Studies on the Structure and Stability of Cyclic Peptide Based

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Studies on the Structure and Stability of Cyclic Peptide Based Nanotubes Using Oligomeric Approach: A Computational Chemistry Investigation R. Vijayaraj, S. Sundar Raman, R. Mahesh Kumar, and V. Subramanian* Chemical Laboratory, Central Leather Research Institute, Council of Scientific and Industrial Research, Adyar, Chennai 600 020, India ReceiVed: June 12, 2010; ReVised Manuscript ReceiVed: October 14, 2010

In this study, an attempt has been made to investigate the structure, dynamics, and stability of cyclic peptide nanotubes (CPNTs) formed by the self-assembly of cyclic peptides (CPs) using classical molecular dynamics (MD) simulation and semiempirical quantum chemistry calculation employing PM6 Hamiltonian with the dispersion correction and hydrogen-bonding interaction (DH2). The structure and energetics of monomer and various oligomeric CPNTs have been investigated by considering the (cyclo-[(D-Ala-L-Ala)4]) peptide as the model for CP. Although the formation of CPNTs has been intensively studied, the present study adds valuable information to the de novo design of CPNTs. Various geometrical parameters extracted from the MD simulation reveal that the terminal residues are loosely hydrogen bonded to the inner subunits regardless of degree of oligomerization. The hydrogen bonds present in the inner core regions are stronger than the terminal residues. As the degree of oligomerization increases, the stability of the tube increases due to the hydrogen-bonding and stacking interactions between the subunits. The results show that the binding free energy increases with the extent of oligomerization and reaches saturation beyond pentamer CPNT. In addition, hydrophobic and electrostatic interactions play crucial roles in the formation of CPNTs. Analysis of both structure and energetics of the formation of CPNTs unveils that the self-assembly of dimer, trimer, and tetramer CPNTs are the essential steps in the growth of CPNTs. Introduction During the past two decades, studies aiming at the design and synthesis of molecules that can self-assemble into supramolecular structures have received increased attention.1 In this context, supramolecular self-assembly of the cyclic peptides (CPs) has attracted widespread attention of the scientific community. CPs can self-assemble into extended hollow tubular structures to form a cyclic peptide nanotube (CPNT) by forming antiparallel hydrogen bonds between the homochiral amino acid residues of the adjacent rings. The structures of CPNTs resemble open-ended tubelike structure in gramicidin A.2-4 The selfassembled CPs have emerging applications in the field of biosensors, antimicrobial agents, selective transport system, and other potential uses in material sciences, biology, optics, and electronics.5-28 A variety of CPs with flat ring-shaped structures consisting of even number of alternate L- and D-R-amino acids has been synthesized and characterized and their potential applications have been explored.29-45 In 1972, Hassall proposed the self-assembly of CPs into tubelike conformation through backbone-backbone hydrogen bonding.46 The same author validated the formation of tubelike structures by backbone-backbone hydrogen bonding using X-ray diffraction studies on the tetrapeptide of cyclo[-(LSer(OtBu)-β-Ala-Gly-β-Asp(OMe))-].47 De Santis and coworkers explored the ability of poly-D,L-R-peptides to form a similar tubelike structure through ring stacking in 1974.48 However, the subsequent experimental work carried out to support their theoretical assumption was not successful due to the extreme insolubility of the peptides.49,50 In 1993, Ghadiri et al. synthesized and characterized the eight amino acid residues * To whom correspondence [email protected].

should

be

addressed.

E-mail:

based (cyclo[-(D-Ala-Glu-D-Ala-Gln)2]) CP and they showed that these can self-assemble into tubular conformation.38 Subsequently, several attempts have been made to design tubular structures based on peptides. The protonated tubular structures have been crystallized into hundreds of nanometer long with the internal van der Waals diameter of 7-8 Å.38 Ghadiri and co-workers proposed the design principles for CPs and their synthesis.12,36 Since the discovery of the formation of alternate D- and L-R-amino acids into tubelike conformation, various nonstandard amino acids have been used to construct CPNT such as (1R,3S)-3-aminocyclohexanecarboxyclic acid (D-γ-Ach), (1R,3S)-3-aminocyclopentanecarboxyclic acid (D-γ-Acp).29 The arrangement of alternate L- and D-amino acid residues in the CP imposes all the amino acid side chains pointing outward with respect to the center of the peptide ring and thus it enables the formation of tubular core structure. The backbone amide functionality lies perpendicular to the plane of the ring. The characteristic arrangements of side chains and backbone CdO and N-H groups facilitate the peptide ring to form flat ring-shaped conformation which further enhances the antiparallel β-sheet like hydrogen bonding with the oppositely oriented neighboring rings. The stacking of CPs into tubelike conformation depends on the specific arrangement of adjacent chain orientations as well as the alignment of L- and D-amino acids in the neighboring rings. The stacking of CPs with oppositely oriented chains is shown in Scheme 1 which reveals the role of β-sheetlike hydrogen-bonding interaction between the adjacent chains. Furthermore, the same chirality of interacting amino acids in the adjacent chains circumvent the aligning of backbone amide functionality with CR-H, and vice versa, which leads to unfavorable alignment of amino acids for hydrogen-bonding interaction (Figure 1). The selection of amino acid to form the

10.1021/jp105403u  2010 American Chemical Society Published on Web 11/18/2010

Stability of Cyclic Peptide Based Nanotubes

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SCHEME 1: Schematic Representation of the Arrangements and Chirality of the Amino Acids in the CP Chainsa

a

The sequential chains are named as CP1 to CP8. The terminals are assumed to be bonded in order to form the cyclic structure.

