Transcript Lecture #5 09/07/04

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)? -> 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?
-> it’s the monomer unit:
3)What exactly is the AMBER program used for? -> 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
5) In section 3.1.2, the text speaks of the "potential energy due to rotation around
the valence cone." ...what is a valence cone? -> 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
xj=rcos(2*pi*j*p/P+phi0)and yj=rsin(2*pi*j*p/P+phi0),because P>p from textbook.
You are correct; this is a typo.
9) Explain Ep in equation (3.4)?
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 -> very hard 3N-6/3N-3 PES; N >1000
Solving Newton’s equations of motions; possibly with restraints/constraints and extra
degrees of freedom
Monte Carlo
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.
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
Bonds
Harmonic Potential
EB  S [r  r0 ]2
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
CT1 C 250.000
dipeptide
1.3750 from experiments on benzene
1.4900 from 6-31G/HF calculations on ala
Bonds
Cubic and higher terms
are used in some force
fields designed for small
molecules. Especially,
the MMFF force field
which is wellparameterized 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
Angle Interactions
E A  S [   0 ]2
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
HB CT1 C
ala dipeptide
40.000 120.00 from experiments on benzene
50.000 109.5000 from 6-31G/HF calculations on
Angle Interactions
E A  S [   0 ]2
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
HB CT1 C
ala dipeptide
40.000 120.00 from experiments on benzene
50.000 109.5000 from 6-31G/HF calculations on
Angle Interactions: Urey-Bradley
E A  S [   0 ]2
Often too floppy for
ring compounds
For a subset of angles add, a Urey-Bradley term
EUB  S[r  r0 ]
2
r
Examples:
CA CA CA
HB CT1 C
40.000 120.00 35.00 2.41620
50.000 109.5000
Bond/Angle interactions
When fitting a potential energy surface experimentally or computationally,
Usually need bond/angle and bond/bond terms
Err '  S[r  r0 ][r  r 0 ]
'
'
Er  S[r  r0 ][  0 ]
E '  S[  0 ][   0 ]
'
'
And more complex forms {stretch/bend/stretch}. Usually ignored in
biomolecules.
Dihedral interactions
Torsions are usually represented by a series:
E=  K n (1 + cos(n( ) -  ))
n
Often reduces to a single term.
E= K(1 + cos(n( ) -  ))
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 crossterms {for at least some amino acids} to properly balance helical forms
Bonded Interactions
EBonded   Si [ri  ri 0 ]   Si [i  i 0 ]   Si [ri  ri 0 ] 
2
bonds
2
angles
2
UB
 V [1 cos(n   )]
ni
1
dihedrals n
The interactions discussed thus far are the “bonded interactions”. They
are used to mimic chemical connectivity.
NonBonded Interactions
Enonbonded  
{ij }
qi q j
rij2
 r0ij
   ij 
r
{ij }
 ij
12

 r0ij 
   

 rij 
6
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
Charge interactions
Eq  
{ij }
qi q j
2
ij
r
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
Nonbonded Interactions
Evdw
 r0ij
   ij 
r
{ij }
 ij
12

 r0ij 
   

 rij 
6
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:
 ij   ii jj
 ij 
 ii   jj
2
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?