Shadow Hamiltonian in classical NVE molecular dynamics simulations: A path to long time stability

Non-unique Hamiltonians for discrete symplectic dynamics

An outstanding property of any Hamiltonian system is the symplecticity of its flow, namely, the continuous trajectory preserves volume in phase space. Given a symplectic but discrete trajectory generated by a transition matrix applied at a fixed time-increment (τ > 0), it was generally believed that there exists a unique Hamiltonian producing a continuous trajectory that coincides at all discrete times (t = nτ with n integers) as long as τ is small enough. However, it is now exactly demonstrated that, for any given discrete symplectic dynamics of a harmonic oscillator, there exist an infinite number of real-valued Hamiltonians for any small value of τ and an infinite number of complex-valued Hamiltonians for any large value of τ. In addition, when the transition matrix is similar to a Jordan normal form with the supradiagonal element of 1 and the two identical diagonal elements of either 1 or -1, only one solution to the Hamiltonian is found for the case with the diagonal elements of 1, but no solution can be found for the other case.

Charge Transfer Mechanism in Guanine-Based Self-Assembled Monolayers on a Gold Surface

In this work, we have theoretically determined the one-electron oxidation potentials and charge transfer mechanisms in complex systems based on a self-assembled monolayer of guanine molecules adsorbed on a gold surface through different organic linkers. Classical molecular dynamics simulations were carried out to sample the conformational space of both the neutral and the cationic species. Thus, the redox potentials were determined for the ensembles of geometries through multiscale quantum-mechanics/molecular-mechanics/continuum solvation model calculations in the framework of the Marcus theory and in combination with an additive scheme previously developed. In this context, conformational sampling, description of the environment, and effects caused by the linker have been considered. Applying this methodology, we unravel the phenomena of electric current transport by evaluating the different stages in which charge transfer could occur. The results revealed how the positive charge migrates from the organic layer to the gold surface. Specifically, the transport mechanism seems to take place mainly along a single ligand and driven with the help of the electrostatic interactions of the surrounding molecules. Aside, several self-assembled monolayers with different linkers have been analyzed to understand how the nature of that moiety can tune the redox properties and the efficiency of the transport. We have found that the conjugation between the guanine and the linker, at the same time conjugated to the gold surface, gives rise to a more efficient transport. In conclusion, the established computational protocol sheds light on the mechanism behind charge transport in electrochemical DNA-based biosensor nanodevices.

Fast, approximation-free molecular simulation of the SPC/Fw water model using non-reversible Markov chains

In a world made of atoms, computer simulations of molecular systems such as proteins in water play an enormous role in science. Software packages for molecular simulation have been developed for decades. They all discretize Hamilton's equations of motion and treat long-range potentials through cutoffs or discretization of reciprocal space. This introduces severe approximations and artifacts that must be controlled algorithmically. Here, we bring to fruition a paradigm for molecular simulation that relies on modern concepts in statistics to explore the thermodynamic equilibrium with an exact and efficient non-reversible Markov process. It is free of all discretizations, approximations, and cutoffs. We explicitly demonstrate that this approach reaches a break-even point with traditional molecular simulation performed at high precision, but without any of its approximations. We stress the potential of our paradigm for crucial applications in biophysics and other fields, and as a practical approach to molecular simulation. We set out a strategy to reach our goal of rigorous molecular simulation.

Unification of Ewald and shifted force methods to calculate Coulomb interactions in molecular simulations

Three new Ewald series are derived using a new strategy that does not start with a proposed charge spreading function. Of these, the Ewald series produced using shifted potential interactions for the Ewald real space series converges relatively slowly, while the corresponding expression using a shifted force (SF) interaction does not converge. A comparison is made between several approximations of the Ewald method and the SF route to include Coulomb interactions in molecular dynamics (MD) computer simulations. MD simulations of a model bulk molten salt and water were carried out. The recently derived α' variant of Ewald, by K. D. Hammonds and D. M. Heyes [J. Chem. Phys. 157, 074108 (2022)], has been developed analytically and found to be more accurate and computationally efficient than SF in part due to the smaller real space truncation distance that can be used. In addition, with α', the number of reciprocal lattice vectors required is reduced considerably compared with the standard Ewald implementations to give the same accuracy. The invention of the α' method shifts the computational balance back toward using an Ewald construction. The SF method shows greater errors in the Coulomb pressure and time dependent fluctuation properties compared to α'. It does not conserve the shadow Hamiltonian in a microcanonical MD simulation, whereas the α' method does, which facilitates long time stability and insignificant drift of properties over time. The speed of the Ewald computer code is improved by using a new lookup table method.

