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Parikh vectors
2MBC_1 2MZH_1 6UCA_1 Letter Amino acid
11 14 28 P Proline
6 11 13 Y Tyrosine
4 11 16 N Asparagine
3 8 18 H Histidine
2 5 6 W Tryptophan
16 11 19 V Valine
14 17 26 K Lycine
10 12 19 T Threonine
14 17 24 A Alanine
9 25 22 G Glycine
4 1 28 C Cysteine
4 9 24 Q Glutamine
9 11 23 E Glutamic acid
7 11 20 I Isoleucine
13 21 44 L Leucine
4 8 6 M Methionine
11 11 26 R Arginine
9 16 23 D Aspartic acid
6 11 29 F Phenylalanine
6 18 28 S Serine 

2MBC_1|Chain A|Protein tyrosine phosphatase type IVA 3|Homo sapiens (9606)
>2MZH_1|Chain A|Matrilysin|Homo sapiens (9606)
>6UCA_1|Chains A, B, C, D, E, F|rRNA N6-adenosine-methyltransferase ZCCHC4|Homo sapiens (9606)
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 \(w=f(c)\)
2MBC , Knot 81 162 0.84 40 122 156 
MARMNRPAPVEVSYKHMRFLITHNPTNATLSTFIEDLKKYGATTVVRVCEVTYDKTPLEKDGITVVDWPFDDGAPPPGKVVEDWLSLVKAKFCEAPGSCVAVHCVAGLGRAPVLVALALIESGMKYEDAIQFIRQKRRGAINSKQLTYLEKYRPKQRLRFKD
2MZH , Knot 114 248 0.84 40 175 241 
LPQEAGGMSELQWEQAQDYLKRFYLYDSETKNANSLEAKLKEMQKFFGLPITGMLNSRVIEIMQKPRCGVPDVAEYSLFPNSPKWTSKVVTYRIVSYTRDLPHITVDRLVSKALNMWGKEIPLHFRKVVWGTADIMIGFARGAHGDSYPFDGPGNTLAHAFAPGTGLGGDAHFDEDERWTDGSSLGINFLYAATHALGHSLGMGHSSDPNAVMYPTYGNGDPQNFKLSQDDIKGIQKLYGKRSNSRKK
6UCA , Knot 187 442 0.86 40 258 428 
SGMEVVLPLDPAVPAPLCPHGPTLLFVKVTQGAAATRRFYACSACRDRKDCNFFQWEDEKLSGARLAAREAHNRRCQPPLSRTQCVERYLKFIELPLTQRKFCQTCQQLLLPDDWGQHSEHQVLGNVSITQLRRPSQLLYPLENAATNAQYLFADRSCQFLVDLLSALGFRRVLCVGTPRLHELIKLTASGDKKSNIKSLLLDIDFRYSQFYMEDSFCHYNMFNHHFFDGKTALEVCRAFLQEDKGEGIIMVTDPPFGGLVEPLAITFKKLIAMWKEGQSQDDSHKELPIFWIFPYFFESRICQFFPSFQMLDYQVDYDNHALYKHGKTGRKQSPVRIFTNIPPNKIILPTEEGYRFCSPCQRYVSLENQHCELCNSCTSKDGRKWNHCFLCKKCVKPSWIHCSICNHCAVPDHSCEGPKHGCFICGELDHKRSTCPNIATS

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 \(c\).

\(|P_{f(2MBC_1)}(2) \setminus P_{f(2MZH_1)}(2)|=57\), \(|P_{f(2MZH_1)}(2) \setminus P_{f(2MBC_1)}(2)|=110\). 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 1:110100111101000010111000100101001100100011001101001000001100011011011100111111011001101101010011100111001111101111111111001100001101100000111000010010000100010100
Pair \(Z_2\) Length of longest common subsequence
2MBC_1,2MZH_1 167 3
2MBC_1,6UCA_1 198 3
2MZH_1,6UCA_1 183 4

Newick tree

 
[
	6UCA_1:98.95,
	[
		2MBC_1:83.5,2MZH_1:83.5
	]:15.45
]

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 \((0.85)(0.8)(\frac{410 }{\log_{20} 410}-\frac{162}{\log_{20}162})=73.9\)
Status Protein1 Protein2 d d1/2
Query variables 2MBC_1 2MZH_1 94 76.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]