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Parikh vectors
5JDS_1 4CJM_1 6EIF_1 Letter Amino acid
10 11 39 L Leucine
5 3 11 M Methionine
5 8 19 Y Tyrosine
11 4 18 A Alanine
7 11 20 R Arginine
3 4 18 N Asparagine
19 7 18 S Serine
6 19 33 K Lycine
5 6 15 P Proline
12 8 15 T Threonine
5 5 24 D Aspartic acid
10 9 14 Q Glutamine
5 9 21 E Glutamic acid
16 14 25 G Glycine
8 2 11 H Histidine
2 1 4 W Tryptophan
8 8 18 V Valine
4 2 6 C Cysteine
1 4 23 I Isoleucine
4 6 16 F Phenylalanine 

5JDS_1|Chain A[auth B]|Nanobody|Camelidae (9835)
>4CJM_1|Chains A, B, C, D|FIBROBLAST GROWTH FACTOR 18|HOMO SAPIENS (9606)
>6EIF_1|Chains A, B, C, D|Dual specificity tyrosine-phosphorylation-regulated kinase 1A|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 \(w=f(c)\)
5JDS , Knot 68 146 0.77 40 105 133 
TGQVQLQESGGGLVQPGGSLRLSCAASGKMSSRRCMAWFRQAPGKERERVAKLLTTSGSTYLADSVKGRFTISQNNAKSTVYLQMNSLKPEDTAMYYCAADSFEDPTCTLVTSSGAFQYWGQGTQVTVSSGSMDPGGSHHHHHHHH
4CJM , Knot 72 141 0.84 40 112 137 
KQLRLYQLYSRTSGKHIQVLGRRISARGEDGDKYAQLLVETDTFGSQVRIKGKETEFYLCMNRKGKLVGKPDGTSKECVFIEKVLENNYTALMSAKYSGWYVGFTKKGRPRKGPKTRENQQDVHFMKRYPKGQPELQKPFK
6EIF , Knot 162 368 0.86 40 228 355 
GASDSSHKKERKVYNDGYDDDNYDYIVKNGEKWMDRYEIDSLIGKGSFGQVVKAYDRVEQEWVAIKIIKNKKAFLNQAQIEVRLLELMNKHDTEMKYYIVHLKRHFMFRNHLCLVFEMLSYNLYDLLRNTNFRGVSLNLTRKFAQQMCTALLFLATPELSIIHCDLKPENILLCNPKRSAIKIVDFGSSCQLGQRIYQYIQSRFYRSPEVLLGMPYDLAIDMWSLGCILVEMHTGEPLFSGANEVDQMNKIVEVLGIPPAHILDQAPKARKFFEKLPDGTWNLKKTKDGKREYKPPGTRKLHNILGVETGGPGGRRAGESGHTVADYLKFKDLILRMLDYDPKTRIQPYYALQHSFFKKTADEGTNTS

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 \(c\).

\(|P_{f(5JDS_1)}(2) \setminus P_{f(4CJM_1)}(2)|=70\), \(|P_{f(4CJM_1)}(2) \setminus P_{f(5JDS_1)}(2)|=77\). 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 1:01010100011111011101010011010100000111100111000001101100010001100101010100001000101010010100011000110010010001100011100110100101001010111000000000
Pair \(Z_2\) Length of longest common subsequence
5JDS_1,4CJM_1 147 3
5JDS_1,6EIF_1 205 4
4CJM_1,6EIF_1 184 4

Newick tree

 
[
	6EIF_1:10.14,
	[
		5JDS_1:73.5,4CJM_1:73.5
	]:30.64
]

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 \((0.85)(0.8)(\frac{287 }{\log_{20} 287}-\frac{141}{\log_{20}141})=45.2\)
Status Protein1 Protein2 d d1/2
Query variables 5JDS_1 4CJM_1 55 54.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]