các con đường tín hiệu khuếch đại hoặc ức chế lẫn nhau. Mô hình dự đoán rằng con đường tăng trưởng sợi khuếch đại phản ứng của con đường pheromone, trong khi con đường pheromone ức chế phản ứng của con đường tăng trưởng sợi. Các tác giả cũng đề xuất các thí nghiệm mới và dự đoán kết quả để kiểm tra các giả thuyết về cơ chế tương tác giữa hai con đường này. Nghiên cứu nhấn mạnh tầm quan trọng của việc phân tích tín hiệu truyền theo thời gian thực để hiểu rõ hơn về sự tương tác động lực học giữa các con đường tín hiệu.

Mục lục chi tiết:

• A modelling approach to quantify dynamic crosstalk between the pheromone and the starvation pathway in baker’s yeast
• Keywords
• Correspondence
• Note
• Cells must be able to process multiple information in parallel and, moreover, they must also be able to combine this information in order to trigger the appropriate response. This is achieved by wiring signalling pathways such that they can interact with each other, a phenomenon often called crosstalk. In this study, we employ mathematical modelling techniques to analyse dynamic mechanisms and measures of crosstalk. We present a dynamic mathematical model that compiles current knowledge about the wiring of the pheromone pathway and the filamentous growth pathway in yeast. We consider the main dynamic features and the interconnections between the two pathways in order to study dynamic crosstalk between these two pathways in haploid cells. We introduce two new measures of dynamic crosstalk, the intrinsic specificity and the extrinsic specificity. These two measures incorporate the combined signal of several stimuli being present simultaneously and seem to be more stable than previous measures. When both pathways are responsive and stimulated, the model predicts that (a) the filamentous growth pathway amplifies the response of the pheromone pathway, and (b) the pheromone pathway inhibits the response of filamentous growth pathway in terms of mitogen activated protein kinase activity and transcriptional activity, respectively. Among several mechanisms we identified leakage of activated Stell as the most influential source of crosstalk. Moreover, we propose new experiments and predict their outcomes in order to test hypotheses about the mechanisms of crosstalk between the two pathways. Studying signals that are transmitted in parallel gives us new insights about how pathways and signals interact in a dynamical way, e.g., whether they amplify, inhibit, delay or accelerate each other.
• Cells respond to their environment based on external cues. A great variety of receptors exist that are able to sense all kinds of stimuli and trigger corresponding responses in the cell through signalling pathways. However, life is complex and in order to make the right decisions concerning growth, proliferation, stress response, etc., cells must not only be able to process multiple information in parallel but also to combine and integrate this information. It can be expected that a cell’s response to multiple stimuli is not just the sum of the individual responses but that signals suppress or amplify each other according to their respective importance. This is achieved by wiring signalling pathways in such a way that they can interact with each other.
• Abbreviations
• J. Schaber et al.
• other, a phenomenon often called crosstalk. Many different ways of pathway interactions have been described in the literature [1-3]. An important question in cell biology is how these systems transduce different extracellular stimuli to produce appropriate responses despite or in exploitation of pathway interactions.
• There have been attempts to quantify crosstalk in signalling networks. In one study crosstalk was categorized by a classification of the input-output relations of signalling networks [4]. Quantification consisted of counting the occurrence of each category in a pairwise comparison of pathways. Another study quantified the degree of crosstalk between two pathways by relating the number of realized interactions between two pathways to the number of hypothetically possible interactions [5]. This definition was restricted to pathways that do not share components. Both studies considered topological and structural properties of signalling networks and did not account for temporal and dynamic aspects. Another study analysed the steady state properties of two simple dynamic three-step kinase cascades with a shared component and concluded that with the proposed wiring scheme selective activation was possible without physical separation of the two cascades [6]. However, an analysis of the temporal behaviour of the two cascades shows that both pathways will always be activated even though not at the same time but subsequently. Thus, in order to understand crosstalk mechanisms, the dynamic behaviour of interacting pathways is important, even more because it is the transient dynamic behaviour that is important in signalling rather than the static or steady state features.
