Martini Force Field for Protonated Polyethyleneimine

Polyethyleneimine (PEI), one of the most widely used nonviral gene carriers, was investigated in the presented work at coarse-grained (CG) level. The main focus was on elaborating a realistic CG force field (FF) aimed to reproduce dynamic structural features of protonated PEI chains and, furthermore, to enable massive simulations of DNA–PEI complex formation and condensation. We parametrized CG Martini FF models for PEI in polarizable and nonpolarizable water by applying Boltzmann inversion techniques to all-atom (AA) probability distributions for distances, angles, and dihedrals of entire monomers. The fine-tuning of the FFs was achieved by fitting simulated CG gyration radii and end-to-end distances to their AA counterparts. The developed Martini FF models are shown to be well suited for realistic large-scale simulations of size/protonation-dependent behavior of solvated PEI chains, either individually or as part of DNA–PEI systems. © 2019 Wiley Periodicals, Inc.     

Implementation of a protein reduced point charge model toward molecular dynamics applications

A reduced point charge model was developed in a previous work from the study of extrema in smoothed charge density distribution functions generated from the Amber99 molecular electrostatic potential. In the present work, such a point charge distribution is coupled with the Amber99 force field and implemented in the program TINKER to allow molecular dynamics (MD) simulations of proteins. First applications to two polypeptides that involve α-helix and β-sheet motifs are analyzed and compared to all-atom MD simulations. Two types of coarse-grained (CG)-based trajectories are generated using, on one hand, harmonic bond stretching terms and, on the other hand, distance restraints. Results show that the use of the unrestrained CG conditions are sufficient to preserve most of the secondary structure characteristics but restraints lead to a better agreement between CG and all-atom simulation results such as rmsd, dipole moment, and time-dependent mean square deviation functions.     

Coarse-Grained Molecular Dynamics Study based on TorchMD

The coarse grained (CG) model implements the molecular dynamics simulation by simplifying atom properties and interaction between them. Despite losing certain detailed information, the CG model is still the first-thought option to study the large molecule in long time scale with less computing resource. The deep learning model mainly mimics the human studying process to handle the network input as the image to achieve a good classification and regression result. In this work, the TorchMD, a MD framework combining the CG model and deep learning model, is applied to study the protein folding process. In 3D collective variable (CV) space, the modified find density peaks algorithm is applied to cluster the conformations from the TorchMD CG simulation. The center conformation in different states is searched. And the boundary conformations between clusters are assigned. The string algorithm is applied to study the path between two states, which are compared with the end conformations from all atoms simulations. The result shows that the main phenomenon of protein folding with TorchMD CG model is the same as the all-atom simulations, but with a less simulating time scale. The workflow in this work provides another option to study the protein folding and other relative processes with the deep learning CG model.     

Aggregation Behavior of Trisiloxane-Tailed Surface Active Ionic Liquids in Aqueous Solution: Coarse-Grained Molecular Dynamics Study

The aggregation behaviors of two trisiloxane-tailed surface active ionic liquids in water have been investigated by coarse-grained (CG) molecular dynamics simulation on the basis of MARTINI force field. The new CG model is developed from the optimized molecule computed by using density functional theory. Direct comparison of angles and bonds obtained from all-atom (AA) simulations with those calculated from the CG model has been conducted to validate the latter model. Excellent agreement between AA and CG demonstrates that the potential of the new CG model can represent the complex system well. The long time CG simulation has been performed to understand the formation process of micelles when dissolving ionic liquids in water. Vesicles were observed at the final stage of the simulation and their partially truncated views and density profiles were obtained to describe the structure in detail.     

Gay-Berne and electrostatic multipole based coarse-grain potential in implicit solvent

A general, transferable coarse-grain (CG) framework based on the Gay-Berne potential and electrostatic point multipole expansion is presented for polypeptide simulations. The solvent effect is described by the Generalized Kirkwood theory. The CG model is calibrated using the results of all-atom simulations of model compounds in solution. Instead of matching the overall effective forces produced by atomic models, the fundamental intermolecular forces such as electrostatic, repulsion-dispersion, and solvation are represented explicitly at a CG level. We demonstrate that the CG alanine dipeptide model is able to reproduce quantitatively the conformational energy of all-atom force fields in both gas and solution phases, including the electrostatic and solvation components. Replica exchange molecular dynamics and microsecond dynamic simulations of polyalanine of 5 and 12 residues reveal that the CG polyalanines fold into "alpha helix" and "beta sheet" structures. The 5-residue polyalanine displays a substantial increase in the "beta strand" fraction relative to the 12-residue polyalanine. The detailed conformational distribution is compared with those reported from recent all-atom simulations and experiments. The results suggest that the new coarse-graining approach presented in this study has the potential to offer both accuracy and efficiency for biomolecular modeling.     

