biowiki - User contributions [en]

Tutorial:amm

2022-08-31T17:31:35Z

Cda923: Added Metadynamics Header and Link to Page

'''Advanced Molecular Modeling Methods'''

= ''Molecular Mechanics and Force Fields (Ren, 3 lectures)'' =

== [[ammm:Mm_gff|Molecular Mechanics and General force fields]] ==

== [[ammm:Mm_mpole|Electrostatic:polarizable multipole]] ==

== [[ammm:Mm_ewald|Ewald and vdw long range correction]] ==

== [[ammm:Mm_aplus|New Generation AMOEBA+ FF]] ==

= ''Molecular Dynamics'' =

== [[ammm:Md_ham|Lagrangian and Hamiltonian]] (Ren) ==

== [[ammm:Md_erg|Liouville Equation and Ergodicity]] ==

== [[ammm:Md_integrator|Integrator and constrain]] ==

== [[ammm:Md_tp|Temperature and Pressure control]] ==

== [[ammm:stoch |Stochastic/Langevin/Brownian/DPD dynamics]] ==

= ''Deriving force field parameters for a new molecule/unit'' =

== [[ammm:Ff_gau_grom_prdrug|Gaussian and gromacs and prodrug server (Fonner)]] ==

== [[ammm:Ff_amber_ligand_parameter|Amber and Antechamber (Chunli)]]==

== [[ammm:Lig_ion_params|Metal ion and ligand parameterizations (Oscar) 9/30]] ==

= [[ammm:QM/MM|QM/MM (Chistina)]] =

= AMOEBA parameterization =
==[[Ammm:Poltype 2|Poltype 2 - Small molecule parameter derivation (2022)]]==

= Free Energy =
== [[Ammm:chgcorr|charge correction]] ==
= ''Implicit Solvent approach'' =

== [[ammm:Gb_gk|GB/GK (Jenny 10/12)]] ==

== [[ammm:PB_(APBS)|PB (APBS)(Yue)]] ==

== [[ammm:Molecular_surfaces|Calculation of molecular surface (Maysam)]] 10/19 ==

== [[ammm:Nonpolar_solvation|Nonpolar Solvation and hydrophobicity (Jenny 10/21)]] ==

= ''Sampling'' =

== [[ammm:Free_energy_simulations|Free energy simulations]] (Johnny) ==

== [[ammm:Umbrella_sampling_and_WHAM|Umbrella sampling and WHAM]] (Xudong Yang) 2022/08/03 ==

== [[AMMM:Metadynamics|Metadynamics]] (Cole Allen) 2022/08/31 ==

== [[ammm:REMD_jenny|REMD with gromacs (Jenny)]] ==

== [[ammm:Adaptive_umbrella_sampling|Multicanonical and adaptive umbrella sampling]] (Bruce) 11/4 ==

== [[Non_equilibrium_method_and_AFM_simulation_w_gromacs|Non equilibrium method and AFM simulation w gromacs]] (Tim) 11/11(out of town on 11/9) ==

= ''Protein-ligand binding'' =

== [https://biomolmd.org/mw/index.php/Ammm:ProteinLigandBFE Protein-Ligand Binding Free Energy (Elizabeth E. Wait) 08/2022] ==

== [[ammm:Flexible_Docking_with_GOLD_and_GLIDE|Docking (Glide and gold) and flexibility (Maysam)]] 11/16 ==

== [[ammm:MM/PBSA_with_amber:_theory_and_application|MM/PBSA with amber: theory and application]](chunli) 11/18 ==

== FEP/BAR, TI (Oscar) cancelled ==
see
* [[ammm:Free_energy_simulations|Free energy simulations (Johnny)]]
* http://alchemistry.org/wiki/Main_Page

Free Energy Perturbation
BAR
Thermodynamic Integration
Metadynamics
Orthogonal Space Random Walk

Read books:

*Molecular Modeling by Andrew Leach
*Free energy calculations (Chipot et al )
*And papers by Ren lab.

