Mechanically tightening,untying and retying a protein trefoil knot by single-molecule force spectroscopy

Knotted conformation is one of the most surprising topological features found in proteins, and understanding the folding mechanism of such knotted proteins remains a challenge. Here, we used optical tweezers (OT) to investigate the mechanical unfolding and folding behavior of a knotted protein Escherichia coli tRNA (guanosine-1) methyltransferase (TrmD). We found that when stretched from its N- and C-termini, TrmD can be mechanically unfolded and stretched into a tightened trefoil knot, which is composed of ca. 17 residues. Stretching of the unfolded TrmD involved a compaction process of the trefoil knot at low forces. The unfolding pathways of the TrmD were bifurcated, involving two-state and three-state pathways. Upon relaxation, the tightened trefoil knot loosened up first, leading to the expansion of the knot, and the unfolded TrmD can then fold back to its native state efficiently. By using an engineered truncation TrmD variant, we stretched TrmD along a pulling direction to allow us to mechanically unfold TrmD and untie the trefoil knot. We found that the folding of TrmD from its unfolded polypeptide without the knot is significantly slower. The knotting is the rate-limiting step of the folding of TrmD. Our results highlighted the critical importance of the knot conformation for the folding and stability of TrmD, offering a new perspective to understand the role of the trefoil knot in the biological function of TrmD.

Optical tweezers are used to stretch a knotted protein along different directions to probe its unfolding–folding behaviors, and the conformational change of its knot structure.      

Calculating potentials of mean force from steered molecular dynamics simulations

Steered molecular dynamics (SMD) permits efficient investigations of molecular processes by focusing on selected degrees of freedom. We explain how one can, in the framework of SMD, employ Jarzynski's equality (also known as the nonequilibrium work relation) to calculate potentials of mean force (PMF). We outline the theory that serves this purpose and connects nonequilibrium processes (such as SMD simulations) with equilibrium properties (such as the PMF). We review the derivation of Jarzynski's equality, generalize it to isobaric--isothermal processes, and discuss its implications in relation to the second law of thermodynamics and computer simulations. In the relevant regime of steering by means of stiff springs, we demonstrate that the work on the system is Gaussian-distributed regardless of the speed of the process simulated. In this case, the cumulant expansion of Jarzynski's equality can be safely terminated at second order. We illustrate the PMF calculation method for an exemplary simulation and demonstrate the Gaussian nature of the resulting work distribution.     

Unbinding of nicotine from the acetylcholine binding protein: steered molecular dynamics simulations

The ligand binding/unbinding process is critical to our understanding of the pharmacology of both the nicotinic acetylcholine receptor (nAChR) and the acetylcholine binding protein (AChBP). Steered molecular dynamics simulations were performed to learn about the unbinding process of the full agonist nicotine. Three different pulling models were designed to investigate the possible binding/unbinding pathways: radial and tangent models, and also a mixed model. Of the three, the tangent pulling model finally failed to dissociate nicotine from the ligand binding pocket. The efficiency of the pulling force profiles was superior, and the opening of the C-loop was smaller in the mixed pulling model than that in the radial model. The most favorable pathway for the cholinergic agonist nicotine to enter or leave the binding pocket is through the principal binding side, following a curvilinear track. Noticeably, it has been seen that the unbinding of the nicotine is concomitant with a global rotation of the protein-ligand complex which could be caused by the interactions of the ligand with protein at the tangent direction.     

Modern protein force fields behave comparably in molecular dynamics simulations

Several molecular dynamics simulations were performed on three proteins--bovine apo-calbindin D9K, human interleukin-4 R88Q mutant, and domain IIA of bacillus subtilis glucose permease--with each of the AMBER94, CHARMM22, and OPLS-AA force fields as implemented in CHARMM. Structural and dynamic properties such as solvent-accessible surface area, radius of gyration, deviation from their respective experimental structures, secondary structure, and backbone order parameters are obtained from each of the 2-ns simulations for the purpose of comparing the protein portions of these force fields. For one of the proteins, the interleukin-4 mutant, two independent simulations were performed using the CHARMM22 force field to gauge the sensitivity of some of these properties to the specific trajectory. In general, the force fields tested performed remarkably similarly with differences on the order of those found for the two independent trajectories of interleukin-4 with CHARMM22. When all three proteins are considered together, no force field showed any consistent trend in variations for most of the properties monitored in the study.     