Replica exchange Monte-Carlo simulations of helix bundle membrane proteins: rotational parameters of helices

We propose a united-residue model of membrane proteins to investigate the structures of helix bundle membrane proteins (HBMPs) using coarse-grained (CG) replica exchange Monte-Carlo (REMC) simulations. To demonstrate the method, it is used to identify the ground state of HBMPs in a CG model, including bacteriorhodopsin (BR), halorhodopsin (HR), and their subdomains. The rotational parameters of transmembrane helices (TMHs) are extracted directly from the simulations, which can be compared with their experimental measurements from site-directed dichroism. In particular, the effects of amphiphilic interaction among the surfaces of TMHs on the rotational angles of helices are discussed. The proposed CG model gives a reasonably good structure prediction of HBMPs, as well as a clear physical picture for the packing, tilting, orientation, and rotation of TMHs. The root mean square deviation (RMSD) in coordinates of C_α atoms of the ground state CG structure from the X-ray structure is 5.03 Å for BR and 6.70 Å for HR. The final structure of HBMPs is obtained from the all-atom molecular dynamics simulations by refining the predicted CG structure, whose RMSD is 4.38 Å for BR and 5.70 Å for HR.     

Modeling real dynamics in the coarse-grained representation of condensed phase systems

This work presents a systematic multiscale methodology to provide a more faithful representation of real dynamics in coarse-grained molecular simulation models. The theoretical formalism is based on the recently developed multiscale coarse-graining (MS-CG) method [S. Izvekov and G. A. Voth, J. Phys. Chem. B. 109, 2469 (2005); J. Chem. Phys. 123, 134105 (2005)] and relies on the generalized Langevin equation approach and its simpler Langevin equation limit. The friction coefficients are determined in multiscale fashion from the underlying all-atom molecular dynamics simulations using force-velocity and velocity-velocity correlation functions for the coarse-grained sites. The diffusion properties in the resulting CG Brownian dynamics simulations are shown to be quite accurate. The time dependence of the velocity autocorrelation function is also well-reproduced relative to the all-atom model if sufficient resolution of the CG sites is implemented.     

A hybrid all-atom/coarse grain model for multiscale simulations of DNA

Hybrid simulations of molecular systems, which combine all-atom (AA) with simplified (or coarse grain, CG) representations, propose an advantageous alternative to gain atomistic details on relevant regions while getting profit from the speedup of treating a bigger part of the system at the CG level. Here we present a reduced set of parameters derived to treat a hybrid interface in DNA simulations. Our method allows us to forthrightly link a state-of-the-art force field for AA simulations of DNA with a CG representation developed by our group. We show that no modification is needed for any of the existing residues (neither AA nor CG). Only the bonding parameters at the hybrid interface are enough to produce a smooth transition of electrostatic, mechanic and dynamic features in different AA/CG systems, which are studied by molecular dynamics simulations using an implicit solvent. The simplicity of the approach potentially permits us to study the effect of mutations/modifications as well as DNA binding molecules at the atomistic level within a significantly larger DNA scaffold considered at the CG level. Since all the interactions are computed within the same classical Hamiltonian, the extension to a quantum/classical/coarse-grain multilayer approach using QM/MM modules implemented in widely used simulation packages is straightforward.     

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.     

A Molecular Mechanics Model for Flavins

Flavin containing molecules form a group of important cofactors that assist a wide range of enzymatic reactions. Flavins use the redox-active isoalloxazine system, which is capable of one- and two-electron transfer reactions and can exist in several protonation states. In this work, molecular mechanics force field parameters compatible with the CHARMM36 all-atom additive force field were derived for biologically important flavins, including riboflavin, flavin mononucleotide, and flavin adenine dinucleotide. The model was developed for important protonation and redox states of the isoalloxazine group. The partial charges were derived using the CHARMM force field parametrization strategy, where quantum mechanics water–solute interactions are used to target optimization. In addition to monohydrate energies and geometries, electrostatic potential around the compound was used to provide additional restraints during the charge optimization. Taking into account the importance of flavin-containing molecules special attention was given to the quality of bonded terms. All bonded terms, including stiff terms and torsion angle parameters, were parametrized using exhaustive potential energy surface scans. In particular, the model reproduces well the butterfly motion of isoalloxazine in the oxidized and reduced forms as predicted by quantum mechanics in gas phase. The model quality is illustrated by simulations of four flavoproteins. Overall, the presented molecular mechanics model will be of utility to model flavin cofactors in different redox states. © 2019 Wiley Periodicals, Inc.     

