Molecular Modeling and Simulation of Mycobacterium tuberculosis

Biomacromolecules 2004, 5, 1066-1077

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Molecular Modeling and Simulation of Mycobacterium tuberculosis Cell Wall Permeability Xuan Hong and A. J. Hopfinger* Laboratory of Molecular Modeling and Design (MC 781), College of Pharmacy, The University of Illinois at Chicago, 833 South Wood Street, Chicago, Illinois 60612-7231 Received December 8, 2003; Revised Manuscript Received February 9, 2004

The low permeability of the mycobacterial cell wall is thought to contribute to the intrinsic drug resistance of mycobacteria. In this study, the permeability of the Mycobacterium tuberculosis cell wall is studied by computer simulation. Thirteen known drugs with diverse chemical structures were modeled as solutes undergoing transport across a model for the M. tuberculosis cell wall. The properties of the solute-membrane complexes were investigated by means of molecular dynamics simulation, especially the diffusion coefficients of the solute molecules inside the cell wall. The molecular shape of the solute was found to be an important factor for permeation through the M. tuberculosis cell wall. Predominant lateral diffusion within, as opposed to transverse diffusion across, the membrane/cell wall system was observed for some solutes. The extent of lateral diffusion relative to transverse diffusion of a solute within a biological cell membrane may be an important finding with respect to absorption distribution, metabolism, elimination, and toxicity properties of drug candidates. Molecular similarity measures among the solutes were computed, and the results suggest that compounds having high molecular similarity will display similar transport behavior in a common membrane/cell wall environment. In addition, the diffusion coefficients of the solute molecules across the M. tuberculosis cell wall model were compared to those across the monolayers of dipalmitoylphosphatidylethanolamine and dimyristoylphosphatidylcholine, are two common phospholipids in bacterial and animal membranes. The differences among these three groups of diffusion coefficients were observed and analyzed. Introduction Tuberculosis (TB) kills approximately 2 million people each year.1 The global incidence of TB is still increasing at approximately 0.4% per year and much faster in some areas.2 The devastating impact of this disease is attributed to three factors: the breakdown in health services, the co-infection with HIV/AIDS, and the emergence of multidrug-resistant TB.1 Mycobacteria infections are, in general, difficult to treat because mycobacteria are resistant to the majority of common antibiotics and chemotherapeutic agents.3,4 An important factor causing this resistance is the barrier imposed by the mycobacterial cell wall.5-10 The mycobacterial cell wall is extraordinarily thick and tight, having two main components: (1) characteristic long chain fatty acids, mycolic acids, and (2) unique polysaccharides, arabinogalactan (AG).11-13 These two constituents are covalently linked together by ester bonds. The mycolyl-AG complex is then attached to peptidoglycan, a porous layer between the cell wall and the plasma membrane, and form the mycolyl-AG peptidoglycan complex. The mycobacterial cell wall also contains many “free” lipid species, the so-called extractable lipids, that are not covalently linked to the AG-peptidoglycan complex and are solvent-extractable. The free lipids include glycolipids, phenolic glycolipids, glycopeptidolipids, and other chemical species.11-17 * Corresponding author. Telephone: 312.996.4816. Fax: 312.413.3479. E-mail: [email protected].

Mycobacterial mycolic acids have several distinctive features compared to most fatty acids: (1) they are longchain molecules having a long branch, mero chain, of 4060 carbons and a short branch, R branch, of typically 24 carbons; and (2) in addition to their extraordinary lengths, mycolic acids contain very few double bonds or cyclopropane groups. The short branch, R branch, is totally saturated, and the long branch, mero chain, only has two positions that are observed to be occupied by functional groups. Of these two positions, the proximal position (nearer the β-hydroxy acid) contains exclusively cis- or trans-olefin or cyclopropane, while the distal position may be the same as the proximal position or may contain one of a variety of oxygen moieties such as R-methyl ketone, R-methyl methyl ether, methylbranched ester, or R-methyl epoxide. There are three kinds of mycolates in the M. tuberculosis cell wall, and they are R-mycolates, methoxymycolates, and ketomycolates (Figure 1). Both the R- and methoxymycolates only have the cis-cyclopropyl group at the proximal position, while 17% of the cyclopropyl groups at the keto proximal position are trans.18 Fifty-one percent of the total mycolates are R-mycolates, 36% are methoxymycolates, and 13% are ketomycolates.19 All three mycolates contain 24 and 26 carbon R branches in approximately the ratio of 10:90, with negligible amounts of 22 carbon R branches. Methoxymycolates and ketomycolates have longer mero chains than R-mycolates. The total carbon numbers for the R, methoxy,

10.1021/bm0345155 CCC: $27.50 © 2004 American Chemical Society Published on Web 04/06/2004

Mycobacterium tuberculosis Cell Wall Permeability

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Figure 1. Structures of mycolic acids found in the M. tuberculosis cell wall. The usual value for k is 23. The sum of n, m, and h is approximately 50. The shorter chain is the R branch, and the longer one is the mero chain. Both R and β carbons have R chirality. (See text for details.) Reprinted with permission from Hong and Hopfinger (2004). Copyright American Chemical Society.

