tailieunhanh - Báo cáo y học: "Research Saturation Behavior: a general relationship described by a simple second-order differential equation"

Tuyển tập các báo cáo nghiên cứu về y học được đăng trên tạp chí y học quốc tế cung cấp cho các bạn kiến thức về ngành y đề tài: Research Saturation Behavior: a general relationship described by a simple second-order differential equation. | Kepner Theoretical Biology and Medical Modelling 2010 7 11 http content 7 1 11 THEORETICAL BIOLOGY AND MEDICAL MODELLING RESEARCH Open Access Saturation Behavior a general relationship described by a simple second-order differential equation Gordon R Kepner Correspondence kepnermsp@ 1 Membrane Studies Project PO Box 14180 Minneapolis MN 55414 USA Full list of author information is available at the end of the article Abstract Background The numerous natural phenomena that exhibit saturation behavior ligand binding and enzyme kinetics have been approached to date via empirical and particular analyses. This paper presents a mechanism-free and assumption-free second-order differential equation designed only to describe a typical relationship between the variables governing these phenomena. It develops a mathematical model for this relation based solely on the analysis of the typical experimental data plot and its saturation characteristics. Its utility complements the traditional empirical approaches. Results For the general saturation curve described in terms of its independent x and dependent y variables a second-order differential equation is obtained that applies to any saturation phenomena. It shows that the driving factor for the basic saturation behavior is the probability of the interactive site being free which is described quantitatively. Solving the equation relates the variables in terms of the two empirical constants common to all these phenomena the initial slope of the data plot and the limiting value at saturation. A first-order differential equation for the slope emerged that led to the concept of the effective binding rate at the active site and its dependence on the calculable probability the interactive site is free. These results are illustrated using specific cases including ligand binding and enzyme kinetics. This leads to a revised understanding of how to interpret the empirical constants in terms of the variables .