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A self-consistent minimal cell model with a physically motivated schema for molecular interaction is introduced and described. The genetic and metabolic reaction network of the cell is modelled by multidimensional nonlinear ordinary differential equations, which are derived from biochemical kinetics. The strategy behind this modelling approach is to keep the model sufficiently simple in order to be able to perform studies on evolutionary optimization in populations of cells. At the same time, the model should be complex enough to handle the basic features of genetic control of metabolism and coupling to environmental factors. Thereby, the model system will provide insight into the mechanisms leading to important biological phenomena, such as homeostasis, (circadian) rhythms, robustness and adaptation to a changing environment. One example of modelling a molecular regulatory mechanism, cooperative binding of transcription factors, is discussed in detail. [ABSTRACT FROM AUTHOR]

Abstract  It is known that the unique thin plate spline interpolant to a function f ∈ C 3 IR sampled at the scaled integers h Z converges at an optimal rate of h 3. In this paper we present results from a recent numerical investigation of the case where the function is sampled at equally spaced points on the unit interval. In this setting the known theoretical error bounds predict a drop in the convergence rate from h 3 to h. However, numerical experiments show that the usual rate of convergence is h 3/2 and that the deterioration occurs near the end points of the interval. We will examine the effect of the boundary on the accuracy of the interpolant and also the effect of the smoothness of the target function. We will show that there exists functions which enjoy an even faster order of convergence of h 5/2. [ABSTRACT FROM AUTHOR]