Figure 1. Schematic representation of the CP stacking. Each chain of the CP is truncated with two amino acids to highlight the stacking interaction. Hydrogen bonds are shown as dotted lines.

CP governs the hydrophilic and hydrophobic nature of the tube surface and thereby stabilizes the tube structure in the water solution. Horne et al. have carried out a detailed study on the adenovirus inhibiting activity of the membrane associated cyclic D- and L-R-peptides by preventing the escape of virions from the endosome.51 Several molecular modeling studies have been carried out on the CPNT employing a variety of computational chemistry approaches. The equilibrium arrangement of water molecules and its diffusion coefficient inside the CPNT have been obtained from the MD simulation.39 Density functional theory (DFT) based calculations on the cyclo[(D-Ala-Glu-D-AlaGln)2] have been carried out by Carloni and co-workers to delineate the geometrical and electron density parameters of the CPNT.52 Lewis et al. calculated the electronic structure, stretching modes of N-H and C-O, and glucose molecule interactions

with the monomer and dimer CPs composed of cyclo[D-AlaGlu-D-Ala-Gln] using the DFT method.53 The enthalphic difference between the parallel and antiparallel arrangement of dimer CPs with N-methylated cyclo-[D-Ala-L-Ala]4 has been calculated using AM1 method.54 They have identified that the enthalphic difference is very small between the parallel and antiparallel systems and the calculated stabilization energy per hydrogen bond is ∼3.6 kcal/mol. Bragin and co-workers have applied the DFT method to study the equilibrium structure and electronic properties of {cyclo[Gly-D-Ala]4}2.55 The geometrical parameters and interaction energy of the monomer and dimer CPs consisting of cyclo[L-Phe-D-Ala]4 have been computed using semiempirical and DFT-based methods.56 The same type of calculations have been carried out to characterize the energetic and structural properties of cyclo[(-β3-HGly)4-] and its oligomers.57 It has been found that the gradual increase in the oligomerization facilitates the enhancement of favorable interaction of the CPNT. It is observed from the molecular dynamics simulation study on CPNT consisting of eight cyclo[(L-Trp-DLeu)3-L-Gln-D-Leu] embedded in a fully hydrated DMPC bilayer that the embedded CPNT function as synthetic, integral transmembrane channels.58 Ion current calculations based on threedimensional Poisson-Nernst-Planck theory performed on the CPNT that consists of 8/10 cyclo[(-L-Trp-D-Leu-)4] embedded in a lipid bilayer membrane reveals that the cation concentration is dominated over the anion concentration inside the CPNT.59 The molecular dynamics simulation study on the dimer CPNT in nonpolar (nonane) and polar (water) solvent shows that the tubelike conformation is stable in the nonpolar solvent than the polar solvent.60 It has been identified from the same study using the nonane/water interfacial system that the monomer CP units prefers to stay close to the nonane phase. Steered molecular dynamics studies on the potential of mean force of Na+ and K+ ions in a CPNT shows that the Na+ ions have a longer residence time inside the nanotube and the permeation of Na+ is less when compared with that of K+.61 Fandino et al. have studied the equilibrium deformability of the CPNT consisting of alternating (1R,3S)-3-aminocyclohexanecarboxyl acid and D-R-amino acid, which has partial hydrophobic inner cavity, in various solvent environments by estimating the free energy required to pull away one terminal CP unit based on steered molecular dynamics simulations.29 Recently, Chiu et al. have carried out MD simulation to characterize the noncovalent functionalization of single-walled carbon nanotubes (SWNT) by reversible cyclic peptides.62 The DFT-based dimerization energy calculated for the R,γ-CP nanotube reveals that the R-R dimerization is energetically favored than the γ-γ dimerization.63 In the present study, we have investigated the structure and dynamics of CPNTs composed of {cyclo[(D-Ala-L-Ala)4]}n,

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Figure 2. Schematic representation of the model systems considered for the simulation study. The numeric value associated with CPNT denotes the number of CPs in the system.

(where n ) 1-8 and n represents the number of CPs) using MD simulations. The energetics of the formation of CPNTs has been calculated employing molecular mechanics/ Possion-Boltzmann surface area (MM-PBSA) approach and semiempirical quantum chemistry method. Despite several theoretical studies having been carried out on CPNTs composed of various amino acids, the relationship between the length and stability of the CPNT has not been addressed comprehensively. Thus, following points related to the self-assembly and stability of CPNTs have been investigated in this study (i) what is the minimum number of CPs required to form stable tubelike conformation; (ii) the role of oligomerization on the selfassembly of CPNTs; and (iii) to understand the interplay of various forces in the self-assembly and stabilization of CPs during the tube formation. Computational Details Rationale for the Selection of Model CP. The choice of Ala as the constituent amino acid in the CPNT reduces the computational cost and enables understanding noncovalent interactions in the formation of CPNT. The stability of the CPNT has been attributed to the ring strain associated with the internal diameter of the CP and ability of the CP to form flat ring-shaped conformation. Previous experimental and molecular modeling studies have shown that CP consists of eight amino acids and has relatively low strain energy and the desired flat ring-shaped conformational stability.37,64,65 Thus, the CP containing eight amino acids was selected for the present study. Molecular Dynamics Simulation Protocol. The initial geometry for the CP was built using Insight II software package.66 The geometry of single CP unit was minimized using various geometry optimization methods like steepest descent and conjugate gradient methods. This final geometry of CP was used to build dimer, trimer, tetramers, and other oligomers. During the model building, necessary care was taken to orient the side chain and the alignment of the amino acids (L and D) in the adjacent chains as shown in Scheme 1. Various CPNT models used in the present study are given in the Figure 2. Both the energy minimization and MD simulations were carried out using AMBER 9.067,68 employing ff99SB69 force field parameters. After sufficient relaxation, the systems were solvated with rectangular box of TIP3P water molecules extending 12 Å away from the solute atoms.70,71 The energy minimization, equilibra-

