Molecular Modelling Notes PDF

1. The difference between a model and reality is that a model is a simplified representation or approximation of reality, while reality is the actual system or phenomenon being modeled. Models make idealizations and approximations in order to study aspects of reality in a simplified way. For example...

1. The difference between a model and reality is that a model is a simplified representation or approximation of reality, while reality is the actual system or phenomenon being modeled. Models make idealizations and approximations in order to study aspects of reality in a simplified way. For example, molecular mechanics force fields use classical mechanics to model atomic interactions, neglecting quantum effects, in order to simulate large molecular systems. 2. The purpose of molecular modeling (MM) is to study molecular systems using computational simulations rather than experiments. This allows probing properties that may be difficult or impossible to measure experimentally. MM contributes to chemistry research by providing insights into reaction mechanisms, predicting properties, aiding in experimental design, and complementing experiments. It allows exploring large regions of configuration space to understand structure-property relationships. 3. Inverse design molecular modeling aims to design new molecules with desired properties, while multiscale modeling bridges different time and length scales, using different levels of theory. Inverse design may use genetic or optimization algorithms, while multiscale combines quantum mechanics for small regions with classical mechanics for larger systems. 4. High performance computing uses many processors in parallel to solve problems much faster than single processors. It is needed for large and complex simulations that would be prohibitive on a single CPU. A simulation might break down if the computational resources are insufficient, such as running out of memory or not completing in a reasonable time. 5. Minima on a potential energy surface (PES) correspond to stable structures, while first order saddle points correspond to transition states between minima. Minima have zero force and positive curvature, while saddle points have zero force and one negative curvature direction. 6. Hybrid quantum mechanics/molecular mechanics (QM/MM) models treat part of a system quantum mechanically and part classically. This allows simulating large biomolecules while accurately describing reactive sites. Examples include modeling enzyme active sites and modeling electron transfers in proteins. 7. Periodic boundary conditions (PBC) make simulations of extended systems efficient by treating a small periodic unit cell as representative of an infinite crystal. Properties outside the cell are images of those inside. This allows modeling properties like lattice constants without explicit treatment of a macroscopic number of atoms. 8. Topology refers to connectivity and types of atoms. Parametrization is the process of deriving force field parameters from data. Functional forms are the mathematical expressions used for energy terms like bonds, angles, torsions. A methanol FF may use harmonic bonds/angles, cosine torsions, and LennardJones and Coulomb terms. 9. For protein folding simulations, a conventional FF with bonded terms and Lennard-Jones/Coulomb nonbonded terms is optimal. It allows conformational changes without bond breaking in a solvated system, improving efficiency and validity. An EAM or many-body potential capturing metallic bonding would be best for simulating metal solid-liquid transitions. 10. Force field parametrization for water involves fitting parameters to reproduce experimental and ab initio reference data for properties of the liquid and ice phases, ensuring transferability between phases. An iterative process is used, where properties are calculated, compared to references, and parameters adjusted to improve agreement. 11. A harmonic potential cannot dissociate bonds, as its force never goes to zero at infinite separation. A Morse potential's force goes to zero at infinite separation, correctly describing bond dissociation. 12. Empirical force fields are computationally efficient classical approximations, while ab initio methods use quantum mechanics. Force fields use functional forms and fitted parameters versus ab initio's explicit electronic structure treatment. 13. Intramolecular force field terms only involve nearby atoms, but intermolecular terms sum over all atom pairs, requiring treatment of long-range interactions which is more computationally expensive, especially for electrostatics. 