• A recent study addressed this problem proposing measures of dynamic crosstalk [7]. By analysing the activation of pathways by the intrinsic and an extrinsic stimulus, respectively, they defined measures for pathway specificity and fidelity. These measures give useful insights into how pathways interact with each other. However, it is important to note that these measures refer to responses to one stimulus at a time. These measures give no clue of how signals interact while being transmitted concomitantly. It can be expected that signals amplify or inhibit each other, when transmitted at the same time. Thus, to understand how signals interact dynamically it does not suffice to study each signal in isolation but also to study the cell’s response to multiple stimuli at the same time.
• The aim of this study was twofold. First, we wanted to map existing literature to a mathematical model to study the dynamic behaviour of two experimentally well characterized pathways and their interactions, i.e., the pheromone and filamentous growth pathway in bakers yeast. Second, we wanted to analyse and compare measures of dynamic crosstalk.
• Modelling dynamic crosstalk in cell signalling
• The mathematical model described here has been submitted to the Online Cellular Systems Modelling Database and can be accessed free of charge at http://jjj.biochem.sun.ac.za/database/schaber/index.html.
• Discussion
• We developed a dynamic mathematical model that represents current knowledge about the wiring of the pheromone pathway and the filamentous growth pathway in yeast. We concentrated on the main dynamic features and the interconnections between the two pathways and on a limited temporal scope. Moreover, we defined new measures of dynamic crosstalk, analysed their relations and conducted simulation studies to explore the contributions of several pathway interactions to crosstalk. As the kinetics of the considered reactions are largely unknown, our results must be viewed with respect to the chosen set of parameters. However, the important dynamic features of the model resembled what is known from experiments and were robust to single parameter perturbation (Fig. 3).
• We defined new measures of crosstalk, i.e., intrinsic specificity S; and extrinsic specificity Se that yield a better understanding of how the two pathways dynamically interact because they consider the combined response of several signals. Crosstalk, in our view, is not something that cells must avoid but rather it is indispensable in order to trigger the appropriate response to multiple simultaneous stimuli. Thus, it is instructive to analyse signal transduction of several pathways in parallel, because this is what the cell has to face.
• The new crosstalk measures characterize how the cells integrate different signals when being transmitted concomitantly. Concerning the pheromone response, they indicate that both signals amplify each other. This result could already be anticipated from the wiring scheme of the pathways, because it contains no direct inhibition of the pheromone pathway by the filamentous growth pathway. In the case of the filamentous growth pathway, however, we saw a crossinhibition by the pheromone pathway. This result was not clear just by studying the wiring scheme, because we considered several promoting and inhibiting influences of the pheromone pathway on the filamentous growth pathway, whose overall effect is not obvious. Our new crosstalk measures complement already existing crosstalk measures and give additional information by a single number that integrates complex time courses in a conceivable and interpretable way. However, it must be stressed that our proposed interpretations of the new crosstalk measures only mirror a phenomenological description of the considered outputs. If the wiring
• scheme is not known, these measures do not allow deriving conclusions about actual molecular interactions. Sensitivity analysis indicated that the new crosstalk measures are more stable than the other crosstalk measures, probably because by integrating both inputs they mutually buffer sensitivities of the other pathway.
• For the pheromone pathway the Komarova-specificity Sk is less than one, meaning that the pheromone stimulus activates its extrinsic response stronger than its intrinsic response. This result is not intuitive. It exemplifies that activation profiles of different components can hardly be compared because in the model these depend strongly on the parameters, and biologically an access of component A over component B does not necessarily mean that component A has a stronger impact than component B.
• In experimental and theoretical studies, the crosstalk measures C (or F), S; and Se (Table 1) can relate the activation profile of one specific component to different stimuli and allow drawing a conclusion about how pathways interact in a dynamical way and how signals are thereby modulated.
