A trade-off relationship between energetic cost and entropic cost for in vitro evolution

In this paper, we consider two complementary cost functions for the landscape exploring processes to obtain the global optimum sequence through in vitro evolution protocol: one is the entropic cost Cetp, which is based on the deviation from the uniformity of a mutant distribution in sequence space, and the other is the energetic cost Ceng, which is based on the total number of sequences to be generated and evaluated. Based on a prior knowledge about the structure of a given fitness landscapes, the conductor of the experiment can think up the efficient search algorithm (ESA), which requires the minimum number of points (=sequences) to be searched up to the global optimum. For five typical fitness landscapes, we considered their respective (putative) ESA, Cetp* and Ceng* based on the ESA. As a result, we found a trade-off relationship between Cetp* and Ceng* for every case, that is, Ceng*+Cetp* is approximately equal to the logarithm of the volume of the sequence space. Cetp* and Ceng* are interpreted in terms of the information-theoretic concepts.