and keto forms are 76-82, 83-90, and 84-89, respectively.20 AG, the other main component of the mycobacterial cell wall, is a polysaccharide consisting of arabinose (Ara) and galactose (Gal).21-23 Within AG, all arabinose and galactose residues are in the furanose form, and mycolic acids are located in clusters of four on the terminal hexaarabinofuranoside through 1,5 linkages. However, only two-thirds of the terminal arabinose residues are mycolated. The linker disaccharidephosphate connects the galactan region of AG to a peptidoglycan. Figure 2 provides an overview of the structure and organization of the mycolyl-AG peptidoglycan complex. In the physical organization model for the mycobacterial cell wall proposed by Minnikin, the mycobacterial cell wall is composed of an asymmetric lipid bilayer (Figure 3).11 The inner leaflet contains mycolic acids covalently linked to AG. In this leaflet, mycolic acid hydrocarbon chains are tightly packed in a parallel fashion, and predominantly oriented in a direction perpendicular to the cell wall surface. The outer leaflet contains the extractable lipids that accommodate the uneven surface of the inner leaflet caused by the two branches of mycolic acid that are not equal in length. It has been shown that the outer leaflet is moderately fluid, while the inner leaflet has very low fluidity.24 This low fluidity of the inner leaflet may be the result of the unique chemical structures of mycolic acids and their tight packing, which, in turn, could account for the low permeability of the overall cell wall. The cell wall permeability barrier prevents drugs

from entering the cell, which attributes, at least in part, to the intrinsic drug resistance of mycobacteria.7 In the study reported in the preceding paper, conformational search and molecular dynamics simulation (MDS) were employed to investigate the conformational profile of AG and subsequently the conformations and structural organization of the mycolyl-AG complex.25 An inner leaflet molecular model of the M. tuberculosis cell wall was constructed. (See the summary given in the Methods section.) The mycolate hydrocarbon chains were determined to be tightly packed and perpendicular to the “plane” formed by the oxygen atoms of the 5-hydroxyl groups of the terminal arabinose residues to which the mycolic acids bind. The average packing distance between mycolic acids of M. tuberculosis was estimated to be approximately 7.3 Å. This previous computational study provides support for the Minnikin model and also presents a way to probe the mechanism of low permeability of the cell wall and, in turn, the intrinsic drug resistance of M. tuberculosis. To investigate M. tuberculosis cell wall permeability to organic solutes in a quantitive manner and to gain more insight into the nature of this barrier, a variety of drugs were modeled as solutes undergoing transport across the M. tuberculosis cell wall. The properties of the solutemembrane complexes were studied by the means of MDS, especially the diffusion coefficients of the solute molecules inside the cell wall. For the purpose of comparing the permeability of the M. tuberculosis cell wall to those of bacterial and animal membranes, models for the complexes

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Figure 2. Overview of the mycolyl-AG peptidoglycan complex (with permission from the Annual Review of Biochemistry, Volume 64, copyright 1995 by Annual Reviews www.annualreviews.org; minor modifications made).

Figure 3. Mycobacterial cell wall model proposed by Minnikin. (The picture is taken from www.niaid.nih.gov/newsroom/focuson/tb02/ target.htm with modifications.) The funnel-shape structure in the center of the cell wall represents a porin (for the description of the function of porins, see ref 25).

of each of the same set of solutes and monolayers of dipalmitoylphosphatidylethanolamine (DPPE) and dimyristoylphosphatidylcholine (DMPC) were also constructed and studied, respectively. In addition, molecular similarity measures among the solutes were computed with the hope of learning more about the solute features that govern permeability across the M. tuberculosis cell wall. Methods 1. Construction of a M. tuberculosis Cell Wall Model. The procedures in the construction of a M. tuberculosis cell wall model have been reported in the preceding paper and are only summarized here to facilitate understanding of this

study.25 As mentioned in the Introduction, the innermost part of the cell wall, consisting solely of mycolic acids, is believed to be the most tightly packed membrane region and has the lowest permeability of the cell wall. Therefore, the mycolic acid region was the focus in the construction of the M. tuberculosis cell wall. Pseudo-mycolic acids (PMAs) were designed to model this cell wall region (Figure 4). There are 24 carbons in the R branch of a PMA molecule. The mero chain was shortened in the modeling to the same length as the R branch. A cis-cyclopropyl group was chosen to be the functional group at the proximal position. The advantages of this structural design are (1) the portions of the mycolic acids that are located in the innermost cell wall, and presumably are responsible for the cell wall low permeability, are adequately represented by PMA molecules and (2) such a PMA molecule represents all of the major types of mycolic acids present in M. tuberculosis because these molecules have similar structures to one another except for the distal moieties (Figure 1) and a cis-cyclopropyl group is the dominant functional group at the proximal position. Even though it is known that the mycolic acids are very tightly packed in the inner leaflet, there is very little data available regarding the actual packing (including distance) between mycolic acids. Therefore, the AG complex, the polysaccharides to which the mycolic acids form ester bonds, was studied. Conformational analysis was applied. However, one AG complex is composed of three arabinans and one galactan, and nearly 100 sugar residues are involved. Consequently, there are hundreds of torsion angle degrees of conformational freedom. A complete systematic torsion angle conformational search of such a complex is not realistic. Thus, the branch containing the 17 arabinose



Figure 4. Chemical structure of a PMA molecule. Carbon atoms located at position 13 on both the R and the mero chains are pointed out.

