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Parikh vectors
7AVE_1 6DZY_1 1TBX_1 Letter Amino acid
2 22 3 P Proline
12 43 8 A Alanine
6 51 6 I Isoleucine
2 11 2 M Methionine
10 35 3 S Serine
6 19 0 W Tryptophan
3 30 8 Y Tyrosine
7 12 3 D Aspartic acid
1 5 6 H Histidine
8 55 8 L Leucine
6 18 13 K Lycine
3 43 7 F Phenylalanine
7 35 7 T Threonine
6 38 3 V Valine
14 18 2 N Asparagine
8 13 0 C Cysteine
3 12 3 Q Glutamine
11 17 4 R Arginine
2 19 9 E Glutamic acid
13 41 4 G Glycine 

7AVE_1|Chain A|Lysozyme C|Gallus gallus (9031)
>6DZY_1|Chain A|Sodium-dependent serotonin transporter|Homo sapiens (9606)
>1TBX_1|Chains A, B|Hypothetical 11.0 kDa protein|Sulfolobus virus 1 (244589)
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 \(w=f(c)\)
7AVE , Knot 66 130 0.82 40 105 128 
GKVFGRCELAAAMKRHGLDNYRGYSLGNWVCAAKFESNFNTQATNRNTDGSTDYGILQINSRWWCNDGRTPGSRNLCNIPCSALLSSDITASVNCAKKIVSDGNGMNAWVAWRNRCKGTDVQAWIRGCRL
6DZY , Knot 212 537 0.82 40 237 490 
RETWGKKVDFLLSVIGYAVDLGNVWRFPYICYQNGGGAFLLPYTIMAIFGGIPLFYMELALGQYHRNGCISIWRKICPIFKGIGYAICIIAFYIASYYNTIMAWALYYLISSFTDQLPWTSCKNSWNTGNCTNYFSEDNITWTLHSTSPAEEFYTRHVLQIHRSKGLQDLGGISWQLALCIMLIFTVIYFSIWKGVKTSGKVVWVTATFPYIALSVLLVRGATLPGAWRGVLFYLKPNWQKLLETGVWIDAAAQIFFSLGPGFGVLLAFASYNKFNNNCYQDALVTSVVNCMTSFVSGFVIFTVLGYMAEMRNEDVSEVAKDAGPSLLFITYAEAIANMPASTFFAIIFFLMLITLGLDSSFAGLEGVITAVLDEFPHVWAKRRERFVLAVVITCFFGSLVTLTFGGAYVVKLLEEYATGPAVLTVALIEAVAVSWFYGITQFCRDVKEMLGFSPGWFWRICWVAISPLFLLFIIASFLMSPPQLRLFQYNYPYWSIILGYAIGTSSFICIPTYIAYRLIITPGTFKERIIKSITPE
1TBX , Knot 50 99 0.77 36 74 94 
MKSTPFFYPEAIVLAYLYDNEGIATYDLYKKVNAEFPMSTATFYDAKKFLIQEGFVKERQERGEKRLYLTEKGKLFAISLKTAIETYKQIKKRHHHHHH

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 \(c\).

\(|P_{f(7AVE_1)}(2) \setminus P_{f(6DZY_1)}(2)|=38\), \(|P_{f(6DZY_1)}(2) \setminus P_{f(7AVE_1)}(2)|=170\). 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 1:1011100011111000110000100110110110100010001000000100001110100011000100110001001100111000101010010011001011011111000001001011101001
Pair \(Z_2\) Length of longest common subsequence
7AVE_1,6DZY_1 208 3
7AVE_1,1TBX_1 133 3
6DZY_1,1TBX_1 193 4

Newick tree

 
[
	6DZY_1:10.29,
	[
		7AVE_1:66.5,1TBX_1:66.5
	]:42.79
]

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 \((0.85)(0.8)(\frac{667 }{\log_{20} 667}-\frac{130}{\log_{20}130})=154.\)
Status Protein1 Protein2 d d1/2
Query variables 7AVE_1 6DZY_1 192 119.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]