14. Molecular dynamics (MD) uses Newton's laws to simulate atomic motion by integrating the equations of motion. It assumes the Born-Oppenheimer and classical approximations, neglecting quantum nuclear effects. This allows access to atomic-level dynamical properties on longer timescales than electronic structure methods. 15. Choosing a time step too large can lead to missed features and instability, while too small wastes computational resources without gaining accuracy. The time step must resolve the fastest motions in the system, usually around 0.5-2 fs for biological systems. 16. Equilibration involves running the simulation for long enough that averaged properties no longer change with additional simulation time. This ensures the system has forgotten its initial conditions and explores configuration space ergodically. Production is the equilibrated phase used to calculate timeaveraged properties. 17. Statistical sampling requires sufficient sampling of configuration space to obtain converged ensemble averages. Ergodicity means time and ensemble averages are equivalent, requiring sufficient sampling to visit all relevant regions. Non-ergodic systems like glasses may get trapped in local minima. 18. To calculate the velocity autocorrelation function, we take the average of the dot product of the velocities at time t with the initial velocities (at t=0) over all particles as a function of time. Its time integral gives the self-diffusion coefficient via the Einstein relation. At t=0 it is equal to the average kinetic energy per particle. 19. The following properties could be dynamic or static observables: I - Static (equilibrium adsorption energy) II - Dynamic (reaction correlation function needed) III - Static (structure at equilibrium) IV - Dynamic (desorption probability as function of time) V,VI - Dynamic (velocity autocorrelation function needed) I. Fundamental methods and approximations in molecular modeling and molecular dynamics simulations: Molecular mechanics (MM) uses classical mechanics approximations to model molecular systems, neglecting quantum effects. This allows simulating large systems computationally (p. 1). The Born-Oppenheimer approximation separates nuclear and electronic motion, allowing use of MM force fields (p. 24). Classical molecular dynamics (MD) uses Newton's laws to simulate atomic motion by integrating equations of motion. It assumes the Born-Oppenheimer and classical approximations, neglecting quantum nuclear effects (p. 14). Periodic boundary conditions (PBC) make simulations of extended systems efficient by treating a small periodic unit cell as representative of an infinite crystal (p. 7). II. Empirical force fields and interatomic potentials: Empirical force fields use functional forms (e.g. harmonic bonds, angles, cosine torsions) and fitted parameters versus ab initio's explicit treatment (p. 12). Topology refers to connectivity and types of atoms. Parametrization derives parameters from data. Functional forms are mathematical energy expressions (p. 8). Force field parametrization fits parameters to reproduce experimental/ab initio reference data, ensuring transferability between phases for water (p. 10). III. Analyzing problems for molecular modeling: For protein folding simulations, a conventional FF is optimal to simulate conformational changes without bond breaking in solvated systems (p. 9). An EAM or many-body potential capturing metallic bonding would be best for simulating metal solid-liquid transitions (p. 9). IV. Applying computational techniques: Statistical sampling requires sufficient configuration space sampling to obtain converged ensemble averages (p. 17). Equilibration runs long enough that averaged properties no longer change, ensuring ergodic sampling (p. 16). V. Connection to statistical mechanics: MD uses statistical mechanics to dynamically sample all configurations and calculate time-averaged properties (p. 21). Velocity autocorrelation functions relate to self-diffusion coefficients via the Einstein relation (p. 18). VI. Property calculations: Dynamic properties include reaction correlation functions and velocity autocorrelation functions (p. 19). Static properties include equilibrium adsorption energies and molecular structures (p. 19). I. Types of Molecular Modeling Methods: Molecular mechanics (MM) uses classical mechanics to model molecular systems, neglecting quantum effects, allowing simulation of large systems computationally (p. 1, 14). Molecular dynamics (MD) simulations dynamically sample molecular configurations using statistical mechanics to calculate time-averaged properties (p. 21). Monte Carlo (MC) simulations statistically sample configuration space to obtain thermodynamic properties (p. 5). II. Empirical Force Fields: Empirical force fields approximate interatomic interactions with functional forms (e.g. Lennard-Jones, Coulombic) and fitted parameters (p. 8-10). Parametrization fits parameters to reproduce experimental/ab initio data, ensuring transferability between phases (p. 10). III. Molecular Modeling Applications: Protein folding simulations typically use conventional force fields to model conformational changes without bond breaking (p. 9). Metal solid-liquid transitions require EAM or many-body potentials capturing metallic bonding (p. 9). Reaction mechanisms and intermediates can be elucidated via MD simulations (p. 7, 30). IV. Best Practices: Equilibration ensures sampling of configuration space and ergodic sampling of ensemble averages (p. 16-17). Velocity autocorrelation functions relate to transport properties via Einstein relations (p. 18). Dynamic properties involve time correlation functions; static properties are time-independent (p. 19). I. Coordinate Systems for Molecular Models: Cartesian coordinates (x,y,z) specify atom positions in 3D space (p. 26) Z-matrix defines internal coordinates (bond lengths, bond angles, dihedral angles) (p. 26) II. Molecular Structure Databases: PubChem, PDB, CCDC, ZINC contain experimental/computed molecular structures (p. 26) III. Molecular Model Building Methods: SMILES provides a line notation for specifying molecular structures using symbols (p. 27) Ball-and-stick, stick, space-filling, ribbon, and other representations visualize molecular geometry and features (p. 34) IV. Molecular Graphics Software: Popular programs like PyMol, VMD, Chimera allow 3D visualization, analysis of structures, electrostatics etc. (p. 34) Force fields are empirical models used to simulate molecular systems using classical mechanics approximations. They describe interatomic interactions using simple functional forms and parameters fitted to experimental/ab initio reference data. The potential energy V(r) of a molecular system is described as a sum of bonded (bond stretching, angle bending, dihedral torsion) and non-bonded (van der Waals, electrostatic) terms. Bonded terms depend only on the geometry of individual molecules while non-bonded terms account for interactions between all atom pairs based on their distance. Common functional forms include harmonic potentials for bond stretching/angle bending and cosine series for dihedral torsions. Van der Waals interactions are typically modeled by Lennard-Jones 6-12 or Buckingham potentials while electrostatics use partial atomic charges. Topology defines connectivity and "atom types", which classify atoms based on hybridization and environment. Parametrization fits force field parameters to reproduce reference data using quantum/statistical mechanics methods. Parameters are transferable between molecules/phases for a given force field. Popular all-atom force fields include AMBER, CHARMM and OPLS-AA. They differ in functional forms, target data, and optimization methods but generally describe protein/nucleic acid structures and dynamics well. Coarser-grained models also exist for larger-scale simulations. Topology defines the list of interaction terms between atom types, including both intramolecular (bonded) and intermolecular (non-bonded) terms. The long-range nature of van der Waals and electrostatic interactions means many atom pairs contribute to the total energy and must be considered in simulations (Question 10). Common functional forms used in force fields include harmonic potentials to describe bond stretching (Vb = k(r - r0)2) and angle bending. The harmonic form implies that at equilibrium (r = r0) the force is zero and curvature is positive, while 1st order saddle points in transition states have one negative curvature direction (Question 2). Force field parametrization fits parameters to reproduce reference data from experiments and ab initio quantum methods. This ensures transferability between different phases for a given molecule, as seen in fitting water models to liquid and vapor properties (Question 7). Periodic boundary conditions are used to efficiently simulate extended systems like crystals by treating a small periodic unit cell as representative of the infinite bulk (Question 5). This allows modeling properties like lattice constants without edge effects from finite size. I. Components of force field potential energy functions (VFF): Bond stretching (VBond) Angle bending (VAngle) Torsional (VTorsion) Improper torsions (VImproper) Van der Waals (VVDW) Electrostatic (VElectrostatic) interactions (p. 2) II. Specific functional forms: Bonds: Harmonic potential or Morse potential (p. 3) Angles: Harmonic potential (p. 3) Torsions: Fourier series (p. 3) VDW: Lennard-Jones 6-12 potential (p. 4) Electrostatic: Coulomb potential (p. 4) III. Additional bonded terms in some force fields: CMAP (correction map) for peptide backbone torsions (p. 5) Urey-Bradley 1-3 interactions (p. 5) IV. Parameterization and derivation of partial charges (p. 6-7) Force fields describe interatomic interactions using simple functional forms (e.g. harmonic, cosine) and parameters fitted to reproduce experimental/ab initio reference data (Q1). Bonded terms depend only on intramolecular geometry while non-bonded terms account for all intermolecular interactions based on distance between atoms (Q13). Lennard-Jones and Buckingham potentials are commonly used to model van der Waals interactions, with the LJ 6-12 potential accounting for Pauli repulsion at short range and dispersion attractions at long range (Q14). Partial atomic charges are usually derived from quantum calculations of the molecular electrostatic potential (ESP) fitted to atomic centers, with methods like Merz-Kollman and CHELPG commonly used (Q15). Parameterization involves fitting force field parameters to reproduce reference data on properties like heats of formation, phase changes, vibrational frequencies etc. to ensure transferability between different phases (Q10). I. Electrostatics and long-range interactions in force fields Coulomb's law models electrostatic interactions between partial charges (p. 2) II. Energy minimization methods (p. 2-4) Steepest descent Conjugate gradients - "Uses step history to speed up convergence" (p. 3) III. Molecular dynamics and Monte Carlo simulations (p. 4-6) Metropolis Monte Carlo is "biased towards low energy" conformations (p. 4) Simulated annealing uses temperature changes to explore multiple minima (p. 6) IV. Potential energy surfaces (p. 6-7) Energy minimization finds local minima while simulated annealing explores global minimum I. Electrostatics and Long-Range Interactions Coulomb's law (Vij = qi qj / 4πε0rij) accounts for interactions between partial charges qi, qj separated by distance rij (p. 2) Dielectric constants ε are used in media other than vacuum to reduce electrostatic forces based on the environment screened charges (p. 2) II. Energy Minimization Methods Steepest descent takes steps proportional to the negative gradient of the potential energy function to iteratively march downhill at each step (p. 2) Conjugate gradients uses previous step directions (conjugacy) to determine search directions, speeding convergence compared to steepest descent (p. 3) III. Molecular Dynamics and Monte Carlo Simulations Metropolis MC randomly perturbs coordinates and only accepts changes lowering energy, allowing exploration of phase space near local minima (p. 4) Simulated annealing uses a temperature schedule, initially allowing uphill moves to escape local wells, gradually restricting to downhill as temperature decreases to global optimization (p. 6) IV. Potential Energy Surfaces Multiple local minima exist due to flexibility of molecular systems (p. 6) Energy minimization becomes trapped in closest minimum while simulated annealing aims to find the global minimum energy structure (p. 6) I. Electrostatics and Long-Range Interactions Coulomb's law (Vij = qi qj / 4πε0rij) accounts for interactions between partial charges qi, qj separated by distance rij (p. 2) Dielectric constants ε are used in media other than vacuum to reduce electrostatic forces based on the environment screened charges (p. 2) II. Energy Minimization Methods Steepest descent takes steps proportional to the negative gradient of the potential energy function to iteratively march downhill at each step (p. 2) Conjugate gradients uses previous step directions (conjugacy) to determine search directions, speeding convergence compared to steepest descent (p. 3) III. Molecular Dynamics and Monte Carlo Simulations Metropolis MC randomly perturbs coordinates and only accepts changes lowering energy, allowing exploration of phase space near local minima (p. 4) Simulated annealing uses a temperature schedule, initially allowing uphill moves to escape local wells, gradually restricting to downhill as temperature decreases to global optimization (p. 6) IV. Potential Energy Surfaces Multiple local minima exist due to flexibility of molecular systems (p. 6) Energy minimization becomes trapped in closest minimum while simulated annealing aims to find the global minimum energy structure (p. 6) I. Molecular Dynamics