Can the conformational response of a corona virus protein with minor difference in substitutional residues be detected by a coarse-grained model? A Mote Carlo simulation on two main (M^pro) protease of SARS (MP1) and COVID-19 (MP2) with minor segmental differences in effective solvent media reveals that the answer is ‘no’ from the overall trends of a global quantity and ‘yes’ from the analysis of specific characteristics of segmental quantities. The coarse-grained model used here involves unique knowledge-based residue-residue interactions and hydropathic residue-solvent interactions with an interaction strength f. The radius of gyration (R_g) of both proteins increases and decreases with f at lower and higher temperatures and converge towards its saturation with strong interactions. The nature of responsiveness of R_g in both MP1 and MP2 is similar due to their overwhelming similarities. Response of the local quantities i.e. the contact profile of the divergent sites in MP1 and MP2 does provide insight into specific differences between two proteins. Distinct structural responses of specific sites of two proteins show that interactions with the underlying medium modulate the segmental conformations of MP1 and MP2 differently despite their overwhelming similarities.