A method for zooming of nonlinear models of biochemical systems

Abstract

BackgroundModels of biochemical systems are typically complex, which may complicate the discovery of cardinal biochemical principles. It is therefore important to single out the parts of a model that are essential for the function of the system, so that the remaining non-essential parts can be eliminated. However, each component of a mechanistic model has a clear biochemical interpretation, and it is desirable to conserve as much of this interpretability as possible in the reduction process. Furthermore, it is of great advantage if we can translate predictions from the reduced model to the original model.ResultsIn this paper we present a novel method for model reduction that generates reduced models with a clear biochemical interpretation. Unlike conventional methods for model reduction our method enables the mapping of predictions by the reduced model to the corresponding detailed predictions by the original model. The method is based on proper lumping of state variables interacting on short time scales and on the computation of fraction parameters, which serve as the link between the reduced model and the original model. We illustrate the advantages of the proposed method by applying it to two biochemical models. The first model is of modest size and is commonly occurring as a part of larger models. The second model describes glucose transport across the cell membrane in baker's yeast. Both models can be significantly reduced with the proposed method, at the same time as the interpretability is conserved.ConclusionsWe introduce a novel method for reduction of biochemical models that is compatible with the concept of zooming. Zooming allows the modeler to work on different levels of model granularity, and enables a direct interpretation of how modifications to the model on one level affect the model on other levels in the hierarchy. The method extends the applicability of the method that was previously developed for zooming of linear biochemical models to nonlinear models.

Model reduction in chemical dynamics: slow invariant manifolds, singular perturbations, thermodynamic estimates, and analysis of reaction graph

“…Semantic zooming can be considering as a simple application of lumping for gradual hiding the details of complex molecular mechanisms. a tool for work on various levels of model granularity [96] and gives a possibility to study interaction between processes at different levels of the hierarchy. The principle of semantic zooming [97] was used for development tools for navigations at different levels, similarly to geological information systems [98] (Fig.4).…”

Analysis of Kinetic Reaction Mechanisms

“…Both symbolic and numerical methods for unconstrained and constrained lumping were developed in Brochot et al (2005) and were demonstrated for 2-and 6-compartment physiologically based pharmacokinetic (PBPK) models for 1,3-butadiene. The approach was generalised for nonlinear systems in Sunnaker et al (2011) and includes methods to determine the inverse transformation, i.e. Sunnaker et al (2010) developed a linear lumping approach with application to a model predicting the observed behaviour of fluorescence emission in photosynthesis.…”

On the relationship between sloppiness and identifiability

“…The idea that a sloppy model is insensitive to parameter changes along sloppy directions, but highly sensitive along stiff combinations of parameters, has been exploited to propose reduced order modelling techniques [42,3,9]. The aim is to obtain a non-sloppy model that captures the relevant dynamics of the original model, but with a reduced number of states and parameters.…”