Free-energy landscape of UvrD conformational ensembles when bound to the fork junction

Based on the information revealed by the PCA analysis, we would like to find the UvrD conformation responsible for the rezipping state when bound to the dsDNA-ssDNA junction. For this purpose, extensive enhanced sampling simulations (12 μs in total) were carried out to characterize the free-energy landscape of UvrD conformations and detect any interesting metastable states in it. See Materials and methods for the setup and simulation details.

We first characterized the 2D potential of mean force (PMF) using the first two PCs as coordinates (middle panel of Figure 3). We identified two conformations located in the two local minima of the 2D PMF map, respectively (right and left panels of Figure 3). These two conformations are defined as ‘closed’ and ‘tilted’ states. The tilted state has features that have not been found in any of the existing crystal structures, as we show in the following sections. The PDB file for the newly found tilted state is provided as Supplementary file 1.

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Figure 3.

Free-energy profile generated using the projections along the first 2 PCs.

The transition state (TS) and an intermediate state (IM) are located between the closed-to-tilted transition (the predicted tilted state PDB is provided as Supplementary file 1). Right and left panels: snapshots for the closed and tilted states are shown along with the gap size, which is defined by the minimal Cα distance between 2B and 1B domains.

Figure 3—figure supplement 1.

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Free-energy profile and key conformations along the transition pathway.

(a) 1D free-energy profile along the lowest free-energy path (LFEP) (Figure 3). The x-axis is the index of the 120 data points (images) along the LFEP. The positions of the transition state TS and the intermediate state IM are labeled in the figure. (b) Conformations of UvrD-DNA complex during the closed to tilted transition.

The closed and tilted conformations served as the initial and final states for a transition path finding protocol, which was employed to find the lowest free-energy path between them (see Materials and methods). The most probable transition happens in two phases, during which the 2B domain undergoes coupled rotational and tilting motions. In the first phase (closed→IM), 2B carries out a large-scale tilting motion along PC2, overcoming a 4.4 kcal/mol barrier before reaching an intermediate state IM. In the second phase (IM→TS→tilted), 2B performs mostly a rotational motion along PC1, overcoming a 1 kcal/mol barrier (GTS−GIM) at the global transition state (TS) before reaching the tilted state. Thus, the rate-limiting step is the first phase, which involves mostly a tilting motion. Figure 3—figure supplement 1 provides the PMF values and intermediate conformations along the lowest free-energy path. Video 1 shows the conformational changes of UvrD during the transition.

One can notice that the region the apo structure represents has a high energy value, which is more than 8 kcal/mol higher than the initial state. This demonstrates that the apo state, which is connected to the closed state by 2B domain rotation, is very unfavorable at the dsDNA-ssDNA junction.

We took the representative protein structure in the final and initial states and measured the gap size, which is defined by the closest Cα atom distance between the 2B and 1B domain. The extended ssDNA has a diameter around 10 Å (Landy et al., 2013). The initial closed state has a very small gap size of 6 Å, through which the ssDNA cannot pass. The final tilted state has a gap size of 14 Å, which is open enough for ssDNA to pass through.

The overall free-energy landscape projected along a progress variable α is plotted in Figure 4. α is proportional to the projection on PC1 and is scaled from 0 to 1.0 between the closed state and the tilted state. The free energy for the metastable tilted state is about 2.5 kcal/mol higher than that of the closed state. The system has to overcome a 4.2 kcal/mol energy barrier at the transition state (TS) to reach the tilted state.

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Figure 4.

Free energy projected along the progress variable α.

The value of α ranges from 0 to 1.0 (the closed state being 0 and the tilted state being 1.0). The standard error is calculated by a bootstrapping error analysis procedure.

Validation of the predicted tilted state

We first tested if the ssDNA can escape from the tilted structure. To accelerate the process, we used targeted molecular dynamics by adding a harmonic potential to the coordination number between UvrD and ssDNA. The targeted coordination number was forced to change from an initial value of 18 to 0 in 30 ns. As shown in Video 2, the ssDNA is seen disengaged from the ssDNA binding domains of UvrD. The final interaction energy between ssDNA and the 1A/2A/1B domains of UvrD gradually drops to zeros (see Figure 5—figure supplement 4). Further below, we also show that this tilted structure can bind stably to the opposing strand to complete the strand-switching process (Figure 8d).