Modeling One-Electron Oxidation Potentials and Hole Delocalization in Double-Stranded DNA by Multilayer and Dynamic Approaches

The number of innovative applications for DNA nowadays is growing quickly. Its use as a nanowire or electrochemical biosensor leads to the need for a deep understanding of the charge-transfer process along the strand, as well as its redox properties. These features are computationally simulated and analyzed in detail throughout this work by combining molecular dynamics, multilayer schemes, and the Marcus theory. One-electron oxidation potential and hole delocalization have been analyzed for six DNA double strands that cover all possible binary combinations of nucleotides. The results have revealed that the one-electron oxidation potential decreases with respect to the single-stranded DNA, giving evidence that the greater rigidity of a double helix induces an increase in the capacity of storing the positive charge generated upon oxidation. In addition, the hole is mainly stored in nucleobases with large reducer character, i.e., purines, especially when those are arranged in a stacked configuration in the same strand. From the computational point of view, the sampling needed to describe biological systems implies a significant computational cost. Here, we show that a small number of representative conformations generated by clustering analysis provides accurate results when compared with those obtained from sampling, reducing considerably the computational cost.

Energy stable scheme for random batch molecular dynamics

The computational bottleneck of molecular dynamics is pairwise additive long-range interactions between particles. The random batch Ewald (RBE) method provides a highly efficient and superscalable solver for long-range interactions, but the stochastic nature of this algorithm leads to unphysical self-heating effect during the simulation. We propose an energy stable scheme (ESS) for particle systems by employing a Berendsen-type energy bath. The scheme removes the notorious energy drift, which exists due to the force error even when a symplectic integrator is employed. Combining the RBE with the ESS, the new method provides a perfect solution to the computational bottleneck of molecular dynamics at the microcanonical ensemble. Numerical results for a primitive electrolyte and all-atom pure water systems demonstrate the attractive performance of the algorithm, including its dramatically high accuracy, linear complexity, and overcoming the energy drift for long-time simulations.

Exploring the role of microbial proteins in controlling environmental pollutants based on molecular simulation

Molecular simulation has been widely used to study microbial proteins' structural composition and dynamic properties, such as volatility, flexibility, and stability at the microscopic scale. Herein, this review describes the key elements of molecular docking and molecular dynamics (MD) simulations in molecular simulation; reviews the techniques combined with molecular simulation, such as crystallography, spectroscopy, molecular biology, and machine learning, to validate simulation results and bridge information gaps in the structure, microenvironmental changes, expression mechanisms, and intensity quantification; illustrates the application of molecular simulation, in characterizing the molecular mechanisms of interaction of microbial proteins with four different types of contaminants, namely heavy metals (HMs), pesticides, dyes and emerging contaminants (ECs). Finally, the review outlines the important role of molecular simulations in the study of microbial proteins for controlling environmental contamination and provides ideas for the application of molecular simulation in screening microbial proteins and incorporating targeted mutagenesis to obtain more effective contaminant control proteins.

One-Electron Oxidation Potentials and Hole Delocalization in Heterogeneous Single-Stranded DNA

The study of DNA processes is essential to understand not only its intrinsic biological functions but also its role in many innovative applications. The use of DNA as a nanowire or electrochemical biosensor leads to the need for a deep investigation of the charge transfer process along the strand as well as of the redox properties. In this contribution, the one-electron oxidation potential and the charge delocalization of the hole formed after oxidation are computationally investigated for different heterogeneous single-stranded DNA strands. We have established a two-step protocol: (i) molecular dynamics simulations in the frame of quantum mechanics/molecular mechanics (QM/MM) were performed to sample the conformational space; (ii) energetic properties were then obtained within a QM1/QM2/continuum approach in combination with the Marcus theory over an ensemble of selected geometries. The results reveal that the one-electron oxidation potential in the heterogeneous strands can be seen as a linear combination of that property within the homogeneous strands. In addition, the hole delocalization between different nucleobases is, in general, small, supporting the conclusion of a hopping mechanism for charge transport along the strands. However, charge delocalization becomes more important, and so does the tunneling mechanism contribution, when the reducing power of the nucleobases forming the strand is similar. Moreover, charge delocalization is slightly enhanced when there is a correlation between pairs of some of the interbase coordinates of the strand: twist/shift, twist/slide, shift/slide, and rise/tilt. However, the internal structure of the strand is not the predominant factor for hole delocalization but the specific sequence of nucleotides that compose the strand.

