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Parikh vectors
5MHS_1 3QHE_1 5BJW_1 Letter Amino acid
7 5 9 Y Tyrosine
13 19 25 V Valine
9 15 23 D Aspartic acid
12 24 19 S Serine
19 17 11 T Threonine
7 6 1 W Tryptophan
8 18 9 R Arginine
15 17 18 G Glycine
7 15 31 I Isoleucine
3 18 37 K Lycine
7 3 11 F Phenylalanine
7 6 12 P Proline
8 34 31 A Alanine
11 14 8 Q Glutamine
5 23 28 E Glutamic acid
6 14 7 M Methionine
11 20 20 N Asparagine
1 12 8 C Cysteine
2 12 13 H Histidine
14 45 45 L Leucine 

5MHS_1|Chains A, B, C|Outer capsid protein sigma-1|Reovirus type 1 (strain Lang) (10884)
>3QHE_1|Chains A, C|Adenomatous polyposis coli protein|Homo sapiens (9606)
>5BJW_1|Chains A, B|WlaL protein|Campylobacter jejuni (197)
Protein code \(c\) LZ-complexity \(\mathrm{LZ}(w)\) Length \(n=|w|\) \(\frac{\mathrm{LZ}(w)}{n /\log_{20} n}\) \(p_w(1)\) \(p_w(2)\) \(p_w(3)\) Sequence \(w=f(c)\)
5MHS , Knot 81 172 0.80 40 130 170 
GVLNQGVTSLPTYRYPLELDTANNRVQVADRFGMRTGTWTGQLQYQHPQLSWRANVTLNLMKVDDWLVLSFSQMTTNSIMADGKFVINFVSGLSSGWQTGDTEPSSTIDPLSTTFAAVQFLNNGQRIDAFRIMGVSEWTDGELEIKNYGGTYTGHTQVYWAPWTIMYPCNVR
3QHE , Knot 142 337 0.81 40 200 314 
DDKRGRREIRVLHLLEQIRAYCETCWEWQEAHEPGMDQDKNPMPAPVEHQICPAVCVLMKLSFDEEHRHAMNELGGLQAIAELLQVDCEMYGLTNDHYSITLRRYAGMALTNLTFGDVANKATLCSMKGCMRALVAQLKSESEDLQQVIASVLRNLSWRADVNSKKTLREVGSVKALMECALEVKKESTLKSVLSALWNLSAHCTENKADICAVDGALAFLVGTLTYRSQTNTLAIIESGGGILRNVSSLIATNEDHRQILRENNCLQTLLQHLKSHSLTIVSNACGTLWNLSARNPKDQEALWDMGAVSMLKNLIHSKHKMIAMGSAAALRNLMAN
5BJW , Knot 152 366 0.81 40 193 349 
ARDISIEDLLARKPKDLDDSAVAAFLKDKVVLVSGAGGTIGSELCKQCIKFGAKHLIMVDHSEYNLYKINDDLNLYKEKITPILLSILDKQSLDEVLKTYKPELILHAAAYKHVPLCEQNPHSAVINNILGTKILCDSAKENKVAKFVMISSDKAVRPTNIMGCTKRVCELYTLSMSDENFEVACVRFGNVLGSSGSVIPKFKAQIANNEPLTLTHPDIVRYFMLVAEAVQLVLQAGAIAKGGELFVLDMGKPVKIIDLAKKMLLLSNRNDLEIKITGLRKGEKLYEELLIDENDAKTQYESIFVAKNEKVDLDWLNKEIENLQICEDISEALLKIVPEFKHNKEGIAAGFNRIPAAALEHHHHHH

Let \(P_w(n)\) be the set of distinct subwords (intervals) in a word \(w\). Let \(p_w(n)\) be the cardinality of \(P_w(n)\). Let \(f(c)\) be the sequence in FASTA with 4-symbol Protein Data Bank code \(c\).

\(|P_{f(5MHS_1)}(2) \setminus P_{f(3QHE_1)}(2)|=65\), \(|P_{f(3QHE_1)}(2) \setminus P_{f(5MHS_1)}(2)|=135\). Let \( Z_k(x,y)=|P_x(k)\setminus P_y(k)|+|P_y(k)\setminus P_x(k)| \) be a LZ76 style (set of subwords) Jaccard distance numerator for \(P(k)\).Hydrophobic-polar version of Sequence 1:1110011001100001101001000101100111001010101000010101010101011010011110100100001110101110110110011001000100010110001111011001001011011110010010101000110001000101111011010010
Pair \(Z_2\) Length of longest common subsequence
5MHS_1,3QHE_1 200 5
5MHS_1,5BJW_1 191 4
3QHE_1,5BJW_1 163 4

Newick tree

 
[
	5MHS_1:10.62,
	[
		5BJW_1:81.5,3QHE_1:81.5
	]:21.12
]

Let d be the Otu--Sayood distance d.
Let d1 be the Otu--Sayood distance d1. (This makes the 4TYN sequence AAAAAA a close match...)
A roughly speaking expected distance is \((0.85)(0.8)(\frac{509 }{\log_{20} 509}-\frac{172}{\log_{20}172})=98.3\)
Status Protein1 Protein2 d d1/2
Query variables 5MHS_1 3QHE_1 122 93
Was not able to put for d
Was not able to put for d1

In notation analogous to [Theorem 16, Kjos-Hanssen, Niraula and Yoon (2022)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]