The model

We were interested in the modeling of potential regulation patterns that could provide a mechanism for the temporal profiles seen in the data and to study, which regulation patterns of the data could potentially be described by a mechanistic model. In the context of chapter 5, the aim was to examine the data set for features of insulation and how further mechanisms could influence the crosstalk in the pathways. For this, we built a model of ordinary differential equations that combines and harmonizes insights from a broad range of past research to a comprehensive view of the signaling mechanisms in the two pathways. The model describes the events as introduced in section 4.1 and 4.2.

A schematic structure of the model can be seen in Fig. 17. We carefully reviewed the known interactions and incorporated them to a combined, but in parts simplified view. In order to create a parametrization for the model, we turned to the data and looked for reasonable overlaps. The phosphopeptides HOG1_174_Y176 and FUS3_T180_Y182 were included in the data an thus used for fitting procedures in our modeling approach. The implementation was done using “Data2Dynamics”⁴⁹ introduced in Raueet al. (2013). The ODE equations as well as parameters and initial values for the model are documented in Appendix A.

Further, species showed a large variability in phosphorylation patterns compared to the anticipated behavior. For example Ste20 facilitates many interactions and thus showed also a large number of regulated phosphopeptides upon both stresses. Yet, the regulation was unspecific to a certain stress. Thus, we decided to disregard the data for now.

As a result of the modeling approach, we obtained a mechanistic view on the two signal transduction pathways that captures the anticipated behavior sufficiently, as can be seen in Fig. 18. In particular, the strong influence of the scaffold proteins Ste5 and Pbs2 could be observed. We see the regulating power of this biochemical functionality in the maintenance of specificity between the two signals. In the model, Ste5 activation of the MAPK signaling cascade Ste50-Ste7-Fus3 depends on the recruitment to the membrane at Ste4 and

49Available athttp://www.data2dynamics.org/. The environment was simulated on MAT-LAB R2015a.

initiates as well as insulates the signal. A similar behavior can be seen by the membrane located signal initiation process of the Sho1-branch in HOG signaling. This behavior already arises with a very simple (and non-biological) parametrization of the model, owed to the strong control that these tethering functions exert in the pathways. This mechanical way of insulating signals thus arises from structure already, emphasizing its importance for biological signal transmission. Even though the modeling process was based on the findings of phospho-proteomic data, we observed a large disparity between our simulations and the data. This proposes that with the knowledge available at the moment, it is not possible to explain the full extend of the data set and further investigations are needed.

As discussed, the data obtained by Vaga et.al. shows that many previously undiscovered regulation patterns of phospho-sites are existent in a crosstalk-like manner between the HOG- and the pheromone-pathway. Further experimental studies are required to either show the significance of the individual regulations or whether certain sites are only byproducts of the crucial signaling. Neverthe-less the data depicts a profound basis to assess further aspects of the complex network and its inter-dependencies.

Remark: The publication of (Vagaet al., 2014, Fig. 8) includes a parallel developed modeling approach employing the boolean ODE simulation frame-work “CellNOpt” published in Terfve et al.(2012). This modeling approach is based on a similar consensus network of the pathways (yet models the separate phosphosites that were detected) and allows for model variant construction by adding or subtracting interactions in the network. This model was used to validate certain proposed mechanisms in the paper by introducing edges in the model graph between different phosphosites. This approach shows that the model then gains a better quality of fit, yet the extend of this is unclear.

Objectively seen, the qualitative behavior of most of the peptides was also imperfect.

Fig. 18: Simulated time courses for an important subset of the species in the model. The expected activation patters can be shown with the model.

Especially appealing is the influence of scaffolding by Ste5 as well as the assembly of Ste20, Ste50, Ste11 and Pbs2 via the activation of Sho1. Both mechanisms insulate efficiently as was observed in previous research. For parametrization, see Appendix A, Tab. 4 and 5.

Consecutive activation patterns The mechanisms that have been identified so far for the functionality of both pheromone and HOG signaling are to a large extend consecutive activations in chains of signaling. There exists an interesting overlap between species and transient as well as longterm feedbacks factor into the system as well. Despite those non-linearities, the chain of activation will (until a certain point) follow an order of activation. In the face of the phospho-proteomic data, a reexamination of this has been suggested. Our modeling approach has shown as well that the behavior of most of the detected phosphosites does not follow the picture painted by scientific studies until now.

And while the data exhibits unfortunate gaps, that would (if filled) presumably show exactly the anticipated consecutive activation pattern, it also suggests that possibly more mechanisms facilitate such a chain. This could be phospho-rylations (or the missing thereof) that unlock certain conformation changes and subsequently allow further activations in the cascade. Yet as to what these mechanisms are, it will be inevitable to go into molecular details that are not in the scope of a modeling approach. Since the significance of the detected phosphosites has not been shown and the observed patterns could merely be by-standing phosphorylations that occur more or less without any consequences, it is vital to follow up this research in order to understand the nature of these patterns. The data provides a critical starting point for that, yet so far is limited in unveiling mechanistic regulations by itself. The model contained in the publication (Vagaet al., 2014, Fig.8) validates proposed mechanisms to a certain degree, yet we believe that more detailed experimental research on single phosphopeptides is necessary to substantiate proofs for their significance and functional mechanisms. The data by Vaga et.al. can thus be primarily viewed as a comprehensive, although non-specific basis for further investigations.