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Parikh vectors
8SXO_1 4OYW_1 3MQT_1 Letter Amino acid
17 27 22 D Aspartic acid
26 30 29 G Glycine
29 40 33 L Leucine
24 19 21 T Threonine
6 14 16 H Histidine
10 21 12 M Methionine
13 21 13 P Proline
27 40 26 V Valine
11 28 22 K Lycine
17 31 12 F Phenylalanine
11 16 14 Y Tyrosine
11 14 15 R Arginine
21 16 18 N Asparagine
14 21 13 Q Glutamine
9 31 32 E Glutamic acid
3 5 10 W Tryptophan
17 26 35 A Alanine
12 11 8 C Cysteine
12 35 30 I Isoleucine
16 23 13 S Serine 

8SXO_1|Chain A|3C-like proteinase nsp5|Severe acute respiratory syndrome coronavirus 2 (2697049)
>4OYW_1|Chain A|Adenylate cyclase type 10|Homo sapiens (9606)
>3MQT_1|Chains A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X|Mandelate racemase/muconate lactonizing protein|Shewanella pealeana (398579)
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 \(w=f(c)\)
8SXO , Knot 134 306 0.83 40 196 290 
SGFRKMAFPSGKVEGCMVQVTCGTTTLNGLWLDDVVYCPRHVICTSEDMLNPNYEDLLIRKSNHNFLVQAGNVQLRVIGHSMQNCVLKLKVDTANPKTPKYKFVRIQPGQTFSVLACYNGSPSGVYQCAMRPNFTIKGSFLNGSCGSVGFNIDYDCVSFCYMHIMELPTGVHAGTDLEGNFYGPFVDRQTAQAAGTDTTITVNVLAWLYAAVINGDRWFLNRFTTTLNDFNLVAMKYNYEPLTQDHVDILGPLSAQTGIAVLDMCASLKELLQNGMNGRTILGSALLEDEFTPFDVVRQCSGVTFQ
4OYW , Knot 199 470 0.86 42 259 447 
XMNTPKEEFQDWPIVRIAAHLPDLIVYGHFSPERPFMDYFDGVLMFVDISGFTAMTEKFSSAMYMDRGAEQLVEILNYHISAIVEKVLIFGGDILKFAGDALLALWRVERKQLKNIITVVIKCSLEIHGLFETQEWEEGLDIRVKIGLAAGHISMLVFGDETHSHFLVIGQAVDDVRLAQNMAQMNDVILSPNCWQLCDRSMIEIESVPDQRAVKVNFLKPPPNFNFDEFFTKCTTFMHYYPSGEHKNLLRLACTLKPDPELEMSLQKYVMESILKQIDNKQLQGYLSELRPVTIVFVNLMFEDQDKAEEIGPAIQDAYMHITSVLKIFQGQINKVFMFDKGCSFLCVFGFPGEKVPDELTHALECAMDIFDFCSQVHKIQTVSIGVASGIVFCGIVGHTVRHEYTVIGQKVNLAARMMMYYPGIVTCDSVTYNGSNLPAYFFKELPKKVMKGVADSGPLYQYWGRTEKV
3MQT , Knot 167 394 0.84 40 221 368 
MSLGANIVSVEFIPVNVAATNWSENTVIVKVTDENGVYGLGEADGPPECMKAFSEIENEHKWLNNIKEAVIGRDPLEFRANYNRMYDTTKWIGMRGLGLFAISGIDMALYDLAGKQLGVPAYKLMGGAQKAQLTPYFTLYPSVAADATLSEIVEAYKPLIAKAKERGAKAVKVCIIPNDKVSDKEIVAYLRELREVIGWDMDMMVDCLYRWTDWQKARWTFRQLEDIDLYFIEACLQHDDLIGHQKLAAAINTRLCGAEMSTTRFEAQEWLEKTGISVVQSDYNRCGGVTELLRIMDICEHHNAQLMPHNWKTGITAAAARHFGIVCHISEYVEYLHPDFWNGTLTQQLTLNEPKIIDGAIEVSDKPGLGIELNIEFVEQVTGHKFEGHHHHHH

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 \(c\).

\(|P_{f(8SXO_1)}(2) \setminus P_{f(4OYW_1)}(2)|=52\), \(|P_{f(4OYW_1)}(2) \setminus P_{f(8SXO_1)}(2)|=115\). 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 1:011001111010101011010010001011110011001001100000110100001110000001110110101011100100011010100101001000110101100101110001010110001101010101011010010111010000101001011011011011001010101111000010111000010101111101111010011100100010010111100000110000101111101001111101010100110011010011101110001011011000011010
Pair \(Z_2\) Length of longest common subsequence
8SXO_1,4OYW_1 167 4
8SXO_1,3MQT_1 191 3
4OYW_1,3MQT_1 188 4

Newick tree

 
[
	3MQT_1:98.21,
	[
		8SXO_1:83.5,4OYW_1:83.5
	]:14.71
]

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 \((0.85)(0.8)(\frac{776 }{\log_{20} 776}-\frac{306}{\log_{20}306})=128.\)
Status Protein1 Protein2 d d1/2
Query variables 8SXO_1 4OYW_1 163 132
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]