Integration Algorithms (p. 17-19) Euler's method directly integrates the equations of motion but is unstable with large time steps. Velocity Verlet method is commonly used as it is time-reversible and conserves the symplectic structure of Hamiltonian dynamics. It involves predicting positions at t + Δt from velocities at t, then updating velocities using forces calculated from the predicted positions. II. Thermostats and Barostats (p. 19-20) Thermostats (e.g. velocity rescaling) couple the system to a heat bath to control temperature by rescaling velocities. Barostats (e.g. Parrinello-Rahman) couple the system to a pressure bath, modifying box dimensions/volumes to control pressure. III. Periodic Boundary Conditions (p. 21) Periodic images allow simulating a small unit cell while capturing properties of an extended system by wrapping atoms that leave the central cell. I. Molecular Dynamics Integration Algorithms (p. 17-19) Velocity Verlet method is commonly used as it is time-reversible, conserves total energy and momentum, and is computationally efficient. This allows ergodic sampling of phase space. II. Thermostats and Barostats (p. 19-20) Thermostats control temperature fluctuations and allow simulation in the canonical (NVT) ensemble. Velocity rescaling ensures the correct Boltzmann distribution of velocities at a given temperature. III. Periodic Boundary Conditions (p. 21) PBCs allow simulating the bulk properties of an infinite system using a finite simulation cell. Atoms interact with primary and periodic images. IV. Ensemble Averages and Ergodicity Averages over a long trajectory converge to ensemble averages, assuming the system is ergodic. Non-ergodic systems like glasses may get trapped in local minima. V. Connecting to Experiment Comparing ensemble-averaged properties like energy, density, heat capacity to experimental measurements validates the model and forcefield parameters. I. Molecular Dynamics Integration Algorithms: Integration algorithms like Velocity Verlet preserve total energy and momentum better than Euler's method, important for NVE/NVE ensemble simulations (Q14). II. Thermostats and Barostats: Thermostats couple the system to a heat bath using algorithms like velocity rescaling to control temperature fluctuations and allow NVT simulations (Q16). III. Periodic Boundary Conditions: PBCs minimize edge effects and allow modeling bulk properties of extended systems using a small periodic unit cell (Q5, Q13). IV. Ensemble Averages: Ergodicity requires sufficient sampling of phase space to obtain converged time averages equivalent to ensemble averages (Q17). V. Connecting to Experiment: Statistical sampling ensures time-averaged properties converge to compare with experimental measurements for validation (Q18). I. Periodic Boundary Conditions (p. 21-24) Images of the simulation cell are replicated in all directions to mimic an infinite bulk system. This allows modeling of extended systems with a finite simulation cell. II. Molecular Dynamics Simulation Setup (p. 29-30) Equilibration phase follows energy minimization to reach equilibrium. Length of production simulation depends on system and properties of interest. Common to fix number of atoms, temperature (via thermostat), and pressure (via barostat). III. Hardware for Molecular Simulations (p. 26-28) Dedicated supercomputers like MDGRAPE and Anton use specialized hardware to accelerate MD simulations. Exascale computers will enable simulations of larger systems and timescales. I. Periodic Boundary Conditions: Images are not physical copies but allow modeling of extended systems by removing surface effects. Atoms interact with closest images within the cutoff distance (Q5). II. Molecular Dynamics Simulation Setup: The equilibration phase involves multiple steps like constant volume (NVT), pressure (NPT) simulations to reach target T and P. Long-range corrections may be needed. Production runs are typically nanoseconds to microseconds for proteins or longer for other systems like liquids. Ensembles like NVE, NVT or NPT are chosen based on experimental conditions. Thermostats like Nosé-Hoover chain and barostats like Berendsen, ParrinelloRahman control T and P. Their parameters require tuning for accurate sampling. III. Hardware: Specialized machines optimize for non-bonded force calculations, the most expensive part of MD. They achieve speedups vs CPUs through parallelization and vectorization. I. Periodic Boundary Conditions: PBCs are used for systems with translational symmetry like solids, liquids, and amorphous systems. They eliminate surface effects and allow modeling an infinite bulk (Q6). II. Molecular