Simulation of conformational transitions

Using correlated motions to determine sufficient sampling times for molecular dynamics

Here we present a time-dependent correlation method that provides insight into how long a system takes to grow into its equal-time (Pearson) correlation. We also show a usage of an extant time-lagged correlation method that indicates the time for parts of a system to become decorrelated, relative to equal-time correlation. Given a completed simulation (or set of simulations), these tools estimate (i) how long of a simulation of the same system would be sufficient to observe the same correlated motions, (ii) if patterns of observed correlated motions indicate events beyond the timescale of the simulation, and (iii) how long of a simulation is needed to observe these longer timescale events. We view this method as a decision-support tool that will aid researchers in determining necessary sampling times. In principle, this tool is extendable to any multidimensional time series data with a notion of correlated fluctuations; however, here we limit our discussion to data from molecular-dynamics simulations.

Balancing Accuracy and Cost of Confinement Simulations by Interpolation and Extrapolation of Confinement Energies

Improvements to the confinement method for the calculation of conformational free energy differences are presented. By taking advantage of phase space overlap between simulations at different frequencies, significant gains in accuracy and speed are reached. The optimal frequency spacing for the simulations is obtained from extrapolations of the confinement energy, and relaxation time analysis is used to determine time steps, simulation lengths, and friction coefficients. At postprocessing, interpolation of confinement energies is used to significantly reduce discretization errors in the calculation of conformational free energies. The efficiency of this protocol is illustrated by applications to alanine n-peptides and lactoferricin. For the alanine-n-peptide, errors were reduced between 2- and 10-fold and sampling times between 8- and 67-fold, while for lactoferricin the long sampling times at low frequencies were reduced 10-100-fold.

Structural integrity of the ribonuclease H domain in HIV-1 reverse transcriptase

The mature form of reverse transcriptase (RT) is a heterodimer comprising the intact 66-kDa subunit (p66) and a smaller 51-kDa subunit (p51) that is generated by removal of most of the RNase H (RNH) domain from a p66 subunit by proteolytic cleavage between residues 440 and 441. Viral infectivity is eliminated by mutations such as F440A and E438N in the proteolytic cleavage sequence, while normal processing and virus infectivity are restored by a compensatory mutation, T477A, that is located more than 10 Å away from the processing site. The molecular basis for this compensatory effect has remained unclear. We therefore investigated structural characteristics of RNH mutants using computational and experimental approaches. Our Nuclear Magnetic Resonance and Differential Scanning Fluorimetry results show that both F440A and E438N mutations disrupt RNH folding. Addition of the T477A mutation restores correct folding of the RNH domain despite the presence of the F440A or E438N mutations. Molecular dynamics simulations suggest that the T477A mutation affects the processing site by altering relative orientations of secondary structure elements. Predictions of sequence tolerance suggest that phenylalanine and tyrosine are structurally preferred at residues 440 and 441, respectively, which are the P1 and P1' substrate residues known to require bulky side chains for substrate specificity. Interestingly, our study demonstrates that the processing site residues, which are critical for protease substrate specificity and must be exposed to the solvent for efficient processing, also function to maintain proper RNH folding in the p66/p51 heterodimer.

Enhanced sampling simulations of DNA step parameters

A novel approach for the selection of step parameters as reaction coordinates in enhanced sampling simulations of DNA is presented. The method uses three atoms per base and does not require coordinate overlays or idealized base pairs. This allowed for a highly efficient implementation of the calculation of all step parameters and their Cartesian derivatives in molecular dynamics simulations. Good correlation between the calculated and actual twist, roll, tilt, shift, and slide parameters is obtained, while the correlation with rise is modest. The method is illustrated by its application to the methylated and unmethylated 5'-CATGTGACGTCACATG-3' double stranded DNA sequence. One-dimensional umbrella simulations indicate that the flexibility of the central CG step is only marginally affected by methylation.

