Section 20.1.2. Methods

Ubiquitin consists of 76 amino acids with 602 non-hydrogen atoms. Hydrogen atoms attached to aliphatic carbon atoms are incorporated into these (the united-atom approach), and the remaining 159 hydrogen atoms are treated explicitly. Ubiquitin crystallizes in the orthorhombic space group , with a = 5.084, b = 4.277 and c = 2.895 nm. There is one molecule in the asymmetric unit. The protein was crystallized at pH 5.6. The amino acids Glu and Asp were taken to be deprotonated, and Lys, Arg and His residues were protonated, leading to a charge of +1 electron charge per chain. Because this is a small value compared with the size of the system, no counter ions were added. Four chains of ubiquitin, making up a full unit cell of the crystal, were simulated together with 692 water molecules modelled using the SPC water model (Berendsen et al., 1981). 232 water molecules were placed at crystallographically observed water sites, and the remaining 460 were added to obtain the experimental density of 1.35 g cm⁻³, leading to a system size of 3044 protein atoms and 5120 atoms total.

The crystal structure of ubiquitin [Protein Data Bank (Bernstein et al., 1977) code 1UBQ] solved at 1.8 Å resolution (Vijay-Kumar et al., 1987) was used as a starting point. To achieve the appropriate total density, noncrystallographic water molecules were added, using a minimum distance of 0.220605 nm between non-hydrogen protein atoms or crystallographic water oxygen atoms and the oxygen atoms of the added water molecules, which were taken from an equilibrated water configuration (van Gunsteren et al., 1996). Initial velocities were assigned from a Maxwell–Boltzmann distribution at 300 K. The protein and solvent were coupled separately to temperature baths of 300 K with a coupling time of 0.1 ps (Berendsen et al., 1984). No pressure coupling was applied. Another simulation (results not shown) including pressure coupling showed no significant change in the box volume. Bonds were kept rigid using the SHAKE method (Ryckaert et al., 1977), with a relative geometric tolerance of . Long-range forces were treated using twin range cutoff radii of 0.8 and 1.4 nm (van Gunsteren & Berendsen, 1990). The pair list for non-bonded interactions was updated every 10 fs. No reaction field correction was applied. All simulations were performed using the GROMOS96 package and force field (van Gunsteren et al., 1996).

The system was initially minimized for 20 cycles using the steepest-descent method. The protein atoms were harmonically restrained (van Gunsteren et al., 1996) to their initial positions with a force constant of 25000 kJ mol⁻¹ nm⁻². This minimized structure was then pre-equilibrated in several short MD runs of 500 steps of 0.002 ps each, gradually lowering the restraining force constant from 25000 kJ mol⁻¹ nm⁻² to zero. The time origin was then set to zero, and the entire unit cell was simulated for 2 ns. The time step was 0.002 ps, and every 500th configuration was stored for evaluation. The first 400 ps of the run were treated as equilibration time, the remaining 1.6 ns were used for analysis.