Designer phospholipid capping ligands for soft metal halide nanocrystals.

The success of colloidal semiconductor nanocrystals (NCs) in science and optoelectronics is inextricable from their surfaces. The functionalization of lead halide perovskite NCs1-5 poses a formidable challenge because of their structural lability, unlike the well-established covalent ligand capping of conventional semiconductor NCs6,7. We posited that the vast and facile molecular engineering of phospholipids as zwitterionic surfactants can deliver highly customized surface chemistries for metal halide NCs. Molecular dynamics simulations implied that ligand-NC surface affinity is primarily governed by the structure of the zwitterionic head group, particularly by the geometric fitness of the anionic and cationic moieties into the surface lattice sites, as corroborated by the nuclear magnetic resonance and Fourier-transform infrared spectroscopy data. Lattice-matched primary-ammonium phospholipids enhance the structural and colloidal integrity of hybrid organic-inorganic lead halide perovskites (FAPbBr3 and MAPbBr3 (FA, formamidinium; MA, methylammonium)) and lead-free metal halide NCs. The molecular structure of the organic ligand tail governs the long-term colloidal stability and compatibility with solvents of diverse polarity, from hydrocarbons to acetone and alcohols. These NCs exhibit photoluminescence quantum yield of more than 96% in solution and solids and minimal photoluminescence intermittency at the single particle level with an average ON fraction as high as 94%, as well as bright and high-purity (about 95%) single-photon emission.

Reduced atomic pair-interaction design (RAPID) model for simulations of proteins.

Increasingly, theoretical studies of proteins focus on large systems. This trend demands the development of computational models that are fast, to overcome the growing complexity, and accurate, to capture the physically relevant features. To address this demand, we introduce a protein model that uses all-atom architecture to ensure the highest level of chemical detail while employing effective pair potentials to represent the effect of solvent to achieve the maximum speed. The effective potentials are derived for amino acid residues based on the condition that the solvent-free model matches the relevant pair-distribution functions observed in explicit solvent simulations. As a test, the model is applied to alanine polypeptides. For the chain with 10 amino acid residues, the model is found to reproduce properly the native state and its population. Small discrepancies are observed for other folding properties and can be attributed to the approximations inherent in the model. The transferability of the generated effective potentials is investigated in simulations of a longer peptide with 25 residues. A minimal set of potentials is identified that leads to qualitatively correct results in comparison with the explicit solvent simulations. Further tests, conducted for multiple peptide chains, show that the transferable model correctly reproduces the experimentally observed tendency of polyalanines to aggregate into ß-sheets more strongly with the growing length of the peptide chain. Taken together, the reported results suggest that the proposed model could be used to succesfully simulate folding and aggregation of small peptides in atomic detail. Further tests are needed to assess the strengths and limitations of the model more thoroughly.

ICSM: An order N method for calculating electrostatic interactions added to TINKER.

We present an order N method for calculating electrostatic interactions that has been integrated into the molecular dynamics portion of the TINKER Molecular Modeling package. This method, introduced in a previous paper [J. Chem. Phys. 131 (2009) 154103] and termed the Image-Charge Solvation Model (ICSM), is a hybrid electrostatic approach that combines the strengths of both explicit and implicit representations of the solvent. A multiple-image method is used to calculate reaction fields due to the implicit part while the Fast Multipole Method (FMM) is used to calculate the Coulomb interactions for all charges, including the explicit part. The integrated package is validated through test simulations of liquid water. The results are compared with those obtained by the Particle Mesh Ewald (PME) method that is built in the TINKER package. Timing performance of TINKER with the integrated ICSM is benchmarked on bulk water as a function of the size of the system. In particular, timing analysis results show that the ICSM outperforms the PME for sufficiently large systems with the break-even point at around 30,000 particles in the simulated system.

The mechanism of the converter domain rotation in the recovery stroke of myosin motor protein.

Upon ATP binding, myosin motor protein is found in two alternative conformations, prerecovery state M* and postrecovery state M**. The transition from one state to the other, known as the recovery stroke, plays a key role in the myosin functional cycle. Despite much recent research, the microscopic details of this transition remain elusive. A critical step in the recovery stroke is the rotation of the converter domain from "up" position in prerecovery state to "down" position in postrecovery state that leads to the swing of the lever arm attached to it. In this work, we demonstrate that the two rotational states of the converter domain are determined by the interactions within a small structural motif in the force-generating region of the protein that can be accurately modeled on computers using atomic representation and explicit solvent. Our simulations show that the transition between the two states is controlled by a small helix (SH1) located next to the relay helix and relay loop. A small translation in the position of SH1 away from the relay helix is seen to trigger the transition from "up" state to "down" state. The transition is driven by a cluster of hydrophobic residues I687, F487, and F506 that make significant contributions to the stability of both states. The proposed mechanism agrees well with the available structural and mutational studies.

