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Parikh vectors
7CJG_1 2BEX_1 6IFG_1 Letter Amino acid
17 5 17 H Histidine
18 12 7 I Isoleucine
12 14 37 P Proline
21 45 31 S Serine
14 3 12 Y Tyrosine
7 6 11 W Tryptophan
33 32 46 A Alanine
27 27 19 D Aspartic acid
16 24 22 Q Glutamine
15 35 27 E Glutamic acid
20 92 56 L Leucine
9 16 6 K Lycine
11 4 15 F Phenylalanine
14 24 35 R Arginine
12 17 6 N Asparagine
35 32 47 G Glycine
19 25 35 V Valine
4 32 1 C Cysteine
10 2 4 M Methionine
19 13 40 T Threonine 

7CJG_1|Chains A, B|Glutamine cyclotransferase-related protein|Porphyromonas gingivalis (strain ATCC BAA-308 / W83) (242619)
>2BEX_1|Chains A, B|RIBONUCLEASE INHIBITOR|HOMO SAPIENS (9606)
>6IFG_1|Chains A, B|Zinc metalloprotease|Deinococcus radiodurans (strain ATCC 13939 / DSM 20539 / JCM 16871 / LMG 4051 / NBRC 15346 / NCIMB 9279 / R1 / VKM B-1422) (243230)
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 \(w=f(c)\)
7CJG , Knot 142 333 0.82 40 199 322 
MGSSHHHHHHSSGLVPRGSHMGNNTSETQGDRTEQAETVQADLFSADSAYTFVQRQVNFGPRIPGTAPHRACGDWLVATLRSFGAAVQEQTAEIKAHDGTMLPMRNIIASYRPEATGRMLLMAHWDTRPVCDQDANPAMHTETFDGADDGGSGVGVLLEIARYLGQQKDLGMGIDIVFFDTEDYGSYGDDESWCLGSQYWSRNPHVAGYKAEAGILLDMVGAKGATFYWEYFSKSYAPGLISAVWQTAAALGYGNYFIQADGGALTDDHVPVIKNLGIPCIDIINYSSKNEHGFGDHWHTQRDNMQIIDKNVLDAVGETVIRYLDEQVKAASH
2BEX , Knot 172 460 0.76 40 186 386 
SLDIQSLDIQCEELSDARWAELLPLLQQCQVVRLDDCGLTEARCKDISSALRVNPALAELNLRSNELGDVGVHCVLQGLQTPSCKIQKLSLQNCCLTGAGCGVLSSTLRTLPTLQELHLSDNLLGDAGLQLLCEGLLDPQCRLEKLQLEYCSLSAASCEPLASVLRAKPDFKELTVSNNDINEAGVRVLCQGLKDSPCQLEALKLESCGVTSDNCRDLCGIVASKASLRELALGSNKLGDVGMAELCPGLLHPSSRLRTLWIWECGITAKGCGDLCRVLRAKESLKELSLAGNELGDEGARLLCETLLEPGCQLESLWVKSCSFTAACCSHFSSVLAQNRFLLELQISNNRLEDAGVRELCQGLGQPGSVLRVLWLADCDVSDSSCSSLAATLLANHSLRELDLSNNCLGDAGILQLVESVRQPGCLLEQLVLYDIYWSEEMEDRLQALEKDKPSLRVIS
6IFG , Knot 182 474 0.78 40 201 417 
MASWSHPQFEKGSSHHHHHHSSGSGGGGGENLYFQGSQSVGDSIFPSLGQRGLDVQHYDLHLTVPRPGEPHLSGDVTLTVGAREPLSRIVLDLLGPRVSAAQWNGQRVRWVQTAQKVEVTLPRPLRPGETGRLRLIYAGTPELSGDPGLPIRPGWQNEAGLSYSLSEPHGTRGFLPCNDHPSDPATFTVRVTVPASASAAASGLFTTQTERNGLKTLTFTQRVPVPTYALGLIVGPLERRTAPDVQLGTQTVHRRDIYAAGLPAGTTVPEGETARMLRVLSDWFGPYPDEVYGVALLPVRQLALETAGLTTMPATSNRERVRLHALAHQWFGDQVTLADWADTWLSEGFATYAELLWAESQGEDGQAMAADWYARLSVLPSRPLRATREEEIFDASAYFRGALALHALRLKVGDAAFGQFLHSYVKTFTGRPVSTTALLTLVKTQLGAEAEQTLRVWVEGRTLPPLPEPVGAPV

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 \(c\).

\(|P_{f(7CJG_1)}(2) \setminus P_{f(2BEX_1)}(2)|=98\), \(|P_{f(2BEX_1)}(2) \setminus P_{f(7CJG_1)}(2)|=85\). 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 1:110000000000111101001100000001000001001010110100100110001011101110110010101111010011111000010101001011110011100010101011111010001100001011100001011001101111110110011000011111011110000010010000101100010001011100101111101111011010100100001111101110011111010011010111100001111001111010110000000011100100000010110001101110011001000101100
Pair \(Z_2\) Length of longest common subsequence
7CJG_1,2BEX_1 183 4
7CJG_1,6IFG_1 164 12
2BEX_1,6IFG_1 159 4

Newick tree

 
[
	7CJG_1:89.20,
	[
		6IFG_1:79.5,2BEX_1:79.5
	]:9.70
]

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 \((0.85)(0.8)(\frac{793 }{\log_{20} 793}-\frac{333}{\log_{20}333})=125.\)
Status Protein1 Protein2 d d1/2
Query variables 7CJG_1 2BEX_1 151 135
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]