PROTECCIÓN

I will be using an ODE system to model TGFβ because my network, although relatively large for an ODE model, will not require excess computing power for any tasks. Using ODE will allow me to generate a detailed understanding of the system that can be altered to match generated data and also make future predictions. As it is also the most commonly used system for TGFβ studies it will give me a wealth of information to draw on. Careful planning of models before starting is important for structure and parameters (Hasdemir et al. 2015).

Therefore having previous models assisted with this design. A PN model would be unfavourable as the intricate details would be difficult to design. Boolean networks are difficult to represent time accurately and also do not allow for deterministic simulation, both of which will be important for matching the model to experimental data. Finally LP and ABM are both in their infancy for examining these types of systems. Therefore, using either system would require

substantially more effort for no reward.

Mass action kinetics will be used for the model, as it is the most used rate law for mathematical and biological studies that some argue requires no justification (Voit et al. 2015). In this case my justification is that the two models that the majority of my network is based on are built using mass action equations, which proves it can be implemented for this type of study. Although they could be adapted, mass action also allows me to switch with ease between deterministic and stochastics simulations, allowing me a deeper understanding of the model

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interactions. Other functions do not allow this, as they are either unsuitable for stochastic simulation or must be modified to accommodate it, which then makes them unsuitable for deterministic. Mass action kinetics works from the principle that the reaction rate is proportional to the probability that reactants will collide (Voit et al. 2015). It takes into account the concentration of reactants, the power of their molecularity and how many are involved in the reaction (Voit et al.

2015).

Advances in computing power have also allowed complex modelling that would have previously been impossible. This has led to an increase in the number of biologists using computational modelling to unravel complex systems. As a result there has been a number of modelling tools designed to facilitate their move into an area that was once exclusively for mathematics and physics researchers. Most approaches have associated programmes, Boolean using CellNetAnalyzer for example (Klamt et al. 2007). However, ODE modelling has been the most used and has resulted in a number of programmes being made available, including but not limited to simbiology, SBTOOLBOX (both Matlab plugins) (MATLAB vR2016a, The MathWorks Inc., Natick, MA) and COPASI (S.

Hoops et al. 2006). My model has been built in COPASI as it contains many tools including pre-set or custom functions; the input of events; deterministic, stochastic and hybrid simulations as well as a multitude of analysis tools such as: sensitivity analyses, parameter estimations and parameter scans amongst others. It is also well maintained and constantly being improved upon. Finally, I believe it has the most user friendly interface.

132 5.1.2 Chapter aims

 Alter and combine two previous computational models to create a model that represents IL-1+OSM+TGFβ signalling, whilst still matching the profiles seen by the original models.

 Match the model simulation output to data created in the previous chapters.

 Test the model by showing its ability to match novel experimental data, without modification. Then alter the structure if it cannot.

 Use the model to explore how TGFβ will affect IL-1+OSM-driven MMP-13 expression with age, as ALK1 becomes the dominant receptor.

133 5.2 Model construction

In order to create my model I first had to alter the previously published models separately to make them compatible. In order to ease the computational burden I also reduced complexity where possible, removing or altering any interactions that were not necessary for what I was studying. Combining both models in their original forms would have resulted in a very large model, which would have been difficult to parameterise and simulate.

5.2.1 IL-1+OSM

The original IL-1+OSM model was presented in three sections, OSM, pro-MMP activation and IL-1 (Proctor et al. 2014) all of which can be seen in appendix 5.1. As I was only looking at MMP-13 mRNA and had no interest, at that time, in its transition to an active MMP, I removed the pro-MMP activation component completely. The remaining two sections were simplified but still fit the same profiles. To achieve this some approximations were made: Three proteins were originally present in the model: DUSP16, MKP1 and PP4. As these were

upregulated by the same source and only relevant for blocking, I replaced all three of these species with one “block” species. This blocked all three reactions that the original proteins did. However, each reaction was blocked at a different rate, in order to have the same effect that the original proteins would have had.

The receptor profile for IL-1 was changed to include an internalisation step that replaced the need for IRAK and TRAF6. The phosphorylation and subsequent nuclear translocation of STAT3 was altered so that it could be represented by a single reaction. Finally any mRNAs that were produced, other than MMP-13, were removed. The resulting model is represented in Figure 5.1.

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Figure 5.1 Network

diagram showing species and reactions involved in the IL-1+OSM response.

Schematic representation of the simplified IL-1+OSM signalling section of my newly developed model.

CellDesigner was used to create the schematic.

135 5.2.2 TGFβ

The TGFβ section of the model is based on the TGFβ section, described in Wang Hui et al. (2014), which can be seen in appendix 5.2. It had only minor alterations in comparison to the IL-1+OSM section. This was for two reasons:

1. It was a smaller model.

2. It was the pathway being explored so required more detail.

The biggest change was the removal of the SOX9, aggrecan and collagen component from the original model as I had no interest in their expression at this time. MMP2 was completely removed as it had no effect on the model in this form. The role of active RUNX2 was also altered, no longer inducing the production of pro-MMP-13 but instead producing MMP-13 mRNA. This change was reasonable as RUNX2 induced upregulation of MMP-13 has been shown to be at the mRNA level (Ijiri et al. 2005).

The original models had not been created to be combined and as a result they did not share any interactions. Therefore, I performed a literature search to identify some ways IL-1, OSM and TGFβ may interact. I then altered my version of the model to facilitate TGFβ and IL-1+OSM interactions. The first alteration was JunB production through SMAD2 (which represents SMAD2/3 as explained in chapter 2.3.3) signalling because there is a substantial body of evidence showing that it is a direct downstream target of SMAD3 (Ponticos et al. 2009; Gervasi et al. 2012) and works to antagonise rapid gene transcription (Mauviel et al. 1996; Verrecchia et al. 2001; Selvamurugan et al. 2004).

Studies have shown it can displace Fos in the AP-1 complex and bind to c-Jun (Ponticos et al. 2009; Mauviel et al. 1996). It has also been demonstrated to limit the effects of IL-1, in particular its effect on MMP synthesis (Emi

Shimizu et al. 2010). Finally it has been shown to repress gene expression in epithelial–mesenchymal transition in cancer due to upregulation by TGFβ. This demonstrates TGFβ can produce significantly high JunB expression to limit gene transcription (Gervasi et al. 2012). SMAD1 signalling could also now lead to an increase in p38 phosphorylation, as shown in C. G. Chen et al. (2012).

Figure 5.2 shows the complete TGFβ section of my model.

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Figure 5.2 Network diagram showing all the species and reactions involved in the TGFβ pathway. Schematic representation of the modified TGFβ section in my newly developed model. CellDesigner was used to create the schematic.

137 5.3 Model parameterisation

After altering the structure of the two model components, I combined them together to form my complete model (Fig 5.3). The original parameters from both models were also incorporated and the parameters for the newly added reactions were assigned default values. With this model I attempted to match the simulation output to the data that were generated in chapters 3 and 4.

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Figure 5.3 Network diagram showing species and reactions involved in the IL-1+OSM+TGFβ model. Schematic representation of my complete model. Detailing all interactions between the IL-1, OSM and TGFβ signalling pathways. The “block” species is involved in multiple reaction but represents one species upregulated by cJun_dimers or cFos_cJun and provides a negative feedback for multiple reactions but at different rates. CellDesigner was used to create the schematic.

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