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Molecular dynamics simulations of Oxprenolol and Propranolol in a DPPC lipid bilayer
Accepted Manuscript Title: Molecular dynamics simulations of Oxprenolol and Propranolol in a DPPC lipid bilayer Author: Khaled Azizi Mokhtar Ganjali Koli PII: DOI: Reference:
S1093-3263(16)30009-2 http://dx.doi.org/doi:10.1016/j.jmgm.2016.01.009 JMG 6653
To appear in:
Journal of Molecular Graphics and Modelling
Received date: Revised date: Accepted date:
9-8-2015 22-1-2016 23-1-2016
Please cite this article as: Khaled Azizi, Mokhtar Ganjali Koli, Molecular dynamics simulations of Oxprenolol and Propranolol in a DPPC lipid bilayer, Journal of Molecular Graphics and Modelling http://dx.doi.org/10.1016/j.jmgm.2016.01.009 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Molecular dynamics simulations of Oxprenolol and Propranolol in a DPPC lipid bilayer Khaled Azizi*, Mokhtar Ganjali Koli Department of Chemistry, University of Kurdistan, Sanandaj, Iran (Email: [email protected]) To whom correspondence should be addressed: Tel: ++98-871-6624133 Fax: ++98-871-6660075 Email: [email protected]
1
Graphical abstract
Highlights Passing across the membrane for Propranolol is easier than Oxprenolol. The electrostatic potential is influenced effectively by the concentrations of drugs. Oxprenolol and Propranolol have the same effect on the water penetration in membrane.
Abstract Extensive microscopic molecular dynamics simulations have been performed to study the effects of
tow
β-blocker
drugs
(Propranolol,
Oxprenolol)
on
fully
hydrated
dipalmitoylphosphatidylcholine (DPPC) in the fluid phase at 323 K. Simulation of 4 systems 2
containing varying concentrations of drugs was carried out. For the purpose of comparison, a fully hydrated DPPC bilayer without drugs was also studied at the same level of simulation technique which has been done on 4 other systems. The length of each simulation was 100 ns. The effects of concentrations of both drugs were analyzed on lipid bilayer properties, such as electrostatic potential, order parameter, diffusion coefficients, and hydrogen bond formation, etc. Penetration of water in the bilayer system was also investigated using radial distribution function analysis. Efficacy of varying concentrations of both drugs has no significant effect on P-N vector. Consistent with experimental results, by increasing the concentration of Propranolol, the thickness of the bilayer was increased. Keywords: Lipid bilayers; β-blocker; molecular dynamics simulation; membrane.
1. Introduction The pharmacological action of a drug is a complex phenomenon. Among the factors that have an important impact on this complexity, a special place should be assigned to drug-membrane interaction. This is due to the fact that the interactions between drugs and bio-membranes play a key role for pharmacokinetic parameters such as absorption, distribution, metabolism and elimination [1, 2]. Therefore, many efforts have been devoted to understanding the nature of interactions between drugs and bio-membranes [3]. Primary partitioning is the pre-requirements condition for permeability of drug molecules through bio-membranes. Typically, a lipophilicity evaluation is built with bulk phase measurements of drug partition coefficients between an aqueous and organic phase (e.g., n-octanol). The basic assumption is that, the lipid bilayer membranes could be effectively represented by bulk phase. This assumption has been brought into question by several investigators [4–6]. The plasma membrane is the most important
3
membrane for drug administration, through which drugs must penetrate to achieve the internal milieu of the target cells [7]. The behavior of the drug in the membrane is controlled by several factors that among these shape, size, hydrophobicity and pKa are the most influential. In order to improve the efficacy and viability of many drugs, understanding the fundamental interactions between the drug and lipid have a special importance [8]. Since Phosphatidylcholines (PC) bilayers are the most abundant lipids in mammalian membranes, they typically used as simple membrane models, although phosphatidylserines, phophatidylethanolamines, sphingomyelins, and cholesterol are also present [9]. β-Blockers are known as the most efficacious agents for the treatment of heart failure, certain types of arrhythmia, hypertrophic obstructive cardiomyopathy, as well as prior myocardial infarction [10]. Propranolol (Fig. 1a) is a non-cardioselective βblocker and a prototype β-adrenoreceptor blocking agent, which has earned far-reaching utilization in the treatment of angina pectoris, cardiac dysrhythmias and hypertension [11,12]. It has been specified that (R) -(+) -enantiomer has a membrane stabilizing effect [12], therefore the membrane activity of Propranolol may be important in study of its toxicity following overdose [11]. Oxprenolol (Fig. 1b) is a non-selective β-Blocker, which has low membrane stabilizing activity and medium intrinsic sympathomimetic activity. Because of its sympathomimetic activity, Oxprenolol displays less negative ionotropic effect than Propranolol. Consequently, Oxprenolol may help for treatment with a beta adrenoceptor antagonist despite peripheral vascular disease or heart failure. Owing to extensive hepatic metabolism, its bioavailability is low and half-life is short [13,14]. Regarding to the above-mentioned, many investigations including studies of the effects of Propranolol and Oxprenolol on the lipid membranes have been performed. The results of differential scanning calorimetry (DSC) studies indicated that the dimyristoylphosphatidylcholine (DMPC) thermotropic phase behavior is modulated by these
4
compounds as follows:
Propranolol > metoprolol = oxprenolol > nadolol [4]. Some of
thermodynamic and structural features of Propranolol-DPPC liposomes interactions were investigated by DSC and X-ray diffraction [11]. The interactions between β-blockers (Oxprenolol, Propranolol, and acebutolol) and palmitoyloleoylphosphatidylcholine (POPC) have been studied by Time-Dependent Fluorescence Shift (TDFS) and Generalized Polarization (GP). It has been shown that by increasing β–blocker concentrations, the lipid bilayer at the glycerol and head group level is significantly rigidifies. The effects are significantly stronger for Propranolol than those of the two other β-blockers [15]. Molecular dynamics simulations are powerful tools that may provide valuable complementary to experiment information about details of interactions between the drug molecules and bio-membranes [8,16]. Despite the enormous development on computer simulations of lipid bilayers and utilizing GROMACS package for MD simulations [17–20], investigations on computer modeling of β–blockers in lipid bilayer are rather scarce. The nonspecific membrane effects (NME) of Oxprenolol and Propranolol β-blockers have been proven [20]. Accordingly in this study neutral form of these βblockers were selected and studied by molecular dynamic simulation method. In addition, the effects of these β–blockers on dipalmitoylphosphatidylcholine (DPPC) lipid bilayer, shown in Fig. 1c, were compared. 2. Methodology 2.1. Molecular structures The molecular structures of DPPC Lipid and β–blockers are shown in Fig. 1. As can be seen, two etheric bonds in Oxprenolol against an attached phenyl ring and one etheric bond in Propranolol could be considered as the most obvious structural differences between the two drugs. In this study, five different systems were chosen to carry out the simulation study. The 5
first system which comprises only lipid and water molecules was utilized as a reference. The second one includes 128 DPPC lipids (64 per leaflet) with one Propranolol molecule in each leaflet, within the bilayer. Another system contains one Oxprenolol molecule in each leaflet. In two system remained, Propranolol and Oxprenolol was just doubled in the same manner. All of these systems were hydrated by 4000 water molecules. Fig. 2 shows the initial configurations of DPPC lipids, water molecules and two drug molecules within the simulation box. As can be seen for both the Propranolol and Oxprenolol, somewhere between the head and tail of DPPC lipids are selected as the initial position of the drug molecule. For lipid bilayer and β–blockers molecules, the united atom model base on the GROMOS force field with modification by Berger was applied [21,22], and for water molecules, the simple point charge model (SPC) was used [55]. The topology and coordinates files of β–blockers based on the GROMOS 53A6 force field were received from the ATB server [23,24]. 2.2. Simulation details In this study, two different types of molecular dynamics simulation were performed. The first study which is run over five different systems was conducted to investigate the behavior of the drugs in the lipid bilayer. The second simulation was set up for PMF calculations in systems containing the 128 DPPC lipids and one of Propranolol or Oxprenolol molecules. All simulations were executed in the NPT ensemble using GROMACS4.5.5 [25]. The systems were maintained at a constant temperature of 323K using the Nose-Hoover thermostat with a coupling time of 0.5 ps [26]. All the bond lengths were constrained with LINCS algorithm [27]. The pressure was held constant at 1 bar by compressibility 4.5 × 10 -5 bar-1 and by coupling the simulation cell to a Parrinello-Rahman barostat, with coupling time constant 2 ps which was used semiisotropically with tow degree of freedom, one in XY direction and another in Z direction [28]. To integrate 6