TABLE 1: Composition of Various CPNTs and Periodic Box Volume

system CPNT1 CPNT2 CPNT3 CPNT4 CPNT5 CPNT6 CPNT7 CPNT8

total no. total no. init periodic no. of CP of amino of water total no. box vol units acids molecules of atoms (Å3) 1 2 3 4 5 6 7 8

8 16 24 32 40 48 56 64

1664 2049 2306 2640 3104 3667 4038 4412

5072 6307 7158 8240 9712 11481 12674 13876

71556 87280 98584 114257 132332 155522 169505 187862

tion, and production runs of various CPNTs were carried out in different stages: (i) solvent minimization for 10 000 cycles by restraining the CPNT with 3 kcal/mol/A2 restrain weight, (ii) a 50 ps solvent equilibration run by restraining the CPNT, (iii) all-atom minimization for 10 000 cycles, (iv) a 200 ps final unconstrained equilibration, and (v) production MD for 4 ns with 2 fs time step. From the production run, a frame for every 0.2 ps was collected for trajectory analysis. All the simulations were carried out in NPT ensemble and the pressure was maintained at 1 bar using Berendsen weak-coupling algorithm with a relaxation time constant of 1 ps.72,73 The particle-mesh Ewald (PME) summation method was used for calculating the long-range electrostatic interaction and the nonbonded interactions were truncated at 12 Å cutoff.74,75 The temperature of the system was maintained at 300 K using Langevin dynamics with collision frequency of 5 ps-1. The SHAKE algorithm was used to constrain all the bonds involving hydrogen atoms.76 Table 1 contains information on the number of CP units in each CPNT, total number of residues, water molecules, and initial volume of the periodic box. MM-PBSA Calculation. The binding free energy of each chain in the CPNT with respect to the remaining CP units was calculated using the MM-PBSA methodology as implemented in AMBER 9.77-79 The dimer and higher oligomeric CPNTs were considered for the binding free energy calculation. The calculation of free energy of binding was carried out for 40 snapshots which were retrieved at every 25 ps interval from the last 1 ns of production run. The water molecules were removed from each snapshot, and the free energy of binding of each CP unit present in the CPNT8 with other CP subunits of the same system was calculated using

Stability of Cyclic Peptide Based Nanotubes n m ∆Gbinding ) Gcomplex - (Gn + Gcomplex )


(1)

where Gn represents the energy of the nth monomer in CPNT8 and the position of the n ranges from CP1 to CP8 (Scheme 1). m denotes the energy of the complex which excludes The Gcomplex the nth monomer (Gn) and Gcomplex represents the complex n is the binding free energy for the nth energy. The ∆Gbinding monomer CP. Similarly, the binding free energy for the CPNT7 system was calculated with n ) CP1 to CP7. The binding free energy for the CPNT2-CPNT6 was calculated using the same protocol. The free energy of binding of each subunit was calculated using the formula

∆Gbinding ) ∆EMM + ∆Gsolv - T∆Ssolute

(2) Figure 3. Average rmsd (in Å) of heavy atoms of various CPNTs with standard deviation.

The molecular mechanics energy, ∆EMM, was divided into

∆EMM ) ∆Einternal + ∆EvdW + ∆Eele

(3)

where ∆Einternal, ∆EvdW, and ∆Eele represent internal, van der Waals, and the electrostatic contributions to the MM energy. The solvation energy term was divided into two terms

∆Gsolv ) ∆Gpol + ∆Gnp

(4)

The polar contribution (∆Gpol) to the free energy of solvation (∆Gsolv) was calculated by solving the Poisson-Boltzmann (PB) equation using the PBSA module of the AMBER9. The nonpolar contribution (∆Gnp) to solvation free energy was calculated from the solvent-accessible surface area (SASA) using the molsurf program with a probe radius of 1.4 Å, according to the equation

∆Gnp ) γSASA + β

(5)

where γ ) 0.0072 kcal mol-1 Å-2 and β ) 0.0 kcal/mol. The interior and exterior dielectric constants were set to 1 and 80, respectively, with a grid spacing set to 0.5 Å, and 1000 linear iterations were performed. Bond radii and a probe radius of 1.4 Å were used for both ∆Gpol and ∆Gnp calculations. The conformational entropy contributions such as translation, rotation, and vibration to the binding free energy were calculated using normal-mode analysis program of MM-PBSA package. In addition to the calculation of the binding energy (BE) of each CP unit in the system, the total binding energy of each CPNT was calculated using n n BEtotal ) Ecomp - nEmono

