**3.2. Coarse grain**

In a similar direction, simulations with the two bupivacaine (BVC) enantiomers helped to elucidate the higher cardiotoxicity observed for the R-form than the S-form [56]. The effect of R-BVCs (at 1:3 molar concentration) is to disorganize the membrane (decrease the order parameters); this effect is seen for both tails [51]. This is essentially related with the empty space in the lower part of the lipid tails due to the localization of the LA and the lateral expansion of the bilayer. On the other hand, S-BVC only promotes a soft disorganization for carbons above 10 (in both tails): in this case, the localization of the LA in the interior of the bilayer

green and violet, respectively. Circles and circles are used for saturated and unsaturated chains of POPC.

**Figure 2.** (A) Electron density profiles (EDPs) of different bilayer components as a function of the membrane normal: POPC in black, water in blue and drug in red. Solid and dotted line are used for protonated and neutral prilocaine, respectively. (B) Calculated order parameter, −SCD, for plain bilayers (black); etidocaine at 1:6 and 1:3 drug:lipid ratio in

Thus, in our hands, molecular simulation of LA in model membranes was found useful to explain different aspects on the anesthesia mechanism and drug encapsulation [57]. Besides, within simulations, it was possible to explain the experimentally observed differences [49] between less (prilocaine/lidocaine) and more hydrophobic (etidocaine) isomers regarding the depth of their preferential insertion into bilayers [50], with possible implication on the increased potency and toxicity of the more hydrophobic analogs (Meyer-

compensates the effects of the lateral expansion.

Overton rule) [5, 58].

80 Molecular Dynamics

Through the reduction of degrees of freedom, CG models are useful to efficiently simulate drug delivery systems, such as liposomes, polymersome, and micelles, relieving the size and time-scale limitations of atomistic simulation but losing in details. One of the crucial factors, representing the capacity of potential drug delivery systems, is the partition coefficient of a potential drug candidate between the aggregate and surrounding water.

In particular, the encapsulation of prilocaine into liposome was studied using this approach (MARTINI-based force field) [59]. Following the atomistic results, neutral PLC was fully encapsulated in the interior part of the lipid membrane where it adopts an asymmetric bimodal distribution. Our simulation results therefore suggest that although protonation leads to a structured interaction between drug and host, hydrophobicity is the major driving force of drug encapsulation. Our results also depend on the protonated PLC initial simulations conditions [59]. This observation suggested different preparation schemes of liposomedrug complexes, leading to prilocaine trapped within vesicles that could increase overall drug encapsulation efficiency.

On the other hand, it is demonstrated that the two LA species (neutral and protonated) are present at physiologic pH, contributing together to the anesthetic effect [50, 57] and they could be important in the development of DDS. For example, in a liposomal formulation prepared at pH 7.4, while the neutral form of the anesthetic is able to quickly and efficiently cross the bilayer, the protonated form is mainly found in the water phase. Both species depend on each other: the protonated needs the neutral one in order to efficiently cross the membrane, reaching the adjacent water compartment, while the uncharged species depends on the high solubility of the protonated LA in the water phase to reach the clinically effective dose.

The protonation/deprotonation reaction cannot be directly simulated using classical MD simulation. In order to partially overcome this, we represented the physiological pH, taking into account Henderson-Hasselbach equation:

$$pH = pKa + \log \frac{[heat\,\,p]a}{[proton\,\,the\,\,t]} \tag{4}$$

and the fact that PLC apparent pKa in membranes is 7.6 [60]; values around 0.4 and 0.6 represent the molar fractions of neutral and protonated species, respectively.

In **Figure 3A**, we illustrated the results with a snapshot. In order to get an idea of how PLCs distribute inside the vesicle, we have calculated the average number of PLCs as a function of the PLC (center of mass) distance to the vesicle center. In **Figure 3**, we also show separated histograms for neutral (B) and protonated (C) PLCs. Considering that the average vesicle radius is 75Å, we can see from **Figure 3C** that all neutral PLCs are essentially found inside the vesicle and show two main peaks, in good agreement with previous results [47, 57]. On the other hand, just a small fraction (~14 molecules on an average) of the protonated PLCs are found inside the vesicle, as we can see in **Figure 3C**, and they only interact with the external monolayer of the vesicle. The results here show that the behavior of PLCs at physiological pH is essentially a combination of high and low pH: This means neutral PLCs are found inside the vesicle, whereas protonated molecules are partitioned into the external monolayer of the vesicle and water regions. However, different than at low pH, the average number of protonated PLCs inside the vesicle is lower at physiological pH (14 than 20) because of the presence of neutral molecules. In this direction, this kind of simulation could guide the LA:lipid molar ratio to enhance the loading capacity of the liposomes, depending on pH.

