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Parikh vectors
3EPC_1 4IPE_1 2ENE_1 Letter Amino acid
11 53 0 A Alanine
4 4 2 C Cysteine
5 21 3 H Histidine
5 20 0 M Methionine
8 31 1 F Phenylalanine
26 40 1 V Valine
10 49 3 R Arginine
12 57 3 E Glutamic acid
20 78 1 L Leucine
6 42 4 K Lycine
15 26 3 P Proline
5 22 2 Y Tyrosine
2 23 2 N Asparagine
3 37 1 I Isoleucine
18 36 2 T Threonine
6 39 0 D Aspartic acid
16 39 1 Q Glutamine
17 32 8 G Glycine
20 63 9 S Serine
4 7 0 W Tryptophan 

3EPC_1|Chain A[auth R]|Poliovirus receptor|Homo sapiens (9606)
>4IPE_1|Chains A, B|TNF receptor-associated protein 1|Danio rerio (7955)
>2ENE_1|Chain A|Zinc finger protein 347|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 \(w=f(c)\)
3EPC , Knot 95 213 0.79 40 143 200 
VVQAPTQVPGFLGDSVTLPCYLQVPNMEVTHVSQLTWARHGESGSMAVFHQTQGPSYSESKRLEFVAARLGAELRDASLRMFGLRVEDEGSYTCLFVTFPQGSRSVDIWLRVLAKPQNTAEVQKVQLTGEPVPMARCVSTGGRPPAQITWHSDLGGMPQTSQVPGFLSGTVTVTSLWILVPSSQVDGKQVTCKVEHESFEKPQLLTVSLTVYY
4IPE , Knot 271 719 0.82 40 281 650 
MIRSLNLLKYSLNVSQRAQLRLLSSSKWTGHRIVPAAFTGVDTNGRQQLHQPRPFRLWSPSCSGVSVHHRSYSTQQHTEPAEEETLHNIITDTENVQGSFSKHEFQAETKKLLDIVARSLYSEKEVFIRELISNGSDALEKLRHRMITAGGDTAPMEIHLQTDSVKGTFTIQDTGVGMNKEDLVSNLGTIARSGSKAFLDALQNQAEASSSIIGQFGVGFYSAFMVADKVEVYSQSAEADAPGYKWSSDGSGVFEVAEASGVRQGTKIVLHLKDDCKEFSSEDRVKEVVTKYSNFVSFPIFLNGRRLNTLQALWMMEPKDISEWQHEEFYRYVAQAYDKPRYTLHYRADAPLNIRSIFYVPEMKPSMFDVSREMGSSVALYSRKILIQTKATDILPKWLRFLRGVVDSEDIPLNLSRELLQESALIRKLRDVLQQRVIRFLLDQSKKDPEKYARFFEDYGLFMREGIVTTGEQSVKEDIAKLLRFESSALPAGQQTSLMEYSSRMKAGTRNIYYLCAPNRHLAEHSPYFEAMKQKDMEVLFCFEQFDELTLLHLREFDRKKLISAETDIVVDHYKEEKFQDSKPASERLSSEQAEDLLAWMRNALVQRVTNIKVTPRLDTHPAMITVLEMGAARHFLRTQQLARSSEERAQILQPTLEINTGHDLIKKLHALKDSNPELAQLLLEQIYDNAMIAAGLNEDPRPMISRLNQLLTRALEKH
2ENE , Knot 25 46 0.69 32 33 38 
GSSGSSGTGEKPYKCNECGKVFRHNSYLSRHQRIHTGEKPSGPSSG

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 \(c\).

\(|P_{f(3EPC_1)}(2) \setminus P_{f(4IPE_1)}(2)|=25\), \(|P_{f(4IPE_1)}(2) \setminus P_{f(3EPC_1)}(2)|=163\). 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 1:110110011111100101100101101010010010110010010111100001100000001011110111010010101111010001000011101101000101110111010001010010101011111001001101110101000111110000111110101010011111100010100100010000100101101010100
Pair \(Z_2\) Length of longest common subsequence
3EPC_1,4IPE_1 188 4
3EPC_1,2ENE_1 138 3
4IPE_1,2ENE_1 262 3

Newick tree

 
[
	4IPE_1:12.47,
	[
		3EPC_1:69,2ENE_1:69
	]:56.47
]

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 \((0.85)(0.8)(\frac{932 }{\log_{20} 932}-\frac{213}{\log_{20}213})=196.\)
Status Protein1 Protein2 d d1/2
Query variables 3EPC_1 4IPE_1 244 157
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)],
\[ \delta= \alpha \mathrm{min} + (1-\alpha) \mathrm{max}= \begin{cases} d &\alpha=0,\\ d_1/2 &\alpha=1/2 \end{cases} \]