Modeling of Evolutionary Progress of Nonstructure Protein 1 Family from Influenza A Virus

The evolutionary progress is mathematically how an indicator changes over time such as the brain weight changes over time. Thus, this can present in x-y coordinates, on where we can use mathematical and statistical methods to build the time-dependent relationships. Of mathematical methods, the mass-balance styled differential equation is most useful because we can use it to predict an evolutionary indicator in the future. We are particularly interested in the evolution of proteins from influenza A virus not only because influenza A virus causes influenza in humans and animals but also the proteins from influenza A virus have the longest records among viruses. Of 10 proteins from influenza A virus, the nonstructural protein 1 (NS1) gets much less attention than others. However, this ignorance does not minimize its importance because more and more functions have been found in NS1.This requires converting a protein into a numeric scale because the y-axis is better to set in a quantitative scale rather than a qualitative scale. Of 540-plus methods to convert amino acids into digital numbers, we developed the amino-acid pair predictability to do the job. In this communication, 2729 NS1 proteins of influenza A viruses filtered from 7826 full-length NS1 proteins of influenza A virus to eliminate identical sequences were employed. (1) We converted them into numeric format using the amino-acid pair predictability. (2) We presented these proteins in the y-axis according to their sampling time over the x-axis. (3) We determined upward and downward half-life as initial estimates for the analytical solution of mass-balance styled differential equations. (4) We used the analytical solution to fit the evolutionary progress of NS1 protein family. (5) We tested the goodness-of-fit to verify the fittings. The results demonstrated the positive possibility of such studies, and paved the pathway to simulate and predict the evolutionary progress of proteins in the future.