of block copolymer amphiphiles that in the presence of water self-assemble in an organized structures, attracting special interest due to their tunable properties for drug delivery. However, since polymersome sizes often range from 100 nm up to the micron diameter size it is difficult to simulate, even at the coarse grain level, a big polymersome. In this direction, the simulation of polymeric bilayers and small polymersomes at a CG level would make possible to study key mechanical and structural properties to better develop these kinds of drug delivery systems, as recently explored by us [12]. Moreover, these simulations are useful to shed light into the effects of the incorporation of model drugs (such as neutral and protonated

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83

Other popular drug delivery systems composed of copolymers are micelles. Several examples are found in literature [61–66]. In this regard, the encapsulation of the hydrophilic antimigraine drug sumatriptan in a polymer micelle was studied by us in a recent work [13]. A micelle composed of the pluronic F127 tri-block copolymer was simulated under different initial conditions. The main results showed that the drug essentially partitioned in the hydrophilic drug with little effect in the overall micellar structure, and size also correlated with

The times required to observe the mechanism of drug release are out of reach using MD simulations. Nevertheless, important information could be obtained by calculating, for instance, the free energy through a given path for the drug leaving the nanostructure. The idea of enhancement of the sampling of configurational space is not new in molecular simulations, and several methods such as umbrella sampling [67, 68], adaptive biasing force (ABF) method [69], the Wang-Landau algorithm [70], steer molecular dynamics [71], and metadynamics have been proposed [53]. In order to investigate the release of the drug using these methods, a reaction path should be chosen. For bilayers, the natural path is the z direction (normal to the bilayer) and for spherical nanoparticles the radius of it, as exemplified

For the case of local anesthetics, very recently, Saaedi et al. estimated the free energy profile of lidocaine and articaine in a DMPC lipid bilayer using well-tempered metadynamics simulations (Slipid force field) [53]. They estimated that the free energy between the well and the water phase was −32.9kj/mol and −25.4 kj/mol for neutral lidocaine and articaine, respectively. On the other hand, this value reduces ~20% for the protonated species. Similar results were obtained by Prates et al. (unpublished results) using ABF, who reported a free energy dif-

These calculations could be also carried out using a CG approach. Nevertheless, qualitative information could come across of these kinds of calculations. For example, Loverde et al. used Steered molecular dynamics to estimate the free energy profile of Taxol (an anticancer drug)

AT ensemble. This means that pH is a

prilocaine), as we explore in a work-in-progress study.

experimental studies.

**3.3. Drug release: free energy calculations**

in **Figure 4A** and **B**, respectively.

ference ~24kj/mol in a POPC membrane using the NPz

when pulled out from a micelle core [72].

determinant factor for the encapsulation/release of these drugs.

Similar to liposomes, polymersomes form a core-shell structure allowing us to encapsulate both hydrophilic and hydrophobic molecules. These synthetic polymer vesicles are composed

**Figure 3.** (A) and (B) Snapshots from the molecular dynamics simulations prilocaine in POPC vesicles at physiological pH. The snapshots correspond to the initial configuration and after 1 μs NVT simulation run. Neutral and protonated PLC molecules are shown in magenta-blue and in brown, respectively, and lipids are in blue and green forming the vesicle. Water sites were removed for visualization purposes. The chlorine counter ions, in red, are only shown in the last configuration. Number of neutral (C) and protonated (B) PLCs as function of the PLCs center of mass distance to the center of the vesicle.

of block copolymer amphiphiles that in the presence of water self-assemble in an organized structures, attracting special interest due to their tunable properties for drug delivery. However, since polymersome sizes often range from 100 nm up to the micron diameter size it is difficult to simulate, even at the coarse grain level, a big polymersome. In this direction, the simulation of polymeric bilayers and small polymersomes at a CG level would make possible to study key mechanical and structural properties to better develop these kinds of drug delivery systems, as recently explored by us [12]. Moreover, these simulations are useful to shed light into the effects of the incorporation of model drugs (such as neutral and protonated prilocaine), as we explore in a work-in-progress study.

