Theory and mathematical methods for bioinformatics: with 59 tables
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2008
|
| Series: | Biological and medical physics, biomedical engineering
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Auch angekündigt als: Shen, Shiyi: Theory and mathematical methods in bioinformatics |
| Physical Description: | XVI, 445 S. graph. Darst. 235 mm x 155 mm |
| ISBN: | 3540748903 9783540748908 |
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| 100 | 1 | |a Shen, Shiyi |e Verfasser |0 (DE-588)134202333 |4 aut | |
| 245 | 1 | 0 | |a Theory and mathematical methods for bioinformatics |b with 59 tables |c Shiyi Shen ; Jack A. Tuszynski |
| 246 | 1 | 3 | |a Theory and mathematical methods in bioinformatics |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2008 | |
| 300 | |a XVI, 445 S. |b graph. Darst. |c 235 mm x 155 mm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Biological and medical physics, biomedical engineering | |
| 500 | |a Auch angekündigt als: Shen, Shiyi: Theory and mathematical methods in bioinformatics | ||
| 650 | 0 | 7 | |a Bioinformatik |0 (DE-588)4611085-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mathematische Methode |0 (DE-588)4155620-3 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Tuszynski, Jack A. |d 1956- |e Verfasser |0 (DE-588)131905708 |4 aut | |
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| adam_text | Contents
Outline...........................
Part
I
Mutations
and Alignments
Introduction...............................................
5
1.1 Mutation
and Alignment
................................. 5
1.1.1
Classification of Biological Sequences
................ 5
1.1.2
Definition of Mutations and Alignments
..............
б
1.1.3
Progress on Alignment Algorithms and Problems
to Be Solved
...................................... 8
1.1.4
Mathematical Problems Driven by Alignment
and Structural Analysis
............................ 12
1.2
Basic Concepts in Alignment and Mathematical Models
...... 13
1.2.1
Mutation and Alignment
........................... 13
1.3
Dynamic Programming-Based Algorithms
for Pairwise Alignment
................................... 17
1.3.1
Introduction to Dynamic Programming-Based
Algorithms
....................................... 17
1.3.2
The Needleman-Wunsch Algorithm, the Global
Alignment Algorithm
.............................. 18
1.3.3
The Smith-Waterman Algorithm
.................... 21
1.4
Other Notations
......................................... 24
1.4.1
Correlation Functions of Local Sequences
............. 24
1.4.2
Pairwise Alignment Matrices Among Multiple
Sequences
........................................ 25
1.5
Remarks
............................................... 26
1.6
Exercises, Analyses, and Computation
..................... 27
X
Contents
2
Stochastic Models of Mutations and Structural Analysis
... 29
2.1
Stochastic Sequences and Independent Sequence Pairs
........ 29
2.1.1
Definitions and Notations of Stochastic Sequences
..... 29
2.1.2
Independently and Identically Distributed Sequences
... 31
2.1.3
Independent Stochastic Sequence Pairs
............... 33
2.1.4
Local Penalty Function and Limit Properties
of 2-Dimensional Stochastic Sequences
............... 36
2.2
Stochastic Models of Flow Raised by Sequence Mutations
..... 37
2.2.1
Bernoulli Processes
................................ 37
2.2.2
Poisson
Flow
..................................... 40
2.2.3
Mutated Flows Resulting from the Four Mutation
Types
............................................ 43
2.3
Stochastic Models of
Туре
-I
Mutated Sequences
............. 45
2.3.1
Description of
Туре
-I
Mutation
..................... 45
2.3.2
Properties of
Туре
-I
Mutations
..................... 47
2.4
Type
-П
Mutated Sequences
............................... 50
2.4.1
Description of
Type
-П
Mutated Sequences
............ 51
2.4.2
Stochastic Models of
Type
-П
Mutated Sequences
..... 51
2.4.3
Error Analysis of
Type
-П
Mutated Sequences
......... 54
2.4.4
The Mixed Stochastic Models Caused by Type-I
and
Type
-П
Mutations
............................. 57
2.5
Mutated Sequences Resulting from Type-Ill and Type-IV
Mutations
.............................................. 58
2.5.1
Stochastic Models of Type-Ill and
Туре
-IV
Mutated
Sequences
........................................ 58
2.5.2
Estimation of the Errors Caused by Type-Ill
and Type-IV Mutations
........................... 59
2.5.3
Stochastic Models of Mixed Mutations
............... 61
2.6
Exercises
............................................... 64
3
Modulus Structure Theory
................................ 67
3.1
Modulus Structure of Expanded and Compressed Sequences
.. 67
3.1.1
The Modulus Structures of Expanded Sequences
and Compressed Sequences
......................... 67
3.1.2
The Order Relation and the Binary Operators
on the Set of Expanded Modes
...................... 71