residues that are close to the termini of the arabinan chain and covalently linked to the mycolic acids was chosen to represent the structural features of the AG complex (Figure 2). Exhaustive random conformational sampling was performed on this structure. The conformations generated were then ranked according to their conformational potential energies. The low energy conformations were chosen to form complexes with the PMAs. Energy minimization was performed on the resultant PMA-AG complexes, and the complex with the lowest conformational potential energy was used as a starting point in extensive MDS. The average distance between the oxygen atoms of the 5-OH groups of the terminal arabinose residues, where the mycolic acids bind, was calculated on the basis of the MD trajectories taken after the complex had reached equilibrium. Because the mycolic acids exist as mycolates in the inner leaflet, a pseudomycolate (PM) was generated by esterifying the carboxyl group of a PMA molecule with methanol. A PM monolayer was then constructed using the average packing distance between the oxygens of the 5-OH groups that, in turn, represents the inner leaflet of the M. tuberculosis cell wall. 2. Construction of the 13 Solutes. Thirteen known drugs were selected as solutes to study the permeability of the M. tuberculosis cell wall. These drugs include seven first- and second-line anti-TB drugs, five general antimycobacterial drugs, and one compound that has no antimycobacterial activity. The structures of these 13 “solutes” are given in Figure 5. The HyperChem 6.01 software26 was used to build the three-dimensional structures of the solutes. The MM+ molecular mechanics force field, also implemented in HyperChem, was utilized in the solute structure optimizations. Each structure was subject to conjugate gradient energy minimization using the Polak-Ribiere first derivative method,27 until a derivative convergence criterion of 0.1 kcal/ (mol Å) was reached or until a maximum number of iterations were performed. The HyperChem software sets the maximum number of iterations to be 15 times the number of atoms in the system. After each structure was energy minimized in the MM+ force field, it was further energy minimized by the AM1 semiempirical method.28 Partial atomic charges were estimated by performing a single point AM1 calculation on the minimized structure. 3. Construction and MDS of the Complexes of the M. tuberculosis Cell Wall Model with the 13 Solutes. On the basis of the estimated average packing distance between mycolic acids from our previous study, the unit cell parameters of the PM monlayer were selected to be a ) 7.3 Å, b ) 7.3 Å, and γ ) 90°.25 Each solute was inserted into the M. tuberculosis cell wall, modeled by the PM monolayer, as is illustrated in Figure 6. The solutes were located in the region defined by the second and third rows and the third

and fourth columns of the PMs. The primary (largest) inertial axis of each solute was aligned parallel to the Z axis of the mycolates (i.e., the direction of the mycolate hydrocarbon chains). The solute was then moved along the Z axis until its center of mass was in the “plane” formed by the carbon13 atoms of the mycolates’ mero chains; see Figure 4. The 13 cell wall-solute complexes generated were each subjected to extensive MDS. The MOLSIM package,29 with an extended MM2 force field,30,31 was used to perform the MDS. The simulation temperature was set at 311 K and held constant during the MDS by coupling the system to an external fixed temperature bath.32 The initial periodic boundary conditions were set at 36.5 Å for the X and Y dimensions, 80 Å for the Z dimension, and 90° for the surface orientation angle, γ. The simulation sampling time was 140 ps with intervals of 0.001 ps for a total sampling of 140 000 conformations for each of the complexes. Geometries generated during the MDS were recorded every 0.1 ps. Three different random seeds were used to initiate the MDS. The MDS routine of the MOLSIM software package, as described above, was applied throughout this study unless stated otherwise. Methyl ester carbons and the terminal carbons of the PM mero chains were each assigned heavy masses of 1000 amu. The purpose of the heavy mass assignment is to take the influence of additional bonded structure into consideration. For example, restrictions in the movement of the terminal carbons would occur in a MDS if the mero chains had not been artificially shortened. The displacement, ∆di, between two adjacent time steps was determined for each atom of each solute from its MD trajectory, and the individual diffusion coefficient of every solute atom was calculated using the mean-square displacement method.33 The mean-square displacement is given as n

χ2 )

∆di2 ∑ i)1 n

(1)

where n is the total number of time steps in MDS. From the Einstein diffusion equation, the diffusion coefficient, D, is given by D)

χ2 2∆t

(2)

where ∆t is the size of one time step.34 The diffusion coefficient of the complete solute molecule is then calculated as the average of the diffusion coefficients of all atoms of the solute. 4. Construction and MDS of the Complexes of the DPPE Monolayer Model with the Solutes. A DPPE

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Figure 5. Chemical structures of the 13 solute molecules considered in this study.

monolayer model was previously built25 (see Figure 7A for the structure of DPPE). The complexes of the DPPE monolayer with the thirteen solutes were constructed using the MI-QSAR software.35 To prevent unfavorable van der Waals interaction between the solute molecule and the membrane DPPE, one of the “center” DPPE molecules was removed from the monolayer model and the solute molecule was inserted in the space created by the missing DPPE molecule. This procedure was not applied in the construction of the solute-PM complex model. In the previous study,25 it was found that the average packing distance of mycolic acids in a PM monolayer is correspondingly less than that of DPPEs in a DPPE monolayer, and the inner leaflet of the

M. tuberculosis cell wall exists in a relatively highly ordered state. Hence, the solutes were inserted into an intact PM monolayer model to mimic this dense and highly ordered state. Each solute molecule was placed between the regions of head groups and aliphatic chains of the monolayer with the most polar group of the solute molecule “facing” toward the head group region of the monolayer. MDSs were performed on the monolayer-solute complex using MOLSIM. The periodic boundary conditions, which were used to build the DPPE monolayer model, were employed (a ) 37.5 Å, b ) 37.5 Å, c ) 80 Å, and γ ) 92°).25 The monolayer-solute complexes were simulated for 70 ps using time intervals of


Biomacromolecules, Vol. 5, No. 3, 2004 1071 Table 1. IPEs Used in the Molecular Similarity Analyses

Figure 6. Illustration of an initial insertion, position, and alignment of a solute molecule into the M. tuberculosis cell wall model using ethambutol as an example.

0.001 ps. The diffusion coefficients of the solutes in the DPPE model membrane were then calculated in the same manner as just described for the M. tuberculosis cell wall model. 5. Construction and MDS of the Complexes of the DMPC Monolayer Model with the Solutes. The complexes of the DMPC monolayer model with the solute molecules were constructed in the same manner as in step 4 for DPPE (see Figure 7B for the structure of DMPC). The MDSs were carried out using the MOLSIM package. The periodic boundary conditions employed are a ) 40 Å, b ) 40 Å, c ) 80 Å, and γ ) 96°. The simulation sampling time was 70 ps using time intervals of 0.001 ps. Diffusion coefficients

Figure 7. Chemical structures of DPPE and DMPC.