To quantitatively validate our simulation results against experimental data, we compared the FRET efficiency distributions predicted for the closed and tilted states computationally to those of the functional states measured experimentally. We first obtained the 1D FRET efficiency distributions for the unwinding and rezipping state based on the raw single-molecule data (see Materials and methods for details). The distributions, shown in Figure 5a, have peak positions at 0.66 and 0.29 for unwinding and rezipping, respectively. By explicitly simulating UvrD in the two states with fluorophore labels (AlexaFluor555/AlexaFluor647) as in the single-molecule experiments, we also determined FRET efficiencies for the closed and tilted states (Figure 5b). The simulations accumulated 500 ns for each state, and we considered the orientation factor of the fluorophores in determining the FRET efficiency (Materials and methods). The predicted FRET efficiency peak for the closed state is at 0.72, whereas the peak for the tilted state is around 0.31. The close agreement between experimental and simulated FRET distributions reaffirms that the tilted state should be the protein conformation responsible for rezipping. As a control, we simulated the apo-state structure with the fluorophore labels for 500 ns as well. The apo-state FRET distribution, which peaks at 0.16, is quite different from the rezipping-state distribution (Figure 5—figure supplement 1), suggesting that the apo structure is not the conformation for UvrD rezipping at the junction.

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Figure 5.

Comparing experimental FRET efficiency distributions to the distributions obtained from simulations.

(a) Experimental distributions for the unwinding and rezipping states. The dotted lines show the peak positions for the two states. (b) Simulated FRET efficiency distribution for the closed and tilted states.

Figure 5—figure supplement 1.

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Simulated apo-state FRET distribution (solid cyan curve) and its comparison with the distributions for the rezipping state (dotted green curve, from experiments) and the tilted state (solid green curve, from simulations).

Figure 5—figure supplement 2.

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Molecular structures of the dyes (AlexaF555/AlexaF647) used in the simulations.

Figure 5—figure supplement 3.

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Averaged fluorophore pair conformations in the tilted state at different FRET efficiency values.

The averaged conformation of the pair at 0.3 FRET efficiency is shown in red. The averaged conformation of the pair at 0.6 FRET efficiency is shown in purple.

Figure 5—figure supplement 4.

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Interaction energy (electrostatic + Van der Waals) between the ssDNA and the ssDNA-binding domains (1A/2A/1B) during the ssDNA disengagement simulation (the protein is restrained in the tilted state).

We further examined the representative fluorophore pair conformations at the local maxima (FRET Efficiency = 0.3 and 0.6) of the tilted state FRET distribution (green curve in Figure 5b). It appears that the fluorophores have different conformations at the two different FRET values (Figure 5—figure supplement 3), due to the conformational dynamics of the dyes with the long linkers. The ‘shoulder’ of the tilted-state FRET distribution curve at 0.6 efficiency is caused by a metastable conformation of AlexaFluor555 with different pair-distance and orientation comparing to the conformation at 0.3 efficiency.

UvrD diffusion along dsDNA

In the UvrD functional switching model, the 2B domain of UvrD has to maintain contact with dsDNA; otherwise the protein might disassociate from the fork junction during the ssDNA strand exchanging. It is known that the GIG motif (motif IVc) of UvrD plays a key role in interacting with dsDNA (Myong et al., 2005), and T422 (a representative residue of GIG) is important for UvrD activity (Lee and Yang, 2006). We thus monitored the changes in the interaction between GIG and dsDNA. Figure 6 shows a free-energy landscape plotted against the DNA base ID in contact with GIG and the distance between them. For each simulation frame, we calculated the distances between every DNA residue’s O2P atom and the OG1 atom of T422. Then, the minimal distance and the corresponding DNA base ID were used as the two coordinates. Note the two strands of dsDNA share the same base ID here: for residue x in strand A (indexing according to pdb), the complementary residue in strand B has the same ID x. In the present case, frames with base ID 18 only involve strand A - T422 interaction; whereas frames with base ID 14 only involve strand B - T422 interaction.

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Figure 6.

Interaction changes between the GIG motif and dsDNA.