3.1.3
Operators Induced by Modes
....................... 73
3.2
Modulus Structure of Sequence Alignment
.................. 76
3.2.1
Modulus Structures Resulting from Multiple Alignment
76
3.2.2
Structure Analysis of Pairwise Alignment
............. 78
3.2.3
Properties of Pairwise Alignment
.................... 81
3.2.4
The Order Relation and the Operator Induced
by Modulus Structure
.............................. 84
Contents
XI
3.3
Analysis of Modulus Structures Resulting
írom
Sequence
Mutations
.............................................. 85
3.3.1
Mixed Sequence Mutations
......................... 85
3.3.2
Structure Analysis of Purely Shifting Mutations
....... 87
3.3.3
Structural Representation of Mixed Mutation
......... 93
3.4
The Binary Operations of Sequence Mutations
.............. 93
3.4.1
The Order Relationship Among the Modes
of Shifting Mutations
.............................. 93
3.4.2
Operators Induced by Modes of Shifting Mutations
.... 96
3.5
Error Analysis for Pairwise Alignment
.....................100
3.5.1
Uniform Alignment of Mutation Sequences
...........100
3.5.2
Optimal Alignment and Uniform Alignment
..........102
3.5.3
Error Analysis of Uniform Alignment
................104
3.5.4
Local Modification of Sequence Alignment
............106
3.6
Exercises
...............................................107
4
Super Pairwise Alignment
.................................109
4.1
Principle of Statistical Decision-Based Algorithms
for Pairwise Sequences
...................................109
4.1.1
Uniform Alignment and Parameter Estimation
for Pairwise Sequences
.............................109
4.1.2
The Locally Uniform Alignment Resulting from Local
Mutation
.........................................
Ill
4.1.3
The Estimations of Mutation Position and Length
.....113
4.2
Operation Steps of the SPA and Its Improvement
............115
4.2.1
Operation Steps of the SPA
.........................115
4.2.2
Some Unsolved Problems and Discussions of SPA
......118
4.2.3
Local Modifications for Sequence Alignment
..........121
4.3
Index Analysis of SPA
...................................122
4.3.1
The Statistical Features of Estimations
...............122
4.3.2
Improvement of the Algorithm to Estimate s*
.........128
4.3.3
The Computational Complexity of the SPA
..........131
4.3.4
Estimation for the Error of Uniform Alignment
Induced by a Hybrid Stochastic Mutation Sequence
.... 132
4.4
Applications of Sequence Alignment and Examples
..........135
4.4.1
Several Applications of Sequence Alignment
..........135
4.4.2
Examples of Pairwise Alignment
....................137
4.5
Exercises
...............................................146
5
Multiple Sequence Alignment
..............................149
5.1
Pairwise Alignment Among Multiple Sequences
.............149
5.1.1
Using Pairwise Alignment to Process Multiple
Sequences
........................................149
5.1.2
Topological Space Induced by Pairwise Alignment
of Multiple Sequences
..............................150
XII Contents
5.2
Optimization Criteria of MA
.............................156
5.2.1
The Definition of MA
.............................156
5.2.2
Uniform Alignment Criteria and SP-Optimization
Criteria for Multiple Sequences
......................156
5.2.3
Discussion of the Optimization Criterion of MA
......160
5.2.4
Optimization Problem Based on Shannon Entropy
.....164
5.2.5
The Similarity Rate and the Rate of Virtual Symbols
. . 170
5.3
Super Multiple Alignment
................................172
5.3.1
The Situation for MA
..............................172
5.3.2
Algorithm of SMA
................................174
5.3.3
Comparison Among Several Algorithms
..............179
5.4
Exercises, Analyses, and Computation
.....................180
6
Network Structures of Multiple Sequences Induced
by Mutation
...............................................183
6.1
General Method of Constructing the Phylogenetic Tree
.......183
6.1.1
Summary
.........................................183
6.1.2
Distance-Based Methods
...........................184
6.1.3
Feature-Based (Maximum Parsimony) Methods
.......188
6.1.4
Maximum-Likelihood Method and the
Bayes
Method
.. 191
6.2
Network Structure Generated by MA
......................197
6.2.1
Graph and Tree Generated by MA
..................197
6.2.2
Network System Generated by Mutations
of Multiple Sequences
..............................200
6.3
The Application of Mutation Network Analysis
..............206
6.3.1
Selection of the Data Sample
.......................206
6.3.2
The Basic Steps to Analyze the Sequences
............208
6.3.3
Remarks on the Alignment and Output Analysis
......210
6.4
Exercises, Analyses, and Computation
.....................216
7
Alignment Space
..........................................219
7.1
Construction of Alignment Space and Its Basic Theorems
.....219
7.1.1
What Is Alignment Space?
