Exact correspondence between walk in nucleotide and protein sequence spaces

In the course of evolution, genes traverse the nucleotide sequence space, which translates to a trajectory of changes in the protein sequence in protein sequence space. The correspondence between regions of the nucleotide and protein sequence spaces is understood in general but not in detail. One of the unexplored questions is how many sequences a protein can reach with a certain number of nucleotide substitutions in its gene sequence. Here I propose an algorithm to calculate the volume of protein sequence space accessible to a given protein sequence as a function of the number of nucleotide substitutions made in the protein-coding sequence. The algorithm utilizes the power of the dynamic programming approach, and makes all calculations within a couple of seconds on a desktop computer. I apply the algorithm to green fluorescence protein, and get the number of sequences four times higher than estimated before. However, taking into account the astronomically huge size of the protein sequence space, the previous estimate can be considered as acceptable as an order of magnitude estimation. The proposed algorithm has practical applications in the study of evolutionary trajectories in sequence space.