(254e) Analyzing High Fidelity Models in Systems Biology Using a Meta-Model Approach: Case Studies in Cellular Signaling and Acute Inflammation

Background:

‘High fidelity’ models have become a commonplace in systems biology [1]. These models encompass sufficient systems levels information on the interacting components enriched with details on regulatory modules like feedbacks and crosstalks. However, these models are associated with large number of parameters that are often ad hocand only a few of them can be simultaneously inferred from experiments. Therefore, it is important to select and analyze the nonlinear contributions of these parameters to the model behavior to rank the parameters by their importance. While several techniques are available for such a ranking process, sensitivity analysis is a common approach. In biological systems, most often researchers use local estimates of sensitivity because of the computational cost associated with global analysis of high fidelity models. However, local analysis of such non-linearly interacting biological models can often be unreliable. Here we present a work-flow for global sensitivity analysis of high fidelity models using a meta-model approach that provides a sufficiently accurate estimate of the sensitivity indices without costly model evaluations.

Methods:

We based our global sensitivity analysis on random sampling high dimensional model representation (RS-HDMR) developed by Rabitz et al [2]. The method has been previously applied to high dimensional models in physical systems like atmospheric chemistry, combustion processes and genetic circuits [3]. Here, we are extending the method to biological systems with significant nonlinear interactions via feedbacks. The technique constructs a meta-model of the original model and by using orthogonal function decomposition techniques, evaluates the well-known Sobol’ sensitivity indices of the input parameters to the model output. At the same time, the component functions of the resulting function decomposition provide a convenient way to analyze the input-output (IO) behavior of the model. The advantage of using RS-HDMR lies in the reduction in number of random samples required (~10³) to estimate the sensitivity indices as compared to computationally expensive brute-force Monte Carlo methods (> 10⁵). For each case study selected, we did a complete analysis of the model IO behavior predicted by RS-HDMR and compared the accuracy of the Sobol’ indices and the relative ranking of the parameters with brute force Monte Carlo methods.

Applications and results:

We selected two ordinary differential equation models as case studies for our current work. Model 1 describes insulin mediated activation of PI3K/AKT pathway with 20 state variables and 25 free parameters [4]. Model 2 describes an acute inflammation process mediated by endotoxin with 15 state variables and 51 free parameters [5]. We selected models that contain a wide range of reactions that are typically encountered in systems biology models. From our analysis, we found RS-HDMR to perform well for models of this complexity and there was considerable reduction in the computational time. Furthermore, we also gained insights into the model behavior in the high dimensional parameter space that was not possible by analyzing each parameter in isolation. In particular, we could efficiently discover regions of the parameter space with distinct behaviors that are experimentally or clinically relevant. RS-HDMR may therefore be a promising technique with sufficient mathematical foundation to be adapted to several problems of interest to systems biology community.

References:

1. Kiparissides A, Kucherenko SS, Mantalaris A, Pistikopoulos EN (2009) Global sensitivity analysis challenges in biological systems modeling. Industrial & Engineering Chemistry Research 48: 7168-7180.

2. Li G, Rabitz H (2012) General formulation of HDMR component functions with independent and correlated variables. Journal of Mathematical Chemistry 50: 99-130.

3. Li G, Rosenthal C, Rabitz H (2001) High dimensional model representations. The Journal of Physical Chemistry A 105: 7765-7777.

4. Sedaghat AR, Sherman A, Quon MJ (2002) A mathematical model of metabolic insulin signaling pathways. American Journal of Physiology-Endocrinology and Metabolism 283: E1084-E1101.

5. Chow CC, Clermont G, Kumar R, Lagoa C, Tawadrous Z, et al. (2005) The acute inflammatory response in diverse shock states. Shock 24: 74-84.