• Chemistry at the Nanoscale: When Every Reaction is a Discrete Event

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    • Keywords


      Chemical kinetics, stochastic chemical kinetics, Gillespie’s stochastic simulation algorithm, synthetic gene oscillators.

    • Abstract


      Traditionally the kinetics of a chemical reaction has been studiedas a set of coupled ordinary differential equations. Thelaw of mass action, a tried and tested principle for reactionsinvolvingmacroscopic quantities of reactants, gives rise to deterministicequations in which the variables are species concentrations.In recent years, though, as smaller and smallersystems – such as an individual biological cell, say – can bestudied quantitatively, the importance of molecular discretenessin chemical reactions has increasingly been realized. Thisis particularly true when the system is far from the ‘thermodynamiclimit’ when the numbers of all reacting molecularspecies involved are several orders of magnitude smaller thanAvogadro’s number. In such situations, each reaction has tobe treated as a probabilistic ‘event’ that occurs by chancewhen the appropriate reactants collide. Explicitly accountingfor such processes has led to the development of sophisticatedstatistical methods for simulation of chemical reactions,particularly those occurring at the cellular and sub-cellularlevel. In this article, we describe this approach, the so-calledstochastic simulation algorithm, and discuss applications tostudy the dynamics of model regulatory networks.

    • Author Affiliations


      Ashwin B R Kumar1 Ram Ramaswamy2

      1. Department of Biochemistry and Biophysics, University of Rochester, Medical Center, Rochester, NY 14642, USA
      2. School of Physical Sciences, Jawaharlal Nehru University, New Delhi 11 0 067, India.
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