.........................219
7.1.2
The Alignment Space Under General Metric
..........221
7.2
The Analysis of Data Structures in Alignment Spaces
........224
7.2.1
Maximum Score Alignment and Minimum Penalty
Alignment
........................................224
7.2.2
The Structure Mode of the Envelope of Pairwise
Sequences
........................................226
7.2.3
Uniqueness of the Maximum Core and Minimum
Envelope of Pairwise Sequences
.....................230
7.2.4
The Envelope and Core of Pairwise Sequences
.........231
7.2.5
The Envelope of Pairwise Sequences and Its Alignment
Sequences
........................................233
Contents XIII
7.3
The Counting Theorem of the Optimal Alignment
and Alignment Spheroid
..................................237
7.3.1
The Counting Theorem of the Optimal Alignment
.....237
7.3.2
Alignment Spheroid
...............................238
7.4
The Virtual Symbol Operation in the Alignment Space
.......241
7.4.1
The Definition of the Virtual Symbol Operator
........241
7.4.2
The Modulus Structure of the Virtual Symbol
Operator
.........................................243
7.4.3
The Isometric Operation and Micro-Adapted
Operation of Virtual Symbols
.......................247
7.5
Exercises, Analyses, and Computation
.....................250
Part II Protein Configuration Analysis
8
Background Information Concerning the Properties
of Proteins
................................................255
8.1
Amino
Acids and
Peptide
Chains
.........................255
8.1.1
Amino
Acids
.....................................255
8.1.2
Basic Structure of
Peptide
Chains
..................257
8.2
Brief Introduction of Protein Configuration Analysis
........259
8.2.1
Protein Structure Database
........................259
8.2.2
Brief Introduction to Protein Structure Analysis
......260
8.3
Analysis and Exploration
.................................263
9
Informational and Statistical Iterative Analysis of Protein
Secondary Structure Prediction
............................265
9.1
Protein Secondary Structure Prediction and Informational
and Statistical Iterative Analysis
..........................265
9.1.1
Protein Secondary Structure Prediction
..............265
9.1.2
Data Source and Informational Statistical Model
of PSSP
..........................................267
9.1.3
Informational and Statistical Characteristic Analysis
on Protein Secondary Structure
.....................269
9.2
Informational and Statistical Calculation Algorithms
for PSSP
...............................................271
9.2.1
Informational and Statistical Calculation for PSSP
___271
9.2.2
Informational and Statistical Calculation Algorithm
for PSSP
.........................................273
9.2.3
Discussion of the Results
..........................275
9.3
Exercises, Analyses, and Computation
.....................277
XIV Contents
10
Three-Dimensional Structure Analysis of the Protein
Backbone and Side Chains
.................................279
10.1
Space Conformation Theory of Four-Atom Points
...........279
10.1.1
Conformation Parameter System of Four-Atom Space
Points
...........................................279
10.1.2
Phase Analysis on Four-Atom Space Points
..........283
10.1.3
Four-Atom Construction of Protein
3D
Structure
.....286
10.2
Triangle Splicing Structure of Protein Backbones
...........288
10.2.1
Triangle Splicing Belts of Protein Backbones
.........288
10.2.2
Characteristic Analysis of the Protein Backbone
Triangle Splicing Belts
............................291
10.3
Structure Analysis of Protein Side Chains
..................292
10.3.1
The Setting of Oxygen Atom
О
and Atom CB
on the Backbones
.................................293
10.3.2
Statistical Analysis of the Structures
of Tetrahedrons VO,VB
.............................295
10.4
Exercises, Analyses, and Computation
.....................297
11
Alignment of Primary and Three-Dimensional Structures
of Proteins
................................................299
11.1
Structure Analysis for Protein Sequences
...................299
11.1.1
Alignment of Protein Sequences
.....................299
11.1.2
Differences and Similarities Between the Alignment
of Protein Sequences and of
DNA
Sequences
..........301
11.1.3
The Penalty Functions for the Alignment of Protein
Sequences
........................................302
11.1.4
Key Points of the Alignment Algorithms of Protein
Sequences
........................................306
