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)? ->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 • 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)?

2. Moleculardynamics/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

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?