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Parikh vectors
8YFQ_1 2LKZ_1 8QNQ_1 Letter Amino acid
104 9 16 A Alanine
104 6 6 D Aspartic acid
34 8 4 H Histidine
56 3 2 F Phenylalanine
133 4 3 P Proline
14 0 2 W Tryptophan
110 5 11 V Valine
64 4 2 N Asparagine
111 4 11 G Glycine
134 10 22 L Leucine
102 5 4 T Threonine
68 1 3 Y Tyrosine
86 3 10 R Arginine
20 0 0 C Cysteine
82 7 7 Q Glutamine
100 9 5 I Isoleucine
115 0 7 E Glutamic acid
91 5 5 K Lycine
55 4 3 M Methionine
160 8 6 S Serine 

8YFQ_1|Chain A|DNA-directed RNA polymerase subunit|Komagataella phaffii (460519)
>2LKZ_1|Chain A|RNA-binding protein 5|Homo sapiens (9606)
>8QNQ_1|Chains A, B, D, E|Antitoxin Xre/MbcA/ParS-like toxin-binding domain-containing protein|Pseudomonas aeruginosa PAO1 (208964)
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 \(w=f(c)\)
8YFQ , Knot 554 1743 0.79 40 360 1336 
MSQFPYSSAPLRSVKEVQFGLLSPEEIRAISVVKIEYPEIMDESRQRPREGGLNDPKLGSIDRNFKCQTCGEGMAECPGHFGHMELAKPVFHIGFIPKIKKVCECICMNCGKLLLDETNPTMAQAIRIRDPKKRFNAVWQLCKTKMVCEADAPVDEYSEQKVVSRGGCGNTQPVVRKDGMKLWGTWKKSGFSDRDAQPERKLLTPGEILNVFKHISPEDCFRLGFNEDYARPEWMIITVLPVPPPQVRPSIAMDETTQGQDDLTHKLSDILKANINVQKLEMDGSPQHIINEVEQLLQFHVATYMDNDIAGQPQALQKSGRPVKAIRARLKGKEGRLRGNLMGKRVDFSARTVISGDPNLELDQVGVPISIAKTLSYPETVTQYNIHRLTEYVRNGPNEHPGAKYVIRDNGDRIDLRYHKRAGDIVLQYGWKVERHLMDDDPVLFNRQPSLHKMSMMAHRVKVMPYSTFRLNLSVTSPYNADFDGDEMNLHVPQSEETRAELSQLCAVPLQIVSPQSNKPVMGIVQDTLCGVRKMTLRDTFIEYEQVMNMLFWVPSWDGVVPQPAILKPKPLWTGKQLLSIAIPSGIHLQRTDGGNSLLSPKDNGMLIVDGKVMFGVVDKKTVGSGGGGLIHTVMREKGPKICAELFGNIQKVVNYWLLHNGFSIGIGDAIADASTMKEITHAISSAKEQVQEIIYKAQHNELELKPGMTLRESFEGEVSRTLNDARDSAGRSAEMNLKDLNNVKQMVSAGSKGSFINIAQMSACVGQQMVEGKRIAFGFADRSLPHFTKDDFSPESKGFVENSYLRGLTPQEFFFHAMAGREGLIDTAVKTAETGYIQRRLVKALEDIMVHYDGTTRNSLGDIIQFLYGEDGLDGTQVERQTIDTIPGSDKAFHKRYYVDLMDEKNSIKPDVIEYAADILGDVELQKELNSEYEQLVSDRKFLREIVFVNGDHNWPLPVNLRRIIQNAQQIFHLDRAKASDLTIPEIIHGVRDLCKKLFVLRGENELIKEAQQNATSLFQCLVRARLATRRILEEFRLNRDAFEWVLGTIEAQFQRSLVHPGEMVGVIAAQSIGEPATQMTLNTFHYAGVSSKNVTLGVPRLKEILNVAKNIKTPALTVYLDREIALDIEKAKVIQSSIEYTTLKNVTSATEIYYDPDPTSTVIEEDFDTVEAYFSIPDEKVEETIDKQSPWLLRLELDRARMLDKQLTMNQVADKISEVFSDDLFVMWSEDNADKLIIRCRVIRDPKAMDEELEAEEDQMLKRIEAHMLDLIALRGIPGISKVYMVKHKVSVPDESGEYKNEELWALETDGINLAEVMAVPGVDSSRTYSNSFVEILSVLGIEATRSSLYKEILNVIAFDGSYVNYRHMALLVDVMTSRGYLMAITRHGINRADTGALMRCSFEETVEILFEAGAAAELDDCRGVSENVMLGQLAPMGTGAFDVMIDEKLLTSLPADYAPTMPLFKGKATQGSATPYDNNAQYDDEFNHDDVADVMFSPMAETGSGDDRSGGLTEYAGIQSPYQPTSPGLSATSPGFAPTSPGFAPTSPRYSPTSPGYSPTSPSYSPTSPSYSPTSPSYSPTSPSYSPTSPSYSPTSPSYSPTSPSYSPTSPSYSPTSPSYSPTSPQYSPTSPQYSPTSPQYSPTSPQYSPTSPQYSPTSPQYSPTSPQYSPTSPQYSPTSPQYSPTSPQYSPTSPQYSPTSPQYSPTSPQYSPTSPQYSPASPQYSPSRHSPNGESKEGE
2LKZ , Knot 50 95 0.80 34 78 90 
MGHHHHHHMDTIILRNIAPHTVVDSIMTALSPYASLAVNNIRLIKDKQTQQNRGFAFVQLSSAMDASQLLQILQSLHPPLKIDGKTIGVDFAKSA
8QNQ , Knot 61 129 0.76 38 94 121 
MADLNWISSALIKERPSADAVLAKAVLAAREQLGLTQLELAGIVGVDRSAISRWKTQGLRVDSKTGELALLLVRVYRALYALFGGQQEDMRHFLRTPNHHLAGEPLALMGQVQGLVHVLEYLDAIRGKV