• The newly proposed crosstalk measures S; and Se can be generalized to more than two interacting pathways. Suppose we have n stimuli f₁, fn corresponding to n intrinsic responses X1, Xn. The intrinsic specificity of pathway k, Si(k), i.e., a measure of how extrinsic signals influences the intrinsic signals when acting in parallel, can be defined as
• Si(k) = X(fk) / X(f1,…, fn)
• and the extrinsic specificity of pathway k, Se(k), i.e., a measure of how the intrinsic signal influences the extrinsic signals when transmitted in parallel, can be defined as
• Se(k) = X(f1,…, fk-1, fk+1,…, fn) / X(f1,…, fn)
• From the Monte Carlo analysis we conclude that it is most instructive to use the time integral I as a measure for activation. First, the integral is biologically meaningful, because it represents the total amount of activated species, which were produced during the presence of a stimulus. It virtually combines both amplitude and time of a response. Second, it was correlated to the maximal concentration, thus the maximal concentration did not give much additional information in our model. Moreover, the integral is also more easily computed than the maximum as there are not pitfalls like local maxima, and it was in our cases more intuitive. In terms of signal timing we found the time of
• reaching the first maximum more useful than the signalling time as it gave a good measure of how fast a first significant response was, rather than the time of an average response.
• In the literature we could not find experiments where a pheromone stimulus and a starvation stimulus were applied in parallel, although from our viewpoint this would be an interesting experiment concerning crosstalk. A prediction of our model for the phenotype that would result from such an experiment is not possible, because the model was not built for such a purpose. Specifically, we disregarded the Ras-dependent activation of the filamentous growth pathway, and additionally, most described effects depend on unknown parameters. Moreover, in our model the pheromone response will always be transient, irrespective of the length of the pheromone stimulus, because activated Stell is degraded without being newly synthesized (Fig. 4). Nevertheless, it would be informative to test experimentally several features that are predicted by the model. On the one hand, the model predicts that a pheromone stimulus inhibits at least transiently the starvation-induced activation of Kss1 and FREP. On the other hand, a starvation stimulus is anticipated to amplify Fus3 activation by a pheromone stimulus. Moreover, we identified leakage of activated Stell as the most influential source of crosstalk. Crosstalk of activated Stell was stronger than crossinhibition by degradation of Ste12/Tec1 induced by activated Fus3. The model also predicts that activating both pathways at the same time results in amplification of the pheromone response and inhibition of the filamentous growth response compared to a single stimulus, indicating that the pheromone response is in this case the dominant factor. In an experiment where cells are first starved until a certain level of activated Kss1 is reached and then a pheromone stimulus is applied, the model predicts a lower pheromone response and a weakened inhibitory effect of the pheromone pathway on the filamentous growth response compared to the effects caused by application of both stimuli at the same time. This result depends of course on the chosen set of parameters, but exemplifies how such a study can lead to new hypotheses about the relative contribution of distinct mechanisms to overall crosstalk. In the model no cell cycle-dependent processes are considered and to test the model predictions by experiments we recommend using synchronized cells, e.g., by counter-flow centrifugal elutriation [39].
• We strongly believe that if we want to understand how pathways interact and crosstalk dynamically, measurements of pathway activation with both pathways being active are indispensable.
• Definition of crosstalk measures
• We assume that a signalling pathway has certain targets it activates and that each target can be assigned a specific or intrinsic stimulus and signal, whose major target it is, and nonspecific or extrinsic stimuli and signals, whose minor target it is (Fig. 2). This leads to an intuitive first description of the term crosstalk, i.e., the activation of a certain pathway component by an extrinsic stimulus. We define crosstalk C of the considered pathway with another pathway as the activation of a pathway component by the extrinsic stimulus e relative to the activation by the intrinsic stimulus i, i.e.,
• C = X(e) / X(i)
• where X(e) and X(i) denote some activation measures of the considered pathway by stimulus e and i, respectively (Fig. 2, for definition of activation measures see below).