(6)

n where n is the total number of CP units in a CPNT, Ecomp is the total energy of the CPNT with n CP units, and Emono is the energy of the monomer CP unit. Various energy contributions (eqs 3 and 4) obtained from the MM-PBSA calculation were used to calculate the gas-phase binding energy and its free energy of solvation as follows

n,gas MM MM BEtotal ) ∆Ecomp - n∆Emono

(7)

n,PB MM solv MM solv ∆Gtotal ) (∆Ecomp + ∆Gcomp ) - n(∆Emono + ∆Gmono ) (8) MM MM and ∆Emono represent the total energy of the where ∆Ecomp complex and monomer systems, respectively, using eq 3. ∆Gsolv comp and ∆Gsolv mono denote the solvation free energy contribution of the complex and monomer systems, respectively, as obtained from n,PB eq 4. BEn,gas total and ∆Gtotal are the gas-phase and solvation binding energies of CPNT, respectively, with n monomer CP units. Calculation of Binding Energy Using Semiempirical Method. The results obtained from the earlier studies using PM6 Hamiltonian confirm that this method can be routinely employed for the modeling of large systems including proteins.80 Recently, Hobza and co-workers have shown that PM6-DH2 method predicts results comparable to that of sophisticated DFT approaches, like B2-PLYP and M06-2X methods.81,82 Thus, binding energies of dimer and other oligomers were calculated using the PM6-DH2 approach using the average structures obtained from the molecular dynamics study. The same structures were optimized using localized molecular orbital method employing MOZYME keyword with PM6 Hamiltonian.83,80 To compute the BEs, single-point energy calculations were carried out with PM6-DH2 Hamiltonian for the geometries obtained from the PM6 (MOZYME) method. The BE of all the clusters were calculated using the following equation

n

BE ) |Ecomp -

∑ Ei|

(9)

i)2

where Ecomp and Ei are energies of the complex and monomers, respectively, and n is the total number of monomers in the CPNT. All semiempirical calculations were performed using the MOPAC2009 package.84 Results and Discussion Structural and Dynamical Properties of Various CPNTs. The analysis of various trajectories of CPNTs confirms that the antiparallel β-sheet tubelike structure is maintained throughout the simulation. Nevertheless, a slight deviation from the tubelike structure is observed at the terminal units of all the CPNTs. Figure 3 shows the average rmsd of heavy atoms of different CPs with reference to the respective starting geometries. It can be observed that the fluctuations in CPNT1, CPNT2, and CPNT3

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Figure 4. Average rmsd (in Å) of CR, C, and N atoms of each CP unit in various CPNTs.

TABLE 2: Average Length (L) and Its Standard Deviation (SD), and Volume of Dimer and Oligomeric CPNTs system

L (Å) (SD)

∆La (Å)

volume (Å3)

CPNT2 CPNT3 CPNT4 CPNT5 CPNT6 CPNT7 CPNT8

5.07 (0.57) 9.53 (0.10) 14.31 (0.12) 19.08 (0.13) 23.87 (0.15) 28.65 (0.16) 33.38 (0.25)

4.46 4.78 4.77 4.79 4.78 4.73

106.75 333.50 485.38 688.18 806.45 916.99 1086.09

a

(CPNTn - (CPNTn-1)), n ) 3-8.

are comparatively higher than that of other oligomers. Particularly, the rmsd of the dimer is higher than that of the monomeric unit. With increase in the length of the tubular structure, the fluctuation decreases (stability increases) due to the synergetic effect of hydrogen-bonding and stacking interactions. The average rmsd of the backbone atoms (CR, C, and N) and the side-chain atoms (Cβ) for each CP unit present in various CPNTs are depicted in Figure 4 and Supporting Information (Figure S1). The plots reinforce similar findings from the rmsd of backbone atoms. It is interesting to note that the fluctuations in the rmsd exhibit odd-even effect. In addition, the fluctuations in odd numbered oligomers are lower than that of even numbered systems. The average distance between the CR planes of the first and last CP units is referred to as tube length (L) of CPNT. The tube lengths of different CPNTs are presented in Table 2 along with volume of the various tubes. In the case of CPNT2, the distance between the two CP units is ∼5.0 Å. In accordance with the elevated fluctuations in CPNT2, it exhibits significantly larger standard deviation in the L value. Upon gradual oligomerization (stepwise addition of CP units), the L decreases due to the attractive hydrogen-bonding and stacking interaction between various CP units. The increase in L (∆L) upon addition of each CP unit is ∼4.7 Å. These values are in close agreement with those values obtained from earlier experimental and molecular dynamics simulations.38,39,85 It has been found from the earlier reports that the average volume occupied by the water molecule diffusing through the CPNT is 47.6 Å3.39 By considering this value, the average number of water molecules that can be accommodated by various CPNTs (CPNT2-CPNT8) range from 2.3 to 23.2. The number of water molecules that can pass

Vijayaraj et al. through the octamer is similar to that observed in the previous investigations.39,58,86 The diameter (D) of various CPs in CPNT1-CPNT8 was calculated by averaging all the four longest CR-CR distances in each CP unit. The results are presented in the Supporting Information (Table S2). The average diameter of various CPs in CPNT8 ranges from 9.84 to 9.86 Å. The diameter of the CPNT1 is 9.02 Å which is appreciably lower than that of higher oligomeric CPNTs. The diameter of the tube reaches a saturation value of ∼9.85 Å beyond CPNT2. Thus, as the length of the tube increases, the diameter attains approximately a constant value due to self-assembly of CPs. However, standard deviations for the terminal units are marginally higher which reveal that inner units are structurally more stable than the outer ones. A similar observation has been reported in previous studies on different CPNT composed of 8, 10, and 12 CP units.33,38 The residuewise φ and ψ values and their standard deviations obtained from the MD trajectories for CPNT8 are given in the Supporting Information (Table S3). The calculated φ and ψ angles are in agreement with the previously reported values obtained from DFT calculation on monomer and dimer.55,56 The terminal residues exhibit larger standard deviation when compared to the same in the middle region. This evidence elicits that terminal residues undergo more dynamical fluctuations in concomitance with the findings from rmsd analysis. The overall observation of various geometrical properties calculated from the present study and its agreement with previously reported geometrical properties suggest that the substitution of various residues on the CP has no significant effect on the global geometrical properties. Hydrogen Bond Analysis. The self-assembly of CPs is mainly driven by the intermolecular hydrogen-bonding interaction. The calculated properties of intermolecular hydrogenbonding interaction between various CP units of CPNT8 are presented in the Supporting Information (Table S4). The hydrogen bond distance (O · · · H-N), angle (CdO · · · H), and occupancy are 2.97 ( 0.14, 160 ( 10, and 99%, respectively. The observed hydrogen bond distance and angle are in good agreement with the earlier results.5,87 Marginal deviations in the geometrical properties of the terminal hydrogen bonds can be seen from the results presented in Table S4. Furthermore, the occupancy of terminal hydrogen bonds is less than that of the middle ones. A similar trend has also been observed from the calculated lifetime of various hydrogen bonds between different CP units. These results reiterate that CPs units present at the core region are held together by strong hydrogen bonds whereas the terminal units are loosely attached to the core unit. The properties of hydrogen-bonding interaction in dimer, trimer, tetramer, and pentamer are given in the Supporting Information, Tables S5-S8. It is obvious from the results that the increase in the number of oligomer augments the percentage of occupancy of hydrogen-bonding interaction and lifetime. Relatively shorter hydrogen bonds are observed in the core regions of trimer and higher oligomeric CPNTs when compared to the dimer. Interactions of Water Molecule with CPNT. The flow of water through a carbon nanotube has attracted several studies.88 Similarly, the flow of water molecules through various CPNTs has been reported. It is found that the distribution of water molecules inside the CPNT is not uniform, rather it is highly scattered in the region between the planes of the CP units that are adjacent to the hydrophilic part of the tube wall. The hydrophobic part of the CR plane is less populated.39,58,86 Furthermore, it is observed that the water molecules interact



