Systems biology involves a combination of mathematical modelling and quantitative experimentation. One of the main goals of systems biology is to build mechanistic mathematical models of biological systems to make valuable predictions about their system-level behaviors. Mechanistic models are based on our existing knowledge about the biological system and they generally describe the underlying functional mechanisms or reactions in form of ordinary differential equations (ODEs). Development of large-scale mechanistic mathematical models is confronted by issues like parameter estimation and model checking. Ideally mechanistic models should include all known components and relevant phenomena so that it can capture cellular biochemistry, but this kind approach will lead to exponential increase in number of ODEs as well as parameters. Otherwise model can be very simple in terms of mechanistic details, but this kind of oversimplification may not capture real time behavior of biological system. A third alternative is model with intermediate resolution, which generally includes mechanistic detail of key components and activities.
A recent article published by Chen et al describes a large-scale mechanistic model of ErbB signaling pathway, which comprised of 499 ODEs, 828 reactions, 201 unique reaction rates and 28 non-zero initial conditions. Whole system was divided in several biological and reaction compartments, and reactions were described using mass action kinetics. Different parameters were collected either from literature or experimental measurements. One of the key feature of the study is the parameter optimization approach used by Chen et al. They fixed the parameter those have good experimental cell-based estimates, while other parameters were estimated by minimizing an objective function comprising the normalized root mean square deviation (RMSD) between time course data and computed model trajectories. Further they performed simulated annealing (SA) to search across a region of parameter space spanning 2.5 log orders above and below a priori values (obtained from either literature or experiments). By focusing simulated annealing on 75 rate constants and initial conditions out of 229 they tried to improve the convergence of parameter optimization. These 75 parameters were selected based on initial sensitivity analysis. SA approach is computationally expensive and finding one good fit requires 100 annealing runs. In general, parameter estimation has four possible outcomes: (i) a single, unique, parameter solution set, making the model fully identifiable, (ii) a countable number of parameter sets, making the model ‘locally identifiable’, (iii) an infinite number of solution sets, making the model non-identifiable and (iv) no solution sets, in which case the model probably has structural flaws. In this case although model was non-identifiable and partially calibrated, quality of the predictions is quite good and it yields meaningful information on parameter sensitivities. For example, based on sensitivity analysis model suggests that phosphorylated Akt levels (or phosphorylation OF Akt) should be more sensitive to changes in EGFR kinase than those of phosphorylated ERK (or phosphorylation OF ERK), which was further confirmed by experiments. Followings are major insights gained from this study

• Large-scale models should include intermediate resolution of mechanistic details
• Non-identifiability is major issue for large and complex models
• Quality of the predictions of a model is our primary concern and not model identifiability
• Sensitivity analysis is a powerful tool, particularly in case of non-identifiable and partially calibrated models
• Non-deterministic fitting procedures such as simulated annealing, are capable of finding a global minimum in a rugged landscape
• Parameter sensitivity is context and target dependent

The study carried out by Chen et al. provides a valuable guideline about modelling of large-scale biological systems, particularly what should be our major concern when we are dealing with parameter optimization and sensitivity analysis . Reporting of large scale models using standard markup languages such as SBML or CellML (in this case authors submitted their model in SBML format along with MATLAB code) with proper annotations should be a regular practice. This will not only allow to reproduce the results, but also improve the model reusability.

Reference:
William W Chen, Birgit Schoeberl, Paul J Jasper, Mario Niepel, Ulrik B Nielsen, Douglas A Lauffenburger, Peter K Sorger (2009). Input–output behavior of ErbB signaling pathways as revealed by a mass action model trained against dynamic data Molecular Systems Biology, 5 DOI: 10.1038/msb.2008.74