Transcript No Slide Title

Protein-Nucleic Acid Dynamics
Ashok Kolaskar
Vice Chancellor
University of Pune
Pune
India
Molecular Dynamics: Introduction
Biomolecules are
polymers of basic building blocks
Proteins
Nucleic acids
Carbohydrates



Amino Acids
Nucleotides
Sugars
Molecular Dynamics: Introduction
• At physiological conditions, the
biomolecules undergo several movements
and changes
• The time-scales of the motions are diverse,
ranging from few femtoseconds to few
seconds
• These motions are crucial for the function
of the biomolecules
Molecular Dynamics: Introduction
Newton’s second law of motion
Molecular Dynamics: Introduction
We need to know
The motion of the
atoms in a molecule, x(t)
and therefore,
the potential energy, V(x)
Molecular Dynamics: Introduction
How do we describe the potential energy V(x) for a
molecule?
Potential Energy includes terms for
Bond stretching
Angle Bending
Torsional rotation
Improper dihedrals
Molecular Dynamics: Introduction
Potential energy includes terms for (contd.)
Electrostatic
Interactions
van der Waals
Interactions
Molecular Dynamics: Introduction
Equation for covalent terms in P.E.
 k (l  l )   k    
Vbonded ( R) 
l
0
bonds


2
2
0
angles
k (   0 ) 2 
impropers
 A [1  cos(n   )]
n
torsions
0
Molecular Dynamics: Introduction
Equation for non-bonded terms in P.E.
Vnonbonded ( R) 

