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El. knyga: Algorithms in Structural Molecular Biology

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(Duke University)
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Using the tools of information technology to understand the molecular machinery of the cell offers both challenges and opportunities to computational scientists. Over the past decade, novel algorithms have been developed both for analyzing biological data and for synthetic biology problems such as protein engineering. This book explains the algorithmic foundations and computational approaches underlying areas of structural biology including NMR (nuclear magnetic resonance); X-ray crystallography; and the design and analysis of proteins, peptides, and small molecules. Each chapter offers a concise overview of important concepts, focusing on a key topic in the field. Four chapters offer a short course in algorithmic and computational issues related to NMR structural biology, giving the reader a useful toolkit with which to approach the fascinating yet thorny computational problems in this area. A recurrent theme is understanding the interplay between biophysical experiments and computational algorithms. The text emphasizes the mathematical foundations of structural biology while maintaining a balance between algorithms and a nuanced understanding of experimental data. Three emerging areas, particularly fertile ground for research students, are highlighted: NMR methodology, design of proteins and other molecules, and the modeling of protein flexibility. The next generation of computational structural biologists will need training in geometric algorithms, provably good approximation algorithms, scientific computation, and an array of techniques for handling noise and uncertainty in combinatorial geometry and computational biophysics. This book is an essential guide for young scientists on their way to research success in this exciting field.

Preface xxiii
How to Use This Book xxv
Courses of Different Lengths xxix
Acknowledgments xxxi
1 Introduction to Protein Structure and NMR
1(6)
1.1 Protein Structure
1(1)
1.2 Structure Determination of Proteins with NMR Spectroscopy
2(5)
2 Basic Principles of NMR
7(8)
2.1 Overview of NMR
7(1)
2.2 The Physical Basis of NMR Spectroscopy
8(2)
2.3 Chemical Shifts
10(1)
2.4 Introduction to NMR Experiments
11(4)
3 Proteins and NMR Structural Biology
15(8)
3.1 COSY
15(1)
3.2 JHN
15(2)
3.3 HNN HSQC
17(1)
3.4 NTOCSY
17(1)
3.5 NOESY
18(1)
3.6 RDC
19(4)
4 MBM, SVD, PCA, and RDCs
23(4)
4.1 MBM
23(1)
4.2 SVD
24(1)
4.2.1 Definition
24(1)
4 2 2 Properties
24(1)
4.3 PCA
25(1)
4.3.1 Calculating PCA by SVD
25(1)
4.4 RDCs
25(2)
5 Principal Components Analysis, Residual Dipolar Couplings, and Their Relationship in NMR Structural Biology
27(20)
Antony K. Yan
Bruce R. Donald
5.1 Introduction
27(1)
5.2 Introduction to PCA
28(6)
5.3 Residual Dipolar Couplings in Structural Biochemistry
34(4)
5.4 RDCs and PCA
38(5)
5.5 Conclusions and Future Work
43(4)
6 Orientational Sampling of Interatomic Vectors
47(6)
6.1 Introduction
47(1)
6.2 Theory
47(2)
6.2.1 Sampling Tensor
47(1)
6.2.2 Generalized Sampling Parameter
48(1)
6.2.3 Average Constant
48(1)
6.2.4 Generalized Quality Factor
48(1)
6.2.5 Geometric Representation
49(1)
6.3 Results
49(2)