= Electrostatics =

== [[ammm:Comparative_Analysis_of_RNA_And_Mfold|Comparative Analysis of RNA And Mfold]] (David) 11/25 ==

= ''Coarse-grained modeling'' =

== [[ammm:Coarse_grain_modeling|Gay-Berne and coarse-grain modeling (Johnny) 11/30]] ==

== [[ammm:Rigid_body_MD_(Steven_12/2) | Rigidbody mechanics]] ==

== Psudo atom RNA model (Bruce) canceled ==

= ''Reaction Path and TST'' =

== Reaction path search (David) canceled ==

== Nudged Elastic Band (NEB) in AMBER (Oscar) canceled ==

[http://ambermd.org/tutorials/advanced/tutorial5/index.htm http://ambermd.org/tutorials/advanced/tutorial5/index.htm]

[http://www.quantumwise.com/documents/manuals/ATK-2008.10/chap.relax.html#chap.relax.neb.intro http://www.quantumwise.com/documents/manuals/ATK-2008.10/chap.relax.html#chap.relax.neb.intro]

= Continuum method for biomolecules (Steven) canceled or merged with above =

*Tetrameric mouse acetylcholinesterase: continuum diffusion rate calculations by solving the steady-state Smoluchowski equation using finite element methods

Mar 21, 2005 Zhang D, Suen J, Zhang Y, Song Y, Radic Z, Taylor P, Holst MJ, Bajaj C, Baker NA, McCammon JA. Tetrameric mouse acetylcholinesterase: continuum diffusion rate calculations by solving the steady-state Smoluchowski equation using finite element methods. Biophys J, 88, 1659-1666, 2005.

*Continuum diffusion reaction rate calculations of wild type and mutant mouse acetylcholinesterase: adaptive finite element analysis

Sep 1, 2004 Song Y, Zhang Y, Bajaj C, Baker NA. Continuum diffusion reaction rate calculations of wild type and mutant mouse acetylcholinesterase: adaptive finite element analysis. Biophys J, 87, 1558-1566, 2004.

*Finite element solution of the steady-state Smoluchowksi equation for rate constant calculations

Apr 1, 2004 Song Y, Zhang Y, Shen T, Bajaj CL, McCammon JA, Baker NA. Finite element solution of the steady-state Smoluchowksi equation for rate constant calculations. Biophys J, 86, 2017-2029, 2004.

*Finite element simulations of acetylcholine diffusion in neuromuscular junctions

Dec 12, 2002 Tai K, Bond SD, MacMillan HR, Baker NA, Holst MJ, McCammon JA. Finite element simulations of acetylcholine diffusion in neuromuscular junctions. Biophys J, 84, 2234-2241, 2003.

= Online Resource =

== Gromacs tutorial ==

[http://www.dddc.ac.cn/embo04/#Practicals http://www.dddc.ac.cn/embo04/#Practicals]

== AMBER tutorial ==

[http://ambermd.org/tutorial/ http://ambermd.org/tutorial/]

[http://ambermd.org/tutorials/ http://ambermd.org/tutorials/]

AMMM:Metadynamics

2022-08-31T17:27:24Z

Cda923: Recreation of correctly named page

==What is Metadynamics?==
•A simulation method normally applied as part of molecular dynamics

•Used to estimate free energy and state functions of systems where ergodicity (given enough time simulation will explore all possible configurations/areas of phase space) is hindered by energy landscape

•Similar to: Adaptively biased MD, Adaptive reaction coordinate forces, Local elevation umbrella sampling

•Suggested and developed by Alessandro Laio and Michele Parrinello
==How does Metadynamics work?==
•Filling free energy wells with computational sand

•Tracking grains of sand placed along collective variables

•Eventually the wells are completely full and you add sand to sand (known as convergence)

•The landscape is opposite of sum of all sand

Movie: https://www.youtube.com/watch?v=IzEBpQ0c8TA
==How Metadynamics Really Work!==
•Collective variables (s): set of variables which accurately describe the system

•CV Examples: Dihedral angle for cis to trans butane, Distance for cation and anion

•Limitations: 3CV or 8CV with multiple replicas coupled together

•Exponential cost increase with each CV

•Grains of sand are bias potentials

•Hamiltonian is augmented with bias potential Vbias shown in Equation 1[[File:Hamiltonian With Bias Potential.png|thumb|Equation 1|link=https://biomolmd.org/mw/index.php/File:Hamiltonian_With_Bias_Potential.png]]

