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Parikh vectors
7EUQ_1 3KBC_1 7FYQ_1 Letter Amino acid
22 44 11 G Glycine
13 10 2 H Histidine
5 17 5 M Methionine
3 16 6 F Phenylalanine
22 10 11 D Aspartic acid
1 2 2 C Cysteine
22 12 9 E Glutamic acid
4 14 14 K Lycine
43 50 6 A Alanine
17 9 6 R Arginine
6 12 2 Q Glutamine
11 15 10 S Serine
12 27 12 T Threonine
5 0 2 W Tryptophan
28 46 17 V Valine
6 11 4 N Asparagine
24 54 5 L Leucine
18 18 1 P Proline
15 40 8 I Isoleucine
4 18 2 Y Tyrosine 

7EUQ_1|Chains A, B|N(omega)-hydroxy-L-arginine amidinohydrolase|Streptomyces lavendulae (1914)
>3KBC_1|Chains A, B, C|425aa long hypothetical proton glutamate symport protein|Pyrococcus horikoshii (53953)
>7FYQ_1|Chain A|Fatty acid-binding protein, adipocyte|Homo sapiens (9606)
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 \(w=f(c)\)
7EUQ , Knot 121 281 0.81 40 150 262 
MIDLIVSQGRVADRAAWMIEGAARTARALEERYGLKGHYVGEPAPHADDDWSVALPQARETLVAVREAATESIKGDNLTVLVNNTHSVSLATLPVVAREHPDAVVLYIDGHGDFNTPETTDTGNLHGMVLSGACGLWDSGHGAGLRPEQAVLVGSRDIDEGERELIRKAGVRVIPPGEATAQAVLDAVKDAPVWISIDWDVLEPGSIPADYTVPDGMLPAQIRAVFEAIPAERLIGVELAELNAPADSERAEQAVAVILDMVAPAFDAAAARPLEHHHHHH
3KBC , Knot 172 425 0.81 38 194 388 
MGLYRKYIEYPVLQKILIGLILGAIVGLILGHYGYAHAVHTYVKPFGDLFVRLLCMLVMPIVFASLVVGAASISPARLGRVGVKIVVYYLLTSAFAVTLGIIMARLFNPGAGIHLAVGGQQFQPHQAPPLVHILLDIVPTNPFGALANGQVLPTIFFAIILGIAITYLMNSENEKVRKSAETLLDAINGLAEAMYKIVNGVMQYAPIGVFALIAYVMAEQGVHVVGELAKVTAAVYVGLTLQILLVYFVLLKIYGIDPISFIKHAKDAMLTAFVTRSSSGTLPVTMRVAKEMGISEGIYSFTLPLGATINMDGTALYQGVATFFIANALGSHLTVGQQLTIVLTAVLASIGTAGVPGAGAIMLCMVLHSVGLPLTDPNVAAAYAMILGIDAILDMGRTMVNVTGDLTGTAIVAKTEGELEKGVIA
7FYQ , Knot 69 135 0.83 40 104 129 
GSHMCDAFVGTWKLVSSENFDDYMKEVGVGFATRKVAGMAKPNMIISVNGDVITIKSESTFKNTEISFILGQEFDEVTADDRKVKSTITLDGGVLVHVQKWDGKSTTIKRKREDDKLVVECVMKGVTSTRVYERA

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 \(c\).

\(|P_{f(7EUQ_1)}(2) \setminus P_{f(3KBC_1)}(2)|=58\), \(|P_{f(3KBC_1)}(2) \setminus P_{f(7EUQ_1)}(2)|=102\). 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 1:11011100101100111110111001011000011010011011101000101111010001111001100010100101110000010110111110001011110101010100100000101011110110111001011110100111110001001000110011101111101010111011001111101010110110111000110111110101110111100111101101011100001001111110111111011110110000000
Pair \(Z_2\) Length of longest common subsequence
7EUQ_1,3KBC_1 160 4
7EUQ_1,7FYQ_1 162 3
3KBC_1,7FYQ_1 176 4

Newick tree

 
[
	7FYQ_1:86.04,
	[
		7EUQ_1:80,3KBC_1:80
	]:6.04
]

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 \((0.85)(0.8)(\frac{706 }{\log_{20} 706}-\frac{281}{\log_{20}281})=117.\)
Status Protein1 Protein2 d d1/2
Query variables 7EUQ_1 3KBC_1 146 118
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]