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Parikh vectors
9CZO_1 5XCB_1 3EXC_1 Letter Amino acid
121 16 11 L Leucine
68 16 2 A Alanine
51 18 6 E Glutamic acid
73 23 8 I Isoleucine
74 27 4 S Serine
58 28 4 N Asparagine
29 0 0 C Cysteine
30 4 3 M Methionine
17 1 2 W Tryptophan
42 2 9 R Arginine
34 12 3 Q Glutamine
22 10 1 H Histidine
60 8 2 F Phenylalanine
42 8 1 P Proline
56 29 2 T Threonine
33 20 1 Y Tyrosine
70 25 10 V Valine
62 23 9 D Aspartic acid
60 18 6 G Glycine
54 37 7 K Lycine 

9CZO_1|Chains A, B, C, D|Isoform 5 of Calcium-activated potassium channel subunit alpha-1|Homo sapiens (9606)
>5XCB_1|Chain A|Probable surface protein|Clostridium perfringens str. 13 (195102)
>3EXC_1|Chain A[auth X]|Uncharacterized protein|Sulfolobus solfataricus (2287)
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 \(w=f(c)\)
9CZO , Knot 391 1056 0.86 40 340 956 
MDALIIPVTMEVPCDSRGQRMWWAFLASSMVTFFGGLFIILLWRTLKYLWTVCCHCGGKTKEAQKINNGSSQADGTLKPVDEKEEAVAAEVGWMTSVKDWAGVMISAQTLTGRVLVVLVFALSIGALVIYFIDSSNPIESCQNFYKDFTLQIDMAFNVFFLLYFGLRFIAANDKLWFWLEVNSVVDFFTVPPVFVSVYLNRSWLGLRFLRALRLIQFSEILQFLNILKTSNSIKLVNLLSIFISTWLTAAGFIHLVENSGDPWENFQNNQALTYWECVYLLMVTMSTVGYGDVYAKTTLGRLFMVFFILGGLAMFASYVPEIIELIGNRKKYGGSYSAVSGRKHIVVCGHITLESVSNFLKDFLHKDRDDVNVEIVFLHNISPNLELEALFKRHFTQVEFYQGSVLNPHDLARVKIESADACLILANKYCADPDAEDASNIMRVISIKNYHPKIRIITQMLQYHNKAHLLNIPSWNWKEGDDAICLAELKLGFIAQSCLAQGLSTMLANLFSMRSFIKIEEDTWQKYYLEGVSNEMYTEYLSSAFVGLSFPTVCELCFVKLKLLMIAIEYKSANRESRILINPGNHLKIQEGTLGFFIASDAKEVKRAFFYCKACHDDITDPKRIKKCGCKRLEDEQPSTLSPKKKQRNGGMRNSPNTSPKLMRHDPLLIPGNDQIDNMDSNVKKYDSTGMFHWCAPKEIEKVILTRSEAAMTVLSGHVVVCIFGDVSSALIGLRNLVMPLRASNFHYHELKHIVFVGSIEYLKREWETLHNFPKVSILPGTPLSRADLRAVNINLCDMCVILSANQNNIDDTSLQDKECILASLNIKSMQFDDSIGVLQANSQGFTPPGMDRSSPDNSPVHGMLRQPSITTGVNIPIITELVNDTNVQFLDQDDDDDPDTELYLTQPFACGTAFAVSVLDSLMSATYFNDNILTLIRTLVTGGATPELEALIAEENALRGGYSTPQTLANRDRCRVAQLALLDGPFADLGDGGCYGDLFCKALKTYNMLCFGIYRLRDAHLSTPSQCTKRYVITNPPYEFELVPTDLIFCLMQFD
5XCB , Knot 136 325 0.80 38 170 299 
MNHKVHHHHHHIEGRHMTPSISKDAPIKGSITISKKGATFTAYKLLDAIKSGDAYEYSVNSDLKDFFNNSNYGSYSQESIQKLNGEQVKEFAINLHKYILENKKSGQELKDGQKNTVDLGYYLVTETSSDSEGAAVASTPIIVSVPQVSGDSWNYDVTINPKDNTPILEKNIVKENQRVKTSSENIGDVVKYEVKASIPVYQKNAQNIMYKFTDTMSKGLTYDEKTGFKVTSGDKVFAKDTDYTVDVKKQEDGSTVITINFVYENIKAYAETGITLNYQATLNKDAVISNKENLGNTNNIQLDYTNNPHVKDSYKKLTDKVTTYT
3EXC , Knot 48 91 0.79 38 73 88 
FQGMKLLVVYDVSDDSKRNKLANNLKKLGLERIQRSAFEGDMDSQRMKDLVRVVKLIVDTNTDIVHIIPLGIRDWERRIVIGREGLEEWLV

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 \(c\).

\(|P_{f(9CZO_1)}(2) \setminus P_{f(5XCB_1)}(2)|=181\), \(|P_{f(5XCB_1)}(2) \setminus P_{f(9CZO_1)}(2)|=11\). 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 1:101111110101100001001111111001101111111111100100110100001100001001001000101010110000011110111100100111111010010101111111110111111011000011000001000101010111011111011101111000111110100110110111111010100011110110110110100110110110000010110110111001101111101100010110010000110010010111101001101010100011011111111111111100110110111000001100011010001110101010010011001100000010101111001010101011100010010100101101001101010010101111000010101001001101101000010101100110000010110110101001001101101011111000110110011101101001101000010000101100010000100111110110100101101011111100001000001110110010100101111110010010011100010000100100100010001000010010100000011100010001011000111111000100100010000001110101100100111000011101101011101110100111110011111010010000100111110100100010010011010111101100101011010100101110100001000010000011101010010100011110100011011110000100011011100101001101111001100001011000000010001010011101011110110011010010001101100110111010101111000110110001001100000011011110111101101100101100110000110111001001010010000000110011001011100111011010
Pair \(Z_2\) Length of longest common subsequence
9CZO_1,5XCB_1 192 4
9CZO_1,3EXC_1 277 3
5XCB_1,3EXC_1 159 3

Newick tree

 
[
	9CZO_1:12.71,
	[
		5XCB_1:79.5,3EXC_1:79.5
	]:50.21
]

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 \((0.85)(0.8)(\frac{1381 }{\log_{20} 1381}-\frac{325}{\log_{20}325})=274.\)
Status Protein1 Protein2 d d1/2
Query variables 9CZO_1 5XCB_1 353 227.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]