Newton’s equations of motion, the leap-frog algorithm with time step 2 fs was applied [29]. Coulomb and Van der Waals interactions were cut-off at 1.2 nm. Long-range electrostatic interactions are important for the true explanation of the lipid bilayer, hence, for long range electrostatic interactions the Particle Mesh Ewald was applied [30]. Starting structure for DPPC lipid bilayer was obtained from the Biocomputing group at the University of Calgary (http://moose.bio.ucalgary.ca/). Periodic boundary conditions were used in all three dimensions. In all systems, steepest descent energy minimization was used to remove undesirable atomic contacts and calm down the water molecules within systems [31]. At first, positions of drugs were restrained and equilibration conducted in the NVT ensemble for 2 ns and then followed by equilibration in NPT ensemble for 8 ns. After equilibration steps, all simulations were run for 100 ns from their starting conditions and coordinates of the atoms. The Grid MAT-MD program [32] was used to measure the thickness of the DPPC membrane and the area per lipid (APL) head group of each lipid forming the bilayer. For free energy calculations, in the biased MD simulation, pre-equilibrated simulation starting frames were generated by pulling the center-ofmass (COM) of drugs against the COM of DPPC lipid bilayer. Drugs was pulled along the bilayer normal (the z-axis) by using a pulling force constant of 1000 kJ mol−1 nm−2 and pulling rate of 0.01 nm ps−1. Pulling exerts a harmonic potential on the drug molecule and moves the potential center with a given pull rate. From the pulling simulation, the snapshots were obtained and among them 18 windows (~0.2 Å apart) along the z-axis, ranging from the bulk water (Z= ±3.5 nm) to the middle of the DPPC lipid bilayer (Z= ± 0.0 nm), were selected. Each window was explored in a separate simulation (10 ns run time each) to avoid any drug interactions. 3. Results and Discussion 3.1. Mass Density 7
Computational mass density of various groups is shown in Fig. 3. Water and lipid density changes are in agreement with whatever reported before [33,34]. As seen here, the maximum of the density of Oxprenolol and Propranolol molecules is very close to each other and located at approximately 1(nm) from the center of membrane. In this area, increasing the number of drugs from 2 to 4, shows a decrease in the DPPC density towards the reference system. Moreover, the maximum density of both drugs is located in the middle layer of hydrocarbon chains of lipid tail. Since the total density has been the same at all simulated systems, it is not presented here; and the water density that indicates equal distribution is shown only for the reference system. 3.2. Potential of mean force Partitioning of the drug throughout the lipid bilayer membrane can be described by free energy (∆G) profile along the normal axis of membrane, which is also known as PMF [56]. In this study, PMF was calculated by using the umbrella sampling method. The forces exerted on the drugs were analyzed, and the free energy profile was calculated using weighted histogram analysis method embedded in GROMACS [57, 58]. Statistical errors were estimated using Bayesian bootstrap analysis (N = 200). Fig. 4 shows the free energy profiles of tow β-blockers, from which we can see that there exists an obvious minimum for Oxprenolol whereas the energy curve is flat for Propranolol. The obvious free energy minimum of Oxprenolol corresponds to distance of 1.0 nm between the COM of drug and the bilayer center, suggesting that Oxprenolol tend to localize in this region. The free energy minimum of Propranolol, occurring at a flat area around -1.0 to +1.0 nm and near the bilayer center, is more negative than that of Oxpreolol. The pictures given by the snapshot of systems in their final configurations, reported in Fig. 5. In agreement with the ∆G profile along the normal axis of membrane, while Oxprenolol chooses areas near the head of DPPC, Propranolol prefers to be in the area near the center of membrane. 8
It seems that because of additional ring, in comparison with Oxprenolol, Propranolol has less polarity and more lipophilicity, and hence is more favorable that is located at the deeper regions of membrane. On the other hand, Oxprenolol because of an ether chain that exerts more polarity and less lipophilicity on the molecule, is placed in the nearby of the polar head group. Comparing of energy barriers in bilayer center for two drugs indicate that it is more difficult for Oxprenolol to pass across membrane. 3.3. Area per lipid and bilayer thickness The area per lipid (APL) amount of all simulated systems is shown in Table 1. As seen in this table, value of APL for reference system is anticipated to be equivalent to 62.7
that is within
range of previously reported amounts [35–39]. It is also in excellent agreement with experimental amount of 62
at 323 K temperature and 1 bar [40]. It is noteworthy that
implementation of 2 units of each of Propranolol and Oxprenolol has approximately similar effect on the increasing of APL of DPPC membrane with respect to reference system (1.70 and 1.36
for Oxprenolol and Propranolol, respectively). However, for 4 unit implementation the
effect is entirely different. While for additional of 4 unit of Propranolol, the APL of DPPC membrane is increased considerably (3.18
with respect to reference system), by adding 4
units of Oxprenolol its value is increased by small amount (0.12
). This effect can be
explained on the basis of existing more aromatic rings in Propranolol and their establishment amongst the lipids. For Oxprenolol, the increase of density leads to the increase of hydrophobic chains and reinforcement of strong attractive interactions between lipid chains, that in turn, remarkably decreases the upward steep of APL. The thickness value of 3.8 nm for reference system is in good agreement with experimental value of 3.9 nm [35,41]. According to Table 1, by adding 2 molecules of Propranolol or Oxprenolol, the thickness of the membrane has 9
increased almost the same for both drugs in the compare with the reference system. An increased number of drug molecules from 2 to 4, leads to a more chance of increasing in the thickness of the membrane. This effect is more obvious for Propranolol-including systems. The increase in thickness of the DPPC membrane by increasing the concentration of Propranolol is in agreement with experimental observations and is in consistent with the increase of APL [11].
3.4. Deuterium order parameter It is found that the movements of lipid chains in a bilayer membrane, including rotation around chemical bonds or lipid axis, trans/gauche isomerization, lateral diffusion and etc. Have a completely dynamic nature [3]. The effect of these configurationally variations can be evaluated by deuterium order parameter which is one of the important quantities for the description of microscopic structure of lipid bilayer [39,42]. On the other hand, deuterium order parameter for each group of CH2 (CD2) can be measured experimentally through nuclear magnetic resonance (NMR) investigations. The order parameter of the lipid chain is given by the following equation [3]: S
3cos θ
1
1
Where θ is the angle between a CD bond (in experimental) or a CH bond (in simulation) and the bilayer normal axis (Z). In this equation the bracket is implying time averaging over two bonds at each group of CH2 in all lipids. Order parameter of SN1 and SN2 chains of DPPC lipids are shown in Fig. 6. As seen in this figure, the calculated values for reference system, are in acceptable agreement with experimental results as well as previous simulation findings [22, 43, 44]. An explanation of the differences between calculated and experimental order parameters are 10
difficult. However, this difference is mainly attributed to subtle defects in hydrocarbon chain potential, incomplete sampling of the chain conformations and/or long time-scale lipid stumble [45]. As seen in Fig. 6, for SN1 chain, the presence of 2 units of Oxprenolol and Propranolol, has led to slight increase and decrease in order parameter, respectively. In SN2 chain, the circumstances are different; while the presence of Oxprenolol leads to more severe increasing in order parameter, except for the first few carbons in chain, the Propranolol does not establish a significant change in lipid order. For the system containing 4 units of each drug, the order parameter of SN1 chain has been increased by slightly more effect for Oxpernolol. In the case of SN2 chain, the increasing in order parameter which was imposed by the presence of Oxprenolol is remarkably higher than Propranolol. These observations are expected because it is shown that various chemical compositions in membrane have different effects on order parameter of lipid chains [16,60]. As seen in Table 1, the increase of both Propranolol and Oxprenolol has led to slower diffusion in lipids. It should be remembered that in the case of the neutral form of Articaine, an increase in the order parameter of lipid bilayers corresponds to faster diffusion in lipids [16]. It seems that the membrane fluidity changes are more complicated to be interpreted based on the order parameter changes. Therefore, more information on orientation of drug molecules within a bilayer should be made available. NA-AC and NB-CB vectors were selected as long axis associated to Oxprenolol and Propranolol, respectively. These distributions are shown in Fig. 7 in which the zero angles correspond to the direction out of the bilayer. From the angular distribution, one can see noticeable differences in the orientation of Propranolol and Oxprenolol. As can be seen, while the most probable angle for the system containing 2 units of Oxprenolol is
77.5 , for 4 units, and a wide distribution between
11
65 until
105
have been obtained. The value of angle for the system containing 2 and 4 units of Propranolol are 99.8 and
86.7 , respectively.
