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In this perspective, we review the theory and methodology of the derivation of force fields (FFs), and their validity, for molecular simulations, from their inception in the second half of the twentieth century to the improved representations at the end of the century. We examine the representations of the physics embodied in various force fields, their accuracy and deficiencies. The early days in the 1950s and 60s saw FFs first introduced to analyze vibrational spectra. The advent of computers was soon followed by the first molecular mechanics machine calculations. From the very first papers it was recognized that the accuracy with which the FFs represented the physics was critical if meaningful calculated structural and thermodynamic properties were to be achieved. We discuss the rigorous methodology formulated by Lifson, and later Allinger to derive molecular FFs, not only obtain optimal parameters but also uncover deficiencies in the representation of the physics and improve the functional form to account for this physics. In this context, the known coupling between valence coordinates and the importance of coupling terms to describe the physics of this coupling is evaluated. Early simplified, truncated FFs introduced to allow simulations of macromolecular systems are reviewed and their subsequent improvement assessed. We examine in some depth: the basis of the reformulation of the H-bond to its current description; the early introduction of QM in FF development methodology to calculate partial charges and rotational barriers; the powerful and abundant information provided by crystal structure and energetic observables to derive and test all aspects of a FF including both nonbond and intramolecular functional forms; the combined use of QM, along with crystallography and lattice energy calculations to derive rotational barriers about ɸ and ψ; the development and results of methodologies to derive “QM FFs” by sampling the QM energy surface, either by calculating energies at hundreds of configurations, or by describing the energy surface by energies, first and second derivatives sampled over the surface; and the use of the latter to probe the validity of the representations of the physics, reveal flaws and assess improved functional forms. Research demonstrating significant effects of the flaws in the use of the improper torsion angle to represent out of plane deformations, and the standard Lorentz–Berthelot combining rules for nonbonded interactions, and the more accurate descriptions presented are also reviewed. Finally, we discuss the thorough studies involved in deriving the 2nd generation all-atom versions of the CHARMm, AMBER and OPLS FFs, and how the extensive set of observables used in these studies allowed, in the spirit of Lifson, a characterization of both the abilities, but more importantly the deficiencies in the diagonal 12-6-1 FFs used. The significant contribution made by the extensive set of observables compiled in these papers as a basis to test improved forms is noted. In the following paper, we discuss the progress in improving the FFs and representations of the physics that have been investigated in the years following the research described above.

In the previous paper, we reviewed the origins of energy based calculations, and the early science of FF development. The initial efforts spanning the period from roughly the early 1970s to the mid to late 1990s saw the development of methodologies and philosophies of the derivation of FFs. The use of Cartesian coordinates, derivation of the H-bond potential, different functional forms including diagonal quadratic expressions, coupled valence FFs, functional form of combination rules, and out of plane angles, were all investigated in this period. The use of conformational energetics, vibrational frequencies, crystal structure and energetics, liquid properties, and ab initio data were all described to one degree or another in deriving and validating both the FF functional forms and force constants. Here we discuss the advances made since in improving the rigor and robustness of these initial FFs. The inability of the simple quadratic diagonal FF to accurately describe biomolecular energetics over a large domain of molecular structure, and intermolecular configurations, was pointed out in numerous studies. Two main approaches have been taken to overcome this problem. The first involves the introduction of error functions, either exploiting torsion terms or introducing explicit 2-D error correction grids. The results and remaining challenges of these functional forms is examined. The second approach has been to improve the representation of the physics of intra and intermolecular interactions. The latter involves including descriptions of polarizability, charge flux aka geometry dependent charges, more accurate representations of spatial electron density such as multipole moments, anisotropic nonbond potentials, nonbond and polarization flux, among others. These effects, though not as extensively studied, likely hold the key to achieving the rigorous reproduction of structural and energetic properties long sought in biomolecular simulations, and are surveyed here. In addition, the quality of training and validation observables are evaluated. The necessity of including an ample set of energetic and crystal observables is emphasized, and the inadequacy of free energy as a criterion for FF reliability discussed. Finally, in light of the results of applications of the two approaches to FF development, we propose a “recipe” of terms describing the physics of inter and intramolecular interactions whose inclusion in FFs would significantly improve our understanding of the energetics and dynamics of biomolecular systems resulting from molecular dynamics and other energy based simulations.

