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Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_5435_Библиотеки_им_академика_М_И_Перельмана
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difficult using any experimental method. (ii) Second, the simulation conditions are pre-
cisely known and can be carefully controlled, including the temperature, voltage across
amembrane,aprotein’s protonation state, the ligands that are bound to it, whether it
has mutations or post-translational modifications, and other molecules in its environ-
ment. By comparing simulations conducted under different conditions, one can identify
the effects of a wide range of different factors.
8.1.4 Theory of molecular dynamics simulation
The theory of MD simulation is rooted in classical mechanics and statistical thermody-
namics. It involves simulating the motion and interactions of atoms and molecules
over time to s tudy their behavior and properties. The fundamental principles and
equations that govern MD simulations can be summarized as follows.
8.1.4.1 Newton’s laws of motion
MD simulations are based on Newton’s laws, which describe the motion of particles in
a classical system. These laws state that the force acting on a particle is equal to the
rate of change of its momentum, and the acceleration of a particle is directly propor-
tional to the force acting on it. By integrating these equations, the positions and veloc-
ities of particles can be determined at each time step.
By using Newton’s laws of motion, it is possible to simulate the way biological sys-
tems dynamically evolve through time:
F =
dp
dt
= m
d
2
r
dt
The finite difference approach is used for the integration of these standard equations
of motion. Using these methods, MD trajectories with continuous potential models can
be generated.
8.1.4.2 Potential energy functions
To describe the interactions between atoms or molecules, a potential energy function
is used. This function quantifies the potential energy of the system, based on the posi-
tions of the particles. It typically consists of bonded terms (e.g., bonds, angles, and di-
hedrals) and nonbonded terms (e.g., van der Waals interactions and electrostatic
interactions). Various force fields, such as chemistry at Harvard molecular mechanics
(CHARMM), AMBER, or OPLS, provide parameterized potential energy functions for
different types of molecules.
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8.1.4.3 Integration algorithms
To numerically solve the equations of motion, integration algorithms such as Verlet or
Leapfrog are employed. These algorithms update the positions and velocities of particles
at discrete time intervals (timesteps), based on the forces acting on them. The choice of a
timestep is important to ensure numerical stability and accurate simulation results.
8.1.4.3.1 Verlet algorithm
In MD, this algorithm is the most fundamental and the often employed algorithm for
integrating the equation of motion [10]. This method has the advantages of being
straightforward, simple, and self-starting, making it simple to derive the new positions
from the previous ones. It also uses less computer memory. The drawback is that until
the position for the following step has been calculated, it is challenging to determine
the velocity at the current position because there is no explicit velocity term.
8.1.4.3.2 Velocity verlet algorithm
The velocity valet method necessitates the information of current position and veloc-
ity of a particle to calculate its position at the next time step while also being storage-
efficient.
8.1.4.3.3 Leapfrog algorithm
This term refers to the evaluation of forces and positions followed by velocities, utiliz-
ing timesteps in a leapfrog fashion. This method shares similarities with the velocity
verlet approach and is also considerably superior in terms of stability and accuracy.
8.1.4.4 Ensemble and temperature
MD simulations often simulate systems in different ensembles such as the NVE ensem-
ble (constant number of particles, volume, and energy), NVT ensemble (constant num-
ber of particles, volume, and temperature), or NPT ensemble (constant number of
particles, pressure, and temperature). The temperature of the system is controlled
using thermostats, which modify the velocities of particles to maintain the desired
temperature.
8.1.4.5 Statistical sampling
MD simulations provide statistical information by sampling the system’s phase space. By
running a simulation for a sufficiently long time, the system explores different configu-
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rations and captures equilibrium properties. Various statistical mechanical methods,
such as averaging over time or ensemble averaging, can be used to extract thermody-
namic quantities like energy, pressure, or diffusion coefficients from the trajectory data.
8.1.4.6 Boundary conditions
To simulate a small portion of a larger system, periodic boundary conditions are
often used. This approach creates replicas of the simulation box in all directions, al-
lowing particles to interact with their periodic images. This approximation ensures
that the system represents an infinite, homogeneous system and avoids edge effects.
8.1.4.7 Long-range interactions
In simulations, long-range interactions, such as electrost atic forces, require special
treatment due to their computational complexity. Techniques like the particle mesh
Ewald method or the smooth particle mesh Ewald method are commonly employed to
efficiently compute long-range interactions in periodic systems.
