ProteinNucleic Acid Dynamics

1
Protein-Nucleic Acid Dynamics

• Ashok Kolaskar
• Vice Chancellor
• University of Pune
• Pune
• India

2
Molecular Dynamics Introduction

• Biomolecules are
• polymers of basic building blocks
• Proteins ? Amino Acids
• Nucleic acids ? Nucleotides
• Carbohydrates ? Sugars

3
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

4
Molecular Dynamics Introduction

• Newtons second law of motion

5
Molecular Dynamics Introduction

• We need to know
• The motion of the
• atoms in a molecule, x(t)
• and therefore,
• the potential energy, V(x)

6
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

7
Molecular Dynamics Introduction

• Potential energy includes terms for (contd.)
• Electrostatic
• Interactions
• van der Waals
• Interactions

8
Molecular Dynamics Introduction

• Equation for covalent terms in P.E.

9
Molecular Dynamics Introduction

• Equation for non-bonded terms in P.E.

10
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
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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)

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Molecular Dynamics Introduction

• The position x2 , of the atom after time interval
  ?t would be,
• and the velocity v2 would be,

13
How a molecule changes during MD
14
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,

15

• Generalizing these ideas, the trajectories for
  all the atoms of a molecule can be calculated.

16
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

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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.

18
An overview of various motions in proteins (1)
19
An overview of various motions in proteins (2)
20
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

21
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)

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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

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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.

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BASIC INFORMATION FLOW IN AMBER
seq
pdb
forcefield
database
prep
link
edit
parm
nmode
constraints
Nmanal, lmanal
Sander, Gibbs, spasms
carnal
anal
mdanal
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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.

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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.

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STARTING DNA MODEL
28
DNA MODEL WITH IONS
29
DNA in a box of water
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SNAPSHOTS
31
SNAPSHOTS
32
SHORTENING
33
AVERAGE ROLL
34
AVERAGE TWIST
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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
  G7C7 and C8G6 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.

36
DOCKING

• The MD frames bearing closest similarity to the
  conformation of the DNA in the PvuII-DNA 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.

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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.

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DOCKING
39
DOCKING
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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