Kinetics of catalytically activated duplication in aggregation growth |
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| Authors: | Wang Hai-Feng Lin Zhen-Quan Gao Yan and Xu Chao |
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| Affiliation: | Key Laboratory of Ecophysics and Department of Physics, Teachers College, Shihezi University, Shihezi 832003, China; Department of Physics, Wenzhou University, Wenzhou 325027, China |
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| Abstract: | We propose a catalytically activated duplication model to mimic the
coagulation and duplication of the DNA polymer system under the
catalysis of the primer RNA. In the model, two aggregates of the
same species can coagulate themselves and a DNA aggregate of any
size can yield a new monomer or double itself with the help of RNA
aggregates. By employing the mean-field rate equation approach we
analytically investigate the evolution behaviour of the system. For
the system with catalysis-driven monomer duplications, the aggregate
size distribution of DNA polymers ak(t) always follows a power
law in size in the long-time limit, and it decreases with time or
approaches a time-independent steady-state form in the case of the
duplication rate independent of the size of the mother aggregates,
while it increases with time increasing in the case of the
duplication rate proportional to the size of the mother aggregates.
For the system with complete catalysis-driven duplications, the
aggregate size distribution ak(t) approaches a generalized or
modified scaling form. |
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| Keywords: | aggregation catalytically
activated reaction rate equation kinetic behavior |
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