These are some of the key theoretical aspects of MD simulation. By implementing
these principles and techniques, MD simulations provide valuable insights into the
structural, dynamic, and thermodynamic properties of molecules and materials at the
atomic level.
8.1.5 Elements of molecular dynamic simulation
The elements of MD simulation can be categorized into four main components: the
system, the force field, the integration algorithm, and the ensemble. Each of these ele-
ments plays a crucial role in the simulation process and contributes to understanding
the behavior of the system being studied. Let us explore each element in detail.
8.1.5.1 System
The system refers to the collection of atoms or molecules that are the subject of the
simulation. It includes the initial positions, velocities, and, possibly, charges or other
properties of the particles. The size and shape of the system are determined by the
scientific question or problem being investigated. The system can range from small
molecules to large biological macromolecules or even extended materials.
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8.1.5.2 Force field
The force field describes the potential energy function that governs the interactions
between the particles in the system. It consists of mathematical expressions that de-
fine the bonded and nonbonded interactions such as bonds, angles, dihedrals, van der
Waals forces, and electrostatic interactions. The force field also includes parameters
that quantify the strength and nature of these interactions. These parameters are de-
rived from experimental data or quantum mechanical calculations and are specific to
a particular force field.
Force fields are mathematical functions that are used to explain the potential en-
ergy of a system of particles (usually molecules and atoms) in the context of molecular
modelling. High-level quantum mechanical computations and experimental studies
both contribute to the development of force field functions and parameter sets.
AMBER, CHARMM, and OPLS are the force fields most frequently employed in MD
simulations according to Abraham et al. [11], Harder et al. [12], Huang et al. [13], and
Robustelli et al. [14]. While these force fields utilize comparable functional forms,
they possess distinct advantages and disadvantages.
In MD simulations, the most commonly used force fields are AMBER, CHARMM,
and OPLS [11–14]. Although utilizing comparable functional forms, each of these force
fields has its pa rticular advantages and limitations. For ex ample, CHARMM36m and
CHARMM General Force Field (CGenFF) are well-suited for simulating proteins, lipids,
and drug-like molecules [15, 16], while A99SB-disp is better suited for simulating disor-
dered proteins. OPLS3 has highly optimized ligand parameters, but these parameters
are not available for third-party evaluation due to their proprietary nature.
Table 8.1: Force fields commonly used in molecular dynamics simulations.
Force field Description
AMBER Assisted model building with energy refinement
CHARM Chemistry at Harvard molecular mechanics
GROMOS GROningen MOlecular Simulation
OPLS Optimized potentials for liquid simulations
MARTINI Coarse-grained force field for biomolecular simulations
AMOEBA Atomic multipole optimized energetics for biomolecular applications
CHARMM Updated version of the CHARMM force field for biomolecular systems
AMBERSB An AMBER force field for protein simulations
GROMOS A force field for biomolecular simulations
ffSBA Protein force field in the AMBER family
ff.r A nucleic acid force field in the AMBER family
GAFF General AMBER force field, for small organic molecules
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Table 8.1 provides an overview of some commonly used force fields in MD simula-
tions. Different force fields are developed for specific purposes such as biomolecular
simulations, small organic molecules, or coarse-grained models. Each force field has
its own parameterization and functional form, designed to accurately describe the in-
teractions between atoms and molecules in a system. When choosing a force field, it
is important to consider the nature of the system being studied and the compatibility
of the force field with the simulation software being used.
Some common force fields are summarized below.
8.1.5.2.1 AMBER (assisted model building with energy refinement)
The late Peter Kolman’s [17] group at the University of California, San Francisco, de-
veloped the AMBER family of force fields for MD modelling of biomolecules. In order
to use the AMBER force fields, parameters such as equilibrium bond lengths and an-
gles, force constants, and charges are needed.
TheAMBERforcefield(GAFF)isdesignedto facilitate simulations of small or-
ganic molecules, including drugs and ligands, in combination with biomolecules. Its
purpose is to provide accurate representations of these molecules in computational
simulations, which can aid in drug design and other applications.
8.1.5.2.2 CHARMM force field
CHARMM, which stands for Chemistry at Harvard macromolecular mechanics, is an
extremely flexible molecular mechanics and dynamics program that was initially de-
veloped in the Harvard University laboratory of Dr. Martin Karplus [18]. It was pa-
rameterized using ab initio energies and small organic model geometries.
