Questions

1
Questions
Blue should have been covered in lecture. If you
still have questions. Please,Ask!

• 1) Are the values of r0/theta0 approximately what
  is listed in the book (in table 3.1 and 3.2)? -gt
  for those atom pairs/triplets yes
• 2) In the equations listed for 3.5, what is the
  j? Is that just the coordinate in space? -gt its
  the monomer unit
• 3)What exactly is the AMBER program used for? -gt
  MD, minimization and free energy calculations we
  will be using other programs
• 4) Topological Restraints-if the are key in
  mainting a well defined structure, how come they
  have been "ignored" in all the calculations we've
  seen so far. The book is slightly dated
• In section 3.1.2, the text speaks of the
  "potential energy due to rotation around the
  valence cone." ...what is a valence cone? -gt see
  figure 1.3, and the lab these are torsions
• 6) Re-explain what the high T approximation is
  used for and why. I don't remember now, for some
  reason?
• 7) What is the AMBER program and how does it
  arrive at its values?
• 8) I think there is something wrong with equation
  (3.5) because I think it should be
• xjrcos(2pijp/Pphi0)and yjrsin(2pijp/Pphi
  0),because Pgtp from textbook. You are correct
  this is a typo.
• 9) Explain Ep in equation (3.4)?

2
Molecular dynamics/mechanics programs
We will use these in lab
They are used to
Model protein structures Study protein folding
with more approximations/tricks Calculate
free energy changes with more
tricks Calculate protein energetics Simulate
conformational flexibility Occasionally, study
protein dynamics Examine motional correlations
across a protein Study binding events Do thought
experiments
Use the force fields to do their work, in
conjunction with Optimization routines
minimization -gt very hard 3N-6/3N-3 PES N
gt1000 Solving Newtons equations of motions
possibly with restraints/constraints and extra
degrees of freedom Monte Carlo
3
Force Fields
Potential energy terms used to determine the
energies and forces during dynamics
There have been changes in the way most
forcefields are computed since Daune was first
published
Many different force fields in existence
Some are designed for organic molecules, some for
biomolecules, some for both. Some for different
types of calculations.
CHARMM22/27 and AMBER force fields are the most
commonly used for biomolecules
Force fields vary in complexity, but CHARMM and
AMBER are similar.
Force field in this context is short for all-atom
force field.
4
Force Fields
Potential energy terms used to determine the
energies and forces during dynamics
There have been changes in the way most
forcefields are computed since Daune was first
published
Force fields have to be determined
self-consistently see paper
Balance different types of interactions
nonbonded vs bonded solute-solute,
Solvent-solvent and solvent-solute interactions
Use experimental data on connectivity
supplemented by ab initio calculations
Back-check a proposed set of parameters with MD
simulations and minimizations, and fiddle with
the parameters until the results are consistent
Use the simplest set of functions to reproduce
physics, and structural properties
5
Bonds
Harmonic Potential
Only good for small vibrations
CANNOT be used to study bond-breaking
Parameters can be obtained from experiments
often, or from QM calculations
Examples CA CA 305.000 1.3750 from
experiments on benzene CT1 C 250.000
1.4900 from 6-31G/HF calculations on ala
dipeptide
6
Bonds
Cubic and higher terms are used in some force
fields designed for small molecules. Especially,
the MMFF force field which is well-parameterized
for many organic molecules.
Morse could allow for bond-breaking but it would
be long-timescale, and expensive
Morse term has been used in conjuction with
standard force fields to study particular bonds
simulate at various points along the morse
oscillator to integrate over the other degrees
of freedom
7
Angle Interactions
Harmonic Potential
Most common form
For a wide range of angles, this term is not
enough!
Parameters can be obtained from experiments
often, or from QM calculations
Examples CA CA CA 40.000 120.00 from
experiments on benzene HB CT1 C 50.000
109.5000 from 6-31G/HF calculations on ala
dipeptide
8
Angle Interactions
Harmonic Potential
Most common form
For a wide range of angles, this term is not
enough!
Parameters can be obtained from experiments
often, or from QM calculations
Examples CA CA CA 40.000 120.00 from
experiments on benzene HB CT1 C 50.000
109.5000 from 6-31G/HF calculations on ala
dipeptide
9
Angle Interactions Urey-Bradley
Often too floppy for ring compounds
For a subset of angles add, a Urey-Bradley term
r
Examples CA CA CA 40.000 120.00 35.00
2.41620 HB CT1 C 50.000 109.5000
10
Bond/Angle interactions
When fitting a potential energy surface
experimentally or computationally, Usually need
bond/angle and bond/bond terms
And more complex forms stretch/bend/stretch.
Usually ignored in biomolecules.
11
Dihedral interactions
Torsions are usually represented by a series
Often reduces to a single term.
There can in principle be cross-terms with angles
and/or dihedrals often when fitting potential
surfaces, but rarely used in biomolecular force
fields. The next version of the CHARMM force
field will include phi/psi cross-terms for at
least some amino acids to properly balance
helical forms
12
Bonded Interactions
The interactions discussed thus far are the
bonded interactions. They are used to mimic
chemical connectivity.
13
NonBonded Interactions
There are two sets of nonbonded interactions
electrostatics and van der Waals. Almost all
pairs of atoms are involved in both interactions.
Note the sums exclude atoms connected by angles,
or bonds some FF also exclude dihedrals This
does imply that FF dihedrals are not exactly the
same as dihedrals from experimentalists
14
Charge interactions
QM calcs are the starting points for charges
atom-centered monopole fits to the electrostatic
potential of a model molecule note two approx
here
Charges are commonly modified as part of the
iterative fitting the approximate fits to QM
potential do not reflect the environment found in
proteins or even in solvent
Some rare force fields use atom-based multipoles
3rd generation force fields will allow for
polarizability
15
Nonbonded Interactions
Vdw parameters are typically considered as the
size of the atom, and the strength of
interaction. However,hydrogens are shrunk
The pairs of parameters are often too many to
fit, so a further approximation is
The vdW parameters are fit , with charges, to
reproduce hydrogen bonds. So the vdW
interactions include parts of H-bonds and
dihedrals steric repulsion
Leaving fewer parameters to fit iteratively,
along with the charges and Sometimes dihedrals.
What has happened to hydrogen bonds?