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Parikh vectors
1JLM_1 7LCV_1 6EWT_1 Letter Amino acid
10 7 3 D Aspartic acid
15 6 2 F Phenylalanine
11 39 5 S Serine
14 5 1 R Arginine
10 7 5 N Asparagine
16 5 4 I Isoleucine
14 13 7 K Lycine
3 2 1 M Methionine
11 19 3 T Threonine
0 5 1 W Tryptophan
15 7 9 E Glutamic acid
4 4 1 H Histidine
9 11 1 P Proline
3 11 1 Y Tyrosine
13 21 2 V Valine
9 14 3 A Alanine
1 5 0 C Cysteine
9 7 4 Q Glutamine
12 23 1 G Glycine
13 16 8 L Leucine 

1JLM_1|Chain A|INTEGRIN|Homo sapiens (9606)
>7LCV_1|Chain A|Immunoglobulin heavy chain Fd fragment|Homo sapiens (9606)
>6EWT_1|Chain A|NRPS Kj12B-NDD|Xenorhabdus stockiae (351614)
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 \(w=f(c)\)
1JLM , Knot 92 192 0.84 38 141 189 
GCPQEDSDIAFLIDGSGSIIPHDFRRMKEFVSTVMEQLKKSKTLFSLMQYSEEFRIHFTFKEFQNNPNPRSLVKPITQLLGRTHTATGIRKVVRELFNITNGARKNAFKILVVITDGEKFGDPLGYEDVIPEADREGVIRYVIGVGDAFRSEKSRQELNTIASKPPRDHVFQVNNFEALKTIQNQLREKIFA
7LCV , Knot 100 227 0.79 40 141 214 
EVQLVESGGGLVQPGGSLRLSCAASGFTFSSYAMSWVRQAPGKGLEWVSAISGSGGSSHYTDSVKGRFTISRDNSKNTLWLQMNSLRAEDTAIYYCAKTSGSYYYHYEIDVWGQGTTVTVSSASTKGPSVFPLAPSSKSTSGGTAALGCLVKDYFPEPVTVSWNSGALTSGVHTFPAVLQSSGLYSLSSVVTVPSSSLGTQTYICNVNHKPSNTKVDKKVEPKSCDK
6EWT , Knot 36 62 0.79 38 54 60 
MKNAAKIVNEALNQGITLFVSDNKLKYKTNRDSIPSELLEEWKQHKQELIDFLTQLESEEES

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 \(c\).

\(|P_{f(1JLM_1)}(2) \setminus P_{f(7LCV_1)}(2)|=92\), \(|P_{f(7LCV_1)}(2) \setminus P_{f(1JLM_1)}(2)|=92\). 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 1:101000001111101010111001001001100110010000011011000001010101001000101001101100111000010110011001101001100011011111001001101110001110100011100111110110000000010011001100011010010110010001000111
Pair \(Z_2\) Length of longest common subsequence
1JLM_1,7LCV_1 184 3
1JLM_1,6EWT_1 127 3
7LCV_1,6EWT_1 153 2

Newick tree

 
[
	7LCV_1:90.55,
	[
		1JLM_1:63.5,6EWT_1:63.5
	]:27.05
]

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 \((0.85)(0.8)(\frac{419 }{\log_{20} 419}-\frac{192}{\log_{20}192})=66.9\)
Status Protein1 Protein2 d d1/2
Query variables 1JLM_1 7LCV_1 84 79.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]