SMA5233
Particle Methods and Molecular Dynamics
Lecture 1: Introduction
A/P Chen Yu Zong
Tel: 6516-6877
Email: phacyz@nus.edu.sg
http://bidd.nus.edu.sg
Room 08-14, level 8, S16
National University of Singapore
What is expected:
To learn basic theory, algorithm of molecular
simulations and their applications
To learn the fundamentals in molecular
modeling
To practice the installation and use of related
software
2
Labs, Exams and Textbook:
Projects and labs of part 1:
Molecular dynamics software (12%).
Simulation of biomolecular motions and dynamics
(12%).
Exams (part 1: 26%)
Text and web:
http://bidd.nus.edu.sg/group/teach/sma5233/sma5233.htm
3
Topics covered in part 1:
Lecture 1: Introduction
Lecture 2: Physical Principles and Design Issues
of MD
Lecture 3: Force Fields
Lecture 4: Integration Methods
Lecture 5: Applications in Biomolecular Simulation
and Drug Design
4
Topics covered in part 2:
Lecture 6, introduction to Monte Carlo method,
random number generators
Lecture 7, Some applications of MC method
Lecture 8, Advanced MC methods, such as parallel
tempering
Lecture 9, Brownian dynamics, stochastic
differential equations
Lecture 10, dissipative particle method
Lecture 11, smoothed particle hydrodynamics
5
Reference Books for Part 1:
"Molcular Modelling. Principles and Applications". Andrew Leach. Publisher: Prentice Hall. ISBN:
0582382106. This book has rapidly become the defacto introductory text for all aspects of simulation.
"Molecular Dynamics Simulation: Elementary Methods". J.M. Haile. Publisher: Wiley. ISBN:
047118439X. This text provides a more focus but slightly more old-fashioned view of simulation. It has
some nice simple examples of how to code (in fortran) some of the algorithms
P.W. Atkins Physical Chemistry (any edition) Chapters 11-14)
Schlick, T. Molecular Modeling and Simulation: An Interdisciplinary Guide. Springer-Verlag, New York,
NY: 2002. ISBN 0-387-95404-X.
MacKerell, A.D., Jr., Empirical Force Fields for Biological Macromolecules: Overview and Issues,
Journal of Computational Chemistry, 25: 1584-1604, 2004
M. P. Allen, D. J. Tildesley (1989) Computer simulation of liquids. Oxford University Press. ISBN
0198556454.
J. A. McCammon, S. C. Harvey (1987) Dynamics of Proteins and Nucleic Acids. Cambridge University
Press. ISBN 0-52-135652-0 (paperback); ISBN 0-52-130750 (hardback).
D. C. Rapaport (1996) The Art of Molecular Dynamics Simulation. ISBN 0521445612.
Daan Frenkel, Berend Smit (2001) Understanding Molecular Simulation. Academic Press. ISBN
0122673514.
J. M. Haile (2001) Molecular Dynamics Simulation: Elementary Methods. ISBN 047118439X
Oren M. Becker, Alexander D. Mackerell Jr, Benoît Roux, Masakatsu Watanabe (2001) Computational
Biochemistry and Biophysics. Marcel Dekker. ISBN 082470455X.
Tamar Schlick (2002) Molecular Modeling and Simulation. Springer. ISBN 038795404X.
6
Molecular Modeling: Goals, Problems,
Perspectives
1. Goal
simulate/predict processes such as
1. DNA migration in nanofluidic tube
2. polypeptide folding
3. biomolecular association
4. partitioning between solvents
5. membrane/micelle formation
thermodynamic
equilibria governed
by weak (nonbonded)
forces
6. drug conformation
7
Example of MD Application:
How can an enzyme metabolite escape?
The enzyme acetylcholinesterase
generates a strong electrostatic field
that can attract the cationic substrate
acetylcholine to the active site.
However, the long and narrow active
site gorge seems inconsistent with the
enzyme's high catalytic rate.
E+S E+P
How does the metabolite P escape?
Acetylcholinesterase (AChE) is the enzyme
responsible for the termination of signaling
in cholinergic synapses (such as the
neuromuscular junction) by degrading the
neurotransmitter acetylcholine. AChE has a
gorge, 2 nm deep, leading to the catalytic
site
8
How can an enzyme metabolite escape?
Metabolite
unlikely
escape from
the entrance
How can it
escape?
9
How can an enzyme metabolite escape?
How can it escape?
Can you tell which of
the following
possibilities is likely or
unlikely, and why?
Protein unfolding
Condensation of
ions on protein
surface to counterbalance the force
Change of electric
charge on
metabolite
Alternative escape
route
10
How can an enzyme metabolite escape?
