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Parikh vectors
3SQP_1 6KVS_1 9CAI_1 Letter Amino acid
11 9 0 Q Glutamine
43 33 984 G Glycine
16 4 0 H Histidine
34 23 0 K Lycine
17 10 0 N Asparagine
10 1 735 C Cysteine
31 22 0 S Serine
17 10 0 R Arginine
34 20 0 L Leucine
29 27 0 I Isoleucine
14 10 0 F Phenylalanine
24 6 0 P Proline
31 19 0 T Threonine
3 4 0 W Tryptophan
13 9 0 Y Tyrosine
42 28 858 A Alanine
21 30 0 D Aspartic acid
44 19 0 V Valine
29 15 0 E Glutamic acid
15 14 0 M Methionine 

3SQP_1|Chains A, B|Glutathione reductase, mitochondrial|Homo sapiens (9606)
>6KVS_1|Chains A, B|3-oxoacyl-[acyl-carrier-protein] synthase 3|Staphylococcus aureus (strain Mu3 / ATCC 700698) (418127)
>9CAI_12|Chain L[auth A5]|28S rRNA|Caenorhabditis elegans (6239)
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 \(w=f(c)\)
3SQP , Knot 198 478 0.85 40 246 462 
ACRQEPQPQGPPPAAGAVASYDYLVIGGGSGGLASARRAAELGARAAVVESHKLGGTCVNVGCVPKKVMWNTAVHSEFMHDHADYGFPSCEGKFNWRVIKEKRDAYVSRLNAIYQNNLTKSHIEIIRGHAAFTSDPKPTIEVSGKKYTAPHILIATGGMPSTPHESQIPGASLGITSDGFFQLEELPGRSVIVGAGYIAVEMAGILSALGSKTSLMIRHDKVLRSFDSMISTNCTEELENAGVEVLKFSQVKEVKKTLSGLEVSMVTAVPGRLPVMTMIPDVDCLLWAIGRVPNTKDLSLNKLGIQTDDKGHIIVDEFQNTNVKGIYAVGDVCGKALLTPVAIAAGRKLAHRLFEYKEDSKLDYNNIPTVVFSHPPIGTVGLTEDEAIHKYGIENVKTYSTSFTPMYHAVTKRKTKCVMKMVCANKEEKVVGIHMQGLGCDEMLQGFAVAVKMGATKADFDNTVAIHPTSSEELVTLR
6KVS , Knot 135 313 0.82 40 179 296 
MNVGIKGFGAYAPEKIIDNAYFEQFLDTSDEWISKMTGIKERHWADDDQDTSDLAYEASVKAIADAGIQPEDIDMIIVATATGDMPFPTVANMLQERLGTGKVASMDQLAACSGFMYSMITAKQYVQSGDYHNILVVGADKLSKITDLTDRSTAVLFGDGAGAVIIGEVSEGRGIISYEMGSDGTGGKHLYLDKDTGKLKMNGREVFKFAVRIMGDASTRVVEKANLTSDDIDLFIPHQANIRIMESARERLGISKDKMSVSVNKYGNTSAASIPLSIDQELKNGKLKDDDTIVLVGFGGGLTWGAMTIKWGK
9CAI , Knot 585 3510 0.45 8 16 64 
CUCAACCUGAACUCAGUCGUGAUUACCCGCUGAACUUAAGCAUAUCAUUUAGCGGAGGAAAAGAAACUAAAAAGGAUUCCCUUAGUAACGGCGAGUGAAACGGGAAGAGCCCAGCGCCGAAUCGAUCAGUCUUUGGCUGCUUCGAAAUGUGGCGUAUAGGUGUAAGUUUCCAGCAGUGUCGUAUGUCCGAAGUCCUUACGAUUGAGGCCAUAAACCAGAGAGGGUGCGAGCCCCGUUCUGGAUAGCGGCACUGUUGGUUCGCUUGCUCCUUGGAGUCGGGUUGCUUGAAAGUGCAGCCUAAAGUGGGUGAUAAACUUCAUCUAAGGCUAAAUAUCGACUCGAUUGCGAUAGCGAACAAGUACCGUGAGGGAAAGUUGCAAAGGACUUUGAAGAGAGAGUUCAAGAGAACGUGAAAUCGCUGGAGUGGAACCGGAGACAGUUGAUGUUGCUUGGAGACAAGCUUGGUGACUGGUCGCUUAGUUGUGAUCGUUGCCGGGUGUCGUUUCCUAUGCUACGCCGACGGCGUUGGCUGCUCGUUCUAGCCCGACAGUGUUGCCCAUCUCGCAAGAGAAGGUGUCUUGCUGGCGGUAGUGGGUUCGUGGCGGCUAGCGUUUAGUUACGCUAGUGUGUGUGACGUCGGUGUGAAAGUCGACGACGUUUCCGACCCGUCUUGAAACACGGAUUGCGGAGUGCUUGUCUACUGCGAGUCAAAGGGUGUUAAAACCUUGCGGCGAAAUGAAAGUAAAGGUCAGUCUCGAAUUGGCCGACGUGGGAUCUGUGUUCUUCGGAGUGCAGCGCACCACGGCCCUGUGCGUGUCACUUGUGACUGUGCAGAGGUUGAGCAGUUGGCAAACGACCCGAAAGAUGGUGAACUAUGCCUGAGCAGGAUGAAGCCAGAGGAAACUCUGGUGGAAGUCCGUAUCGGUUCUGACGUGCAAAUCGAUCGAUAGACUUGGGUAUAGGGGCGAAAGACUAAUCGAACCAUCUAGUAGCUGGUUCCUUCCGAAGUUUCCCUCAGGAUAGCUGGAUCUCAGGCAGUUAUAUUCGGUAAAGCUAAUGAUUAGAGGCCUUGGGGACGUAAUGUCCUCAACCUAUUCUCAAACUUUCAAUGGAUAUGAAGUUGCAGUUUCUUUAGUGAACUGUCAACGUGAAUGCGAGGUCCAAGUGGGCCAUUUUUGGUAAGCAGAACUGGCGCUGUGGGAUGAACCAAACGUGGAGUUAAGGUGCCUAACUUCUCGCUCAUGAGACCCCAUAAAAGGUGUUGGUUGAUAUUGACAGCAGGACGGUGGCCAUGGAAGUCGGUAUCCGCUAAGGAGUGUGUAACAACUCACCUGCCGAAUCAACUAGCCCUGAAAAUGGAUGGCGCUUAAGCGAGAGACCUAUACUCCGCCGUUGCGACAUGUGCGUUGUCUAGCGCCAGGUCGUAACGAGUAGGAAGGUCGUGGCGGUUGCGUUGAAGGCUAUGAGCGUAGGCUCGGCUGGAGCUUCCGUCAGUGCAGAUCGUAAUGGUAGUAGCAAAUAUUCAAGUUCGAUCCUUGAAGACUGAAGUGGAGAAGGGUUCCACGUGAACAGUAGUUGGAUGUGGGUCAGUCGAUCCUAAGGUACUGGCGAACGCCUUGUAUCAUCGGUGGCGAAAAGCUUGCUUUUAGUCCCCGCUUGUCGAAAGGGAAUAGGGUUAAUAUUCCCUAACUGAGAUGCAAAGAUUGUGUUCUUCGGAGCACAAGCGCGGUAACGCAUUCGAACUUGGUUAGUCGCUCAAAGACCGAGCUAGAGUUUUCUUCUCUAGUUAAGGAACGGACUCCCUGGAAUUGGUUCAGCCAGAGAUGGGGACGUUGUUUCCGAAAAGCACCGCGGUUUCUGUGGUGUCUCGUGCUCUUUGAACGGCCCUUAAAACACCAAGGGAGGCUAUUAAUUUGCACUCAAUCGUACCGAUAUCCGCAUUAGGUCUCCAAGGUGAACAGCCUCUAGUCGAUAGAAUAAUGUAGGUAAGGGAAGUCGGCAAACUAGAUCCGUAACUUCGGGAAAAGGAUUGGCUCCAGUGGUUGGAACGGUUGGCCAGUUGGUUGAUGCUUGUCCGGCGCAGUUCUGUCUGCUUGAUACUUUCGGGUUGAUGGCGGACUAGUGAUUGUGCUUGCUUGCGGACGCUUUCUGGUGUGUGCUUGGACCUCGGUUCUAGUAUCCUGAUCGCUCAUCUAAACAACCGUACUGGAACCGGUACGGACUCAGGGAAUCCGACUGUCUAAUUAAAACAGAGGUGACAGAUGGUCCUUGCGGACGUUGACUGUCACUGAUUUCUGCCCAGUGCUCUGAAUGUUAAAUCGUAGUAAUUCGAGUAAGCGCGGGUAAACGGCGGGAGUAACUAUGACUCUCUUAAGGUAGCCAAAUGCCUCGUCAUUUAAUUGUUGACGCGCAUGAAUGGAUUAACGAGAUUCCUACUGUCCCUAACUACUUUCUAGCGAAACCACAGCCAAGGGAACGGGCUUGGCAAAAAUAGCGGGGAAAGAAGACCCUGUUGAGCUUGACUCUAGUUUGACAUUGUGAAGAGUCAUGAGAGGUGUAGCAUAGGUGGGAGUCUUCGGACGACAGUGAAAUACCACCACUUUCAUCGACUCUUUACUUAUUCGGUUAAAAGAGAAUUGGCUUCACGGCCUUUUUUCGAAGCAUUAAGCGGAGCCAUUUUAUGGCACCGUGACUCUCCUCGAAGACAGUGUCAAGCGGGGAGUUUGACUGGGGCGGUACAUCUAUCAAAUCGUAACGUAGGUGUCCUAAGGCGAGCUCAGAGAGGACGGAAACCUCUCGUAGAGCAAAAGGGCAAAAGCUUGCUUGAUCUUGACUUUCAGUACGAGUACAGACCGCGAAAGCGUGGCCUAUCGAUCCUUUUAAUCCUGAUUGUUUCAGGUAAGAGGUGUCAGAAAAGUUACCACAGGGAUAACUGGCUUGUGGCAGCCAAGCGUCCAUAGCGACGUUGCUUUUUGAUCCUUCGAUGUCGGCUCUUCCUAUCAUUGCGAAGCAGAAUUCGCCAAGCGUUGGAUUGUUCACCCACUAAUAGGGAACGUGAGCUGGGUUUAGACCGUCGUGAGACAGGUUAGUUUUACCCUACUGUUGACUUGUUAUUGCGAAAGUAAUCCUGCUUAGUACGAGAGGAACAGCGGGUUCAAACAUUUGGUUCAUAGACUUGAUCGACAGAUCAAUGGUCUGAAGCUACCAUUUGAGAGAUUAUAACUGAACGCCUCUAAGUUAGAAUCUCGCCUUGUCAAGGCGAAAAUUUCUUGCUUCCCGGUGUCGGGAGGCAUCUCUAUCUCGUGGCAACACGAGAGCUUAUGCCCUAUGUAUGGCCUUGGCGUCGUAGUGAAUUCUGCGACGCUUGCCAACGCCAGAUCACUCUGGUUCAAUGUCGGGGCGCUAAAUCACUUGCAUACGACUUGGUCUCUUGGUCAAGGUGUUGUAUUCAGUAGAGCAGUCCUUUUAUACUGCGAUCUGUUGAGACUAUCCUUUGAUUGAGUUUUUUGU

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 \(c\).

\(|P_{f(3SQP_1)}(2) \setminus P_{f(6KVS_1)}(2)|=121\), \(|P_{f(6KVS_1)}(2) \setminus P_{f(3SQP_1)}(2)|=54\). 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 1:1000010101111111111000011111101111010011011101111000011100101101100111001100011000100111000101010110000010100101100001000010110101110001010101010000110111101111001000011110111000111010011100111111011101111101110000111000011001001100000001001110110100100100010110101101111011110111010011111101100001010011100000101110010000101101110101011101111111001100110000000100001101110011110111000011000110010000001011001100000001101101000001111010111000110111111011100101000111010000011010
Pair \(Z_2\) Length of longest common subsequence
3SQP_1,6KVS_1 175 4
3SQP_1,9CAI_1 246 4
6KVS_1,9CAI_1 185 4

Newick tree

 
[
	9CAI_1:11.05,
	[
		3SQP_1:87.5,6KVS_1:87.5
	]:27.55
]

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 \((0.85)(0.8)(\frac{791 }{\log_{20} 791}-\frac{313}{\log_{20}313})=130.\)
Status Protein1 Protein2 d d1/2
Query variables 3SQP_1 6KVS_1 165 135.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]