Enzyme kinetics far from the standard quasi-steady-state and equilibrium approximations

Analytic approximations of the time-evolution of the single enzyme-substrate reaction are valid for all but a small region of parameter space in the positive initial enzyme-initial substrate concentration plane. We find velocity equations for the substrate decomposition and product formation with the aid of the total quasi-steady-state approximation and an aggregation technique for cases where neither the more normally employed standard nor reverse quasi-steady-state approximations are valid. Applications to determining reaction kinetic parameters are discussed

A century of enzyme kinetics. Should we believe in the Km and vmax estimates?

The application of the quasi-steady-state approximation (QSSA) in biochemical kinetics allows the reduction of a complex biochemical system with an initial fast transient into a simpler system. The simplified system yields insights into the behavior of the biochemical reaction, and analytical approximations can be obtained to determine its kinetic parameters. However, this process can lead to inaccuracies due to the inappropriate application of the QSSA. Here we present a number of approximate solutions and determine in which regions of the initial enzyme and substrate concentration parameter space they are valid. In particular, this illustrates that experimentalists must be careful to use the correct approximation appropriate to the initial conditions within the parameter space

Bulletin of Mathematical Biology - facts, figures and comparisons

The Society for Mathematical Biology (SMB) owns the Bulletin of Mathematical Biology (BMB). This is an international journal devoted to the interface of mathematics and biology. At the 2003 SMB annual meeting in Dundee the Society asked the editor of the BMB to produce an analysis of impact factor, subject matter of papers, submission rates etc. Other members of the society were interested in the handling times of articles and wanted comparisons with other (appropriate) journals. In this article we present a brief history of the journal and report on how the journal impact factor has grown substantially in the last few years. We also present an analysis of subject areas of published papers over the past two years. We finally present data on times from receipt of paper to acceptance, acceptance to print (and to online publication) and compare these data with some other journals

Two-stage Turing model for generating pigment patterns on the leopard and the jaguar

Based on the results of phylogenetic analysis, which showed that flecks are the primitive pattern of the felid family and all other patterns including rosettes and blotches develop from it, we construct a Turing reaction-diffusion model which generates spot patterns initially. Starting from this spotted pattern, we successfully generate patterns of adult leopards and jaguars by tuning parameters of the model in the subsequent phase of patterning

Oscillatory Turing Patterns in a Simple Reaction-Diffusion System

Turing suggested that, under certain conditions, chemicals can react and diffuse in such a way as to produce steady-state inhomogeneous spatial patterns of chemical concentrations. We consider a simple two-variable reaction-diffusion system and find there is a spatio-temporally oscillating solution (STOS) in parameter regions where linear analysis predicts a pure Turing instability and no Hopf instability. We compute the boundary of the STOS and spatially non-uniform solution (SSNS) regions and investigate what features control its behavior

Multiscale modeling in biology

The 1966 science-fction film Fantastic Voyage captured the public imagination with a clever idea: what fantastic things might we see and do if we could minaturize ourselves and travel through the bloodstream as corpuscles do? (This being Hollywood, the answer was that we'd save a fellow scientist from evildoers.

Formation of vertebral precursors: Past models and future predictions

Disruption of normal vertebral development results from abnormal formation and segmentation of the vertebral precursors, called somites. Somitogenesis, the sequential formation of a periodic pattern along the antero-posterior axis of vertebrate embryos, is one of the most obvious examples of the segmental patterning processes that take place during embryogenesis and also one of the major unresolved events in developmental biology. We review the most popular models of somite formation: Cooke and Zeeman's clock and wavefront model, Meinhardt's reaction-diffusion model and the cell cycle model of Stern and co-workers, and discuss the consistency of each in the light of recent experimental findings concerning FGF-8 signalling in the presomitic mesoderm (PSM). We present an extension of the cell cycle model to take account of this new experimental evidence, which shows the existence of a determination front whose position in the PSM is controlled by FGF-8 signalling, and which controls the ability of cells to become competent to segment. We conclude that it is, at this stage, perhaps erroneous to favour one of these models over the others

Mathematical models of avascular cancer

This review will outline a number of illustrative mathematical models describing the growth of avascular tumours. The aim of the review is to provide a relatively comprehensive list of existing models in this area and discuss several representative models in greater detail. In the latter part of the review, some possible future avenues of mathematical modelling of avascular tumour development are outlined together with a list of key questions