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Parikh vectors
6TYY_1 7XHG_1 3DTB_1 Letter Amino acid
3 6 19 M Methionine
5 8 28 F Phenylalanine
1 0 16 W Tryptophan
10 8 48 A Alanine
8 8 18 Q Glutamine
14 11 51 L Leucine
5 7 42 K Lycine
9 8 29 R Arginine
5 11 27 N Asparagine
10 10 56 G Glycine
10 5 23 T Threonine
23 15 33 V Valine
11 5 52 E Glutamic acid
3 7 13 H Histidine
4 3 39 I Isoleucine
11 7 33 S Serine
4 7 26 D Aspartic acid
2 1 13 C Cysteine
6 5 44 P Proline
2 7 14 Y Tyrosine 

6TYY_1|Chain A|Protein hedgehog|Drosophila melanogaster (7227)
>7XHG_1|Chains A, B, C, D|Ras GTPase-activating protein-binding protein 1|Homo sapiens (9606)
>3DTB_1|Chains A, B|Phosphoenolpyruvate carboxykinase, cytosolic [GTP]|Rattus norvegicus (10116)
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 \(w=f(c)\)
6TYY , Knot 72 146 0.82 40 117 142 
CFTPESTALLESGVRKPLGELSIGDRVLSMTANGQAVYSEVILFMHRNLEQMQNFVQLHTDGGAVLTVTPAHLVSVWQPESQKLTFVFADRIEEKNQVLVRDVETGELRPQRVVKVGSVRSKGVVAPLTREGTIVVNSVAASCYAV
7XHG , Knot 69 139 0.81 38 114 135 
MVMEKPSPLLVGREFVRQYYTLLNQAPDMLHRFYGKNSSYVHGGLDSNGKPADAVYGQKEIHRKVMSQNFTNCHTKIRHVDAHATLNDGVVVQVMGLLSNNNQALRRFMQTFVLAPEGSVANKFYVHNDIFRYQDEVFG
3DTB , Knot 255 624 0.87 40 281 579 
GSMPPQLHNGLDFSAKVIQGSLDSLPQEVRKFVEGNAQLCQPEYIHICDGSEEEYGRLLAHMQEEGVIRKLKKYDNCWLALTDPRDVARIESKTVIITQEQRDTVPIPKSGQSQLGRWMSEEDFEKAFNARFPGCMKGRTMYVIPFSMGPLGSPLAKIGIELTDSPYVVASMRIMTRMGTSVLEALGDGEFIKCLHSVGCPLPLKKPLVNNWACNPELTLIAHLPDRREIISFGSGYGGNSLLGKKCFALRIASRLAKEEGWLAEHMLILGITNPEGKKKYLAAAFPSACGKTNLAMMNPTLPGWKVECVGDDIAWMKFDAQGNLRAINPENGFFGVAPGTSVKTNPNAIKTIQKNTIFTNVAETSDGGVYWEGIDEPLAPGVTITSWKNKEWRPQDEEPCAHPNSRFCTPASQCPIIDPAWESPEGVPIEGIIFGGRRPAGVPLVYEALSWQHGVFVGAAMRSEATAAAEHKGKVIMHDPFAMRPFFGYNFGKYLAHWLSMAHRPAAKLPKIFHVNWFRKDKNGKFLWPGFGENSRVLEWMFGRIEGEDSAKLTPIGYVPKEDALNLKGLGDVNVEELFGISKEFWEKEVEEIDKYLEDQVNADLPYEIERELRALKQRISQM

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 \(c\).

\(|P_{f(6TYY_1)}(2) \setminus P_{f(7XHG_1)}(2)|=65\), \(|P_{f(7XHG_1)}(2) \setminus P_{f(6TYY_1)}(2)|=62\). 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 1:01010001110011001110101100110101010110001111100010010011010001111101011011011010000101111001000001110010010101001101101000111111000101110011100011
Pair \(Z_2\) Length of longest common subsequence
6TYY_1,7XHG_1 127 3
6TYY_1,3DTB_1 204 3
7XHG_1,3DTB_1 229 3

Newick tree

 
[
	3DTB_1:11.71,
	[
		6TYY_1:63.5,7XHG_1:63.5
	]:56.21
]

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 \((0.85)(0.8)(\frac{285 }{\log_{20} 285}-\frac{139}{\log_{20}139})=45.3\)
Status Protein1 Protein2 d d1/2
Query variables 6TYY_1 7XHG_1 56 54
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]