IPE code

symbol

definitions

0 1 2 3 4 5 6 7

ALL NP P+ PHBA HBD ARO HS

all atoms in the molecule nonpolar atoms polar atoms with positive charge polar atoms with negative charge hydrogen bond acceptor atoms hydrogen bond donor atoms aromatic atoms non-hydrogen atoms (hydrogen suppressed)

were calculated for the solute molecules in the same manner as in PM and DPPE. Additional information regarding the construction of a phospholipid monolayer, and its complexes with solutes, using the MI-QSAR software can be found in refs 36-38. 6. Molecular Similarity Analysis of the 13 Solutes. The 4D-MS module of the 4D-QSAR software package was used to perform the four-dimensional molecular similarity study of the 13 solutes.39,40 4D-QSAR molecular similarity analysis considers both the three-dimensional molecular structure and the corresponding complete conformational ensemble of states of a molecule in estimating molecular similarity. The formalism measures relative molecular similarity (RMS) that is dependent upon an alignment constraint (an external reference frame) and absolute molecular similarity (AMS) that is alignment-independent. This method also allows estimation of molecular similarity measures on the basis of atom types composing molecules. 4D-QSAR defines eight atom types and names them as interaction pharmacophore elements, IPEs (Table 1). In this study, AMS analysis based on the eight IPE types was applied. MDS was performed to generate a conformational ensemble profile (CEP) for every solute molecule. The MOLSIM package was again used to perform the simulations. The simulation sampling time was 70 ps using time intervals of 0.001 ps. The atomic coordinates of all conformations sampled for every solute were recorded every 0.1 ps and stored in a trajectory file that, in turn, constituted the corresponding CEP of the solute. For the detailed methodology of 4D-MS formalism, see ref 40.

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Hong and Hopfinger Table 2. MW and Calculated log P (calcd log P) Values of the Solute Molecules solute

MW

calcd log Pa

First- and Second-Line Anti-TB Drugs isoniazid 137.14 PAS 153.14 ethionamide 166.24 ethambutol 204.31 ciprofloxacin 331.34 ofloxacin 361.37 clofazimine 473.40

0.49 0.68 1.97 0.29 0.67 0.62 6.98

General Antimycobacterial Drugs amithiazone 236.29 dapsone 248.30 hydnocarpic acid 252.40 chaulmoogric acid 280.45 thiocarlide 400.58

1.24 1.31 4.78 5.57 6.72

phencycline

Non-Antimycobacterial Drug 243.39

3.98

a

Calcd log P values were calculated from the calcd log P module in the HyperChem 6.01 package.

Figure 8. Three-dimensional structures of clofazimine, ethionamide, and ethambutol after structure optimization: H (white), C (grey), N (blue), Cl (green), S (yellow), and O (red).

Results 1. Permeation of the Solute Molecules through the M. tuberculosis Cell Wall Model. The 13 solute molecules considered in this study can be classified into three categories according to their molecular shapes: (1) bulky, as represented by clofazimine, and including clofazimine, phencycline, ciprofloxacin, and ofloxacin, where the first two molecules are much bulkier than the last two (phencycline, the only non-antimycobacterial drug in the dataset, was chosen for its bulky and “football”-like molecular shape.); (2) flat, as represented by ethionamide, and including isoniazide, ethionamide, p-aminosalicyclic acid (PAS), amithiazone, dapsone, and thiocarlide; and (3) linear, as represented by ethambutol, and including ethambutol, hydnocarpic acid, and chaulmoogric acid. The three-dimensional structures of the three representative molecules, clofazimine, ethionamide, and ethambutol, after structure optimization, are shown in Figure 8. In addition to steric features, the molecular size, reflected by molecular weight (MW), of the solute molecules also varies significantly (Table 2). Isoniazid is the smallest molecule in the dataset and has a MW of 137 amu, while clofazimine has the highest MW of 473 amu. The solute molecules also possess a considerable range in lipophilicity (Table 2) and can be grouped into two classes based on their log P values being greater (class 1) or less (class 2) than 2. Clofazimine, hydnocarpic acid, chaulmoogric acid, thiocarlide, and phencycline belong to the first class, and the rest of the compounds fall into the second class. Overall, this

Figure 9. Relationship between mean-square displacement of the solute (10-20 cm2) and simulation time (ps). The thick green-colored curve is made of data points. The regression line (in red) and fit are shown. The diffusion coefficient calculated here corresponds to Dma (2) in Table 3.

dataset of 13 solutes covers a relatively large and diverse chemical space regarding molecular shape, size, and polarity. Figure 9 illustrates the relationship between mean-square displacements (χ2) of the solutes in the M. tuberculosis cell wall model and simulation time (t), using ethambutol as an example. The diffusion coefficients of the solute molecules, calculated as 1/2 of the slope of the linear regression line of χ2 versus time (see eq 2), are given in Table 3 in the form of Dma, where “D” stands for diffusion coefficient and “ma” stands for mycolic acid. Bulky solutes have a lower Dma than flat and linear solutes, while there is no significant difference between solutes in the latter two classes. Moreover, it is difficult to find a straightforward relationship between Dma values of the solutes and their molecular shapes and polarities. The geometry of a M. tuberculosis cell wall-solute complex, at the end of MDS, is exemplified using ethambutol (Figure 10). The hydrocarbon chains of the mycolates remain tightly packed and perpendicular to the cell surface throughout the MDS.



