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Parikh vectors
7QAV_1 7AFZ_1 5LBS_1 Letter Amino acid
15 25 51 G Glycine
12 5 13 F Phenylalanine
5 2 12 C Cysteine
18 8 28 E Glutamic acid
16 19 19 P Proline
30 10 33 S Serine
27 16 16 R Arginine
15 10 13 Q Glutamine
40 27 31 L Leucine
2 5 9 W Tryptophan
17 6 13 N Asparagine
17 20 27 D Aspartic acid
8 10 18 H Histidine
21 9 16 I Isoleucine
9 8 27 K Lycine
5 6 14 M Methionine
12 19 35 T Threonine
11 8 10 Y Tyrosine
29 43 29 A Alanine
23 15 33 V Valine 

7QAV_1|Chains A, B|Multiple virulence factor regulator MvfR|Pseudomonas aeruginosa (strain ATCC 15692 / DSM 22644 / CIP 104116 / JCM 14847 / LMG 12228 / 1C / PRS 101 / PAO1) (208964)
>7AFZ_1|Chain A|Metallo-beta-lactamase L1|Stenotrophomonas maltophilia (40324)
>5LBS_1|Chains A, B|envelope protein E|Zika virus (64320)
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 \(w=f(c)\)
7QAV , Knot 144 332 0.84 40 192 309 
MPIHNLNHVNMFLQVIASGSISSAARILRKSHTAVSSAVSNLEIDLCVELVRRDGYKVEPTEQALRLIPYMRSLLNYQQLIGDIAFNLNKGPRNLRVLLDTAIPPSFCDTVSSVLLDDFNMVSLIRTSPADSLATIKQDNAEIDIAITIDEELKISRFNQCVLGYTKAFVVAHPQHPLCNASLHSIASLANYRQISLGSRSGQHSNLLRPVSDKVLFVENFDDMLRLVEAGVGWGIAPHYFVEERLRNGTLAVLSELYEPGGIDTKVYCYYNTALESERSFLRFLESARQRLRQLGRQRFDDAPAWQPSIVETAQRRSGPKALAYRQRAAPE
7AFZ , Knot 113 271 0.77 40 158 256 
GPAEVPLPQLRAYTVDASWLQPMAPLQIADHTWQIGTEDLTALLVQTPDGAVLLDGGMPQMASHLLDNMKARGVTPRDLRLILLSHAHADHAGPVAELKRRTGAKVAANAESAVLLARGGSDDLHFGDGITYPPANADRIVMDGEVITVGGIVFTAHFMAGHTPGSTAWTWTDTRNGKPVRIAYADSLSAPGYQLQGNPRYPHLIEDYRRSFATVRALPCDVLLTPHPGASNWDYAAGARAGAKALTCKAYADAAEQKFDGQLAKETAGAR
5LBS , Knot 187 447 0.85 40 246 417 
IRCIGVSNRDFVEGMSGGTWVDVVLEHGGCVTVMAQDKPTVDIELVTTTVSNMAEVRSYCYEASISDMASDSRCPTQGEAYLDKQSDTQYVCKRTLVDRGWGNGCGLFGKGSLVTCAKFACSKKMTGKSIQPENLEYRIMLSVHGSQHSGMIVNDTGHETDENRAKVEITPNSPRAEATLGGFGSLGLDCEPRTGLDFSDLYYLTMNNKHWLVHKEWFHDIPLPWHAGADTGTPHWNNKEALVEFKDAHAKRQTVVVLGSQEGAVHTALAGALEAEMDGAKGRLSSGHLKCRLKMDKLRLKGVSYSLCTAAFTFTKIPAETLHGTVTVEVQYAGTDGPCKVPAQMAVDMQTLTPVGRLITANPVITESTENSKMMLELDPPFGDSYIVIGVGEKKITHHWHRSGSTIGGPFEDDDDKAGWSHPQFEKGGGSGGGSGGGSWSHPQFEK

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 \(c\).

\(|P_{f(7QAV_1)}(2) \setminus P_{f(7AFZ_1)}(2)|=96\), \(|P_{f(7AFZ_1)}(2) \setminus P_{f(7QAV_1)}(2)|=62\). 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 1:11100100101110111010100110110000011001100101010101100010010100011011101001100001110111010011001011100111101000100111001011011000110011010000101011101000101001000111000111110100110010100110110000101100010000110110001111001001101101111111110011000100101111001001111000100000011000001101100100010011000100111101011001000011011100001110
Pair \(Z_2\) Length of longest common subsequence
7QAV_1,7AFZ_1 158 4
7QAV_1,5LBS_1 192 3
7AFZ_1,5LBS_1 174 3

Newick tree

 
[
	5LBS_1:95.44,
	[
		7QAV_1:79,7AFZ_1:79
	]:16.44
]

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 \((0.85)(0.8)(\frac{603 }{\log_{20} 603}-\frac{271}{\log_{20}271})=93.3\)
Status Protein1 Protein2 d d1/2
Query variables 7QAV_1 7AFZ_1 119 107
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]