| Chapter title |
Mathematical Models of Quasi-Species Theory and Exact Results for the Dynamics
|
|---|---|
| Chapter number | 471 |
| Book title |
Quasispecies: From Theory to Experimental Systems
|
| Published in |
Current topics in microbiology and immunology, January 2015
|
| DOI | 10.1007/82_2015_471 |
| Pubmed ID | |
| Book ISBNs |
978-3-31-923897-5, 978-3-31-923898-2
|
| Authors |
David B. Saakian, Chin-Kun Hu, Saakian, David B., Hu, Chin-Kun |
| Abstract |
We formulate the Crow-Kimura, discrete-time Eigen model, and continuous-time Eigen model. These models are interrelated and we established an exact mapping between them. We consider the evolutionary dynamics for the single-peak fitness and symmetric smooth fitness. We applied the quantum mechanical methods to find the exact dynamics of the evolution model with a single-peak fitness. For the smooth symmetric fitness landscape, we map exactly the evolution equations into Hamilton-Jacobi equation (HJE). We apply the method to the Crow-Kimura (parallel) and Eigen models. We get simple formulas to calculate the dynamics of the maximum of distribution and the variance. We review the existing mathematical tools of quasi-species theory. |
Mendeley readers
Geographical breakdown
| Country | Count | As % |
|---|---|---|
| Unknown | 5 | 100% |
Demographic breakdown
| Readers by professional status | Count | As % |
|---|---|---|
| Professor | 2 | 40% |
| Researcher | 2 | 40% |
| Student > Doctoral Student | 1 | 20% |
| Readers by discipline | Count | As % |
|---|---|---|
| Biochemistry, Genetics and Molecular Biology | 3 | 60% |
| Medicine and Dentistry | 1 | 20% |
| Unknown | 1 | 20% |