Coarse-grained force field for simulating polymer-tethered silsesquioxane self-assembly in solution

A coarse-grained model has been developed for simulating the self-assembly of nonyl-tethered polyhedral oligomeric silsesquioxane (POSS) nanoparticles in solution. A mapping scheme for groups of atoms in the atomistic molecule onto beads in the coarse-grained model was established. The coarse-grained force field consists of solvent-mediated effective interaction potentials that were derived via a structural-based coarse-graining numerical iteration scheme. The force field was obtained from initial guesses that were refined through two different iteration algorithms. The coarse-graining scheme was validated by comparing the aggregation of POSS molecules observed in simulations of the coarse-grained model to that observed in all-atom simulations containing explicit solvent. At 300 K the effective coarse-grained potentials obtained from different initial guesses are comparable to each other. At 400 K the differences between the force fields obtained from different initial guesses, although small, are noticeable. The use of a different iteration algorithm employing identical initial guesses resulted in the same overall effective potentials for bare cube corner bead sites. In both the coarse-grained and all-atom simulations, small aggregates of POSS molecules were observed with similar local packings of the silsesquioxane cages and tether conformations. The coarse-grained model afforded a savings in computing time of roughly two orders of magnitude. Further comparisons were made between the coarse-grained monotethered POSS model developed here and a minimal model developed in earlier work. The results suggest that the interactions between POSS cages are long ranged and are captured by the coarse-grained model developed here. The minimal model is suitable for capturing the local intermolecular packing of POSS cubes at short separation distances.     

CHARMM-GUI Nanodisc Builder for modeling and simulation of various nanodisc systems

Nanodiscs are discoidal protein–lipid complexes that have wide applications in membrane protein studies. Modeling and simulation of nanodiscs are challenging due to the absence of structures of many membrane scaffold proteins (MSPs) that wrap around the membrane bilayer. We have developed CHARMM-GUI Nanodisc Builder ( http://www.charmm-gui.org/input/nanodisc ) to facilitate the setup of nanodisc simulation systems by modeling the MSPs with defined size and known structural features. A total of 11 different nanodiscs with a diameter from 80 to 180 Å are made available in both the all-atom CHARMM and two coarse-grained (PACE and Martini) force fields. The usage of the Nanodisc Builder is demonstrated with various simulation systems. The structures and dynamics of proteins and lipids in these systems were analyzed, showing similar behaviors to those from previous all-atom and coarse-grained nanodisc simulations. We expect the Nanodisc Builder to be a convenient and reliable tool for modeling and simulation of nanodisc systems. © 2019 Wiley Periodicals, Inc.     

Tandem mass spectrometry of poly(ethylene imine)s by electrospray ionization (ESI) and matrix‐assisted laser desorption/ionization (MALDI)

In this contribution, linear poly(ethylene imine) (PEI) polymers, which are of importance in gene delivery, are investigated in detail by using electrospray ionization‐quadrupole‐time of flight (ESI‐Q‐TOF) and matrix‐assisted laser desorption/ionization‐time of flight (MALDI‐TOF) mass spectrometry (MS). The analyzed PEIs with different end groups were synthesized using the polymerization of substituted 2‐oxazoline via a living cationic ring‐opening polymerization (CROP) and a subsequent hydrolysis under acidic conditions. The main goal of this study was to identify linear PEI polymers in a detailed way to gain information about their fragmentation pathways. For this purpose, a detailed characterization of three different linear PEIs was performed by using ESI‐Q‐TOF and MALDI‐TOF MS in combination with collision‐induced dissociation (CID) experiments. In ESI‐MS as well as MALDI‐MS analysis, the obtained spectra of PEIs resulted in fitting mass distributions for the investigated PEIs. In the tandem MS analysis, a 1,2‐hydride shift with a charge‐remote rearrangement via a four‐membered cyclic transition state, as well as charge‐induced fragmentation reactions, was proposed as the main fragmentation mechanisms according to the obtained fragmentation products from the protonated parent peaks. In addition, heterolytic and homolytic cleavages were proposed as alternative fragmentation pathways. Moreover, a 1,4‐hydrogen elimination was proposed to explain different fragmentation products obtained from the sodiated parent peaks. Copyright © 2012 John Wiley & Sons, Ltd.     