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 \(c\).

\(|P_{f(8YFQ_1)}(2) \setminus P_{f(2LKZ_1)}(2)|=283\), \(|P_{f(2LKZ_1)}(2) \setminus P_{f(8YFQ_1)}(2)|=1\). 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 1:100110001110010010111101001011011010010110000001001110010110100010000010111001101101011011101111101001000101001011100001011011010010001011101000011001011100000001100110100011100011011101000110000101000110110110110010100010111000010101111011111110101011100000100010001001101010100101010100110010011010110010001110101100010110110101010010101011100101010011010101010011111011001001001000010010001001100011100110001001010000011011100110100011000111100010100101110010111000101010100100101010010101100000010100101111011010000111111000101100101000110000110111111010111101111010111010011011110110100001100110100011111010111111000011011111100110001101010111010011001110011011110111010010010011001000100110010000101011101000101010001001000110010101001001001101100101101101010110011010011111100011010000101000111000010110100111011110011100110010010100011011001110001000001101101101001101001000010011100011000001011000001010110011011101010001000000110000110011110100011111010011001001101001010010110110110010001111010001100100010011001101011000110010100011011110101010001101101111111001101100101001001110000101111010011011001001110101000111010010110001000010010010010001010001100010010101011000100010000111101010010110001010011001001100011111000010011100011001011000101000011001010110111101111100101100010110001000000111100011011011111110000000001101101111010000100011011110100100001111101100010111100011001001111000100010111011111010000110001111011111011101110001100111001101111010100101010000100000100001101110111001010000111000111001001001110100111110011111001000100110010010001001000100100010010001001000100100010010001001000100100010010001001000100100010010001001000100100010010001001000100100010010001001000100100010010001001000110100010000101000010
Pair \(Z_2\) Length of longest common subsequence
8YFQ_1,2LKZ_1 284 4
8YFQ_1,8QNQ_1 274 4
2LKZ_1,8QNQ_1 120 3

Newick tree

 
[
	8YFQ_1:15.33,
	[
		8QNQ_1:60,2LKZ_1:60
	]:97.33
]

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 \((0.85)(0.8)(\frac{1838 }{\log_{20} 1838}-\frac{95}{\log_{20}95})=455.\)
Status Protein1 Protein2 d d1/2
Query variables 8YFQ_1 2LKZ_1 531 279.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]