11.2
Alignment of Protein Three-Dimensional Structures
..........307
11.2.1
Basic Idea and Method of the Alignment
of Three-Dimensional Structures
....................307
11.2.2
Example of Computation in the Discrete Case
........310
11.2.3
Example of Computation in Consecutive Case
........314
11.3
Exercises, Analyses, and Computation
.....................323
12
Depth Analysis of Protein Spatial Structure
...............325
12.1
Depth Analysis of
Amino
Acids in Proteins
.................325
12.1.1
Introduction to the Concept of Depth
................325
12.1.2
Definition and Calculation of Depth
.................327
12.1.3
Proof of Theorem
40...............................329
12.1.4
Proof of Theorem
41...............................334
12.2
Statistical Depth Analysis of Protein Spatial Particles
........335
12.2.1
Calculation for Depth Tendency Factor of
Amino
Acid
. 335
12.2.2
Analysis of Depth Tendency Factor of
Amino
Acid
.... 338
Contents
XV
12.2.3
Prediction for Depth of Multiple
Peptide
Chains
in Protein Spatial Structure
........................342
12.2.4
The Level Function in Spatial Particle System
........347
12.2.5
An Example
......................................347
12.3
Exercises
...............................................353
13
Analysis of the Morphological Features of Protein Spatial
Structure
..................................................355
13.1
Introduction
............................................355
13.1.1
Morphological Features of Protein Spatial Structure
. .. 355
13.1.2
Several Basic Definitions and Symbols
...............357
13.1.3
Preliminary Analysis of the Morphology of Spatial
Particle System
...................................360
13.1.4
Example
.........................................362
13.2
Structural Analysis of Cavities and Channels in a Particle
System
.................................................366
13.2.1
Definition, Classification and Calculation of Cavity
.... 366
13.2.2
Relationship Between Cavities
......................368
13.2.3
Example
.........................................371
13.3
Analysis of 7-Accessible Radius in Spatial Particle System
.... 371
13.3.1
Structural Analysis of a Directed Polyhedron
.........371
13.3.2
Definition and Basic Properties of
7-
Accessible Radius
. 377
13.3.3
Basic Principles and Methods of
7-
Accessible Radius.
.. 378
13.4
Recursive Algorithm of 7-Function
.........................382
13.4.1
Calculation of the
7-
Function Generated by 0-Level
Convex Hull
......................................382
13.4.2
Recursive Calculation of 7-Function
.................384
13.4.3
Example
.........................................387
13.5
Proof of Relative Theorems and Reasoning of Computational
Formulas
...............................................387
13.5.1
Proofs of Several Theorems
.........................387
13.5.2
Reasoning of Several Formulas
......................390
13.6
Exercises
...............................................394
14
Semantic Analysis for Protein Primary Structure
.........395
14.1
Semantic Analysis for Protein Primary Structure
............395
14.1.1
The Definition of Semantic Analysis for Protein
Primary Structure
.................................395
14.1.2
Information-Based Stochastic Models in Semantic
Analysis
..........................................397
14.1.3
Determination of Local Words Using Informational
and Statistical Means and the Relative Entropy
Density Function for the Second and Third Ranked
Words
...........................................400
14.1.4
Semantic Analysis for Protein Primary Structure
.....402
XVI Contents
14.2
Permutation
and Combination Methods for Semantic
Structures
..............................................412
14.2.1
Notation Used in Combinatorial Graph Theory
.......416
14.2.2
The Complexity of Databases
......................420
14.2.3
Key Words and Core Words in a Database
...........421
14.2.4
Applications of Combinatorial Analysis
..............425
14.3
Exercises, Analyses, and Computation
.....................429
Epilogue
.......................................................431
References
.....................................................433
Index
..........................................................441
|
| adam_txt |
Contents
Outline.
Part
I
Mutations
and Alignments
Introduction.
5
1.1 Mutation
and Alignment
. 5
1.1.1
Classification of Biological Sequences
. 5
1.1.2
Definition of Mutations and Alignments
.
