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Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_5443_Библиотеки_им_академика_М_И_Перельмана
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can be used to investigate the behavior of a many-body system [26]. Although the
Born-Oppenheimer approach can be used to distinguish between the wave functions
of electrons and nuclei, numerically solving the Schrödinger equation for large biolog-
ical systems is impossible. MD simulations offer an alternative, allowing the applica-
tion of classical mechanics to investigate atomistic-level difficulties. Because classical
models hold true for systems with thermal wavelength that is significantly less than
the distance between the nearest neighbors in a diluted gas model, each atom can be
viewed as a particle. Using semiempirical parameterizations and conventional effec-
tive potentials, this method can be utilized to explore biomolecular interactions and
processes. In an MD s imulation, macroscopic observables like pressure and energy
may be calculated using the position and velocity data of each particle. Chemical reac-
tions and high-frequency vibrations, however , are not included in standard treat-
ments [27].
13.6 Applications of molecular dynamic simulations
in polymeric nanoparticles drug delivery
systems
Due to their numerous benefits, including high stability, biocompatibility, and tar-
geted drug delivery, polymeric NPs have gained considerable attention in drug deliv-
ery [28]. Their effectiveness as DDSs is contingent upon their stability, self-assembly
process, interaction with biological membranes, and drug release efficiency. Simula-
tions of MD have proven to be effective methods for studying the properties of poly-
meric NPs [29]. In this compilation, recent advances in the use of MD simulations in
polymeric NP DDSs were discussed. The stability and dynamics of polymeric NPs have
been extensively predicted using MD simulations. Specifically, they can shed light on
the conformational changes and aggregation behavior of polymer chains in NPs,
which play an essential role in their stability. Zhao et al. [30], investigated the confor-
mational changes of polyethylene glycol (PEG) chains in PEGylated polylactic-co-
glycolic acid (PLGA) NPs using MD simulations. They discovered that PEG chains can
adopt various conformations, such as loops, tails, and brushes, which affect the NPs’
stability. In a separate study, Wu et al. [31] utilized MD simulations to examine the
aggregation behavior of polymeric NPs with varying surface charges [31]. The surface
charge and chain flexibili ty of the polymers were found to have a substantial effect
on the aggregation behavior. Additionally, MD simulations have been utilized to com-
prehend the self-assembly process of polymeric NPs. Specifically, they can shed light
on the kinetics and thermodynamics of the self-assembly process and identify the fac-
tors that affect the size, shape, and surface properties of NPs. For instance, Sun et al.
[32] investigated the self-assembly process of PLGA-based nanoparticles using MD sim-
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ulations. They found that the molecular weight of the polymer, the quality of the sol-
vent,andthetemperatureaffectedthesizeandshapeofthenanoparticles.Inaseparate
study, Huo Jun et al. [33] utilized MD simulations to examine the effect of hydrophobic
and electrostatic interactions on the self-assembly of polyelectrolyte-coated nanopar-
ticles. They discovered that the interactions between polyelectrolyte chains and the sol-
vent play a crucial role in the process of self-assembly. In addition, MD simulations have
been utilized to examine the interaction between polymeric NPs and biological mem-
branes. Specifically, they can shed light on the mechanism of NP–membrane interaction
and the factors influencing membrane permeability and NP toxicity. Ruirui Zhang et al.
[34] investigated the interaction between PLGA-based NPs and a lipid bilayer membrane
using MD simulations. They discovered that NPs are capable of penetrating lipid bilayer
membranes and inducing membrane thinning and deformation, which can lead to the
release of encapsulated drugs. In a separate study, Md. Zaved et al. [35] used MD simula-
tions to examine the interaction of graphene oxide (GO) NPs with cell membranes. They
discovered that the surface charge and functional groups of the GO NPs significantly af-
fected the interaction. In addition, MD simulations have been utilized to improve the
drug release performance of polymeric NPs. Specifically, they can shed light on the
mechanism of drug release and the factors that affect its rate and profile. For example,
Wang et al. [27] investigated the drug using MD simulations.
13.7 Mechanical statistics: arithmetic mean
It is a challenging area of physics to understand the relationship between the visible
characteristics of a macroscopic system and their underlying microscopic dynamics
or fluctuations [36]. Certain interparticle interactions and microscopic principles gov-
ern the behavior of subatomic particles like atoms, molecules, electrons, and nuclei.