Van der Waals (vdW) interactions are ubiquitous in molecules and condensed matter, and play a crucial role in determining the structure, stability, and function for a wide variety of systems. The accurate prediction of these interactions from first principles is a substantial challenge because they are inherently quantum mechanical phenomena that arise from correlations between many electrons within a given molecular system. We introduce an efficient method that accurately describes the nonadditive many-body vdW energy contributions arising from interactions that cannot be modeled by an effective pairwise approach, and demonstrate that such contributions can significantly exceed the energy of thermal fluctuations—a critical accuracy threshold highly coveted during molecular simulations—in the prediction of several relevant properties. Cases studied include the binding affinity of ellipticine, a DNA-intercalating anticancer agent, the relative energetics between the A-and B-conformations of DNA, and the thermodynamic stability among competing paracetamol molecular crystal polymorphs. Our findings suggest that inclusion of the many-body vdW energy is essential for achieving chemical accuracy and therefore must be accounted for in molecular simulations.

To study the microscopic thermal aging mechanism of insulating paper cellulose through molecular dynamics simulation, it is important to select suitable DP (Degree of Polymerization) and force field for the cellulose model to shorten the simulation time and obtain correct and objective simulation results. Here, the variation of the mechanical properties and solubility parameters of models with different polymerization degrees and force fields were analyzed. Numerous cellulose models with different polymerization degrees were constructed to determine the relative optimal force field from the perspectives of the similarity of the density of cellulose models in equilibrium to the actual cellulose density, and the volatility and repeatability of the mechanical properties of the models through the selection of a stable polymerization degree using the two force fields. The results showed that when the polymerization degree was more than or equal to 10, the mechanical properties and solubility of cellulose models with the COMPASS (Condensed-phase Optimized Molecular Potential for Atomistic Simulation Studies) and PCFF (Polymer Consistent Force Field) force fields were in steady states. The steady-state density of the cellulose model using the COMPASS force field was closer to the actual density of cellulose. Thus, the COMPASS force field is favorable for molecular dynamics simulation of amorphous cellulose.

“Plant-type” ferredoxins (Fds) in the thylakoid membranes of plants, algae, and cyanobacteria possess a single [2Fe-2S] cluster in active sites and mediate light-induced electron transfer from Photosystem I reaction centers to various Fd-dependent enzymes. Structural knowledge of plant-type Fds is relatively limited to static structures, and the detailed behavior of oxidized and reduced Fds has not been fully elucidated. It is important that the investigations of the effects of active-center reduction on the structures and dynamics for elucidating electron-transfer mechanisms. In this study, model systems of oxidized and reduced Fds were constructed from the high-resolution crystal structure of Chlamydomonas reinhardtii Fd1, and three 200 ns molecular dynamics simulations were performed for each system. The force field parameters of the oxidized and reduced active centers were independently obtained using quantum chemical calculations. There were no substantial differences in the global conformations of the oxidized and reduced forms. In contrast, active-center reduction affected the hydrogen-bond network and compactness of the surrounding residues, leading to the increased flexibility of the side chain of Phe61, which is essential for the interaction between Fd and the target protein. These computational results will provide insight into the electron-transfer mechanisms in the Fds.

Intrinsically disordered proteins (IDPs) pose challenges to conventional experimental techniques due to their large-scale conformational fluctuations and transient structural elements. This work presents computational methods for studying IDPs at various resolutions using the Amber and Gromacs packages with both all-atom (Amber ff19SB with the OPC water model) and coarse-grained (Martini 3 and SIRAH) approaches. The effectiveness of these methodologies is demonstrated by examining the monomeric form of amyloid-β (Aβ42), an IDP, with and without disulfide bonds at different resolutions. Our results clearly show that the addition of a disulfide bond decreases the β-content of Aβ42; however, it increases the tendency of the monomeric Aβ42 to form fibril-like conformations, explaining the various aggregation rates observed in experiments. Moreover, analysis of the monomeric Aβ42 compactness, secondary structure content, and comparison between calculated and experimental chemical shifts demonstrates that all three methods provide a reasonable choice to study IDPs; however, coarse-grained approaches may lack some atomistic details, such as secondary structure recognition, due to the simplifications used. In general, this study not only explains the role of disulfide bonds in Aβ42 but also provides a step-by-step protocol for setting up, conducting, and analyzing molecular dynamics (MD) simulations, which is adaptable for studying other biomacromolecules, including folded and disordered proteins and peptides.