б
1.1.3
Progress on Alignment Algorithms and Problems
to Be Solved
. 8
1.1.4
Mathematical Problems Driven by Alignment
and Structural Analysis
. 12
1.2
Basic Concepts in Alignment and Mathematical Models
. 13
1.2.1
Mutation and Alignment
. 13
1.3
Dynamic Programming-Based Algorithms
for Pairwise Alignment
. 17
1.3.1
Introduction to Dynamic Programming-Based
Algorithms
. 17
1.3.2
The Needleman-Wunsch Algorithm, the Global
Alignment Algorithm
. 18
1.3.3
The Smith-Waterman Algorithm
. 21
1.4
Other Notations
. 24
1.4.1
Correlation Functions of Local Sequences
. 24
1.4.2
Pairwise Alignment Matrices Among Multiple
Sequences
. 25
1.5
Remarks
. 26
1.6
Exercises, Analyses, and Computation
. 27
X
Contents
2
Stochastic Models of Mutations and Structural Analysis
. 29
2.1
Stochastic Sequences and Independent Sequence Pairs
. 29
2.1.1
Definitions and Notations of Stochastic Sequences
. 29
2.1.2
Independently and Identically Distributed Sequences
. 31
2.1.3
Independent Stochastic Sequence Pairs
. 33
2.1.4
Local Penalty Function and Limit Properties
of 2-Dimensional Stochastic Sequences
. 36
2.2
Stochastic Models of Flow Raised by Sequence Mutations
. 37
2.2.1
Bernoulli Processes
. 37
2.2.2
Poisson
Flow
. 40
2.2.3
Mutated Flows Resulting from the Four Mutation
Types
. 43
2.3
Stochastic Models of
Туре
-I
Mutated Sequences
. 45
2.3.1
Description of
Туре
-I
Mutation
. 45
2.3.2
Properties of
Туре
-I
Mutations
. 47
2.4
Type
-П
Mutated Sequences
. 50
2.4.1
Description of
Type
-П
Mutated Sequences
. 51
2.4.2
Stochastic Models of
Type
-П
Mutated Sequences
. 51
2.4.3
Error Analysis of
Type
-П
Mutated Sequences
. 54
2.4.4
The Mixed Stochastic Models Caused by Type-I
and
Type
-П
Mutations
. 57
2.5
Mutated Sequences Resulting from Type-Ill and Type-IV
Mutations
. 58
2.5.1
Stochastic Models of Type-Ill and
Туре
-IV
Mutated
Sequences
. 58
2.5.2
Estimation of the Errors Caused by Type-Ill
and Type-IV Mutations
. 59
2.5.3
Stochastic Models of Mixed Mutations
. 61
2.6
Exercises
. 64
3
Modulus Structure Theory
. 67
3.1
Modulus Structure of Expanded and Compressed Sequences
. 67
3.1.1
The Modulus Structures of Expanded Sequences
and Compressed Sequences
. 67
3.1.2
The Order Relation and the Binary Operators
on the Set of Expanded Modes
. 71
3.1.3
Operators Induced by Modes
. 73
3.2
Modulus Structure of Sequence Alignment
. 76
3.2.1
Modulus Structures Resulting from Multiple Alignment
76
3.2.2
Structure Analysis of Pairwise Alignment
. 78
3.2.3
Properties of Pairwise Alignment
. 81
3.2.4
The Order Relation and the Operator Induced
by Modulus Structure
. 84
Contents
XI
3.3
Analysis of Modulus Structures Resulting
írom
Sequence
Mutations
. 85
3.3.1
Mixed Sequence Mutations
. 85
3.3.2
Structure Analysis of Purely Shifting Mutations
. 87
3.3.3
Structural Representation of Mixed Mutation
. 93
3.4
The Binary Operations of Sequence Mutations
. 93
3.4.1
The Order Relationship Among the Modes
of Shifting Mutations
. 93
3.4.2
Operators Induced by Modes of Shifting Mutations
. 96
3.5
Error Analysis for Pairwise Alignment
.100
3.5.1
Uniform Alignment of Mutation Sequences
.100
3.5.2
Optimal Alignment and Uniform Alignment
.102
3.5.3
Error Analysis of Uniform Alignment
.104
3.5.4
Local Modification of Sequence Alignment
.106
3.6
Exercises
.107
4
Super Pairwise Alignment
.109
4.1
Principle of Statistical Decision-Based Algorithms
for Pairwise Sequences
.109
4.1.1
Uniform Alignment and Parameter Estimation
for Pairwise Sequences
.109
4.1.2
The Locally Uniform Alignment Resulting from Local
Mutation
.
