protein K-mer connection

Question

[kartik.aier.gta]

Hello everyone, I came across a problem in my work and would be grateful if anyone can help me out. The problem is stated below : Considering two protein sequence, S1 and S2 of length m and n respectively, we have bags M1 and M2, which contain (m-k+1) from S1, and (n-k+1) k-mers from S2, respectively. I would like to make the connection between k-mer in M1 and k-mer in M2 based on Blosum62 similarity. Is there any mathematical function or procedure available for this? Example:

let k=4
S1 = GCHYY, m=5  then  M1 = {GCHY,CHYY} contain [5-4+1=2] 4-mer
S2 = ACRTYV, n=6  then M2={ACRT,CRTY,RTYV} contain [6-4+1=3] 4-mer

Thank you in advance.