6622 Nucleic Acids Research, 2005, Vol. 33, No. 20 the nick), and (ii) the strand-rotation model (21) (in which one end of the nick is driven to rotate around the intact strand by the supercoiling free energy). For the type IA subfamily, evid- ence in favor of the enzyme-bridging model, suggested by structural data (22,23), was conﬁrmed by recent single- molecule manipulations (11,12). For the type IB subfamily, structural evidence points toward the strand-rotation model (see below). While an exciting recent single-molecule work (appeared during the submission phase of this manuscript) on vaccinia topo I (a smaller topo IB enzyme) found that its activity is torque-dependent (24), no molecular dynamical details of the actual mechanism involving the protein are cur- rently available. Moreover, while topo IB enzymes relax, unlike topo IA, both positive and negative supercoils (i.e. overwound or underwound), no attempt to discriminate between the two types of DNA substrates has been made for human topoi- somerase. Here, we present the ﬁrst dynamical model that includes the protein response to the large-scale motion of the two supercoiled DNA states by atomistic simulations. Available data on human topoisomerase I In a crystallographic tour de force, Holl, Champoux and coworkers (25–27) have obtained both covalent (i.e. after DNA nicking) and non-covalent (i.e. with intact DNA) com- plexes between human topoisomerase I and a 22 bp DNA duplex. Human topoisomerase I is a monomeric protein of 765 amino acids and is composed (2,25,28) of four major regions: the N-terminal, core, linker and the C-terminal domains. As seen in Figure 1A and B, the core subdomains I and II constitute an ‘upper cap’, which is connected by a ﬂexible hinge to a ‘lower cap,’ containing the C-terminal domain, the core subdomain III, and the anti-parallel coiled-coil linker domain. Two contiguous a-helices (a5 and a6 in Figure 1A) form a V-shaped ‘nose cone,’ believed to be important in the topoisomerization mechanism (21), and belong to the upper-cap core subdomains II and I, respectively. When closed, the upper and lower caps bring together two opposable ‘lips’. These regions are positioned diametrically opposite the hinge region. The upper lip is part of the core subdomain I; the lower lip belongs to core subdomain III (see Figure 1A and B). The protein is believed (21) to open up its lips widely (hinging on the hinge region) in order to bind the incoming DNA duplex; this is then to be followed by the closing of the lips around the DNA strand (see binding step in Figure 1C). The steps of the cycle of activity of human topo I continue with cleavage of one of the two DNA strands through nucleophilic attack by the active site tyrosine (Tyr723 in Figure 1B). This results in covalent attachment of the protein to the 30 phosphate at the site of cleavage. The resulting nick allows rotation of the DNA duplex down- stream of the nick (see Figure 1B and C). This strand-rotation mechanism explains why topo IB enzymes can relax multiple supercoils, of either sign, at a time: the number of times the downstream part rotates equals the change in DNA’s linking number [i.e. the number of times the two strands cross, a topological invariant under continuous deformations (29)]. The driving torque required for DNA rotation is thought to derive from the supercoiling energy; the direction of rotation depends on whether DNA is overwound (positively supercoiled) or underwound (negatively supercoiled). After a number of rotations occur [number believed to be, at least for vaccinia topos, torque-dependent (24)], a religation reaction sutures back the nick and the enzyme opens up to release a less-supercoiled DNA product. Based on the crystal structures of the covalent and nonco- valent complex, Champoux and coworkers (21) have proposed what is now the prevalent model for human topo I activity, the so called ‘controlled-rotation’ mechanism: the downstream part of the DNA scissile strand, rather than being driven to rotate freely, rotates under the control of the surrounding pro- tein. An important role in this process is thought to be played by charged residues of the nose cone and linker interacting electrostatically with the DNA downstream part. Eight addi- tional crystal structures (26) exhibited signiﬁcant crystal-to- crystal non-isomorphism and sizable differences in the trace of the backbone, documenting the remarkable ﬂexibility needed by the closed enzyme to accommodate duplex rotation inside a cylinder-like space of large radius inside an enzyme maintain- ing its grip on the DNA. This indication of large-scale dynam- ical motions, together with available studies for related type IB topos (24,30–33), provided an incentive basis for our studies of the dynamical mechanisms important for the function of human topo I. However, it is very important to note that our simulations and the resultant ﬁndings are all based on the previously proposed ‘controlled-rotation’ mechanism (21), i.e., rotation of the downstream DNA around the intact strand. Therefore, if the DNA relaxes through another mechanism, our results should not be regarded as physiological. 1 2 MATERIALS AND METHODS Torque-applied molecular dynamics Constant-temperature molecular dynamics using the Nose– Hoover thermostat (34,35) and taking 2 fs steps by utilizing the SHAKE algorithm (36) were performed, with the non- bonded interactions (force) shifted to zero over 8–12 A˚ . The system was biased half-harmonically, i.e., only when it moved away from the target (37), with an external potential of the form a Wðr‚ tÞ ¼ 2 ðr r0Þ2‚ in which a is chosen to be 1000 kcal/mol/A4, (value adjusted so that full 360 rotations can be performed within the ns time scale). The reaction coordinate r leading from the initial state to the ﬁnal state is given by rðtÞ ¼ NðN 1 1 XN XN ðrijðtÞ Þ i¼1 j6¼i R 2 rijÞ where rij ¼ |ri rj| is the distance between atoms i and j, R labels the coordinates of the ﬁnal reference structure, and N represents the total number of atoms biased. In this set-up, downstream DNA experienced forces from 0 to 2 nN, yielding an average effective torque of about 8.4 nN·A˚ . The reference structures towards which DNA was biased were obtained by applying a rotation transformation to the backbone atoms of DNA duplex in 10 angular increments until a full