Figure 5. Average, maximum, and minimum number of hydrogen bonds observed between the carbonyl oxygen and solvent molecules.

with the amide functionality from the lumen. The analysis of the molecular dynamics trajectory of the CPNT8 shows that, in addition to the interaction of water molecules with the amide group, the presence of small residue (alanine) can facilitate the formation of hydrogen bond between the water and the amide groups from the surface of the tube. A similar interaction can also be observed from the water molecules present in the outer surface of the CPNT. Figure 5 illustrates the average, minimum, and maximum number of hydrogen bonds observed between the carbonyl oxygen and O-H of water. It is evident that the average and maximum number of hydrogen bonds involving the carbonyl oxygen and water are 38 and 50, respectively for CPNT8. It is found from the previous studies that the CR plane and mid-CR plane can accommodate one and two water molecules, respectively. Thus, CPNT8 can accommodate approximately 22 water molecules inside the tube. The calculated volume from the present study ensures the presence of 22 water molecules inside the tube. In addition to the inside water molecules, some water molecules may interact with the outer surface. Figure 6 depicts the interaction of water molecules with the carbonyl oxygen of CP from the surface of the octamer CPNT. It reveals that in addition to the interaction of water molecules with the carbonyl oxygen from the lumen of the CPNT, some of the water molecules are observed between the Cβ atoms of a CP unit. They form carbonyl-water hydrogenbonding interaction (CdO · · · HsO). It can be noted that these kind of hydrogen bonds are intrinsic property of the alaninebased CPs. The calculated percentages of occupancies for these hydrogen bonds are significantly low. Free Energy of Binding. Although the estimation of free energy of binding is usually calculated on a large collection of equilibrated structures sampled from molecular dynamics study, it has been proved that the free energy calculation on single, relaxed complex structure is adequate to gain insight into the nature of interaction.89,90 Thus, the MM-PBSA method was used to calculate the free energy of binding with frames collected from the last 1 ns simulation. Various contributions to the free energy of binding obtained from the MM-PBSA calculations are listed in Table 3 and in the Supporting Information (Table S9). It can be seen from the results that the electrostatic contribution of each subunit (∆Eele) increases up to pentamer and then attains saturation at the core

Figure 6. Water molecule (green) interaction with the CP carbonyl O from the surface of the octamer CPNT. The surface coloring is based on the depth of the tube. Half of tube molecular surface is sliced to enhance the visibility.

regions. It is noteworthy that the electrostatic contribution for the dimer CPNT is considerably lower than for the other systems. The electrostatic contributions for the trimer and higher oligomeric CPNTs range from -80.3 to -87.10 kcal/mol. This observation indicates that the electrostatic contribution of each subunit does not vary significantly after the formation of pentamer. Since the backbone carbonyl and amide hydrogenbonding interaction is the predominant one, average electrostatic energy contribution of each subunit per hydrogen bond has been calculated using the ∆Eele. The CP unit in the middle of the tube forms 16 hydrogen bonds with the adjacent subunits

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TABLE 3: Contribution of Various Energy Components to the Free Energy of Binding for Dimer and Oligomeric CPNTs (kcal/mol)a ∆Eele

∆Eele CP

system CPNT2 CPNT3 CPNT4 CPNT5

1

2

CP

3

4

5

6 7 8 system

1

2

3

4

5

CPNT2 CPNT3 CPNT4 CPNT5

∆EvdW

∆EvdW

1

2

CP

3

4

5

6 7 8 system

-16.12 -19.56 -36.88 -19.08 -19.70 -37.81 -37.32 -19.21 -19.08 -37.08 -36.71 -36.00 -19.10