Other popular drug delivery systems composed of copolymers are micelles. Several examples are found in literature [61–66]. In this regard, the encapsulation of the hydrophilic antimigraine drug sumatriptan in a polymer micelle was studied by us in a recent work [13]. A micelle composed of the pluronic F127 tri-block copolymer was simulated under different initial conditions. The main results showed that the drug essentially partitioned in the hydrophilic drug with little effect in the overall micellar structure, and size also correlated with experimental studies.

## **3.3. Drug release: free energy calculations**

PLCs are found inside the vesicle, as we can see in **Figure 3C**, and they only interact with the external monolayer of the vesicle. The results here show that the behavior of PLCs at physiological pH is essentially a combination of high and low pH: This means neutral PLCs are found inside the vesicle, whereas protonated molecules are partitioned into the external monolayer of the vesicle and water regions. However, different than at low pH, the average number of protonated PLCs inside the vesicle is lower at physiological pH (14 than 20) because of the presence of neutral molecules. In this direction, this kind of simulation could guide the LA:lipid molar ratio to enhance the loading capacity of the liposomes, depending

Similar to liposomes, polymersomes form a core-shell structure allowing us to encapsulate both hydrophilic and hydrophobic molecules. These synthetic polymer vesicles are composed

**Figure 3.** (A) and (B) Snapshots from the molecular dynamics simulations prilocaine in POPC vesicles at physiological pH. The snapshots correspond to the initial configuration and after 1 μs NVT simulation run. Neutral and protonated PLC molecules are shown in magenta-blue and in brown, respectively, and lipids are in blue and green forming the vesicle. Water sites were removed for visualization purposes. The chlorine counter ions, in red, are only shown in the last configuration. Number of neutral (C) and protonated (B) PLCs as function of the PLCs center of mass distance to

on pH.

82 Molecular Dynamics

the center of the vesicle.

The times required to observe the mechanism of drug release are out of reach using MD simulations. Nevertheless, important information could be obtained by calculating, for instance, the free energy through a given path for the drug leaving the nanostructure. The idea of enhancement of the sampling of configurational space is not new in molecular simulations, and several methods such as umbrella sampling [67, 68], adaptive biasing force (ABF) method [69], the Wang-Landau algorithm [70], steer molecular dynamics [71], and metadynamics have been proposed [53]. In order to investigate the release of the drug using these methods, a reaction path should be chosen. For bilayers, the natural path is the z direction (normal to the bilayer) and for spherical nanoparticles the radius of it, as exemplified in **Figure 4A** and **B**, respectively.

For the case of local anesthetics, very recently, Saaedi et al. estimated the free energy profile of lidocaine and articaine in a DMPC lipid bilayer using well-tempered metadynamics simulations (Slipid force field) [53]. They estimated that the free energy between the well and the water phase was −32.9kj/mol and −25.4 kj/mol for neutral lidocaine and articaine, respectively. On the other hand, this value reduces ~20% for the protonated species. Similar results were obtained by Prates et al. (unpublished results) using ABF, who reported a free energy difference ~24kj/mol in a POPC membrane using the NPz AT ensemble. This means that pH is a determinant factor for the encapsulation/release of these drugs.

These calculations could be also carried out using a CG approach. Nevertheless, qualitative information could come across of these kinds of calculations. For example, Loverde et al. used Steered molecular dynamics to estimate the free energy profile of Taxol (an anticancer drug) when pulled out from a micelle core [72].

**Author details**

**References**

738664

Juan M.R. Albano1,2, Eneida de Paula3

DOI: 10.1039/C5CS00798D

2174/1567201813666160512145800

DOI: 10.2147/AABC.S70333

DOI: 10.1002/qua.24124

Paulo, Brazil: Editora Livraria da Física; 2007

\*Address all correspondence to: monicapickholz@gmail.com

3 Biology Institute of the University of Campinas, Campinas, Brazil

and Monica Pickholz1,2\*

Molecular Dynamics Simulations to Study Drug Delivery Systems

http://dx.doi.org/10.5772/intechopen.75748

85

1 Physics Institute of Buenos Aires (IFIBA, UE UBA-CONICET), Buenos Aires, Argentina 2 Physics Department of the FCEyN (University of Buenos Aires), Buenos Aires, Argentina

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**Figure 4.** Schematic representations (A) a free energy profile over the lipid bilayer normal and (B) a micelle, as generic DDS, showing the reaction pathway.
