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Parikh vectors
6UDJ_1 6CQU_1 1MGQ_1 Letter Amino acid
8 24 7 D Aspartic acid
19 54 7 G Glycine
5 13 0 W Tryptophan
25 52 10 V Valine
11 51 2 A Alanine
8 39 7 R Arginine
10 16 6 N Asparagine
13 7 3 K Lycine
14 47 3 P Proline
38 30 7 S Serine
2 11 1 H Histidine
16 56 11 L Leucine
6 27 2 F Phenylalanine
22 24 2 T Threonine
5 6 0 C Cysteine
8 20 2 Q Glutamine
7 30 5 E Glutamic acid
6 9 6 I Isoleucine
2 7 1 M Methionine
13 19 1 Y Tyrosine 

6UDJ_1|Chains A, B[auth K], C[auth Q]|10-1074 Fab Heavy Chain|Homo sapiens (9606)
>6CQU_1|Chains A, B|Acetylcholinesterase|Homo sapiens (9606)
>1MGQ_1|Chains A, B, C, D, E, F, G|SM-LIKE PROTEIN|Methanothermobacter thermautotrophicus (145262)
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 \(w=f(c)\)
6UDJ , Knot 104 238 0.79 40 151 226 
QVQLQESGPGLVKPSETLSVTCSVSGDSMNNYYWTWIRQSPGKGLEWIGYISDRESATYNPSLNSRVVISRDTSKNQLSLKLNSVTPADTAVYYCATARRGQRIYGVVSFGEFFYYYSMDVWGKGTTVTVSSASTKGPSVFPLAPSSKSTSGGTAALGCLVKDYFPEPVTVSWNSGALTSGVHTFPAVLQSSGLYSLSSVVTVPSSSLGTQTYICNVNHKPSNTKVDKRVEPKSCDKT
6CQU , Knot 213 542 0.82 40 236 495 
GREDAELLVTVRGGRLRGIRLKTPGGPVSAFLGIPFAEPPMGPRRFLPPEPKQPWSGVVDATTFQSVCYQYVDTLYPGFEGTEMWNPNRELSEDCLYLNVWTPYPRPTSPTPVLVWIYGGGFYSGASSLDVYDGRFLVQAERTVLVSMNYRVGAFGFLALPGSREAPGNVGLLDQRLALQWVQENVAAFGGDPTSVTLFGESAGAASVGMHLLSPPSRGLFHRAVLQSGAPNGPWATVGMGEARRRATQLAHLVGCPPGGTGGNDTELVACLRTRPAQVLVNHEWHVLPQESVFRFSFVPVVDGDFLSDTPEALINAGDFHGLQVLVGVVKDEGSYFLVYGAPGFSKDNESLISRAEFLAGVRVGVPQVSDLAAEAVVLHYTDWLHPEDPARLREALSDVVGDHNVVCPVAQLAGRLAAQGARVYAYVFEHRASTLSWPLWMGVPHGYEIEFIFGIPLDPSRNYTAEEKIFAQRLMRYWANFARTGDPNEPRDPKAPQWPPYTAGAQQYVSLDLRPLEVRRGLRAQACAFWNRFLPKLLSAT
1MGQ , Knot 44 83 0.78 36 70 81 
GSVIDVSSQRVNVQRPLDALGNSLNSPVIIKLKGDREFRGVLKSFDLHMNLVLNDAEELEDGEVTRRLGTVLIRGDNIVYISP

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 \(c\).

\(|P_{f(6UDJ_1)}(2) \setminus P_{f(6CQU_1)}(2)|=46\), \(|P_{f(6CQU_1)}(2) \setminus P_{f(6UDJ_1)}(2)|=131\). 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 1:0101000111110100010100010100100001011000110110111010000010001010001110000000010101001011001100010100100101110110110000101110100101001000110111111000000110111101100011011010100111001100111110001100100110110001100001001000100001000101000000
Pair \(Z_2\) Length of longest common subsequence
6UDJ_1,6CQU_1 177 5
6UDJ_1,1MGQ_1 137 4
6CQU_1,1MGQ_1 196 3

Newick tree

 
[
	6CQU_1:10.29,
	[
		6UDJ_1:68.5,1MGQ_1:68.5
	]:31.79
]

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 \((0.85)(0.8)(\frac{780 }{\log_{20} 780}-\frac{238}{\log_{20}238})=150.\)
Status Protein1 Protein2 d d1/2
Query variables 6UDJ_1 6CQU_1 191 135.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]