Interactions between relay helix and Src homology 1 (SH1) domain helix drive the converter domain rotation during the recovery stroke of myosin II.

Myosin motor protein exists in two alternative conformations, prerecovery state M* and postrecovery state M**, on adenosine triphosphate binding. The details of the M*-to-M** transition, known as the recovery stroke to reflect its role as the functional opposite of the force-generating power stroke, remain elusive. The defining feature of the postrecovery state is a kink in the relay helix, a key part of the protein involved in force generation. In this article, we determine the interactions that are responsible for the appearance of the kink. We design a series of computational models that contain three other segments, relay loop, converter domain, and Src homology 1 (SH1) domain helix, with which relay helix interacts and determine their structure in accurate replica exchange molecular dynamics simulations in explicit solvent. By conducting an exhaustive combinatorial search among different models, we find that: (1) the converter domain must be attached to the relay helix during the transition, so it does not interfere with other parts of the protein and (2) the structure of the relay helix is controlled by SH1 helix. The kink is strongly coupled to the position of SH1 helix. It arises as a result of direct interactions between SH1 and the relay helix and leads to a rotation of the C-terminal part of the relay helix, which is subsequently transmitted to the converter domain.

Ionic solvation studied by image-charge reaction field method.

In a preceding paper [J. Chem. Phys. 131, 154103 (2009)], we introduced a new, hybrid explicit/implicit method to treat electrostatic interactions in computer simulations, and tested its performance for liquid water. In this paper, we report further tests of this method, termed the image-charge solvation model (ICSM), in simulations of ions solvated in water. We find that our model can faithfully reproduce known solvation properties of sodium and chloride ions. The charging free energy of a single sodium ion is in excellent agreement with the estimates by other electrostatics methods, while offering much lower finite-size errors. Similarly, the potentials of mean force computed for Na-Cl, Na-Na, and Cl-Cl pairs closely reproduce those reported previously. Collectively, our results demonstrate the superior accuracy of the proposed ICSM method for simulations of mixed media.

Role of the familial Dutch mutation E22Q in the folding and aggregation of the 15-28 fragment of the Alzheimer amyloid-beta protein.

Amyloid fibrils, large ordered aggregates of amyloid beta proteins (Abeta), are clinical hallmarks of Alzheimer's disease (AD). The aggregation properties of amyloid beta proteins can be strongly affected by single-point mutations at positions 22 and 23. The Dutch mutation involves a substitution at position 22 (E22Q) and leads to increased deposition rates of the AbetaE22Q peptide onto preseeded fibrils. We investigate the effect of the E22Q mutation on two key regions involved in the folding and aggregation of the Abeta peptide through replica exchange molecular dynamics simulations of the 15-28 fragment of the Abeta peptide. The Abeta15-28 peptide encompasses the 22-28 region that constitutes the most structured part of the Abeta peptide (the E22-K28 bend), as well as the central hydrophobic cluster (CHC) (segment 17-21), the primary docking site for Abeta monomers depositing onto fibrils. Our simulations show that the 22-28 bend is preserved in the Abeta(15-28) peptide and that the CHC, which is mostly unstructured, interacts with this bend region. The E22Q mutation does not affect the structure of the bend but weakens the interactions between the CHC and the bend. This leads to an increased population of beta-structure in the CHC. Our analysis of the fibril elongation reaction reveals that the CHC adopts a beta-strand conformation in the transition state ensemble, and that the E22Q mutation increases aggregation rates by lowering the barrier for Abeta monomer deposition onto a fibril. Thermodynamic signatures of this enhanced fibrillization process from our simulations are in good agreement with experimental observations.

On the Mechanism of Alkylammonium Ligands Binding to the Surface of CsPbBr3 Nanocrystals.

