opinion
Opinion: FMO meets MD – Achievements and Future Directions
2025 Volume 25 Pages 71-78
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2025 Volume 25 Pages 71-78
The interplay between the fragment molecular orbital method (FMO) and molecular dynamics (MD) simulations is reviewed. Subsequently, opinions and aspirations related to the further enhancement of this interplay are presented, referring to recent advancements in reactive force fields and machine learning MD, with regard to the simulation of enzymatic reactions. Overall, the interplay between FMO and MD represents a promising frontier in the fields of computational chemistry and quantum life science.
This article provides an overview of the interplay between fragment molecular orbital (FMO) [1] and molecular dynamics (MD) methods. It also includes the opinions of the author regarding the future of this interplay. FMO is a highly parallelizable ab initio quantum method applicable to the electronic state calculations of macromolecular systems [2], whereas MD simulates the time-dependent evolution of molecular configurations [3]. The merging of FMO and MD therefore sheds light on the dynamic aspects of target molecules, while also considering the corresponding electronic state changes.
This article discusses the current status of FMO interfaced with MD (Section 2), significant recent improvements in MD methods (Section 3), and the future of simulating chemical and biological reactions by combining FMO and MD (Section 4).
Notes: This article is an adaptation and reformation of some parts of Chapter 14 from a previous publication [3], and all figures have been reproduced from [3] with slight modifications and with permission from the publisher. This article does not provide a comprehensive review of related subjects, but readers can refer to the cited literature and references therein for further information.
To date, a range of MD methods have been developed. Hence, to facilitate further discussion, these methods have been classified into five categories based on their molecular models and physical principles (Figure 1). In the context of quantum mechanical MD (QM MD, Figure 1A), both the nuclei and electrons are handled by quantum mechanics (QM). However, in first-principles or ab initio MD (FP-MD, Figure 1B), only the electrons are subject to QM, whereas the nuclei are handled by classical (Newtonian) mechanics. In molecular mechanics (MM)-based MD (MM-MD, Figure 1C), only the nuclei are explicitly simulated and the effect of the surrounding electrons is represented by the MM force field parameters. In MM-MD, atoms are regarded as charged elastic spheres and their movements are determined by classical mechanics. Additionally, coarse-grained MD (CG-MD, Figure 1D) refers to any MD method in which groups of atoms unite into larger units. Moreover, QM/MM-MD (Figure 1E) applies QM only to a specified part of the molecule, whereas the remainder is handled by classical MM.
Figure 1. Classification of different MD methods
Classification of the molecular model of CH3OH according to MD methods [A]–[D] and their corresponding physical principles. The yellow regions in [A] and [B] represent the electron clouds. The gray spheres in [A] represent quantum nuclei, whereas the black spheres in [B] represent classical nuclei. In [E], certain parts of the molecular system are subjected to QM, whereas others are subjected to MM.
For the above methods, both the model accuracy and the computational cost decrease in the order [A] > [B] > [C] > [D], which indicates that a greater accuracy corresponds to a higher cost. Users should therefore select an appropriate MD method that meets their requirements while considering their computational resources. Additionally, the accuracy and cost of QM/MM-MD fall between those of FP-MD and MM-MD, and the effectiveness of this approach depends mainly on the choice and size of the QM and MM regions.
The FMO method was interfaced with the five aforementioned MD categories to give the combinations described below.
[A] FMO and QM-MD: FMO-PIMD
Upon merging the FMO method with the path integral MD (PIMD) approach, a kind of QM-MD method, the resulting FMO-PIMD model successfully simulated pure water [4]. However, the practical applications of FMO-PIMD are limited by its high computational cost. Therefore, accelerating the FMO-PIMD simulation and/or developing an alternative QM-MD method is desirable because the quantum effects of protons play important roles in various biological reactions.
[B] FMO and FP-MD: ab initio FMO-MD
Ab initio FMO-MD represents an FP-MD method in which the forces exerted on the nuclei are calculated by FMO and are employed by MD to integrate the Newtonian equations of motion for the nuclei (Figure 2) [5]. FMO-MD has been applied to the analyses of various chemical reactions of small molecules in solution, the vibration of molecular clusters, and the hydration of ions [2]. However, to simulate enzymatic reactions, drastic improvements and acceleration of the FMO-MD algorithms are required.
