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Parikh vectors
1NWK_1 7TQX_1 7XSQ_1 Letter Amino acid
21 34 73 V Valine
18 21 110 R Arginine
12 16 101 N Asparagine
26 32 150 L Leucine
19 19 161 K Lycine
16 10 18 M Methionine
19 20 76 P Proline
16 19 60 Y Tyrosine
5 12 27 C Cysteine
11 16 41 Q Glutamine
28 37 138 E Glutamic acid
30 27 112 I Isoleucine
4 4 28 W Tryptophan
29 36 62 A Alanine
23 23 108 S Serine
27 29 86 T Threonine
22 27 121 D Aspartic acid
28 36 135 G Glycine
9 13 39 H Histidine
12 20 76 F Phenylalanine

1NWK_1|Chain A|Actin, alpha skeletal muscle|Oryctolagus cuniculus (9986)
>7TQX_1|Chain A|Tubulin alpha-1B chain|Sus scrofa (9823)
>7XSQ_1|Chain A|RAMP superfamily protein|Candidatus Scalindua brodae (237368)
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 \(w=f(c)\)
1NWK , Knot 159 375 0.83 40 219 360
DEDETTALVCDNGSGLVKAGFAGDDAPRAVFPSIVGRPRHQGVMVGMGQKDSYVGDEAQSKRGILTLKYPIEHGIITNWDDMEKIWHHTFYNELRVAPEEHPTLLTEAPLNPKANREKMTQIMFETFNVPAMYVAIQAVLSLYASGRTTGIVLDSGDGVTHNVPIYEGYALPHAIMRLDLAGRDLTDYLMKILTERGYSFVTTAEREIVRDIKEKLCYVALDFENEMATAASSSSLEKSYELPDGQVITIGNERFRCPETLFQPSFIGMESAGIHETTYNSIMKCDIDIRKDLYANNVMSGGTTMYPGIADRMQKEITALAPSTMKIKIIAPPERKYSVWIGGSILASLSTFQQMWITKQEYDEAGPSIVHRKCF
7TQX , Knot 192 451 0.86 40 258 426
MRECISIHVGQAGVQIGNACWELYCLEHGIQPDGQMPSDKTIGGGDDSFNTFFSETGAGKHVPRAVFVDLEPTVIDEVRTGTYRQLFHPEQLITGKEDAANNYARGHYTIGKEIIDLVLDRIRKLADQCTGLQGFLVFHSFGGGTGSGFTSLLMERLSVDYGKKSKLEFSIYPAPQVSTAVVEPYNSILTTHTTLEHSDCAFMVDNEAIYDICRRNLDIERPTYTNLNRLISQIVSSITASLRFDGALNVDLTEFQTNLVPYPRIHFPLATYAPVISAEKAYHEQLSVAEITNACFEPANQMVKCDPRHGKYMACCLLYRGDVVPKDVNAAIATIKTKRSIQFVDWCPTGFKVGINYQPPTVVPGGDLAKVQRAVCMLSNTTAIAEAWARLDHKFDLMYAKRAFVHWYVGEGMEEGEFSEAREDMAALEKDYEEVGVDSVEGEGEEEGEEY
7XSQ , Knot 591 1722 0.85 40 353 1387
MKSNDMNITVELTFFEPYRLVEWFDWDARKKSHSAMRGQAFAQWTWKGKGRTAGKSFITGTLVRSAVIKAVEELLSLNNGKWEGVPCCNGSFQTDESKGKKPSFLRKRHTLQWQANNKNICDKEEACPFCILLGRFDNAGKVHERNKDYDIHFSNFDLDHKQEKNDLRLVDIASGRILNRVDFDTGKAKDYFRTWEADYETYGTYTGRITLRNEHAKKLLLASLGFVDKLCGALCRIEVIKKSESPLPSDTKEQSYTKDDTVEVLSEDHNDELRKQAEVIVEAFKQNDKLEKIRILADAIRTLRLHGEGVIEKDELPDGKEERDKGHHLWDIKVQGTALRTKLKELWQSNKDIGWRKFTEMLGSNLYLIYKKETGGVSTRFRILGDTEYYSKAHDSEGSDLFIPVTPPEGIETKEWIIVGRLKAATPFYFGVQQPSDSIPGKEKKSEDSLVINEHTSFNILLDKENRYRIPRSALRGALRRDLRTAFGSGCNVSLGGQILCNCKVCIEMRRITLKDSVSDFSEPPEIRYRIAKNPGTATVEDGSLFDIEVGPEGLTFPFVLRYRGHKFPEQLSSVIRYWEENDGKNGMAWLGGLDSTGKGRFALKDIKIFEWDLNQKINEYIKERGMRGKEKELLEMGESSLPDGLIPYKFFEERECLFPYKENLKPQWSEVQYTIEVGSPLLTADTISALTEPGNRDAIAYKKRVYNDGNNAIEPEPRFAVKSETHRGIFRTAVGRRTGDLGKEDHEDCTCDMCIIFGNEHESSKIRFEDLELINGNEFEKLEKHIDHVAIDRFTGGALDKAKFDTYPLAGSPKKPLKLKGRFWIKKGFSGDHKLLITTALSDIRDGLYPLGSKGGVGYGWVAGISIDDNVPDDFKEMINKTEMPLPEEVEESNNGPINNDYVHPGHQSPKQDHKNKNIYYPHYFLDSGSKVYREKDIITHEEFTEELLSGKINCKLETLTPLIIPDTSDENGLKLQGNKPGHKNYKFFNINGELMIPGSELRGMLRTHFEALTKSCFAIFGEDSTLSWRMNADEKDYKIDSNSIRKMESQRNPKYRIPDELQKELRNSGNGLFNRLYTSERRFWSDVSNKFENSIDYKREILRCAGRPKNYKGGIIRQRKDSLMAEELKVHRLPLYDNFDIPDSAYKANDHCRKSATCSTSRGCRERFTCGIKVRDKNRVFLNAANNNRQYLNNIKKSNHDLYLQYLKGEKKIRFNSKVITGSERSPIDVIAELNERGRQTGFIKLSGLNNSNKSQGNTGTTFNSGWDRFELNILLDDLETRPSKSDYPRPRLLFTKDQYEYNITKRCERVFEIDKGNKTGYPVDDQIKKNYEDILDSYDGIKDQEVAERFDTFTRGSKLKVGDLVYFHIDGDNKIDSLIPVRISRKCASKTLGGKLDKALHPCTGLSDGLCPGCHLFGTTDYKGRVKFGFAKYENGPEWLITRGNNPERSLTLGVLESPRPAFSIPDDESEIPGRKFYLHHNGWRIIRQKQLEIRETVQPERNVTTEVMDKGNVFSFDVRFENLREWELGLLLQSLDPGKNIAHKLGKGKPYGFGSVKIKIDSLHTFKINSNNDKIKRVPQSDIREYINKGYQKLIEWSGNNSIQKGNVLPQWHVIPHIDKLYKLLWVPFLNDSKLEPDVRYPVLNEESKGYIEGSDYTYKKLGDKDNLPYKTRVKGLTTPWSPWNPFQVIAEHEEQEVNVTGSRPSVTDKIERDGKMV

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 \(c\).

\(|P_{f(1NWK_1)}(2) \setminus P_{f(7TQX_1)}(2)|=59\), \(|P_{f(7TQX_1)}(2) \setminus P_{f(1NWK_1)}(2)|=98\). 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 1:000000111000101110111110011011110111010001111111000001100100001110100110011100100100110001000101110001011001110101000010011100101111011101110101010001111001011000111001011101110101110010001101100010011001000110010001001110100011011000010000011010110110001001001101011110011100000001100010100010100110110010111100100010111100101011111000001111101110100100111000000011101100001
Pair \(Z_2\) Length of longest common subsequence
1NWK_1,7TQX_1 157 5
1NWK_1,7XSQ_1 172 5
7TQX_1,7XSQ_1 135 4

Newick tree

 
[
	1NWK_1:86.71,
	[
		7TQX_1:67.5,7XSQ_1:67.5
	]:19.21
]

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 \((0.85)(0.8)(\frac{826 }{\log_{20} 826}-\frac{375}{\log_{20}375})=121.\)
Status Protein1 Protein2 d d1/2
Query variables 1NWK_1 7TQX_1 152 138
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]