Solving the equation of motion for a system with multiple bodies is challenging, even
with today’s computational power. Macroscopic samples with a large number of par-
ticles in a wide variety of conformations are commonly used in experiments [37]. To
determine the experimental observables in statistical mechanics, the observable A is
averaged over a large number of system copies (the ensemble). Particle positions and
velocities, which together form a multidimensional space, characte rize the system’s
microscopic state. The quantities that can be observed experimentally are the ensem-
ble averages, not the temporal averages. To reconcile this discrepancy between tem-
poral and ensemble means, scientists have turned to MD simulations, which use
thousands of atoms or beads to sample a mechanical-statistical ensemble. One of the
cornerstones of statistical mechanics is the ergodic hypothesis, which states that an
observable’s ensemble average is identical to its temporal average. The steady values
of the thermodynamic variables that characterize the state of the system are what dis-
tinguish an ensemble from another [38]. For instance, the NPT ensemble maintains a
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steady temperature, pressure, and particle count. There is a corresponding state equa-
tion for each possible state of the system, determined by these parameters. The statis-
tical ensemble is the experimental settings in MD simulations. Nevertheless, periodic
boundary conditions that limit bilayer undulations can affect the impression of sur-
face tension in simulations. As a result, NPT ensembles, in which the simulation box
is completely relaxed, are preferred for such systems.
13.8 Regression model
To analyze the connection between a dependent and an independent variable, statisti-
cians employ regression models. Given the intrinsic features of the polymer and the
physicochemical conditions of the system, regression models may be used to predict the
quantity of drug uptake by the polymer in the context of drug delivery. In this section,
we introduce a regression model that links the interaction energy of a polymer with the
drug to the extent to which the polymer may absorb the drug [39]. The model is depicted
in Figure 13.2(A) and is founded on the resultsofpreviousexperiments.Thepercentage
of medication absorption can be predicted using the linear equation %Drug uptake=
0.0218IE – 8366.9. The model is a good fit for the data as shown by the R
2
value of 0.65
and the F
2
value of 30.25 (P = 0.001). Figure 13.2(B) shows the various ways in which poly-
mers and pharmaceuticals interact with one another. Chitosan has the weakest interac-
tion with doxorubicin, while the Gantrez AN119 polymer had the strongest interactions
with all three drugs. At intermediate concentrations, the polymers alginate, sodium algi-
nate, alginate, and Eudragit RSPO and Eudragit L100 interact with the drugs.
The results show that polymer selection can have a major impact on the pharma-
cokinetics of a drug. The degree to which a polymer dissolves in water is a crucial
factor that can affect how well a drug is administered. In the research by Plazinska
et al. [40], hydrophilic polymers like chitosan, sodium alginate, and alginic acid exhib-
ited hydrophilic interactions, while hydrophobic polymers like Gantrez, ERSPO, and
EL100 exhibited a hydrophobic effect due to polarization effects. These results are
consistent with previous studies and highlight the importance of taking into account
the physicochemical properties of polymers when developing DDSs. Interactions be-
tween biopolymers and environmental parameters, including temperature, pH, and
ionic strength, can affect the drug’s stability, transport, and release. Complex chemis-
try in polymer carrier systems must be developed for real patient benefit. The devel-
opment of more effective drug delivery methods can be aided by our study of drug
interaction and absorption by very biocompatible and biodegradable polymer NPs. As
a result, regression models are useful tools for analyzing the connection between
medication uptake and polymer properties. New research provides important under-
standing of the factors that affect drug uptake by polymers and highlights the impor-
tance of considering polymers’ physicochemical properties when developing DDSs.
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13.9 Structural optimization of periodic systems
in molecular dynamics
When looking into the behavior of polymeric NPs in DDSs, MD simulations are com-
monly used. Polymeric NPs’ structures are optimized in these simulations to reduce
the total energy of the system [41]. To obtain the most stable structure in MD simula-
tions, structural optimization of periodic systems requires a number of steps, includ-
ing the choice of a suitable force field, the determination of the initial structure, and
the application of optimization algorithms. The choice of a suitable force field is a cru-
cial part of structural optimization in MD simulations. The interactions between par-
ticles in a system are modeled mathematically by what are called “force fields” [42].