Here, we use the DNA base ID to represent the closest DNA residue in contact with T422 (part of the GIG motif) on strand A (red) or its complementary residue on strand B (blue). T422 engages with the backbone phosphate of residue 18 of strand A in the closed state, whereas it engages with the phosphate of residue 14 of strand B in the tilted state.

Figure 6—figure supplement 1.

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Evolution of the DNA base ID in contact with the GIG motif during the transition from the closed state to the tilted state (along the lowest free-energy path).

In the closed state, residue 18 of strand A contacts the GIG motif, whereas in the tilted state, residue 14 of strand B contacts the GIG motif. Thus, there is a diffusional motion along the dsDNA during the conformational change (see Figure 6). In such a way, UvrD is able to switch the binding dsDNA strand and finds an energetically favorable configuration for the ssDNA strand-switching that will happen in the next step. The diffusion happens in a way that the DNA and T422 are disengaged first, and T422 then re-engages with another DNA residue along the double strand. The base ID in contact with T422 during the transition path from the closed state to the tilted state is shown in Figure 6—figure supplement 1. One can see that the 2B diffusion happens late during the transition. Although UvrD diffuses along dsDNA during the transition, there is no base pair unwound during the closed-to-tilted transition.

A physical model for UvrD functional switching

A schematic model can be established based on the simulation results (Figure 8a,b). The corresponding molecular models are shown in Figure 8d. The UvrD functional switching happens in a two-step manner. A first step is the opening of the 2B domain, followed by a second step of the switching of the bound ssDNA strand, in which the original ssDNA disengages from the 1A/2A/1B domain binding site and the other strand fills in.

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Figure 8.

Physical mechanism of UvrD functional switching.

(a) Illustration for the whole free-energy landscape of ssDNA strand switching enabled by UvrD conformational transition. (b) Schematic representation showing the 2-step process of how UvrD switches the ssDNA strand along which the motor domain walks. (c) Dwell time distributions for the unwinding and rezipping states at 10 μM and 2.5 μM ATP concentration based on the measured traces from optical tweezers (Materials and methods). (d) The structural models for the unwinding, tilted and rezipping states are shown from left to right. The structural model for the rezipping state was obtained from the tilted state after the ssDNA strand switching as illustrated in Methods. Strands A and B of the dsDNA are shown in red and blue, respectively.

Figure 8—figure supplement 1.

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Projection of crystal structures onto the first two principal components from PCA (same data points used in Figure 2).

Here, the UvrD structures with ATP or non-hydrolysable analog molecules bound are colored in red.

Figure 8—figure supplement 2.

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Rezipping-state RMSD (calculated using the protein non-hydrogen atoms) from the tilted state during the 100 ns equilibration simulation.

Figure 8—figure supplement 3.

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The apo structure is not accessible after the closed-to-tilted transition at the DNA junction.

(A) The tilted conformation obtained from the simulations. The 2B domain is shown in cyan, whereas 1A/2A/1B are shown in gray. Strands A and B of the dsDNA are shown in red and blue, respectively. (B) After aligning the apo structure to the tilted structure, geometric clashes between the apo 2B domain and the dsDNA of the tilted state are detected (shown in orange dotted circle).

To obtain the free-energy difference between the unwinding and rezipping states, we performed a dwell time analysis based on past single-molecule measurements (Comstock et al., 2015). The dwell times of the unwinding and rezipping states of UvrD monomers are plotted in a histogram and the calculated averaged rates for both transitions are almost equal (kunwind→rezip= 6.6 s^-1 and krezip→unwind = 7.0 s^-1) at 10 μM ATP (see Figure 8c). Thus, the equilibrium constant is around one and the unwinding and the re-zipping conformations should have similar free energy. This is consistent with the picture that the tilted state is a little bit less favorable than the initial state but as soon as the ssDNA releases and the other ssDNA strand binds to the UvrD, the system returns to a lower free energy (the rezipping state) (Figure 8a). For the mutant UvrD303, the free energy for the closed state drops around 3 kcal/mol, whereas Gtilted and Grezip remain the same. The relative stabilization of the closed state leads to more persistent unwinding.