Assessment of biomolecular force fields for molecular dynamics simulations in a protein crystal

Different biomolecular force fields (OPLS‐AA, AMBER03, and GROMOS96) in conjunction with SPC, SPC/E and TIP3P water models are assessed for molecular dynamics simulations in a tetragonal lysozyme crystal. The root mean square deviations for the C_a atoms of lysozymes are about 0.1 to 0.2 nm from OPLS‐AA and AMBER03, smaller than 0.4 nm from GROMOS96. All force fields exhibit similar pattern in B‐factors, whereas OPLS‐AA and AMBER03 accurately reproduce experimental measurements. Despite slight variations, the primary secondary structures are well conserved using different force fields. Water diffusion in the crystal is approximately ten‐fold slower than in bulk phase. The directional and average water diffusivities from OPLS‐AA and AMBER03 along with SPC/E model match fairly well with experimental data. Compared to GROMOS96, OPLS‐AA and AMBER03 predict larger hydrophilic solvent‐accessible surface area of lysozyme, more hydrogen bonds between lysozyme and water, and higher percentage of water in hydration shell. SPC, SPC/E and TIP3P water models have similar performance in most energetic and structural properties, but SPC/E outperforms in water diffusion. While all force fields overestimate the mobility and electrical conductivity of NaCl, a combination of OPLS‐AA for lysozyme and the Kirkwood‐Buff model for ions is superior to others. As attributed to the steric restraints and surface interactions, the mobility and conductivity in the crystal are reduced by one to two orders of magnitude from aqueous solution. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Ranking protein–protein docking results using steered molecular dynamics and potential of mean force calculations

Crystallization of protein–protein complexes can often be problematic and therefore computational structural models are often relied on. Such models are often generated using protein–protein docking algorithms, where one of the main challenges is selecting which of several thousand potential predictions represents the most near‐native complex. We have developed a novel technique that involves the use of steered molecular dynamics (sMD) and umbrella sampling to identify near‐native complexes among protein–protein docking predictions. Using this technique, we have found a strong correlation between our predictions and the interface RMSD (iRMSD) in ten diverse test systems. On two of the systems, we investigated if the prediction results could be further improved using potential of mean force calculations. We demonstrated that a near‐native (<2.0 Å iRMSD) structure could be identified in the top‐1 ranked position for both systems. © 2016 Wiley Periodicals, Inc.     

Comparative analysis of nucleotide translocation through protein nanopores using steered molecular dynamics and an adaptive biasing force

The translocation of nucleotide molecules across biological and synthetic nanopores has attracted attention as a next generation technique for sequencing DNA. Computer simulations have the ability to provide atomistic‐level insight into important states and processes, delivering a means to develop a fundamental understanding of the translocation event, for example, by extracting the free energy of the process. Even with current supercomputing facilities, the simulation of many‐atom systems in fine detail is limited to shorter timescales than the real events they attempt to recreate. This imposes the need for enhanced simulation techniques that expand the scope of investigation in a given timeframe. There are numerous free energy calculation and translocation methodologies available, and it is by no means clear which method is best applied to a particular problem. This article explores the use of two popular free energy calculation methodologies in a nucleotide‐nanopore translocation system, using the α‐hemolysin nanopore. The first uses constant velocity‐steered molecular dynamics (cv‐SMD) in conjunction with Jarzynski's equality. The second applies an adaptive biasing force (ABF), which has not previously been applied to the nucleotide‐nanpore system. The purpose of this study is to provide a comprehensive comparison of these methodologies, allowing for a detailed comparative assessment of the scientific merits, the computational cost, and the statistical quality of the data obtained from each technique. We find that the ABF method produces results that are closer to experimental measurements than those from cv‐SMD, whereas the net errors are smaller for the same computational cost. © 2014 The Authors Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