They may incorporate terms for bond stretching, angle ben ding, torsional rotation,
and nonbonded interactions like van der Waals and electrostatic interactions, based
on empirical parameters derived from experimental data. The precision required and
the characteristics of the polymeric NP system under study dictate the choice of force
field. The next step in structural optimization is to establish the starting structure of
the polymeric NP. Creating a foundational structure from either experimental data or
Figure 13.2: (A) Interaction energy (IE) versus drug efficacy scatter plot. Embedded dots Confidence
interval of 95% (permission obtained for the reuse of the figure; order number 501803212). (B) Structure
of how drugs and polymers interact with each other (orange dashes show non-hydrogen bonds).
Interaction of (a) doxorubicin with Gantrez AN119, (b) gliclazide with Gantrez AN119, and (c) silymarin with
Gantrez AN119. Green Drug, blue polymer (permission obtained for the reuse of the figure; license
number: 5517300461669).
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computational models is the first step. The initial structure is then optimized for en-
ergy to yield a more stable arrangement. In order to find the configuration with the
lowest energy, energy minimization algorithms like steepest descent, conjugate gradi-
ent, and quasi-Newton must be used. It is possible that further iterations of optimiza-
tion will be required to reach the most stable configuration after the initial structure
has been optimized. Advanced optimization algorithms like simulated annealing, ge-
netic algorithms, and basin hopping may be used at this stage. Genetic algorithms
mimic natural selection processes to optimize the structure, while simulated anneal-
ing involves gradually cooling of the system to achieve a more stable configuration.
The goal of “basin hopping” is to find the most stable state of the system by analyzing
its potential energy landscape. Polymeric NPs in DDSs can be studied using MD simu-
lations’ structural optimization of periodic systems. It can be used to improve drug
targeting, decrease drug release, or maximize drug loading in polymeric NPs. Poly-
meric NPs’ structure and behavior can be studied in relation to environmental factors
like temperature, pH, and ionic strength. In conclusion, structural optimization of pe-
riodic systems in MD simulations is necessary for studying the behavior of polymeric
NPs in DDSs. The most stable configuration can be achieved through careful consider-
ation of the force field, the determination of the initial structure, and the application
of optimization algorithms. Maximizing the efficiency of DDSs, structural optimization
of polymeric NPs can yield important insights into their behavior.
The computational method of structural optimization of periodic systems is used to
optimize the molecular model of a polymer prodrug. It entails simulating the molecular
structure to identify any illogical structures and optimizing them to achieve the lowest
energy state while maintaining equilibrium. This method facilitates the development of
more efficient and targeted DDSs. The structural optimization of periodic systems was
used to optimize the molecular model of the mPEG-PLGA-SS-DOX prodrug in light of the
findings of Junxu Hao et al., 43. The optimization of the molecular model of the polymer
prodrug mPEG-PLGA-SS-DOX is depicted in Figure 13.3A. The simulation aided in opti-
mizing the molecule’s unreasonable structure, and when the energy reached the lowest
level while maintaining equilibrium, structural optimization step was complete. The pe-
riodic system’s annealing produced results regarding the cell, density, energy, and tem-
perature. Molecular structure optimization refers to the procedure of determining the
atomic arrangements within a molecule that are both stable and energetically prefera-
ble. The atoms’ behavior in the molecule is simulated, and the least-energy configuration
is found using this technique. The given example illustrates (Figure 13.3B) a molecule in
an unstable, high-energy state, with an initial total energy of 3,823.448309 kcal/mol. The
atom positions were then optimized by the simulation to decrease the overall energy of
the system. The system’s energy gradually decreased throughout the simulation, eventu-
ally reaching a minimum of 279.604513 kcal/mol. When a molecule reaches this lower-
energy state, it has settled into a configuration that is more stable. The molecule under-
went a series of optimization steps until it reached a stable equilibrium in which the
system’s energy was minimized. When convergence was achieved, it was determined
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Figure 13.3: (A) System composed of mPEG-PLGA-SS-DOX/DOX, mPEG-PLGA/DOX, mPEG-PLL-SS-DOX/DOX, and mPEG-PPHE-SS-DOX/DOX. (B) Findings from an
optimization of the molecular geometry of mPEG-PLGA-SS-DOX. Energy and unification are the focus of this spirited expression (permission obtained for the
reuse of the figure; license number: 5516910045708).