Coupled binding-bending-folding: The complex conformational dynamics of protein-DNA binding studied by atomistic molecular dynamics simulations

BACKGROUND

Protein-DNA binding often involves dramatic conformational changes such as protein folding and DNA bending. While thermodynamic aspects of this behavior are understood, and its biological function is often known, the mechanism by which the conformational changes occur is generally unclear. By providing detailed structural and energetic data, molecular dynamics simulations have been helpful in elucidating and rationalizing protein-DNA binding.

SCOPE OF REVIEW

This review will summarize recent atomistic molecular dynamics simulations of the conformational dynamics of DNA and protein-DNA binding. A brief overview of recent developments in DNA force fields is given as well.

MAJOR CONCLUSIONS

Simulations have been crucial in rationalizing the intrinsic flexibility of DNA, and have been instrumental in identifying the sequence of binding events, the triggers for the conformational motion, and the mechanism of binding for a number of important DNA-binding proteins.

GENERAL SIGNIFICANCE

Molecular dynamics simulations are an important tool for understanding the complex binding behavior of DNA-binding proteins. With recent advances in force fields and rapid increases in simulation time scales, simulations will become even more important for future studies. This article is part of a Special Issue entitled Recent developments of molecular dynamics.

Protein aggregation: mechanisms and functional consequences

Understanding the mechanisms underlying protein misfolding and aggregation has become a central issue in biology and medicine. Compelling evidence show that the formation of amyloid aggregates has a negative impact in cell function and is behind the most prevalent human degenerative disorders, including Alzheimer's Parkinson's and Huntington's diseases or type 2 diabetes. Surprisingly, the same type of macromolecular assembly is used for specialized functions by different organisms, from bacteria to human. Here we address the conformational properties of these aggregates, their formation pathways, their role in human diseases, their functional properties and how bioinformatics tools might be of help to study these protein assemblies.

Cy3-DNA stacking interactions strongly depend on the identity of the terminal basepair

We characterized the effect of the first basepair on the conformational dynamics of the fluorescent dye Cy3 attached to the 5' end of double-stranded DNA using gaussian-mixture adaptive umbrella sampling simulations. In the simulations, the sampling of all five dihedral angles along the linker was enhanced, so that both stacked and unstacked states were sampled. The affinity of Cy3 for a T·A basepair (with the dye attached to T) was found to be significantly less than for the other basepairs. This was verified experimentally by measuring the activation energies for cis-trans isomerization of the dye. The simulation and experimental results indicate the existence of partially unstacked conformations amenable to photoisomerization. The simulations also showed that stacking of Cy3 straightens the DNA while stabilizing the first basepair. Our findings indicate that fluorescence is modulated by Cy3-DNA interactions in a sequence-dependent manner.

Structural evolution of protein-biofilms: Simulations and experiments

The control of biofilm formation is a challenging goal that has not been reached yet in many aspects. One unsolved question is the role of van der Waals forces and another is the importance of mutual interactions between the adsorbing and the adsorbed biomolecules ("critical crowding"). In this study, a combined experimental and theoretical approach is presented, which fundamentally probes both aspects. On three model proteins-lysozyme, α-amylase, and bovine serum albumin-the adsorption kinetics is studied experimentally. Composite substrates are used enabling a separation of the short- and the long-range forces. Although usually neglected, experimental evidence is given for the influence of van der Waals forces on the protein adsorption as revealed by in situ ellipsometry. The three proteins were chosen for their different conformational stabilities in order to investigate the influence of conformational changes on the adsorption kinetics. Monte Carlo simulations are used to develop a model for these experimental results by assuming an internal degree of freedom to represent conformational changes. The simulations also provide data on the distribution of adsorption sites. By in situ atomic force microscopy we can also test this distribution experimentally, which opens the possibility to, e.g., investigate the interactions between adsorbed proteins.