CsPbBr3 nanocrystals (NCs) suffer from instabilities caused by the dynamic and labile nature of both the inorganic core and the organic-inorganic interface. Surface ligand engineering thus remains an imminent research topic. In this study, classical molecular dynamics simulations with an explicit solvent are used to gain insights into the inherent binding properties of three different alkylammonium ligands-primary dodecylammonium (DA), secondary didodecylammonium (DDA), and quaternary dimethyldi- dodecylammonium (DMDDA). Our simulations uncover three main factors that govern the effective ligand-substrate interactions: (i) the ability of the head-group to penetrate into the binding pocket, (ii) the strength of head-group interactions with the polar solvent, and (iii) the higher barrier for ligand adsorption/desorption in the case of multiple alkyl chains. The interplay between these factors causes the following order of the binding free energies: DDA < DA ≈ DMDDA, while surface capping with DDA and DMDDA ligands is additionally stabilized by the kinetic barrier. These findings are in agreement with previous experimental observations and with the results of presented ligand-exchange experiments, wherein DDA is found to loosely bind to the CsPbBr3 surface, while DMDDA capping is more stable than capping with the primary oleylammonium ligand. The presented mechanistic understanding of the ligand-NC interactions will aid in the design of cationic ligands that make perovskite NC surfaces more robust.

Amyloid beta-protein: experiment and theory on the 21-30 fragment.

The structure of the 21-30 fragment of the amyloid beta-protein (Abeta) was investigated by ion mobility mass spectrometry and replica exchange dynamics simulations. Mutations associated with familial Alzheimer's disease (E22G, E22Q, E22K, and D23N) of Abeta(21-30) were also studied, in order to understand any structural changes that might occur with these substitutions. The structure of the WT peptide shows a bend and a perpendicular turn in the backbone which is maintained by a network of D23 hydrogen bonding. Results for the mutants show that substitutions at E22 do little to alter the overall structure of the fragment. A substitution at D23 resulted in a change of structure for Abeta(21-30). A comparison of these gas-phase studies to previous solution-phase studies reveals that the peptide can fold in the absence of solvent to a structure also seen in solution, highlighting the important role of the D23 hydrogen bonding network in stabilizing the fragment's folded structure.

Removing systematic errors in interionic potentials of mean force computed in molecular simulations using reaction-field-based electrostatics.

The performance of reaction-field methods to treat electrostatic interactions is tested in simulations of ions solvated in water. The potential of mean force between sodium chloride pair of ions and between side chains of lysine and aspartate are computed using umbrella sampling and molecular dynamics simulations. It is found that in comparison with lattice sum calculations, the charge-group-based approaches to reaction-field treatments produce a large error in the association energy of the ions that exhibits strong systematic dependence on the size of the simulation box. The atom-based implementation of the reaction field is seen to (i) improve the overall quality of the potential of mean force and (ii) remove the dependence on the size of the simulation box. It is suggested that the atom-based truncation be used in reaction-field simulations of mixed media.

An image-based reaction field method for electrostatic interactions in molecular dynamics simulations of aqueous solutions.

In this paper, a new solvation model is proposed for simulations of biomolecules in aqueous solutions that combines the strengths of explicit and implicit solvent representations. Solute molecules are placed in a spherical cavity filled with explicit water, thus providing microscopic detail where it is most needed. Solvent outside of the cavity is modeled as a dielectric continuum whose effect on the solute is treated through the reaction field corrections. With this explicit/implicit model, the electrostatic potential represents a solute molecule in an infinite bath of solvent, thus avoiding unphysical interactions between periodic images of the solute commonly used in the lattice-sum explicit solvent simulations. For improved computational efficiency, our model employs an accurate and efficient multiple-image charge method to compute reaction fields together with the fast multipole method for the direct Coulomb interactions. To minimize the surface effects, periodic boundary conditions are employed for nonelectrostatic interactions. The proposed model is applied to study liquid water. The effect of model parameters, which include the size of the cavity, the number of image charges used to compute reaction field, and the thickness of the buffer layer, is investigated in comparison with the particle-mesh Ewald simulations as a reference. An optimal set of parameters is obtained that allows for a faithful representation of many structural, dielectric, and dynamic properties of the simulated water, while maintaining manageable computational cost. With controlled and adjustable accuracy of the multiple-image charge representation of the reaction field, it is concluded that the employed model achieves convergence with only one image charge in the case of pure water. Future applications to pKa calculations, conformational sampling of solvated biomolecules and electrolyte solutions are briefly discussed.

The structure of the Alzheimer amyloid beta 10-35 peptide probed through replica-exchange molecular dynamics simulations in explicit solvent.

The conformational states sampled by the Alzheimer amyloid beta (10-35) (Abeta 10-35) peptide were probed using replica-exchange molecular dynamics (REMD) simulations in explicit solvent. The Abeta 10-35 peptide is a fragment of the full-length Abeta 40/42 peptide that possesses many of the amyloidogenic properties of its full-length counterpart. Under physiological temperature and pressure, our simulations reveal that the Abeta 10-35 peptide does not possess a single unique folded state. Rather, this peptide exists as a mixture of collapsed globular states that remain in rapid dynamic equilibrium with each other. This conformational ensemble is dominated by random coil and bend structures with insignificant presence of an alpha-helical or beta-sheet structure. The 3D structure of Abeta 10-35 is seen to be defined by a salt bridge formed between the side-chains of K28 and D23. This salt bridge is also observed in Abeta fibrils and our simulations suggest that monomeric conformations of Abeta 10-35 contain pre-folded structural motifs that promote rapid aggregation of this peptide.

