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Parikh vectors
6UZA_1 6AEK_1 8JLA_1 Letter Amino acid
38 40 6 G Glycine
26 53 5 P Proline
48 37 6 V Valine
33 27 6 Q Glutamine
13 11 0 W Tryptophan
31 41 3 Y Tyrosine
69 46 7 E Glutamic acid
18 28 3 H Histidine
49 33 4 F Phenylalanine
39 40 4 D Aspartic acid
12 17 2 C Cysteine
58 37 7 I Isoleucine
97 89 11 L Leucine
62 41 7 K Lycine
61 23 12 A Alanine
32 30 14 R Arginine
44 36 1 N Asparagine
27 12 3 M Methionine
63 65 5 S Serine
27 32 6 T Threonine 

6UZA_1|Chains A, B, C, D|Short transient receptor potential channel 6|Homo sapiens (9606)
>6AEK_1|Chain A|Ectonucleotide pyrophosphatase/phosphodiesterase 1, isoform CRA_d|Mus musculus (10090)
>8JLA_1|Chains A, E|Histone H3.1|Homo sapiens (9606)
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 \(w=f(c)\)
6UZA , Knot 326 847 0.86 40 308 780 
AYMFSDRSTSLSIEEERFLDAAEYGNIPVVRKMLEECHSLNVNCVDYMGQNALQLAVANEHLEITELLLKKENLSRVGDALLLAISKGYVRIVEAILSHPAFAEGKRLATSPSQSELQQDDFYAYDEDGTRFSHDVTPIILAAHCQEYEIVHTLLRKGARIERPHDYFCKCNDCNQKQKHDSFSHSRSRINAYKGLASPAYLSLSSEDPVMTALELSNELAVLANIEKEFKNDYKKLSMQCKDFVVGLLDLCRNTEEVEAILNGDVETLQSGDHGRPNLSRLKLAIKYEVKKFVAHPNCQQQLLSIWYENLSGLRQQTMAVKFLVVLAVAIGLPFLALIYWFAPCSKMGKIMRGPFMKFVAHAASFTIFLGLLVMNAADRFEGTKLLPNETSTDNAKQLFRMKTSCFSWMEMLIISWVIGMIWAECKEIWTQGPKEYLFELWNMLDFGMLAIFAASFIARFMAFWHASKAQSIIDANDTLKDLTKVTLGDNVKYYNLARIKWDPSDPQIISEGLYAIAVVLSFSRIAYILPANESFGPLQISLGRTVKDIFKFMVIFIMVFVAFMIGMFNLYSYYIGAKQNEAFTTVEESFKTLFWAIFGLSEVKSVVINYNHKFIENIGYVLYGVYNVTMVIVLLNMLIAMINSSFQEIEDDADVEWKFARAKLWFSYFEEGRTLPVPFNLVPSPKSLFYLLLKLKKWISELFQGHKKGFQEDAEMNKINEEKKLGILGSHEDLSKLSLDKKQVGHNKQPSIRSSEDFHLNSFNNPPRQYQKIMKRLIKRYVLQAQIDKESDEVNEGELKEIKQDISSLRYELLEEKSQNTEDLAELIRELGEKLSMEPNQEETNR
6AEK , Knot 287 738 0.85 40 299 677 
GPKSWVEETCESIDTPECPAEFESPPTLLFSLDGFRAEYLHTWGGLLPVISKLKNCGTYTKNMRPMYPTKAFPNHYSIVTGLYPESHGIIDNKMYDPKMNASFSLKSKEKFNPLWYKGQPIWVTANHQEVKSGTYFWPGSDVEIDGILPDIYKVYNGSVPFEERILAVLEWLQLPSHERPHFYTLYLEEPDSSGHSHGPVSSEVIKALQKVDRLVGMLMDGLKDLGLDKCLNLILISDHGMEQGSCKKYVYLNKYLGDVNNVKVVYGPAARLRPTDVPETYYSFNYEALAKNLSCREPNQHFRPYLKPFLPKRLHFAKSDRIEPLTFYLDPQWQLALNPSERKYCGSGFHGSDNLFSNMQALFIGYGPAFKHGAEVDSFENIEVYNLMCDLLGLIPAPNNGSHGSLNHLLKKPIYNPSHPKEEGFLSQCPIKSTSNDLGCTCDPWIVPIKDFEKQLNLTTEDDDIYHMTVPYGRPRILLKQHRVCLLQQQQFLTGYSLDLLMPLWASYTFLSNDQFSRDDFSNCLYQDLRIPLSPVHKCSYYKSNSKLSYGFLTPPRLNRVSNHIYSEALLTSNIVPMYQSFQVIWHYLHDTLLQRYAHERNGINVVSGPVFDFDYDGRYDSLEILKQNSRVIRSQEILIPTHFFIVLTSCKQLSETPLECSALESSAYILPHRPDNIESCTHGKRESSWVEELLTLHRARVTDVELITGLSFYQDRQESVSELLRLKTHLPIFSQED
8JLA , Knot 59 112 0.82 38 99 109 
GSHMSAPATGGVKKPHRYRPGTVALREIRRYQKSTELLIRKLPFQRLVREIAQDFKTDLRFQSSAVMALQEACEAYLVGLFEDTNLCAIHAKRVTIMPKDIQLARRIRGERA

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 \(c\).

\(|P_{f(6UZA_1)}(2) \setminus P_{f(6AEK_1)}(2)|=64\), \(|P_{f(6AEK_1)}(2) \setminus P_{f(6UZA_1)}(2)|=55\). 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 1:1011000000101000011011001011110011000001010010011001101111000101001110000100110111111001010110111001111010011001000010000101000010010001011111100000011001100110100100010000000000000010000001010011101101010000111011010001111101000100000010100001111110100000010111010100100100101010010111000100111010000011011000101100001110111111111111111110111100011011011110111011010111111110110010100111000000010011010000101101111011111111000011001100011011011011111111101110111110100100110100010010010110010000110101010010110011011111101001101111000111101011001001101111111111111111101000011100001100100010011111111001001110000011001101101100101111110111111000100100010101011010111001001001111101110100110111010011001101000110001010010000011111000010010100001100001010000010100100110000011001100011010100000010010100100010010001100000000011011001100101010000000
Pair \(Z_2\) Length of longest common subsequence
6UZA_1,6AEK_1 119 5
6UZA_1,8JLA_1 243 4
6AEK_1,8JLA_1 248 3

Newick tree

 
[
	8JLA_1:13.52,
	[
		6UZA_1:59.5,6AEK_1:59.5
	]:78.02
]

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 \((0.85)(0.8)(\frac{1585 }{\log_{20} 1585}-\frac{738}{\log_{20}738})=210.\)
Status Protein1 Protein2 d d1/2
Query variables 6UZA_1 6AEK_1 271 251
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]