6.4 Applications
51(2)
7 Solution Structures of Native and Denatured Proteins Using RDCs
53(6)
7.1 Determining Native Protein Structure
53(2)
7.1.1 Theoretical Background
53(1)
7.1.2 The Algorithm
54(1)
7.1.3 Results
55(1)
7.2 Determination of Denatured or Disordered Proteins
55(4)
7.2.1 A Probabilistic Interpretation of Restraints in the Denatured State
56
7.2.2 The Algorithm
56(2)
7.2.3 Applications to Biological Systems
58(1)
8 JIGSAW and NMR
59(8)
8.1 Overview of JIGSAW
59(1)
8.2 NMR Spectra Used in JIGSAW
59(1)
8.3 Graph Representation of Atom Interactions in NOESY Spectra
60(1)
8.3.1 Graph Representation
60(1)
8.3.2 Graph Constraints for Identifying Secondary Structure
61(1)
8.4 Secondary Structure Pattern Discovery
61(3)
8.5 Assignment by Alignment of Side-Chain Fingerprints
64(3)
8.5.1 Experimental Results
65(2)
9 Peptide Design
67(10)
9.1 Peptides
67(1)
9.2 Peptide Backbone Reconstruction
68(2)
9.2.1 Problem Statement
68(1)
9.2.2 Motivation
68(1)
9.2.3 Algorithm
69(1)
9.2.4 Results
69(1)
9.3 Peptides That Target Transmembrane Helices
70(1)
9.3.1 Algorithm
70(1)
9.3.2 Results
71(1)
9.4 Foldamers
71(6)
9.4.1 Types of Monomer Frameworks
72(1)
9.4.2 Foldamer Structure
72(1)
9.4.3 Foldamer Function
72(1)
9.4.4 Foidamer Benefits
73(4)
10 Protein Interface and Active Site Redesign
77(10)
10.1 Minimalist Active Site Redesign
77(6)
10.1.1 Subtilisin
78(1)
10.1.2 Interconverting Homologous Enzymes
79(1)
10.1.3 Introduction of Catalytic Machinery
80(1)
10.1.4 Removal of Catalytic Nucleophiles
81(1)
10.1.5 Partitioning of Reaction Intermediates
81(1)
10.1.6 Controlling Stereo- and Regiochemistry
81(1)
10.1.7 Improving Promiscuity
82(1)
10.2 Protein Domain Interface Redesign via Directed Evolution
83(4)
11 Computational Protein Design
87(10)
11.1 Introduction
87(1)
11.2 Overview of Methodology
87(1)
11.3 Algorithm Design
88(3)
11.4 Intuition: Dead-End Elimination
91(1)
11.5 Complexity Analysis
92(1)
11.6 Experimental Validation: Interplay of Computational Protein Design and NMR
92(5)
12 Nonribosomal Code and K Algorithms for Ensemble-Based Protein Design
97(18)
12.1 Nonribosomal Peptide Synthetase (NRPS) Enzymes
97(1)
12.2 K-star (K) Algorithm Basics
98(4)
12.3 Energy Functions
102(3)
12.4 Redesigning Enzymes with K
105(1)
12.5 Minimized Dead-End Elimination (minDEE)
106(1)
12.5.1 A Search and minDEE
106(1)
12.6 Backbone Flexibility in DEE for Protein Design
107(2)
12.6.1 Continuous Backbone Flexibility DEE
107(1)
12.6.2 Backrub DEE
108(1)
12.7 Application to Negative Design
109(1)
12.8 Discussion
110(5)
13 RDCs In NMR Structural Biology
115(4)
13.1 Residual Dipolar Couplings
115(1)
13.2 Computational Topics Related to RDCs
116(3)
13.2.1 Assignment Problem
116(1)
13.2.2 Structure Determination Problem
116(1)
13.2.3 Estimation of Alignment Tensor Without Assignments
117(1)
13.2.4 Structural Homology Detection
117(2)
14 Nuclear Vector Replacement
119(8)
14.1 Experimental Input
119(1)
14.2 Nuclear Vector Replacement
119(3)
14.2.1 Tensor Estimation
120(1)
14.2.2 Resonance Assignment
121(1)
14.3 An Expectation/Maximization NVR Algorithm
122(1)
14.4 3D Structural Homology Detection via NVR
123(1)
14.5 Matching Modulo a Group, and Clustering Modulo a Group
123(4)
15 Short Course: Automated NMR Assignment and Protein Structure Determination
18 Using Sparse Residual Dipolar Couplings
127(60)
Bruce R. Donald