Ill
4.1.3
The Estimations of Mutation Position and Length
.113
4.2
Operation Steps of the SPA and Its Improvement
.115
4.2.1
Operation Steps of the SPA
.115
4.2.2
Some Unsolved Problems and Discussions of SPA
.118
4.2.3
Local Modifications for Sequence Alignment
.121
4.3
Index Analysis of SPA
.122
4.3.1
The Statistical Features of Estimations
.122
4.3.2
Improvement of the Algorithm to Estimate s*
.128
4.3.3
The Computational Complexity of the SPA
.131
4.3.4
Estimation for the Error of Uniform Alignment
Induced by a Hybrid Stochastic Mutation Sequence
. 132
4.4
Applications of Sequence Alignment and Examples
.135
4.4.1
Several Applications of Sequence Alignment
.135
4.4.2
Examples of Pairwise Alignment
.137
4.5
Exercises
.146
5
Multiple Sequence Alignment
.149
5.1
Pairwise Alignment Among Multiple Sequences
.149
5.1.1
Using Pairwise Alignment to Process Multiple
Sequences
.149
5.1.2
Topological Space Induced by Pairwise Alignment
of Multiple Sequences
.150
XII Contents
5.2
Optimization Criteria of MA
.156
5.2.1
The Definition of MA
.156
5.2.2
Uniform Alignment Criteria and SP-Optimization
Criteria for Multiple Sequences
.156
5.2.3
Discussion of the Optimization Criterion of MA
.160
5.2.4
Optimization Problem Based on Shannon Entropy
.164
5.2.5
The Similarity Rate and the Rate of Virtual Symbols
. . 170
5.3
Super Multiple Alignment
.172
5.3.1
The Situation for MA
.172
5.3.2
Algorithm of SMA
.174
5.3.3
Comparison Among Several Algorithms
.179
5.4
Exercises, Analyses, and Computation
.180
6
Network Structures of Multiple Sequences Induced
by Mutation
.183
6.1
General Method of Constructing the Phylogenetic Tree
.183
6.1.1
Summary
.183
6.1.2
Distance-Based Methods
.184
6.1.3
Feature-Based (Maximum Parsimony) Methods
.188
6.1.4
Maximum-Likelihood Method and the
Bayes
Method
. 191
6.2
Network Structure Generated by MA
.197
6.2.1
Graph and Tree Generated by MA
.197
6.2.2
Network System Generated by Mutations
of Multiple Sequences
.200
6.3
The Application of Mutation Network Analysis
.206
6.3.1
Selection of the Data Sample
.206
6.3.2
The Basic Steps to Analyze the Sequences
.208
6.3.3
Remarks on the Alignment and Output Analysis
.210
6.4
Exercises, Analyses, and Computation
.216
7
Alignment Space
.219
7.1
Construction of Alignment Space and Its Basic Theorems
.219
7.1.1
What Is Alignment Space?
.219
7.1.2
The Alignment Space Under General Metric
.221
7.2
The Analysis of Data Structures in Alignment Spaces
.224
7.2.1
Maximum Score Alignment and Minimum Penalty
Alignment
.224
7.2.2
The Structure Mode of the Envelope of Pairwise
Sequences
.226
7.2.3
Uniqueness of the Maximum Core and Minimum
Envelope of Pairwise Sequences
.230
7.2.4
The Envelope and Core of Pairwise Sequences
.231
7.2.5
The Envelope of Pairwise Sequences and Its Alignment
Sequences
.233
Contents XIII
7.3
The Counting Theorem of the Optimal Alignment
and Alignment Spheroid
.237
7.3.1
The Counting Theorem of the Optimal Alignment
.237
7.3.2
Alignment Spheroid
.238
7.4
The Virtual Symbol Operation in the Alignment Space
.241
7.4.1
The Definition of the Virtual Symbol Operator
.241
7.4.2
The Modulus Structure of the Virtual Symbol
Operator
.243
7.4.3
The Isometric Operation and Micro-Adapted
Operation of Virtual Symbols
.247
7.5
Exercises, Analyses, and Computation
.250
Part II Protein Configuration Analysis
8
Background Information Concerning the Properties
of Proteins
.255
8.1
Amino
Acids and
Peptide
Chains
.255
8.1.1
Amino
Acids
.255
8.1.2
Basic Structure of
Peptide
Chains
.257
8.2
Brief Introduction of Protein Configuration Analysis
.259
8.2.1
Protein Structure Database
.259
8.2.2
Brief Introduction to Protein Structure Analysis
.260
8.3