3.5. Radial distribution function It is well known that the APL can be influenced by interactions between the head group and water molecules [46]. Radial distribution function (RDF) of water molecules in membrane was applied to gain a better understanding of effect of type and concentration of drugs on water penetration, lipid hydration, and mutual water-lipid interactions. The RDFs of water oxygen around the phosphate oxygen for reference and systems including various densities of both drugs are shown in Fig. 8. As can be seen, the RDF schemes of the systems are nearly the same. For all RDFs the first minimum is occurred at 3.2 Å indicating the hydrogen bonding between water and phosphate oxygen; and the second maximum for all systems is located at 5.0 Å. Coordination numbers which are obtained from the appropriate integration of RDF up to the first minimum, are shown in Table 2. For all systems containing Oxprenolol and Propranolol, the first maximum peak is higher than reference system. This can be treated as the increase in water penetration into the head groups in the presence of Oxprenolol and Propranolol molecules. For systems containing 2 units of the drugs, the peak in the presence of the Oxprenolol is higher than Propranolol while for systems containing 4 units a trend reversal is observed that the higher peak belongs to Propranolol. As a result, the increase of APL in drug containing systems, can be attributed to an increase in water penetration and coordination number, (Table 2). The apparent increase in coordination number of 4 units containing Propranolol with respect to Oxprenolol, can be mentioned as an acceptable reason for difference in APL values of systems, (Table 1). 3.6. Hydrogen bonds
12
Regarding the ability of the hydrogen bonding formation by both β-blocker and polar head groups of lipids, a competition between these molecules for hydrogen bonding formation with water molecules is inevitable. Therefore, the formation of different types of hydrogen bonds between β–blockers and lipid molecules, β–blockers and water molecules, lipids and water molecules, and also between β–blocker molecules with each others, has been studied. At the present study, hydrogen bonds are determined by a maximum distance of 3.5 Å between acceptor and hydrogen and also maximum angle of 30 between acceptor-hydrogen and hydrogen- donor vectors [47]. The results of various types of hydrogen bonds in simulated systems are collected in Table 3. According to this table, in systems including 2 β–blockers, the number of hydrogen bonds between DPPC and water are slightly more than the reference systems. This result is in full agreement with more penetration of water into the membrane, which mentioned in the previous section. Moreover, the number of hydrogen bonds between water and DPPC in Propranolol containing system is more than Oxprenolol. As can be seen from Table 3, for systems containing 4 β–blockers a similar situation is existed, however, here extend of the hydrogen bonding formation for Propranolol containing systems are somewhat more evident than for Oxprenolol. This is in full agreement with more water penetration into the bilayer. For system containing Oxprenolol, due to low penetration of water, the number of hydrogen bonds is similar to the reference system. For 2 units of drug containing system, the total numbers of hydrogen bonds terminated to Oxprenolol (either from DPPC or water) are remarkably higher than Propranolol. As seen, with the increasing of the number of drug units from 2 to 4, the number of hydrogen bonds of β–blockers with DPPC and water will become almost double. The superiority of Oxprenolol on Propranolol in formation hydrogen bonding, may be attributed to higher number of oxygen atoms in Oxprenolol and the large amount of negative electrostatic
13
charge on OA2 (Fig. 1b). It seems that the larger number of hydrogen bonding in Oxprenolol including system can be considered as strong reason for lower diffusion of drug in bilayer membrane. 3.7. Lateral diffusion It is shown that many cell signaling processes related to membrane, are under the control of lipid molecules diffusion, an indicator of lipid viscosity [33]. Therefore, we calculated the lateral diffusion coefficients of β–blockers and lipids in all simulated systems. In this study, MD trajectories are applied for calculating the mean square displacement (MSD) of single molecules and the lateral diffusion coefficient is calculated by the Einstein formula in two dimensions in the following form [48]: D
where
|∆r t |
lim →
1d 4 dt
|∆r t |
2
is the MSD in XY plane during the time t, starting from the initial time t0
and D stands for the lateral diffusion coefficient. Averaging is taken over all molecules and over all initial time t0. Time dependence of lateral MSD of Propranolol and Oxprenolol in DPPC is shown in Fig. 9. In practical calculations, the limit of the derivative in equation 2 is calculated from the slope of linear region of the MSD vs. time curve. At shorter times, due to non-Brownian character of the diffusion a non-linear character may be exerted on the MSD curve. As times approach to the total simulation time, the poor statistics led to large fluctuations in MSD curves [16]. Here in, the time interval 5–35 ns, where the MSD curves show behavior most close to linear, is used for the slope fitting. Lateral diffusion coefficients calculated for drug molecules and lipids are listed in Table 1. As seen, the value of diffusion coefficient, DL, for reference system is in very good agreement with experimental result (that is around 16 14
10
) [49].
Furthermore, insertion of β-blocker molecules in DPPC leds to a substantial reduction in the lateral diffusion coefficient of lipids. This can be explained by considering the reduction of DL due to occupation of some free volumes by Propranolol aromatic ring. On the other hand, the higher diffusion coefficient of Propranolol comparing to Oxprenolol, can be attributed to the formation of less hydrogen bonds by Propranolol. The diffusion coefficient in the membrane indicates an inverse relationship with the number of drug molecules. The main reason is that with increasing the concentration of drug, some barriers to molecular movements such as the number of intermolecular interactions between drugs, molecular packing, and molecular accumulation are increased. 3.8. Electrostatic potential One of the important properties of lipid bilayers that may be useful in understanding the mechanisms behind the functioning of ion channels, is the electrostatic potential across the membrane [50]. This potential which is often referred to as the bilayer dipole potential, arises as a result of specific preferential orientations of the lipid head group dipoles and water dipoles at the membrane-water interface. The electrostatic potential can be influenced by the presence of the ions and other charged components [16,48]. Due to translational symmetry in X and Y directions, the electrostatic potential depends only on Z-coordinate. In Fig. 10, the electrostatic potential is presented for all five simulations. The values of electrostatic potential in the middle of the membrane (
) and the maximum potential values (
)
are presented in Table 1. For
reference system, the results of a positive dipole potential shows 500-600 mV in the center of the membrane that is in good agreement with the results of previous simulations carried by GROMOS force field [50,59]. Experimental determination of the exact value of dipole potential is difficult and several references have reported different values in the center of the membrane 15
ranging from 300 to 800 mV [51]. In some experimental studies, a lower value ranging 220-280 mV was reported for a phosphatidylcholine membrane with fully saturated chains [52] and in another study, 510 mV was reported for diphytanoylphosphatidylcholine (ester - DphPC) [53] that is very close to the obtained results of the present work for the reference system. As seen in Fig. 10, in head group area, by adding of 2 units of Propranolol to DPPC membrane causes around 23 mV increases in electrostatic potential while for Oxprenalol an amount of 20 mV reduction is obtained. By addition of 2 units of drugs, the presence of Propranolol remarkably increases the potential in hydrocarbon region of lipid, while Oxprenolol has no significant effects. It seems that this effect can be attributed to the more rigidity of Propranolol molecule in compare with Oxprenolol. This conclusion can be supported by the angular distributions of drug molecules shown in Fig. 7. This molecular rigidity in turn limits the interactions between lipid chains. By increasing of the concentration of drug up to 4 units, as seen in Fig. 10, in the head group region, the insertion of Propranolol causes an 80 mV decrease in electrostatic potential; while for Oxprenolol a 10 mV increase is obtained. In hydrocarbon region, in the presence of Propranolol and Oxprenolol the potentials are 30 mV decreased and 50 mV increased, respectively. Although it is difficult to justify this effect, however, in case of Propranolol, it is observed that the drug-drug interactions are stronger than drug-lipid or lipid-lipid interactions. 3.9. P-N tilt angle The head group tilt is a very important property of a phospholipid bilayer that exhibits a characteristic tilt toward the bilayer normal, which can be analyzed by calculating the distribution of the vector connecting the phosphorus and the nitrogen atoms, averaged over the course of the simulation and all lipid molecules [54]. It has been found that many properties of the bilayer are affected by dipole moment associated with zwitterionic head group that is 16
involved in long-range electrostatic interactions [48,49]. Fig. 8 shows the distribution of the head group P–N vector of DPPC lipids relative to the bilayer normal at different concentration of drugs as well as for the reference system. The average angles between the P–N vector and the bilayer normal are given in Table 2. According to the data presented in Table 2 and Fig. 11, neutral forms of Oxprenolol and Propranolol have no significant effect on the orientation of the P – N vector in the bilayer. At both drug concentrations, average of P-N angle is almost the same (~90) as reference system. With regard to the Fig. 11, the number of configurations with an angle of 90 in the Oxperanolol (2 units) and Propranolol (4 units) containing systems are slightly increased and slightly decreased, respectively. As shown by Fig. 3 and 4, since the drug molecules are mostly located in the middle tail region of lipids, the P–N vector angles have not been significantly affected by drugs. Similar behavior of the P–N vector was also observed in previous simulation for the reference system [54]. 4. Conclusion A molecular dynamics simulation study was conducted to compare the effects of different concentrations of tow β-blockers (Propranolol and Oxprenolol) on DPPC bilayer. According to the results, it can be concluded that the bilayer thickness and the APL are increased by the neutral form of both β-blockers and the effect is more prominent in the case of Propranolol . Free energy profiles were shown that location of Oxprenolol corresponds to distance of 1.0 nm between the COM of drug and the bilayer center, while the location of Propranolol in membrane was much deeper, occurring at a flat area around -1.0 to +1.0 nm near the bilayer center. The order parameters in lipid tails are increased in neutral form of Oxprenolol in both concentrations while a slightly increase is just observed in high concentration (4 units) for Propranolol. In compare with Propranolol, Oxprenolol forms more hydrogen bonds with lipids and due to more 17
rigidity Propranolol was caused slower DL than Oxprenolol. The most interesting result of this study is that neutral form of Propranolol and Oxprenolol in different concentrations, leads to very different results on electrostatic potential. In low concentration systems (2 units), Propranolol increased the electrostatic potential, while for Oxprenolol, it was increased in high concentration systems (4 units).
