Prediction of viscoelastic properties with coarse‐grained molecular dynamics and experimental validation for a benchmark polyurea system

To explore the relationship between microscopic structure and viscoelastic properties of polyurea, a coarse‐grained (CG) model is developed by a structure matching method and validated against experiments conducted on a controlled, benchmark material. Using the Green‐Kubo method, the relaxation function is computed from the autocorrelation of the stress tensor, sampled over equilibrium MD simulations, and mapped to a real time scale established by matching self‐diffusion rates of atomistic and CG models. Master curves computed from the predicted stress relaxation function are then compared with dynamic mechanical analysis experiments mapped to a wide frequency range by time–temperature superposition, as well as measurements of ultrasonic shear wave propagation. Computational simulations from monodisperse and polydisperse configurations, representative of the benchmark polyurea, show excellent agreement with the experimental measurements over a multidecade range of loading frequency. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 797–810     

Brownian dynamics simulation of protein association

Summary The Brownian Dynamics (BD) method is applied to study the diffusive dynamics and interaction of two proteins, cytochrome c (CYTC) and cytochrome c peroxidase (CYP). We examine the role of protein electrostatic charge distribution in the facilitation of protein-protein docking prior to the electron transfer step, assessing the influence of individual charged amino acid residues. Accurate interaction potentials are computed by iterating the linearized Poisson-Boltzmann (PB) equation around the larger protein CYP. The low dielectric constant inside proteins, electrolyte screening effects and irregular protein surface topography are taken into account. We observe a large ensemble of electrostatically stable encounter complexes seemingly with acceptable geometric requirements for electron transfer rather than a single dominant complex. Stabilities of the large variety of docking complexes are rationalized in terms of generalized charged residue complementarities. However, it is found that the electrostatic interactions giving rise to complex stabilities are somewhat nonspecific in nature. A large series of additional simulations are performed in which individual charged residues on CYTC have been chemically modified. Resulting perturbations of the association rate are significant and qualitatively similar to results observed in comparable kinetics experiments. We therefore demonstrate the potential of the Brownian dynamics method to estimate the effects of site-directed mutagenesis on protein-protein and protein-ligand diffusional association rates.     

Melting thermodynamics of oligonucleic acids conjugated with relatively solvophobic linear polymers: A coarse‐grained molecular simulation study

Oligonucleic acids (ONAs), such as DNA and RNA, are used in various biotechnology and nanotechnology applications due to their ability to form a double helix that is stable at low temperature and melts at high temperatures. The melting temperature (T_m) of ONA duplexes can be tuned by the ONA composition, sequence, length and concentration, solvent quality, and salt concentration and by conjugation to other macromolecules. In this article, we use coarse‐grained (CG) molecular simulations to study ONAs conjugated with linear homopolymers that are relatively more solvophobic than the ONA. We study charged and stiff 8‐mer ONAs (e.g., DNA) and neutral and flexible 8‐mer ONAs (e.g., peptide nucleic acids or PNA), and vary the composition (or G‐C content) and sequence of ONA, conjugated homopolymer lengths and solvent quality for the polymer. For neutral and flexible ONAs, as the solvent quality worsens for the polymer, the ONA melting temperature increases from that of unconjugated ONA. The melting curves broaden with polymer length and worsening solvent quality, especially for ONAs with higher G‐C content. For charged and stiff ONAs, as the solvent quality worsens, the ONA melting temperature decreases compared to unconjugated ONA while the width of the melting curve remains the same. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1196–1208     

Singularity‐Free Brownian Dynamics Analyses of Rotational Dynamics: Non‐Spherical Nanoparticles in Solution

Summary: From kinetic theory we have rigorously derived singularity‐free Brownian dynamics analyses of nanoparticle rotational dynamics. The rigid non‐spherical nanoparticles incorporate all three rotational degrees of freedom. This was achieved by using the components of Cartesian rotation vectors as the generalized coordinates describing angular orientation. The new results constitute an important advance compared to the situation when Eulerian angles specify angular orientation. Our finding eliminates one of the main longstanding obstacles to detailed studies of nanoparticle rotational dynamics in the diffusion time domain. The described formalism is applicable to a wide range of nanoparticle systems including liquid crystals, biopolymers, and colloids.