Table 3. Diffusion Coefficients (10-8 cm2/s) of the Solute Molecules in the M. tuberculosis Cell Wall (Dma)a solute

〈Dma〉

Dma (1)

Dma (2)

Dma (3)

isoniazid PAS ethionamide ethambutol ciprofloxacin ofloxacin clofazimine amithiazone dapsone hydnocarpic acid chaulmoogric acid thiocarlide phencycline

1.0 1.0 1.0 1.3 0.8 0.7 0.7 0.9 1.3 1.1 1.1 1.1 0.8

1.1 1.0 0.9 1.2 0.8 0.7 0.8 0.8 1.6 1.1 1.1 1.2 0.7

0.9 1.0 1.0 1.3 0.7 0.7 0.6 1.0 1.1 1.0 1.1 1.1 0.7

1.0 1.0 1.0 1.3 0.8 0.7 0.7 0.9 1.1 1.2 1.1 1.1 0.9

a The D ma (1-3) were calculated from the molecular dynamics trajectories using three different random seeds to inititate the MDS. The 〈Dma〉 values reported in the second column are the average values from the three MDSs.

Figure 11. Axial ∆d2 (10-20 cm2) components of clofazimine, ethambutol, and chaulmoogric acid in the membrane models over the course of the MDS. The unit of simulation time is ps. The color coding for the X, Y (lateral diffusion), and Z (transverse diffusion) is given in the clofazimine plot.

Figure 10. Structure of the membrane-solute complex of the M. tuberculosis cell wall with ethambutol at the end of MDS. The hydrogen atoms of the cell wall are shown in white, the carbon atoms in gray, and the oxygen atoms in red. The solute, ethambutol, is shown in CPK form.

Some solutes during the MDS diffusion experiments predominantly move inside the membrane in directions other than through the cell. These molecules may have high diffusion coefficients, but their actual uptake into the interior of a cell is low. The measurement of a diffusion coefficient cannot detect this lateral component to net diffusion. Thus, the observed diffusion coefficient can, perhaps, be misleading of the cellular uptake of the compound. For the solutes in Figure 5, the individual movements along the X, Y, and Z axes of each solute were calculated from the distance that the molecule moves parallel to each axis during every single MDS time step. These distances

are referred to as ∆dX2, ∆dY2, and ∆dZ2, respectively. According to the different patterns of movement exhibited by the solutes inside the cell wall model, the solute molecules can be classified into three groups. Solutes in the first group move in small ranges relative to each of the three axes. These solutes are clofazimine, ciprofloxacin, ofloxacin, and phencycline. The second group of solutes also moves uniformly along all three axes, but the overall movement is larger than that of solutes in the first group. Ethambutol, dapsone, isoniazid, ethionamide, amithiazone, PAS, and thiocarlide exhibit group 2 behavior. Chaulmoogric acid and hydnocarpic acid have considerably different movements from the solutes of groups 1 and 2. These two solutes do not move equally along each axis, instead they undergo much more movement in the membrane, the X and Y directions, than through the membrane, the Z direction. Chaulmoogric acid and hydnocarpic acid, thus, make up the third group of solutes. Clofazimine, ethambutol, and chaulmoogric acid are representative of the three solute groupings with respect to

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Table 4. Components of the Diffusion Coefficients with Respect to the Individual Axes (10-8 cm2/s) for the Solute Molecules in the M. tuberculosis Cell Walla 〈Dma〉

Dma (1)

Dma (2)

Dma (3)

solute

〈Dx〉

〈Dy〉

〈Dz〉

Dx

Dy

Dz

Dx

Dy

Dz

Dx

Dy

Dz


0.4 0.4 0.3 0.5 0.3 0.3 0.3 0.3 0.5 0.4 0.5 0.3 0.3

0.4 0.4 0.4 0.5 0.3 0.3 0.3 0.4 0.5 0.5 0.5 0.2 0.3

0.3 0.3 0.3 0.3 0.2 0.2 0.2 0.3 0.4 0.2 0.2 0.2 0.2

0.4 0.4 0.4 0.5 0.3 0.3 0.3 0.3 0.6 0.4 0.5 0.3 0.3

0.4 0.4 0.3 0.5 0.3 0.3 0.3 0.3 0.5 0.5 0.4 0.3 0.3

0.3 0.4 0.3 0.3 0.3 0.2 0.3 0.2 0.6 0.2 0.2 0.2 0.2

0.3 0.4 0.3 0.5 0.3 0.3 0.2 0.3 0.4 0.4 0.4 0.3 0.3

0.4 0.4 0.4 0.4 0.2 0.3 0.2 0.4 0.4 0.5 0.6 0.2 0.3

0.3 0.3 0.3 0.4 0.2 0.2 0.2 0.3 0.4 0.2 0.2 0.2 0.2

0.4 0.4 0.3 0.5 0.3 0.2 0.3 0.3 0.4 0.5 0.4 0.2 0.2

0.4 0.4 0.4 0.5 0.3 0.3 0.3 0.4 0.4 0.5 0.5 0.2 0.3

0.3 0.3 0.3 0.4 0.2 0.2 0.2 0.3 0.3 0.2 0.2 0.2 0.2

a The indices, (1-3), represent the MDS experiments initiated by three different random seeds. The diffusion coefficients reported in the second to fourth columns are the average values from the three MDS experiments. The diffusion coefficients of hydnocarpic acid and chaulmoogric acid, which exhibit significant lateral diffusion, are shown in bold.