The mechanism of vesicle fusion as revealed by molecular dynamics simulations

We describe molecular dynamics simulations elucidating the molecular details of the process of fusion for small lipid vesicles. The simulations are based on a coarse grained (CG) lipid model that accurately represents the lamellar state of a variety of phospholipids and enables us to observe intermediate stages during fusion at near atomic detail. Simulations were conducted on a variety of systems containing common phospholipids such as phosphatidylcholine (PC), phosphatidylethanolamine (PE), lysoPC, and mixtures of the above. The fusion intermediates found are in general agreement with the stalk-pore mechanism. Transient pores sometimes form adjacent to the stalk, however, resulting in the mixing of lipids from the outer and inner monolayers. The speed of stalk formation and the opening of the fusion pore can be modulated by altering the lipid composition in qualitative agreement with experimental observations.     

Dual function of the hydration layer around an antifreeze protein revealed by atomistic molecular dynamics simulations

Atomistic molecular dynamics simulations are used to investigate the mechanism by which the antifreeze protein from the spruce budworm, Choristoneura fumiferana, binds to ice. Comparison of structural and dynamic properties of the water around the three faces of the triangular prism-shaped protein in aqueous solution reveals that at low temperature the water structure is ordered and the dynamics slowed down around the ice-binding face of the protein, with a disordering effect observed around the other two faces. These results suggest a dual role for the solvation water around the protein. The preconfigured solvation shell around the ice-binding face is involved in the initial recognition and binding of the antifreeze protein to ice by lowering the barrier for binding and consolidation of the protein:ice interaction surface. Thus, the antifreeze protein can bind to the molecularly rough ice surface by becoming actively involved in the formation of its own binding site. Also, the disruption of water structure around the rest of the protein helps prevent the adsorbed protein becoming covered by further ice growth.     

G protein- and agonist-bound serotonin 5-HT2A receptor model activated by steered molecular dynamics simulations

A 5-HT(2A) receptor model was constructed by homology modeling based on the β(2)-adrenergic receptor and the G protein-bound opsin crystal structures. The 5-HT(2A) receptor model was transferred into an active conformation by an agonist ligand and a G(αq) peptide in four subsequent steered molecular dynamics (MD) simulations. The driving force for the transformation was the addition of several known intermolecular and receptor interhelical hydrogen bonds enforcing the necessary helical and rotameric movements. Subsquent MD simulations without constraints confirmed the stability of the activated receptor model as well as revealed new information about stabilizing residues and bonds. The active 5-HT(2A) receptor model was further validated by retrospective ligand screening of more than 9400 compounds, whereof 182 were known ligands. The results show that the model can be used in drug discovery for virtual screening and structure-based ligand design as well as in GPCR activation studies.     

Hydrophobic attraction as revealed by AFM force measurements and molecular dynamics simulation

Spherical calcium dioleate particles ( approximately 10 mum in diameter) were used as AFM (atomic force microscope) probes to measure interaction forces of the collector colloid with calcite and fluorite surfaces. The attractive AFM force between the calcium dioleate sphere and the fluorite surface is strong and has a longer range than the DLVO (Derjaguin-Landau-Verwey-Overbeek) prediction. The AFM force between the calcium dioleate sphere and the mineral surfaces does not agree with the DLVO prediction. Consideration of non-DLVO forces, including the attractive hydrophobic force and the repulsive hydration force, was necessary to explain the experimental results. The non-DLVO interactions considered were justified by the different interfacial water structures at calcite- and fluorite-water interfaces as revealed by the numerical computation experiments with molecular dynamics simulation.     