     

Use of the Rotation Vector in Brownian Dynamics Simulation of Transient Electro‐Optical Properties

We have recently developed a new singularity‐free algorithm for Brownian dynamics simulation of free rotational diffusion. The algorithm is rigorously derived from kinetic theory and makes use of the Cartesian components of the rotation vector as the generalized coordinates describing angular orientation. Here, we report on the application of this new algorithm in Brownian dynamics simulations of transient electro‐optical properties. This work serves two main purposes. Firstly, it demonstrates the integrity of the new algorithm for BD‐simulations of the most common transient electro‐optic experiments. Secondly, it provides new insight into the performance of the new algorithm compared to algorithms that make use of the Euler angles. We study the transient electrically induced birefringence in dilute solutions of rigid particles with anisotropic polarization tensor in response to external electric field pulses. The use of both one single electric pulse and two electric pulses with opposite polarity are being analyzed. We document that the new singularity‐free algorithm performs flawlessly. We find that, for these types of systems, the new singularity‐free algorithm, in general, outperforms similar algorithms based on the Euler angles. In a wider perspective, the most important aspect of this work is that it serves as an important reference for future development of efficient BD‐algorithms for studies of more complex systems. These systems include polymers consisting of rigid segments with single‐segment translational–rotational coupling, segment–segment fluid‐dynamic interactions and holonomic constraints.

     

Coarse‐grained A‐graft‐B model of poly(lactic acid) for molecular dynamics simulations

A mesoscopic model of poly(lactic acid) is developed where the polymer is represented as an A‐graft‐B chain with monomer units consisting of two covalently connected beads. A coarse‐graining algorithm is proposed to convert an atomistic model of PLA into a coarse‐grained one. The developed model is based on atomistic simulations of oligolactides to take into account terminal groups correctly. It was used for coarse‐grained simulations of polylactide. Gyration radii and end to end distances of polymer chains as well as the density of the polymer melt are shown to be in a good agreement with those obtained from atomistic simulations. The thermal expansion coefficients of the OLA melts calculated using the coarse‐grained model are in reasonable agreement with those obtained from all‐atom molecular dynamics. The model provides a 17‐fold speedup compared with atomistic calculations. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 604–612     

Effect of internal viscosity on Brownian dynamics of DNA molecules in shear flow

The results of Brownian dynamics simulations of a single DNA molecule in shear flow are presented taking into account the effect of internal viscosity. The dissipative mechanism of internal viscosity is proved necessary in the research of DNA dynamics. A stochastic model is derived on the basis of the balance equation for forces acting on the chain. The Euler method is applied to the solution of the model. The extensions of DNA molecules for different Weissenberg numbers are analyzed. Comparison with the experimental results available in the literature is carried out to estimate the contribution of the effect of internal viscosity.     

Reconstruction of atomistic details from coarse‐grained structures

We present an algorithm to reconstruct atomistic structures from their corresponding coarse‐grained (CG) representations and its implementation into the freely available molecular dynamics (MD) program package GROMACS. The central part of the algorithm is a simulated annealing MD simulation in which the CG and atomistic structures are coupled via restraints. A number of examples demonstrate the application of the reconstruction procedure to obtain low‐energy atomistic structural ensembles from their CG counterparts. We reconstructed individual molecules in vacuo (NCQ tripeptide, dipalmitoylphosphatidylcholine, and cholesterol), bulk water, and a WALP transmembrane peptide embedded in a solvated lipid bilayer. The first examples serve to optimize the parameters for the reconstruction procedure, whereas the latter examples illustrate the applicability to condensed‐phase biomolecular systems. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