diffusion and their movement patterns are shown in Figure 11. These movement patterns, especially those of the third group, can also be seen in Table 4, where Dma is partitioned into Dma-x, Dma-y and Dma-z. The Dma-z of hydnocarpic acid and chaulmoogric acid (in bold) are significantly smaller than the corresponding Dma-x and Dma-y (in bold). There is a correlation between the steric shape of a molecule and its movement pattern inside the M. tuberculosis cell wall. All the spherical and bulky molecules are in the first group, while linear and flat molecules compose the second and third groups. For every solute in the first and second groups, the extent of its movement relative to each reference axis is proportional to its Dma value. However, the large Dma values of the third group of solutes do not reflect their penetration rates. Chaulmoogric acid and hydnocarpic acid both resemble the shape, charge distribution, and polar/nonpolar asymmetry of a PM molecule, which may promote their preferred lateral movements within, as opposed to through, the membrane. In fact, these two molecules are readily taken up into the PM monolayer, and by the end of MDS the polar head groups of these acid solutes are located in the same region as the head groups of mycolates. Lateral movement is, in fact, quite common for molecules composing membranes and includes phospholipids and membrane proteins.41,42 The first observation of this event using MDS has been reported by Moore and co-workers recently.43 Table 5 lists the two-dimensional and four-dimensional (alignment independent) AMSs for the solute molecules. The AMS consists of measurements based on the eight IPE types. Only molecule pairs having their similarity measures greater than 0.900 are considered similar in this study and are given in Table 5. Most spherical and bulky compounds are similar to one another, such as ciprofloxacin and ofloxacin, having the ALL-AMS, ARO-AMS and HS-AMS measures greater than 0.900. Some flat-shaped molecules are also similar, including isoniazid and PAS, and amithiazone and dapsone, and so forth. Chaulmoogric acid and hydnocarpic acid are similar, having a two-dimensional molecular similarity measure of 0.906 and the AMS P+-AMS and HBDAMS have measured similarities of 1.000.

Table 5. Two-Dimensional and Four-Dimensional AMS Molecular Similarity Measurements between Pairs of Solute Moleculesa Part A. Two-Dimensional Molecular Similarity chaulmoogric acid hydnocarpic acid 2D 0.906

ALL

Part B. Four-Dimensional AMS amithiazone isoniaid ciprofloxacin dapsone PAS ofloxacin 0.938 0.935 0.901

NP

isoniaid PAS 0.961

P+

chaulmoogric acid hydnocarpic acid 1.000

isoniazid ofloxacin 0.942

P-

PAS ethambutol 0.957

isoniazid ethambutol 0.907

HBA

clofazimine ethambutol 0.961

PAS ethambutol 0.957

isoniazid PAS ethionamide amithiazone 0.939 0.917

PAS clofazimine 0.937

isoniazid ethambutol 0.907

chaulmoogric acid ciprofloxacin amithiazone PAS hydnocarpic acid thiocarlide ethambutol amithiazone HBD 1.000 0.954 0.925 0.917

ARO

ofloxacin PAS 1.000

phencycline ciprofloxacin ciprofloxacin PAS ofloxacin phencycline 0.999 0.999 0.999

ARO

ofloxacin phencycline 0.999

isoniazid amithiazone amithiazone ethionamide PAS ciprofloxacin 0.999 0.999 0.999

ARO

amithiazone ofloxacin 0.999

amithiazone PAS phencycline ciprofloxacin 0.999 0.999

HS

PAS ethionamide 0.941

ciprofloxacin ofloxacin 0.922

a A value of 0.000 means there is no similarity and a value of 1.000 implies identical similarity.

It is a core working hypothesis in medicinal chemistry that structurally similar molecules are likely to express similar



Table 6. Diffusion Coefficients (10-8 cm2/s) of the Solute Molecules in the DPPE and DMPC Monolayers (DDPPE, DDMPC) solute

〈DDPPE〉

DDPPE (1)

DDPPE (2)

DDPPE (3)

〈DDMPC〉

DDMPC (1)

DDMPC (2)

DDMPC (3)


1.5 1.6 1.5 1.7 1.2 1.0 1.0 1.7 1.7 1.6 1.4 1.3 1.2

1.6 1.7 1.6 1.8 1.2 1.0 1.0 1.8 1.7 1.5 1.4 1.3 1.2

1.5 1.5 1.5 1.6 1.2 1.1 0.9 1.5 1.8 1.6 1.4 1.4 1.2

1.5 1.5 1.5 1.6 1.1 0.9 1.0 1.7 1.7 1.6 1.5 1.3 1.2

1.3 1.2 1.3 1.6 1.0 0.9 0.8 1.4 1.4 1.4 1.5 1.2 0.9

1.4 1.3 1.3 1.6 1.0 0.9 0.8 1.3 1.5 1.4 1.4 1.1 0.9

1.2 1.3 1.3 1.6 1.0 0.9 0.9 1.4 1.4 1.4 1.5 1.2 0.9

1.3 1.1 1.4 1.7 1.0 1.0 0.8 1.3 1.4 1.3 1.5 1.2 1.0

biological behavior profiles including absorption distribution, metabolism, elimination, and toxicity (ADMET) properties. In this case, it would appear that similar compounds have similar permeation behavior within a common cell wall environment. This conclusion is supported by several examples, such as chaulmoogric acid and hydnocarpic acid, isoniazid and PAS, amithiazone and dapsone, and the spherical and bulky solutes. 2. Comparison of Diffusion Coefficients from the DPPE and the DMPC Monolayer Models. There is no significant difference between the DDPPE and the DDMPC values for the solute molecules studied (Table 6). But, as expected, solutes in both phospholipid membrane models have correspondingly larger diffusion coefficients than the Dma of the M. tuberculosis cell wall model. Most solutes retain three-dimensional movement patterns in both the DPPE and DMPC monolayers such as those observed in the M. tuberculosis cell wall model, except for chaulmoogric acid. This molecule moves uniformally with respect to the three reference axes in the DPPE and DMPC monolayers. Only hydnocarpic acid from the solute dataset retains its principal movement within, as opposed to through, the membrane in the DPPE and DMPC monolayers. That is, hydnocarpic acid undergoes significant lateral diffusion in both DPPE and DMPC membranes. Discussion The molecular shape of a solute is found to be an important factor for the permeation behavior of a solute through the M. tuberculosis cell wall. For example, clofazimine and thiocarlide have similar MWs. However, bulky-shaped clofazimine has a Dma value significantly lower than that of the flat-shaped thiocarlide. Moreover, phencycline and clofazimine have the same Dma values even though the MW of phencycline is only half that of clofazimine. A major finding of this MDS study is the observation for some solutes of predominant lateral diffusion within, as opposed to transverse diffusion across, the M. tuberculosis cell wall model. Chaulmoogric acid is one of the solutes that prefers to move “parallel” to the cell surface inside the cell wall structure (lateral diffusion) as opposed to moving along the hydrocarbon chains of mycolates (transverse diffusion). As a result of preferred lateral diffusion, such solutes remain inside the cell wall. Overall, the apparent penetration rate