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[33] R.R. Gullapalli, M.C. Demirel, P.J. Butler, Molecular dynamics simulations of DiI-C 18 (3) in a DPPC lipid bilayer, Phys. Chem. Chem. Phys. 10 (2008) 3548–3560. [34] Z.E. Hughes, A.E. Mark, R.L. Mancera, Molecular dynamics simulations of the interactions of DMSO with DPPC and DOPC phospholipid membranes, J. Phys. Chem. B. 116 (2012) 11911–11923. [35] N. Kučerka, M.-P. Nieh, J. Katsaras, Fluid phase lipid areas and bilayer thicknesses of commonly used phosphatidylcholines as a function of temperature, Biochim. Biophys. Acta (BBA)-Biomembranes. 1808 (2011) 2761–2771. [36] Y. Song, V. Guallar, N.A. Baker, Molecular dynamics simulations of salicylate effects on the micro-and mesoscopic properties of a dipalmitoylphosphatidylcholine bilayer, Biochemistry. 44 (2005) 13425–13438. [37] M. Patra, E. Salonen, E. Terama, I. Vattulainen, R. Faller, B.W. Lee, et al., Under the influence of alcohol: the effect of ethanol and methanol on lipid bilayers, Biophys. J. 90 (2006) 1121–1135. [38] M. Patra, M. Karttunen, M.T. Hyvönen, E. Falck, P. Lindqvist, I. Vattulainen, Molecular dynamics simulations of lipid bilayers: major artifacts due to truncating electrostatic interactions, Biophys. J. 84 (2003) 3636–3645. [39] C. Hofsäß, E. Lindahl, O. Edholm, Molecular dynamics simulations of phospholipid bilayers with cholesterol, Biophys. J. 84 (2003) 2192–2206. [40] J.F. Nagle, Area/lipid of bilayers from NMR., Biophys. J. 64 (1993) 1476. [41] J.F. Nagle, R. Zhang, S. Tristram-Nagle, W. Sun, H.I. Petrache, R.M. Suter, X-ray structure determination of fully hydrated L alpha phase dipalmitoylphosphatidylcholine 22
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Comput. 6(12) (2010) 3713–3720. [59] J. Wohlert and O. Edholm, “The range and shielding of dipole-dipole interactions in phospholipid bilayers,” Biophys. J., vol. 87, no. 4, pp. 2433–2445, 2004. [60] R.D. Porasso, W.F. Drew Bennett, S.D. Oliveira-Costa, J.J. Lopez Cascales, Study of the benzocaine transfer from aqueous solution to the interior of a biological membrane, J. Phys. Chem. B. 113 (2009) 9988–9994. Figures and Tables captions Fig. 1. Molecular structures of Propranolol (a) and Oxprenolol (b) with partial atom charges and atom names referred in the text along with the structure of DPPC lipid (c). Fig. 2. Snapshots of the initial configurations of DPPC lipids, water molecules and two molecules of (a) Propranolol and (b) Oxprenolol. Fig. 3. Mass density of different components for DPPC lipid bilayer system: 2 Neutral βblockers system (a), 4 Neutral β-blockers system (b). Fig. 4. Free energy profiles for tow β -blockers along the bilayer z-axis. Fig. 5. Snapshots of the final configuration of the DPPC lipids and water molecules and two molecules of (a) Propranolol and (b) Oxprenolol. Fig. 6. The deuterium order parameters for different carbon atoms in the SN-1 and SN-2 chains in presence tow kind of β-blocker. Fig. 7. Angular distribution of the NA–CA vector of Oxprenolol (a) and the NB-CB vector of Propranolol (b) in the DPPC bilayer relative to the bilayer normal.
25
Fig. 8. The radial distribution function of water oxygen around phosphate oxygen (OC1 and OC2) of DPPC lipid molecules. Fig. 9. The mean square displacement of the drugs in the simulated systems. Fig. 10. Electrostatic potential of the simulated systems.
Fig. 11. Distribution of the head group orientation vector (P-N) with respect to the bilayer normal for different systems.