The strand switching is mostly driven by Brownian motion and does not require energy from ATP hydrolysis. To address the possible effect of ATP on strand switching, we (1) analyzed additional data from the optical tweezers experiments and compared the switching rate at two different ATP concentrations and (2) also analyzed the X-ray structures of the closed state with and without ATP. The dwell time distributions at 10 μM ATP and 2.5 μM ATP concentration are plotted in Figure 8c. The equilibrium constants of switching measured for the two concentrations are very similar (both around 1), which suggests that strand switching is likely an ATP-independent process. Furthermore, although our simulated system is based on an ATP-free UvrD crystal structure (2IS2), our computational approach covered the structural information from ATP (or its analogs) bound structures (Figure 8—figure supplement 1). One can see that the 2B motion between the ATP-substrate bound and empty UvrD in the closed state is small relative to the large closed-tilted conformational change. Therefore, it is not very likely that ATP binding has a noticeable impact on the closed-to-tilted transition.

DNA-UvrD conformation at the rezipping state

To explore the structure of the rezipping state further, we built a rezipping structure starting from the tilted conformation after ssDNA strand switching has occurred (see Figure 8d and Materials and methods). After a 100 ns equilibration simulation, the modeled system was stable and had a rmsd around 3 Å from the tilted state (Figure 8—figure supplement 2). The newly obtained rezipping structure satisfies the following considerations: (1) The protein conformation is very similar to the tilted conformation. (2) The interaction configuration between 2B and dsDNA remains the same between the tilted state and the rezipping state. Note that during our simulations of the closed to tilted transition, the 2B domain changed its contact from one strand of dsDNA to the other (4 bp shift, from the red strand A to the blue strand B in Figure 6). (3) The ATPase domains 1A-2A are in the correct orientation along the ssDNA (3’ to 5’), pointing away from the junction. Such a conformation enables UvrD to translocate along ssDNA, allowing the duplex to rezip behind it. In examining the rezipping structure, we found a small loop forming between the dsDNA junction and the ssDNA-1A binding site. A similar feature was proposed by a translocation model of PcrA helicase in Park et al. (2010), which suggested that PcrA can extrude a ssDNA loop while it attaches to dsDNA and translocates the 5’ ssDNA tail in an open conformation.

The apo state seen in the crystal structures without DNA bound is likely not a functional state of UvrD at the fork junction. First, the simulated apo-structure FRET distribution is quite different from the rezipping-state FRET distribution. Upon completion of the ssDNA strand-switch, we expect the conformation of UvrD to stay close to the tilted structure. The FRET signal from the single-molecule experiment shows a clear two-state distribution, and our FRET distribution for the tilted state from simulations agrees very well with the experiment. Second, we aligned the apo state structure to the tilted state in Figure 8—figure supplement 3, and there are serious clashes between the apo structure and the dsDNA. Thirdly, the apo state is highly unfavorable at the fork junction according to our simulations.

MD simulation setup

Our simulations were initiated from the closed state (pdb 2IS2) of UvrD (see Figure 1c). The protein-DNA system was solvated in a 100 Å ×100 Å ×130 Å water box with 55 mM NaCl (the system had ∼140K atoms in total). A 2×104-step energy minimization was carried out and the system was then heated to 310 K in 30 ps, employing harmonic constraints with 1 kcal/(mol Å2) spring constant to the Cα atoms. Keeping the spring constant, a 1 ns equilibration in the NPT ensemble (1 atm at 310 K) was performed with a Langevin thermostat for temperature coupling. This was followed by a 1 ns NVT-ensemble simulation, during which the spring constant was gradually decreased to zero. The system was then equilibrated for 60 ns, and the resulting configuration is referred to as the closed state. All MD simulations in our study were performed using NAMD 2.10 (Phillips et al., 2005) with the CHARMM36 force field (Best et al., 2012; Hart et al., 2012).

