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Journal of Biomolecular Structure and Dynamics Publication details, including instructions for authors and subscription information: http://www.tandfonline.com/loi/tbsd20
Variability Analysis of HIV-1 gp120 V3 Region: IV. Distribution Functions for Intra- and Inter- Subtype Amino Acid Hamming Distances Michael Yu Shchelkanov
a b
d
, Nicole S. Starikov
O. Tsvetkov , Alex N. Yudin Alexander A. Vedenov
a e
a b
a b
c
, Ilya V. Yaroslavtsev , Philip a
, Maxim V. Denisov , Alexander A. Slavsky
& Edward V. Karamov
a b
,
b f
a
Moscow Institute of Physics and Technology, Faculty of Physicochemical Biology, Department of Molecular Biophysics , Dolgoprudny , Moscow region , 141700 , Russia b
D. I. Ivanovsky Institute of Virology, Immunochemistry Group , Gamaley 16, Moscow , 123098 , Russia c
Moscow Aviation Institute, Faculty of Mathematics, Department of Mathematical , Cybernetics , Moscow , 115098 , Russia d
Institute of Molecular Biology , Moscow , 117989 , Russia
e
Russian Scientific Center Kurchatov Institute , Kurchatov s., Moscow , 123182 , Russia f
Moscow State University, Institute of Applied Research, Laboratory of Virology , Lenin's Hills, Moscow , 119899 , Russia Published online: 21 May 2012.
To cite this article: Michael Yu Shchelkanov , Nicole S. Starikov , Ilya V. Yaroslavtsev , Philip O. Tsvetkov , Alex N. Yudin , Maxim V. Denisov , Alexander A. Slavsky , Alexander A. Vedenov & Edward V. Karamov (1998) Variability Analysis of HIV-1 gp120 V3 Region: IV. Distribution Functions for Intra- and Inter- Subtype Amino Acid Hamming Distances, Journal of Biomolecular Structure and Dynamics, 15:5, 877-885, DOI: 10.1080/07391102.1998.10508209 To link to this article: http://dx.doi.org/10.1080/07391102.1998.10508209
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Journal of Biomolecular Structure & Dynamics. ISSN 0739-1102 Volume 15, Issue Number 5, (1998) ©Adenine Press (1998)
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Variability Analysis of HIV-1 gp120 V3 Region: IV. Distribution Functions for Intra- and InterSubtype Amino Acid Hamming Distances. http://www.albany.edu/chemistry/sarmaljbsd.html Abstract
Distribution functions for intra- and inter- HIV-1 V3-Ioop subtypes amino acid Hamming distances were calculated (850 V3-loop sequences from the Los Alamos HIV-1 Database (1996) were used). These functions have pronounced bell-like shape. Such shapes of the histograms for HIV-1 V3 intra- and inter-subtype distriutions are discussed to confirm the applicability of different hierarchical cluster procedures (see ref. 17) for HIV-1 V3 classification. Two-mode distribution for the subtype E could sertificate that this subtype includes two thinner taxons.
Michael Yu. Shchelkanov1,2, Nicole S. Starikovl.Z, Ilya V. Yaroslavtsev3, Philip 0. Tsvetkov4, Alex N. Yudin1,2, Maxim V. Denisovl, Alexander A. Slavskyl,2, Alexander A. Vedenovl.S and Edward V. Karamov2,6* 1Moscow
Institute of Physics and
Technology, Faculty of Physicochemical Biology, Department of Molecular Biophysics,
Introduction
Dolgoprudny, Moscow region, Human Immunodeficiency Virus (HN) is etiological agent of lethal incurable Acquired ImmunoDeficiency Syndrome (AIDS) (1, 2). Development of the effective anti-HN vaccine and treatment needs the detail investigations of HIV evolution both in individual organisms (3,4) and in the large human populations (5,6). The key feature of these evolutionary processes is the requirement to take into account their stochastic nature which leads to the simultaneous existence of the wide virus variants range. The extremely high level of reverse transcription errors (10-3-1Q-4 mutations per genome per replication cycle (7,8) versus usual 10-8-10-9 ones (9)) and genetic recombinations (10) are the main sources of HN variability.
141700 Russia 2D. I. Ivanovsky Institute of Virology, Immunochemistry Group, Gamaley 16, Moscow, 123098 Russia 3Moscow Aviation Institute, Faculty of
Mathemati~s.
Department of Mathematical Cybernetics,
Modem HN classification includes two large taxons: HN-1 and HN-2 (11). The first is widely spread everywhere and is divided into two groups: M (Major) and 0 (Outlier). The M-group consists of 10 subtypes designated by capital latin alphabet letters from A to J. These subtypes are extracted on the basis of the differences in gag and env gene nucleic acid sequences ( 10) and have not completely characterized serological (5,6), neutralizational (12,13) and phenotypical (14,15) distinctions. Many of the referred properties are modulated by the amino acid sequence of gp120 V3-loop (16-18) flanked by S-S-bounded cysteines in the 303-th and 337 -th positions (according to the HN-1MN-strain (10)). In this work we utilize sequences belonging to 8 HN1 M-group subtypes (from A through H). Subtypes I (19,20) and J (21) are excluded from the analysis since information about them seems to be still preliminary. Hamming distance (the number of mismatching symbols - see ref. 22) is one of the most obvious measures between symbol sequences. Since each HIV-1 subtype is a set of such sequences we analyze in this work the distribution functions for intraand inter-subtype amino acid sequences.
Distribution Functions for Hamming Distances Between Two Symbol Sequence Sets According to designations introduced previously (16-18) let X be a disordered IX
1-
Moscow, 115098 Russia 4Institute of Molecular Biology, Moscow, 117989 Russia 5Russian Scientific Center Kurchatov Institute, Kurchatov s., Moscow, 123182 Russia 6Moscow State University, Institute of Applied Research, Laboratory of Virology, Lenin's Hills, Moscow, 119899 Russia
*Author to whom correspondence should be addressed. Phone: 7 095 190 3048; Fax: 7 095 190 2867; E-mail:
[email protected]
877
878 Shchelkanov et a/.
power set of symbol sequences X;, which are ordered lx; l-power symbol sets containing elements from alphabet n: X= {x;}
= {[a/]},
i = 1,2•... ,
lx I,
i= 1,2•...•
lx;
I, af en.
[1]
Further we will use the following alphabet: n = [ A,C,D,E,F,G,H,I,K,L,M,N,P,Q,R,S,T,V,W,Y,., X].
[2]
In I= 22 because of«.» and = "Liil, (X,Y)' ;
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CJ"_\T
=
[8]
·)
IXI·IYI lxl · IX 1·1Y1- l r"LH;(X,Y)·(l< H(X,Y) >) l
l
.
Variability Analysis of HIV-1 gp120 V3 Region
[9] Figure 1, part 3
882 Shchelkanov et a/.
< H(X,Y)> and O'xy values are presented in Table I and Table II. Comparison of mean Hamming distances< H(X,Y)> with Hamming-transformed euclidean measures between mean sequences Euc(, ) (see ref. 16) reveals that
> HTEM(< x >, < y >),
[10]
for all (X,Y) pairs where X andY are HIV-1 taxons (of course, inequality 10 is true
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Figure 1, part 4
=
and for the case when X coincides with Y since < H(X, Y)> >0 Euc( < x >, < x >) ). Nevertheless, inequality 10 can be shown to reflect basis relationships between < H(X, Y)> and Euc(< x >, < y >) for any symbol sets X and Y.
883 Variability Analysis of HIV-1 gp120 V3 Region
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The value of