and the corresponding absorption of solute inside the cell are both low even though the diffusion coefficient may be large. Lateral diffusion may also affect cell wall function. In fact, lipid analysis of M. Vaccae grown in the presence of chaulmoogric acid has demonstrated that chaulmoogric acid is taken up by the organism and incorporated into cell wall components.44 It is also observed that cell growth is retarded by the addition of chaulmoogric acid to the growth medium.44 Therefore, it is interesting to postulate that the antimycobacterial properties of chaulmoogric acid result from its uptake into or distortion of the cell wall structure. In the bacterial and animal membranes modeled by DPPE and DMPC monolayers, respectively, chaulmoogric acid undergoes transverse diffusion across the membrane equally well compared to lateral diffusion. Thus, this compound is not readily retained inside the phospholipid membranes and its cellular absorption and distribution properties are likely to reflect its diffusion coefficients in these membranes. Although chaulmoogric acid is traditionally used to treat leprosy, this molecule might also provide a promising antiTB mechanism: the uptake into or disruption of the M. tuberculosis cell wall structure. Thus, chaulmoogric acid could be an important lead for future anti-TB drug development. Hydnocarpic acid, similar to chaulmoogric acid, is also used to treat leprosy, and its antimycobacterial effects may also be due to the uptake into or distortion of the mycobacterial cell wall structure. The resolution of solute diffusion into transverse and lateral components in membranes might be very important in studying ADMET properties of drug candidates. It is shown that lateral diffusion plays a significant role in the transport of molecules across tissues, including the blood-brain barrier, corneal membrane, and intestinal membranes (Figure 12).45 However, to get inside a target cell and exert its action, the drug candidate has to have good transverse diffusion properties. Among the solute molecules currently studied, hydnocarpic acid is the only molecule that displays predominant lateral diffusion in the bacterial and animal membrane models, while the rest of the solutes exhibit, essentially, equal lateral and transverse diffusion. Considering that these solute molecules are actual drugs and have clinically acceptable ADMET properties, it is not clear from the results of this study what the delicate balance between

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Hong and Hopfinger

Figure 12. Illustration of lateral diffusion and transverse diffusion processes across three cells of a tissue. The green circles represent the plasma membrane. The red arrows represent nonpolar solutes, and the red circle stands for the lateral diffusion of the solute molecules inside the membrane. The diffusion processes are driven by the concentration gradient of the solute molecules.

lateral and transverse diffusion should be to realize an effective drug for a particular therapy. The molecular similarity analysis suggests that compounds having markedly high features of molecular similarity will display similar transport behavior in a common membrane/ cell wall environment. What is not clear is if a set of 13 diverse compounds is sufficient to extend the similar structure-similar transport behavior observation into a design rule. Moreover, there remains the nagging problem that, in general, building in favorable ADMET properties in a drug candidate correspondingly diminishes biological potency. Dma is generally smaller than both DDPPE and DDMPC, indicating it is more difficult for a solute to diffuse through a tightly packed M. tuberculosis cell wall inner leaflet than to pass through a more liquid-crystal-like phospholipid membrane structure. This observation is consistent with the results from the M. tuberculosis cell wall construction study.25 However, the calculated variations in diffusion coefficients of the same solute in the different membrane/cell wall environments and the computed diffusion coefficients of the different solutes in the same membrane/cell wall environment are markedly small (1 order of magnitude) in terms of both the different membrane environments and the diversity in chemical structures of the solutes. The role AG plays in formation and stabilization of the M. tuberculosis cell wall may not have been adequately modeled and could be responsible for this small range, overall, in the computed diffusion coefficients (Figures 2 and 3).25 When a bulky solute is inserted into the cell wall model, it introduces significant deformations to the structure of the M. tuberculosis model cell wall. For example, in the cell wallclofazimine complex, the PM molecules in the center of the cell wall are “squeezed” out by clofazimine, and as a result, the “surface” formed by the head groups of the PM molecules is no longer flat (Figure 13). The “chain reaction” induced by this structural deformation might disrupt the extensive inter-residue and intra-residue hydrogen bonds among the hydroxyl groups of arabinose and galactose residues of AG.25 In turn, changes in this hydrogen bonding pattern might alter the stability of the original mycolyl-AG complex structure. Consequently, the mycolyl-AG complex likely tries to keep the solute molecule out and “push” it back to the relatively

Figure 13. Structure of the membrane-solute complex of the M. tuberculosis cell wall with clofazimine at the end of MDS. Molecules are represented in the same manner as in Figure 10.

