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Parikh vectors
7GIB_1 8FFO_1 8QBD_1 Letter Amino acid
21 26 8 N Asparagine
14 38 23 Q Glutamine
7 20 4 H Histidine
11 24 12 Y Tyrosine
11 43 20 R Arginine
17 31 26 D Aspartic acid
26 45 19 G Glycine
11 39 19 I Isoleucine
17 35 9 F Phenylalanine
13 32 17 P Proline
24 42 15 T Threonine
17 56 26 A Alanine
12 15 0 C Cysteine
3 13 3 W Tryptophan
9 46 44 E Glutamic acid
29 99 30 L Leucine
11 23 20 K Lycine
10 24 2 M Methionine
16 41 29 S Serine
27 47 13 V Valine 

7GIB_1|Chains A, B|3C-like proteinase|Severe acute respiratory syndrome coronavirus 2 (2697049)
>8FFO_1|Chains A, B, C, D|Transient receptor potential cation channel subfamily V member 5|Oryctolagus cuniculus (9986)
>8QBD_1|Chains A, B, C, D, E, F, G, H, I, J, K, L, M, N|Sphingolipid long chain base-responsive protein PIL1|Saccharomyces cerevisiae (4932)
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 \(w=f(c)\)
7GIB , Knot 134 306 0.83 40 196 290 
SGFRKMAFPSGKVEGCMVQVTCGTTTLNGLWLDDVVYCPRHVICTSEDMLNPNYEDLLIRKSNHNFLVQAGNVQLRVIGHSMQNCVLKLKVDTANPKTPKYKFVRIQPGQTFSVLACYNGSPSGVYQCAMRPNFTIKGSFLNGSCGSVGFNIDYDCVSFCYMHHMELPTGVHAGTDLEGNFYGPFVDRQTAQAAGTDTTITVNVLAWLYAAVINGDRWFLNRFTTTLNDFNLVAMKYNYEPLTQDHVDILGPLSAQTGIAVLDMCASLKELLQNGMNGRTILGSALLEDEFTPFDVVRQCSGVTFQ
8FFO , Knot 281 739 0.83 40 305 676 
MGACPPKAKGPWAQLQKLLISWPVGEQDWEQYRDRVNMLQQERIRDSPLLQAAKENDLRLLKILLLNQSCDFQQRGAVGETALHVAALYDNLEAATLLMEAAPELAKEPALCEPFVGQTALHIAVMNQNLNLVRALLARGASVSARATGAAFRRSPHNLIYYGEHPLSFAACVGSEEIVRLLIEHGADIRAQDSLGNTVLHILILQPNKTFACQMYNLLLSYDEHSDHLQSLELVPNHQGLTPFKLAGVEGNTVMFQHLMQKRKHVQWTCGPLTSTLYDLTEIDSWGEELSFLELVVSSKKREARQILEQTPVKELVSFKWKKYGRPYFCVLASLYILYMICFTTCCIYRPLKLRDDNRTDPRDITILQQKLLQEAYVTHQDNIRLVGELVTVTGAVIILLLEIPDIFRVGASRYFGQTILGGPFHVIIITYASLVLLTMVMRLTNMNGEVVPLSFALVLGWCSVMYFARGFQMLGPFTIMIQKMIFGDLMRFCWLMAVVILGFASAFHITFQTEDPNNLGEFSDYPTALFSTFELFLTIIDGPANYSVDLPFMYCITYAAFAIIATLLMLNLFIAMMGDTHWRVAQERDELWRAQVVATTVMLERKMPRFLWPRSGICGYEYGLGDRWFLRVENHHDQNPLRVLRYVEAFKCSDKEDGQEQLSEKRPSTVESGMLSRASVAFQTPSLSRTTSQSSNSHRGWEILRRNTLGHLNLGLDLGEGDGEEVYHFTETSQVAPA
8QBD , Knot 141 339 0.80 38 181 314 
MHRTYSLRNSRAPTASQLQNPPPPPSTTKGRFFGKGGLAYSFRRSAAGAFGPELSRKLSQLVKIEKNVLRSMELTANERRDAAKQLSIWGLENDDDVSDITDKLGVLIYEVSELDDQFIDRYDQYRLTLKSIRDIEGSVQPSRDRKDKITDKIAYLKYKDPQSPKIEVLEQELVRAEAESLVAEAQLSNITRSKLRAAFNYQFDSIIEHSEKIALIAGYGKALLELLDDSPVTPGETRPAYDGYEASKQIIIDAESALNEWTLDSAQVKPTLSFKQDYEDFEPEEGEEEEEEDGQGRWSEDEQEDGQIEEPEQEEEGAVEEHEQVGHQQSESLPQQTTA

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 \(c\).

\(|P_{f(7GIB_1)}(2) \setminus P_{f(8FFO_1)}(2)|=37\), \(|P_{f(8FFO_1)}(2) \setminus P_{f(7GIB_1)}(2)|=146\). 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 1:011001111010101011010010001011110011001001100000110100001110000001110110101011100100011010100101001000110101100101110001010110001101010101011010010111010000101001001011011011001010101111000010111000010101111101111010011100100010010111100000110000101111101001111101010100110011010011101110001011011000011010
Pair \(Z_2\) Length of longest common subsequence
7GIB_1,8FFO_1 183 6
7GIB_1,8QBD_1 175 4
8FFO_1,8QBD_1 182 4

Newick tree

 
[
	8FFO_1:92.46,
	[
		7GIB_1:87.5,8QBD_1:87.5
	]:4.96
]

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 \((0.85)(0.8)(\frac{1045 }{\log_{20} 1045}-\frac{306}{\log_{20}306})=197.\)
Status Protein1 Protein2 d d1/2
Query variables 7GIB_1 8FFO_1 250 174.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]