i j
rijmin 12
rijmin 6
qi q j
( ij [(
)  2(
) ]
rij
rij
4 r  0rij
Molecular Dynamics: Introduction
• Each of these interactions exerts a force
onto a given atom of the molecule
• The total resulting force on each atom is
calculated using the PE function
Knowing the force on an
atom, its movement due
to the force is then
calculated:
Molecular Dynamics: Introduction
To do this, we should know
at given time t,
• initial position of the atom
x1
• its velocity
v1 = dx1/dt
• and the acceleration
a1 = d2x1/dt2 = m-1F(x1)
Molecular Dynamics: Introduction
The position x2 , of the atom after time
interval t would be,
x2  x1  v1t
and the velocity v2 would be,
1
v2  v1  a1t  v1  m F ( x1)t  v1  m
1 dV
dx
x 1 t
How a molecule changes during MD
Molecular Dynamics: Introduction
In general, given the values x1, v1 and the
potential energy V(x), the molecular
trajectory x(t) can be calculated, using,
xi  xi 1  vi 1t
1 dV ( x)
vi  vi 1  m
xi1 t
dx
• Generalizing these ideas, the trajectories for
all the atoms of a molecule can be
calculated.
The Necessary Ingredients
• Description of the structure: atoms and
connectivity
• Initial structure: geometry of the system
• Potential Energy Function: force field
• AMBER
• CVFF
• CFF95
• Universal
Protein-specific Applications of MD
• Calculation of thermodynamic properties
such as internal energy, free energy
• Studying the protein folding / unfolding
process
• Studying conformational properties and
transitions due to environmental conditions
• Studying conformational distributions in
molecular system.
An overview of various motions in proteins (1)
Motion
Spatial extent
(nm)
Log10 of
characteristic
time (s)
Relative vibration of
bonded atoms
0.2 to 0.5
-14 to –13
Elastic vibration of
globular region
1 to 2
-12 to –11
Rotation of side
chains at surface
0.5 to 1
-11 to –10
Torsional libration
of buried groups
0.5 to 1
-14 to –13
An overview of various motions in proteins (2)
Spatial
Extent (nm)
Log10 of
characteristic
time (s)
1 to 2
-11 to –7
0.5
-4 to 0
Allosteric transitions
0.5 to 4
-5 to 0
Local denaturation
0.5 to 1
-5 to 1
Protein folding
???
-5 to 2
Motion
Relative motion of
different globular regions
(hinge bending)
Rotation of medium-sized
side chains in interior
A typical MD simulation protocol
•
•
•
•
Initial random structure generation
Initial energy minimization
Equilibration
Dynamics run – with capture of
conformations at regular intervals
• Energy minimization of each captured
conformation
Essential Parameters for MD
(to be set by user)
•
•
•
•
•
•
•
Temperature
Pressure
Time step
Dielectric constant
Force field
Durations of equilibration and MD run
pH effect (addition of ions)
WHAT IS AMBER?
AMBER (Assisted Model Building with Energy
Refinement).
Allows users to carry out molecular dynamics
simulations
Updated forcefield for proteins and nucleic acids
Parallelized dynamics codes
Ewald sum periodicity
New graphical and text-based tools for building
molecules
Powerful tools for NMR spectral simulations
New dynamics and free energy program
WHY AMBER?
Most widely used program: approximately 5000 users
world over.
Over 1000 research papers have been published using
AMBER.
Program available at a nominal price for academic
users.
Complete source code available with the package.
Available for most machine configurations.
Developed by Prof.Peter Kollman at the University of
California San Francisco: An authority in the area of
molecular simulations.
BASIC INFORMATION FLOW IN AMBER
database
prep
seq
link
pdb
edit
forcefield
parm
nmode
Nmanal,
constraints
lmanal
Sander,
Gibbs,
spasms
carnal
anal
mdanal
CASE STUDY
• Type II restriction endonucleases recognize DNA
sequences of 4 to 8 base pairs in length and require
Mg2+ to hydrolyse DNA.
• The recognition of DNA sequences by endonucleases
is still an open question.
• PvuII endonuclease, recognizes the sequence 5’CAGCTG-3’ and cleaves between the central G and C
bases in both strands.
• Though crystal structure of the PvuII-DNA complex
have been reported, very little is known about the
steps involved in the recognition of the cleavage site
by the PvuII enzyme.
• Molecular dynamics (MD) simulation is a powerful
computational approach to study the macromolecular
structure and motions.
CASE STUDY: METHODS (MD Simulations)
• Simulations were carried out on the sequence
–
–
–
–
–
–
–
5’-TGACCAGCTGGTC-3’
Rectangular box (60 X 48 X 54 Å3) containing 24 Na+, using PBC
SHAKE algorithm
Integration time step of 1 fs
283 K with Berendsen coupling
Particle Mesh Ewald (PME) method
9.0 Å cutoff was applied to the Lennard-Jones interaction term.
• Equilibration was performed by slowly raising the
temperature from 100 to 283 K. Production run was
initiated for 1.288 ns and the structures were saved at
intervals of one picosecond.
• The trajectory files were imaged using the RDPARM
program and viewed and analysed using the MOIL-VIEW
and CURVES packages respectively.
STARTING DNA MODEL
DNA MODEL WITH IONS
DNA in a box of water
SNAPSHOTS
SNAPSHOTS
SHORTENING
AVERAGE ROLL
AVERAGE TWIST
RESULTS
Particle Mesh Ewald simulations of PvuII substrate
• The simulations carried out using PME method, points out that
the initial straight B-helix conformation bends significantly as the
simulation progresses. The DNA molecule bends maximally by
18% and 22% at 616 ps and 1243 ps respectively. The base pair
rise (h) between G7:C7’ and C8:G6’ observed in this simulation,
shows large fluctuations around the normal value.
• The average roll value is seen to increase with simulation time and
this indicates bending of the DNA molecule.
• The offset values, for each base pair showed that the maximum
bending of the DNA molecule occurs at G7 and C8 bases.
• When viewed from the top, the snapshots of DNA structures
captured at 50 ps interval show that the DNA structures move
from a B-DNA structure to a close to an A-DNA.
• The average helical twist at the beginning of the simulation is an
ideal B-DNA, and is about 31 upto 500 ps and beyond 500 ps, the
twist is below that of an ideal A-DNA (28). This, along with phase
indicates that the molecule is neither in an A-DNA nor a B-DNA
form.
DOCKING
• The MD frames bearing closest similarity to
the conformation of the DNA in the PvuIIDNA crystal structure, were selected for
docking, using the Affinity module in the
MSI package.
• The molecules were subjected to MC
minimization with a maximum translational
move of 8 Å and a maximum rotational
move of 360 Å. An energy tolerance
parameter of 1000 was used.
DOCKING RESULTS
• In order to understand the phenomena of the recognition and
cleavage of the DNA substrate by the PvuII enzyme, the
conformation of the PvuII enzyme as obtained from the complex
crystal structure was docked to various frames of the DNA from
the MD trajectory.
• The structure at the 1230 ps gave good stable energy of –1898
Kcal/mol after optimization due to stabilization arising from
hydrogen bonds and nonbonded contacts between the amino acid
side chains and the bases in the DNA. The structure at 1230 ps also
showed a very high shortening of 22.31 % indicating that the
molecule is highly curved.
• This suggests that the PvuII enzyme recognizes the bent
conformation of the substrate DNA and binds to it.
• The shortening of the docked DNA was seen to be about 20.71 %
as compared to 3.73 % for that of the DNA in the complex crystal
structure, indicating that the enzyme prefers the bent DNA
structure.
DOCKING
DOCKING
CONCLUSION
• Our studies reported here for nanosecond MD
simulations point out that the 13-mer DNA
substrate for PvuII bends considerably.
• Docking studies showed that the PvuII enzyme
recognizes the bent DNA conformation.
• The local distortions in the helical
conformation at the base pair level may be
playing an important role during the cleavage
of the phosphodiester bond