Jeffrey Martin
15.1 Introduction
127(7)
15.1.1 Motivation
127(1)
15.1.2 Glossary of Abbreviations
128(6)
15.1.3 Background
129
16.1 The Power of Exact Solutions
134(11)
16.1.1 Computing the Globally Optimal Solution
142(2)
16.1.2 Limitations and Extensions
144(1)
17.1 NMR Structure Determination Algorithms Using Sparse RDCs
145(4)
17.2 Nuclear Vector Replacement for Automated NMR Assignment and Structure Determination
149(4)
17.3 Protein Fold Determination via Unassigned Residual Dipolar Couplings
153(2)
17.4 Automated NOE Assignment Using a Rotamer Library Ensemble and RDCs
155(3)
17.5 NMR Structure Determination of Symmetric Homo-Oligomers
158(2)
17.6 Applications and Connections to Other Biophysical Methods
160(1)
18.1 Looking Under the Hood: How the Algorithms Work, and Outlook for Future Developments
160(27)
18.1.1 Exact Solutions for Computing Backbone Dihedral Angles from RDCs
161(5)
18.1.2 Nuclear Vector Replacement and Fold Recognition Using Unassigned RDCs
166(5)
18.1.3 Automated NOE Assignment
171(1)
18.1.4 NMR Structure Determination of Symmetric Oligomers
172(15)
19 Proteomic Disease Classification Algorithm
187(4)
19.1 Proteomic Disease Classification
187(2)
19.1.1 Methods
187(1)
19.1.2 Q5: An MSCA Algorithm
188(1)
19.2 Results and Discussion
189(2)
20 Protein Flexibility: Introduction to Inverse Kinematics and the Loop Closure Problem
191(6)
20.1 Loop Closure Problem and Exact Inverse Kinematics
191(2)
20.1.1 Protein Backbone Representations
191(1)
20.1.2 Loop Closure Problem
191(1)
20.1.3 Denavit-Hartenberg Local Frames
192(1)
20.2 Probik
193(1)
20.2.1 Overview
193(1)
20.2.2 Algorithm Description
193(1)
20.2.3 Exploring Control Parameters Based on Principal Component Analysis
193(1)
20.3 ChainTweak
193(2)
20.3.1 Overview
193(1)
20.3.2 Algorithm Description
194(1)
20.4 Comparisons Between Probik and ChainTweak
195(2)
21 Normal Mode Analysis (NMA) and Rigidity Theory
197(8)
21.1 Normal Mode Analysis
197(3)
21.1.1 Introduction
197(2)
21.1.2 Different Normal Modes
199(1)
21.2 Protein Flexibility Predictions Using Graph Theory
200(5)
21.2.1 Overview of FIRST
200(1)
21.2.2 Rigidity Theory
200(1)
21.2.3 Pebble Came Analysis
201(4)
22 ROCK and FRODA for Protein Flexibility
205(8)
22.1 The ROCK Algorithm
205(3)
22.1.1 Terminology
205(1)
22.1.2 Overview
205(1)
22.1.3 Conformation Sampling in Single-Ring Closure
206(1)
22.1.4 Conformation Sampling in Multiple-Ring Closure
206(1)
22.1.5 Conformation Sampling in Side Branches
207(1)
22.1.6 Hydrophobic Interactions and Ramachandran Checks
207(1)
22.2 Application of ROCK in Flexible Docking
208(1)
22.3 FRODA
208(5)
22.3.1 Overview
208(1)
22.3.2 The FRODA Algorithm
208(2)
22.3.3 Comparisons Between ROCK and FRODA
210(3)
23 Applications of NMA to Protein-Protein and Ligand-Protein Binding
213(6)
23.1 Structure Changes for Protein Binding in the Unbound State
213(2)
23.1.1 Classical Models for Protein-Protein Interactions
213(1)
23.1.2 Gaussian Network Model (GNM)
213(1)
23.1.3 Anisotropic Network Model (ANM)
214(1)
23.2 Receptor Flexibility Representation Through Relevant Normal Modes
215(4)
23.2.1 Methodology Overview
215(1)
23.2.2 Determination of the Relevant Normal Mode
215(1)
23.2.3 Generation of MRCs
216(1)
23.2.4 Side-Chain Optimization
216(1)
23.2.5 Small-Scale Virtual Screening Using RED
216(3)