26
27
Fig 1
Fig 2
28
Fig 3
Fig 4
29
Fig 5
Fig 6 30
Fig 7
31
Fig 8
32
Fig 9
Fig 10
Fig 11
33
Table 1 The values of area per lipid (APL), thickness of bilayer (DB), lipid lateral diffusion coefficient (DL), β-blocker lateral diffusion coefficient (DA), electrostatic potential in the middle of membrane (ωMid), maximum electrostatic potential (ωMax) and DPPC head group P–N tilt angle (αP-N) of the simulated bilayer systems. DPPC in presence of 2 Oxprenolol
DPPC in presence of 2 Propranolol
DPPC reference (Without drug)
DPPC in presence of 4 Propranolol
DPPC in presence of 4 Oxprenolol
APL (Å2)
64.40 (±0.48)
64.06 (±0.49)
62.70 (±0.50)
65.88 (±0.55)
62.82 (±0.52)
DB (nm)
3.81 (±0.23)
3.85 (±0.25)
3.80 (±0.31)
3.90 (±0.23)
3.88 (±0.28)
DL 10
12.2 (±1.5)
4.6 (±2.1)
15.7 (±3.1)
1.5 (±0.9)
6.4 (±2.0)
DA 10
17.2 (±1.6)
36.4 (±4.0)
------
34.2 (±2.8)
20.3 (±1.2)
ωMid (V)
0.56 (±0.01)
0.60 (±0.01)
0.56 (±0.01)
0.53 (±0.01)
0.61(±0.01)
ωMax (V)
0.76 (±0.02)
0.80 (±0.02)
0.78 (±0.02)
0.70 (±0.02)
0.79 (±0.02)
αP-N (degree)
90.20 (±1.79)
89.90 (±1.72)
89.7 (±1.8)
89.4 (±1.7)
90.00 (±1.81)
Table 2 Coordination numbers in the simulated systems. System
Coordination number
DPPC reference
1.2653 (±0.0015)
2 Propranolol in DPPC
1.2683 (±0.0012)
2 Oxprenolol in DPPC
1.2703 (±0.0009)
4 Propranolol in DPPC
1.2760 (±0.0017)
4 Oxprenolol in DPPC
1.2683 (±0.0013)
Table 3 Average number of different hydrogen bonds in the simulated systems. Simulation System
Number of Drugs
H-bonds between Drug and DPPC
H-bonds between Drug and Water
H-bonds between Drug and Drug
H-bonds between DPPC and Water
DPPC+Water+Propranolol
2
0.292(±0.434)
0.251(±0.394)
0.025(±0.048)
782.296(±15.152)
DPPC+Water+Oxprenolol
2
1.472(±0.740)
2.154(±1.245)
0.070(±0.130)
781.955(±14.820)
DPPC+Water (Reference)
0
-----
-----
-----
778.580(±16.392)
DPPC+Water+Propranolol
4
0.528(±0.626)
0.454(±0.585)
0.057(±0.109)
784.223(±16.084)
DPPC+Water+Oxprenolol
4
2.896(±0.933)
4.198(±1.580)
0.183(±0.305)
778.720(±14.605)
34
S1093-3263(16)30009-2 http://dx.doi.org/doi:10.1016/j.jmgm.2016.01.009 JMG 6653
To appear in:
Journal of Molecular Graphics and Modelling
Received date: Revised date: Accepted date:
9-8-2015 22-1-2016 23-1-2016
Please cite this article as: Khaled Azizi, Mokhtar Ganjali Koli, Molecular dynamics simulations of Oxprenolol and Propranolol in a DPPC lipid bilayer, Journal of Molecular Graphics and Modelling http://dx.doi.org/10.1016/j.jmgm.2016.01.009 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Molecular dynamics simulations of Oxprenolol and Propranolol in a DPPC lipid bilayer Khaled Azizi*, Mokhtar Ganjali Koli Department of Chemistry, University of Kurdistan, Sanandaj, Iran (Email: [email protected]) To whom correspondence should be addressed: Tel: ++98-871-6624133 Fax: ++98-871-6660075 Email: [email protected]
1
Graphical abstract
Highlights Passing across the membrane for Propranolol is easier than Oxprenolol. The electrostatic potential is influenced effectively by the concentrations of drugs. Oxprenolol and Propranolol have the same effect on the water penetration in membrane.
Abstract Extensive microscopic molecular dynamics simulations have been performed to study the effects of
tow
β-blocker
drugs
(Propranolol,
Oxprenolol)
on
fully
hydrated
dipalmitoylphosphatidylcholine (DPPC) in the fluid phase at 323 K. Simulation of 4 systems 2
containing varying concentrations of drugs was carried out. For the purpose of comparison, a fully hydrated DPPC bilayer without drugs was also studied at the same level of simulation technique which has been done on 4 other systems. The length of each simulation was 100 ns. The effects of concentrations of both drugs were analyzed on lipid bilayer properties, such as electrostatic potential, order parameter, diffusion coefficients, and hydrogen bond formation, etc. Penetration of water in the bilayer system was also investigated using radial distribution function analysis. Efficacy of varying concentrations of both drugs has no significant effect on P-N vector. Consistent with experimental results, by increasing the concentration of Propranolol, the thickness of the bilayer was increased. Keywords: Lipid bilayers; β-blocker; molecular dynamics simulation; membrane.
1. Introduction The pharmacological action of a drug is a complex phenomenon. Among the factors that have an important impact on this complexity, a special place should be assigned to drug-membrane interaction. This is due to the fact that the interactions between drugs and bio-membranes play a key role for pharmacokinetic parameters such as absorption, distribution, metabolism and elimination [1, 2]. Therefore, many efforts have been devoted to understanding the nature of interactions between drugs and bio-membranes [3]. Primary partitioning is the pre-requirements condition for permeability of drug molecules through bio-membranes. Typically, a lipophilicity evaluation is built with bulk phase measurements of drug partition coefficients between an aqueous and organic phase (e.g., n-octanol). The basic assumption is that, the lipid bilayer membranes could be effectively represented by bulk phase. This assumption has been brought into question by several investigators [4–6]. The plasma membrane is the most important
3
membrane for drug administration, through which drugs must penetrate to achieve the internal milieu of the target cells [7]. The behavior of the drug in the membrane is controlled by several factors that among these shape, size, hydrophobicity and pKa are the most influential. In order to improve the efficacy and viability of many drugs, understanding the fundamental interactions between the drug and lipid have a special importance [8]. Since Phosphatidylcholines (PC) bilayers are the most abundant lipids in mammalian membranes, they typically used as simple membrane models, although phosphatidylserines, phophatidylethanolamines, sphingomyelins, and cholesterol are also present [9]. β-Blockers are known as the most efficacious agents for the treatment of heart failure, certain types of arrhythmia, hypertrophic obstructive cardiomyopathy, as well as prior myocardial infarction [10]. Propranolol (Fig. 1a) is a non-cardioselective βblocker and a prototype β-adrenoreceptor blocking agent, which has earned far-reaching utilization in the treatment of angina pectoris, cardiac dysrhythmias and hypertension [11,12]. It has been specified that (R) -(+) -enantiomer has a membrane stabilizing effect [12], therefore the membrane activity of Propranolol may be important in study of its toxicity following overdose [11]. Oxprenolol (Fig. 1b) is a non-selective β-Blocker, which has low membrane stabilizing activity and medium intrinsic sympathomimetic activity. Because of its sympathomimetic activity, Oxprenolol displays less negative ionotropic effect than Propranolol. Consequently, Oxprenolol may help for treatment with a beta adrenoceptor antagonist despite peripheral vascular disease or heart failure. Owing to extensive hepatic metabolism, its bioavailability is low and half-life is short [13,14]. Regarding to the above-mentioned, many investigations including studies of the effects of Propranolol and Oxprenolol on the lipid membranes have been performed. The results of differential scanning calorimetry (DSC) studies indicated that the dimyristoylphosphatidylcholine (DMPC) thermotropic phase behavior is modulated by these
4
compounds as follows:
Propranolol > metoprolol = oxprenolol > nadolol [4]. Some of
thermodynamic and structural features of Propranolol-DPPC liposomes interactions were investigated by DSC and X-ray diffraction [11]. The interactions between β-blockers (Oxprenolol, Propranolol, and acebutolol) and palmitoyloleoylphosphatidylcholine (POPC) have been studied by Time-Dependent Fluorescence Shift (TDFS) and Generalized Polarization (GP). It has been shown that by increasing β–blocker concentrations, the lipid bilayer at the glycerol and head group level is significantly rigidifies. The effects are significantly stronger for Propranolol than those of the two other β-blockers [15]. Molecular dynamics simulations are powerful tools that may provide valuable complementary to experiment information about details of interactions between the drug molecules and bio-membranes [8,16]. Despite the enormous development on computer simulations of lipid bilayers and utilizing GROMACS package for MD simulations [17–20], investigations on computer modeling of β–blockers in lipid bilayer are rather scarce. The nonspecific membrane effects (NME) of Oxprenolol and Propranolol β-blockers have been proven [20]. Accordingly in this study neutral form of these βblockers were selected and studied by molecular dynamic simulation method. In addition, the effects of these β–blockers on dipalmitoylphosphatidylcholine (DPPC) lipid bilayer, shown in Fig. 1c, were compared. 2. Methodology 2.1. Molecular structures The molecular structures of DPPC Lipid and β–blockers are shown in Fig. 1. As can be seen, two etheric bonds in Oxprenolol against an attached phenyl ring and one etheric bond in Propranolol could be considered as the most obvious structural differences between the two drugs. In this study, five different systems were chosen to carry out the simulation study. The 5
