Overview of Classical and Quantum Molecular Dynamics Simulations

Given the significant time and financial costs involved in developing commercial drugs, it remains important to continuously revolutionize the drug discovery pipeline with new technologies that can narrow down candidate compounds to the most promising lead compounds for clinical trials. The last decade has seen a huge increase in computing power, enabling computer simulation methods to speed up drug discovery. Molecular dynamics (MD) has become a particularly important tool in drug design and discovery. From classical MD methods to more complex hybrid classical/quantum mechanical (QM) methods, molecular dynamics simulations are now able to provide extraordinary insights into ligand-receptor interactions.

Figure 1: MD simulation results sample graph. (Hu, Xia et al.,2023)

In this article, we discuss basic MD concepts and principles and show how these applications can significantly change current drug discovery and development efforts.

Introduction to Molecular Dynamics Simulations

When selecting specific targets and libraries of compounds, virtual high-throughput screening based on molecular docking is used to identify only those compounds that have a higher affinity for the protein's active site. These proteins are dynamic biomolecules, and their flexibility plays a crucial role in the ligand recognition process, and therefore also in SBDD. In addition, ligand binding also tends to induce conformational changes at measurable levels in proteins to accommodate biophysical states suitable for the formation of strongly binding complexes (known as the "inducible fit" effect). However, accounting for receptor flexibility remains a major challenge, and conventional molecular docking methods are mostly unable to capture such conformational changes in proteins. For SBDD, you can refer to the previous article Structure-Based vs Ligand-Based Drug Design.

MD is a computational approach that addresses this challenge and predicts the time-dependent behavior of molecular systems, making it a valuable tool for SBDD. It is particularly valuable in exploring the energy landscape of proteins and identifying their physiological conformations, which in many cases are not even available through high-resolution experimental techniques. MD can also be used for structural refinement of post-docking complexes, so the complementarity between ligand and receptor is enhanced in the complex state, allowing for better re-scoring of complexes.

What is Molecular Dynamics Simulation?

Molecular Dynamics Simulation is a computation-based scientific method for studying the physical motion of atoms and molecules over time scales. By applying classical mechanics (such as Newton's laws of motion), the method can simulate the trajectories of particles in a molecular system, thus predicting the dynamical behavior and physicochemical properties of the system. Molecular dynamics simulations typically rely on potential energy functions (such as force field models) to describe interactions between molecules and analyze molecular structural changes, energy transfers, and kinetic processes by calculating the generated trajectory data. This technique is widely used in biology (such as protein folding), materials science (such as nanomaterials design), and chemical reaction kinetics studies, and is an important tool for connecting theoretical research with experimental observation.

Figure 2: MD simulation basic process diagram. (Hu, Xia et al.,2023)

Applications of Molecular Dynamics in Modern Science

Early docking methods assumed that the ligand-protein binding phenomenon could be modeled as a simple "lock and key" scheme. That is, the aim is to identify ligands (i.e., bonds) with precise shape complementarities to fit the rigid active site cavity (as a keyhole) of the protein. In this way, most early docking algorithms treated the ligand and receptor as two rigid counterparts. However, this assumption applies only in rare cases, such as the trypsin-BPTI complex, where the interfaces of the bound and unbound states are nearly identical in conformation. However, it does not reflect the reality in most cases, where both ligand and receptor undergo mutual changes to adapt to each other in complex states. With the increase of the types in algorithms, many software methods to achieve ligand flexibility in virtual screening based on docking have made great progress. In contrast, protein flexibility has been virtually ignored in docking calculations. Very little technology has been developed to solve this problem.

An effective solution is to model protein flexibility in molecular docking with a set-based strategy that explicitly considers multiple individual receptor conformations and docking ligands against all of these target structures. In the absence of these experimental structures, modeling, and MD simulations can be performed to glean statistically significant protein conformations from the resulting (MD) trajectories. Our Molecular Dynamics Simulation Services offer advanced MD solutions to help you explore protein flexibility, optimize ligand-receptor interactions, and simulate real-world biological processes with high precision. MD simulations can be used to explain protein flexibility in docking-based virtual screening. As a result, the MD approach is now considered a valuable tool for SBDD.