24 Modeling Equilibrium Fluctuations in Proteins
219(8)
24.1 Missing Loops and Protein Flexibility
219(1)
24.2 Materials and Methods
220(6)
24.2.1 Fragment Ensemble Method (FEM)
220(1)
24.2.2 Protein Ensemble Method (PEM)
221(5)
24.3 Results
226(1)
25 Generalized Belief Propagation, Free Energy Approximations, and Protein Design
227(18)
25.1 Free Energy
227(1)
25.2 Graphical Models
228(1)
25.2.1 Bayesian Networks
228(1)
25.2.2 Pairwise Markov Random Fields
229(1)
25.2.3 Factor Graphs
229(1)
25.3 Belief Propagation (BP)
229(1)
25.4 The Connection Between Belief Propagation and Free Energy
230(1)
25.5 Generalized Belief Propagation (GBP)
231(1)
25.6 An Application of GBP: Estimating the Free Energy of Protein Structures
231(2)
25.6.1 Results and Discussion
232(1)
25.7 Application: Graphical Models for Protein Design
233(12)
25.7.1 Protein Design Problem
235(1)
25.7.2 Graphical Models and Belief Propagation for Protein Design
236(1)
25.7.3 Multiple Low-Energy Sequences Through BP
237(1)
25.7.4 Graphical Models for Probabilistic Protein Design
238(2)
25.7.5 Discussion and Future Directions
240(5)
26 Ligand Configurational Entropy
245(4)
26.1 Experimental Input
245(1)
26.2 Entropy
245(1)
26.3 Entropy in Ligand Binding
246(1)
26.3.1 Conformational Entropy
246(1)
26.3.2 Vibrational Entropy
246(1)
26.4 Entropy and Amprenavir
246(1)
26.5 Implications for Design
247(2)
27 Carrier Protein Structure and Recognition in Peptide Biosynthesis
249(4)
27.1 Carrier Proteins
249(4)
28 Kinetic Studies of the Initial Module PheATE of Gramicidin S Synthetase
253(6)
28.1 Background
253(1)
28.2 Binding of the Amino Acid Substrate to the A Domain of GrsA
254(1)
28.3 Aminoacyl-AMP Formation Catalyzed by the A Domain
254(1)
28.3.1 The Steady-State Assays
254(1)
28.3.2 The Pre-Steady-State Assay
255(1)
28.4 Loading of the Amino Acid Substrate to the T Domain
255(1)
28.5 Epimerization of the L-Form Substrate-Enzyme Complex to D-Form by the E Domain
256(1)
28.6 Free Energy Profiles for HoloPheATE Catalysis
256(3)
29 Protein-Ligand NOE Matching
259(6)
29.1 Background
259(1)
29.2 Methods
260(2)
29.3 Results and Discussion
262(3)
30 Side-Chain and Backbone Flexibility in Protein Core Design
265(8)
30.1 Protein Modeling with Fixed or Flexible Backbone
265(1)
30.2 SoftROC
266(2)
30.2.1 Initializing Backbone Population
266(1)
30.2.2 Optimization with Genetic Algorithm
266(2)
30.2.3 Refining the Model with Monte Carlo Sampling
268(1)
30.2.4 Final Model
268(1)
30.3 Issues on Energy Calculations
268(1)
30.4 Results: Comparison to ROC Variants
269(4)
30.4.1 ROC Settings
269(1)
30.4.2 Experiments on 434 cro
269(1)
30.4.3 Experiments on T4 Lysozyme
270(3)
31 Distance Geometry
273(6)
31.1 The Molecule Problem
273(1)
31.2 Divide and Conquer
274(1)
31.3 Conditions for Unique Realizibility
274(1)
31.4 Graph Partitioning
275(1)
31.5 Realizing Subgraphs
276(1)
31.6 Conclusion
277(2)
32 Distance Geometry: NP-Hard, NP-Hard to Approximate
279(6)
32.1 Introduction
279(1)
32.1.1 Review: Reductions
279(1)
32.1.2 NP-Hard Problems
280(1)
32.2 Reduction from Partition to 1-Embeddability
280(1)
32.3 Reduction from 3SATto {1,2} 1-Embeddability
280(2)
32.4 Reduction from 3SAT to Integer 1-Embeddability
282(1)
32.5 Adding Dimensions
282(1)
32.6 Approximation
282(3)
32.6.1 Definition of E-Approximate K-Embeddability
282(3)
33 A Topology-Constrained Network Algorithm for NOESY Data Interpretation