•Bias potential Vbias is continuously updated by adding bias (more grains of sand) visualized in Figure 1[[File:Energy Landscape Filled With Gaussians.png|thumb|Figure 1|link=https://biomolmd.org/mw/index.php/File:Energy_Landscape_Filled_With_Gaussians.png]]

[[File:Bias Potential Equation and Integral.png|thumb|Equation 2|link=https://biomolmd.org/mw/index.php/File:Bias_Potential_Equation_and_Integral.png]]

Defined Variables for Equation 2:

•Vbias: bias potential

•tsim: simulation time

•s: collective variable

•st: instantaneous collective variable at time t

•ω: bias deposition rate

•F: free energy

•C: constant (irrelevant)

•Evaluating the integral of bias potential over the time duration of the simulation returns free energy F with a negative sign given enough time
==How to make Metadynamics efficient and computationally viable?==
[[File:Efficient Bias Potential Equation.png|thumb|Equation 3|link=https://biomolmd.org/mw/index.php/File:Efficient_Bias_Potential_Equation.png]]•Time is discretized into T time intervals

•The Dirac delta function is replaced with a Gaussian function

•Time intervals (T), bias deposition rate (ω), and width of Gaussian functions (σ) are constants determined as inputs

•Vbias equation for efficient implementation shown in Equation 3
==Two types of Metadynamics==
•Everything so far has been “original” or “plain” metadynamics

•Well-tempered metadynamics scales Gaussian height down as wells are filled[[File:Gaussian Height Scaling Equation.png|thumb|Equation 4|link=https://biomolmd.org/mw/index.php/File:Gaussian_Height_Scaling_Equation.png]]Defined Variables for Equation 4 and 5:

•w: Gaussian height

•ω: bias deposition rate

•Vb: estimate of free energy at current CV position and time step

•ΔT: tunable parameter controls how quickly Gaussian height reduces as wells are filled[[File:Free Energy Equation Using Well-Tempered Metadynamics.png|thumb|Equation 5|link=https://biomolmd.org/mw/index.php/File:Free_Energy_Equation_Using_Well-Tempered_Metadynamics.png]]•F: free energy

•Final value of biasing potential is a scaled approximation of free energy as shown in Equation 5

• Well-tempered metadynamics allows for rapid exploration of phase space as the wells are filled quickly (at Vbias=0 the amount of bias deposited is relatively large, at Vbias=infinity the amount of bias deposited is infinitely small)

•As wells fill progressively smaller perturbations to bias potential lead to "smooth convergence" (less excess bias potential or sand deposited on 'top')

•Suggested and developed by Alessandro Barducci, Giovanni Bussi, and Michele Parrinello

Movie Comparing MD, MTD, and WTMTD: https://www.youtube.com/watch?v=IzEBpQ0c8TA
==Applications of Metadynamics==
•Able to sample free energy curve even when ergodicity is limited by energy landscape

•Keys to successful metadynamics simulation are choice and definition of CVs

•Applicable systems: Protein folding, Molecular docking, Phase transitions, Chemical reactions, Simple to complex systems as long as CVs are sufficient to describe system

•Widely integrated as PLUMED and Collective Variable Module:

•PLUMED: AMBER, GROMACS, LAMMPS, NAMD, Q ESPRESSO, CP2K, OpenMM

•Collective Variable Module: LAMMPS, NAMD, GROMACS, ORAC, CP2K, Desmond

Metadynamics

2022-08-31T17:24:54Z

Cda923: Updated figures and variable definitions for clarity

== What is Metadynamics? ==
•A simulation method normally applied as part of molecular dynamics

•Used to estimate free energy and state functions of systems where ergodicity (given enough time simulation will explore all possible configurations/areas of phase space) is hindered by energy landscape

•Similar to: Adaptively biased MD, Adaptive reaction coordinate forces, Local elevation umbrella sampling

•Suggested and developed by Alessandro Laio and Michele Parrinello

== How does Metadynamics work? ==
•Filling free energy wells with computational sand

•Tracking grains of sand placed along collective variables

•Eventually the wells are completely full and you add sand to sand (known as convergence)

•The landscape is opposite of sum of all sand

Movie: https://www.youtube.com/watch?v=IzEBpQ0c8TA

== How Metadynamics Really Work! ==
•Collective variables (s): set of variables which accurately describe the system