In addition, MD simulations are widely used in the characterization of biomolecular systems, including membrane structure and organization, membrane permeability, lipid-protein interactions, lipid-drug interactions, protein-ligand interactions, and protein structure and dynamics. Leveraging our comprehensive MD simulation services can accelerate your research and bring deeper insights into complex biological systems.

A classic example is the study by Cardoso et al., inhibition of tyrosinase activity was analyzed using kojic acid (KA) derivatives designed with aromatic aldehydes and malonitrile. In this study, whole-atom MD simulations were used on various mutants and CATR-AAC complexes, revealing a detailed description of this transport mechanism. The results provide new insights into the highly conserved but variable m-gate network in a family of large mitochondrial carriers.

Classical Molecular Dynamics Simulations

Principles of Classical Molecular Dynamics

Classical Molecular Dynamics is a computational method that uses the principles of classical mechanics to simulate the motion of particles in a molecular system. By solving Newton's equation of motion numerically, it simulates the dynamic evolution process of molecules under certain temperature and pressure conditions, so as to obtain the structure, thermodynamics, and dynamics properties of the system.

Solving Newton's Equations of Motion

In CMD, each particle in the system obeys Newton's second law of motion:

• F_i is the force acting on particle i
• m_i is the particle's mass
• a_i is the particle's acceleration
• r_i is the particle's position

By numerically integrating these equations using algorithms like the Verlet algorithm, Leapfrog algorithm, or Velocity Varlet algorithm, the velocities and positions of particles can be updated iteratively to generate their trajectories over time.

Potential Energy Functions and Force Fields

The interactions between particles in CMD are described using force fields, which are mathematical models for potential energy. The total energy is a sum of bonded and non-bonded interactions:

• Bond stretching (harmonic potential):

• Angle bending (harmonic angle potential):

• Non-bonded interactions:

Van der Waals interactions (Lennard-Jones potential):

Electrostatic interactions (Coulomb potential):

Temperature and pressure control

During the simulation, the temperature and pressure of the system need to be controlled by specific algorithms:

Temperature control methods: such as Berendsen thermostat, Nose-Hoover thermostat, etc., by adjusting the particle speed to maintain the temperature of the system.

Pressure control methods, such as the Berendsen pressure controller and the Parrinello-Rahman method, maintain pressure by changing the volume of the system.

Periodic boundary condition (PBC)

In order to simulate infinitely large systems, molecular dynamics uses periodic boundary conditions, that is, the particles in the simulated box are copied into the surrounding space, and when the particle leaves the simulated box, it re-enters from the other side of the box, thus avoiding the boundary effect.

Energy conservation and stability

In the simulation process, energy conservation is an important index to measure the accuracy of the simulation results. Numerical integration algorithms need to ensure that the total energy of the system remains as stable as possible over a long period of time.

Software and Tools for Classical Simulations

Classical molecular dynamics simulations rely on powerful computational software and tools to achieve efficient simulations. The commonly used molecular dynamics software has different application scenarios because of its characteristics. For details, see the article Top 10 Molecular Dynamics Simulation Software: Free, Open-Source, and Commercial Options.

GROMACS

GROMACS (GROningen MAchine for Chemical Simulations) is a highly efficient molecular dynamics simulation package for biomolecules, chemical molecules, and materials science. It supports a variety of force fields (such as GROMOS, AMBER, CHARMM, etc.) and optimizes support for multi-core and parallel computing. Supports efficient long-term simulations and large-scale systems such as proteins and macromolecular systems.

LAMMPS

LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator) is an open-source, parallel, and powerful molecular dynamics simulation software that is widely used in solid, liquid, gas, and materials research. Supports a variety of simulation methods, including classical molecular dynamics, particle simulation, quantum molecular dynamics, etc.

It can handle different types of force fields (such as EAM, Tersoff, ReaxFF, etc.), and can perform particle fluid simulation, nanoscale material simulation, etc.

