中国物理B ›› 2009, Vol. 18 ›› Issue (8): 3577-3584.doi: 10.1088/1674-1056/18/8/074

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Kinetics of catalytically activated duplication in aggregation growth

林振权1, 王海锋2, 高艳2, 胥超2   

  1. (1)Department of Physics, Wenzhou University, Wenzhou \rm 325027, China; (2)Key Laboratory of Ecophysics and Department of Physics, Teachers College, Shihezi University, Shihezi 832003, China
  • 收稿日期:2009-01-07 修回日期:2009-02-10 出版日期:2009-08-20 发布日期:2009-08-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10275048, 10305009 and 10875086) and by the Zhejiang Provincial Natural Science Foundation of China (Grant No 102067).

Kinetics of catalytically activated duplication in aggregation growth

Wang Hai-Feng(王海锋)a)†, Lin Zhen-Quan(林振权)b), Gao Yan(高艳)a), and Xu Chao(胥超)a)   

  1. a Key Laboratory of Ecophysics and Department of Physics, Teachers College, Shihezi University, Shihezi 832003, China; b Department of Physics, Wenzhou University, Wenzhou 325027, China
  • Received:2009-01-07 Revised:2009-02-10 Online:2009-08-20 Published:2009-08-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10275048, 10305009 and 10875086) and by the Zhejiang Provincial Natural Science Foundation of China (Grant No 102067).

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摘要： 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.

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.

Key words: aggregation, catalytically activated reaction, rate equation, kinetic behavior