I.D.L. Bogle

Detailed mathematical modelling of membrane modules

Abstract Membrane technology is used for a wide range of separations from particle-liquid separations to gaseous and liquid–liquid separations. In this paper, we introduce a detailed model that describes a general membrane separation. The model disregards many common assumptions such as plug flow; constant temperature; constant pressure; binary mixture; steady-state conditions; and constant physical properties. Our approach is applicable to any membrane separation and in this paper we demonstrate its application to both liquid mixture separation (pervaporation) and gas separation in hollow-fibre modules. Both cases are seen to exemplify the need for a detailed model.

Simulation and optimization of metabolic pathways

A program to simulate metabolic pathways on the basis of either kinetic data or data on the steady state levels and fluxes using Biochemical Systems Theory is presented. Having established such a model it is possible to determine the rate-controlling enzymes and metabolites for the system. While this in itself yields extremely valuable information pinpointing the limiting fluxes through the system, a more usual objective is to maximise a production rate or flux or to minimise byproducts or toxic intermediates. For this reason the problem is posed as a constrained optimization. While we recognise that the optimum thus found may be unachievable in practical terms due to limitations in experimental techniques, it is important in that it (a) gives an upper or lower bound to the production rate or flux, and (b) indicates the ideal combination of variables which should be aimed at. The model system used to test the software is a pathway for the degradation of toluene encoded by the TOL plasmid from Pseudomonas putida transformed into Escherichia coli. Kinetic data has been obtained, partly from the literature and partly by approximation, and realistic metabolite and enzyme concentrations are chosen.

Addressing the challenges of multiscale model management in systems biology

Mathematical and computational modelling are emerging as important techniques for studying the behaviour of complex biological systems. We argue that two advances are necessary to properly leverage these techniques: firstly, the ability to integrate models developed and executed on separate tools, without the need for substantial translation and secondly, a comprehensive system for storing and man-ageing not only the models themselves but also the parameters and tools used to execute those models and the results they produce. A framework for modelling with these features is described here. We have developed of a suite of XML-based services used for the storing and analysis of models, model parameters and results, and tools for model integration. We present these here, and evaluate their effectiveness using a worked example based on part of the hepatocyte glycogenolysis system.

Global optimisation of constrained non-convex programs using reformulation and interval analysis

Abstract In this paper the interval global optimisation approach is recast, by reformulation of the global optimisation problem, as a bound constrained linear relaxation. Two new classes of linear under-estimator, derived from the natural extension and mean value forms of interval analysis, respectively, and applicable to any once differentiable function, are introduced. These under-estimators are combined with the interval bounded linear program to create a rigorous global optimisation algorithm for constrained global optimisation. The value of the approach is validated by application to selected test problems from the process engineering and global optimisation literature. The results indicate that the interval LP is more efficient than other interval methods for constrained problems whilst retaining a wide applicability.

A composite computational model of liver glucose homeostasis. I. Building the composite model

A computational model of the glucagon/insulin-driven liver glucohomeostasis function, focusing on the buffering of glucose into glycogen, has been developed. The model exemplifies an ‘engineering’ approach to modelling in systems biology, and was produced by linking together seven component models of separate aspects of the physiology. The component models use a variety of modelling paradigms and degrees of simplification. Model parameters were determined by an iterative hybrid of fitting to high-scale physiological data, and determination from small-scale in vitro experiments or molecular biological techniques. The component models were not originally designed for inclusion within such a composite model, but were integrated, with modification, using our published modelling software and computational frameworks. This approach facilitates the development of large and complex composite models, although, inevitably, some compromises must be made when composing the individual models. Composite models of this form have not previously been demonstrated.

A composite computational model of liver glucose homeostasis. II. Exploring system behaviour

Using a composite model of the glucose homeostasis system, consisting of seven interconnected submodels, we enumerate the possible behaviours of the model in response to variation of liver insulin sensitivity and dietary glucose variability. The model can reproduce published experimental manipulations of the glucose homeostasis system and clearly illustrates several important properties of glucose homeostasis—boundedness in model parameters of the region of efficient homeostasis, existence of an insulin sensitivity that allows effective homeostatic control and the importance of transient and oscillatory behaviour in characterizing homeostatic failure. Bifurcation analysis shows that the appearance of a stable limit cycle can be identified.

An accelerated interval method for global optimisation

Many optimisation problems in Chemical and Process Engineering are nonconvex resulting in multiple local solutions. A modified interval algorithm for obtaining global minimisers is presented. The modifications accelerate the convergence of the interval algorithm and identify minimisers lying on constraints to provide a single rigorous globally optimal point to a general optimisation problem. The results of application to test problems indicate that a substantial performance increase is obtained when solving multiextremal problems.

Modelling and simulation of fractional precipitation — comparison with pilot plant data

This paper describes the modelling and simulation of fractional precipitation and centrifugation, two common operations in the downstream processing of intracellular proteins, and demonstrates how the developed models are validated against pilot plant scale data.

An analysis of the recycle dynamics of a high pressure production process

Control schemes have been developed for a continuous pilot plant for vitamin production using the approach recommended by Luyben. The plant was simulated using Speedup and accurate physical property prediction. The approach was modified to fit the plant but it was confirmed that the basic premise of requiring one stream in the recycle loop under flow control was confirmed.