285(8)
33.1 Algorithms
285(6)
33.2 Results
291(2)
34 MARS: An Algorithm for Backbone Resonance Assignment
293(8)
34.1 MARS---Backbone Assignment of Proteins
293(3)
34.1.1 Backbone Resonance Assignment
293(1)
34.1.2 Method
293(3)
34.1.3 Results and Discussion
296(1)
34.2 Backbone Assignment with Known Structure Using RDCs
296(5)
34.2.1 Method
298(1)
34.2.2 Results and Discussion
298(3)
35 Errors in Structure Determination by NMR Spectroscopy
301(6)
35.1 Errors in Published Protein Folds
301(1)
35.2 Case Study: Dynein Light Chain
301(2)
35.3 Identifying the Problems: Problems in Identifiers
303(4)
36 SemiDefinite Programming and Distance Geometry with Orientation Constraints
307(8)
36.1 SemiDefinite Programming and Two Applications
307(3)
36.1.1 Overview of SemiDefinite Programming
307(1)
36.1.2 Application in the Side-Chain Positioning Problem
307(2)
36.1.3 Application in the Sensor Network Localization Problem
309(1)
36.2 Distance Geometry with Orientation Constraints
310(5)
36.2.1 Graph Embedding with Angle Information
310(1)
36.2.2 Protein Structure Determination from RDCs
311(4)
37 Graph Cuts for Energy Minimization and Assignment Problems
315(8)
37.1 Construction of the Energy Function
315(1)
37.2 Optimizing the Energy Function by Graph Cuts
316(2)
37.2.1 Graph Construction
316(1)
37.2.2 The MultiWay Cut Formulation
317(1)
37.2.3 The MultiWay Cut Algorithm
317(1)
37.3 Graph Cuts for Computing Visual Correspondence with Occlusions
318(5)
37.3.1 Notation
318(1)
37.3.2 Energy Function
318(1)
37.3.3 The a-Expansion Move Algorithm
319(4)
38 Classifying the Power of Graph Cuts for Energy Minimization
323(10)
38.1 Feature Space Clustering
323(1)
38.2 Energy Minimization Framework for Feature Space Clustering
323(3)
38.2.1 The Pixel Labeling Problem
324(1)
38.2.2 An EM-Style Energy Minimization Algorithm
324(2)
38.3 Approaches to Incorporating Spatial Coherence
326(1)
38.4 Classifying Energy Functions that Can Be Minimized Efficiently Using Graph Cuts
326(1)
38.4.1 Using Graph Cuts in Energy Minimization
327(1)
38.5 Representation of Energy Functions by Graphs
327(1)
38.6 The Class F2
328(2)
38.6.1 Graph Construction for F2
328(1)
38.6.2 NP-Hardness of General E2 Functions
329(1)
38.7 The Class F3
330(2)
38.7.1 Graph Construction for F3
330(2)
38.8 Comments
332(1)
39 Protein Unfolding by Using Residual Dipolar Couplings
333(8)
39.1 Motivation and Overview
333(1)
39.2 Ensemble Computation Using Only Local Sampling
333(2)
39.3 Ensemble Computation with Both Local Sampling and Long-Range Order
335(2)
39.4 An Unfolded Protein Structure Model from RDCs and Small-Angle X-Ray Scattering (SAXS) Data
337(4)
39.4.1 Generation of the Conformation Ensemble
337(1)
39.4.2 RDC Computation from the Conformational Ensemble
337(1)
39.4.3 Prediction of SAXS Data from the Conformational Ensemble
337(4)
40 Structure-Based Protein-Ligand Binding
341(4)
40.1 Uncertainty in Experimentally Derived Structures
341(1)
40.1.1 Uncertainty in X-Ray Structures
341(1)
40.1.2 Uncertainty in NMR Structures
342(1)
40.2 Protein Dynamics
342(1)
40.3 Probabilistic Representations of Uncertainty and Dynamics
343(1)
40.4 Representation of Protein Flexibility: Ensemble Docking
343(1)
40.5 FDS: Flexible Ligand and Receptor Docking with a Continuum Solvent Model and Soft-Core Energy Function
