Shen S., Tuszynski J.A. Theory and Mathematical Methods for Bioformatics
Подождите немного. Документ загружается.
7.5 Exercises, Analyses, and Computation 251
Exercise 37. Based on the minimum penalty alignment sequences in the Ex-
ercise 3 in Chap. 1 with the Hamming matrix, construct the maximum core
and minimum envelope of the pairwise sequences.
Exercise 38. Based on Exercise 35, discuss the counting problem of the op-
timal alignment sequences of pairwise sequences. That is to say, estimate the
number of all the optimal alignment sequences of the pairwise sequences.
Part II
Protein Configuration Analysis
8
Background Information Concerning
the Properties of Proteins
Proteins are among the most significant biological macromolecules which per-
form the key functions involved in life processes. The activity of a protein
is not only related to its chemical components, but is also affected by its
three-dimensional configuration. Our main focus in this chapter is the topic
of protein configuration analysis. First, we introduce some background con-
cerning the physical properties of proteins.
8.1 Amino Acids and Peptide Chains
Proteins are formed by different amino acids, of which 20 types are commonly
found in nature. Different amino acids are arranged in a specific sequence to
form the primary structure of proteins, and their three-dimensional configu-
ration defines the three-dimensional structure of the protein. Parts of these
segments are called chains. Some specific motifs formed by peptide chains (for
example, α-helices, β-sheets) determine what is called the secondary struc-
ture of the proteins. We introduce first the chemical components and related
notations of these 20 commonly occurring amino acids.
8.1.1 Amino Acids
Amino acids are the basic structural units of proteins. The chemical compo-
nents of an amino acid refer to the types, amounts, and interactional structure
of the atoms that it consists of. Therefore, different amino acids have distinct
chemical components, three-dimensional configurations and physical chem-
istry characteristics. To properly analyze protein structures, we need some
basic information on amino acids.
Fixed Parts and Movable Parts of Amino Acid Components
The chemical components of an amino acid comprise two parts: the “fixed
part” and the “movable part.” The “fixed part” is the common part of the 20
256 8 Background Information Concerning the Properties of Proteins
Fig. 8.1. The fixed part and the movable part of amino acid components
amino acids, consisting of an amine group (NH
2
), a carboxyl group (COOH),
and a carbon atom (C
A
). When several carbon atoms are contained in an
amino acid, where C
α
is a specific one, it is called an α-carbon in molecular
biology, and is denoted by A in this book.
The “movable part” of an amino acid refers to the various component
elements of different amino acids. In molecular biology, the “fixed part” of an
amino acid is denoted by L while the “movable part” (also called the “side
chain” of the amino acid) is denoted by R. Here, L is formed by fixed elements,
while the formation of R is not fixed, or distinctive for different amino acids
(Fig. 8.1).
Names, Codes, and Chemical Components of Amino Acids
The names, codes, chemical structures, and physical chemistry characteristics
of the 20 commonly occurring amino acids will be used frequently in this book.
These are summarized in the following figures and tables.
The names, three-letter codes, and one-letter codes of the 20 commonly
occurring amino acids are shown in Table 8.1.
In a database, we usually denote Gln and/or Glu by a three-letter code
Glx, or a one-letter code Z; similarly for Asn and/or Asp we use Asx or a one-
letter code B; and undetermined amino acids are given the symbol X.
Physical Chemistry Characteristic Indices of the Commonly
Occurring 20 Amino Acids
The physical chemistry properties of an amino acid include: chemical type,
molecular weight, volume, frequency, hydrophobicity, polarity, electron prop-
erty, specific volume, dissociation degree, etc. Some key properties of the 20
commonly occurring amino acids are listed in Table 8.2.
8.1 Amino Acids and Peptide Chains 257
Table 8.1. Names, three-letter codes, and one-letter codes of the 20 commonly
occurring amino acids
No. Name Three- One- No. Name Three- One-
letter letter letter letter
code code code code
1 Alanine Ala A 11 Leucine Leu L
2 Arginine Arg R 12 Lysine Lys K
3 Asparagine Asn N 13 Methionine Met M
4 Aspartic acid Asp D 14 Phenylalanine Phe F
5 Cysteine Cys C 15 Proline Pro P
6 Glutamine Gln Q 16 Serine Ser S
7 Glutamic acid Glu E 17 Threonine Thr T
8 Glycine Gly G 18 Tryptophane Trp W
9 Histidine His H 19 Tyrosine Tyr Y
10 Isoleucine Ile I 20 Valine Val V
8.1.2 Basic Structure of Peptide Chains
Figure 8.2 shows the common expression of the protein/peptide chain struc-
ture. The horizontal line is called the “backbone,” while the sequence
R={R
1
, R
2
, ··· , R
n
} , (8.1)
is called the “side chain” of the peptide chain, and R
j
is the movable part of
the jth amino acid. If R
j
is the name of an amino acid, then R in (8.1) is the
primary structure sequence of the protein.