Folding landscapes of the Alzheimer amyloid-beta(12-28) peptide.

The energy landscape for folding of the 12-28 fragment of the Alzheimer amyloid beta (Abeta) peptide is characterized using replica-exchange molecular dynamics simulations with an all-atom peptide model and explicit solvent. At physiological temperatures, the peptide exists mostly as a collapsed random coil, populating a small fraction (less than 10%) of hairpins with a beta-turn at position V18F19, with another 10% of hairpin-like conformations possessing a bend rather than a turn in the central VFFA positions. A small fraction of the populated states, approximately 14%, adopt polyproline II (PPII) conformations. Folding of the structured hairpin states proceeds through the assembly of two locally stable segments, VFFAE and EDVGS. The interactions stabilizing these locally folded structural motifs are in conflict with those stabilizing the global fold of A12-28, a signature of underlying residual frustration in this peptide. At increased temperature, the population of both beta-strand and PPII conformations diminishes in favor of beta-turn and random-coil states. On the basis of the conformational preferences of Abeta 12-28 monomers, two models for the molecular structure of amyloid fibrils formed by this peptide are proposed.

Amyloid beta-protein monomer structure: a computational and experimental study.

The structural properties of the Abeta42 peptide, a main constituent of the amyloid plaques formed in Alzheimer's disease, were investigated through a combination of ion-mobility mass spectrometry and theoretical modeling. Replica exchange molecular dynamics simulations using a fully atomic description of the peptide and implicit water solvent were performed on the -3 charge state of the peptide, its preferred state under experimental conditions. Equilibrated structures at 300 K were clustered into three distinct families with similar structural features within a family and with significant root mean square deviations between families. An analysis of secondary structure indicates the Abeta42 peptide conformations are dominated by loops and turns but show some helical structure in the C-terminal hydrophobic tail. A second calculation on Abeta42 in a solvent-free environment yields compact structures turned "inside out" from the solution structures (hydrophobic parts on the outside, polar parts on the inside). Ion mobility experiments on the Abeta42 -3 charge state electrosprayed from solution yield a bimodal arrival time distribution. This distribution can be quantitatively fit using cross-sections from dehydrated forms of the three families of calculated solution structures and the calculated solvent-free family of structures. Implications of the calculations on the early stages of aggregation of Abeta42 are discussed.

Structure of the 21-30 fragment of amyloid beta-protein.

Folding and self-assembly of the 42-residue amyloid beta-protein (Abeta) are linked to Alzheimer's disease (AD). The 21-30 region of Abeta, Abeta(21-30), is resistant to proteolysis and is believed to nucleate the folding of full-length Abeta. The conformational space accessible to the Abeta(21-30) peptide is investigated by using replica exchange molecular dynamics simulations in explicit solvent. Conformations belonging to the global free energy minimum (the "native" state) from simulation are in good agreement with reported NMR structures. These conformations possess a bend motif spanning the central residues V24-K28. This bend is stabilized by a network of hydrogen bonds involving the side chain of residue D23 and the amide hydrogens of adjacent residues G25, S26, N27, and K28, as well as by a salt bridge formed between side chains of K28 and E22. The non-native states of this peptide are compact and retain a native-like bend topology. The persistence of structure in the denatured state may account for the resistance of this peptide to protease degradation and aggregation, even at elevated temperatures.

The influence of different treatments of electrostatic interactions on the thermodynamics of folding of peptides.

Replica exchange molecular dynamics simulations were performed to investigate the effects of different electrostatic treatments on the structure and thermodynamics of a small beta-hairpin forming peptide. Three different electrostatic schemes were considered: regular cutoffs, generalized reaction field (GRF), and particle mesh Ewald (PME), with the peptide modeled using OPLS/AA all-atom force field with explicit TIP3P water. Both the GRF and PME methods yielded results consistent with experiment, with free energy surfaces displaying a single minimum corresponding to the native beta-hairpin structure. In contrast, use of straight cutoffs led to the population of an additional local minimum corresponding to nonhairpin conformations that compete with the formation of the native beta-hairpin at low temperatures. This extra minimum would not be apparent in conventional constant-temperature molecular dynamics simulations run for a few nanoseconds. This result points to the critical need of careful sampling of conformational space to assess the quality of different numerical treatments of long-range forces. While differences emerged in the nature of the unfolded states populated using PME and GRF approaches, simulations on the beta-hairpin forming peptide and on two additional control peptides indicate that the GRF treatment of electrostatics offers a satisfactory compromise between accuracy and computational speed for the identification of low-energy conformations. A GRF-based approach emerges as a viable means for treating larger biological systems that would be prohibitively costly to simulate using PME methods.