AMBER

AMBER (Assisted Model Building with Energy Refinement) is a set of molecular simulation software specially developed for biological molecules (especially proteins, nucleic acids, etc.). Strong biomolecular force fields (e.g. ff14SB, RNA, DNA force fields). Support conventional molecular dynamics simulation, free energy calculation, molecular docking, and other functions. It has advantages in the accurate simulation of biomolecules and drug design, providing comprehensive analytical tools.

CHARMM

CHARMM (Chemistry at Harvard Macromolecular Mechanics) is a powerful molecular dynamics simulation software specifically designed for the study of macromolecules and biomolecules. Support a variety of force fields (such as CHARMM27, CHARMM36, etc.), very suitable for the simulation of proteins, lipids, nucleic acids, and other biological macromolecules. It provides a wide range of simulation functions, including molecular docking, free energy calculation, dynamic path analysis, etc.

Applications of Classical Molecular Dynamics

Classical molecular dynamics is used to simulate the structure, dynamic behavior, and interaction of biological macromolecules such as proteins and nucleic acids. These simulations contribute to the understanding of biological processes such as protein folding, the catalytic mechanisms of enzymes, and the binding patterns of drugs to targets. In materials research, classical molecular dynamics can be used to model the mechanical properties of nanomaterials, the reactivity of material surfaces, and the stability and properties of materials under different environmental conditions. Molecular dynamics is used to simulate the motion of molecules in liquids and gases and to explore their thermodynamic properties, transport properties, and chemical reaction processes, which is of great significance for understanding complex fluid behavior. By simulating the interaction between molecules, the kinetic process, reaction mechanism, and energy conversion path of chemical reactions are revealed, which is helpful in designing more efficient catalysts and functional materials.

Classical molecular dynamics can be used to model the binding patterns of drug molecules to receptors, predict drug efficacy, optimize drug design, and help understand drug mechanisms of action and drug molecule delivery routes.

More detailed information can be found in the articles Molecular Dynamics Simulation in Drug Discovery and Pharmaceutical Development.

Quantum Molecular Dynamics Simulations

Introduction to Quantum Molecular Dynamics

Quantum Molecular Dynamics (QMD) is an advanced computational technique that takes into account quantum mechanical effects on the basis of classical molecular dynamics. Unlike classical molecular dynamics (CMD), which describes the motion of particles (atoms and molecules) only through classical mechanics, QMD can accurately simulate atomic and molecular systems by introducing the principles of quantum mechanics, which is especially suitable for studying processes involving quantum effects such as electron behavior and bond formation. In classical molecular dynamics, the motion of particles follows Newton's laws, and position and velocity are classical variables. In QMD, the evolution of the system is governed by the Schrodinger equation, which describes the behavior of quantum particles (electrons and nuclei). The quantum properties of the electron are explicitly incorporated, and the motion of the nucleus can be treated in different ways, either classically or quantized, depending on the computational method employed.

QMD simulations need to deal with a large number of quantum mechanical calculations, which are often more complex and time-consuming than classical molecular dynamics (MD) and require the support of high-performance computing resources. At present, QMD is mainly used to explore quantum effects at the atomic scale, such as studying electronic structure, material properties and reaction dynamics in materials science. Compared with classical MD, its application scenario is relatively narrow, which limits its scope of large-scale application. Therefore, there is not much data for reference and comparison, so it is not compared with traditional MD technology.

Applications of Quantum Molecular Dynamics

Quantum molecular dynamics (QMD) has a wide range of applications in several scientific fields, especially those involving important studies of quantum effects. It is widely used in the study of chemical reactions, helping to reveal reaction mechanisms, electron transfer, and intermolecular interactions. In materials science, QMD is able to deeply study the electronic structure and mechanical properties of materials, providing a theoretical basis for the design and optimization of new materials. In catalytic research, QMD can accurately simulate the reaction mechanism and energy changes of catalytic reactions, and provide support for the development of efficient catalysts. In addition, QMD is applied in the field of nanotechnology to the study of the electronic, mechanical, and thermodynamic properties of nanomaterials to help understand and design novel nanodevices. In the field of biology, QMD simulates the structure and function of biomolecules, reveals quantum effects in enzyme catalysis, molecular recognition, and other processes, and promotes the development of drug design and biomedical research. In general, quantum molecular dynamics, which accurately describes the behavior of atoms and molecules through quantum mechanics, plays an important role in the fields of chemistry, materials science, biology, and other fields, and promotes the frontier development of multiple disciplines.

Challenges and Future Directions

Challenges in Molecular Dynamics Simulations

Classical MD simulation remains a valuable tool in drug design. They contribute to the understanding of key molecular motions, energetics, ligand-protein interactions, receptor flexibility, and conformational changes in molecular systems, helping to identify potential candidate genes with higher affinity for targets. However, it is also important to acknowledge that MD also has some potential limitations and drawbacks, particularly in terms of time constraints, force field issues, and quantum effects. Currently, typical MD simulations are performed on systems containing hundreds of millions to millions of atoms, with durations ranging from nanoseconds to microseconds. Despite these impressive advances in the (MD) field, such time limits may not be enough to loosen the system to study certain quantities. For example, some of the physical properties of biological systems, such as protein folding, ligand binding, and unbinding processes, mostly occur on very long timescales, which are often not possible with traditional mechanical MD simulations.

The MM force field used in the simulation plays a crucial role in determining the structural model of the system under study. Force fields are often developed by combining existing experimental data with advanced ab initio results that form small models of larger systems, and as such, they are essentially approximations. In addition, force fields are parameterized, so they include several types of atoms that describe different cases of the same atom (or functional group). Therefore, the transitivity of the electric field is limited. Therefore, the results of a dynamic simulation are reliable only if the potential energy function (or force field) is consistent with the forces exerted on the atoms in the actual system under study. QM/MM MD (Quantum Mechanics/Molecular Mechanics Molecular Dynamics) is a computational chemistry method that combines the molecular dynamics simulation techniques of quantum mechanics and molecular mechanics. Part of the system (such as the active site, reaction center, etc.) is accurately described by quantum mechanical method (QM), while the rest (such as the surrounding environment, macromolecular background, etc.) is described by molecular mechanical method (MM). The core idea of this approach is to use more accurate quantum mechanical calculations to deal with important chemical or physical processes when needed, while at the same time dealing with a larger range of molecular dynamic behavior through molecular mechanical simulations.

However, QM/MM MD simulation also has some significant disadvantages. One of the most important problems in QM/MM simulations is dealing with the interfacial regions that connect the QM part and the MM part, especially when they are covalent bonds, such as in ligand-protein systems. When a complete system is explicitly cut into QM and MM parts, it leaves incomplete valence states in the former region, which can cause QM processing to fail. The most common strategy to overcome this problem is to cover the boundary QM residue being allocated with hydrogen atoms. However, this hydrogen cap introduces atoms into quantum-managed regions that are different from the atoms that originally existed in the real system, which can lead to artifacts. In addition, QM/MM MD simulations of large protein-ligand systems are still computationally expensive. Therefore, they can only be applied to selected systems in drug design, such as those with top-ranked hit values filtered from thorough virtual screening and classical MD simulations, where subsequent details about key ligand-protein interactions for pharmacophore modeling are computationally sound.

Future Trends in MD

With the continuous progress of computational techniques and algorithms, molecular dynamics simulation will develop towards higher accuracy, wider application range, and stronger computational efficiency in the future. Firstly, multi-scale simulation will become an important trend in MD. By combining simulation methods at different scales, such as quantum mechanics/molecular mechanics (QM/MM) methods, it is possible to deal with physical phenomena at both micro and macro scales, resulting in more accurate simulation of complex systems. In addition, the combination of machine learning and artificial intelligence will promote the automation and acceleration of MD, especially in the field of force field development, simulation parameter optimization, and big data analysis, machine learning can significantly improve the efficiency and accuracy of MD. Improvements in high-performance computing will also allow researchers to simulate systems on larger scales and longer timescales, driving the application of MD in materials science, life science and other fields. With the development of quantum computing technology, future MD simulation may further break through the current computational bottleneck and solve more complex quantum mechanical problems through quantum computers. In short, the development of MD in the future will enable it to achieve more significant progress in accurate simulation, efficiency improvement, and wide application, especially in the fields of chemical reaction, material design, and biology.