Molecular Dynamics: Bridge between Theory and Experiment !

Molecular dynamics (MD) is a technique of computer simulation in which time evolution of large set of interacting atoms is followed by tracing their trajectory so that their corresponding equation of motion can be understood.  Molecular dynamics is becoming a celebrating technique which is now being used routinely, mostly in applied investigation of a wide range of dynamic properties and processes by researchers in numerous fields, including structural biochemistry, biophysics, molecular biology, pharmaceutical chemistry, and biotechnology. So the number of publications regarding MD theory and application of MD to biological systems is growing at an extraordinary pace. Using MD simulations, one is able to study thermodynamic properties and time-dependent (i.e., kinetic) phenomena of infinitely large complex structure of interacting atoms. Understanding the thermodynamics of the system one can develop various dynamic simulations using variety of algorithms in computer. In the simulation procedure, it has been considered the systems as small as an atom and a diatomic molecule undergoing a chemical reaction as large as a galaxy. Before doing MD simulation one needs to have knowledge of interaction potential for the particles, force due to these interactions, and the equation of motion that leads the particle dynamics. The interaction potential may vary with the mass and the distance between the interaction particles i.e the simple gravitational interaction between stars to the complex many-body forces between atoms and molecules. In conventional MD simulations, the energy function for non-bonded interactions tends to be a simple pair wise additive function (for computational reasons) of nuclear coordinates only. This use of a single nuclear coordinate to represent atoms is justified in terms of the Born-Oppenheimer approximation.The basic idea of molecular dynamics is the solution of the Newton’s law of motion in classical dynamics.

It has been noticed that the classical Newtonian equations of motion are adequate for many systems, including large biomolecules but for the systems with tunneling reactions, quantum corrections are important and need to include relativistic effects if we consider evolution of galaxy. In the MD simulation and its algorithm, it is supposed that the single particle motions as a function of time so they can be understood more easily than experiments to answer lots of properties of the system. To run the MD simulation, energy of the system is taken as a function of the atomic co-ordinates. We know, forces acting on the atoms of any system can be calculated by taking first derivative of the potential with respect to the atom positions. The force thus calculated gives dynamic behavior of the system by solving Newton’s equations of motion for the atoms as a function of time (M. Karplus, 1990). So, the major component in MD simulations is the force evaluation, specifically the long-range van der Waals and electrostatic interactions that must be computed for each pair of interacting components.

MD simulations are designed such a way that the result/simulation obtained is largely consistent with basic physical principles which can be validated by experiments. It is therefore, the Nobel Prize for Chemistry in 2013 [1] was awarded to Marin Karplus, Micheal Leavitt, and Arieh Warshall, who pioneered the MD simulations methodology for bimolecular systems. They explored that MD simulations evaluate the interactions between particles as a function of the coordinates of their individual substituent particles (e.g., atoms, residues/nucleotides, etc.). The foundation of MD is several theories from mathematics, physics, and chemistry, and it contains algorithms from computer science and information theory. The idea was originally conceived within theoretical physics but is applied today mostly in materials science and modeling of biomolecules. Before it became possible to simulate molecular dynamics with computers, some undertook the hard work of trying it with physical models such as macroscopic spheres.

Molecular dynamics is a specialized discipline of molecular modeling and computer simulation based on statistical mechanics; the main justification of the MD method is that statistical ensemble averages are equal to time averages of the system, known as the ergodic hypothesis. As stated by ergodic hypothesis, statistical ensemble averages are equal to time averages of the system if integration is performed to higher order. However, it is found that long MD simulations are mathematically limited because of cumulative errors in numerical integration of equations of motion. This error can be minimized with proper selection of algorithms and parameters, but cannot eliminate entirely. Furthermore, current potential functions are, in many cases, not sufficiently accurate to reproduce the dynamics of molecular systems, so researchers are taking use of computationally demanding Ab-Initio Molecular Dynamics method. Nevertheless, MD method allows detailed time and space resolution into representative behavior in phase space and thermodynamic properties of the large system.

It is found that there is a significant difference between the focus and methods used by various chemists and physicists while doing MD simulation and this is the key differences in the way used by the different fields. In chemistry and biophysics, the interaction between the particles is either described by a force field (classical MD), a quantum chemical model, or a mix between these two as a hybrid.

In applied mathematics and theoretical physics, molecular dynamics is considered as part of the research realm of dynamical systems i.e ergodic theory and statistical mechanics in general. So, theories of thermodynamics can be used to analyze the concepts of energy conservation and molecular entropy.

Some techniques to calculate conformational entropy such as principal components analysis come from information theory. Mathematical techniques such as the transfer operator become applicable when MD is seen as a Markov chain. Also, there is a large community of mathematicians working on volume preserving, symplectic integrators for more computationally efficient MD simulations. MD can also be seen as a special case of the discrete element method (DEM) in which the particles have spherical shape (e.g. with the size of their van der Waals radii.) Some authors in the DEM community employ the term MD rather loosely, even when their simulations do not model actual molecules.

 

References:

[1] The Nobel Prize in Chemistry. http://www.nobelprize.org, 2013.

[2] Gongpu Zhao, Juan R. Perilla, Ernest L. Yufenyuy, Xin Meng, Bo Chen, Jiying Ning,    Jinwoo Ahn, Angela M. Gronenborn, Klaus Schulten, Christopher Aiken, and Peijun Zhang. Mature HIV-1 capsid structure by cryo-electron microscopy and all-atom molecular dynamics. Nature, 497(7451):643–646, May 2013.

Image Copyright: Universität Stuttgart, IMWF

Chetanath Neupane

He is a graduate researcher of Astrophysics and Biophysics in St. Xavier's College, Kathmandu, Nepal. His research domain includes VMD/NAMD interface to study Large Structure Biomolecules; see some of his research interest in 'Research works section of the website. More Importantly, he actively leading his project "Science for Society-SS" which aims to promote Science ethics/principles to the society of Nepal.

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