Picosecond to Millisecond Structural Dynamics in Human Ubiquitin

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Picosecond to Millisecond Structural Dynamics in Human Ubiquitin Kresten Lindorff-Larsen, Paul Maragakis, Stefano Piana, and David E. Shaw J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.6b02024 • Publication Date (Web): 15 Apr 2016 Downloaded from http://pubs.acs.org on April 18, 2016

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The Journal of Physical Chemistry

Picosecond to Millisecond Structural Dynamics in Human Ubiquitin

Kresten Lindorff-Larsen,1,†,§,* Paul Maragakis,1,† Stefano Piana,1,† and David E. Shaw1,2,* 1

2

D. E. Shaw Research, New York, NY 10036, USA

Department of Biochemistry and Molecular Biophysics, Columbia University, New York, NY 10032, USA

† These authors contributed equally to this work. § Current address: Structural Biology and NMR Laboratory, Department of Biology, University of Copenhagen.

* To whom correspondence should be addressed. Kresten Lindorff-Larsen E-mail:

[email protected]

Phone:

+45 3532 2027

David E. Shaw E-mail:

[email protected]

Phone:

(212) 478-0260

Fax:

(212) 845-1286

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Abstract Human ubiquitin has been extensively characterized using a variety of experimental and computational methods, and has become an important model for studying protein dynamics. Nevertheless, it has proven difficult to characterize the microsecond-timescale dynamics of this protein with atomistic resolution. Here we use an unbiased computer simulation to describe the structural dynamics of ubiquitin on the picosecond to millisecond timescale. In the simulation, ubiquitin interconverts between a small number of distinct states on the microsecond to millisecond timescale. We find that the conformations visited by free ubiquitin in solution are very similar to those found various crystal structures of ubiquitin in complex with other proteins, a finding in line with previous experimental studies. We also observe weak but statistically significant correlated motions throughout the protein, including long-range concerted movement across the entire β sheet, consistent with recent experimental observations. We expect that the detailed atomistic description of ubiquitin dynamics provided by this unbiased simulation may be useful in interpreting current and future experiments on this protein.

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Introduction A large number of experimental and computational studies have demonstrated that the structural dynamics of proteins often play a crucial role in their functions. The ability to describe a protein’s various structural states, and the rates at which those states interconvert, is thus key to our understanding of protein function.

Among the experimental tools that can be used to study protein dynamics, nuclear magnetic resonance (NMR) spectroscopy has become a central technique, as NMR experiments can be used to probe dynamics on a wide range of timescales.1 NMR relaxation techniques can be used both to measure the amplitude of motions on the fastest (ps–ns) timescale and to study slower (µs–ms) protein motions.2 Residual dipolar couplings (RDCs) are sensitive to motions on an even wider range of timescales (ps–ms) and can, in combination with relaxation measurements, be used to probe the ns–µs motions that cannot easily be determined solely using current relaxation techniques.3

Molecular dynamics (MD) simulations provide an alternative approach to study protein dynamics. By aiming to model the physical forces that determine the structure and dynamics of molecules, MD simulations can provide an atomic-level description of protein motions— information that is inherently more detailed than that afforded by experimental techniques alone. Recent developments in the physical models (force fields) used in MD simulations,4 along with dramatic increases in the period of time that can be feasibly simulated using available computational techniques and technologies,5 have made it possible to use MD simulations for the study of protein dynamics on timescales ranging from ps to ms, facilitating comparisons with a broad range of experimentally accessible timescales. MD simulations and results from experimental techniques such as NMR spectroscopy can thus be used in a complementary fashion.