1

2

3

4

5

1

2

3


-3.21 -3.80 -3.79 -3.78

-7.59 -7.56 -7.55

-3.79 -7.56 -7.56

1 17.98 35.27 34.53 34.47

2

5

-3.78 -7.59

6

7

8

-3.79

system

1

2

3

4

5

6

7

8

CPNT6 CPNT7 CPNT8

-3.80 -3.79 -3.78

-7.55 -7.55 -7.54

-7.53 -7.54 -7.53

-7.55 -7.55 -7.53

-7.55 -7.54 -7.53

-3.78 -7.58 -7.52

-3.81 -7.56

-3.79

∆Gpol

3

71.19 71.69 71.62

CP

4

35.19 73.01 73.57

5

36.31 72.37

6

7

8

system

1

2

3

4

5

6

7

8

CPNT6 CPNT7 CPNT8

36.35 36.44 35.61

72.98 74.09 73.12

73.45 74.56 74.29

73.49 74.28 73.79

72.49 74.13 74.00

35.73 72.38 74.91

35.12 73.25

35.41

35.67

∆Gele

∆Gele CP

system

1

2

CP

3

4

5

6 7 8 system

CPNT2 5.20 CPNT3 -4.91 -9.17 -4.04 CPNT4 -3.49 -8.90 -10.60 -5.19 CPNT5 -5.18 -11.77 -13.59 -13.15 -5.96

1

2

3

4

3

4

5

6 7 8 system

-14.13 -28.27 -53.63 -26.91 -26.98 -54.35 -55.49 -28.18 -28.05 -56.40 -57.86 -56.74 -28.85

2

8

1

2

3

4

5

3

6

7

8

CPNT6 -28.00 -55.51 -57.13 -56.60 -54.96 -27.95 CPNT7 -28.16 -55.80 -56.23 -56.21 -56.78 -55.69 -28.11 CPNT8 -27.52 -54.93 -56.83 -57.01 -56.64 -57.11 -55.62 -27.57 ∆Gbinding

CP 1

7

CP

∆Gbinding

system

6

∆GPB CP

2

5

CPNT6 -5.27 -11.42 -11.87 -10.22 -9.91 -5.38 CPNT7 -5.16 -11.30 -11.50 -11.70 -11.87 -10.58 -4.81 CPNT8 -4.33 -10.04 -11.12 -10.86 -10.84 -11.79 -10.7 -4.31

∆GPB

1

8

CP 4

CP system

7

∆Gnp

∆Gpol


6

CPNT6 -18.93 -36.54 -37.73 -38.82 -37.49 -18.79 CPNT7 -19.21 -36.95 -37.19 -36.95 -37.36 -37.53 -19.49 CPNT8 -19.41 -37.34 -38.18 -38.62 -38.27 -37.79 -37.36 -19.47

CP system

system

8

CPNT6 -41.62 -84.39 -85.32 -83.71 -82.4 -41.11 CPNT7 -41.60 -85.39 -86.06 -85.99 -85.99 -82.96 -39.94 CPNT8 -39.94 -83.16 -85.41 -84.65 -84.83 -86.70 -83.95 -39.72

∆Gnp


7

-12.78 -40.19 -80.36 -39.23 -38.02 -80.66 -83.61 -41.5 -39.65 -83.39 -87.16 -85.52 -41.62

CP system

6

CP 4

5

CPNT2 4.04 CPNT3 -9.42 -34.82 -7.73 CPNT4 -8.37 -34.69 -35.69 -9.44 CPNT5 -9.48 -36.6 -35.55 -37.07 -10.15

6 7 8 system

1

2

3

4

5

6

7

8

CPNT6 -9.24 -35.66 -33.82 -33.46 -35.09 -9.33 CPNT7 -9.67 -35.95 -33.97 -32.44 -33.70 -35.76 -9.41 CPNT8 -8.93 -35.04 -34.37 -33.42 -33.08 -34.15 -35.83 -8.95

a ∆Eele and ∆EvdW represent the electrostatic and van der Waals interactions, respectively. ∆Gnp and ∆Gpol denote the nonpolar and polar contributions to solvation. ∆Gele results from the addition of ∆Gpol + ∆Eele. ∆GPB represents the total binding energy calculated from ∆EMM + ∆Gsolv. ∆Gbinding stands for the final free energy of binding calculated from ∆GPB - T∆S. All the values are represented in kcal/mol units.



TABLE 4: Average Interaction Energy (kcal/mol) Per Hydrogen Bond Calculated from the MM-PBSA Electrostatic Energy Component

TABLE 5: Gas Phase Binding Energy (BE) and Its Free Energy of Solvation (∆G) Calculated for Dimer and Oligomeric CPNTs Using Energy Components Obtained from the MM-PBSA Method