344(1)
41 Flexible Ligand-Protein Docking
345(6)
41.1 Predicting Binding Energetics from Structure
345(1)
41.2 Flexible Docking in Solution Using Metadynamics
346(5)
41.2.1 Overview of Metadynamics
346(1)
41.2.2 Application of Metadynamics in Flexible Docking
347(2)
41.2.3 Results
349(2)
42 Analyzing Protein Structures Using an Ensemble Representation
351(4)
42.1 Mathematical Results
351(4)
42.1.1 Terminology
351(1)
42.1.2 Results
352(1)
42.1, 3 Brief Proof
352(3)
42.2 Biological Significance
353
43 NMR Resonance Assignment Assisted by Mass Spectrometry
355(8)
43.1 Motivation
355(1)
43.2 Mass Spectrometry-Assisted NMR Assignment
355(2)
43.2.1 Principle of the Approach
355(1)
43.2.2 Extracting HX Rates by HSQC
355(2)
43.2.3 Extracting HX Rates by MS
357(1)
43.2.4 Correlating HX Rates Between NMR and MS
357(1)
43.2.5 MS-Assisted Assignment
357(1)
43.3 MS-Assisted NMR Assignment in Reductivcly 13C-Methylated Proteins
357(6)
44 Autollnk: An Algorithm for Automated NMR Resonance Assignment
363(8)
44.1 Algorithm Overview
363(2)
44.2 Spin System Pair Scoring
365(2)
44.2.1 Spin Density Bias
365(1)
44.2.2 Assigned Spin Bias
365(2)
44.2.3 Offset Bias
367(1)
44.2.4 Atomic Assignment Bias
367(1)
44.2.5 Overall Spin System Pair Scoring
367(1)
44.3 Hypothesis Evaluation/Reevaluation Cycles
367(4)
44.3.1 Calculation of the Base Priority Prime List
367(2)
44.3.2 Calculation of the Relative Priority Prime List
369(2)
45 CS-Rosetta: Protein Structure Generation from NMR Chemical Shift Data
371(6)
45.1 Introduction
371(3)
45.1.1 Rosetta
372(1)
45.1.2 CS-Rosetta
373(1)
45.2 Results
374(3)
46 Enzyme Redesign by SVM
377(6)
46.1 Overview
377(1)
46.2 Data Representation
377(1)
46.3 The Support Vector Machine (SVM) Approach
378(3)
46.4 Results
381(2)
47 Cross-Rotation Analysis Algorithm
383(4)
47.1 CRANS
383(4)
47.1.1 Methods
384(1)
47.1.2 Complexity
384(3)
48 Molecular Replacement and NCS in X-ray Crystallography
387(6)
48.1 Background
387(1)
48.1.1 The Phase Problem
387(1)
48.1.2 Molecular Replacement
387(1)
48.2 NMA in Molecular Replacement
388(2)
48.2.1 Objectives
388(1)
48.2.2 Normal Modes and Elastic Network Models (ENM)
389(1)
48.2.3 Summary
390(1)
48.3 NCS-Constrained Exhaustive Search Using Oligomeric Models
390(3)
48.3.1 Methods
391(1)
48.3.2 Examples
391(2)
49 Optimization of Surface Charge-Charge Interactions
393(6)
49.1 Algorithm Input
393(1)
49.2 Genetic Algorithm
393(2)
49.2.1 Chromosome Scoring
394(1)
49.2.2 Parental Chromosome Selection and Crossover
395(1)
49.2.3 Child Chromosome Mutation
395(1)
49.3 Computational and Experimental Validations
395(4)
49.3.1 Computational Validations
397(1)
49.3.2 Experimental Validation
397(2)
50 Computational Topology and Protein Structure
399(16)
50.1 Topology
399(1)
50.2 Homology
400(1)
50.3 Stmpfccial Complexes
401(1)
50.4 Homology Type Is Effectively Computable
402(2)
50.4.1 Complexity
403(1)
50.4.2 Applications
403(1)
50.4.3 Foundations
404(1)
50.5 Computing Homology Croups
404(6)
50.5.1 Stmpboal Homology
404(1)
50.5.2 Computing the Homology Groups
405(2)
50.5.3 The Algorithm for Homology Group Computation
407(3)
50.6 Alpha Shapes (Shapes) and Applications to Protein Structure
410(1)
50.7 CorHiuwwK and Future Work
411(4)
Index 415
Daugiau apie elektronines knygas Daugiau apie elektronines knygas
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