Tài liệu Báo cáo khoa học: Optimal observability of sustained stochastic competitive inhibition

Optimal observability of sustained stochastic competitive

inhibition oscillations at organellar volumes

Kevin L. Davis* and Marc R. Roussel

Department of Chemistry and Biochemistry, University of Lethbridge, Lethbridge, Alberta, Canada

When a system contains only a small number of work￾ing units, whether these be molecules in a chemical sys￾tem or individuals in a biological population, random

changes in the number of individuals of a population

play an important dynamical role. Living cells in par￾ticular often have biochemical components which are

present in very small numbers. In these cases, the usual

deterministic differential equations may give mislead￾ing results and a stochastic description, incorporating

the essentially random nature of individual reaction

events, is required. If we are interested in biochemical

kinetics, a mesoscopic description, i.e. one which does

not take into account the microscopic details of the

positions and internal states of the molecules involved,

is often sufficient. This is the level of description adop￾ted in this study.

Noise can have a variety of effects in nonlinear

systems [1–4]. In some cases, these effects are more

quantitative than qualitative [5–9]. In others, new

behaviours are observed when either internal [10,11]

or externally imposed noise is considered. It is now

relatively well known that external noise can excite

Keywords

stochastic kinetics; enzyme inhibition;

oscillation; stochastic resonance

Correspondence

M.R. Roussel, Department of Chemistry

and Biochemistry, University of Lethbridge,

Lethbridge, Alberta, T1K 3M4, Canada

Tel: +1 403 329 2326

Fax: +1 403 329 2057

E-mail: [email protected]

Website: http://people.uleth.ca/
roussel

Note

The mathematical model described here has

been submitted to the Online Cellular Sys￾tems Modelling Database and can be

accessed free of charge at http://jjj.biochem.

sun.ac.za/database/davis/index.html

*Present address

Centre for Nonlinear Dynamics in Physiology

and Medicine, McGill University, Montre´ al,

Que´bec, Canada

(Received 19 August 2005, revised 12

October 2005, accepted 31 October 2005)

doi:10.1111/j.1742-4658.2005.05043.x

When molecules are present in small numbers, such as is frequently the

case in cells, the usual assumptions leading to differential rate equations

are invalid and it is necessary to use a stochastic description which takes

into account the randomness of reactive encounters in solution. We display

a very simple biochemical model, ordinary competitive inhibition with sub￾strate inflow, which is only capable of damped oscillations in the deter￾ministic mass-action rate equation limit, but which displays sustained

oscillations in stochastic simulations. We define an observability parameter,

which is essentially just the ratio of the amplitude of the oscillations to the

mean value of the concentration. A maximum in the observability is seen

as the volume is varied, a phenomenon we name system-size observability

resonance by analogy with other types of stochastic resonance. For the

parameters of this study, the maximum in the observability occurs at vol￾umes similar to those of bacterial cells or of eukaryotic organelles.

Abbreviations

CI, competitive inhibition; PSD, power spectral density; SSA, steady-state approximation.

84 FEBS Journal 273 (2006) 84–95 ª 2005 The Authors Journal compilation ª 2005 FEBS