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Parikh vectors
7OLE_1 9JDG_1 4HXA_1 Letter Amino acid
12 34 11 Y Tyrosine
13 17 10 N Asparagine
44 26 12 E Glutamic acid
36 53 15 G Glycine
10 6 3 H Histidine
40 44 9 I Isoleucine
8 43 7 F Phenylalanine
29 32 20 T Threonine
21 19 9 D Aspartic acid
6 19 5 C Cysteine
18 13 7 Q Glutamine
41 27 12 K Lycine
17 35 10 P Proline
24 42 36 S Serine
33 34 10 A Alanine
18 19 5 R Arginine
42 70 11 L Leucine
13 18 5 M Methionine
0 20 4 W Tryptophan
31 49 12 V Valine 

7OLE_1|Chains A, C, E|RuvB-like 1|Homo sapiens (9606)
>9JDG_1|Chain A|Sodium- and chloride-dependent taurine transporter|Homo sapiens (9606)
>4HXA_1|Chain A[auth L]|13D9 FAB LIGHT CHAIN|MUS MUSCULUS (10090)
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 \(w=f(c)\)
7OLE , Knot 185 456 0.82 38 231 434 
MKIEEVKSTTKTQRIASHSHVKGLGLDESGLAKQAASGLVGQENAREACGVIVELIKSKKMAGRAVLLAGPPGTGKTALALAIAQELGSKVPFCPMVGSEVYSTEIKKTEVLMENFRRAIGLRIKETKEVYEGEVTELTPCETENPMGGYGKTISHVIIGLKTAKGTKQLKLDPSIFESLQKERVEAGDVIYIEANSGAVKRQGRCDTYATEFDLEAEEYVPLPKGDVHKKKEIIQDVTLHDLDVANARPQGGQDILSMMGQLMKPKKTEITDKLRGEINKVVNKYIDQGIAELVPGVLFVDEVHMLDIECFTYLHRALESSIAPIVIFASNRGNCVIRGTEDITSPHGIPLDLLDRVMIIRTMLYTPQEMKQIIKIRAQTEGINISEEALNHLGEIGTKTTLRYSVQLLTPANLLAKINGKDSIEKEHVEEISELFYDAKSSAKILADQQDKYMK
9JDG , Knot 245 620 0.84 40 280 577 
MATKEKLQCLKDFHKDILKPSPGKSPGTRPEDEAEGKPPQREKWSSKIDFVLSVAGGFVGLGNVWRFPYLCYKNGGGAFLIPYFIFLFGSGLPVFFLEIIIGQYTSEGGITCWEKICPLFSGIGYASVVIVSLLNVYYIVILAWATYYLFQSFQKELPWAHCNHSWNTPHCMEDTMRKNKSVWITISSTNFTSPVIEFWERNVLSLSPGIDHPGSLKWDLALCLLLVWLVCFFCIWKGVRSTGKVVYFTATFPFAMLLVLLVRGLTLPGAGAGIKFYLYPDITRLEDPQVWIDAGTQIFFSYAICLGAMTSLGSYNKYKYNSYRDCMLLGCLNSGTSFVSGFAIFSILGFMAQEQGVDIADVAESGPGLAFIAYPKAVTMMPLPTFWSILFFIMLLLLGLDSQFVEVEGQITSLVDLYPSFLRKGYRREIFIAFVCSISYLLGLTMVTEGGMYVFQLFDYYAASGVCLLWVAFFECFVIAWIYGGDNLYDGIEDMIGYRPGPWMKYSWAVITPVLCVGCFIFSLVKYVPLTYNKTYVYPNWAIGLGWSLALSSMLCVPLVIVIRLCQTEGPFLVRVKYLLTPREPNRWAVEREGATPYNSRTVMNGALVKPTHIIVETMM
4HXA , Knot 98 213 0.82 40 150 204 
EEVLTQSPAIMSASPGEKVTMTCSVSSSVNYMHWYQQKSSTSPKLWIYDTSNLASGVPGRFSGSGSGISYSLTISSMEAEDVATYYCFQGSGYPLTFGGGTKLEIKRADAAPTVSIFPPSSEQLTSGGASVVCFLNNFYPKDINVKWKIDGSERQNGVLNSWTDQDSKDSTYSMSSTLTLTKDEYERHNSYTCEATHKTSTSPIVKSFNRNEC

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 \(c\).

\(|P_{f(7OLE_1)}(2) \setminus P_{f(9JDG_1)}(2)|=60\), \(|P_{f(9JDG_1)}(2) \setminus P_{f(7OLE_1)}(2)|=109\). 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 1:101001000000001100001011110001110011011110001001011110110000111011111111101001111111001100111011110010000100001110010011110100000100101001010000011110100100111110010100010101011001000010110110101001110001000001001010100011110101000001100101001011010101100110111011010000100010101001100010011101111111100101101001001001100011111111000100110100010010111101100111100110010010011010100011010001100110110000100010110110111010100010000100100110010001011100000010
Pair \(Z_2\) Length of longest common subsequence
7OLE_1,9JDG_1 169 4
7OLE_1,4HXA_1 169 3
9JDG_1,4HXA_1 200 4

Newick tree

 
[
	4HXA_1:95.11,
	[
		7OLE_1:84.5,9JDG_1:84.5
	]:10.61
]

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 \((0.85)(0.8)(\frac{1076 }{\log_{20} 1076}-\frac{456}{\log_{20}456})=162.\)
Status Protein1 Protein2 d d1/2
Query variables 7OLE_1 9JDG_1 212 181.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]