8.1.5.3 Integration algorithm
The integration algorithm is responsible for numerically solving the equations of mo-
tion and updating the positions and velocities of the particles at each time step. Vari-
ous algorithms, such as the Verlet algorithm, leapfrog algorithm, or higher-order
symplectic integrators, can be employed. These algorithms ensure the accurate propa-
gation of particle trajectories while conserving energy and maintaining the stability
of the simulation.
8.1.5.4 Ensemble
The ensemble represents the set of conditions under which the simulation is per-
formed. Different ensembles correspond to different constraints imposed on the sys-
tem. Commonly used ensembles in MD simulations are given below.
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8.1.5.4.1 NVE ensemble
In this microcanonical ensemble, the number of particles (N), volume (V), and total
energy (E) of the system are conserved. The simulation evolves without any external
influence, resulting in a constant energy trajectory.
8.1.5.4.2 NVT ensemble
In this canonical ensemble, the number of particles (N), volume (V), and temperature
(T) are kept constant. A thermostat is employed to control the system’s temperature
and maintain it at the desired value.
8.1.5.4.3 NPT ensemble
In this isothermal-isobaric ensemble, the number of particles (N), pressure (P), and
temperature (T) are maintained. In addition to a thermostat, a barostat is used to con-
trol both temperature and pressure, allowing the system to equilibrate under constant
external pressure.
8.1.5.4.4 Grand canonical ensemble
This ensemble allows for fluctuations in the number of particles, volume, and temper-
ature. It is often used in simulations involving exchange of particles with a reservoir
or simulations of systems with variable particle numbers.
These four elements, namely the system, force field, integration algorithm, and
ensemble, form the foundation of MD simulations. By carefully defining and combin-
ing these elements, researchers c an investigate the dynamic behavior, structural
changes, thermodynamics, and other properties of molecular systems, providing valu-
able insights into various scientific and engineering problems.
8.1.6 Types of MD
There are several types of MD simulations that can be employed to study different as-
pects of molecular systems. Here are some commonly used types of MD simulations:
8.1.6.1 Canonical ensemble (NVT)
In this simulation, the number of particles (N), volume (V), and temperature (T)are
kept constant. The system is typically coupled to a thermostat to maintain a fixed tem-
perature throughout the simulation. This ensemble is useful for studying the equilib-
rium properties of the system at a specific temperature.
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8.1.6.2 Isothermal-isobaric ensemble (NPT)
This simulation maintains the number of particles (N), pressure (P), and temperature
(T) at constant values. The system is coupled to both a thermostat and a barostat to
control temperature and pressure simultaneously. This ensemble is often employed to
simulate systems under near-constant pressure conditions, such as in solution or
membrane environments.
8.1.6.3 Grand canonical ensemble (μVT)
In this simulation, the chemical potential (μ), volume (V), and temperature (T)are
held constant. The grand canonical ensemble is used when simulating systems with
variable particle numbers, such as adsorption or desorption processes.
8.1.6.4 Replica exchange molecular dynamics (REMD)
REMD involves running multiple independent MD simulations, in parallel, at different
temperatures. Periodically, neighboring replicas swap temperatures, allowing the sys-
tem to explore a broader range of conformations and overcome energy barriers.
REMD is particularly useful for sampling conformational space and studying tempera-
ture-dependent phenomena.
8.1.6.5 Umbrella sampling
Umbrella sampling is a technique used to calculate free energy profiles along a spe-
cific reaction coordinate. It involves restraining the system at different positions
along the reaction coordinate and running multiple MD simulations under these re-
straints. The resulting data is then used to reconstruct the free energy landscape
using methods such as weighted histogram analysis.
8.1.6.6 Steered molecular dynamics (SMD)
SMD simulations are used to study the mechanical properties of molecules or probe
the forces required to induce conformational changes. An external force is applied to
specific atoms or groups of atoms to steer the system along a predefined path or in-
duce a specific reaction.
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8.1.6.7 Coarse-grained molecular dynamics (CG-MD)
CG-MD simulations simplify the representation of molecular systems by grouping multi-
ple atoms into a single interaction site. This approach reduces the computational cost
and allows for the study of larger time and length scales. CG-MD is often employed in
studying phenomena like self-assembly, membrane fusion, or protein folding.
These are just a few examples of the various types of MD simulations available.
Each type has its own specific purpose and application. The choice of simulation type
depends on the research question, system complexity, time and length scales of inter-
est, and available computational resources.