Alternative
route
An “open
back door”
policy:
Transient
opening of a
channel to
allow the
metabolite to
escape
11
MD simulation of acetylcholinesterase
MD simulation clearly
reveals transient opening
of a channel “back door”
Science 263, 1276-1278
(1994)
The open “back door”
allows the metabolite P
to escape
12
Molecular Modeling: Goals, Problems,
Perspectives
1. Goal
Common characteristics:
-
Degrees of freedom: atomic, coarse-grain
(solute + solvent)
Equations of motion: classical dynamics
Governing theory: statistical mechanics
Hamiltonian or
force field
entropy
13
Processes: Thermodynamic Equilibrium
Folding
folded/native
Micelle Formation
denatured
Complexation
bound
unbound
micelle
mixture
Partitioning
in membrane
in water in mixtures
14
Definition of a model for molecular simulation
Every molecule consists of atoms that are very strongly bound to each other
Degrees of freedom:
atoms are the
elementary particles
Forces or
interactions
between atoms
Boundary conditions
MOLECULAR
MODEL
Force Field =
physicochemical
knowledge
Methods for
generating
configurations of
atoms: Newton
system
temperature
pressure
15
Molecular Modeling: Goals, Problems,
Perspectives
Four Problems
1. Force field
A very small (free) energy
differences
B entropic effects
C size problem
3. Ensemble problem
4. Experimental problem
A averaging
B insufficient accuracy
2. Search problem
A the search problem alleviated
B the search problem aggravated
16
Four Problems
1. The Force Field Problem
A very small (free) energy differences (kBT = 2.5 kJ/mol)
resulting from summation over very many contributions (atoms)
i
i
106 – 108
must be very accurate
energy
E(x)
B accounting for entropic effects
not only energy minima are of
importance but whole range of
x-values with energies ~kBT
must be included in the
force field parameter calibration
may have higher energy
but lower free energy
than
coordinate x
17
Four Problems
C size problem
The larger the system, the more accurate the individual energy
contributions (from atoms) must be to reach the same overall
accuracy
Calibrate force field using thermodynamic data for small molecules in
the condensed phase keep force field physical + simple
transferable
computable
18
Choice of Model, Force Field, Sampling
3. Scoring Function, Energy Function, Force Field
-
-
Continuous n Lattice
Basis for force field or scoring function:
1. Structural data
- Large molecules:
crystal structures
solution structures of proteins
2. Thermodynamic data
- Small molecules:
heat of vaporization, density
in condensed phase partition coefficients
e, D, h, etc.
3. Theoretical data
- Small molecules:
in gas phase
electrostatic potential and gradient
torsion–angle rotation profiles
19
Determination of Force Field Parameters
Calibration sets of small molecules
1. Non-polar molecules
2. Polar molecules
3. Ionic molecules
Calibration set: 28 compounds
2. Polar Molecules
methanol
ethanol
ethers, alcohols, esters, ketones,
acids, amines, amides, aromatics,
2-propanol
sulfides, thiols
diethylether
butanol
20
Determination of Force Field Parameters
Calibration set: 28 compounds
ethylamine
acetone
1-butylamine
2-butanone
ethyldiamine
3-pentanone
acetic acid
diethylamine
n-methylacetamide
21
Applications of Molecular Simulation in
(Bio)Chemistry and Physics
1. Types of Systems
-
-
liquids
solutions
electrolytes
polymers
- proteins
- DNA, RNA
- sugars
- other
polymers
membranes
crystals
glasses
zeolites
metals
…
2. Types of Processes
3. Types of Properties
- melting
- structural
- adsorption
- mechanical
- segregation
- dynamical
- complex formation
- thermodynamical
- protein folding
- electric
- order-disorder
- …
transitions
- crystallisation
- reactions
- protein stabilisation
- membrane
permeation
- membrane
formation
- …
22
Objectives
Characterization of the populated microscopic states of
molecules by molecular dynamics of spontaneous reversible
motions in solution
Investigate the effect of
Thermodynamic conditions
Solvent environment
Amino acid composition, chain length
on the peptide folding behavior
Characterization of the unfolded state
23
Four Problems
4. The Experimental Problem
A Any experiment involves averaging over time and space (molecules)
So it determines the average of a distribution, not the distribution itself
However:
Very different
distributions may
yield same average
probability
P(Q)
(linear) average
<Q>
quantity Q
Example:
circular dichroism(CD)-spectra b-peptides
NOE’s + J-values of peptides in
crystal
solution
NOE: Nuclear Overhauser effect leads to changes in the intensity of signal(s) of a set of nuclei as
a function of their respective distances. The use of NOE allows to obtain structural information on
peptides and proteins in solution as well as the study of interactions between small ligands and
biomolecules.
24
Four Problems
NOE’s:
J-values:
X-ray:
are notoriously insensitive to the (atom-atom-distance)
distribution provided a small part satisfies the NOE bounds
may be sensitive to dihedral angle distribution
crystal contains a much narrower distribution than a
(aqueous) solution
Experimental data cannot define a conformational ensemble
B Experimental data have insufficient accuracy for force field calibration
and testing
accuracy of NOE’s, J-values, structure factors, etc. is limited but may
improve with methodological and technical progress
Example: NMR data on beta-hexapeptide, alpha-octapeptide
Experimental data may converge over time towards simulation results
25
Molecular Simulations
Molecular Mechanics: energy minimization
Molecular Dynamics: simulation of motions
Monte Carlo methods: sampling techniques
26
What is molecular mechanics?