Backbone dynamics of proteins studied by two-dimensional heteronuclear NMR spectroscopy and molecular dynamics simulations

To investigate the backbone dynamics of proteins ¹⁵N longitudinal and transverse relaxation experiments combined with {¹H, ¹⁵N{ NOE measurements together with molecular dynamics simulations were carried out using ribonuclease T₁ and the complex of ribonuclease T₁ with 2′GMP as a model protein. The intensity decay of individual amide cross peaks in a series of (¹H, ¹⁵N)HSQC spectra with appropriate relaxation periods was fitted to a single exponential by using a simplex algorithm in order to obtain ¹⁵N T₁ and T₂ relaxation times. The relaxation times were analyzed in terms of the “model-free” approach introduced by Lipari and Szabo. In addition, a nanosecond molecular dynamics (MD ) simulation of ribonuclease T₁ and its 2′GMP complex in water was carried out. The angular reorientations of the backbone amide groups were classified with several coordinate frames following a transformation of NH vector trajectories. In this study, NH librations and backbone dihedral angle fluctuations were distinguished. The NH bond librations were found to be similar for all amides as characterized by correlation times of librational motions in a subpicosecond scale. The angular amplitudes of these motions were found to be about 10°–12° for out-of-plane displacements and 3°–5° for the in-plane displacement. The contributions from the much slower backbone dihedral angle fluctuations strongly depend on the secondary structure. The dependence of the amplitude of local motion on the residue location in the backbone is in good agreement with the results of NMR relaxation measurements and the X-ray data. The protein dynamics is characterized by a highly restricted local motion of those parts of the backbone with defined secondary structure as well as by a high flexibility in loop regions. Comparison of the MD and NMR data of the free liganded enzyme ribonuclease T₁ clearly indicates a restriction of the mobility within certain regions of the backbone upon inhibitor binding. © 1996 John Wiley & Sons, Inc.     

A method for predicting protein conformational pathways by using molecular dynamics simulations guided by difference distance matrices

Here, an efficient method that predicts natural transition pathways between two endpoint states of an allosteric protein has been proposed. This method helps create structures that bridge these endpoints through multiple iterative and unbiased molecular dynamics simulations with explicit water. Difference distance matrices provide an approach for identifying states involving concerted slow motion. A series of structures are readily generated along the transition pathways of adenylate kinase. Predicted structures may be useful for an initial pathway to evaluate free energy landscapes via umbrella sampling and chain‐of‐states methods. © 2016 Wiley Periodicals, Inc.     

Gating motions in voltage-gated potassium channels revealed by coarse-grained molecular dynamics simulations

Voltage-gated potassium (Kv) channels are ubiquitous transmembrane proteins involved in electric signaling of excitable tissues. A fundamental property of these channels is the ability to open or close in response to changes in the membrane potential. To date, their structure-based activation mechanism remains unclear, and there is a large controversy on how these gates function at the molecular level, in particular, how movements of the voltage sensor domain are coupled to channel gating. So far, all mechanisms proposed for this coupling are based on the crystal structure of the open voltage-gated Kv1.2 channel and structural models of the closed form based on electrophysiology experiments. Here, we use coarse-grain (CG) molecular dynamics simulations that allow conformational changes from the open to the closed form of the channel (embedded in its membrane environment) to be followed. Despite the low specificity of the CG force field, the obtained closed structure satisfies several experimental constraints. The overall results suggest a gating mechanism in which a lateral displacement the S4-S5 linker leads to a closing of the gate. Only a small up-down movement of the S4 helices is noticed. Additionally, the study suggests a peculiar upward motion of the intracellular tetramerization domain of the channel, hence providing a molecular view on how this domain may further regulate conduction in Kv channels.     

Local order and dynamics in supercooled water: a study by IR spectroscopy and molecular dynamic simulations

Micron-sized water droplets in a cryogenic flow tube were probed by IR spectroscopy. The analysis of the IR spectra suggests that there is a relative increase of about 30% in the fraction, f(L), of low density domains in water on cooling over the temperature range between 300 and 240 K. The results derived from the experiments agree qualitatively with those of molecular dynamics (MD) simulations in terms of the increase in the f(L) values. The MD simulations show that the intensities of the mode at about 100 cm(-1) for the molecules in the low density domains are reduced in comparison to the average, while the intensities and frequencies of the librational mode at 600 cm(-1) are increased. Furthermore, the reorientations (dielectric relaxation times) in these domains are found to be somewhat slower, pointing to the fact that these low density "cages" live longer than the average local molecular environments in supercooled water.     

