6624 Nucleic Acids Research, 2005, Vol. 33, No. 20 360 turn (clock- or counter-clockwise) was obtained. Each simulation was 1.8 ns long, and took around 18 days on a 4 dual-node cluster of 8 AMD-Opteron-1.7GHz-64Bit CPUs. The rotation axis is chosen to be a hypothetical axis that passes through the phosphate of the 1 adenine and the phos- phate of the +10 adenine on the intact strand. The choice of the 1 Ade phosphate is motivated by the fact that, on one hand, it is exactly opposite the phosphate on the scissile strand which forms the phospodiester bond with the protein, and, on the other hand, it sits at the middle of the intact backbone part that connects the 1 Ade and +1 Ade. Choosing the rotation axis to pass through other atoms (or points in space) in this region will shift the rotation axis 1–2 A˚ on the helical curve, which is not expected to signiﬁcantly affect the overall protein motion. The +10 Ade phosphate is chosen because it sits just below the 1 Ade phosphate in the 3D structure. Thus, the rotation axis becomes parallel with the helical axis of the rotating downstream duplex, which is needed for a proper (i.e. without base-pair opening) duplex rotation as hypothesized by the strand-rotation model. If our choice of the axis of rotation for DNA is incorrect, all of the described conformational changes in topo I should be regarded as artifacts of the simulations and one should not expect to observe them experimentally. The CHARMM simulation package (38) was used for all calculations. A covalent model of the DNA–topoisomerase complex was set-up, with the position of the linker domain (missing in the covalent structure, PDB code 1a31) built using the non-covalent structure (PDB code 1a36). The protein–DNA complex was completely immersed into a 60 A˚ -radius sphere of TIP3P (39) water molecules with at least 6 A˚ distance between the spherical boundary and the complex; waters overlapping by up to 2.8 A˚ were removed. A stochastic boundary potential was applied (40) and the system was equi- librated for 0.2 ns. Charge neutralization was performed by replacing 19 waters with sodium ions in the places where water oxygens had highest electrostatic energies. The systems was then equilibrated for an additional 100 ps without SHAKE (36) and 200 ps with the SHAKE algorithm. The ﬁnal equilibrated structure has an 2.7 A˚ average RMS deviation from the ori- ginal crystal structure. Six distinct simulations (corresponding to distinct ways to manipulate the rotating DNA) were set-up (see Table 1 in the main text) and analyzed in the light of each other. Table 1. Descriptions of the six systems used for MD simulations System 1 System 2 System 3 System 4 System 5 System 6 External potential is applied to: Both downstream and upstream parts Both downstream and upstream parts Both downstream and upstream parts Both downstream and upstream parts Only downstream part Only downstream part aWhen looking from the perspective in Figure 1A, i.e. from the linker side of the protein. The resultant biasing forces mimic the effective torque arising from the twist energy contribution stored in the super- coiling free energy of the DNA substrate [estimated, based on measurements of the torsional modulus (15) to have the value, for an entire DNA molecule, on the average 4.5 cm long, at 5% supercoiled state, of around 12 kcal/mol]. How- ever, the resultant torques in the simulation exceed by at least two orders of magnitude the physiologically-relevant torques expected in vivo. The strategy to apply forces or torques much larger than the actual ones is a necessity dictated by the limitations in the time scale accessible to molecular dynamics and has been used in several other studies (37,41–43). Given the large degree of forcing imposed to DNA on a short time scale (shorter than the intrinsic rotation time scale under physiological conditions), there exists, in principle, the possibility that protein motion was exaggerated because of the lack of relaxation time. Based on the reaction coordinate generated by the present study, calculations of the potential of mean force (in which the angle of DNA rotation is ﬁxed and the protein is allowed to relax), as equilibrium calculations, surpass time scale limitations by restraining the system along a reaction pathway and are an obvious continua- tion of the work presented here. [While the method will be immune to a possible criticism of the shortness of reaction time scales, it will still have to address the issue of time to converge at the restraint points on the reaction path.] Systems 1 and 2 represent the original strand rotation scheme where only the downstream part rotates. Although system 5 and system 6 may also be seen as representatives of a strand rotation scheme, they do not produce the desired motion (relative rotation of the downstream part) due to the fact that upstream DNA, together with the covalently attached protein, follow the downstream part when it is left free. The results of the simulations done on the system 5 and system 6 are found to be overall system rotations as a rigid body. This is because the upstream duplex is left free while the downstream part is subjected to a harmonic potential that drives the rota- tion. Such uneven treatment of the upstream part combined with the fact that the rotations are done on a rapid, ns time scale, causes the upstream duplex to rotate, unless external potentials are applied as in systems 1,2 and 3,4. Secondly, as explained above, applied potentials mimic the torque in the supercoiled DNA (although not quantitatively, but in what the resultant motions are concerned), and both the downstream Direction of the biased rotationa Downstream!Counterclockwise Upstream!No rotation Downstream!Clockwise Upstream!No rotation Downstream!Counterclockwise Upstream!Clockwise Downstream!Clockwise Upstream!Counterclockwise Downstream!Counterclockwise Upstream!No rotation Downstream!Clockwise Upstream!No rotation Rotation increments 10 0 10 0 10 10 10 10 10 0 10 0 The system relaxes: Positive supercoils Negative supercoils Positive supercoils Negative supercoils Positive supercoils Negative supercoils