Solvation free energies and partition coefficients with the coarse-grained and hybrid all-atom/coarse-grained MARTINI models

We present the estimation of solvation free energies of small solutes in water, n-octanol and hexane using molecular dynamics simulations with two MARTINI models at different resolutions, viz. the coarse-grained (CG) and the hybrid all-atom/coarse-grained (AA/CG) models. From these estimates, we also calculate the water/hexane and water/octanol partition coefficients. More than 150 small, organic molecules were selected from the Minnesota solvation database and parameterized in a semi-automatic fashion. Using either the CG or hybrid AA/CG models, we find considerable deviations between the estimated and experimental solvation free energies in all solvents with mean absolute deviations larger than 10 kJ/mol, although the correlation coefficient is between 0.55 and 0.75 and significant. There is also no difference between the results when using the non-polarizable and polarizable water model, although we identify some improvements when using the polarizable model with the AA/CG solutes. In contrast to the estimated solvation energies, the estimated partition coefficients are generally excellent with both the CG and hybrid AA/CG models, giving mean absolute deviations between 0.67 and 0.90 log units and correlation coefficients larger than 0.85. We analyze the error distribution further and suggest avenues for improvements.     

A simple, efficient polarizable coarse-grained water model for molecular dynamics simulations

The development of coarse-grained (CG) models that correctly represent the important features of compounds is essential to overcome the limitations in time scale and system size currently encountered in atomistic molecular dynamics simulations. Most approaches reported in the literature model one or several molecules into a single uncharged CG bead. For water, this implicit treatment of the electrostatic interactions, however, fails to mimic important properties, e.g., the dielectric screening. Therefore, a coarse-grained model for water is proposed which treats the electrostatic interactions between clusters of water molecules explicitly. Five water molecules are embedded in a spherical CG bead consisting of two oppositely charged particles which represent a dipole. The bond connecting the two particles in a bead is unconstrained, which makes the model polarizable. Experimental and all-atom simulated data of liquid water at room temperature are used for parametrization of the model. The experimental density and the relative static dielectric permittivity were chosen as primary target properties. The model properties are compared with those obtained from experiment, from clusters of simple-point-charge water molecules of appropriate size in the liquid phase, and for other CG water models if available. The comparison shows that not all atomistic properties can be reproduced by a CG model, so properties of key importance have to be selected when coarse graining is applied. Yet, the CG model reproduces the key characteristics of liquid water while being computationally 1-2 orders of magnitude more efficient than standard fine-grained atomistic water models.     

A Monte Carlo simulation of grafted poly(ethylene oxide) chains

Conformational changes of a simplified model of grafted poly(ethylene oxide) (PEO) chains were simulated using an off-lattice Monte Carlo model. A random-walk scheme was used in our simulations. The initial polymer structure was modeled with molecular mechanics and models of grafted polymer chains were built using programs developed in our laboratory. During the simulation, all bond angles and bond lengths were kept fixed while the dihedral angles of backbones were changed to search for energy-favorite conformations. Torsional energy, van der Waals interaction, and Coulombic interaction were considered. Periodic boundary conditions were implemented. In addition, the solvent quality was simulated implicitly by modifying the Lennard-Jones 12–6 van der Waals expression. Each PEO chain, 50-monomer long, was represented with a united-atom model. Eight series of simulations with varying solvent quality, simulation temperature, and Coulombic interaction were carried out. For each series, nine different initial grafting densities of grafted PEO chains were considered. Five different conformations were simulated at each grafting density. The calculated system energies, scaling properties, and atom density profiles were studied. Changes in solvent quality produced different structural behaviors. As the grafting density increased, there was a mushroom-to-brush transition, and the scaling property of average layer thickness was dependent on the grafting density.     

Control of structure and photophysical properties by protonation and subsequent intramolecular hydrogen bonding

Protonation and subsequent intramolecular hydrogen bonding as methods to control chain structure and tune luminescence in heteroatomic conjugated polymers were reported experimentally [A. P. Monkman et al., J. Am. Chem. Soc. 124, 6049 (2002)]. In this paper, the structure and photophysical properties of the model teraryl compound of phenylene-pyridylene copolymer before and after protonation are theoretically studied with quantum chemistry methods. From the optimized ground states, intramolecular hydrogen bonding to the adjacent oxygen atom in the alkoxy substituent planarizes the backbone of the molecules, and the optimized detailed results of compound 9 before and after protonation, such as the dihedral angles between the central benzene and the two pyridyl rings, the bond lengths, and the bond angles, are consistent with the experimental results. From the results of the calculated excited states, the protonation and subsequent intramolecular hydrogen bonding result in the redshifts of the absorption, the increase of the ionization energy, the increase of the electron affinity, the decrease of the energy difference of the highest occupied molecular orbital and lowest unoccupied molecular orbital, the decrease of the binding gap, and the delocalization of the electron-hole coherence. The photophysical properties of compound 9 before and after protonation are further studied with a three-dimensional real-space analysis method of transition and charge difference densities (study transition dipole moment and charge transfer in the absorption and fluorescence processes) and two-dimensional real-space analysis method of transition density matrices (study the electron-hole coherence and the excitation delocalization). The calculated results show theoretically an insight understanding on the influence of the protonation and subsequent intramolecular hydrogen bonding to chain structure and photophysical properties.     