first system which comprises only lipid and water molecules was utilized as a reference. The second one includes 128 DPPC lipids (64 per leaflet) with one Propranolol molecule in each leaflet, within the bilayer. Another system contains one Oxprenolol molecule in each leaflet. In two system remained, Propranolol and Oxprenolol was just doubled in the same manner. All of these systems were hydrated by 4000 water molecules. Fig. 2 shows the initial configurations of DPPC lipids, water molecules and two drug molecules within the simulation box. As can be seen for both the Propranolol and Oxprenolol, somewhere between the head and tail of DPPC lipids are selected as the initial position of the drug molecule. For lipid bilayer and β–blockers molecules, the united atom model base on the GROMOS force field with modification by Berger was applied [21,22], and for water molecules, the simple point charge model (SPC) was used [55]. The topology and coordinates files of β–blockers based on the GROMOS 53A6 force field were received from the ATB server [23,24]. 2.2. Simulation details In this study, two different types of molecular dynamics simulation were performed. The first study which is run over five different systems was conducted to investigate the behavior of the drugs in the lipid bilayer. The second simulation was set up for PMF calculations in systems containing the 128 DPPC lipids and one of Propranolol or Oxprenolol molecules. All simulations were executed in the NPT ensemble using GROMACS4.5.5 [25]. The systems were maintained at a constant temperature of 323K using the Nose-Hoover thermostat with a coupling time of 0.5 ps [26]. All the bond lengths were constrained with LINCS algorithm [27]. The pressure was held constant at 1 bar by compressibility 4.5 × 10 -5 bar-1 and by coupling the simulation cell to a Parrinello-Rahman barostat, with coupling time constant 2 ps which was used semiisotropically with tow degree of freedom, one in XY direction and another in Z direction [28]. To integrate 6
Newton’s equations of motion, the leap-frog algorithm with time step 2 fs was applied [29]. Coulomb and Van der Waals interactions were cut-off at 1.2 nm. Long-range electrostatic interactions are important for the true explanation of the lipid bilayer, hence, for long range electrostatic interactions the Particle Mesh Ewald was applied [30]. Starting structure for DPPC lipid bilayer was obtained from the Biocomputing group at the University of Calgary (http://moose.bio.ucalgary.ca/). Periodic boundary conditions were used in all three dimensions. In all systems, steepest descent energy minimization was used to remove undesirable atomic contacts and calm down the water molecules within systems [31]. At first, positions of drugs were restrained and equilibration conducted in the NVT ensemble for 2 ns and then followed by equilibration in NPT ensemble for 8 ns. After equilibration steps, all simulations were run for 100 ns from their starting conditions and coordinates of the atoms. The Grid MAT-MD program [32] was used to measure the thickness of the DPPC membrane and the area per lipid (APL) head group of each lipid forming the bilayer. For free energy calculations, in the biased MD simulation, pre-equilibrated simulation starting frames were generated by pulling the center-ofmass (COM) of drugs against the COM of DPPC lipid bilayer. Drugs was pulled along the bilayer normal (the z-axis) by using a pulling force constant of 1000 kJ mol−1 nm−2 and pulling rate of 0.01 nm ps−1. Pulling exerts a harmonic potential on the drug molecule and moves the potential center with a given pull rate. From the pulling simulation, the snapshots were obtained and among them 18 windows (~0.2 Å apart) along the z-axis, ranging from the bulk water (Z= ±3.5 nm) to the middle of the DPPC lipid bilayer (Z= ± 0.0 nm), were selected. Each window was explored in a separate simulation (10 ns run time each) to avoid any drug interactions. 3. Results and Discussion 3.1. Mass Density 7
Computational mass density of various groups is shown in Fig. 3. Water and lipid density changes are in agreement with whatever reported before [33,34]. As seen here, the maximum of the density of Oxprenolol and Propranolol molecules is very close to each other and located at approximately 1(nm) from the center of membrane. In this area, increasing the number of drugs from 2 to 4, shows a decrease in the DPPC density towards the reference system. Moreover, the maximum density of both drugs is located in the middle layer of hydrocarbon chains of lipid tail. Since the total density has been the same at all simulated systems, it is not presented here; and the water density that indicates equal distribution is shown only for the reference system. 3.2. Potential of mean force Partitioning of the drug throughout the lipid bilayer membrane can be described by free energy (∆G) profile along the normal axis of membrane, which is also known as PMF [56]. In this study, PMF was calculated by using the umbrella sampling method. The forces exerted on the drugs were analyzed, and the free energy profile was calculated using weighted histogram analysis method embedded in GROMACS [57, 58]. Statistical errors were estimated using Bayesian bootstrap analysis (N = 200). Fig. 4 shows the free energy profiles of tow β-blockers, from which we can see that there exists an obvious minimum for Oxprenolol whereas the energy curve is flat for Propranolol. The obvious free energy minimum of Oxprenolol corresponds to distance of 1.0 nm between the COM of drug and the bilayer center, suggesting that Oxprenolol tend to localize in this region. The free energy minimum of Propranolol, occurring at a flat area around -1.0 to +1.0 nm and near the bilayer center, is more negative than that of Oxpreolol. The pictures given by the snapshot of systems in their final configurations, reported in Fig. 5. In agreement with the ∆G profile along the normal axis of membrane, while Oxprenolol chooses areas near the head of DPPC, Propranolol prefers to be in the area near the center of membrane. 8
It seems that because of additional ring, in comparison with Oxprenolol, Propranolol has less polarity and more lipophilicity, and hence is more favorable that is located at the deeper regions of membrane. On the other hand, Oxprenolol because of an ether chain that exerts more polarity and less lipophilicity on the molecule, is placed in the nearby of the polar head group. Comparing of energy barriers in bilayer center for two drugs indicate that it is more difficult for Oxprenolol to pass across membrane. 3.3. Area per lipid and bilayer thickness The area per lipid (APL) amount of all simulated systems is shown in Table 1. As seen in this table, value of APL for reference system is anticipated to be equivalent to 62.7
that is within
range of previously reported amounts [35–39]. It is also in excellent agreement with experimental amount of 62
at 323 K temperature and 1 bar [40]. It is noteworthy that
implementation of 2 units of each of Propranolol and Oxprenolol has approximately similar effect on the increasing of APL of DPPC membrane with respect to reference system (1.70 and 1.36
for Oxprenolol and Propranolol, respectively). However, for 4 unit implementation the
effect is entirely different. While for additional of 4 unit of Propranolol, the APL of DPPC membrane is increased considerably (3.18
with respect to reference system), by adding 4
units of Oxprenolol its value is increased by small amount (0.12
). This effect can be
explained on the basis of existing more aromatic rings in Propranolol and their establishment amongst the lipids. For Oxprenolol, the increase of density leads to the increase of hydrophobic chains and reinforcement of strong attractive interactions between lipid chains, that in turn, remarkably decreases the upward steep of APL. The thickness value of 3.8 nm for reference system is in good agreement with experimental value of 3.9 nm [35,41]. According to Table 1, by adding 2 molecules of Propranolol or Oxprenolol, the thickness of the membrane has 9
increased almost the same for both drugs in the compare with the reference system. An increased number of drug molecules from 2 to 4, leads to a more chance of increasing in the thickness of the membrane. This effect is more obvious for Propranolol-including systems. The increase in thickness of the DPPC membrane by increasing the concentration of Propranolol is in agreement with experimental observations and is in consistent with the increase of APL [11].
