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Parikh vectors
3PHW_1 6IPV_1 3HDO_1 Letter Amino acid
14 17 36 A Alanine
11 18 27 G Glycine
6 10 7 M Methionine
14 18 30 E Glutamic acid
8 4 12 F Phenylalanine
12 10 15 T Threonine
1 3 4 C Cysteine
5 15 11 H Histidine
14 11 21 S Serine
3 7 3 W Tryptophan
6 11 10 K Lycine
6 9 22 P Proline
10 13 29 R Arginine
6 10 12 N Asparagine
14 17 16 D Aspartic acid
7 7 8 Q Glutamine
12 13 23 I Isoleucine
18 18 36 L Leucine
8 14 19 Y Tyrosine
10 14 19 V Valine 

3PHW_1|Chains A, C, E, G|RNA-directed RNA polymerase L|Crimean-Congo hemorrhagic fever virus strain IbAr10200 (652961)
>6IPV_1|Chains A, B, C, D|CqsB2|Streptomyces exfoliatus (1905)
>3HDO_1|Chains A, B|Histidinol-phosphate aminotransferase|Geobacter metallireducens GS-15 (269799)
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 \(w=f(c)\)
3PHW , Knot 93 185 0.87 40 144 180 
GPMDFLRSLDWTQVIAGQYVSNPRFNISDYFEIVRQPGDGNCFYHSIAELTMPNKTDHSYHYIKRLTESAARKYYQEEPEARLVGLSLEDYLKRMLSDNEWGSTLEASMLAKEMGITIIIWTVAASDEVEAGIKFGDGDVFTAVNLLHSGQTHFDALRILPQFETDTREALSLMDRVIAVDQLTS
6IPV , Knot 116 239 0.88 40 169 229 
MSQRVPDESGLAQNYVLDRSDLQGLDLVWNENTGMDDMMKLMESKTKETYDHGEIFGQYCSLAEHINVPYDIVFEYAANARSLEEWTYSIRNMKHLGGGLYRADEMIQPNTDIYIRAEAQKGPEHGLVVYPCAWDQGHELWMRYYMTIIDSSKVLDKPGTVVLWTNCKHPYYDRSTENVPDYIAEGRARTDRVWVGDIWPVFHAGHSIEMGNLKRILEHRFGAGKAKLAAALEHHHHHH
3HDO , Knot 150 360 0.81 40 198 336 
MSLIPLRQNIASMKGYIPGYQPPDIASWIKLNTNENPYPPSPEVVKAILEELGPDGAALRIYPSASSQKLREVAGELYGFDPSWIIMANGSDEVLNNLIRAFAAEGEEIGYVHPSYSYYGTLAEVQGARVRTFGLTGDFRIAGFPERYEGKVFFLTTPNAPLGPSFPLEYIDELARRCAGMLVLDETYAEFAESNALELVRRHENVVVTRTLSKSYSLAGMRIGLAIARPEVIAALDKIRDHYNLDRLAQAACVAALRDQAYLSECCRRIRETREWFTTELRSIGYDVIPSQGNYLFATPPDRDGKRVYDGLYARKVLVRHFSDPLLAHGMRISIGTREEMEQTLAALKEIGEGHHHHHH

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 \(c\).

\(|P_{f(3PHW_1)}(2) \setminus P_{f(6IPV_1)}(2)|=74\), \(|P_{f(6IPV_1)}(2) \setminus P_{f(3PHW_1)}(2)|=99\). 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 1:11101100101001111001001010100010110011010010001101011000000000100100011000000010101111010001001100001100101011100111011110111000101110110101101101100100010110111010000001101100111100100
Pair \(Z_2\) Length of longest common subsequence
3PHW_1,6IPV_1 173 3
3PHW_1,3HDO_1 174 4
6IPV_1,3HDO_1 159 6

Newick tree

 
[
	3PHW_1:89.03,
	[
		6IPV_1:79.5,3HDO_1:79.5
	]:9.53
]

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 \((0.85)(0.8)(\frac{424 }{\log_{20} 424}-\frac{185}{\log_{20}185})=70.5\)
Status Protein1 Protein2 d d1/2
Query variables 3PHW_1 6IPV_1 89 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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]