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Parikh vectors
7AXZ_1 4FEI_1 4RCA_1 Letter Amino acid
5 0 6 C Cysteine
24 2 12 Q Glutamine
32 13 23 G Glycine
44 5 22 S Serine
27 8 23 T Threonine
32 9 25 R Arginine
28 1 20 I Isoleucine
71 13 18 L Leucine
16 0 7 M Methionine
30 3 8 F Phenylalanine
30 9 25 P Proline
2 2 3 W Tryptophan
21 0 6 Y Tyrosine
29 11 19 A Alanine
39 7 15 D Aspartic acid
33 9 28 V Valine
19 0 15 N Asparagine
57 7 21 E Glutamic acid
11 2 1 H Histidine
59 1 11 K Lycine 

7AXZ_1|Chain A|X-ray repair cross-complementing protein 6|Homo sapiens (9606)
>4FEI_1|Chain A|Heat shock protein-related protein|Deinococcus radiodurans (243230)
>4RCA_1|Chain A|Receptor-type tyrosine-protein phosphatase delta|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 \(w=f(c)\)
7AXZ , Knot 235 609 0.82 40 253 559 
MSGWESYYKTEGDEEAEEEQEENLEASGDYKYSGRDSLIFLVDASKAMFESQSEDELTPFDMSIQCIQSVYISKIISSDRDLLAVVFYGTEKDKNSVNFKNIYVLQELDNPGAKRILELDQFKGQQGQKRFQDMMGHGSDYSLSEVLWVCANLFSDVQFKMSHKRIMLFTNEDNPHGNDSAKASRARTKAGDLRDTGIFLDLMHLKKPGGFDISLFYRDIISIAEDEDLRVHFEESSKLEDLLRKVRAKETRKRALSRLKLKLNKDIVISVGIYNLVQKALKPPPIKLYRETNEPVKTKTRTFNTSTGGLLLPSDTKRSQIYGSRQIILEKEETEELKRFDDPGLMLMGFKPLVLLKKHHYLRPSLFVYPEESLVIGSSTLFSALLIKCLEKEVAALCRYTPRRNIPPYFVALVPQEEELDDQKIQVTPPGFQLVFLPFADDKRKMPFTEKIMATPEQVGKMKAIVEKLRFTYRSDSFENPVLQQHFRNLEALALDLMEPEQAVDLTLPKVEAMNKRLGSLVDEFKELVYPPDYNPEGKVTKRKHDNEGSGSKRPKVEYSEEELKTHISKGTLGKFTVPMLKEACRAYGLKSGLKKQELLEALTKHFQD
4FEI , Knot 49 102 0.74 32 69 96 
QGGPWTPAADWRDAGTHLDLLLDVPGVDAGTLALAEDGGQLTVSGERPGTEHLLRSERPSGRFVRELAFPEPVRPASGVASLAGGVLTVRFEKLRPTIDVTA
4RCA , Knot 132 308 0.81 40 188 288 
ETPPRFTRTPVDQTGVSGGVASFICQATGDPRPKIVWNKKGKKVSNQRFEVIEFDDGSGSVLRIQPLRTPRDEAIYECVASNNVGEISVSTRLTVLREDQIPRGFPTIDMGPQLKVVERTRTATMLCAASGNPDPEITWFKDFLPVDTSNNNGRIKQLRSESIGGTPIRGALQIEQSEESDQGKYECVATNSAGTRYSAPANLYVRELREVRRVPPRFSIPPTNHEIMPGGSVNITCVAVGSPMPYVKWMLGAEDLTPEDDMPIGRNVLELNDVRQSANYTCVAMSTLGVIEAIAQITVKALSRLVPR

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 \(c\).

\(|P_{f(7AXZ_1)}(2) \setminus P_{f(4FEI_1)}(2)|=202\), \(|P_{f(4FEI_1)}(2) \setminus P_{f(7AXZ_1)}(2)|=18\). 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 1:101100000001000100000001010100000100011111010011100000001011010100100101001100000111111010000000101001011001001110011010010100100010011101000010011110101100101010000111100000101000101001000110100011110110100111101011000110110000101010000010011001010000001100101010001110111001100110111101000000110000001000011111100000001010001110000000100100111111110111110000010101110100011110001101111001000111100001000111011111100001000010101111011111110000011100011101001101011100101000000100111000100101111011010011010110101100011011001001101100010101000000001010001010000001000100101101011110010010110011000011011000100
Pair \(Z_2\) Length of longest common subsequence
7AXZ_1,4FEI_1 220 4
7AXZ_1,4RCA_1 157 5
4FEI_1,4RCA_1 163 4

Newick tree

 
[
	4FEI_1:10.17,
	[
		7AXZ_1:78.5,4RCA_1:78.5
	]:23.67
]

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 \((0.85)(0.8)(\frac{711 }{\log_{20} 711}-\frac{102}{\log_{20}102})=175.\)
Status Protein1 Protein2 d d1/2
Query variables 7AXZ_1 4FEI_1 222 127.5
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]