Intramolecular and intermolecular hole delocalization rules the reducer character of isolated nucleobases and homogeneous single-stranded DNA

The use of DNA strands as nanowires or electrochemical biosensors requires a deep understanding of charge transfer processes along the strand, as well as of the redox properties. These properties are computationally assessed in detail throughout this study. By applying molecular dynamics and hybrid QM/continuum and QM/QM/continuum schemes, the vertical ionization energies, adiabatic ionization energies, vertical attachment energies, one-electron oxidation potentials, and delocalization of the hole generated upon oxidation have been determined for nucleobases in their free form and as part of a pure single-stranded DNA. We show that the reducer ability of the isolated nucleobases is explained by the intramolecular delocalization of the positively charged hole, while the enhancement of the reducer character when going from aqueous solution to the strand correlates very well with the intermolecular hole delocalization. Our simulations suggest that the redox properties of DNA strands can be tuned by playing with the balance between intramolecular and intermolecular charge delocalization.

Shadow energy functionals and potentials in Born-Oppenheimer molecular dynamics

In Born-Oppenheimer molecular dynamics (BOMD) simulations based on the density functional theory (DFT), the potential energy and the interatomic forces are calculated from an electronic ground state density that is determined by an iterative self-consistent field optimization procedure, which, in practice, never is fully converged. The calculated energies and forces are, therefore, only approximate, which may lead to an unphysical energy drift and instabilities. Here, we discuss an alternative shadow BOMD approach that is based on backward error analysis. Instead of calculating approximate solutions for an underlying exact regular Born-Oppenheimer potential, we do the opposite. Instead, we calculate the exact electron density, energies, and forces, but for an underlying approximate shadow Born-Oppenheimer potential energy surface. In this way, the calculated forces are conservative with respect to the approximate shadow potential and generate accurate molecular trajectories with long-term energy stabilities. We show how such shadow Born-Oppenheimer potentials can be constructed at different levels of accuracy as a function of the integration time step, δt, from the constrained minimization of a sequence of systematically improvable, but approximate, shadow energy density functionals. For each energy functional, there is a corresponding ground state Born-Oppenheimer potential. These pairs of shadow energy functionals and potentials are higher-level generalizations of the original "zeroth-level" shadow energy functionals and potentials used in extended Lagrangian BOMD [Niklasson, Eur. Phys. J. B 94, 164 (2021)]. The proposed shadow energy functionals and potentials are useful only within this extended dynamical framework, where also the electronic degrees of freedom are propagated as dynamical field variables together with the atomic positions and velocities. The theory is quite general and can be applied to MD simulations using approximate DFT, Hartree-Fock, or semi-empirical methods, as well as to coarse-grained flexible charge models.

An Efficient Multilayer Approach to Model DNA-Based Nanobiosensors

In this work, we present a full computational protocol to successfully obtain the one-electron reduction potential of nanobiosensors based on a self-assembled monolayer of DNA nucleobases linked to a gold substrate. The model is able to account for conformational sampling and environmental effects at a quantum mechanical (QM) level efficiently, by combining molecular mechanics (MM) molecular dynamics and multilayer QM/MM/continuum calculations within the framework of Marcus theory. The theoretical model shows that a guanine-based biosensor is more prone to be oxidized than the isolated nucleobase in water due to the electrostatic interactions between the assembled guanine molecules. In addition, the redox properties of the biosensor can be tuned by modifying the nature of the linker that anchor the nucleobases to the metal support.

Graph-based quantum response theory and shadow Born-Oppenheimer molecular dynamics

Graph-based linear scaling electronic structure theory for quantum-mechanical molecular dynamics simulations [A. M. N. Niklasson et al., J. Chem. Phys. 144, 234101 (2016)] is adapted to the most recent shadow potential formulations of extended Lagrangian Born-Oppenheimer molecular dynamics, including fractional molecular-orbital occupation numbers [A. M. N. Niklasson, J. Chem. Phys. 152, 104103 (2020) and A. M. N. Niklasson, Eur. Phys. J. B 94, 164 (2021)], which enables stable simulations of sensitive complex chemical systems with unsteady charge solutions. The proposed formulation includes a preconditioned Krylov subspace approximation for the integration of the extended electronic degrees of freedom, which requires quantum response calculations for electronic states with fractional occupation numbers. For the response calculations, we introduce a graph-based canonical quantum perturbation theory that can be performed with the same natural parallelism and linear scaling complexity as the graph-based electronic structure calculations for the unperturbed ground state. The proposed techniques are particularly well-suited for semi-empirical electronic structure theory, and the methods are demonstrated using self-consistent charge density-functional tight-binding theory both for the acceleration of self-consistent field calculations and for quantum-mechanical molecular dynamics simulations. Graph-based techniques combined with the semi-empirical theory enable stable simulations of large, complex chemical systems, including tens-of-thousands of atoms.