•CV Examples: Dihedral angle for cis to trans butane, Distance for cation and anion

•Limitations: 3CV or 8CV with multiple replicas coupled together

•Exponential cost increase with each CV

•Grains of sand are bias potentials

•Hamiltonian is augmented with bias potential Vbias shown in Equation 1
[[File:Hamiltonian With Bias Potential.png|thumb|Equation 1]]

•Bias potential Vbias is continuously updated by adding bias (more grains of sand) visualized in Figure 1
[[File:Energy Landscape Filled With Gaussians.png|thumb|Figure 1]]

[[File:Bias Potential Equation and Integral.png|thumb|Equation 2]]

Defined Variables for Equation 2:

•Vbias: bias potential

•tsim: simulation time

•s: collective variable

•st: instantaneous collective variable at time t

•ω: bias deposition rate

•F: free energy

•C: constant (irrelevant)

•Evaluating the integral of bias potential over the time duration of the simulation returns free energy F with a negative sign given enough time

== How to make Metadynamics efficient and computationally viable? ==
[[File:Efficient Bias Potential Equation.png|thumb|Equation 3]]
•Time is discretized into T time intervals

•The Dirac delta function is replaced with a Gaussian function

•Time intervals (T), bias deposition rate (ω), and width of Gaussian functions (σ) are constants determined as inputs

•Vbias equation for efficient implementation shown in Equation 3

== Two types of Metadynamics ==
•Everything so far has been “original” or “plain” metadynamics

•Well-tempered metadynamics scales Gaussian height down as wells are filled
[[File:Gaussian Height Scaling Equation.png|thumb|Equation 4]]
Defined Variables for Equation 4 and 5:

•w: Gaussian height

•ω: bias deposition rate

•Vb: estimate of free energy at current CV position and time step

•ΔT: tunable parameter controls how quickly Gaussian height reduces as wells are filled
[[File:Free Energy Equation Using Well-Tempered Metadynamics.png|thumb|Equation 5]]
•F: free energy

•Final value of biasing potential is a scaled approximation of free energy as shown in Equation 5

• Well-tempered metadynamics allows for rapid exploration of phase space as the wells are filled quickly (at Vbias=0 the amount of bias deposited is relatively large, at Vbias=infinity the amount of bias deposited is infinitely small)

•As wells fill progressively smaller perturbations to bias potential lead to "smooth convergence" (less excess bias potential or sand deposited on 'top')

•Suggested and developed by Alessandro Barducci, Giovanni Bussi, and Michele Parrinello

Movie Comparing MD, MTD, and WTMTD: https://www.youtube.com/watch?v=IzEBpQ0c8TA

== Applications of Metadynamics ==
•Able to sample free energy curve even when ergodicity is limited by energy landscape

•Keys to successful metadynamics simulation are choice and definition of CVs

•Applicable systems: Protein folding, Molecular docking, Phase transitions, Chemical reactions, Simple to complex systems as long as CVs are sufficient to describe system

•Widely integrated as PLUMED and Collective Variable Module:

•PLUMED: AMBER, GROMACS, LAMMPS, NAMD, Q ESPRESSO, CP2K, OpenMM

•Collective Variable Module: LAMMPS, NAMD, GROMACS, ORAC, CP2K, Desmond

Metadynamics

2022-08-31T17:18:11Z

Cda923: Made Page Filled with Information from AMMM Presentation

== What is Metadynamics? ==
•A simulation method normally applied as part of molecular dynamics

•Used to estimate free energy and state functions of systems where ergodicity (given enough time simulation will explore all possible configurations/areas of phase space) is hindered by energy landscape

•Similar to: Adaptively biased MD, Adaptive reaction coordinate forces, Local elevation umbrella sampling

•Suggested and developed by Alessandro Laio and Michele Parrinello

== How does Metadynamics work? ==
•Filling free energy wells with computational sand

•Tracking grains of sand placed along collective variables

•Eventually the wells are completely full and you add sand to sand (known as convergence)

•The landscape is opposite of sum of all sand

Movie: https://www.youtube.com/watch?v=IzEBpQ0c8TA

== How Metadynamics Really Work! ==
•Collective variables (s): set of variables which accurately describe the system

