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Parikh vectors
2LIT_1 1LTH_1 2CKX_1 Letter Amino acid
2 2 0 C Cysteine
5 8 4 H Histidine
8 25 7 L Leucine
5 5 2 Y Tyrosine
7 16 1 N Asparagine
4 19 7 D Aspartic acid
2 11 5 Q Glutamine
12 25 3 G Glycine
15 16 4 K Lycine
4 18 3 S Serine
3 12 8 R Arginine
7 19 5 E Glutamic acid
4 26 1 I Isoleucine
3 17 4 P Proline
8 35 10 A Alanine
2 8 1 M Methionine
4 7 2 F Phenylalanine
9 21 4 T Threonine
1 2 3 W Tryptophan
3 27 9 V Valine 

2LIT_1|Chain A|Cytochrome c iso-1|Saccharomyces cerevisiae (559292)
>1LTH_1|Chains A[auth R], B[auth T]|L-LACTATE DEHYDROGENASE (T- AND R- STATE TETRAMER COMPLEX)|Bifidobacterium longum subsp. longum (1679)
>2CKX_1|Chain A|TELOMERE BINDING PROTEIN TBP1|NICOTIANA TABACUM (4097)
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 \(w=f(c)\)
2LIT , Knot 59 108 0.85 40 92 105 
TEFKAGSAKKGATLFKTRCLQCHTVEKGGPHKVGPNLHGIFGRHSGQAEGYSYTDANIKKNVLWDENNMSEYLTNHAKYIPGTKMAFGGLKKEKDRNDLITYLKKATE
1LTH , Knot 137 319 0.82 40 184 308 
AETTVKPTKLAVIGAGAVGSTLAFAAAQRGIAREIVLEDIAKERVEAEVLDMQHGSSFYPTVSIDGSDDPEICRDADMVVITAGPRQKPGQSRLELVGATVNILKAIMPNLVKVAPNAIYMLITNPVDIATHVAQKLTGLPENQIFGSGTNLDSARLRFLIAQQTGVNVKNVHAYIAGEHGDSEVPLWESATIGGVPMSDWTPLPGHDPLDADKREEIHQEVKNAAYKIINGKGATNYAIGMSGVDIIEAVLHDTNRILPVSSMLKDFHGISDICMSVPTLLNRQGVNNTINTPVSDKELAALKRSAETLKETAAQFGF
2CKX , Knot 47 83 0.83 38 75 80 
RPFSVAEVEALVEAVEHLGTGRWRDVKMRAFDNADHRTYVDLKDKWKTLVHTASIAPQQRRGEPVPQDLLDRVLAAHAYWSQQ

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 \(c\).

\(|P_{f(2LIT_1)}(2) \setminus P_{f(1LTH_1)}(2)|=43\), \(|P_{f(1LTH_1)}(2) \setminus P_{f(2LIT_1)}(2)|=135\). 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 1:001011010011011000010000100111001110101111000101010000010100011100001000100010011100111111000000001100100100
Pair \(Z_2\) Length of longest common subsequence
2LIT_1,1LTH_1 178 4
2LIT_1,2CKX_1 135 2
1LTH_1,2CKX_1 177 3

Newick tree

 
[
	1LTH_1:94.78,
	[
		2LIT_1:67.5,2CKX_1:67.5
	]:27.28
]

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 \((0.85)(0.8)(\frac{427 }{\log_{20} 427}-\frac{108}{\log_{20}108})=96.6\)
Status Protein1 Protein2 d d1/2
Query variables 2LIT_1 1LTH_1 120 80.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]