Onsager-Machlup action-based path sampling and its combination with replica exchange for diffusive and multiple pathways

For sampling multiple pathways in a rugged energy landscape, we propose a novel action-based path sampling method using the Onsager-Machlup action functional. Inspired by the Fourier-path integral simulation of a quantum mechanical system, a path in Cartesian space is transformed into that in Fourier space, and an overdamped Langevin equation is derived for the Fourier components to achieve a canonical ensemble of the path at a finite temperature. To avoid "path trapping" around an initially guessed path, the path sampling method is further combined with a powerful sampling technique, the replica exchange method. The principle and algorithm of our method is numerically demonstrated for a model two-dimensional system with a bifurcated potential landscape. The results are compared with those of conventional transition path sampling and the equilibrium theory, and the error due to path discretization is also discussed.

Transient non-native hydrogen bonds promote activation of a signaling protein

Phosphorylation is a common mechanism for activating proteins within signaling pathways. Yet, the molecular transitions between the inactive and active conformational states are poorly understood. Here we quantitatively characterize the free-energy landscape of activation of a signaling protein, nitrogen regulatory protein C (NtrC), by connecting functional protein dynamics of phosphorylation-dependent activation to protein folding and show that only a rarely populated, pre-existing active conformation is energetically stabilized by phosphorylation. Using nuclear magnetic resonance (NMR) dynamics, we test an atomic scale pathway for the complex conformational transition, inferred from molecular dynamics simulations (Lei et al., 2009). The data show that the loss of native stabilizing contacts during activation is compensated by non-native transient atomic interactions during the transition. The results unravel atomistic details of native-state protein energy landscapes by expanding the knowledge about ground states to transition landscapes.

Segmented transition pathway of the signaling protein nitrogen regulatory protein C

Recent advances in experimental methods provide increasing evidence that proteins sample the conformational substates that are important for function in the absence of their ligands. An example is the receiver domain of nitrogen regulatory protein C, a member of the phosphorylation-mediated signaling family of "two-component systems." The receiver domain of nitrogen regulatory protein C samples both inactive conformation and the active conformation before phosphorylation. Here we determine a possible pathway of interconversion between the active state and the inactive state by targeted molecular dynamics simulations and quasi-harmonic analysis; these methods are used because the experimental conversion rate is in the high microsecond range, longer than those that are easily accessible to atomistic molecular dynamics simulations. The calculated pathway is found to be composed of four consecutive stages described by different progress variables. The lowest quasi-harmonic principal components from unbiased molecular dynamics simulations on the active state correspond to the first stage, but not to the subsequent stages of the transition. The targeted molecular dynamics pathway suggests that several transient nonnative hydrogen bonds may facilitate the transition.

An optimized replica exchange molecular dynamics method

We introduce a new way to perform swaps between replicas in replica exchange molecular dynamics simulations. The method is based on a generalized canonical probability distribution function and flattens the potential of mean force along the temperature coordinate, such that a random walk in temperature space is achieved. Application to a Go model of protein A showed that the method is more efficient than conventional replica exchange. The method results in a constant probability distribution of the replicas over the thermostats, yields a minimum round-trip time between extremum temperatures, and leads to faster ergodic convergence.

Gaussian-mixture umbrella sampling

We introduce the Gaussian-mixture umbrella sampling method (GAMUS) , a biased molecular dynamics technique based on adaptive umbrella sampling that efficiently escapes free energy minima in multidimensional problems. The prior simulation data are reweighted with a maximum likelihood formulation, and the new approximate probability density is fit to a Gaussian-mixture model, augmented by information about the unsampled areas. The method can be used to identify free energy minima in multidimensional reaction coordinates. To illustrate GAMUS , we apply it to the alanine dipeptide (2D reaction coordinate) and tripeptide (4D reaction coordinate).