A coarse‐grained MARTINI‐like force field for DNA unzipping in nanopores

In nanopore force spectroscopy (NFS) a charged polymer is threaded through a channel of molecular dimensions. When an electric field is applied across the insulating membrane, the ionic current through the nanopore reports on polymer translocation, unzipping, dissociation, and so forth. We present a new model that can be applied in molecular dynamics simulations of NFS. Although simplified, it does reproduce experimental trends and all‐atom simulations. The scaled conductivities in bulk solution are consistent with experimental results for NaCl for a wide range of electrolyte concentrations and temperatures. The dependence of the ionic current through a nanopore on the applied voltage is symmetric and, in the voltage range used in experiments (up to 2 V), linear and in good agreement with experimental data. The thermal stability and geometry of DNA is well represented. The model was applied to simulations of DNA hairpin unzipping in nanopores. The results are in good agreement with all‐atom simulations: the scaled translocation times and unzipping sequence are similar. © 2015 Wiley Periodicals, Inc.     

Modeling dimerizations of transmembrane proteins using Brownian dynamics simulations

The dimerizations of membrane proteins, Outer Membrane Phospholipase A (OMPLA) and glycophorin A (GPA), have been simulated by an adapted Brownian Dynamics program. To mimic the membrane protein environment, we introduced a hybrid electrostatic potential map of membrane and water for electrostatic interaction calculations. We added a van der Waals potential term to the force field of the current version of the BD program to simulate the short-range interactions of the two monomers. We reduced the BD sampling space from three dimensions to two dimensions to improve the efficiency of BD simulations for membrane proteins. The OMPLA and GPA dimers predicted by our 2D-BD simulation and structural refinement is in good agreement with the experimental structures. The adapted 2D-BD method could be used for prediction of dimerization of other membrane proteins, such as G protein-coupled receptors, to help better understanding of the structures and functions of membrane proteins.     

Statistics of polymer capture by a nanopore: A Brownian dynamics simulation study

We investigate the statistics of polymer capture by a nanopore using Brownian dynamics simulations. It is found that when the velocity flux is greater than a critical velocity flux, the capture picture is a random selection process, otherwise it tends to a statistical process governed by energetic considerations. In addition, the chain ends capture probability decreases as the chain length increases and satisfies a power-law scaling of P0(N)~N-0.8.     

Brownian dynamics simulation of polyelectrolyte dilute solutions: Relaxation time and elongational flow

The authors used the bead‐and‐spring model and the Brownian dynamics simulation technique including hydrodynamic interaction to study the behavior of dilute polyelectrolyte solutions under elongational flow. First they carried out simulations to determine the longest relaxation time of a polyelectrolyte, finding that the relaxation time depends on the ionic strength of the solution. Then, they studied the coil‐stretch transition of polyelectrolyte molecules in elongational flow and determined the critical value of the elongational rate necessary in order this transition to occur. In this way, they could compute the value of the Deborah number at which coil‐stretch transition sets in for polyelectrolyte dilute solutions. Finally, they studied the power law relationship that relates the critical elongational rate with the molecular weight of the polyelectrolyte. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 714–722, 2007     

RedMD—Reduced molecular dynamics package

We developed a software package (RedMD) to perform molecular dynamics simulations and normal mode analysis of reduced models of proteins, nucleic acids, and their complexes. With RedMD one can perform molecular dynamics simulations in a microcanonical ensemble, with Berendsen and Langevin thermostats, and with Brownian dynamics. We provide force field and topology generators which are based on the one‐bead per residue/nucleotide elastic network model and its extensions. The user can change the force field parameters with the command line options that are passed to generators. Also, the generators can be modified, for example, to add new potential energy functions. Normal mode analysis tool is available for elastic or anisotropic network models. The program is written in C and C++ languages and the structure/topology of a molecule is based on an XML format. OpenMP technology for shared‐memory architectures was used for code parallelization. The code is distributed under GNU public licence and available at http://bionano.icm.edu.pl/software/ . © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

Understanding Creep Behavior of Semicrystalline Polymer via Coarse‐Grained Modeling