Free-energy simulation protocol

To determine the free-energy profile along a reaction coordinate, we employed the Hamiltonian replica-exchange (HREX) method (Park et al., 2012; Jiang et al., 2012; Jiang et al., 2014). HREX uses a series of replicas (j=1, 2,. .., M) of the system, which are simulated concurrently with slightly different Hamiltonians and are exchanged frequently among themselves based on the Metropolis exchange criterion (Sugita et al., 2000). HREX can be very powerful in reconstructing rugged free-energy landscapes by exchanging external biasing potentials, which, with different biasing parameters, are added to the replicas to enhance the sampling throughout the reaction coordinate (RC). The biasing potential (or the window potential) for each replica j usually assumes the form of Um(ξj)=km(ξj−pm)2/2, where ξj is the current value of the reaction coordinate for replica j, m (m=1, 2,. .., M) is the index for the biasing potentials (windows), pm is the preassigned parameter for the center of the harmonic potential, and km is the spring constant. The centers of the biasing potentials (pm) are selected as an ordered list of values (p1<p2<...<pM) all over the RC to cover the reaction of interest fully. Exchanges between two neighboring replicas (replicas with neighboring pm values) are attempted periodically during the simulations. Without the replica-exchange strategy, this protocol reduces to the conventional umbrella sampling, which often suffers from the inefficient sampling of degrees of freedom orthogonal to the reaction coordinate (Jiang et al., 2012).

The present study chooses the projection on the first PC (v1) as the reaction coordinate ξ and includes M = 120 biasing windows between the closed state and the tilted state. The initial configurations for the M windows were generated through a 5 ns targeted MD simulation (Schlitter et al., 1994), by driving UvrD from the closed state to the tilted state. An exchange between two neighboring replicas was attempted every 10 ps and the spring constant of the harmonic potential was set to 100 kcal/(mol Å2). The production run of each replica lasted 100 ns, and the total simulation time added up to 12 μs (100 ns × 120). Eventually the weighted histogram analysis method (WHAM) (Kumar et al., 1992) was applied to obtain the unbiased 1D and 2D free-energy landscapes in Figures 4 and ​and3.3. We performed the Monte Carlo bootstrap error analysis (Stine, 1989; Hub et al., 2010) to estimate the uncertainty along the reaction coordinate. The basic idea of bootstrapping is to obtain several estimates (we obtained 10 trials) for the free energy based on randomly generated subpopulations from the histogram in each window. Our simulations with HREX benefitted from a scalable multiple copy algorithm (Jiang et al., 2014) which enables simulating hundreds of replicas simultaneously on a petascale supercomputer.

As stated in Results, the tilted state structure was identified as one of the most important metastable states. Based on the free-energy landscape using the projections on the first two PCs, the lowest free-energy path describing the most probable reaction mechanism was localized between closed state and the tilted state using the optimization algorithm in (Ensing et al., 2005). The path was then smoothed and 120 images were chosen uniformly along the 2D pathway applying the curve-fitting protocol in (Ma and Schulten, 2015).

FRET efficiency calculation based on simulations with dye molecules

To check if the simulated closed and tilted states generate the FRET signals of the respective unwinding and rezipping states measured by the single-molecule experiments, we carried out equilibrium simulations with the actual dye molecules for both states. AlexaFluor555 and AlexaFluor647 maleimides (Molecular Probes, Eugene, OR) were modeled according to (Vrljic et al., 2010) and (Gust et al., 2014) (see Figure 5—figure supplement 2). Then the two dyes were, respectively, attached to UvrD residues 473 and 100, which were mutated to cysteine from alanine. Force field parameters for the dyes linked to a cysteine residue were obtained from the CHARMM General Force Field (CGenFF) (Vanommeslaeghe et al., 2010) using the ParamChem server. The total charges were set to 0 and −3 for the two dyes respectively (Gust et al., 2014). Partial charges on the atoms were further refined by the Force Field Toolkit (ffTK) (Mayne et al., 2013) in VMD (Humphrey et al., 1996). Parameters for bonds, angles and dihedrals from CGenFF with high penalty scores were validated or refined by ffTK.

To sample dye dynamics efficiently, we launched 50 independent standard MD simulations with random initial velocity seeds for the closed, tilted and apo states. Every single simulation lasted 10 ns and a total 500 ns simulation time was accumulated for each state.