•CV Examples: Dihedral angle for cis to trans butane, Distance for cation and anion

•Limitations: 3CV or 8CV with multiple replicas coupled together

•Exponential cost increase with each CV

•Grains of sand are bias potentials
[[File:Hamiltonian With Bias Potential.png|thumb]]

•Bias potential Vbias is continuously updated by adding bias (more grains of sand)
[[File:Energy Landscape Filled With Gaussians.png|thumb]]

[[File:Bias Potential Equation and Integral.png|thumb]]

•Vbias: bias potential

•tsim: simulation time

•s: collective variable

•st: instantaneous collective variable at time t

•ω: bias deposition rate

•F: free energy

•C: constant (irrelevant)

•Evaluating the integral of bias potential over the time duration of the simulation returns free energy F with a negative sign given enough time

== How to make Metadynamics efficient and computationally viable? ==
[[File:Efficient Bias Potential Equation.png|thumb]]
•Time is discretized into T time intervals

•The Dirac delta function is replaced with a Gaussian function

•Time intervals (T), bias deposition rate (ω), and width of Gaussian functions (σ) are constants determined as inputs

== Two types of Metadynamics ==
•Everything so far has been “original” or “plain” metadynamics

•Well-tempered metadynamics scales Gaussian height down as wells are filled
[[File:Gaussian Height Scaling Equation.png|thumb]]
•w: Gaussian height

•ω: bias deposition rate

•Vb: estimate of free energy at current CV position and time step

•ΔT: tunable parameter controls how quickly Gaussian height reduces as wells are filled
[[File:Free Energy Equation Using Well-Tempered Metadynamics.png|thumb]]
•Final value of biasing potential is a scaled approximation of free energy

• Well-tempered metadynamics allows for rapid exploration of phase space as the wells are filled quickly (at Vbias=0 the amount of bias deposited is large, at Vbias=infinity the amount of bias deposited is infinitely small)

•As wells fill progressively smaller perturbations to bias potential lead to "smooth convergence" (less excess potential or sand)

•Suggested and developed by Alessandro Barducci, Giovanni Bussi, and Michele Parrinello

Movie Comparing MD, MTD, and WTMTD: https://www.youtube.com/watch?v=IzEBpQ0c8TA

== Applications of Metadynamics ==
•Able to sample free energy curve even when ergodicity is limited by energy landscape

•Keys to successful metadynamics simulation are choice and definition of CVs

•Applicable systems: Protein folding, Molecular docking, Phase transitions, Chemical reactions, Simple to complex systems as long as CVs are sufficient to describe system

•Widely integrated as PLUMED and Collective Variable Module:

•PLUMED: AMBER, GROMACS, LAMMPS, NAMD, Q ESPRESSO, CP2K, OpenMM

•Collective Variable Module: LAMMPS, NAMD, GROMACS, ORAC, CP2K, Desmond

File:Free Energy Equation Using Well-Tempered Metadynamics.png

2022-08-31T17:09:22Z

Cda923:

Well tempered metadynamics yields a scaled approximation of free energy using the final value of the biasing potential scaled by deltaT

File:Gaussian Height Scaling Equation.png

2022-08-31T17:07:42Z

Cda923:

Equation scaling Gaussian height according to parameter deltaT and magnitude of bias potential

File:Efficient Bias Potential Equation.png

2022-08-31T17:06:12Z

Cda923:

Equation of bias potential made to be computationally efficient

File:Bias Potential Equation and Integral.png

2022-08-31T17:03:31Z

Cda923:

Equation for bias potential and evaluated integral to obtain free energy with opposite sign

File:Energy Landscape Filled With Gaussians.png

2022-08-31T17:01:26Z

Cda923:

Figure with wells being filled with Gaussian functions.
Rozanov, E.O., Protsenko, S.P. & Baidakov, V.G. Study of the Activation Barrier of Crystallization of a Metastable Liquid Using Metadynamics. Phys. Solid State 64, 22–25 (2022). https://doi.org/10.1134/S1063783422010176

File:Hamiltonian With Bias Potential.png

2022-08-31T16:58:26Z

Cda923:

Hamiltonian of a system with the added bias potential