3.4. Deuterium order parameter It is found that the movements of lipid chains in a bilayer membrane, including rotation around chemical bonds or lipid axis, trans/gauche isomerization, lateral diffusion and etc. Have a completely dynamic nature [3]. The effect of these configurationally variations can be evaluated by deuterium order parameter which is one of the important quantities for the description of microscopic structure of lipid bilayer [39,42]. On the other hand, deuterium order parameter for each group of CH2 (CD2) can be measured experimentally through nuclear magnetic resonance (NMR) investigations. The order parameter of the lipid chain is given by the following equation [3]: S
3cos θ
1
1
Where θ is the angle between a CD bond (in experimental) or a CH bond (in simulation) and the bilayer normal axis (Z). In this equation the bracket is implying time averaging over two bonds at each group of CH2 in all lipids. Order parameter of SN1 and SN2 chains of DPPC lipids are shown in Fig. 6. As seen in this figure, the calculated values for reference system, are in acceptable agreement with experimental results as well as previous simulation findings [22, 43, 44]. An explanation of the differences between calculated and experimental order parameters are 10
difficult. However, this difference is mainly attributed to subtle defects in hydrocarbon chain potential, incomplete sampling of the chain conformations and/or long time-scale lipid stumble [45]. As seen in Fig. 6, for SN1 chain, the presence of 2 units of Oxprenolol and Propranolol, has led to slight increase and decrease in order parameter, respectively. In SN2 chain, the circumstances are different; while the presence of Oxprenolol leads to more severe increasing in order parameter, except for the first few carbons in chain, the Propranolol does not establish a significant change in lipid order. For the system containing 4 units of each drug, the order parameter of SN1 chain has been increased by slightly more effect for Oxpernolol. In the case of SN2 chain, the increasing in order parameter which was imposed by the presence of Oxprenolol is remarkably higher than Propranolol. These observations are expected because it is shown that various chemical compositions in membrane have different effects on order parameter of lipid chains [16,60]. As seen in Table 1, the increase of both Propranolol and Oxprenolol has led to slower diffusion in lipids. It should be remembered that in the case of the neutral form of Articaine, an increase in the order parameter of lipid bilayers corresponds to faster diffusion in lipids [16]. It seems that the membrane fluidity changes are more complicated to be interpreted based on the order parameter changes. Therefore, more information on orientation of drug molecules within a bilayer should be made available. NA-AC and NB-CB vectors were selected as long axis associated to Oxprenolol and Propranolol, respectively. These distributions are shown in Fig. 7 in which the zero angles correspond to the direction out of the bilayer. From the angular distribution, one can see noticeable differences in the orientation of Propranolol and Oxprenolol. As can be seen, while the most probable angle for the system containing 2 units of Oxprenolol is
77.5 , for 4 units, and a wide distribution between
11
65 until
105
have been obtained. The value of angle for the system containing 2 and 4 units of Propranolol are 99.8 and
86.7 , respectively.
3.5. Radial distribution function It is well known that the APL can be influenced by interactions between the head group and water molecules [46]. Radial distribution function (RDF) of water molecules in membrane was applied to gain a better understanding of effect of type and concentration of drugs on water penetration, lipid hydration, and mutual water-lipid interactions. The RDFs of water oxygen around the phosphate oxygen for reference and systems including various densities of both drugs are shown in Fig. 8. As can be seen, the RDF schemes of the systems are nearly the same. For all RDFs the first minimum is occurred at 3.2 Å indicating the hydrogen bonding between water and phosphate oxygen; and the second maximum for all systems is located at 5.0 Å. Coordination numbers which are obtained from the appropriate integration of RDF up to the first minimum, are shown in Table 2. For all systems containing Oxprenolol and Propranolol, the first maximum peak is higher than reference system. This can be treated as the increase in water penetration into the head groups in the presence of Oxprenolol and Propranolol molecules. For systems containing 2 units of the drugs, the peak in the presence of the Oxprenolol is higher than Propranolol while for systems containing 4 units a trend reversal is observed that the higher peak belongs to Propranolol. As a result, the increase of APL in drug containing systems, can be attributed to an increase in water penetration and coordination number, (Table 2). The apparent increase in coordination number of 4 units containing Propranolol with respect to Oxprenolol, can be mentioned as an acceptable reason for difference in APL values of systems, (Table 1). 3.6. Hydrogen bonds
12
Regarding the ability of the hydrogen bonding formation by both β-blocker and polar head groups of lipids, a competition between these molecules for hydrogen bonding formation with water molecules is inevitable. Therefore, the formation of different types of hydrogen bonds between β–blockers and lipid molecules, β–blockers and water molecules, lipids and water molecules, and also between β–blocker molecules with each others, has been studied. At the present study, hydrogen bonds are determined by a maximum distance of 3.5 Å between acceptor and hydrogen and also maximum angle of 30 between acceptor-hydrogen and hydrogen- donor vectors [47]. The results of various types of hydrogen bonds in simulated systems are collected in Table 3. According to this table, in systems including 2 β–blockers, the number of hydrogen bonds between DPPC and water are slightly more than the reference systems. This result is in full agreement with more penetration of water into the membrane, which mentioned in the previous section. Moreover, the number of hydrogen bonds between water and DPPC in Propranolol containing system is more than Oxprenolol. As can be seen from Table 3, for systems containing 4 β–blockers a similar situation is existed, however, here extend of the hydrogen bonding formation for Propranolol containing systems are somewhat more evident than for Oxprenolol. This is in full agreement with more water penetration into the bilayer. For system containing Oxprenolol, due to low penetration of water, the number of hydrogen bonds is similar to the reference system. For 2 units of drug containing system, the total numbers of hydrogen bonds terminated to Oxprenolol (either from DPPC or water) are remarkably higher than Propranolol. As seen, with the increasing of the number of drug units from 2 to 4, the number of hydrogen bonds of β–blockers with DPPC and water will become almost double. The superiority of Oxprenolol on Propranolol in formation hydrogen bonding, may be attributed to higher number of oxygen atoms in Oxprenolol and the large amount of negative electrostatic
13
charge on OA2 (Fig. 1b). It seems that the larger number of hydrogen bonding in Oxprenolol including system can be considered as strong reason for lower diffusion of drug in bilayer membrane. 3.7. Lateral diffusion It is shown that many cell signaling processes related to membrane, are under the control of lipid molecules diffusion, an indicator of lipid viscosity [33]. Therefore, we calculated the lateral diffusion coefficients of β–blockers and lipids in all simulated systems. In this study, MD trajectories are applied for calculating the mean square displacement (MSD) of single molecules and the lateral diffusion coefficient is calculated by the Einstein formula in two dimensions in the following form [48]: D
where
|∆r t |
lim →
1d 4 dt
|∆r t |
2
is the MSD in XY plane during the time t, starting from the initial time t0
and D stands for the lateral diffusion coefficient. Averaging is taken over all molecules and over all initial time t0. Time dependence of lateral MSD of Propranolol and Oxprenolol in DPPC is shown in Fig. 9. In practical calculations, the limit of the derivative in equation 2 is calculated from the slope of linear region of the MSD vs. time curve. At shorter times, due to non-Brownian character of the diffusion a non-linear character may be exerted on the MSD curve. As times approach to the total simulation time, the poor statistics led to large fluctuations in MSD curves [16]. Here in, the time interval 5–35 ns, where the MSD curves show behavior most close to linear, is used for the slope fitting. Lateral diffusion coefficients calculated for drug molecules and lipids are listed in Table 1. As seen, the value of diffusion coefficient, DL, for reference system is in very good agreement with experimental result (that is around 16 14
10
) [49].