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that no further structural changes were necessary and the optimization was complete.
Further evidence depicts the optimization procedure’s output, which most likely repre-
sents the final atomic positions and configuration of the molecule. The best possible
structure would be the one with the lowest possible energy and the highest stability.
Drug design, materials science, and computational chemistry are just some of the fields
that could benefit from this approach. By fine-tuning molecular structures, scientists can
foresee how molecules will behave, information that can be used to create better medi-
cines, materials, and technologies.
13.10 Challenges in molecular dynamic simulations
of polymeric nanoparticles drug delivery
systems
Polymeric NPs in DDSs are frequently made up of thousands of atoms and molecules.
Modeling such large systems necessitates a significant amount of computational
power and lengthy simulation times, which can be problematic for MD simulations.
Sachin et al. [44] for example, used MD simulations to study the self-assembly of poly-
meric NPs in the presence of surfactants. The simulation times required to observe
the self-assembly process increased with system size, making it difficult to accurately
model large systems. MD simulations rely on force fields to describe the interactions
between atoms and molecules in polymeric NPs. Force fields, on the other hand, have
limited precision, particularly in polymeric systems. Recent research has emphasized
the importance of improving the precision of force fields for polymeric NPs. Hao et al.
[30] investigated the accuracy of different force fields in simulating the interaction of
PLGA NPs with cell membranes. They discovered that some force fields produced un-
realistic results and recommended that PLGA NP force fields be developed further.
Polymeric NPs are frequently surrounded by water molecules in DDSs, which can af-
fect their behavior and properties. However, modeling the water–polymer interface
in MD simulations is difficult, especially for polymeric NPs. For example, Chen et al.
[45] used MD simulations to investigate the stability of PEGylated PLGA NPs in water.
They discovere d that the hydration layer surrounding the NPs was highly dynamic
and affected the stability of the NPs, highlighting the need for a more accurate model
of the water–polymer interface. Simulations of polymeric NP DDSs using MD necessi-
tate a significant amount of computational power, particularly for large systems with
long simulation times. High-performance computing resources, such as supercom-
puters and graphics processing units (GPUs), are frequently required to perform MD
simulations effectively. Using MD simulations, Le Grand et al. [46] investigated the ef-
fect of NP size and surface charge on their interaction with cell membranes. They dis-
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covered that GPU-accelerated MD simulations were necessary for accurately simulat-
ing large systems with long simulation times.
13.11 Modeling the mPEG-PLGA-SS-DOX/DOX micelle
generation process
This section provides a model for the formation of polymer micelles in water utilizing
mPEG-PLGA-SS-DOX/DOX. The simulation showed that the polymer molecules, through
both hydrophilic and hydrophobic interactions, clustered together to form spheres.
These micelles reorganized themselves into a stable core–shell polymer micelle struc-
ture. DOX was found to be located in the middle as the hydrophobic core, PLGA envel-
oped DOX, and mPEG formed the outermost hydrophilic shell to maintain the stability
of the system, as determined by an examination of their relative positions inside the
micelle. The results of the simulation verify the interaction parameters and system con-
figuration necessary for the formation of micelles in an aqueous mPEG-PLGA-SS-
DOX/DOX copolymer solution (Figure 13.4).
Figure 13.4: mPEG-PLGA-SS-DOX DPD modeling. (a) The structure of the simulation at various times. (b) A
micelle’s shape is identical to a ball. (c) DOX, PLGA, and mPEG concentration profiles (permission obtained
for the reuse of the figure; license number: 5516910045708).