8.1.7 Software packages for MD
Prior to running a MD simulation, the molecular system must be prepared by adding
missing atoms, such as hydrogen atoms, which may not be present in crystal struc-
tures. Several simulation software packages now include tools for system preparation,
and newer packages have been developed to streamline this process.
There are several software packages available for performing MD simulations.
Here are some widely used software packages for MD simulations:
8.1.7.1 GROMACS
GROMACS (Groningen machine for chemical simulations) is a highly efficient and popu-
lar software package for MD simulations. It is known for its scalability and performance
on a wide range of computer architectures. GROMACS provides a comprehensive set of
tools for system setup, energy minimization, equilibration, and production MD runs. It
also offers various analysis tools to extract properties from the simulation trajectories.
8.1.7.2 AMBER
AMBER (assisted model building with energy refinement) is a suite of software tools
for MD simulations and structure analysis. AMBER provides a user-friendly interface
and wide range of features including system preparation, energy minimization, equil-
ibration, and production MD runs. It also offers advanced methods for free energy
calculations and enhanced sampling techniques.
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8.1.7.3 NAMD
NAMD (nanoscale molecular dynamics) is a high-performance software package de-
signed for large-scale molecular simulations [19]. It is particularly efficient in simulat-
ing systems with a large number of atoms, such as biomolecular complexes and
membranes. NAMD employs parallel computing techniques and is known for its scal-
ability on high-performance computing (HPC) clusters. It provides a range of features
for system setup, equilibration, production MD runs, and analysis.
8.1.7.4 CHARMM
CHARMM [20] is a versatile software package for molecular modeling and simulations.
It offers a wide range of force fields and methods for simulating various molecular sys-
tems. CHARMM provides tools for system setup, energy minimization, equilibration,
and production MD simulations. It also includes advanced features for free energy cal-
culations, protein folding, and structure refinement.
8.1.7.5 Desmond
Desmond is a MD software package developed by D.E. Shaw Research. It is specifically
designed for simulations of biomolecular systems and is known for its high-performance
capabilities. Desmond offers features for system preparation, energy minimization, equili-
bration, and production MD simulations. It alsoincludesspecializedmethodsforstudying
protein–ligand binding and membrane systems.
8.1.7.6 OpenMM
OpenMM is an open-source MD toolkit that provides a programming interface for per-
forming MD simulations [21]. It supports a wide range of force fields and algorithms,
making it flexible and customizable. OpenMM can be integrated w ith various pro-
gramming languages and used to develop customized simulation workflows and
protocols.
These are just a few examples of the many so ftware packages available for MD
simulations. Each software package has its own features, strengths, and user interfa-
ces, so the choice of software often depends on the specific research goals, system re-
quirements, and user preferences.
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8.1.8 Impact of molecular dynamics simulations on
understanding biological systems
By applying classical mechanics and mathematical algorithms to simulate the motion
of atoms and molecules over time, MD simulations provide a detailed understanding
of the behavior, interactions, and dynamics of molecular systems. This technique has
revolutionized the field of computationa lchemistryandhasbroadapplicationsin
drug discovery, material science, biophysics, and many other areas of research. MD
simulations have had a profound impact on advancing our understanding of biologi-
cal systems. They provide unique insights into the dynamic behavior, structure-
function relationships, and thermodynamics of biomolecules at the atomic level. Here
are some key impacts of MD simulations on our understanding of biological systems
8.1.8.1 Protein structure and function
MD simulations have significantly contributed to elucidating the structure-function
relationship of proteins. Simulations can explore protein folding pathways, protein
stability, and conformational changes. They have helped uncover the mechanisms of
protein–ligand interactions, enzyme catalysis, and protein–protein interactions. MD
simulations have also been instrumental in studying protein dynamics, allosteric reg-
ulation, and protein misfolding associated with diseases.
8.1.8.2 Membrane biology
MD simulations have played a crucial role in studying the properties and behavior of bio-
logical membranes. They have provided insights into membrane dynamics, lipid–protein
interactions, membrane permeability, and the formation of lipid rafts. Simulations have
also helped unravel the mechanisms of membrane transport, ion channels, and the inser-
tion and folding of membrane proteins.
8.1.8.3 Drug design and discovery
MD simulations have revolutionized the field of computer-aided drug design. They en-
able the study of drug–target interactions, ligand binding, and conformational changes
in drug targets. MD simulations can provide insights into drug-binding affinities, selec-
tivity, and off-target effects. They are used to optimize drug candidates, predict binding
modes, and guide the design of new therapeutics.
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