Furthermore, insertion of β-blocker molecules in DPPC leds to a substantial reduction in the lateral diffusion coefficient of lipids. This can be explained by considering the reduction of DL due to occupation of some free volumes by Propranolol aromatic ring. On the other hand, the higher diffusion coefficient of Propranolol comparing to Oxprenolol, can be attributed to the formation of less hydrogen bonds by Propranolol. The diffusion coefficient in the membrane indicates an inverse relationship with the number of drug molecules. The main reason is that with increasing the concentration of drug, some barriers to molecular movements such as the number of intermolecular interactions between drugs, molecular packing, and molecular accumulation are increased. 3.8. Electrostatic potential One of the important properties of lipid bilayers that may be useful in understanding the mechanisms behind the functioning of ion channels, is the electrostatic potential across the membrane [50]. This potential which is often referred to as the bilayer dipole potential, arises as a result of specific preferential orientations of the lipid head group dipoles and water dipoles at the membrane-water interface. The electrostatic potential can be influenced by the presence of the ions and other charged components [16,48]. Due to translational symmetry in X and Y directions, the electrostatic potential depends only on Z-coordinate. In Fig. 10, the electrostatic potential is presented for all five simulations. The values of electrostatic potential in the middle of the membrane (
) and the maximum potential values (
)
are presented in Table 1. For
reference system, the results of a positive dipole potential shows 500-600 mV in the center of the membrane that is in good agreement with the results of previous simulations carried by GROMOS force field [50,59]. Experimental determination of the exact value of dipole potential is difficult and several references have reported different values in the center of the membrane 15
ranging from 300 to 800 mV [51]. In some experimental studies, a lower value ranging 220-280 mV was reported for a phosphatidylcholine membrane with fully saturated chains [52] and in another study, 510 mV was reported for diphytanoylphosphatidylcholine (ester - DphPC) [53] that is very close to the obtained results of the present work for the reference system. As seen in Fig. 10, in head group area, by adding of 2 units of Propranolol to DPPC membrane causes around 23 mV increases in electrostatic potential while for Oxprenalol an amount of 20 mV reduction is obtained. By addition of 2 units of drugs, the presence of Propranolol remarkably increases the potential in hydrocarbon region of lipid, while Oxprenolol has no significant effects. It seems that this effect can be attributed to the more rigidity of Propranolol molecule in compare with Oxprenolol. This conclusion can be supported by the angular distributions of drug molecules shown in Fig. 7. This molecular rigidity in turn limits the interactions between lipid chains. By increasing of the concentration of drug up to 4 units, as seen in Fig. 10, in the head group region, the insertion of Propranolol causes an 80 mV decrease in electrostatic potential; while for Oxprenolol a 10 mV increase is obtained. In hydrocarbon region, in the presence of Propranolol and Oxprenolol the potentials are 30 mV decreased and 50 mV increased, respectively. Although it is difficult to justify this effect, however, in case of Propranolol, it is observed that the drug-drug interactions are stronger than drug-lipid or lipid-lipid interactions. 3.9. P-N tilt angle The head group tilt is a very important property of a phospholipid bilayer that exhibits a characteristic tilt toward the bilayer normal, which can be analyzed by calculating the distribution of the vector connecting the phosphorus and the nitrogen atoms, averaged over the course of the simulation and all lipid molecules [54]. It has been found that many properties of the bilayer are affected by dipole moment associated with zwitterionic head group that is 16
involved in long-range electrostatic interactions [48,49]. Fig. 8 shows the distribution of the head group P–N vector of DPPC lipids relative to the bilayer normal at different concentration of drugs as well as for the reference system. The average angles between the P–N vector and the bilayer normal are given in Table 2. According to the data presented in Table 2 and Fig. 11, neutral forms of Oxprenolol and Propranolol have no significant effect on the orientation of the P – N vector in the bilayer. At both drug concentrations, average of P-N angle is almost the same (~90) as reference system. With regard to the Fig. 11, the number of configurations with an angle of 90 in the Oxperanolol (2 units) and Propranolol (4 units) containing systems are slightly increased and slightly decreased, respectively. As shown by Fig. 3 and 4, since the drug molecules are mostly located in the middle tail region of lipids, the P–N vector angles have not been significantly affected by drugs. Similar behavior of the P–N vector was also observed in previous simulation for the reference system [54]. 4. Conclusion A molecular dynamics simulation study was conducted to compare the effects of different concentrations of tow β-blockers (Propranolol and Oxprenolol) on DPPC bilayer. According to the results, it can be concluded that the bilayer thickness and the APL are increased by the neutral form of both β-blockers and the effect is more prominent in the case of Propranolol . Free energy profiles were shown that location of Oxprenolol corresponds to distance of 1.0 nm between the COM of drug and the bilayer center, while the location of Propranolol in membrane was much deeper, occurring at a flat area around -1.0 to +1.0 nm near the bilayer center. The order parameters in lipid tails are increased in neutral form of Oxprenolol in both concentrations while a slightly increase is just observed in high concentration (4 units) for Propranolol. In compare with Propranolol, Oxprenolol forms more hydrogen bonds with lipids and due to more 17
rigidity Propranolol was caused slower DL than Oxprenolol. The most interesting result of this study is that neutral form of Propranolol and Oxprenolol in different concentrations, leads to very different results on electrostatic potential. In low concentration systems (2 units), Propranolol increased the electrostatic potential, while for Oxprenolol, it was increased in high concentration systems (4 units).
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Comput. 6(12) (2010) 3713–3720. [59] J. Wohlert and O. Edholm, “The range and shielding of dipole-dipole interactions in phospholipid bilayers,” Biophys. J., vol. 87, no. 4, pp. 2433–2445, 2004. [60] R.D. Porasso, W.F. Drew Bennett, S.D. Oliveira-Costa, J.J. Lopez Cascales, Study of the benzocaine transfer from aqueous solution to the interior of a biological membrane, J. Phys. Chem. B. 113 (2009) 9988–9994. Figures and Tables captions Fig. 1. Molecular structures of Propranolol (a) and Oxprenolol (b) with partial atom charges and atom names referred in the text along with the structure of DPPC lipid (c). Fig. 2. Snapshots of the initial configurations of DPPC lipids, water molecules and two molecules of (a) Propranolol and (b) Oxprenolol. Fig. 3. Mass density of different components for DPPC lipid bilayer system: 2 Neutral βblockers system (a), 4 Neutral β-blockers system (b). Fig. 4. Free energy profiles for tow β -blockers along the bilayer z-axis. Fig. 5. Snapshots of the final configuration of the DPPC lipids and water molecules and two molecules of (a) Propranolol and (b) Oxprenolol. Fig. 6. The deuterium order parameters for different carbon atoms in the SN-1 and SN-2 chains in presence tow kind of β-blocker. Fig. 7. Angular distribution of the NA–CA vector of Oxprenolol (a) and the NB-CB vector of Propranolol (b) in the DPPC bilayer relative to the bilayer normal.
25
Fig. 8. The radial distribution function of water oxygen around phosphate oxygen (OC1 and OC2) of DPPC lipid molecules. Fig. 9. The mean square displacement of the drugs in the simulated systems. Fig. 10. Electrostatic potential of the simulated systems.
Fig. 11. Distribution of the head group orientation vector (P-N) with respect to the bilayer normal for different systems.
26
27
Fig 1
Fig 2
28
Fig 3
Fig 4
29
Fig 5
Fig 6 30
Fig 7
31
Fig 8
32
Fig 9
Fig 10
Fig 11
33
Table 1 The values of area per lipid (APL), thickness of bilayer (DB), lipid lateral diffusion coefficient (DL), β-blocker lateral diffusion coefficient (DA), electrostatic potential in the middle of membrane (ωMid), maximum electrostatic potential (ωMax) and DPPC head group P–N tilt angle (αP-N) of the simulated bilayer systems. DPPC in presence of 2 Oxprenolol
DPPC in presence of 2 Propranolol
DPPC reference (Without drug)
DPPC in presence of 4 Propranolol
DPPC in presence of 4 Oxprenolol
APL (Å2)
64.40 (±0.48)
64.06 (±0.49)
62.70 (±0.50)
65.88 (±0.55)
62.82 (±0.52)
DB (nm)
3.81 (±0.23)
3.85 (±0.25)
3.80 (±0.31)
3.90 (±0.23)
3.88 (±0.28)
DL 10
12.2 (±1.5)
4.6 (±2.1)
15.7 (±3.1)
1.5 (±0.9)
6.4 (±2.0)
DA 10
17.2 (±1.6)
36.4 (±4.0)
------
34.2 (±2.8)
20.3 (±1.2)
ωMid (V)
0.56 (±0.01)
0.60 (±0.01)
0.56 (±0.01)
0.53 (±0.01)
0.61(±0.01)
ωMax (V)
0.76 (±0.02)
0.80 (±0.02)
0.78 (±0.02)
0.70 (±0.02)
0.79 (±0.02)
αP-N (degree)
90.20 (±1.79)
89.90 (±1.72)
89.7 (±1.8)
89.4 (±1.7)
90.00 (±1.81)
Table 2 Coordination numbers in the simulated systems. System
Coordination number
DPPC reference
1.2653 (±0.0015)
2 Propranolol in DPPC
1.2683 (±0.0012)
2 Oxprenolol in DPPC
1.2703 (±0.0009)
4 Propranolol in DPPC
1.2760 (±0.0017)
4 Oxprenolol in DPPC
1.2683 (±0.0013)
Table 3 Average number of different hydrogen bonds in the simulated systems. Simulation System
Number of Drugs
H-bonds between Drug and DPPC
H-bonds between Drug and Water
H-bonds between Drug and Drug
H-bonds between DPPC and Water
DPPC+Water+Propranolol
2
0.292(±0.434)
0.251(±0.394)
0.025(±0.048)
782.296(±15.152)
DPPC+Water+Oxprenolol
2
1.472(±0.740)
2.154(±1.245)
0.070(±0.130)
781.955(±14.820)
DPPC+Water (Reference)
0
-----
-----
-----
778.580(±16.392)
DPPC+Water+Propranolol
4
0.528(±0.626)
0.454(±0.585)
0.057(±0.109)
784.223(±16.084)
DPPC+Water+Oxprenolol
4
2.896(±0.933)
4.198(±1.580)
0.183(±0.305)
778.720(±14.605)
34