fluid outer leaflet where the solute first enters the cell wall. This “pushing back” likely involves some kind of collaborative movement between the AG backbone and the mycolate chains. As a result, the permeation rates of the solutes will be reduced. However, in the MDS experiments conducted in this study, the impact of cell wall structure deformation on solute diffusion processes may not be adequately modeled. Another possible reason for the small variation in computed diffusion coefficients may arise from neglect of the concentration gradients of the solute molecules in the MDS experiments. That is, the solubility of the solute in the membrane (a component of permeation) has not been considered. However, the variations in the computed diffusion coefficients, although small, are still consistent with the observed trends in the biological behavior of the different solute molecules in the different membrane/cell wall environments. For example, the differences in the Dma values of clofazimine, ethambutol, and chaulmoogric acid reveal quite different behaviors among these solutes in the M. tuberculosis cell wall model (Tables 3 and 4, Figure 11). In future work, a model for the entire mycolyl-AG complex will be constructed and used to simulate the permeability of the M. tuberculosis cell wall. A means to include the concentration gradient of the solutes in the membrane/cell wall (solute solubility in the membrane) should also be developed to actually represent permeation, as opposed to diffusion, processes for the solutes. Acknowledgment. Resources of the Laboratory of Molecular Modeling and Design were used in performing this study. We gratefully appreciate financial support from The


Chem21 Group, Inc., and X.H. acknowledges a University Fellowship from UIC. We also thank Mr. Jianzhong Liu of our research group and Professor Scott G. Franzblau of the Institute for Tuberculosis Research at UIC for their helpful comments and discussions over the course of this work. References and Notes (1) WHO Tuberculosis Fact Sheet. http://www.who.int/mediacentre/ factsheets/who104/en/index.html (accessed May 2003). (2) WHO report 2003. http://www.who.int/gtb/publications/globrep/ index.html (accessed June 2003). (3) Dolin, P. J.; Raviglione, M. C.; Kochi, A. Global tuberculosis incidence and mortality during 1990-2000. Bull. W. H. O. 1994, 72, 213-220. (4) Jarlier, V.; Nikaido, H. Mycobacterial cell wall: structure and role in natural resistance to antibiotics. FEMS Microbiol. Lett. 1994, 123, 11-18. (5) Brennan, P. J.; Nikaido, H. The envelope of mycobacteria. Annu. ReV. Biochem. 1995, 64, 29-63. (6) Barry, C. E., III; Mdluli, K. Drug sensitivity and environmental adaptation of mycobacterial cell wall components. Trends Microbiol. 1996, 4, 275-281. (7) Jarlier, V.; Nikaido, H. Permeability barrier to hydrophilic solutes in Mycobacterium chelonei. J. Bacteriol. 1990, 172, 1418-1423. (8) Trias, J.; Benz, R. Permeability of the cell wall of Mycobacterium smegmatis. Mol. Microbiol. 1994, 14, 283-290. (9) Chambers, H. F.; Moreau, D.; Yajko, D.; Miick, C.; Wagner, C.; Hackbarth, C.; Kocagoz, S.; Rosenberg, E.; Hadley, W. K.; Nikaido, H. Can penicillins and other beta-lactam antibiotics be used to treat tuberculosis? Antimicrob. Agents Chemother. 1995, 39, 2620-2624. (10) Jarlier, V.; Gutmann, L.; Nikaido, H. Interplay of cell wall barrier and beta-lactamase activity determines high resistance to beta-lactam antibiotics in Mycobacterium chelonae. Antimicrob. Agents Chemother. 1991, 35, 1937-1939. (11) Minnikin, D. E. In The biology of the Mycobacteria; Ratledge, C., Standford, J. L., Eds.; Academic: London, 1982; Vol. 1, pp 95184. (12) Minnikin, D. E.; Goodfellow, M. In Microbiological classification and identification; Goodfellow, M., Board, R. G., Eds.; Academic: London, 1980; pp 189-256. (13) Dobson, G.; Minnikin, D. E.; Minnikin, S. M.; Parlett, J. H.; Goodfellow, M. In Chemical methods in bacterial systematics; Goodfellow, M., Minnikin, D. E., Eds.; Academic: London, 1985; pp 237-265. (14) Brennan, P. J. In Microbial lipids; Ratledge, C., Wilkinson, S. G., Eds.; Academic: London, 1988; Vol. 1, pp 203-298. (15) Brennan, P. J. Structure of mycobacteria: recent developments in defining cell wall carbohydrates and proteins. ReV. Infect. Dis. 1989, 11 (Suppl.), 420-430. (16) Hunter, S. W.; Murphy, R. C.; Clay, K.; Goren, M. B.; Brennan, P. J. Trehalose-containing lipooligosaccharides. A new class of speciesspecific antigens from mycobacterium. J. Biol. Chem. 1983, 258, 10481-10487. (17) Hunter, S. W.; Gaylord, H.; Brennan, P. J. Structure and antigenicity of the phosphorylated lipopolysaccharide antigens from the leprosy and tubercle bacilli. J. Biol. Chem. 1986, 261, 12345-12351. (18) Liu, J.; Barry, C. E., III; Besra, G. S.; Nikaido, H. Mycolic acid structure determines the fluidity of the mycobacterial cell wall. J. Biol. Chem. 1996, 271 (47), 29545-29551. (19) Yuan, Y.; Crane, D. C.; Musser, J. M.; Sreevatsan, S. Barry, C. E., III. MMAS-1, the branch point between cis- and trans-cyclopropanecontaining oxygenated mycolates in Mycobacterium tuberculosis. J. Biol. Chem. 1997, 272 (15), 10041-10049. (20) Barry, C. E., III; Lee, R. E.; Mdluli, K.; Sampson, A. E.; Schroeder, B. G.; Slayden, R. A.; Yuan, Y. Mycolic acids: structure, biosynthesis and physiological functions. Prog. Lipid Res. 1998, 37, 143-179. (21) Daffe, M.; Brennan, P. J.; McNeil, M. Predominant structural features of the cell wall arabinogalactan of Mycobacterium tuberculosis as revealed through characterization of oligoglycosyl alditol fragments by gas chromatography/mass spectrometry and by 1H and 13C NMR analysis. J. Biol. Chem. 1990, 265, 6734-6743.

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BM0345155

Molecular Modeling and Simulation of Mycobacterium tuberculosis

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