A one-dimensional (1D) virtual force field (VFF) algorithm for real-time reflexive local path planning of mobile robots is proposed. The 1D-VFF is composed of the virtual steering, obstacle and integrated force fields (IFFs). The steering force field (SFF) is generated by the local or global goal position. This SFF leads a mobile robot to the goal. The obstacle force field (OFF) is created by the raw data of a range measurement sensor (RMS). By this OFF, a mobile robot avoids obstacles. The IFF is produced by combining the steering and OFFs in which weights between 0 and 1 are multiplied. Through this IFF, a final steering command by which a mobile robot reaches a goal by avoiding obstacles is generated. Various simulations compare the performance of the proposed 1D-VFF with the weighted virtual tangential vector (WVTV), which is the recently suggested local path planning method to overcome the U-shaped enclosure problem.

Mechano-sensitive channels are ubiquitous membrane proteins that activate in response to increasing tension in the lipid membrane. They facilitate a sudden, nonselective release of solutes and water that safeguards the integrity of the cell in hypo- or hyper-osmotic shock conditions. We have simulated the rapid release of content from a pressurized liposome through a particular mechano-sensitive protein channel, MscL, embedded in the liposomal membrane. We show that a single channel is able to relax the liposome, stressed to the point of bursting, in a matter of microseconds. We map the full activation-deactivation cycle of MscL in near-atomic detail and are able to quantify the rapid decrease in liposomal stress as a result of channel activation. This provides a computational tool that opens the way to contribute to the rational design of functional nano-containers.

Understanding the behavior of carbon dioxide (CO2) under varying thermodynamic conditions is essential for optimizing processes such as Carbon Capture and Storage (CCS) and supercritical fluid extraction. This study employs molecular dynamics (MD) simulations with the EPM2 and TraPPE-small force fields to examine CO2 phase behavior, structural characteristics, and transport properties across a temperature range of 228–500 K and pressures from 1 to 150 atm. Our findings indicate a good agreement between simulated and experimental liquid–vapor coexistence curves, validating the capability of both force fields to model CO2 accurately in a wide range of thermodynamical conditions. Radial distribution functions (RDFs) reveal distinct interaction patterns in liquid and supercritical phases, while mean squared displacement (MSD) analyses show diffusivity increasing from 5.2×10−9 m2/s at 300 K to 1.8×10−8 m2/s at 500 K. Additionally, response functions such as the heat capacity effectively capture phase transitions. These findings provide quantitative insights into CO2 phase behavior and transport properties, enhancing the predictive reliability of simulations for CCS and related industrial technologies. This work bridges gaps in the CO2 modeling literature and highlights the potential of MD simulations in advancing sustainable applications.

Context Nanoscrolls are tube-shaped structures formed when a sheet or ribbon of material is rolled into a cylinder, creating a hollow tube with a diameter on the nanoscale, similar to the papyrus. Carbon nanoscrolls have unique properties that make them useful in various applications, such as energy storage, catalysis, and drug delivery. In this study, we employed classical molecular dynamics simulations to investigate the formation and stability of nanoscrolls composed of graphene and hexagonal boron nitride (hBN) nanoribbons. Using a carbon nanotube (CNT) as a template to trigger their collapsing, we found that graphene/graphene, graphene/hBN, and hBN/hBN could form CNT-wrapped nanoscrolls at ultrafast speeds. We also confirmed that these nanoscrolls are thermally stable and discussed the other products formed from the interaction of these complexes and their temperature dependence. Gr/Gr and hBN/Gr nanoscrolls exhibit similar interlayer distances, while hBN/hBN nanoscrolls have wider interlayer distances than the other two composite nanoscrolls. These features suggest that hBN/hBN composite nanoscrolls could more efficiently capture small molecules because of their greater interlayer spacing. Methods We conducted molecular dynamics simulations using the Forcite package in the Biovia Materials Studio software, which employs the Universal and Dreiding force fields. We considered an NVT ensemble with a fixed time step of 1.0 fs for a duration of 500 ps. The velocity Verlet algorithm was adopted to integrate the equations of motion of the entire system. We employed the Nosé-Hoover-Langevin thermostat to control the system temperature. The simulations were carried out without periodic boundary conditions, so there was no pressure coupling.