Contents -- Preface -- 1 Introduction -- 1.1 Protein Structure -- 1.1.1. DNA, RNA, and protein -- 1.1.2. Hierarchy of structures -- 1.1.3. Properties of amino acids -- 1.1.4. Sequence, structure, and function -- 1.2 Structure Determination -- 1.2.1. Experimental approaches -- 1.2.2. Theoretical approaches -- 1.2.3. Knowledge-based methods -- 1.2.4. Structural refinement -- 1.3 Dynamics Simulation -- 1.3.1. Potential energy and force field -- 1.3.2. Monte Carlo simulation -- 1.3.3. Solution of equations of motion -- 1.3.4. Normal mode analysis -- 1.4 The Myth of Protein Folding -- 1.4.1. Folding of a closed chain -- 1.4.2. Biological and physical basis -- 1.4.3. Computer simulation -- 1.4.4. Alternative approaches -- Selected Further Readings -- Protein structure -- Structure determination -- Dynamics simulation -- Protein folding -- 2 X-ray Crystallography Computing -- 2.1 The Phase Problem -- 2.1.1. X-ray diffraction -- 2.1.2. Electron scattering -- 2.1.3. Atomic scattering factor -- 2.1.4. Crystal lattice -- 2.2 Least Squares Solutions -- 2.2.1. Diffraction equations -- 2.2.2. Sayre's equations -- 2.2.3. Cochran distributions -- 2.2.4. Minimal principles -- 2.3 Entropy Maximization -- 2.3.1. Entropy vs. probability -- 2.3.2. Maximizing entropy -- 2.3.3. Newton method -- 2.3.4. Fast Fourier transform (FFT) and discrete convolution -- 2.4 Indirect Methods -- 2.4.1. Patterson function -- 2.4.2. Isomorphous replacement -- 2.4.3. Molecular replacement -- 2.4.4. Anomalous scattering -- Selected Further Readings -- The phase problem -- Least squares solutions -- Entropy maximization -- Indirect methods -- 3 NMR Structure Determination -- 3.1 Nuclear Magnetic Resonance -- 3.1.1. Nuclear magnetic fields -- 3.1.2. NMR spectra -- 3.1.3. COSY experiment -- 3.1.4. Nuclear Overhauser effect (NOE) -- 3.2 Distance Geometry -- 3.2.1. The fundamental problem.

3.2.2. Exact distances -- 3.2.3. Sparse distances -- 3.2.4. Distance bounds -- 3.3 Distance-based Modeling -- 3.3.1. Embedding -- 3.3.2. Least squares method -- 3.3.3. Geometric buildup -- 3.3.4. Potential energy minimization -- 3.4 Structural Analysis -- 3.4.1. The coordinate root mean square deviation -- 3.4.2. NMR structure evaluation -- 3.4.3. Ramachandran plot -- 3.4.4. Structure refinement -- Selected Further Readings -- Nuclear magnetic resonance -- Distance geometry -- Distance-based protein modeling -- Structural analysis -- 4 Potential Energy Minimization 99 -- 4.1 Potential Energy Function -- 4.1.1. Quantum chemistry calculation -- 4.1.2. Semiempirical approximation -- 4.1.3. Protein energy landscape -- 4.1.4. Implicit and explicit solvent effects -- 4.2 Local Optimization -- 4.2.1. Steepest-descent direction method -- 4.2.2. Conjugate gradient method -- 4.2.3. Newton method -- 4.2.4. The quasi-Newton method -- 4.3 Global Optimization -- 4.3.1. Multi-start method -- 4.3.2. Stochastic search -- 4.3.3. Branch and bound -- 4.3.4. Simulated annealing -- 4.4 Energy Transformation -- 4.4.1. Integral transform -- 4.4.2. Solution to the diffusion equation -- 4.4.3. Smoothing properties -- 4.4.4. Computation of transformation -- Selected Further Readings -- Potential energy minimization -- Local optimization -- Global optimization -- Function transformation -- 5 Molecular Dynamics Simulation -- 5.1 Equations of Motion -- 5.1.1. Least-action principle -- 5.1.2. Principle of variation -- 5.1.3. Equation for molecular motion -- 5.1.4. Force field calculation -- 5.2 Initial-Value Problem -- 5.2.1. Initial positions and velocities -- 5.2.2. The Verlet algorithm -- 5.2.3. Leap-frog algorithm -- 5.2.4. Shake and Rattle -- 5.3 Boundary-Value Problem -- 5.3.1. Initial and ending positions -- 5.3.2. Finite difference -- 5.3.3. Stochastic path following.

5.3.4. Multiple shooting -- 5.4 Normal Mode Analysis -- 5.4.1. Equilibrium state approximation -- 5.4.2. Normal modes -- 5.4.3. Thermodynamic properties -- 5.4.4. Gaussian network modeling -- Selected Further Readings -- Equation of motion -- Initial-value problem -- Boundary-value problem -- Normal mode analysis -- 6 Knowledge-based Protein Modeling -- 6.1. Sequence/Structural Alignment -- 6.1.1. Sequence alignment -- 6.1.2. Shortest path problem -- 6.1.3. Optimal alignment -- 6.1.4. Structural alignment -- 6.2 Fold Recognition/Inverse Folding -- 6.2.1. Fold recognition -- 6.2.2. Inverse folding -- 6.2.3. Scoring functions -- 6.2.4. Complexities of threading -- 6.3 Knowledge-based Structural Refinement -- 6.3.1. Deriving structural constraints -- 6.3.2. Distance distributions -- 6.3.3. Mean force potentials -- 6.3.4. Structure refinement -- 6.4 Structural Computing and Beyond -- 6.4.1. Structural bioinformatics -- 6.4.2. High-performance computing -- 6.4.3. Structural genomics -- 6.4.4. Biocomplexes and biosystems -- Selected Further Readings -- Sequence/structural alignment -- Fold recognition/threading -- Knowledge-based structural re.nement -- Beyond structural computing -- Appendix A Design and Analysis of Computer Algorithms -- A.1 Evaluation of Algorithms -- A.1.1. Computational model -- A.1.2. Computing time -- A.1.3. Memory space -- A.1.4. Example analysis -- A.2 Intractability -- A.2.1. NP-completeness -- A.2.2. Satis.ability problem -- A.2.3. Set partition problem -- A.2.4. Polynomial time reduction -- A.3 Lists, Arrays, Graphs, and Trees -- A.3.1. Lists -- A.3.2. Arrays -- A.3.3. Graphs -- A.3.4. Trees -- A.4 Sorting, Searching, and Optimization -- A.4.1. Sorting -- A.4.2. Searching -- A.4.3. Solution to the shortest path problem -- A.4.4. Minimal weight spanning tree -- Selected Further Readings -- Appendix B Numerical Methods.

B.1 Numerical Linear Algebra -- B.1.1. Matrix-vector operations -- B.1.2. Matrix factorizations -- B.1.3. Linear systems of equations -- B.1.4. Singular value decomposition -- B.2 Numerical Optimization -- B.2.1. Steepest descent direction method -- B.2.2. Conjugate gradient method -- B.2.3. Newton method -- B.2.4. Quasi-Newton method -- B.3 Numerical Solutions to Initial-Value Problems -- B.3.1. Existence and uniqueness of the solution -- B.3.2. Single-step method -- B.3.3. Multistep method -- B.3.4. Accuracy and convergence -- B.4 Numerical Solutions to Boundary-Value Problems -- B.4.1. Existence and uniqueness of the solution -- B.4.2. Single shooting -- B.4.3. Multiple shooting -- B.4.4. Finite difference -- Selected Further Readings -- Index.