Understanding the deformational and failure behaviors of thermoplastic semicrystalline polymers is crucial due to the practical usages in various engineering applications. Taking isotactic polypropylene (iPP) as a semicrystalline polymer model system, atomistically informed coarse‐grained (CG) molecular dynamics (MD) simulations are employed to investigate the creep behavior of iPP. The simulations reveal that there exists a threshold stress of about 20.0 MPa, above which the maximum strain of iPP within the simulation time span increases dramatically. From the strain‐time analysis, it is observed that the iPP exhibits an initial elastic deformation stage and a subsequent plastic stage at lower stress levels, while a three‐stage creep behavior including a third fracture stage is observed at higher stress levels. Specifically, at lower stress levels, the bonded energy increases continuously as the chains stretch steadily, while the nonbonded energy shows an initial increase followed by a steady decrease due to the interchain sliding. At higher stress levels, both bonded and nonbonded energies change dramatically at the third stage, resulting from accelerated chain stretching, unfolding, sliding, and breaking. This study provides physical insight into the creep behavior of iPP at a fundamental molecular level and highlights the important role of microstructural evolution of chains in the deformation of semicrystalline polymer materials. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1779–1791     

Coarse‐grained molecular dynamics simulations of protein–ligand binding

Coarse‐grained molecular dynamics (CGMD) simulations with the MARTINI force field were performed to reproduce the protein–ligand binding processes. We chose two protein–ligand systems, the levansucrase–sugar (glucose or sucrose), and LinB–1,2‐dichloroethane systems, as target systems that differ in terms of the size and shape of the ligand‐binding pocket and the physicochemical properties of the pocket and the ligand. Spatial distributions of the Coarse‐grained (CG) ligand molecules revealed potential ligand‐binding sites on the protein surfaces other than the real ligand‐binding sites. The ligands bound most strongly to the real ligand‐binding sites. The binding and unbinding rate constants obtained from the CGMD simulation of the levansucrase–sucrose system were approximately 10 times greater than the experimental values; this is mainly due to faster diffusion of the CG ligand in the CG water model. We could obtain dissociation constants close to the experimental values for both systems. Analysis of the ligand fluxes demonstrated that the CG ligand molecules entered the ligand‐binding pockets through specific pathways. The ligands tended to move through grooves on the protein surface. Thus, the CGMD simulations produced reasonable results for the two different systems overall and are useful for studying the protein–ligand binding processes. © 2014 Wiley Periodicals, Inc.     

Fracture of flexible polymer chains in dilute solution under transient extensional flow

 Applying the technique of Brownian dynamics simulation, we have studied the fracture process of flexible polymer chains when they encounter an extensional flow field of transient character. For this purpose, a mathematical model was made of an experimental device used earlier by other authors to study fracture of polystyrene in dilute solution. The polymer/solvent system studied was a very dilute solution in theta conditions. The polymer molecule was modeled as a FENE bead-spring chain, including a modification to allow for chain fracture. The simulation results showed that the fracture yield depended strongly on flow rate and on molecular weight. We have characterized the molecular-weight dependence of the critical flow rate which is necessary for fracture to occur. The distribution of the result-ing fragments is interpreted in terms of the conformation of the chains prior to fracture. Received: 17 September 1996 Accepted: 29 May 1997     

Polarizable coarse‐grained models for molecular dynamics simulation of liquid cyclohexane

Force field parameters for polarizable coarse‐grained (CG) supra‐atomic models of liquid cyclohexane are proposed. Two different bead sizes were investigated, one representing two fine‐grained (FG) CH₂r united atoms of the cyclohexane ring, and one representing three FG CH₂r united atoms. Electronic polarizability is represented by a massless charge‐on‐spring particle connected to each CG bead. The model parameters were calibrated against the experimental density and heat of vaporization of liquid cyclohexane, and the free energy of cyclohexane hydration. Both models show good agreement with thermodynamic properties of cyclohexane, yet overestimate the self‐diffusion. The dielectric properties of the polarizable models agree very well with experiment. © 2015 Wiley Periodicals, Inc.