Furthermore, an oxygen atom is preserved in each amino acid residue, so
an oxygen atom sequence exists within a peptide chain:
O={O
1
, O
2
, ··· , O
n
} . (8.2)
In this book, we call oxygen sequences O the oxygen chains of the peptide
chains, where O
j
is the oxygen atom of the jth amino acid. Apart from side
Fig. 8.2. Structural connection of backbone and side chains in common peptide
chains
258 8 Background Information Concerning the Properties of Proteins
Table 8.2. Properties of the 20 commonly occurring amino acids
One- Cate- Cate- Molecular Volume Surface Specific pK
a
FR Hydrophobicity factors
letter gory gory weight area volume K-D Eisenberg Meek F-P Wolfenden
code 1
a
2
b
(D) (
˚
A
3
)(
˚
A
2
) (mL/g) (%)
A A I 71.08 88.6 115 0.748 7.9 1.80(7) 0.25(7) 0.20(8) 0.31(10) 1.49(6)
R D II 156.20 173.4 225 0.666 12 5.4 −4.0(20) −1.8(20) −1.3(20) −1.0(20) −19.9(20)
N B III 114.11 117.7 160 0.619 4.1 −3.5(15) −0.64(16) −0.69(15) −0.60(16) −0.97(16)
D C III 115.09 111.1 150 0.579 4.5 5.4 −3.5(15) −0.72(18) −0.72(16) −0.77(18) −10.9(19)
C B IV 103.13 108.5 135 0.613 9.3 1.5 2.5(5) 0.04(9) 0.67(3) 1.54(5) 1.24(8)
Q B III 128.14 143.9 180 0.674 3.9 −3.5(13) −0.69(17) −0.74(17) −0.22(15) −9.4(14)
E C III 129.12 138.4 190 0.643 6.7 −3.5(15) −0.62(15) −1.1(18) −0.64(17) −10.2(17)
G B I 57.06 60.1 75 0.632 7.0 0.4(8) 0.16(8) 0.06(9) 0.0(13) 2.4(2)
H D II 137.15 153.2 195 0.670 6.2 2.3 −3.2(14) −0.40(14) −0.0(10) −0.13(12) −10.3(18)
I A I 113.17 166.7 175 0.884 5.9 4.5(1) 0.73(1) 0.74(1) 1.8(2) 2.15(4)
L A I 113.17 166.7 170 0.884 9.6 3.8(3) 0.53(4) 0.65(5) 0.17(4) 2.28(3)
K D II 128.18 168.7 200 0.789 10.4 5.9 −3.9(19) −1.1(19) −2.0(19) −0.99(19) −9.5(15)
M A IV 131.21 162.9 185 0.745 2.4 1.9(6) 0.26(6) 0.71(2) 1.23(6) 1.48(9)
F A V 147.18 189.9 210 0.774 4.0 2.8(4) 0.61(2) 0.67(3) 1.79(3) −0.76(7)
P A V 97.12 122.7 145 0.758 4.8 −1.6(11) −0.07(11) −0.44(14) −0.72(9) 5.40(1)
S B IV 87.08 89.0 115 0.613 6.8 −0.8(10) −0.26(13) −0.34(13) −0.04(14) −
5.06(11)
T B IV 101.11 116.1 140 0.689 5.4 −0.7(9) −0.18(12) −0.26(12) −0.34(11) −4.88(10)
W A V 186.21 227.8 255 0.734 1.1 −0.9(11) 0.37(5) 0.45(7) 2.25(1) −5.88(12)
Y B V 163.18 193.6 230 0.712 9.7 3.0 −1.3(12) −0.02(10) −0.22(11) −0.96(8) −6.11(13)
V A I 99.14 140.0 155 0.847 6.8 4.2(2) 0.54(3) 0.61(6) 1.22(7) 1.99(5)
The molecular weight is given in units of 1.07 × 10
−24
g. The results may vary using different samples in amino acid frequency statistics, and there would
be a little difference in the amounts obtained. The unit in the table is a percentage. pK
a
denotes the dissociation constant of the side chains [65]. More
specifically, using K
a
as the equilibrium constant for the dissociation reaction of an acid, pK
a
= −log
10
K
a
. For example, the dissociation constant of the
amide group are 6.8–7.9, while those of the carboxyl group are 3.5–5.1. The last five columns are the hydrophobicity factors of each amino acid under
different statistical means and grades (in parentheses ).