CP system CPNT2 CPNT3 CPNT4 CPNT5 CPNT6 CPNT7 CPNT8

1 -1.59 -5.02 -4.75 -4.96 -5.02 -5.20 -4.99

2 -5.02 -5.04 -5.21 -5.27 -5.34 -5.20

3 -4.90 -5.22 -5.44 -5.33 -5.38 -5.34

4

-5.19 -5.34 -5.23 -5.37 -5.29

5

-5.20 -5.15 -5.37 -5.30

6

-5.14 -5.18 -5.42

7

-4.99 -5.25

BE

8

-4.97

whereas the terminal units form only eight hydrogen bonds. The calculated average electrostatic energy contribution per hydrogen bond for each sub unit using the MM-PBSA method is listed in the Table 4. It ranges from -4.75 to -5.44 kcal/mol. Previous theoretical studies on the similar systems predicted comparable estimates (-3.6 and -5.7 kcal/mol).37,54,56 The average electrostatic contribution per hydrogen bond for CNPT2 is ∼-1.59 kcal/mol. In fact, CNPT2 has the lowest electrostatic energy contribution when compared to other systems. The hydrogen bond energy difference between the dimer and trimer CPNT as depicted in the Table 4 highlights the increase in electrostatic contribution from dimer onward. The hydrogen bond strength increases from trimer and reaches saturation from CPNT5. Comparatively low electrostatic contribution per hydrogen bond has been observed for the terminal CP units which reiterates that the association of these units with the core is weak. The van der Waals energy (∆EvdW) contributions of each CP unit present in the dimer and other CPNTs are shown in Table 3. The van der Waals energy is constant for trimer and higher oligomers except for CPNT2. It can also be observed that the van der Waals energy contributions corresponding to the core regions are 2-fold higher than that of terminal CP units due to the absence of interacting partners at the terminals. The comparison of ∆Eele and ∆EvdW contributions reveals that the electrostatic contribution is approximately 2 times larger than the van der Waals energy. Further, the electrostatic contribution to the free energy of binding is opposed by unfavorable contributions owing to the polar part of the solvation free energy (∆Gele ) ∆Gpol + ∆Eele). Thus, solvation effect reduces the electrostatic contribution in the self-assembling process. The total electrostatic contribution (∆Gele) for the self-assembly of CPs at the core region ranges from -9.0 to -13.0 kcal/mol. As expected, the same contributions for the terminal regions are lower than the core. The van der Waals and nonpolar solvation contributions account for approximately -45.0 kcal/ mol (∆EvdW + ∆Gnp). On the other hand, the electrostatic and polar solvation interactions amount to ∼-11.0 kcal/mol (∆Gele) for the core regions of various CPNTs. These values clearly demonstrate that the van der Waals interaction plays a dominant role in the self-assembly of alanine-based CPs in polar environment. This observation is concomitant with the previous molecular dynamics study of CPNTs in various solvent environments.60 The calculated results from the PB method (∆GPB) reveal that the BE for the core and terminal CPs are ∼-56.0 and -28 kcal/mol, respectively. The ∆GPB of CPNT2 is -14.13 kcal/ mol. The same for the core region of the CPNT3 is -53.63 kcal/mol. It has been found from the previous study that the gas-phase BE calculated from the DFT method for dimer CPNT consists of {cyclo[L-Phe-D-Ala]4}2 is -47.6 kcal/mol.56 In a recent study on the dimer CPNT composed of alternating D-Ramino acid and (1R,3S)-3-aminocyclohexane (or cyclopentane)

system

n,gas BEtotal

n,gas a ∆BEtotal

n,PB ∆Gtotal

n,PB b ∆∆Gtotal


-29.18 -118.06 -178.37 -239.06 -299.90 -361.35 -418.51

-88.88 -60.31 -60.69 -60.84 -61.45 -57.16

-14.40 -56.80 -85.21 -111.75 -138.66 -165.08 -191.86

-42.40 -28.41 -26.54 -26.91 -26.42 -26.78

a ∆BE ) BECPNTn - BECPNT(n-1). ∆GCPNT(n-1), where n ) 3-8.

b

∆∆G ) ∆GCPNTn -

carboxylic acid octapeptides, the gas-phase dimer interaction energy is calculated as -44.1 ( 2 and -69 ( 2 kcal/mol using B3LYP and M05-2x methods, respectively.63 The comparison of dimer BE calculated from PB method with that of DFT methods reveals that the addition of solvation effect to the DFT methods may produce trends comparable to molecular mechanics methods. These results show that the nature of amino acids present in the CP dictates the stability of various tubular structures. The calculated entropies for various systems are listed in Supporting Information (Table S9). It can be found that entropy contributions to the core regions are less when compared to the terminal subunits. The fluctuations in the terminal residues cause the disorderliness in the terminal regions. The increased order in the core regions of tubular structures arises from the self-assembly of various CP units and thereby the surface area exposed to water is reduced. As a consequence, the structural water molecules are released, resulting in overall gain in entropy which stabilizes the CPNTs. Using the steered molecular dynamics, the potential of mean force associated with the detachment of a CP unit from the assembly of CPNTs has been calculated.29,60 Detachment energy has been found to be 6.69 kcal/mol for the hexamer and 7.0 ( 1 kcal/mol for the dimer. In the present investigation, the calculated free energy of binding (∆Gbinding) as shown in Table 3 for the terminal CP units of CPNT3 and higher oligomers ranges from -8.37 to -10.15 kcal/mol, which is in agreement with the previous computational studies. It is interesting to note that the terminal CPs of trimer CPNT have comparatively low free energy of binding (-7.73 kcal/mol) than that of the terminal CPs of higher oligomers. For core regions, free energy of binding varies from -33 to -37 kcal/mol. The total BE calculated using the eqs 7 and 8 is presented in the Table 5. It describes that the BEs for trimer and higher oligomeric CPNTs are additive in nature whereas the dimer CPNT shows comparatively lower binding energy. It can be seen from the relative BE that the self-assembly of CPNTs up to trimer is cooperative in nature and interaction becomes additive for the tetramer and higher oligomeric CPNTs. A linear relationship is observed between the gas-phase and solvation BEs. Since the BE calculation was carried out using the MM-PBSA energy contribution of the monomer CP unit present in central part of the CPNT, the results may show (15 kcal/mol energy variation for the selection different CP unit. On the other hand, the use of energy of CPNT1 for the calculation of BEs of various oligomers does not yield appropriate trend due to the structural fluctuations during MD simulation. Semiempirical Binding Energy. Table 6 illustrates the total energy and BE (using eq 9) calculated for the dimer and higher

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Vijayaraj et al.