Functionally rigid and degenerate molecular shuttles

The preparation and dynamic behavior of two functionally rigid and degenerate [2]rotaxanes (14 PF(6) and 24 PF(6)) in which a pi-electron deficient tetracationic cyclophane, cyclobis(paraquat-p-phenylene) (CBPQT(4+)) ring, shuttles back and forth between two pi-electron-rich naphthalene (NP) stations by making the passage along an ethynyl-phenylene-(PH)-ethynyl or butadiyne rod, are described. The [2]rotaxanes were synthesized by using the clipping approach to template-directed synthesis, and were characterized by NMR spectroscopic and mass spectrometric analyses. (1)H NMR spectra of both [2]rotaxanes show evidence for the formation of mechanically interlocked structures, resulting in the upfield shifts of the resonances for key protons on the dumbbell-shaped components. In particular, the signals for the peri protons on the NP units in the dumbbell-shaped components experienced significant upfield shifts at low temperatures, just as has been observed in the flexible [2]rotaxanes. Interestingly, the resonances for the same protons did not exhibit a significant upfield shift at 298 K, but rather only a modest shift. This phenomenon arises from the much reduced binding of the ethynyl-NP unit compared to the 1,5-dioxy-NP unit. This effect, in turn, increases the shuttling rate when compared to the 1,5-dioxy-NP-based rotaxane systems investigated previously. The kinetic and thermodynamic data of the shuttling behavior of the CBPQT(4+) ring between the NP units were obtained by variable-temperature NMR spectroscopy and using the coalescence method to calculate the free energies of activation (DeltaG(c) ( not equal)) of 9.6 and 10.3 kcal mol(-1) for 14 PF(6) and 24 PF(6), respectively, probed by using the rotaxane's alpha-bipyridinium protons. The solid-state structure of the free dumbbell-shaped compound (3) shows the fully rigid ethynyl-PH-ethynyl linker with a length (8.1 A) twice as long as that (3.8 A) of the butadiyne linker. Full-atomistic simulations were carried out with the DREIDING force field (FF) to probe the degenerate molecular shuttling processes, and afforded shuttling energy barriers (DeltaG( not equal)=10.4 kcal mol(-1) for 14 PF(6) and 24 PF(6)) that are in good agreement with the experimental values (DeltaG(c) ( not equal)=9.6 and 10.3 kcal mol(-1) for 14 PF(6) and 24 PF(6), respectively, probed by using their alpha-bipyridinium protons).

Minimum free energy pathways and free energy profiles for conformational transitions based on atomistic molecular dynamics simulations

An efficient method for the calculation of minimum free energy pathways and free energy profiles for conformational transitions is presented. Short restricted perturbation-targeted molecular dynamics trajectories are used to generate an approximate free energy surface. Approximate reaction pathways for the conformational change are constructed from one-dimensional line segments on this surface using a Monte Carlo optimization. Accurate free energy profiles are then determined along the pathways by means of one-dimensional adaptive umbrella sampling simulations. The method is illustrated by its application to the alanine "dipeptide." Due to the low computational cost and memory demands, the method is expected to be useful for the treatment of large biomolecular systems.

Metadynamics in Essential Coordinates: Free Energy Simulation of Conformational Changes

We propose an approach that combines an extraction of collective motions of a molecular system with a sampling of its free energy surface. A recently introduced method of metadynamics allows exploration of the free energy surface of a molecular system by means of coarse-grained dynamics with flooding of free energy minima. This free energy surface is defined as a function of a set of collective variables (e.g., interatomic distances, angles, torsions, and others). In this study, essential coordinates determined by essential dynamics (principle component analysis) were used as collective variables in metadynamics. First, dynamics of the model system (explicitly solvated alanine dipeptide, Ace-Ala-Nme) was simulated by a classical molecular dynamics simulation. The trajectory (1 ns) was then analyzed by essential dynamics to obtain essential coordinates. The free energy surface as a function of the first and second essential coordinates was then explored by metadynamics. The resulting free energy surface is in agreement with other studies of this system. We propose that a combination of these two methods (metadynamics and essential dynamics) has great potential in studies of conformational changes in peptides and proteins.