Chapter 4 Self-test questions

Chapter 4 Self-test questions

Molecular Mechanics Methods

1. The bond-bending contribution to the molecular mechanics energy of a water molecule, for a structure with an angle of 120.6°, is 4.34 kcal mol-1. If the bending force constant kbend of equation (4.1) is 55 kcal mol-1 radian-2, what is the equilibrium bond angle θ0?

2. Which of the following is not the name of a forcefield?

3. For an MM model of a system containing four water molecules, the forcefield includes eight bond stretching terms and 6 oxygen-oxygen non-bonded terms. How many of each would be present in a system with 10,000 water molecules?

4. A peptide carbonyl carbon atom is positioned 10 Å from the peptide nitrogen atom of another residue. What is the Lennard-Jones interaction energy of eq. (4.5) if the σCC and σNN parameters are 2.00 and 1.85 Å, εCC and εNN are 0.11 and 0.20 kcal mol-1, and the combining rules of eq. (4.7) are used?

5. How many methanol molecules (RMM 32.04 g mol-1) are present in a cubic box with an edge length of 30 Å, assuming a density of 0.792 g cm-3?

6. When using periodic boundary conditions, every atom present in the simulation box, with coordinates (x, y, z), is accompanied by an infinite number of periodic images with coordinates (x+nxLx, y+nyLy, z+nzLz), where the n's are integers, and Lx, Ly and Lz are the length of the box in each direction. Consider a cubic box (L = 30 Å in each direction) and two atoms A and B with (xA, yA, zA) = (29, 14, 28) and (xB, yB, zB) = (2, 15, 1). What is the distance between the two closest images of A and B?

7. A molecular mechanics calculation is carried out on a protein which is roughly spherical, with a diameter of 40 Å. Periodic boundary conditions are used with a cubic box, whose length L is chosen so that if the protein is in the centre of the box, each part of the protein is at least 20 Å from the edge of the box. How many water molecules will be needed to fill the rest of the box, assuming that one water molecule occupies 29.9 Å3?

8. A Ca2+ ion interacts with a sulfate ion SO42- that is 20 Å away. How strong is the interaction due to Coulomb's law?

9. Combination rules lead to a requirement for many fewer parameters when developing forcefields. Consider a forcefield that is to be used for a system with 100 different atom types. How many Lennard-Jones radius parameters σ must be obtained if they are defined for each pair of atoms, or if combining rules are used, respectively?

10. Calculations are performed on a water droplet with radius r = 80 Å. Assuming each water molecule occupies 29.9 Å3, and that the layer with thickness 3.85 Å at the surface of the sphere corresponds to 'surface' molecules, how many molecules are present in total and at the surface, respectively?

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