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Parikh vectors
7LCM_1 3OFS_1 5WVI_1 Letter Amino acid
1 8 3 W Tryptophan
9 10 18 G Glycine
7 12 8 P Proline
6 18 21 T Threonine
7 14 16 R Arginine
10 21 24 D Aspartic acid
2 12 5 C Cysteine
4 13 16 Q Glutamine
5 18 38 K Lycine
7 4 6 M Methionine
5 13 14 F Phenylalanine
6 20 33 S Serine
10 10 32 A Alanine
4 8 23 N Asparagine
7 16 42 E Glutamic acid
2 7 4 H Histidine
1 5 26 Y Tyrosine
11 17 28 V Valine
7 14 22 I Isoleucine
21 17 50 L Leucine 

7LCM_1|Chain A|Regulator of RpoS|Escherichia coli (562)
>3OFS_1|Chains A, B, C, D, E, F|ADP-ribosyl cyclase 1|Homo sapiens (9606)
>5WVI_14|Chain N[auth R]|26S proteasome regulatory subunit RPN7|Saccharomyces cerevisiae (strain ATCC 204508 / S288c) (559292)
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 \(w=f(c)\)
7LCM , Knot 66 132 0.81 40 105 128 
GPHMTQPLVGKQILIVEDEQVFRSLLDSWFSSLGATTVLAADGVDALELLGGFTPDLMICDIAMPRMNGLKLLEHIRNRGDQTPVLVISATENMADIAKALRLGVEDVLLKPVKDLNRLREMVFACLYPSMF
3OFS , Knot 119 257 0.85 40 177 250 
EFWRQTWSGPGTTKRFPETVLARCVKYTEIHPEMRHVDCQSVWDAFKGAFISKHPCDITEEDYQPLMKLGTQTVPCNKILLWSRIKDLAHQFTQVQRDMFTLADTLLGYLADDLTWCGEFDTSKINYQSCPDWRKDCSNNPVSVFWKTVSRRFAEAACDVVHVMLDGSRSKIFDKDSTFGSVEVHNLQPEKVQTLEAWVIHGGREDSRDLCQDPTIKELESIISKRNIQFSCKNIYRPDKFLQCVKNPEDSSCTSEI
5WVI , Knot 172 429 0.81 40 208 397 
MVDVEEKSQEVEYVDPTVNRVPNYEVSEKAFLLTQSKVSIEQRKEAAEFVLAKIKEEEMAPYYKYLCEEYLVNNGQSDLEHDEKSDSLNEWIKFDQELYNELCKKNESKIKELNEKIQKLEEDDEGELEQAQAWINLGEYYAQIGDKDNAEKTLGKSLSKAISTGAKIDVMLTIARLGFFYNDQLYVKEKLEAVNSMIEKGGDWERRNRYKTYYGIHCLAVRNFKEAAKLLVDSLATFTSIELTSYESIATYASVTGLFTLERTDLKSKVIDSPELLSLISTTAALQSISSLTISLYASDYASYFPYLLETYANVLIPCKYLNRHADFFVREMRRKVYAQLLESYKTLSLKSMASAFGVSVAFLDNDLGKFIPNKQLNCVIDRVNGIVETNRPDNKNAQYHLLVKQGDGLLTKLQKYGAAVRLTGSDRV

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 \(c\).

\(|P_{f(7LCM_1)}(2) \setminus P_{f(3OFS_1)}(2)|=55\), \(|P_{f(3OFS_1)}(2) \setminus P_{f(7LCM_1)}(2)|=127\). 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 1:110100111100111100001100110011001110011110110110111110101110011110101101100100010001111101000110110110111001110110010010011110101011
Pair \(Z_2\) Length of longest common subsequence
7LCM_1,3OFS_1 182 4
7LCM_1,5WVI_1 185 3
3OFS_1,5WVI_1 181 4

Newick tree

 
[
	7LCM_1:92.16,
	[
		3OFS_1:90.5,5WVI_1:90.5
	]:1.66
]

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 \((0.85)(0.8)(\frac{389 }{\log_{20} 389}-\frac{132}{\log_{20}132})=77.8\)
Status Protein1 Protein2 d d1/2
Query variables 7LCM_1 3OFS_1 101 75
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]