Combining SBML Models in the Context of Cellular Aging Mechanisms
Authors:   , Kounis Dimitrios , Kriete Andres , Sacan Ahmet 
Published: April 2024

Complex biological processes like aging require a broad investigation of multiple mechanisms (Cohen et al., 2022). Computational modeling has been proven successful in studying specific pathways, but the interaction of these pathways on a cellular level is not well understood. Here we introduce a method to combine established pathway models developed in the standardized Systems Biology Markup Language (SBML). The models chosen are relevant to cellular aging pathways. Some of the difficulties in reaching this goal include overlapping components of the models, and refitting the parameters based on adding components to maintain consistency with experimental data. We developed and applied a computational pathway combination method to assist us in understanding cellular aging. There are many complexities in the aging process. One of these complexities is the property of tradeoffs, where cells prioritize robustness, function, and efficacy over fragility and longevity (Kriete, 2013). Accumulative damage and an unresponsive repair mechanism stimulates these aging pathways (Maynard et al., 2015; Yousefzadeh et al., 2021). This can be seen in oxidative proteins, irradiation, DNA damage, metabolic decline, and other processes (Maynard et al., 2015; Yousefzadeh et al., 2021). Each stress response introduces a new steady state as damage slowly accumulates over time and increases stress and mutations (Kriete, 2013). Some relevant and important pathways include mTOR, p53, NF-kB, IKK, AKT, and AMPK (Alfego & Kriete, 2017; Kriete et al., 2010; Rodríguez-Rodero et al., 2011; Takahashi et al., 2000). Here we combine three SBML models which include key nodes to accomplish the goal of creating a more complex and comprehensive approach to studying the process of biological aging. This is done by creating a protocol for adding multiple models together into a singular complex functional model that can be further extended to increase complexity. Models are combined by keeping components separate but connect through a ratio scaling factor based on steady state values between matching elements allowing each model to influence the other. We initially seed our modeling approach with a SBML model of the mTOR pathways by Sonntag and a senescence mitochondrial dysfunction model from Dalle Pezze (Dalle Pezze et al., 2014; Sonntag et al., 2012). Subsequently, proteolysis models by Proctor were investigated (Proctor et al., 2005; Proctor et al., 2007) and the most suitable model was chosen due to added mechanistic detail on the accumulation of aggregated misfolded damaged proteins. The models were implemented using Tellurium package in Python (Choi et al., 2018). Scripts were written to assist in making choices when combining models and support model compatibility. The behavior of the models, in isolation and combined, and differences in steady state values were analyzed along with varying perturbations. A sensitivity analysis was performed showing that there is a change in sensitivity of different parameters both inside and outside the models. Sensitivities alter when models including an increase in sensitivity in external model connections. Combining SBML models allows studying cellular mechanisms on a broader scale that arise out of the interaction of individual pathways models, which influence each other in a communicative fashion. This method used to combine models was biologically relevant as species behaved similar to how prior literature described. However, limitations and feasibility issues exist with adding more models, computing, and managing manual steps that were used. Further testing is recommended before exploring larger models. While our approach is a step towards SBML model combinations and opens new opportunities to investigate complex biological mechanisms more comprehensively, some recommendations to improve the process can be made.