FR the frequency rate found using the Swiss-Prot’2006 Database.
a
A nonpolar, B polar and uncharged, C electronegative, D electropositive
b
I fatty hydroxyl, II alkaline group, III acid group, IV hydroxyl and sulfur, V aryl and loop
8.2 Brief Introduction of Protein Configuration Analysis 259
chain R
j
and oxygen chain O
j
, the remaining part
L = {(N
1
, A
1
, C
1
), (N
2
, A
2
, C
2
), ··· , (N
n
, A
n
, C
n
)} , (8.3)
is the backbone of the peptide chain, where (N
j
, A
j
, C
j
)isanα-carbon and
carbon atom in the fixed part of the jth amino acid, which appear alternately.
In Fig. 8.2, B
i
is the C
B
atom of the ith amino acid.
We see from the above that proteins are made up of one or more peptide
chain(s), while peptide chains are sequences composed of amino acids. This
is the primary structure of the proteins. Within peptide chains, every amino
acid and its atoms have a relevant three-dimensional configuration and form
various geometrical structures. This is the tertiary structure or high level
structure, called in general the three-dimensional structure of the proteins.
The target of this book is to investigate the characteristics of the primary,
secondary (motifs), and three-dimensional structures of proteins.
8.2 Brief Introduction of Protein Configuration Analysis
In this section, we introduce briefly the research status on protein config-
uration analysis, including protein structure databases, related issues in the
study of three-dimensional structures of proteins and the bioinformatics issues
emphasized in this book.
8.2.1 Protein Structure Database
There are many types of protein structure databases, which can be classified
as follows.
Database of Protein Common Information
Protein common information databases involve information on primary struc-
ture sequence, and other information concerned with the commentary. The
commentary deals with other aspects of the proteins, such as the origin, class,
function, domain, key words and the connection to other databases, etc. The
most popular ones are:
• PIR (Protein Information Resource) [9]: http://pir.georgetown.edu/
• Swiss-Prot [8]: http://expasy.org/sprot/
By December 2005, the number of proteins collected in PIR and Swiss-Prot
exceeded 100,000 each.
260 8 Background Information Concerning the Properties of Proteins
Databases of Protein Structures
The main characteristic of protein structure databases is that they contain
information regarding the three-dimensional structure of proteins. It can be
as specific as providing the three-dimensional location of each atom. The most
popular ones are:
• PDB (Protein Data Bank) [13]: http://www.rcsb.org/pdb/
• CSD (Cambridge Structural Database) [1]:
http://www.ccdc.cam.ac.uk/prods/csd.html
Other Types of Databases
There are many other types of protein database. According to incomplete
statistics, there are 120 well-known ones, of many types, including:
1. Databases concerning proteins together with peptides, such as
TrEMBL [71] and GenPept database [11]. These are databases of pro-
teins translated by nucleic acids.
2. Databases that derive from the original databases (such as PIR [9], Swiss-
Prot [8], PDB [13]), such as a database of the similar proteins, for instance,
PIR-ASDB is a database of similar proteins in PIR. PIR-ALN contains
the sequence pairs whose similarity error is below 55% after sequence
alignment [97].
3. Protein secondary structure databases and structure classification data-
bases. For instance, the DSSP database [50] is a protein secondary struc-
ture database built upon PDB, while the SCOP (Structural Classification
of Proteins) database [59] contains the protein domains, and classifies
protein structure by seven hierarchies.
The database used frequently in this book, the PDB-Select database [41],
is obtained by deleting homologous proteins (or peptide chains) from the
PDB database. Its characteristic is that each individual protein then has
more independence.
4. Relatively specialized databases, such as a database of protein functions,
classifications, enzymes, etc., which are not elaborated on here.