The term molecular mechanics refers to the use of Newtonian
mechanics to model molecular systems.
Molecular mechanics approaches are widely applied in
molecular structure refinement, molecular dynamics simulations,
Monte Carlo simulations and ligand docking simulations.
Molecular mechanics can be used to study small molecules as
well as large biological systems or material assemblies with
many thousands to millions of atoms.
27
What is molecular mechanics?
All-atomistic molecular mechanics methods have the
following properties:
– Each atom is simulated as a single hard spherical particle
– Each such particle is assigned a radius (typically the van der
Waals radius) and a constant net charge (generally derived
from high-level quantum calculations and/or experiment)
– Bonded interactions are treated as "springs" with an
equilibrium distance equal to the experimental or calculated
bond length
28
What is molecular mechanics?
Molecular Mechanics (MM) finds the geometry that
corresponds to a minimum energy for the system - a
process known as energy minimization.
A molecular system will generally exhibit numerous
minima, each corresponding to a feasible conformation.
Each minimum will have a characteristic energy, which
can be computed. The lowest energy, or global minimum,
will correspond to the most likely conformation.
29
What is molecular dynamics simulation?
Simulation that shows how the atoms in the
system move with time
Typically on the nanosecond timescale
Atoms are treated like hard balls, and their
motions are described by Newton’s laws.
30
What is molecular dynamics simulation?
Beginning in theoretical physics, the method of MD gained
popularity in material science and since the 1970s also in
biochemistry and biophysics.
In chemistry, MD serves as an important tool in protein
structure determination and refinement (see also
crystallography, NMR)
In physics, MD is used to examine the dynamics of atomiclevel phenomena that cannot be observed directly, such as
thin film growth. It is also used to examine the physical
properties of nanotechnology devices that have not or
cannot yet be created.
31
What is molecular dynamics simulation?
Note that there is a large difference between the focus and
methods used by chemists and physicists, and this is
reflected in differences in the jargon used by the different
fields.
In Chemistry, the interaction between the objects is either
described by a force field (chemistry) (classical MD), a
quantum chemical model, or a mix between the two. These
terms are not used in Physics, where the interactions are
usually described by the name of the theory or
approximation being used.
32
Why MD simulations?
Link physics, chemistry and biology
Model phenomena that cannot be observed
experimentally
Understand protein folding…
Access to thermodynamics quantities (free
energies, binding energies,…)
33
Molecular Dynamics Simulations
Schrödinger equation
Born-Oppenheimer approximation
Nucleic motion described classically
Empirical force field
34
Molecular Dynamics Simulations
Interatomic interactions
35
Molecular dynamics Simulations of Biopolymers
d2
(  ) ma 2 R   Eel ( R1 ,..., RN ),   1,..., N .
dt
•
Motions of nuclei are described classically,
•
Potential function Eel describes the electronic influence on motions of the nuclei and
is approximated empirically  „classical MD“:
E el 

Eibond 
Bindungen
i
E
Bindungs
winkel j
angle
j

E
Dihedral
winkel k
Covalent bonds
dihe
k
.
rep .
vdW
  ( ECoul
,b  E ,b  E ,b )  ...,
Non-bonded interactions
Eibond
approximated
exact
=
=
R
KBT {
0
|R|
36
Computational task:
Solve the Newtonian equations of motion:
37
Molecular dynamics is very expensive ...
Example: F1-ATPase in water (183 674 atoms), 1 nanosecond:
106 integration steps
8.4 * 1011 flop per step [n(n-1)/2 interactions]
total:
8.4 * 1017 flop
on a 100 MFLOPS workstation:
250 years
...but performance has been improved by use of:
multiple time stepping
25 years
+ structure adapted multipole methods
6 years
+ FAMUSAMM
2 years
+ parallel computers
55 days
•
FLOPS : Floating Point Operations Per Second on a standard benchmark such as LINPACK
benchmark
•
Many other factors affect computation speed: I/O, inter-processor communication, cache coherence,
memory hierarchy.
•
Typical systems: 2GHz Pentium 4 (few GFLOPS); IBM Blue Gene/L 131,072 processors (207.3
TFLOPS); SETI@home (100 TFLOPS); Pocket calculator (10 FLOPS); Human (milliFLOPS)
38
Limits of MD-Simulations
• Classical description:
Chemical reactions not described
Poor description of H-atoms (proton-transfer)
Poor description of low-T (quantum) effects
Simplified electrostatic model
Simplified force field
• Only small systems accessible (104 ... 106 atoms)
• Only short time spans accessible (ps ... μs)
39
MD as a tool for minimization
Energy
Molecular dynamics
uses thermal energy
to explore the energy
surface
State A
State B
Energy minimization
stops at local minima
40
Position
Energy
Crossing energy barriers
I
DG
State B
State A
A
B
time
Position
The actual transition time from A to B is very quick (a few pico seconds).
What takes time is waiting. The average waiting time for going from A to B can be
expressed as:
 AB  Ce
DG
kT
41