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Parikh vectors
8OSH_1 6FOF_1 2XVR_1 Letter Amino acid
25 9 16 R Arginine
11 17 15 N Asparagine
3 1 2 C Cysteine
11 9 10 F Phenylalanine
7 2 10 M Methionine
5 7 10 Y Tyrosine
27 20 33 G Glycine
11 5 7 H Histidine
23 10 17 I Isoleucine
39 15 28 L Leucine
29 9 18 D Aspartic acid
13 6 11 Q Glutamine
22 8 21 K Lycine
35 14 29 V Valine
21 7 23 T Threonine
1 2 0 W Tryptophan
27 14 51 A Alanine
32 6 20 E Glutamic acid
20 22 9 P Proline
18 13 15 S Serine 

8OSH_1|Chains A, B, C, D, E|Magnesium-chelatase subunit ChlI|Nostoc sp. PCC 7120 = FACHB-418 (103690)
>6FOF_1|Chains A, B, C, D, E, F, G, H, I, J, K, L|Galectin-3,Galectin-3|Homo sapiens (9606)
>2XVR_1|Chains A, B, C, D, E, F, G|MAJOR CAPSID PROTEIN 10A|ENTEROBACTERIA PHAGE T7 (10760)
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 \(w=f(c)\)
8OSH , Knot 155 380 0.80 40 202 360 
MHHHHHHTPTAQTTASARRVVFPFTAIVGQEEMKLALLLNVIDPKIGGVMIMGDRGTGKSTTIRALADLLPEIPVVANDPFNSDPSDPDLMSDEVRQKSGTGAEIPIEFKKVQMVDLPLGATEDRVCGTIDIEKALSEGVKAFEPGLLAKANRGILYVDEVNLLDDHLVDVLLDSAASGWNTVEREGISIRHPARFVLVGSGNPEEGELRPQLLDRFGMHAEIHTVKEPALRVQIVEQRSEFDQNPPTFLEKYNPEQTALQKKIVEAQKLLPEVKLDYDLRVKISEVCSELDVDGLRGDIVTNRAAKALTAYEGRTEVTVDDIRRVITLCLRHRLRKDPLESIDSGYKVEKVFARIFGVELLEDDSSQKNGAGQIKTGVR
6FOF , Knot 92 196 0.82 40 140 191 
ADNFSLHDALSGSGNPNPQGWPGVYPGPPSGPGAYPSSGQPSATGAYPATGPYGAPAGPLIVPYNLPLPGGVVPRMLITILGTVKPNANRIALDFQRGNDVAFHFNPRFNENNRRVIVCNTKLDNNWGREERQSVFPFESGKPFKIQVLVEPDHFKVAVNDAHLLQYNHRVKKLNEISKLGISGDIDLTSASYTMI
2XVR , Knot 144 345 0.81 38 194 327 
MASMTGGQQMGTNQGKGVVAAGDKLALFLKVFGGEVLTAFARTSVTTSRHMVRSISSGKSAQFPVLGRTQAAYLAPGENLDDKRKDIKHTEKVITIDGLLTADVLIYDIEDAMNHYDVRSEYTSQLGESLAMAADGAVLAEIAGLCNVESKYNENIEGLGTATVIETTQNKAALTDQVALGKEIIAALTKARAALTKNYVPAADRVFYCDPDSYSAILAALMPNAANYAALIDPEKGSIRNVMGFEVVEVPHLTAGGAGTAREGTTGQKHVFPANKGEGNVKVAKDNVIGLFMHRSAVGTVKLRDLALERARRANFQADQIIAKYAMGHGGLRPEAAGAVVFKVE

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 \(c\).

\(|P_{f(8OSH_1)}(2) \setminus P_{f(6FOF_1)}(2)|=111\), \(|P_{f(6FOF_1)}(2) \setminus P_{f(8OSH_1)}(2)|=49\). 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 1:10000000101000101001111101111000101111101101011111111001010000101110111011111001100010010110001000010110111010010110111110000101010100110011011011111010011101001011000110111001101100100011010011011111010100101010110011101010010011101011000001000110110000100011000110100111010100010101001000101011010110001101101001000101001001101010001000110010010010011101111011000000001110100110
Pair \(Z_2\) Length of longest common subsequence
8OSH_1,6FOF_1 160 5
8OSH_1,2XVR_1 140 4
6FOF_1,2XVR_1 166 4

Newick tree

 
[
	6FOF_1:85.00,
	[
		8OSH_1:70,2XVR_1:70
	]:15.00
]

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 \((0.85)(0.8)(\frac{576 }{\log_{20} 576}-\frac{196}{\log_{20}196})=108.\)
Status Protein1 Protein2 d d1/2
Query variables 8OSH_1 6FOF_1 133 101.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]