Analysis and Exploration
.263
9
Informational and Statistical Iterative Analysis of Protein
Secondary Structure Prediction
.265
9.1
Protein Secondary Structure Prediction and Informational
and Statistical Iterative Analysis
.265
9.1.1
Protein Secondary Structure Prediction
.265
9.1.2
Data Source and Informational Statistical Model
of PSSP
.267
9.1.3
Informational and Statistical Characteristic Analysis
on Protein Secondary Structure
.269
9.2
Informational and Statistical Calculation Algorithms
for PSSP
.271
9.2.1
Informational and Statistical Calculation for PSSP
_271
9.2.2
Informational and Statistical Calculation Algorithm
for PSSP
.273
9.2.3
Discussion of the Results
.275
9.3
Exercises, Analyses, and Computation
.277
XIV Contents
10
Three-Dimensional Structure Analysis of the Protein
Backbone and Side Chains
.279
10.1
Space Conformation Theory of Four-Atom Points
.279
10.1.1
Conformation Parameter System of Four-Atom Space
Points
.279
10.1.2
Phase Analysis on Four-Atom Space Points
.283
10.1.3
Four-Atom Construction of Protein
3D
Structure
.286
10.2
Triangle Splicing Structure of Protein Backbones
.288
10.2.1
Triangle Splicing Belts of Protein Backbones
.288
10.2.2
Characteristic Analysis of the Protein Backbone
Triangle Splicing Belts
.291
10.3
Structure Analysis of Protein Side Chains
.292
10.3.1
The Setting of Oxygen Atom
О
and Atom CB
on the Backbones
.293
10.3.2
Statistical Analysis of the Structures
of Tetrahedrons VO,VB
.295
10.4
Exercises, Analyses, and Computation
.297
11
Alignment of Primary and Three-Dimensional Structures
of Proteins
.299
11.1
Structure Analysis for Protein Sequences
.299
11.1.1
Alignment of Protein Sequences
.299
11.1.2
Differences and Similarities Between the Alignment
of Protein Sequences and of
DNA
Sequences
.301
11.1.3
The Penalty Functions for the Alignment of Protein
Sequences
.302
11.1.4
Key Points of the Alignment Algorithms of Protein
Sequences
.306
11.2
Alignment of Protein Three-Dimensional Structures
.307
11.2.1
Basic Idea and Method of the Alignment
of Three-Dimensional Structures
.307
11.2.2
Example of Computation in the Discrete Case
.310
11.2.3
Example of Computation in Consecutive Case
.314
11.3
Exercises, Analyses, and Computation
.323
12
Depth Analysis of Protein Spatial Structure
.325
12.1
Depth Analysis of
Amino
Acids in Proteins
.325
12.1.1
Introduction to the Concept of Depth
.325
12.1.2
Definition and Calculation of Depth
.327
12.1.3
Proof of Theorem
40.329
12.1.4
Proof of Theorem
41.334
12.2
Statistical Depth Analysis of Protein Spatial Particles
.335
12.2.1
Calculation for Depth Tendency Factor of
Amino
Acid
. 335
12.2.2
Analysis of Depth Tendency Factor of
Amino
Acid
. 338
Contents
XV
12.2.3
Prediction for Depth of Multiple
Peptide
Chains
in Protein Spatial Structure
.342
12.2.4
The Level Function in Spatial Particle System
.347
12.2.5
An Example
.347
12.3
Exercises
.353
13
Analysis of the Morphological Features of Protein Spatial
Structure
.355
13.1
Introduction
.355
13.1.1
Morphological Features of Protein Spatial Structure
. . 355
13.1.2
Several Basic Definitions and Symbols
.357
13.1.3
Preliminary Analysis of the Morphology of Spatial
Particle System
.360
13.1.4
Example
.362
13.2
Structural Analysis of Cavities and Channels in a Particle
System
.366
13.2.1
Definition, Classification and Calculation of Cavity
. 366
13.2.2
Relationship Between Cavities
.368
13.2.3
Example
.371
13.3
Analysis of 7-Accessible Radius in Spatial Particle System
. 371
13.3.1
Structural Analysis of a Directed Polyhedron
.371
13.3.2
Definition and Basic Properties of
7-
Accessible Radius
. 377
13.3.3
Basic Principles and Methods of
7-
Accessible Radius.