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13.12 Atomistic simulations
This section w ould elaborate on the difficulty of utilizing atomistic simulations to
fully model nano-carriers such cyclodextrins, calixarenes, and dendrimers. Hence, sci-
entists have turned to alternative methods, such as using simplified models, focusing
on the interaction of a particular medication, or treating bilayers as a stand-in for lip-
osomes, polymersomes, and niosomes. The text elaborates on the latter method, de-
scribing how simulations can be used to learn more about drug partition in various
bilayer regions and discover how pharmaceuticals interact with lipids. As the chapter
progresses, it explains how simulations can be used to influence the development of
DDSs for the treatment of both acute and chronic pain, and specifically how local
anesthetics (LAs) interact with membranes [47]. Simulations have demonstrated that
neutral LAs partition in the hydrophobic portion of the bilayer, while protonated LAs
segregate in the lipid head/water interface and water phase, demonstrating that LAs
exhibit distinct ionization states, depending on the pH. Computer simulation s have
also revealed that different LAs are distri buted in the bilayer in distinct ways, with
more hydrophobic LAs encouraging greater lipid chain disorder. The tilt angle of the
lipid chains and the trans-gauche distribution of chain dihedrals are two factors that
can be employed in simulations to determine the order parameter. The impact of
guest molecules, such as LAs, on lipid packing can be assessed experimentally by mea-
suring the carbon–deuterium segmental order parameter along the lipid chain.
13.13 Coarse grain
CG MD simulations are discussed herein as a tool for studying DDSs [48]. By reducing
the degrees of freedom, CG models can efficiently simulate systems like liposomes, poly-
mersomes, and micelles, overcoming the size and time-scale limitations of atomistic sim-
ulation at the cost of some details. Potential DDSs are largely characterized by their
ability to effectively partition a drug candidate between the aggregate and the surround-
ing water. Liposomal encapsulation of prilocaine was studied using this technique. Drug
encapsulation seems to be driven by hydrophobicity, while protonation leads to a more
ordered interaction between the drug and the host [49]. At physiological pH, both the
neutral and protonated LA species are present, each contributing to the anesthetic effect
and potentially playing a pivotal role in future DDS research. This section provides a
more in-depth analysis of why protonation/deprotonation reactions cannot be directly
simulated by means of classical MD simulations. That is why the Henderson–Hasselbach
equation was used to represent pH in a body. The average number of PLCs calculated as
a function of PLC distance from the vesicle center is also presented in this passage for
context [50]. The passage then moves on to discuss polymersomes, which, due to their
core–shell structure, can house both hydrophilic and hydrophobic molecules. Block co-
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polymer amphiphiles make up the bulk of these synthetic polymer vesicles, and they
form a coherent structure when exposed to water. To better develop these types of
DDSs, CG-level simulations of polymeric bilayers and small polymersomes can be used
to investigate key mechanical and structural properties [51]. Micelles, which are made of
copolymers and are used as DDSs, are discussed to round out the passage. CG MD simu-
lations were used to study the encapsulation of the hydrophilic antimigraine drug suma-
triptan in a polymer micelle, and the results showed that the drug partitioned in the
hydrophilic drug with negligible effects on the overall micellar structure and size. Drug
delivery systems can be studied with CG MD simulations, which can then be used to in-
form the creation of more efficient drug delivery strategies.
13.14 Free energy calculations for drug release
It is often difficult to observe the mechanism of drug release due to the long timescales
involved in molecular simulations. However, there are paths to acquiring essential de-
tails about the process. To determine how much free energy the drug needs to leave the
nanostructure is one such approach. Several methods, such as the umbrella sampler,
the adaptive biasing force method, the Wang–Landau algorithm, steer MD, and metady-
namics, have been proposed to increase the accuracy with which the configurational
space is sampled [52]. Choosing a reaction path is essential for studying drug release
using these techniques. The z-axis (normal to the bilayer) is the most direct route for
molecules in a bilayer, while the NP radius is the most direct route for spherical NPs.
Using well-tempered metadynamic simulations, Saaedi et al. estimated the free energy
profile of lidocaine and articaine in a DMPC lipid bilayer. For neutral lidocaine, they
measured a free energy of –32.9 kJ/mol between the well and the water phase, while for
articaine, they measured –25.4 kJ/mol . On the other hand, protonated species have
about 20% lower free energy. Similar findings were reported by Prates et al. using the
ABF method; they found that the NPzAT ensemble produced a free energy difference of
around 24 kJ/mol in a POPC membrane [53]. The significance of pH in the encapsulation
and release of these drugs is demonstrated. These computations could also be done
using a CG method. Computer simulations may only provide qualitative information,
however. The anticancer drug Taxol’s free energy profile during its release from a mi-
celle core was estimated by Loverde et al. using steered MD.
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