Figure 2. Outline of the FMO-MD algorithm
[C] FMO and MM-MD: MM-MD/FMO
In the MM-MD/FMO protocol, the molecular structures were modeled using MM-MD and subjected to FMO calculations. This protocol, which is often abbreviated as MD+FMO, enables FMO calculations to be performed for fluctuating snapshots of large biological molecules [6]. Although MM-MD/FMO is widely employed, it has an inherent inconsistency in that FMO energy calculations are applied to molecular configurations prepared under an MM force field. Further details regarding the advantages and disadvantages of this protocol can be found in the literature [2]. One potential method for alleviating this inconsistency is discussed later.
[D] FMO and CGMD: FMO-DPD
FMO has been interfaced with the dissipative particle dynamics (DPD) simulation method [7, 8], which is a class of CG-MD. DPD is often applied to the simulation of mesoscopic systems such as complex fluids, soft matter, polymers, and biological membranes. In a DPD simulation, a group of atoms is considered as a single particle, and the interactions between pairs of particles are calculated and characterized by a parameter named “χ.” In the FMO-DPD method, the χ parameter is calculated using FMO, thereby bridging the two methods.
[E] FMO and QM/MM-MD: FMO-QM/MM-MD
FMO-QM/MM-MD refers to a QM/MM-MD simulation in which the QM region is treated using FMO. This simulation has been implemented by combining the AMBER MM-MD software with the PAICS FMO program [2, 9].
In the previous section, various combinations of FMO and MD were considered, while in the subsequent section, FMO-MD and MM-MD/FMO are considered. However, before moving on, an overview of the convergence of FP-MD and MM-MD is required, since this convergence represents an important and recent trend in MD simulations.
Currently, FP-MD (Figure 1B) and MM-MD (Figure 1C) are being merged to improve the simulation of chemical reactions. This shift has been driven by advancements in reactive force fields and machine learning force fields (ML-FF). From an MM-MD perspective, progress in reactive force fields allows one to obtain information at the FP-MD level without significantly increasing the computational cost. Conversely, from an FP-MD standpoint, ML-FFs enable the simulation of the same phenomena while reducing the computational costs to the level of MM-MD. The following subsections provide an overview of these developments, which are described in detail in the literature [10, 11].
3.1. Reactive force fields
The term "reactive force field" refers to force field parameters that are designed for performing classical MM-MD simulations of chemical reactions. As previously mentioned, FP-MD calculates the electronic states using QM, which provides a description of the polarization, charge transfer, bond formation, and bond cleavage behaviors. Ultimately, this enables chemical reaction simulations to be carried out. However, solving the Schrödinger equation using QM requires extensive computational resources. In contrast, MM-MD uses empirical force field parameters to calculate the force and energy, rendering the calculations significantly faster than those of the FP-MD approach. Therefore, improving the MM force field parameters to describe polarization, charge transfer, and bond formation and cleavage could allow the MM-MD method to offer similar capabilities. This represents the key goal of the reactive force fields.
Several reactive force fields have been developed over the years; however, ReaxFF is the most widely used. Since its introduction in 2001 [12], ReaxFF has undergone continuous refinement to expand its capabilities and applications [13]. The functional forms and parameters of ReaxFF are significantly more complex than those of conventional MM force fields. Its most notable feature is the incorporation of the bond order into the force field, which allows ReaxFF to describe the formation and dissociation of covalent bonds. ReaxFF has been particularly successful in material simulations, but has also been applied to biological systems, such as in the analysis of radical reactions in nucleic acids.
3.2. Machine learning force fields
An ML-FF is a force-field parameter set that is constructed using ML. Although various ML methods exist, the majority of ML-FFs currently use neural networks (NNs) as the ML method. In this section, ML-FFs that use NNs to achieve FP-MD-level accuracy at MM-MD computational speeds are considered. Hereafter the MD simulations performed using ML-FFs are referred to as ML-MD simulations.