. 378
13.4
Recursive Algorithm of 7-Function
.382
13.4.1
Calculation of the
7-
Function Generated by 0-Level
Convex Hull
.382
13.4.2
Recursive Calculation of 7-Function
.384
13.4.3
Example
.387
13.5
Proof of Relative Theorems and Reasoning of Computational
Formulas
.387
13.5.1
Proofs of Several Theorems
.387
13.5.2
Reasoning of Several Formulas
.390
13.6
Exercises
.394
14
Semantic Analysis for Protein Primary Structure
.395
14.1
Semantic Analysis for Protein Primary Structure
.395
14.1.1
The Definition of Semantic Analysis for Protein
Primary Structure
.395
14.1.2
Information-Based Stochastic Models in Semantic
Analysis
.397
14.1.3
Determination of Local Words Using Informational
and Statistical Means and the Relative Entropy
Density Function for the Second and Third Ranked
Words'
.400
14.1.4
Semantic Analysis for Protein Primary Structure
.402
XVI Contents
14.2
Permutation
and Combination Methods for Semantic
Structures
.412
14.2.1
Notation Used in Combinatorial Graph Theory
.416
14.2.2
The Complexity of Databases
.420
14.2.3
Key Words and Core Words in a Database
.421
14.2.4
Applications of Combinatorial Analysis
.425
14.3
Exercises, Analyses, and Computation
.429
Epilogue
.431
References
.433
Index
.441 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Shen, Shiyi Tuszynski, Jack A. 1956- |
| author_GND | (DE-588)134202333 (DE-588)131905708 |
| author_facet | Shen, Shiyi Tuszynski, Jack A. 1956- |
| author_role | aut aut |
| author_sort | Shen, Shiyi |
| author_variant | s s ss j a t ja jat |
| building | Verbundindex |
| bvnumber | BV023169801 |
| classification_rvk | WC 7000 WC 7700 |
| ctrlnum | (OCoLC)244014031 (DE-599)DNB985774266 |
| dewey-full | 570.285 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 570 - Biology |
| dewey-raw | 570.285 |
| dewey-search | 570.285 |
| dewey-sort | 3570.285 |
| dewey-tens | 570 - Biology |
| discipline | Biologie Informatik Mathematik |
| discipline_str_mv | Biologie Informatik Mathematik |
| format | Book |
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| id | DE-604.BV023169801 |
| illustrated | Illustrated |
| index_date | 2024-07-02T19:57:10Z |
| indexdate | 2024-07-09T21:12:11Z |
| institution | BVB |
| isbn | 3540748903 9783540748908 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016356481 |
| oclc_num | 244014031 |
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| owner_facet | DE-703 DE-355 DE-BY-UBR DE-11 DE-83 |
| physical | XVI, 445 S. graph. Darst. 235 mm x 155 mm |
| publishDate | 2008 |
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| publisher | Springer |
| record_format | marc |
| series2 | Biological and medical physics, biomedical engineering |
| spelling | Shen, Shiyi Verfasser (DE-588)134202333 aut Theory and mathematical methods for bioinformatics with 59 tables Shiyi Shen ; Jack A. Tuszynski Theory and mathematical methods in bioinformatics Berlin [u.a.] Springer 2008 XVI, 445 S. graph. Darst. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Biological and medical physics, biomedical engineering Auch angekündigt als: Shen, Shiyi: Theory and mathematical methods in bioinformatics Bioinformatik (DE-588)4611085-9 gnd rswk-swf Mathematische Methode (DE-588)4155620-3 gnd rswk-swf Bioinformatik (DE-588)4611085-9 s Mathematische Methode (DE-588)4155620-3 s DE-604 Tuszynski, Jack A. 1956- Verfasser (DE-588)131905708 aut Erscheint auch als Online-Ausgabe 978-3-540-74891-5 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016356481&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Shen, Shiyi Tuszynski, Jack A. 1956- Theory and mathematical methods for bioinformatics with 59 tables Bioinformatik (DE-588)4611085-9 gnd Mathematische Methode (DE-588)4155620-3 gnd |
| subject_GND | (DE-588)4611085-9 (DE-588)4155620-3 |
| title | Theory and mathematical methods for bioinformatics with 59 tables |
| title_alt | Theory and mathematical methods in bioinformatics |
| title_auth | Theory and mathematical methods for bioinformatics with 59 tables |
| title_exact_search | Theory and mathematical methods for bioinformatics with 59 tables |
| title_exact_search_txtP | Theory and mathematical methods for bioinformatics with 59 tables |
| title_full | Theory and mathematical methods for bioinformatics with 59 tables Shiyi Shen ; Jack A. Tuszynski |
| title_fullStr | Theory and mathematical methods for bioinformatics with 59 tables Shiyi Shen ; Jack A. Tuszynski |
| title_full_unstemmed | Theory and mathematical methods for bioinformatics with 59 tables Shiyi Shen ; Jack A. Tuszynski |
| title_short | Theory and mathematical methods for bioinformatics |
| title_sort | theory and mathematical methods for bioinformatics with 59 tables |
| title_sub | with 59 tables |
| topic | Bioinformatik (DE-588)4611085-9 gnd Mathematische Methode (DE-588)4155620-3 gnd |
| topic_facet | Bioinformatik Mathematische Methode |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016356481&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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