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Parikh vectors
6YJK_1 4DHT_1 1FHF_1 Letter Amino acid
10 3 3 H Histidine
15 5 20 F Phenylalanine
19 17 3 K Lycine
23 10 26 T Threonine
25 24 18 A Alanine
5 2 8 C Cysteine
27 29 9 E Glutamic acid
35 24 35 L Leucine
12 13 23 G Glycine
10 9 3 M Methionine
17 13 15 R Arginine
21 7 30 N Asparagine
15 14 20 D Aspartic acid
13 7 13 Q Glutamine
9 10 5 Y Tyrosine
19 12 17 V Valine
15 10 16 I Isoleucine
13 5 17 P Proline
21 19 22 S Serine
1 2 1 W Tryptophan 

6YJK_1|Chain A|CYRI-B (FAM49B)|Rhincodon typus (259920)
>4DHT_1|Chain A|14-3-3 PROTEIN SIGMA|Homo sapiens (9606)
>1FHF_1|Chains A, B, C|SEED COAT PEROXIDASE|Glycine max (3847)
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 \(w=f(c)\)
6YJK , Knot 146 325 0.86 40 203 309 
SMGNLIKVLTRDIDHNASHFFLDFENAQPTEAEREIFNQVNVVLKDAEGILNDLQSYRGAGHEIREAIQHPNDENLQEKAWSAVCPLVGKLKKFYEFSQRLEAALHGLLGALTSTPYSPTQHLEREQALAKQFAEILHFTLRFDELKMTNPAIQNDFSYYRRTLSRMRINNVPAEGENEVNNELANRMSLFYAEATPMLKTLSDATTKFVSDNKSLPIENTTDCLSTMASVCRVMLETPEYRSRFASEETVSFCLRVMVGVIILYDHVHPVGAFAKTSKIDMKGCIKVLKDQPPNSVEGLLNALRYTTKHLNDETTSKQIKTMLQ
4DHT , Knot 109 235 0.84 40 164 228 
AMGSMERASLIQKAKLAEQAERYEDMAAFMKGAVEKGEELSCEERNLLSVAYKNVVGGQRAAWRVLSSIEQKSNEEGSEEKGPEVREYREKVETELQGVCDTVLGLLDSHLIKEAGDAESRVFYLKMKGDYYRYLAEVATGDDKKRIIDSARSAYQEAMDISKKEMPPTNPIRLGLALNFSVFHYEIANSPEEAISLAKTTFDEAMADLHTLSEDSYKDSTLIMQLLRDNLTLWT
1FHF , Knot 132 304 0.82 40 182 287 
QLTPTFYRETCPNLFPIVFGVIFDASFTDPRIGASLMRLHFHDCFVQGCDGSVLLNNTDTIESEQDALPNINSIRGLDVVNDIKTAVENSCPDTVSCADILAIAAEIASVLGGGPGWPVPLGRRDSLTANRTLANQNLPAPFFNLTQLKASFAVQGLNTLDLVTLSGGHTFGRARCSTFINRLYNFSNTGNPDPTLNTTYLEVLRARCPQNATGDNLTNLDLSTPDQFDNRYYSNLLQLNGLLQSDQELFSTPGADTIPIVNSFSSNQNTFFSNFRVSMIKMGNIGVLTGDEGEIRLQCNFVNG

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 \(c\).

\(|P_{f(6YJK_1)}(2) \setminus P_{f(4DHT_1)}(2)|=93\), \(|P_{f(4DHT_1)}(2) \setminus P_{f(6YJK_1)}(2)|=54\). 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 1:0110110110001000100111010010100100011001011100101110010000111001001100100001000110110111101001001000101110111111000100100010000111001101101010100101001110001000000100101001110100010001100101101010111001001000110000011100000010011010011100100000110000101010111111110001011111100001010101011000110010111011000000100000000100110
Pair \(Z_2\) Length of longest common subsequence
6YJK_1,4DHT_1 147 3
6YJK_1,1FHF_1 149 3
4DHT_1,1FHF_1 156 4

Newick tree

 
[
	1FHF_1:77.17,
	[
		6YJK_1:73.5,4DHT_1:73.5
	]:3.67
]

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 \((0.85)(0.8)(\frac{560 }{\log_{20} 560}-\frac{235}{\log_{20}235})=92.5\)
Status Protein1 Protein2 d d1/2
Query variables 6YJK_1 4DHT_1 114 98
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]