Electric field as a disaggregating agent for amyloid fibrils.

Folding and aggregation lie on competing reaction pathways in proteins. Altering the occupancy of one pathway is automatically relayed to the other pathway, leading to a shift in the balance between the two processes. In particular, it is known that the stabilization of the native state through mutations or solvent alterations is able to halt aggregation. In this work, we explore the feasibility of using external electric field as an agent preventing aggregation through the promotion of folding. We use an atomically accurate protein model and computer simulations to investigate folding and aggregation of alanine polypeptides in electric field of varying strength. The studied peptides are mostly unstructured in the absence of the field but experience a transition into α-helical states when the field is applied. The transition is accompanied by the disassembly of preseeded stacked ß-sheets, which are used as a model of amyloid fibrils, suggesting that electric field can be employed to control aggregation propensity of intrinsically disordered peptides. According to our calculations, the strength of the field required for the disaggregation could be suitable for both controlled in vitro experiments as well as for experiments on live cells. Additionally, our estimates suggest that endogenous electric fields may have a significant effect on in vivo amyloid formation.

Effect of the Reaction Field on Molecular Forces and Torques Revealed by an Image-Charge Solvation Model.

We recently developed the Image-Charge Solvation Model (ICSM), which is an explicit/implicit hybrid model to accurately account for long-range electrostatic forces in molecular dynamics simulations [Lin et al., J. Chem. Phys., 131, 154103, 2009]. The ICSM has a productive spherical volume within the simulation cell for which key physical properties of bulk water are reproduced, such as density, radial distribution function, diffusion constants and dielectric properties. Although the reaction field (RF) is essential, it typically accounts for less than 2% of the total electrostatic force on a water molecule. This observation motivates investigating further the role of the RF within the ICSM. In this report we focus on distributions of forces and torques on water molecules as a function of distance from the origin and make extensive tests over a range of model parameters where Coulomb forces are decomposed into direct interactions from waters modeled explicitly and the RF. Molecular torques due to the RF typically account for 20% of the total torque, revealing why the RF plays an important role in the dielectric properties of simulated water. Moreover, it becomes clear that the buffer layer in the ICSM is essential to mitigate artifacts caused by the discontinuous change in dielectric constants at the explicit/implicit interface.

Effect of atom- and group-based truncations on biomolecules simulated with reaction-field electrostatics.

The performance of the reaction-field method of electrostatics is tested in molecular dynamics simulations of protein human interleukin-4 and a short DNA fragment in explicit solvent. Two truncation schemes are considered: one based on the position of atomic charges in water molecules and the other on the position of groups of charges. The group-based truncation leads to the melting of the DNA double helix. In contrast, the atom-based truncation maintains the helical structure intact. Similarly for the protein, the group-based truncation leads to an unfolding at pH 2 while the atom-based truncation produces stable trajectories at low and normal pH, in agreement with experiment. Artificial repulsion between charged residues associated with the group-based truncation is identified as the microscopic reason behind unfolding of the protein. Implications of different truncation schemes in reaction-field simulations of biomolecules are discussed.

Early stages of the recovery stroke in myosin II studied by molecular dynamics simulations.

The recovery stroke is a key step in the functional cycle of muscle motor protein myosin, during which pre-recovery conformation of the protein is changed into the active post-recovery conformation, ready to exersice force. We study the microscopic details of this transition using molecular dynamics simulations of atomistic models in implicit and explicit solvent. In more than 2 µs of aggregate simulation time, we uncover evidence that the recovery stroke is a two-step process consisting of two stages separated by a time delay. In our simulations, we directly observe the first stage at which switch II loop closes in the presence of adenosine triphosphate at the nucleotide binding site. The resulting configuration of the nucleotide binding site is identical to that detected experimentally. Distribution of inter-residue distances measured in the force generating region of myosin is in good agreement with the experimental data. The second stage of the recovery stroke structural transition, rotation of the converter domain, was not observed in our simulations. Apparently it occurs on a longer time scale. We suggest that the two parts of the recovery stroke need to be studied using separate computational models.