Preparing the Starting Structure

1
Preparing the Starting Structure

• Employ a PDB file or hand build the structure
• Read the header remarks in the PDB file, view the
  structure with VMD, Deepview-Swiss PDB Viewer,
  Rasmol etc.
• X-ray structure
• Add hydrogens consider pH
• Build missing residue
• Generate biologically functional unit based on
  symmetry information in the header
• Address bound water molecules
• Select in case multiple side chain conformations
  are available
• NMR structure
• Select appropriate average structure

2
Generating the Input Structure
3
Sander Input File
4
Temperature Control

• To generate NVT, NPT ensembles
• To study the system behavior as temperature
  changes
• Protein unfolding
• Perform simulated annealing
• Searching conformational space

5
Constant Temperature Dynamics

• Kinetic Energy
• Velocity Reassignment Maxwell-Boltzmann
  Distribution
• Velocity Scaling

6
Constant Temperature Dynamics

• Berendsen Temperature Coupling Scheme

Rate of change of temperature is proportional to
the difference in temperature between bath and
the system ? a coupling parameter whose
magnitude determines how tightly the bath and
system are coupled
Amber simulation ? 0.5- 5.0 ps

• Artifact Hot solvent, sold solute

7
Constant Temperature Dynamics

• Stochastic collisions method Anderson et al.
• Randomly choose a particle and reassign its
  velocities from a Maxwell-Boltzmann distribution
• Trajectory Collection of mini microcanonical
  simulations
• Extended system method Nosé et al., Hoover et
  al.
• Thermal reservoir is part of the system,
  represented by additional degrees of freedom
• A fictitious mass parameter of the extra degree
  of freedom controls energy flow between the
  reservoir and system, larger the value of this
  parameter, slower the energy flow

8
Constant Pressure Dynamics

• Isothermal-isobaric ensemble
• Pressure is related to virial product of
  position and the derivative of PE
• Pressure is maintained by volume fluctuations of
  the simulation cell
• Volume fluctuations is related to isothermal
  compressibility, ?

9
Constant Pressure Dynamics

• Box side 20 Å (volume 8000 Å3) at 300 K
• For an ideal gas ? 1 atm-1, fluctuation 18100
  Å3
• for water ? 44.75x10-6 atm-1, fluctuation 121
  Å3

10
Constant Pressure Dynamics

• Weak Coupling method Berendsen
• Extended Pressure-Coupling method Anderson et
  al.
• Introduce an extra degree of freedom (piston)
  corresponding to the volume of the box

11
Boundary Conditions

• Vacuum Boundary Condition
• Spherical Boundary Condition

• Periodic Boundary Condition
• Extended Wall Boundary Condition

12
Nonbonded Computations

• Minimum Image Convention
• ?(N2) Computational Problem
• Cutoff Schemes ?(N) Computation
• cutoff lt L/2 , neighbor list
• Lennard-Jones term converges early but not the
  Coulomb term !

13
Particle Mesh Ewald

• A system of charged particles
• The charges are interpolated onto a grid
• Using FFT, the force and potential are calculated
  at the grid points
• Analytically differentiate the energies to
  calculate the force and update coordinates

?(NlogN) Computation
14
Constraint vis-à-vis Restraint

• Constraint implies absolutely fixed values for
  the selected dof (degree of freedom) of interest
  during the simulation
• Restraints means the use of a biasing energy
  function to maintain the dof of interest close to
  a reference state
• The SHAKE procedure constraints the heavy atom
  hydrogen bonds to a constant value so that the
  simulation can focus on other more important low
  frequency dof (implies we can use 2 fs timesteps
  instead of 1 fs or lower)
• The TIP3P water model constraints both the bond
  lengths and H-O-H angle in the water molecule
• The dof that can be placed under constrain or
  restrain include both cartesian coordinates or
  internal coordinates

15
Elements of MD Simulation

• Prepare the starting structure
• Parameters and topology
• Neutralize charge of the system
• Solvate
• Minimization
• Heating
• Equilibration
• Production
• Analysis

16
Following the Simulations Progress
Note Pressure fluctuations are higher than
temperature fluctuations!
17
Issues to Watch For!

• Imaging Simulation of infinite lattice under PBC
  could cause molecules from the original box to
  move out of the box. To obtain visually
  appropriate structure, wrapping of the molecules
  into the original box might be required.
• Vacuum bubbles The way solute molecules are
  soaked in water to obtain a solvated box causes
  improper density of the system, hence constant
  pressure simulations are required to properly
  equilibrate the system.
• Shake failures Common Causes bad steric
  contacts, some atoms moving too fast, incorrect
  potential being used?

18
Issues to Watch For!

• Hot solvent/Cold solute While employing uniform
  pressure rescaling procedure, energy drain from
  particular modes (eg. low freq modes of water)
  could result in imbalances in atomic
  temperatures.
• Flying Ice Cube Related to uniform velocity
  scaling procedures, with incomplete energy
  conservation. Regularly remove COM motion during
  the simulation.

19
Analysis of MD simulations

• Structural Properties
• RMSD
• Radius of gyration
• Temperature factors
• Distribution functions
• Energetic Properties
• Energy fluctuations
• Free Energy Studies
• Dynamical Properties
• Diffusion constants
• Time correlation functions
• PCA, QuasiHarmonic Analysis