Dynamics Simulation Setup: Initial velocities are usually assigned from a Maxwell-Boltzmann distribution at the desired temperature. This is important for equilibration in the NVT ensemble (Q14). Integrators like Velocity Verlet are time-reversible and conserve total energy and momentum, important for ergodic sampling in NVE simulations (Q14). III. Hardware: Purpose-built machines like MDGRAPE and Anton optimize the non-bonded force calculations, the most expensive part of MD, through parallelization and vectorization (Q18). Exascale supercomputing will enable atomistic simulations of much larger systems and timescales through high performance computing (Q19). I. Example Molecular Modeling Experiments: Molecular dynamics simulations of proteins can study folding, binding, allostery, and more. Parameters like temperature, pressure, force fields must be carefully chosen. Quantum chemistry calculations elucidate reaction mechanisms by modeling transition states and potential energy surfaces. Density functional theory (DFT) is commonly used for accuracy. Monte Carlo simulations model polymer behavior under different conditions like solutions, providing insights into phase transitions, self-assembly, and thermodynamics. II. Free Energy Calculation Methods: Free energy perturbation (FEP) computes free energy differences between two states by perturbing the Hamiltonian. It's accurate but computationally expensive. Potential of mean force (PMF) uses umbrella sampling or steered MD to calculate free energy as a function of a reaction coordinate like distance. Well-tempered metadynamics (WTMetaD) enhances sampling by adding a history-dependent bias potential to the PMF calculation. It's efficient but convergence must be carefully monitored. III. Analysis of Simulations: MDAnalysis and MDTraj allow extracting structural, kinetic, thermodynamic, and other data like RMSDs, contacts, densities. Custom analysis scripts can calculate additional metrics like hydrogen bonding, clustering, and correlations between observables. Convergence testing of ensemble averages is important to obtain statistically robust results.. Free Energy Calculations: Free energy perturbation (FEP) computes free energy differences between two states by perturbing the Hamiltonian. It requires good overlap between the states' potential energy distributions (Q16). Umbrella sampling enhances sampling along a reaction coordinate by applying a biasing potential. The PMF is reconstructed from the biased distributions (Q17). II. Analysis Methods: Radial distribution functions (RDFs) provide information about local liquid structure and can be compared to experimental data like from neutron scattering (Q10). Correlation functions like the velocity autocorrelation function give insights into dynamical properties like diffusion (Q18). Clustering algorithms can group simulation snapshots based on similarity metrics, identifying dominant conformations (Q20). I. Protein Folding (p. 2-5) Classical MD simulations are limited to small, fast folding proteins due to timescale limitations. Biased techniques like replica exchange can enhance sampling. II. AlphaFold (p. 6-9) AlphaFold revolutionized protein structure prediction using deep learning trained on 170 million protein sequences. It provides accurate 3D structure predictions. III. Applications of Protein Structure Prediction (p. 10-11) Structural predictions enable studying protein-protein interactions, evolutionary relationships, functional mechanisms, and designing drugs targeting disease-related proteins. IV. Contact Prediction & Protein Complexes (p. 12-14) AlphaFold can predict residue-residue contacts from sequence alone, enabling modeling of protein complexes. ColabFold and RoseTTAFold provide access to AlphaFold predictions. I. Protein Folding (p. 2-5) Classical MD uses empirical force fields that cannot capture all interactions and timescales are limited. Quantum methods are too computationally expensive (Q6, Q9). Biased methods like replica exchange molecular dynamics enhance conformational sampling by exchanging configurations between simulations at different temperatures (Q16). II. AlphaFold (p. 6-9) It predicts contact maps and residue-residue distances from sequence alone using deep learning on a huge training dataset (Q1). III. Applications (p. 10-11) Structure predictions allow studying allostery and conformational changes involved in protein function using simulations (Q12, Q18). IV. Contact Prediction (p. 12-14) Predicted contacts enable modeling of quaternary structure and proteinprotein interactions which are important for many cellular processes (Q5).