• This definition is the reciprocal of the pathway fidelity introduced by Komarova et al. [7]. Given the intuitive understanding that the activation by the extrinsic signal X(e) is smaller than the activation by the intrinsic signal X(i), this results in a measure between zero and one for no and strong crosstalk, respectively. Of course, we can also get C > 1, meaning that the activation by the extrinsic signal is stronger than the activation by the intrinsic signal.
• As stated above, cells may be subjected to multiple stimuli at a time that can call for conflicting responses. In this case, the cell has to combine signals to trigger the appropriate response. Therefore, we introduce the two new measures, i.e., the intrinsic specificity S; and the extrinsic specificity Se.
• We define intrinsic specificity S; as the activation of the target of the considered pathway by the intrinsic stimulus i relative to the activation by both stimuli i and e, i.e.,
• Si = X(i) / X(i, e)
• where X(i,e) is the pathway activation when both stimuli are present (Fig. 2). The intrinsic specificity is a measure of how the intrinsic signal is influenced by the extrinsic signal when both are transmitted concomitantly. S; < 1 means that the combined signal of i and e yields a stronger response than the intrinsic signal alone, and indicates that the extrinsic signal amplifies the intrinsic signal when both are transduced, i.e., it points to crossactivation. The smaller Si, the stronger is the amplification by extrinsic signals and, thus, the less is the specificity of activation concerning the intrinsic signal. In cases where S; > 1, the activation by the intrinsic signal is stronger than the integrated response and indicates that when both signals are transmitted the extrinsic signal inhibits the intrinsic signal, which can be called a crossinhibition. The greater S₁, the stronger is the inhibition by the extrinsic signal and, thus, the pathway is activated more specifically by the intrinsic signal alone.
• We can also define a measure of how the extrinsic signal is affected by the intrinsic signal, when both are transmitted, i.e., the extrinsic specificity Se:
• Se = X(e) / X(i, e).
• If Se > 1, we encounter a situation where both signals together produce a smaller activation than the extrinsic signal alone. This indicates that the intrinsic signal inhibits the extrinsic signal, i.e., there is a crossinhibition. The larger the value of Se the stronger the inhibition by the intrinsic signal and, thus, the more specific the pathway is activated by an extrinsic signal alone. A value of S < 1 hints to a situation where the intrinsic signal amplifies the extrinsic signal. The lower Se the less specific is the pathway activation in relation to an extrinsic signal. A number close to zero shows a dominance of the intrinsic signal over the extrinsic signal or a weak crossactivation, and a number close to one shows a dominance of the extrinsic signal over the intrinsic signal, i.e., a strong crossactivation.
• Table 1 gives an overview of these measures and proposed interpretations of their respective values. Both measures of crosstalk should always be considered in parallel. Table 2 lists how the combinations of both crosstalk measures can be interpreted.
• The definitions above only consider activation measures explicitly and not the input stimuli. These activation measures relate to time series of protein activation profiles
• obtained by western blot analysis or time series of mRNA expression profiles obtained by microarrays, for example. These profiles are much easier to compare between pathways than input stimuli, like, for instance, a pheromone and a starvation stimulus, simply because they have the same units. It is not clear what would be the strength of a pheromone stimulus compared to a starvation stimulus, whereas the activation of a kinase or gene expression under two different conditions can be much better compared. Obviously, the measure of activation of a pathway by a single stimulus, like X(i), and to several stimuli, like X(i,e), can only be obtained by distinct time series experiments. In order to calculate the crosstalk measures the readouts from both experiments must be comparable, not only by using, in this case, the same input stimulus i in both experiments, but also by relating the readout in a quantitative way. In the case of western blots this can be achieved by blotting the protein activation time series of both experiments on the same gel. In the case of microarrays the signal values must be comparable not only between time points for one experimental condition, but also between experimental conditions by appropriate normalization techniques.
• The mathematical model
• The balance between two opposing goals guided the mathematical model development, i.e., to be as comprehensive and yet as