Methods of model reduction for large-scale biological systems: a survey of current methods and trends

Complex models of biochemical reaction systems have become increasingly common in the systems biology literature. The complexity of such models can present a number of obstacles for their practical use, often making problems difficult to intuit or computationally intractable. Methods of model reduction can be employed to alleviate the issue of complexity by seeking to eliminate those portions of a reaction network that have little or no effect upon the outcomes of interest, hence yielding simplified systems that retain an accurate predictive capacity. This review paper seeks to provide a brief overview of a range of such methods and their application in the context of biochemical reaction network models. To achieve this, we provide a brief mathematical account of the main methods including timescale exploitation approaches, reduction via sensitivity analysis, optimisation methods, lumping, and singular value decomposition-based approaches. Methods are reviewed in the context of large-scale systems biology type models, and future areas of research are briefly discussed

Storage of chemical kinetic information

This chapter describes various methods for storing chemical kinetic mechanistic information within combustion models. The most obvious way is the definition of the kinetic system of differential equations by a detailed reaction mechanism. Parameterisation of such reaction mechanisms is commented upon here. Another possible approach is to store the solution of the system of ordinary or partial differential equations that defines the model within look-up tables. Such data can then be “retrieved” during combustion simulations within complex reacting flow models instead of solving the kinetic system of differential equations, often at much lower computational cost. Several such methods for storage and retrieval are reviewed here. As an alternative approach, functional representations of the time dependant kinetic changes or the look-up table contents can be achieved, using for example polynomial functions or artificial neural networks and these are also discussed

Investigation and improvement of reaction mechanisms using sensitivity analysis and optimization

The Chapter will describe a range of mathematical tools for model sensitivity and uncertainty analysis which may assist in the evaluation of large combustion mechanisms. The aim of such methods is to determine key model input parameters that drive the uncertainty in predicted model outputs. Approaches based on linear sensitivity, linear uncertainty and global uncertainty analysis will be described as well as examples of their application to chemical kinetic modelling in combustion. Improving the robustness of model predictions depends on reducing the extent of uncertainty within the input parameters. This can be achieved via a variety of methods including measurements and theoretical calculations. Optimization techniques which bring together wide sources of data can assist in further constraining the input parameters of a model and therefore reducing the overall model uncertainty. Such methods and their recent application to several combustion mechanisms will be described here

Mechanism reduction to skeletal form and species lumping

The numerical simulation of practical combustion devices such as engines and gas turbines requires the coupling of descriptions of complex physical flows with complex chemistry in order to accurately predict phenomena such as ignition and flame propagation. For three-dimensional simulations, this becomes computationally challenging where interactions between large numbers of chemical species are involved. Historically therefore, such simulations used highly simplified descriptions of chemistry, which limited the applicability of the models. More recently, however, a range of techniques for reducing the size of chemical schemes have been developed, where the resulting reduced schemes can be shown to have accuracies which are almost as good as much larger comprehensive mechanisms. Such techniques will be described in this chapter. Skeletal reduction techniques are first introduced which aim to identify redundant species and reactions within a mechanism over wide ranges of conditions. Approaches based on sensitivity analysis, optimization and direct relation graphs are introduced. Lumping techniques are then discussed which exploit similarities between the structure and reactivity of species in describing lumped components, which can represent the sum of several isomers of a particular hydrocarbon species for example. Both approaches can lead to a substantial reduction in the size of chemical mechanisms (numbers of species and reactions) without having a significant impact on model accuracy. They are combined in the chemistry-guided reduction approach, which is shown to generate reduced chemical schemes which are small enough be used within simulations of ignition behaviour in a homogeneous charge compression ignition (HCCI) engine

Analysis of Kinetic Reaction Mechanisms

Chemical processes in many fields of science and technology, including combustion, atmospheric chemistry, environmental modelling, process engineering, and systems biology, can be described by detailed reaction mechanisms consisting of numerous reaction steps. This book describes methods for the analysis of reaction mechanisms that are applicable in all these fields. Topics addressed include: how sensitivity and uncertainty analyses allow the calculation of the overall uncertainty of simulation results and the identification of the most important input parameters, the ways in which mechanisms can be reduced without losing important kinetic and dynamic detail, and the application of reduced models for more accurate engineering optimizations. This monograph is invaluable for researchers and engineers dealing with detailed reaction mechanisms, but is also useful for graduate students of related courses in chemistry, mechanical engineering, energy and environmental science and biology

Determination of the adsorption and desorption parameters for ethene and propene from measurements of the. heterogeneous ignition temperature

If a cold catalyst is exposed to a mixture of fuel + oxygen, the surface coverage of the catalyst can be dominated by either the fuel or the oxygen, depending on the actual catalyst and the composition of the gaseous mixture. If the temperature is increased, heterogeneous ignition occur

Determination of adsorption and desorption parameters from ignition temperature measurements in catalytic combustion systems

When a cold catalyst is exposed to a fuel-oxygen mixture, the surface gets covered with the more effectively adsorbing species. When the temperature is increased, this species is desorbed and the ignition temperature is determined by the rate of desorption. Based on the equations for the heat balance, expressions were derived for the calculation of ignition temperature from the parameters of the experimental setup, the preexponential factor Ad and activation energy E-d of desorption, the ratio of sticking coefficients, and the ratio of adsorption orders of fuel and oxygen. Published experimental data for the catalytic ignition of CO, H-2, and CH4 were reinterpreted using the expressions obtained, and the following parameters were determined for polycrystalline platinum catalyst: E-d(H-2/Pt) = 43.3+/-5.2 kJ/mol, E-d(CO/Pt) = 107.2+/-12.7 kJ/mol, E-d(O-2/Pt) = 190 34 kJ/mol, S-H2,S-0/S-O2,S-0 = 36.7+/-9.6, S-CO,S-0/S-O2,S-0 = 41.2+/-8.5, S-O2,S-0/SCH4,0 = 5.9+/-0.3. Error limits refer to a confidence level of 0.95. The activation energy of desorption for CO and O-2 and the ratio of zero coverage sticking coefficients of O-2 and CH4 are the first experimentally based determinations of these parameters. Experimental ignition temperatures could be reproduced assuming second-order ' adsorption of CO, H-2, and O-2 on the Pt surface. These reaction orders have been debated in the literature