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In addition to its central role in biology, ubiquitin has become one of the most important model systems for studying protein dynamics, and has been the subject of many studies, including some that combine experimental and computational approaches. Simulations guided by experimental NMR relaxation data, for example, have shown that, from a dynamical perspective, ubiquitin can be described as having liquid-like side chains attached to a solid-like backbone.6 Simulations restrained by RDCs have demonstrated that a subset of ubiquitin residues display motions on a timescale beyond that of rotational diffusion (i.e., beyond the nanosecond timescale); as there is no evidence of substantial motion beyond the millisecond timescale, this finding suggests that the additional dynamics occur on a ns–µs timescale.3,7 Such studies have also suggested that the conformational ensemble sampled by ubiquitin in solution includes many of the structures that it adopts in complex with various binding partners,3,8,9 and have revealed long-range concerted motions in ubiquitin.10,11 Due to the relatively long (µs–ms) timescale involved in these conformational changes, it has been difficult so far to provide an unbiased, atomistic description of ubiquitin motions using simulations.

Here we have performed a millisecond-long unbiased MD simulation of ubiquitin to obtain an atomic-level description of its motions on a wide range of timescales. We find that the protein is remarkably stable throughout our simulation: The root-mean-square deviation (RMSD) of the core Cα atoms is 0.9 Å when averaged over the entire simulation. We compared the ps–nstimescale motions observed in simulation to the corresponding experimental data and found good agreement. Using a kinetic-clustering algorithm,5,12 we also discovered several independent movements in ubiquitin that occur on the µs–ms timescale. These results, which we describe below, offer a detailed structural model that may aid in the interpretation of a large body of experimental data, and they provide information about the timescales involved in protein motions that cannot easily be obtained from experiments alone.


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Methods The native-state structure of ubiquitin was solvated in a box of 5581 water molecules together with 15 chloride and 15 sodium ions. We used the CHARMM-h force field13 for ubiquitin and the TIP3P model for water. The volume of the box was equilibrated in the NPT ensemble at 300 K, resulting in a box size of (56 Å)3. The 1-ms production simulation was performed in the NVT ensemble at a temperature of 300 K using Anton.14 A 9.4 Å cutoff was used—together with a force-shifting method15,16—for the Lennard-Jones and electrostatic interactions. The S2 values shown in Fig. 1 were calculated by first aligning all frames (over residues 2–71) and then, for each time window, calculating P2(cos(θ)) as previously described.17 To calculate autocorrelation functions—both for the kinetic-clustering and dynamical-content calculations— we first transformed each dihedral angle, θ, using cos − ̅, where ̅ is the average angle calculated over the entire trajectory. By transforming the entire set of backbone φ and ψ dihedral angles in this way, we performed the kinetic clustering as previously described,5 aiming to match the correlation function for lag times between 250 ns and 5 µs. The circular correlation of backbone dihedral angles was performed as previously described.10 The data shown in Fig. 3 are only for those correlations whose mean value was more than 4.5 standard deviations from being zero (Z = 4.5 corresponds roughly to p = 0.05 using a Bonferroni correction for 76 * 76 comparisons). Calculations of Rex were performed as previously described.18,19 Briefly explained, we calculated (using either CamShift or SPARTA+) 15N chemical shift for frames sampled at 1-ns intervals throughout the trajectory. The autocorrelation functions of the resulting chemical-shift time series were then integrated and used to calculate Rex at a magnetic field of 11.7 T.



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Results and Discussion

Structural dynamics on the microsecond timescale Using a special-purpose machine for MD simulations, called Anton,14 we have performed a 1-ms simulation of ubiquitin. Experiments have shown that ubiquitin is a rather stable protein that mostly displays local motions on this timescale, an observation that is consistent with the low RMSD value observed throughout our simulation (Fig. 1a). Very good agreement is also observed with the experimental backbone J-couplings20 (RMSD 0.65 Hz) and RDCs21 (average Q-score 0.29), indicating that the simulation provides a reasonable description of the average structure and ps–ns fluctuations in the native state 4,13. The RMSD values show very fast fluctuations, but also hint at slower motions on the microsecond timescale. In addition to a conformational change observed around 0.7 ms, there were also several brief excursions visible in the RMSD plot (e.g., around 0.04 ms, 0.32 ms, and 0.94 ms).

To further investigate the timescales and structural locations of such motions, we calculated NMR order parameters (S2; 0

Picosecond to Millisecond Structural Dynamics in Human Ubiquitin

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