CHARMM force field and molecular dynamics simulations of protonated polyethylenimine

As a gene delivery vector, polyethylenimine (PEI) shows one of the highest transfection efficiencies, while effectively protecting DNA from enzyme degradation. The distinctive charge pattern of protonated PEI is widely considered responsible for fundamental process such as DNA condensation into PEI/DNA polyplexes (which are able to enter cells via endocytosis), proton sponge effect (which triggers the release of polyplexes from endosome), and release of DNA from polyplexes (to be further processed inside the nucleus). Our investigations are largely motivated by the crucial need for a realistic molecular mechanics force field (FF) for PEI, and, accordingly, we focus on two major issues: (1) development of a new atomistic (CHARMM) FF for PEI in different protonation states, rigorously derived from high‐quality ab initio calculations performed on model polymers, and (2) molecular dynamics investigations of solvated PEI, providing a detailed picture of the dynamic structuring thereof in dependence on their size and protonation state. The modeled PEI chains are essentially described in terms of gyration radius, end‐to‐end distance, persistence length, radial distribution functions, coordination numbers, and diffusion coefficients. They turn out to be more rigid than in other computational studies and we find diffusion coefficients in fair agreement with experimental data. The developed atomistic FF proves adequate for the realistic modeling of the size and protonation behavior of linear PEI, either as individual chains or composing polyplexes. © 2017 Wiley Periodicals, Inc.     

Hydration-dependent protein dynamics revealed by molecular dynamics simulation of crystalline staphylococcal nuclease

Molecular dynamics simulations of crystalline Staphylococcal nuclease in full and minimal hydration states were performed to study hydration effects on protein dynamics at temperatures ranging from 100 to 300 K. In a full hydration state (hydration ratio in weight, h=0.49), gaps are fully filled with water molecules, whereas only crystal waters are included in a minimal hydration state (h=0.09). The inflection of the atomic mean-square fluctuation of protein as a function of temperature, known as the glass-like transition, is observed at approximately 220 K in both cases, which is more significant in the full hydration state. By examining the temperature dependence of residual fluctuation, we found that the increase of fluctuations in the loop and terminal regions, which are exposed to water, is much greater than that in other regions in the full hydration state, but the mobilities of the corresponding regions are relatively restricted in the minimal hydration state by intermolecular contact. The atomic mean-square fluctuation of water molecules in the full hydration state at 300 K is 1 order of magnitude greater than that in the minimal hydration state. Above the transition temperature, most water molecules in the full hydration state behave like bulk water and act as a lubricant for protein dynamics. In contrast, water molecules in the minimal hydration state tend to form more hydrogen bonds with the protein, restricting the fluctuation of these water molecules to the level of the protein. Thus, intermolecular interaction and solvent mobility are important to understand the glass-like transition in proteins.     

Paramfit: Automated optimization of force field parameters for molecular dynamics simulations

The generation of bond, angle, and torsion parameters for classical molecular dynamics force fields typically requires fitting parameters such that classical properties such as energies and gradients match precalculated quantum data for structures that scan the value of interest. We present a program, Paramfit, distributed as part of the AmberTools software package that automates and extends this fitting process, allowing for simplified parameter generation for applications ranging from single molecules to entire force fields. Paramfit implements a novel combination of a genetic and simplex algorithm to find the optimal set of parameters that replicate either quantum energy or force data. The program allows for the derivation of multiple parameters simultaneously using significantly fewer quantum calculations than previous methods, and can also fit parameters across multiple molecules with applications to force field development. Paramfit has been applied successfully to systems with a sparse number of structures, and has already proven crucial in the development of the Assisted Model Building with Energy Refinement Lipid14 force field. © 2014 Wiley Periodicals, Inc.