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Some Mathematical Refinements Concerning Error Minimization in the Genetic Code
September/October 2011 (vol. 8 no. 5)
pp. 1358-1372
Harry Buhrman, Centrum voor Wiskunde en Informatica (CWI), Amsterdam
Peter T.S. van der Gulik, Centrum voor Wiskunde en Informatica (CWI), Amsterdam
Steven M. Kelk, Centrum voor Wiskunde en Informatica (CWI), Amsterdam
Wouter M. Koolen, Centrum voor Wiskunde en Informatica (CWI), Amsterdam
Leen Stougie, Centrum voor Wiskunde en Informatica (CWI) and Vrije Universiteit, Amsterdam
The genetic code is known to have a high level of error robustness and has been shown to be very error robust compared to randomly selected codes, but to be significantly less error robust than a certain code found by a heuristic algorithm. We formulate this optimization problem as a Quadratic Assignment Problem and use this to formally verify that the code found by the heuristic algorithm is the global optimum. We also argue that it is strongly misleading to compare the genetic code only with codes sampled from the fixed block model, because the real code space is orders of magnitude larger. We thus enlarge the space from which random codes can be sampled from approximately 2.433 \times 10^{18} codes to approximately 5.908 \times 10^{45} codes. We do this by leaving the fixed block model, and using the wobble rules to formulate the characteristics acceptable for a genetic code. By relaxing more constraints, three larger spaces are also constructed. Using a modified error function, the genetic code is found to be more error robust compared to a background of randomly generated codes with increasing space size. We point out that these results do not necessarily imply that the code was optimized during evolution for error minimization, but that other mechanisms could be the reason for this error robustness.

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Index Terms:
Genetic code, error robustness, origin of life.
Citation:
Harry Buhrman, Peter T.S. van der Gulik, Steven M. Kelk, Wouter M. Koolen, Leen Stougie, "Some Mathematical Refinements Concerning Error Minimization in the Genetic Code," IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol. 8, no. 5, pp. 1358-1372, Sept.-Oct. 2011, doi:10.1109/TCBB.2011.40
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