Monte Carlo vs molecular dynamics for all-atom polypeptide folding simulations

An efficient Monte Carlo (MC) algorithm including concerted rotations is directly compared to molecular dynamics (MD) in all-atom statistical mechanics folding simulations of small polypeptides. The previously reported algorithm "concerted rotations with flexible bond angles" (CRA) has been shown to successfully locate the native state of small polypeptides. In this study, the folding of three small polypeptides (trpzip2/H1/Trp-cage) is investigated using MC and MD, for a combined sampling time of approximately 10(11) MC configurations and 8 micros, respectively. Both methods successfully locate the experimentally determined native states of the three systems, but they do so at different speed, with 2-2.5 times faster folding of the MC runs. The comparison reveals that thermodynamic and dynamic properties can reliably be obtained by both and that results from folding simulations do not depend on the algorithm used. Similar to previous comparisons of MC and MD, it is found that one MD integration step of 2 fs corresponds to one MC scan, revealing the good sampling of MC. The simplicity and efficiency of the MC method will enable its future use in folding studies involving larger systems and the combination with replica exchange algorithms.     

Coarse-grained molecular dynamics simulations of nanopatterning with multivalent inks

A coarse-grained molecular dynamics (MD) model is developed to study the multivalent, or multisite, binding of small functionalized dendrimer molecules to beta-cyclodextrin-terminated self-assembled monolayers, the so-called "molecular printboards" used to print "ink" molecules on surfaces with a high degree of positional control and specificity. Some current and future bionanotechnology applications are in the creation of nanoparticle assemblies, directed protein assembly, platforms for biosensing, and cell:surface attachment. The coarse-grained model allows us to probe up to microsecond timescales and model ink diffusion, crucial for the application of the printboard in, for example, medical diagnostics. Recent all-atom MD simulations identified and quantified the molecular strain limiting the stability of nanopatterns created with small dendrimer inks, and explained the different patterns obtained experimentally with different dendrimer inks. In the present work, the all-atom simulations are "scaled up" to longer timescales via coarse graining, without incurring significant additional computational expense, and, crucially, without significant loss in atom-scale detail, the coarse-grained MD simulations yielding properties similar to those obtained from the all-atom simulations. The anchoring of the ink molecules to the monolayer is of multivalent nature and the degree of multivalency shows a sharp dependence on temperature, control of temperature thus providing a further operational "switch" for directed molecular assembly. The computational protocol developed can, in principle, be extended to model any multivalent assembly, for example, virus-cell complexation.     

Poly(ether imide)s with tailored end groups

Poly(ether imide) (PEI) from polycondensation of 2,2-bis[4-(3,4-dicarboxyphenoxy) phenyl] propane dianhydride (BPADA) and m-phenylenediamine (mPD) is a type of high-temperature engineering thermoplastics that have high glass transition temperature and outstanding mechanical properties. Owing to its wide use in many fields including automotive, aircraft, and electronics, the research of PEI has surged in the last few decades. As science and technology continue to progress rapidly, there is a growing demand for PEIs with better properties. Although a few approaches have successfully improved the properties of PEI, it is recognized that these approaches require complex procedures and are uneconomical. Contrastingly, end-group modification of PEI is highly effective, simple, and economical. Over the last few years, our group has extensively studied the methods for improving the properties of PEI through end-group modification. The end-group moieties and polymer blocks introduce multiple hydrogen bonding, electrostatics, and microphase separation to PEI. In this article, we first classify the end groups based on their characteristics. Then, we compare their effects on the properties of PEIs, including thermal, rheological, mechanical, optical, flame-retardant, and morphological, and discuss the roots of these effects. The in-depth comparisons and discussion generate principles to guide the synthesis of PEIs with tailored properties by modifying the end groups. This timely article will provide insights into the synthesis of other novel high-temperature polymers and entice endeavors to develop novel end groups.