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| 1. | Kumar, A B R; Ramaswamy, R Chemistry at the Nanoscale: When Every Reaction is a Discrete Event Journal Article Resonance, 23 , pp. 23-40, 2018, ISSN: 0973-712X. Abstract | Links | BibTeX | Tags: Chemical Kinetics, Gillespie’s Algorithm, Stochasticity, Synthetic Gene Oscillators @article{Kumar2018, title = {Chemistry at the Nanoscale: When Every Reaction is a Discrete Event}, author = {A B R Kumar and R Ramaswamy}, url = {https://ramramaswamy.org/papers/169.pdf}, doi = {10.1007/s12045-018-0592-4}, issn = {0973-712X}, year = {2018}, date = {2018-01-01}, journal = {Resonance}, volume = {23}, pages = {23-40}, abstract = {Traditionally the kinetics of a chemical reaction has been stud- ied as a set of coupled ordinary differential equations. The law of mass action, a tried and tested principle for reactions involving macroscopic quantities of reactants, gives rise to de- terministic equations in which the variables are species con- centrations. In recent years, though, as smaller and smaller systems ‚Äì such as an individual biological cell, say ‚Äì can be studied quantitatively, the importance of molecular discrete- ness in chemical reactions has increasingly been realized. This is particularly true when the system is far from the ‚Äòthermo- dynamic limit’ when the numbers of all reacting molecular species involved are several orders of magnitude smaller than Avogadro’s number. In such situations, each reaction has to be treated as a probabilistic ‚Äòevent’ that occurs by chance when the appropriate reactants collide. Explicitly accounting for such processes has led to the development of sophisticated statistical methods for simulation of chemical reactions, particularly those occurring at the cellular and sub-cellular level. In this article, we describe this approach, the so-called stochastic simulation algorithm, and discuss applications to study the dynamics of model regulatory networks.}, keywords = {Chemical Kinetics, Gillespie’s Algorithm, Stochasticity, Synthetic Gene Oscillators}, pubstate = {published}, tppubtype = {article} } Traditionally the kinetics of a chemical reaction has been stud- ied as a set of coupled ordinary differential equations. The law of mass action, a tried and tested principle for reactions involving macroscopic quantities of reactants, gives rise to de- terministic equations in which the variables are species con- centrations. In recent years, though, as smaller and smaller systems ‚Äì such as an individual biological cell, say ‚Äì can be studied quantitatively, the importance of molecular discrete- ness in chemical reactions has increasingly been realized. This is particularly true when the system is far from the ‚Äòthermo- dynamic limit’ when the numbers of all reacting molecular species involved are several orders of magnitude smaller than Avogadro’s number. In such situations, each reaction has to be treated as a probabilistic ‚Äòevent’ that occurs by chance when the appropriate reactants collide. Explicitly accounting for such processes has led to the development of sophisticated statistical methods for simulation of chemical reactions, particularly those occurring at the cellular and sub-cellular level. In this article, we describe this approach, the so-called stochastic simulation algorithm, and discuss applications to study the dynamics of model regulatory networks. |