Yakubovich’s Oscillatority of Circadian Oscillations Models

in Mathematical Biosciences (2008), 216

The testing procedure of Yakubovich’s oscillatority property is presented. The procedure is applied for two models of circadian oscillations [10], [11]. Analytical conditions of these models oscillatority ... [more ▼]

The testing procedure of Yakubovich’s oscillatority property is presented. The procedure is applied for two models of circadian oscillations [10], [11]. Analytical conditions of these models oscillatority are established and bounds on oscillation amplitude are calculated. [less ▲]

Approximations and their consequences for dynamic modelling of signal transduction pathways

in Mathematical Biosciences (2007), 207(1), 40-57

Signal transduction is the process by which the cell converts one kind of signal or stimulus into another. This involves a sequence of biochemical reactions, carried out by proteins. The dynamic response ... [more ▼]

Signal transduction is the process by which the cell converts one kind of signal or stimulus into another. This involves a sequence of biochemical reactions, carried out by proteins. The dynamic response of complex cell signalling networks can be modelled and simulated in the framework of chemical kinetics. The mathematical formulation of chemical kinetics results in a system of coupled differential equations. Simplifications can arise through assumptions and approximations. The paper provides a critical discussion of frequently employed approximations in dynamic modelling of signal transduction pathways. We discuss the requirements for conservation laws, steady state approximations, and the neglect of components. We show how these approximations simplify the mathematical treatment of biochemical networks but we also demonstrate differences between the complete system (c) 2006 Elsevier Inc. All rights reserved. [less ▲]