ML-FFs are generally created using the procedure outlined in Figure 3. Initially, a trial FP-MD simulation generates coordinates (r) along with the corresponding force (f) and energy (E) data. These serve as the training data for constructing an appropriate NN model. Ideally, the constructed NN model should predict the force and energy outputs with FP-MD-level precision from the given molecular coordinates at each MD step (Figure 4). Thus, ML-MD should achieve computational speeds far exceeding those of FP-MD, while maintaining an equivalent trajectory accuracy using the NN model.
Figure 3. Basic outline of training an NN model for the construction of an MM-FF
Figure 4. Outline of the ML-MD simulation, in which the trained NN model (Figure 3) is fed with coordinates r and outputs f and E
As mentioned above, the core concept of the ML-FF is to train NN models to predict f and E based on the atomic coordinates (r). However, rather than directly inputting individual atomic three-dimensional (3D) Cartesian coordinates for training, certain transformations have been applied in the practical implementation of ML-MD methods (Figure 5). This is necessary because the direct use of Cartesian coordinates limits the ability of the model to generalize, thereby requiring a new NN model for each change in system size. Additionally, it disrupts the translational and rotational symmetries during potential energy calculations. As illustrated in Figure 5, Transformation A converts the Cartesian coordinates into characteristic features before inputting them into the NN model. Transformation B then converts the outputs to the force exerted on the Cartesian coordinates. Transformations A and B include the use of symmetry functions to represent atomic environments [14], along with graph-based representations of the atomic configurations [15, 16].
Figure 5. Schematic representation of an ML-MD simulation step
The 3D coordinates of the molecules are subjected to Transformation A and fed into the trained NN model (Figure 4). The output data of the NN model are then subjected to Transformation B and converted into f.
Despite these advances, several challenges remain unresolved. Specifically, as of 2025, ML-FFs will be primarily used for inorganic material simulations, and the development of organic and biomolecular systems will lag behind because of their complex atomic compositions and structures.
In Section 2, the current status of the interplay between FMO and MD was described. Subsequently, in Section 3, an overview of the convergence between MM-MD and FP-MD was presented. Based on these discussions, the most important challenge regarding FMO, namely the simulation of enzymatic reactions, is discussed.
Ideally, QM-MD approaches such as FMO-PIMD are the most rigorous tools for performing reaction simulations; however, they are essentially impractical for the majority of molecular systems. A more practical choice is the FP-MD approach (e.g., FMO-MD). As mentioned previously, FMO-MD successfully simulated several chemical reactions involving small molecules in an aqueous solution. However, further improvements and acceleration of the FMO-MD method are mandatory for simulating medium-sized molecules and enzymes.
The construction of an MM force field parameter set compatible with the FMO method is therefore expected to replace part of the ab initio FMO-MD process and also to prepare more appropriate molecular structures for the MM-MD/FMO protocol. Although several trial FMO force fields have been developed [17, 18], they have not yet been used in practice. Although a more practical FMO force field can be developed using ML (Figures 3–5), the ML-FFs of organic/biological molecules may be hindered by the large variety of atomic components and configurations associated with these molecules. To overcome this difficulty, it is necessary to select appropriate features to describe the environment of each atom, ideally referring to the reactive force fields. In this regard, an algorithm has been developed that predicts the interaction energy from low-cost FMO using Random Forest, another ML method [19, 20]. This algorithm has the potential to accelerate FMO-MD simulations in the near future.
Additionally, ML-FF can address the inherent issues of the MM-MD/FMO protocol discussed in Section 2 [C]. Specifically, the inconsistency between the molecular structure and the FMO energy can be mitigated by generating MM-MD snapshots under ML-FF, a force field similar to that of FMO.
To achieve an FMO-based ML-FF, it is necessary to accelerate the FMO-MD simulation itself, for example, by enhancing the parallel efficiency. Since the target molecular system is heterogeneous and contains molecules of various sizes, including proteins, nucleotides, ions, and water molecules, it is necessary to implement an algorithm that can define fragments with fine-grained granularity by merging small fragments into large evenly sized fragments.
In conclusion, the interplay between FMO and MD represents a promising frontier in computational chemistry and quantum life science [21]. Continued efforts in methodological development, algorithm optimization, and integration with ML are crucial for realizing the full potential of FMO in simulating complex chemical and biological phenomena.
