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Parikh vectors
9MCZ_1 8WPN_1 2GUC_1 Letter Amino acid
11 45 6 F Phenylalanine
15 40 3 P Proline
30 38 6 T Threonine
34 55 4 V Valine
15 41 7 D Aspartic acid
35 36 22 G Glycine
6 19 3 H Histidine
12 61 11 I Isoleucine
22 54 2 K Lycine
9 16 2 M Methionine
2 18 0 W Tryptophan
15 52 5 R Arginine
10 43 7 N Asparagine
27 116 7 L Leucine
19 72 19 S Serine
11 34 2 Q Glutamine
13 69 3 E Glutamic acid
12 31 8 Y Tyrosine
32 60 4 A Alanine
0 15 0 C Cysteine 

9MCZ_1|Chain A|Penicillin-binding protein 2|Neisseria gonorrhoeae 35/02 (528346)
>8WPN_1|Chains A, B, C, D|Short transient receptor potential channel 4|Homo sapiens (9606)
>2GUC_1|Chains A, B|griffithsin|Griffithsia (35158)
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 \(w=f(c)\)
9MCZ , Knot 144 330 0.84 38 191 316 
GSGGALSLDQRIQTLAYEELNKAVEYHQAKAGTVVVLDARTGEILALVNTPGRNRAVTDMIEPGSAMKPFTIAKALDSGKVDATDTFNTLPYKIGSATVQDTHVYPTLDVRGIMQKSSNVGTSKLSAMFTPKEMYDFYHDLGVGVRMHSGFPGETAGLLRSWRRWQKIEQATMSFGYGLQLSLLQLARAYTVLTHDGELLPVSFEKQAVAPKGKRVIKASTAKKVRELMVSVTEAGGTGTAGAVDGFDVGAKTGTARKLVNGRYVDYKHVATFIGFAPAKNPRVIVAVTIDEPTANGYYSGVVTGPVFKQVMGGSLNILGVSPTKPLTNV
8WPN , Knot 346 915 0.86 40 329 836 
MAQFYYKRNVNAPYRDRIPLRIVRAESELSPSEKAYLNAVEKGDYASVKKSLEEAEIYFKININCIDPLGRTALLIAIENENLELIELLLSFNVYVGDALLHAIRKEVVGAVELLLNHKKPSGEKQVPPILLDKQFSEFTPDITPIILAAHTNNYEIIKLLVQKGVSVPRPHEVRCNCVECVSSSDVDSLRHSRSRLNIYKALASPSLIALSSEDPFLTAFQLSWELQELSKVENEFKSEYEELSRQCKQFAKDLLDQTRSSRELEIILNYRDDNSLIEEQSGNDLARLKLAIKYRQKEFVAQPNCQQLLASRWYDEFPGWRRRHWAVKMVTCFIIGLLFPVFSVCYLIAPKSPLGLFIRKPFIKFICHTASYLTFLFLLLLASQHIDRSDLNRQGPPPTIVEWMILPWVLGFIWGEIKQMWDGGLQDYIHDWWNLMDFVMNSLYLATISLKIVAFVKYSALNPRESWDMWHPTLVAEALFAIANIFSSLRLISLFTANSHLGPLQISLGRMLLDILKFLFIYCLVLLAFANGLNQLYFYYEETKGLTCKGIRCEKQNNAFSTLFETLQSLFWSIFGLINLYVTNVKAQHEFTEFVGATMFGTYNVISLVVLLNMLIAMMNNSYQLIADHADIEWKFARTKLWMSYFEEGGTLPTPFNVIPSPKSLWYLIKWIWTHLCKKKMRRKPESFGTIGRRAADNLRRHHQYQEVMRNLVKRYVAAMIRDAKTEEGLTEENFKELKQDISSFRFEVLGLLRGSKLSTIQSANASKESSNSADSDEKSDSEEEVARQQAAGPLERNIQLESRGLASRGDLSIPGLSEQCVLVDHRERNTDTLGLQVGKRVCPFKSEKVVVEDTVPIIPKEKHAKEEDSSIDYDLNLPDTVTHEDYVTTRLSRASTVPRARDPPVATLEVLFQ
2GUC , Knot 56 122 0.73 38 83 107 
XSLTHRKFGGSGGSPFSGLSSIAVRSGSYLDAIIIDGVHHGGSGGNLSPTFTFGSGEYISNMTIRSGDYIDNISFETNMGRRFGPYGGSGGSANTLSNVKVIQINGSAGDYLDSLDIYYEQY

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 \(c\).

\(|P_{f(9MCZ_1)}(2) \setminus P_{f(8WPN_1)}(2)|=22\), \(|P_{f(8WPN_1)}(2) \setminus P_{f(9MCZ_1)}(2)|=160\). 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 1:101111010001001100010011000010110111101001011111001100011001101101101101101100101010001001100110101000010101010111000001100010111010010010001111101001111001111001001001001010110110101101101001100010111101000111101001101001001001110100111010111101101110010100110100100001101111111001011111010010101000111011110011110101111010011001
Pair \(Z_2\) Length of longest common subsequence
9MCZ_1,8WPN_1 182 4
9MCZ_1,2GUC_1 164 4
8WPN_1,2GUC_1 258 3

Newick tree

 
[
	8WPN_1:11.88,
	[
		9MCZ_1:82,2GUC_1:82
	]:37.88
]

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 \((0.85)(0.8)(\frac{1245 }{\log_{20} 1245}-\frac{330}{\log_{20}330})=239.\)
Status Protein1 Protein2 d d1/2
Query variables 9MCZ_1 8WPN_1 309 208
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]