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Parikh vectors
7NDH_1 1DZD_1 2DAM_1 Letter Amino acid
8 6 3 N Asparagine
2 3 1 C Cysteine
3 5 2 H Histidine
14 15 6 L Leucine
14 8 1 K Lycine
3 1 1 M Methionine
10 5 2 P Proline
6 4 3 A Alanine
11 9 9 E Glutamic acid
3 8 4 T Threonine
3 1 1 W Tryptophan
3 6 8 Q Glutamine
11 5 2 I Isoleucine
9 10 8 S Serine
3 7 0 Y Tyrosine
9 12 7 G Glycine
17 7 4 D Aspartic acid
10 4 1 F Phenylalanine
15 5 1 V Valine
15 6 3 R Arginine 

7NDH_1|Chains A, B|Probable ribonuclease ZC3H12C|Mus musculus (10090)
>1DZD_1|Chain A|ACIDIC FIBROBLAST GROWTH FACTOR|HOMO SAPIENS (9606)
>2DAM_1|Chain A|ETEA protein|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 \(w=f(c)\)
7NDH , Knot 81 169 0.82 40 123 164 
DDGENLRPVVIDGSNVAMSHGNKEVFSCRGIKLAVDWFLERGHKDITVFVPAWRKEQSRPDALITDQEILRKLEKEKILVFTPSRRVQGRRVVCYDDRFIVKLAFESDGIIVSNDNYRDLANEKPEWKKFIDERLLMYSFVNDKFMPPDDPLGRHGPSLDNFLRKKPIV
1DZD , Knot 64 127 0.81 40 101 123 
LYCSNGGHFLRILPDGTVDGTRDRSDQHIQLQLSAESVGEVYIKSTETGQYLAMDTDGLLYGSQTPNEECLFLERLEENHYNTYISKKHAEKNWFVGLKKNGSCKRGPRTHYGQKAILFLPLPVSSD
2DAM , Knot 37 67 0.77 38 52 61 
GSSGSSGAPEERDLTQEQTEKLLQFQDLTGIESMDQCRHTLEQHNWNIEAAVQDRLNEQEGSGPSSG

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 \(c\).

\(|P_{f(7NDH_1)}(2) \setminus P_{f(1DZD_1)}(2)|=85\), \(|P_{f(1DZD_1)}(2) \setminus P_{f(7NDH_1)}(2)|=63\). 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 1:0010010111101001110010001100011011101110010001011111100000010111000011001000011110100010100110000011101110001111000000011000101001100011100110001111001110011010011000111
Pair \(Z_2\) Length of longest common subsequence
7NDH_1,1DZD_1 148 4
7NDH_1,2DAM_1 129 3
1DZD_1,2DAM_1 111 2

Newick tree

 
[
	7NDH_1:73.46,
	[
		2DAM_1:55.5,1DZD_1:55.5
	]:17.96
]

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 \((0.85)(0.8)(\frac{296 }{\log_{20} 296}-\frac{127}{\log_{20}127})=52.5\)
Status Protein1 Protein2 d d1/2
Query variables 7NDH_1 1DZD_1 71 60.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]