TABLE 6: Total Energy and Binding Energy Calculated for Dimer and Oligomeric CPNTs Using the Semiempirical PM6-DH2 Method system

ETOT (eV)

BE (kcal/mol)

∆BEa


-14515.22 -21773.88 -29032.55 -36291.22 -43549.90 -50808.57 -58067.24

-52.47 -104.28 -157.14 -209.93 -262.73 -315.55 -368.71

-51.81 -52.85 -52.80 -52.80 -52.82 -53.16

a

∆BE ) BECPNTn - BECPNT(n-1), where n ) 3-8.

Figure 7. Plot of the binding energies (in kcal/mol) calculated using n,gas semiempirical PM6 method and MM-PBSA-based BEtotal (BEgas) and n,PB ∆Gtotal (BEsolv).

oligomeric CPNTs using the semiempirical approach. It is evident from Table 6 that there is a linear relationship between the BE of the system and the degree of oligomerization. The incremental BE for the addition of each CP unit confirms similar findings. The difference between the BEs of CPNT2 and CPNT3 is -51.81 kcal/mol. The difference in the BEs increases marginally with the increase in the degree of oligomerization. The total BE calculated using the semiempirical method is compared with the MM-PBSA-based gas-phase and solvation total BEs (Table 5) and the same is plotted in Figure 7. The calculated correlation coefficient (r2) of 0.99 which explains that trend in BEs calculated using semiempirical and force field based methods is the same. Conclusion In summary, we have investigated the structure, dynamics, and stability of tubular structures formed by the CPs using both classical molecular dynamics simulation and semiempirical quantum chemistry calculation employing PM6 Hamiltonian with dispersion correction and hydrogen-bonding interaction (DH2). The calculated rmsd values confirm that higher oligomers (>CPNT3) have less fluctuation and more structural stability. Furthermore, it is observed that the terminal CP units of all the CPNTs are loosely attached to the inner core irrespective of the size of the tube. The average length per CP unit and diameter of the tube are ∼4.7 and ∼9.8 Å, respectively. Minor deviations in the diameter of the terminal units are seen due to dynamical fluctuations and the interaction of water molecules with the free amide group of the terminal CPs. The

calculated hydrogen bond parameters illustrate that the hydrogen bonds formed by the core regions are stronger than the terminal units. In addition to the formation of hydrogen bonds between the amide group and water molecule from the lumen of the CPNT, the alanine residue further facilitates the formation of carbonyl CdO and water O-H hydrogen bonds from the surface of the tube. The electrostatic interaction energy per hydrogen bond calculated from the MM-PBSA approach explains that the strength of the hydrogen bond increases gradually from dimer to pentamer CPNT and then it attains saturation. It is interesting to note that the van der Waals contribution to the binding free energy is constant for various CPNTs. It is evident from the solvation contributions to the electrostatic and van der Waals energy that the self-assembly of the alanine-based CPs are governed by the van der Waals interaction in the polar environment and the self-assembled CPNTs are further organized by the electrostatic interaction in addition to the van der Waals interaction. The BE calculated from PM6-DH2 shows that it varies linearly with the number of subunits. Further, it can be seen that the BE is additive. The overall observation suggests that the structural and energetic properties of the terminal CP units are similar for all the CPNTs and hence the stability of the tubelike conformation depends on the length of the core region. The results obtained for the different CPNTs highlight that the increase in degree of oligomerization enhances the core region of the same and thus increases the stability of the tube. The calculated structural parameters and energetics of various CPNTs demonstrate that the self-assembly of dimer, trimer, and tetramer CPNTs is the critical step in the formation of long tubular structures based on CPs. Acknowledgment. We thank the Council of Scientific and Industrial Research (CSIR), New Delhi, for financial assistance. R.V. thanks Mr. Satheesh Patel and Mr. Sree Ram for their help in preparing the initial model. Supporting Information Available: Average rmsd of Cβ atoms and average diameter of each CP unit in various CPNTs, the calculated φ/ψ angles and their standard deviations (SD) for each residue in CPNT8, results obtained from the hydrogen bond analysis, and various energy contributions from free energy calculation using the MM-PBSA method. We are thankful for the financial support from the Board of Research in Nuclear Sciences (BRNS), Mumbai, India, for funding (Sanction No. 2007/37/52/BRNS/2911). This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Desiraju, G. R. Nature 2001, 412, 397–400. (2) Arseniev, A. S.; Barsukov, I. L.; Bystrov, V. F.; Lomize, A. L.; Ovchinnikov, Y. A. FEBS Lett. 1985, 186, 168–174. (3) Ketchem, R. R.; Roux, B.; Cross, T. Structure 1997, 5, 1655–1669. (4) Roux, B. Acc. Chem. Res. 2002, 35, 366–375. (5) Ghadiri, M. R.; Granja, J. R.; Buehler, L. K. Nature 1994, 369, 301–304. (6) Granja, J. R.; Ghadiri, M. R. J. Am. Chem. Soc. 1994, 116, 10785– 10786. (7) Motesharei, K.; Ghadiri, M. R. J. Am. Chem. Soc. 1997, 119, 11306–11312. (8) Clark, T. D.; Buehler, L. K.; Ghadiri, M. R. J. Am. Chem. Soc. 1998, 120, 651–656. (9) Janshoff, A.; Dancil, K. P. S.; Steinem, C.; Greiner, D.; Lin, P. V. S. Y.; Gurtner, C.; Motesharei, K.; Sailor, M. J.; Ghadiri, M. R. J. Am. Chem. Soc. 1998, 120, 12108–12116. (10) Vollmer, M. S.; Clark, T. D.; Steinem, C.; Ghadiri, M. R. Angew. Chem., Int. Ed. 1999, 38, 1598–1601. (11) Sanchez-Quesada, J.; Ghadiri, M. R.; Bayley, H.; Braha, O. J. Am. Chem. Soc. 2000, 122, 11757–11766.

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