Molecular Dynamics Methods for Antibody Design

Complex and coordinated dynamics are closely connected with protein functions, including the binding of antibodies to antigens. Knowledge of such dynamics could improve the design of antibodies. Molecular dynamics (MD) simulations provide a "computational microscope" that can resolve atomic motions and inform antibody design efforts.

Molecular Dynamics Study of Structural and Transport Properties of Silver Iodide Using Effective Charges

The superionic conductor, solid state, and body-centered cubic structure, silver iodide at room temperature, has been studied via molecular dynamics simulations. The calculated results using pairwise Coulomb-Buckingham potential, zero pressure on the sample, a semi-rigid model system of 1000 Ag and 1000 I ions, (NVE) as a statistical ensemble, and an effective charge of Z=0.63 for the pairs Ag-Ag and I-I, were found to be consistent with experimental data and one study using Z=0.60, different potential, and simulation software. For the pair Ag-I, there is a discrepancy due to the high silver ion diffusion. The calculated value of the diffusion constant of the silver ion is greater than iodide ion. The dynamic transport properties (mean square displacement, velocity autocorrelation function) results indicated typical behavior reported by other authors, using different potentials in their DM simulations for iodine and silver ions.

Optimization of the Ewald method for calculating Coulomb interactions in molecular simulations

Practical implementations of the Ewald method used to compute Coulomb interactions in molecular dynamics simulations are hampered by the requirement to truncate its reciprocal space series. It is shown that this can be mitigated by representing the contributions from the neglected reciprocal lattice vector terms as a simple modification of the real space expression in which the real and reciprocal space series have slightly different charge spreading parameters. This procedure, called the α′ method, enables significantly fewer reciprocal lattice vectors to be taken than is currently typical for Ewald, with negligible additional computational cost, which is validated on model systems representing different classes of charged system, a CsI crystal and melt, water, and a room temperature ionic liquid. A procedure for computing accurate energies and forces based on a periodic sampling of an additional number of reciprocal lattice vectors is also proposed and validated by the simulations. The convergence characteristics of expressions for the pressure based on the forces and the potential energy are compared, which is a useful assessment of the accuracy of the simulations in reproducing the Coulomb interaction. The techniques developed in this work can reduce significantly the total computer simulation times for medium sized charged systems, by factors of up to ∼5 for those in the classes studied here.

Computation of Oxidation Potentials of Solvated Nucleobases by Static and Dynamic Multilayer Approaches

The determination of the redox properties of nucleobases is of paramount importance to get insight into the charge-transfer processes in which they are involved, such as those occurring in DNA-inspired biosensors. Although many theoretical and experimental studies have been conducted, the value of the one-electron oxidation potentials of nucleobases is not well-defined. Moreover, the most appropriate theoretical protocol to model the redox properties has not been established yet. In this work, we have implemented and evaluated different static and dynamic approaches to compute the one-electron oxidation potentials of solvated nucleobases. In the static framework, two thermodynamic cycles have been tested to assess their accuracy against the direct determination of oxidation potentials from the adiabatic ionization energies. Then, the introduction of vibrational sampling, the effect of implicit and explicit solvation models, and the application of the Marcus theory have been analyzed through dynamic methods. The results revealed that the static direct determination provides more accurate results than thermodynamic cycles. Moreover, the effect of sampling has not shown to be relevant, and the results are improved within the dynamic framework when the Marcus theory is applied, especially in explicit solvent, with respect to the direct approach. Finally, the presence of different tautomers in water does not affect significantly the one-electron oxidation potentials.

Molecular simulations of proteins: From simplified physical interactions to complex biological phenomena

Molecular dynamics simulation is the most popular computational technique for investigating the structural and dynamical behaviour of proteins, in search of the molecular basis of their function. Far from being a completely settled field of research, simulations are still evolving to best capture the essential features of the atomic interactions that govern a protein's inner motions. Modern force fields are becoming increasingly accurate in providing a physical description adequate to this purpose, and allow us to model complex biological systems under fairly realistic conditions. Furthermore, the use of accelerated sampling techniques is improving our access to the observation of progressively larger molecular structures, longer time scales, and more hidden functional events. In this review, the basic principles of molecular dynamics simulations and a number of key applications in the area of protein science are summarized, and some of the most important results are discussed. Examples include the study of the structure, dynamics and binding properties of 'difficult' targets, such as intrinsically disordered proteins and membrane receptors, and the investigation of challenging phenomena like hydration-driven processes and protein aggregation. The findings described provide an overall picture of the current state of this research field, and indicate new perspectives on the road ahead to the upcoming future of molecular simulations.