8.2.2 Brief Introduction to Protein Structure Analysis
For protein structure analysis, we mainly discuss the following topics in
this book: sequence alignment of the protein primary structure and three-
dimensional structure; prediction of protein secondary structure; in-depth
analysis of protein three-dimensional particle systems; configuration analy-
sis of the protein three-dimensional structure, and semantic analysis of the
protein primary structure. We briefly introduce these topics here:
8.2 Brief Introduction of Protein Configuration Analysis 261
Sequence Alignment of the Protein Primary Structure
and Three-Dimensional Structure
The sequence alignment of the protein primary structure and three-dimen-
sional structure is an extension of Part I of this book. In the primary structure
sequence alignment, the main difference between DNA sequences and protein
sequences is that the data set is not V
4
but V
20
, which represents the set of the
20 commonly occurring amino acids. As well, the penalty (or scoring) matrix
between the 20 amino acids and the dummy notations is represented in terms
of the PAM or BLOSUM matrix series.
In the protein three-dimensional structure sequence alignment, we mostly
adopt in this book the sequence alignment represented by the protein back-
bone torsion angle. From these, we give a series of definitions and calculations
concerned with protein three-dimensional structure similarity.
Prediction of Protein Secondary Structure
Many methods are used in the prediction of protein secondary structures,
while in this book we mainly introduce only those concerning informatics
and statistics. From this, we can see the difficulties which lie in the protein
secondary structure commonly predicted using the PDB database. This re-
stricts the accuracy of predicting the protein secondary structure, in view of
informatics and statistics issues. Furthermore, in this chapter we discuss the
relationship between the protein secondary structure and the torsion angles
resulting from a particular sequence.
In-Depth Analysis of the Protein Three-Dimensional Particle
System
If we take the atoms in a protein as a three-dimensional particle system, then
a series of geometric calculations can be done on these particles, including an
in-depth analysis of each particle in the system. Many approaches are appli-
cable to the depth calculation of particles within proteins, such as hydropho-
bicity maps that are useful in biology, etc. In this book we use mathematical
(originating from statistics) calculations. At the same time we discuss biolog-
ical consequences of these calculations.
Calculations and Analysis of the Protein Three-Dimensional
Configuration Structure
The discussion in this part forms the centrepiece of this book. Protein three-
dimensional structure is tightly related to its functions. Therefore, the study
of protein functions, such as virus analysis, rational drug design, etc. are all
key problems investigated in bioinformatics.
262 8 Background Information Concerning the Properties of Proteins
Protein three-dimensional structure analysis covers many issues and struc-
ture types. For instance, in the SCOP database [5, 60, 66], the 7-hierarchy
classification from the secondary structure jumping-off point i, is a discus-
sion of protein structure and characteristics in view of the existing structure
types. The emphasis in this book is on: protein secondary structure predic-
tion, three-dimensional configuration alignment, analysis and calculations of
the depth function and three-dimensional structure characteristics. These top-
ics address the various properties of protein structures using different points
of view, which will be helpful when further investigating structure-to-function
relationships for proteins.
Characteristic Analysis of the Protein Three-Dimensional
Structure Configuration
In recent years, much attention has been paid to characteristic analysis of
the protein three-dimensional structure configuration [14, 42]. This problem
mainly arose from the study of virus analysis and rational drug design. These
two issues can be generalized to the ligand-receptor interaction, including the
configuration characteristics and the causal requirements for interactions ac-
companied by configuration characteristics. Ligands can be represented by
viruses, micromolecular and macromolecular drug entities that bind to re-
ceptors. Their interactions include ligand adsorption and penetration upon
receptors, the analysis of which has to do with the interaction of molecules
and atoms and the geometrical configuration. For instance, for a ligand to
penetrate a receptor (such as those present in cell membranes), both the
possibility and the driving force for binding are required. The possibility for
binding refers to whether the ligand will be able to find its way to the receptor
site, while the driving force refers to the free energy reduction upon binding
of the ligand to the receptor.
Apart from three-dimensional structure prediction, many methods and ap-
proaches are conducted in protein three-dimensional structure investigations,
which we generalize in this book to the following problems:
1. The comparison of the protein three-dimensional structural homology.
This is to what extent the protein three-dimensional configurations could
be called homologous; how to measure this similarity, and the definition
of their comparison.
2. The in-depth analysis of the protein three-dimensional particle system. If
we take the amino acids (or atoms of the amino acids) in a protein as
spatially distributed particles, we can do depth calculations upon these
particles. The definition of the depth varies and some of the problems
there can be reduced to geometric calculations.
3. Characteristic analysis of protein three-dimensional configuration. This
characteristic analysis has different aims, whether analyzing ligands or
receptors. For ligands, we need only know the spatial configuration. The