Distributions of activation energy barriers that produce stretched exponential probability distributions for the time spent in each state of the two state reaction AB
✍ Scribed by Larry S. Liebovitch; Tibor I. Tóth
- Book ID
- 104272020
- Publisher
- Springer
- Year
- 1991
- Tongue
- English
- Weight
- 610 KB
- Volume
- 53
- Category
- Article
- ISSN
- 1522-9602
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✦ Synopsis
Many biochemical reactions consist of the spontaneous fluctuation between two states: A~,~-B. For example these two states could be a ligand bound to an enzyme and the ligand and the enzyme separated from each other. A typical case would be the unbinding of CO from myoglobin (Mb), namely, MbCO,~-Mb + CO. Another example is the fluctuation in the ion channel protein in the cell membrane between conformations that are closed to the passage of ions and those that are open to the passage of ions, namely, elosed~-open. Such chemical reactions can be described as two energy levels corresponding to the two states, separated by a distribution of activation energy barriers. Since a kinetic rate can be associated with each energy barrier, this is also equivalent to a distribution of kinetic rate constants. We derive the distribution of the kinetic rates that produces the stretched exponential probability distribution, exp(-at b) where 0 < b-%< 1, which has been observed for such reactions. We also derive the form of the cumulative probability distribution when the pathways connecting the states have minimum or maximum rate constants.
Introduction. Many biochemical reactions consist of the spontaneous fluctuations between two states of a system. For example, a ligand such as CO can be bound or unbound to an enzyme such as myoglobin (Mb) in the reaction MbCO~.~-Mb + CO. Another example is the fluctuation of the conformation of the ion channel protein that spans the lipid cell membrane. The channel can have a closed conformation that prevents the passage of ions, or an open conformation that permits such ion movement. These fluctuations are described by the reaction closed~--open. The times spent in the closed and open states are characterized by the