Mapping global sensitivity of cellular network dynamics: sensitivity heat maps and a global summation law

Abstract

The dynamical systems arising from gene regulatory, signalling and metabolic networks are strongly nonlinear, have high-dimensional state spaces and depend on large numbers of parameters. Understanding the relation between the structure and the function for such systems is a considerable challenge. We need tools to identify key points of regulation, illuminate such issues as robustness and control and aid in the design of experiments. Here, I tackle this by developing new techniques for sensitivity analysis. In particular, I show how to globally analyse the sensitivity of a complex system by means of two new graphical objects: the sensitivity heat map and the parameter sensitivity spectrum. The approach to sensitivity analysis is global in the sense that it studies the variation in the whole of the model's solution rather than focusing on output variables one at a time, as in classical sensitivity analysis. This viewpoint relies on the discovery of local geometric rigidity for such systems, the mathematical insight that makes a practicable approach to such problems feasible for highly complex systems. In addition, we demonstrate a new summation theorem that substantially generalizes previous results for oscillatory and other dynamical phenomena. This theorem can be interpreted as a mathematical law stating the need for a balance between fragility and robustness in such systems.

Sensitivity analysis approaches applied to systems biology models

“…SBML-SAT, SensSB and Systems Biology Toolbox 2). Recently, a new method and tool have been developed to map the sensitivity of the model outputs by sensitivity heat maps and a global summation law [88]. Most of these sensitivity analysis tools support the models encoded in systems biology markup language (SBML) [89].…”

Sensitivity analysis of infectious disease models: methods, advances and their application

“…Much would remain to be known, however, about the parameter sensitivity of other model outputs of interest, leaving ample room for useful SA. Performing SA prior to data collection can also benefit our comprehension of a modelled complex system; indeed, SA can help to determine what data need be collected in order to most informatively narrow parameter and output uncertainty [11]. Similar approaches exist in many disciplines and guises, e.g.…”

“…It should also be noted that SA techniques such as these may be used to explore the parameter sensitivity of the log-likelihood surface itself, with the Fisher Information Matrix describing gradients on this surface and identifying the most profitable parameters to measure experimentally [11]. There is, therefore, both a strong direct and indirect link between SA and parameter estimation.…”

“…GSA techniques have been broadly applied in systems biology [11,21], environmental modelling [22,23] and infectious disease modelling. Examples of recent published infectious disease models that describe and carry out an SA are shown in table 1, and, among these, LHS-PRCC [26][27][28]32] and other simple sensitivity methods [24,25,31] are frequently used.…”

Biological switches and clocks

“…In this regard, the paper by Rand (2008) in this special issue presents a sophisticated and promising new approach to the thorny problem of parameter estimation in complex network models with many parameters.…”