The FRET efficiency was determined by E=R06/(R6+R06), where R is the distance between the donor and acceptor, and R0 is the Föster radius (or the 50% energy transfer distance). R0 is given by the relationship (Wu and Brand, 1994) R0=(8.79×10−5n−4ϕDJκ2)1/6, where n is the index of refraction, ϕD is the donor quantum yield, J is the spectral overlap integral, and κ2 is the orientation factor. R0 is determined to be 51 Å when κ2 equals 2/3, assuming that the dyes randomize their orientations by rapid diffusion prior to energy transfer. Such an assumption can be problematic, and in the present study the orientation factor is calculated using κ2=(cosθT−3cosθDcosθA)2, where θT is the angle between the donor and acceptor transition dipole moments and θD and θA are the angles between these two dipoles and the vector connecting the donor and acceptor (Corry and Jayatilaka, 2008). The transition dipole moments for AlexaFluor555/647 or very similar dyes have been determined in (Corry and Jayatilaka, 2008) and (Graen, 2009). The simulated FRET data were integrated to four ns per point to obtain its probability distribution using the density kernel estimation method (Parzen, 1962; Comstock et al., 2015).

Analysis of single-molecule data

To validate our simulation results, analysis based on the raw data from single-molecule experiments was carried out. Comstock et al. (2015) combined optical tweezers (to detect UvrD unwinding activity) and single-molecule FRET (to detect UvrD conformation) measuring both simultaneously. Example raw time traces of UvrD activity and conformation are shown in Fig. 3 and Fig. S5 in Comstock et al. (2015) (at 10 μM ATP concentration). Time traces from the optical tweezers were sampled at 267 Hz. Time traces for donor and acceptor intensities were integrated to 30–60 ms per data point. The time-dependent FRET efficiency E(t) was calculated by E(t)=1/(1+γ(ID(t)/IA(t))) (Ha et al., 1999; Choi et al., 2010), where ID(t) and IA(t) are the measured donor and acceptor intensities, and γ is a correction factor accounting for the different detection efficiencies for the two dyes, and can be measured from photobleaching events. γ=ΔIA/ΔID is determined to be 0.78 from 20 acceptor photobleaching events, where ΔIA and ΔID are the acceptor and donorintensity changes upon acceptor photobleaching, respectively.

To measure the FRET efficiency distribution for the unwinding and rezipping states individually, we needed to assign each raw data point to the two states separately. Since the helicase velocity and FRET efficiency were measured concurrently, we used helicase velocity to define whether each data point in the traces belonged to unwinding or rezipping states (see Fig. S5 in [Comstock et al., 2015]). Time intervals were determined during which the helicase was either unwinding, rezipping, or paused (positive velocity indicates UvrD is in the unwinding state; negative velocity indicates rezipping; absolute unwinding velocity smaller than 20 bp/s indicates a pause). Paused states were not considered in the analysis. FRET efficiencies over each time interval were collected for the unwinding and rezipping states from 141 time intervals (13 molecules in total). We then used the density kernel estimation method to obtain the experimental FRET distribution (Parzen, 1962; Comstock et al., 2015). A density kernel plot is a summation of small Gaussians centered at each FRET data point. We used a standard deviation of 0.06 for the Gaussians.

We also analyzed the dwell times for both the unwinding state (high FRET) and the rezipping state (low FRET) of UvrD monomers. For this purpose, the duration of each time interval defined above was measured using the traces from optical tweezers measurements. We chose to select intervals and calculate the dwell time using the tweezers signal because it has a higher time resolution than the FRET signal (about one order of magnitude higher). The dwell time distribution was obtained by histogramming the collected duration values for the unwinding and rezipping state separately. In order to assess the effect of ATP concentration on UvrD functional switching, we analyzed optical tweezers data of UvrD activity at two different ATP concentrations. Figure 8c plots the distributions of dwell times at 10 μM and 2.5 μM ATP concentration. The rates of the transitions were estimated by the inverse of the averaged dwell times.

The present contribution is dedicated to Klaus Schulten (1947–2016), whose visionary developments in high performance simulation tools for molecular dynamics permit characterizing biomolecular motor action at biologically relevant timescales. This work has been supported by grants from the NIH (9P41GM104601 to ZL-S and KS; R01 GM120353 to YRC) and from the NSF PHY-1430124 (Center for the Physics of Living Cells to YRC, ZL-S and KS). The authors gladly acknowledge supercomputer time provided by the Texas Advanced Computing Center via Extreme Science and Engineering Discovery Environment grant NSF-MCA93S028 and the Blue Waters sustained-petascale computing project, which is supported by NSF (OCI-0725070 and ACI-1238993) and the State of Illinois. We also thank former Chemla lab member Dr. Matthew J Comstock for scientific discussions.