Chapter 6 Self-test questions

. A dynamical simulation is performed by carrying out a certain number of structural updates using the Verlet method of equation (6.5). Assuming that the simulated phenomenon takes 200 fs to occur, and that a timestep of 0.1 fs is used, how many timesteps are needed?

2,000

200

10

4,000

. Carrying out a molecular dynamics simulation requires choosing an initial structure R₀, as shown in Figure 6.2. Concerning this initial structure, which of the following statements is not true?

For a long enough simulation, the average properties generated from the simulation will not depend on the choice of R₀.

The initial structure must be chosen to be a minimum on the potential energy surface.

In many cases, a poor choice of R₀ will lead to incorrect results.

The impact of the choice of R₀ will differ depending on the nature of the system – systems that reach equilibrium rapidly such as simple liquids will be less sensitive to R₀ than other systems.

. Biomolecular simulation using molecular dynamics or Monte Carlo methods is one of the major fields of computational science nowadays. Which of the following statements is correct?

Modelling proteins is harder than modelling simpler systems such as liquid water, as the normal molecular dynamics method cannot be applied to biomolecules.

Only small proteins such as crambin can be simulated, given the huge number of solvent and protein atoms present in larger proteins.

Using state of the art codes and computers, it is possible to carry out simulations of systems containing many millions of atoms.

Proteins are modelled using special forcefields describing secondary structure elements such as α-helices instead of the atoms making up the protein.

. Molecular dynamics approaches use classical mechanics in the form of Newton's laws of motion because:

Quantum mechanics only applies to light particles such as electrons.

Scientists have not yet developed any methods able to describe motion of atoms using quantum mechanics.

Vibrational frequencies of proteins are so incredibly small that it would be dangerous to attempt a quantum mechanical description of them.

Given the relatively high mass of atoms, it is often an acceptable approximation to neglect quantum mechanical effects when describing their motion.

. A molecular dynamics simulation is performed for a model of liquid 1-phenyloctane (density 0.858 g cm⁻³, molecular mass 190.3 g mol⁻¹). Assuming that the code used cannot simulate more than 20,000 atoms, what is the length of the edge for the largest cubic box that can be modelled?

200,000 Å³

49 Å

1 cm

59 Å

. A molecular dynamics simulation is performed for a system representing liquid argon, using periodic boundary conditions with a box containing 953 atoms. At a particular timestep during the simulation, the total kinetic energy of all the atoms is equal to 1.67 × 10⁻¹⁸ J. What is the implied temperature of the system?

84.5 K

62.4 °C

126.8 K

123.2 K

. Based on the radial distribution function for water shown in Figure 6.3, and the description of the meaning of this function, which of the following is not correct for the radial distribution function g(r_ArAr) of a system representing a box containing compressed argon gas?

It will drop to zero for small values of r, as the probability of two atoms occupying the same region of space is zero.

It will drop to zero for long r, as the density of a gas is much lower than that of a liquid.

There will be a maximum at a distance near twice the van der Waals radius of the argon atom, due to attractive van der Waals attractions.

The function is expected to show relatively little structure in terms of local maxima or minima, due to the unstructured nature of gases.

. The Monte Carlo method is an alternative approach to molecular dynamics for simulating the behaviour of large collections of atoms. Which of the following statements is correct?

A move to a structure with higher potential energy is impossible in Monte Carlo simulations, so these tend to sample only low-energy regions.

Monte Carlo methods are always preferable because the randomness of the moves used is essential for modelling the complex motion of atoms.

Monte Carlo methods have the advantage that they do not usually require that it be possible to calculate the gradient of the energy with respect to the positions of the atoms.

In its original form, the Monte Carlo algorithm required the use of a roulette wheel to generate random moves.

. A molecular dynamics simulation is performed for a system containing water as solvent and a protein which has at its surface, among other groups, an isoleucine residue (containing a -CH(CH₃)CH₂CH₃ sidechain) and a lysine residue (containing a -CH₂CH₂CH₂CH₂NH₃⁺ sidechain). Which of the following statements is correct?

The water molecules will tend to approach the isoleucine residues more strongly due to the hydrophobic interactions.

Hydrogen-bonding will lead to frequent observations of short N-O distances between the N atom in the distal NH₃⁺ group and the O atoms of water molecules.

The charged group of the lysine residue will tend to 'bury' itself in the surface of the protein, to avoid contact with water molecules.

Isoleucine is an amino acid, and amino acids are soluble in water, so the simulation will show that this residue detaches itself from the protein and moves into the solvent.

. Which of the following problems would most strongly require the use of NPT conditions in a molecular dynamics (or Monte Carlo) simulation?

Modelling the flexibility of a loop region in a protein solvated in a large box of water molecules.

Modelling the radial distribution function of liquid water.

Modelling the pattern of preferred structures of a liquid crystal.

Identifying the preferred density of a supercritical fluid as a function of temperature.

Chapter 6 Self-test questions

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