Post-translational modification patterns on β-myosin heavy chain are altered in ischemic and nonischemic human hearts

Phosphorylation and acetylation of sarcomeric proteins are important for fine-tuning myocardial contractility. Here, we used bottom-up proteomics and label-free quantification to identify novel post-translational modifications (PTMs) on β-myosin heavy chain (β-MHC) in normal and failing human heart tissues. We report six acetylated lysines and two phosphorylated residues: K34-Ac, K58-Ac, S210-P, K213-Ac, T215-P, K429-Ac, K951-Ac, and K1195-Ac. K951-Ac was significantly reduced in both ischemic and nonischemic failing hearts compared to nondiseased hearts. Molecular dynamics (MD) simulations show that K951-Ac may impact stability of thick filament tail interactions and ultimately myosin head positioning. K58-Ac altered the solvent-exposed SH3 domain surface - known for protein-protein interactions - but did not appreciably change motor domain conformation or dynamics under conditions studied. Together, K213-Ac/T215-P altered loop 1's structure and dynamics - known to regulate ADP-release, ATPase activity, and sliding velocity. Our study suggests that β-MHC acetylation levels may be influenced more by the PTM location than the type of heart disease since less protected acetylation sites are reduced in both heart failure groups. Additionally, these PTMs have potential to modulate interactions between β-MHC and other regulatory sarcomeric proteins, ADP-release rate of myosin, flexibility of the S2 region, and cardiac myofilament contractility in normal and failing hearts.

Chemical computational approaches for optimization of effective surfactants in enhanced oil recovery

The surfactant flooding becomes an attractive method among several Enhanced Oil Recovery (EOR) processes to improve the recovery of residual oil left behind in the reservoir after secondary oil recovery process. The designing of a new effective surfactant is a comparatively complex and often time consuming process as well as cost-effective due to its dependency on the crude oil and reservoir properties. An alternative chemical computational approach is focused in this article to optimize the performance of effective surfactant system for EOR. The molecular dynamics (MD), dissipative particle dynamics (DPD) and density functional theory (DFT) simulations are mostly used chemical computational approaches to study the behaviour in multiple phase systems like surfactant/oil/brine. This article highlighted a review on the impact of surfactant head group structure on oil/water interfacial property like interfacial tensions, interface formation energy, interfacial thickness by MD simulation. The effect of entropy in micelle formation has also discussed through MD simulation. The polarity, dipole moment, charge distribution and molecular structure optimization have been illustrated by DFT. A relatively new coarse-grained method, DPD is also emphasized the phase behaviour of surfactant/oil/brine as well as polymer-surfactant complex system.

Analysis of an all-solid state nanobattery using molecular dynamics simulations under an external electric field

Present Li-ion battery (LIB) technology requires strong improvements in performance, energy capacity, charging-time, and cost to expand their application to e-mobility and grid storage. Li-metal is one of the most promising materials to replace commercial anodes such as graphite because of its 10 times higher specific capacity. However, Li-metal has high reactivity with commercial liquid electrolytes; thus, new solid materials are proposed to replace liquid electrolytes when Li-metal anodes are used. We present a theoretical analysis of the charging process in a full nanobattery, containing a LiCoO2 cathode, a Li7P2S8I solid-state electrolyte (SSE), a Li-metal anode as well as Al and Cu collectors for the cathode and anode, respectively. In addition, we added a Li3P/Li2S film as a solid electrolyte interphase (SEI) layer between the Li-anode and SSE. Thus, we focus this study on the SEI and SSE. We simulated the charging of the nanobattery with an external voltage by applying an electric field. We estimated temperature profiles within the nanobattery and analyzed Li-ion transport through the SSE and SEI. We observed a slight temperature rise at the SEI due to reactions forming PS3- and P2S74- fragments at the interfaces; however, this temperature profile changes due to the charging current under the presence of the external electric field ε = 0.75 V Å-1. Without the external field, the calculated open-circuit voltage (OCV) was 3.86 V for the battery, which is within the range of values of commercial cobalt-based LIBs. This voltage implies a spontaneous fall of available Li-ions from the anode to the cathode (during discharge). The charge of this nanobattery requires overcoming the OCV plus an additional voltage that determines the charging current. Thus, we applied an external potential able to neutralize the OCV, plus an additional 1.6 V to induce the transport of Li+ from the cathode up to the anode. Several interesting details about Li+ transport paths through the SSE and SEI are discussed.