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J. Phys. Chem. B 2009, 113, 5234–5238
Conformational Study of the PCU Cage Monopeptide: A Key Role of Some Force-Field Parameters Krishna Bisetty*,† and Juan J. Perez‡ Department of Chemistry, Durban UniVersity of Technology, P.O. Box 1334, Durban, 4000, South Africa, and Departament d’Enginyeria Quı´mica, UniVersitat Polite`cnica de Catalunya, ETS d’Enginyeria Industrial, AVenida Diagonal, 647, 08028 Barcelona, Spain ReceiVed: July 23, 2008; ReVised Manuscript ReceiVed: February 5, 2009
As had been previously reported standard AMBER parameters do not reproduce adequately ab initio calculations performed on the pentacycloundecane cage residue. The analysis of the geometries of the minimum energy structures compared with other residues allowed us to suspect the importance of bond stretching parameters in this case. Accordingly, we proceeded to compute new stretching and bending parameters from density functional theory calculations. Accordingly, the reliability of these parameters have been validated by predicting the correct conformational Ramachandran map. This is an example where the geometry of the side chain constrains the geometry of the residue backbone in such a way that you can get the right conformational profile by simple modification of some stretching and bending parameters. Introduction The field of peptide design and protein engineering has recently been expanded due to the synthesis of unnatural amino acids, which in turn has resulted in the design of molecules as potentially useful medicinal agents.1-3 The incorporation of cage frameworks into bioactive molecules has been the aim of many research groups over the past few years.4-7 Specifically, the incorporation of 1-amino-adamantane (1) into peptides has been shown to induce a range of positive effects on the pharmacokinetic properties of drugs.8 The incorporation of cage frameworks (2-3) into drugs should also have the added advantage that metabolic degradation is retarded by the inherent steric bulk of the cage skeleton, thus prolonging the activity and reducing the frequency of drug administration to the patient.
The synthesis of the first trishomocubane amino acid (3) and its pharmaceutical characteristics are well documented.9-11 The hydrophobicity of the hydrocarbon cagelike structures (2-3) enhances the transport of drugs across cell membranes and increases their affinity for lipophilic regions in receptor molecules. The rigid cagelike structure in some cases also induces * Towhomcorrespondenceshouldbeaddressed.E-mail:
[email protected]. † Durban University of Technology. ‡ Universitat Polite`cnica de Catalunya.
Figure 1. Schematic structures of Ac-Norbonane-NHMe (A), Ac-PCU Cage-NHMe (B) and Ac-Trishomocubane-NHMe (C) residues.
receptor site specificity in areas such as antibacterial activity, anabolic action, and analgesic activity.8 The inherent steric bulk of rigid cage structures could potentially be advantageous in the slowing down of drug degradation thus making drug administration to patients less frequent. Recent theoretical studies undertaken in our laboratory revealed that the introduction of pentacycloundecane (PCU) cage residues and trishomocubane (trish) residues (Figure 1) to a peptide chain imposes a constrained conformational profile hampering it to attend C5 extended conformations, although exhibiting a high propensity to adopt 310- as well as RL-helical secondary structures.12-14 This renders the residues an interesting role as a building block for the design of constrained peptide analogs. Furthermore, in addition to its conformational features its side chain features a large hydrophobic moiety that can be used to mimic hydrophobic side chains of residues like leucine, isoleucine, or valine being an added value in peptidomimetic design. These features support experimental evidence published in the literature revealing that the rigid cagelike structure in some cases also induces receptor site specificity in areas such as antibacterial activity, anabolic action, and analgesic activity.15,16 Although the specific conformational features of a peptide residue are dictated by its side chain, it is not always obvious the reason of the conformational profile inferred. In a previous work,12 we studied the conformational profile of the PCU Cage residue using ab initio calculations, finding that the C7ax appears as the lowest energy conformation independently of the size of
10.1021/jp8091946 CCC: $40.75 2009 American Chemical Society Published on Web 03/23/2009
Force-Field Parametrization of PCU Cage Peptides the basis set and even beyond the Hartree-Fock (HF) approximation. This same result is confirmed using density functional theory (DFT) calculations reported in the present work. In contrast, the conformational profile of the residue cannot be reproduced using some set of force field parameters of AMBER. Specifically, molecular mechanics calculations using either the parm94, parm96 wrongly identify the C7eq as the global minimum. However the parm99 set provides a correct qualitative rank order of the minima, although quantitatively the energy difference between the different minima is not well reproduced. These results clearly suggest that some parameters need to be refined, and in turn this analysis can provide us clues to understand the reason the residue exhibits its conformational features. However in the absence of experimental data, quantum mechanical approach appears to be a suitable alternative. Thus our main interest is in the parametrization of the PCU Cage residues for a simple force field such as AMBER.17-19 Accordingly, the primary goal of this paper is to undertake a parametrization study that can provide an explanation to the unsatisfactory description of the conformational preferences of the PCU cage residue provided by the standard AMBER parameters.12 Since the PCU cage is a CR,R disubstituted R-amino acid residue with a cyclic side chain, for comparative purposes and in order to have a better understanding of its geometrical features we have also studied an aliphatic CR,R disubstituted R-amino acid residue like the R-aminoisobutyric acid (Aib) and two cyclic CR,R disubstituted R-amino acid residues, trishomo and norbonaneacetylmethylamide, shown in Figure 1. A number of molecular mechanics force fields have been developed to date, and these differ mainly in the number and complexity of the potential energy functions and in the parameter sets defined. The earlier force fields developed for proteins like ECEPP 20 assumed rigid internal geometries for bonds and bond angles. On the other hand for the more sophisticated ones like MM221 or MM3,22 which are able accurately to reproduce the experimental vibrational frequencies and structures of organic molecules in the gas phase, the complexity of the potential functions and the parameter sets increases significantly, but so does their predictive accuracy. Force fields like SYBYL,23 YETI,24 GROMOS,25 CHARMM,26 OPLS/AMBER,27 and AMBER,17-19,28 which tend to be minimalist in the treating of the contributing functions for the conformational energy, nevertheless compensate for the imposed simplifications with well-tuned empirically derived force field parameters. The historical development of the AMBER program, leading to the more recent versions of the suite of AMBER molecular modeling programs,19 has its origins in the previous force field of the same name developed for proteins and nucleic acids by Weiner et al.17,18 The growth in computer power and the development of more efficient algorithms during the past decade has enabled the improvement of the force field in different aspects of its theoretical formulation and application. Of particular relevance for the distinction between the previous and the latest versions is an improved representation of electrostatics and van der Waals interactions, influenced by the philosophy of the optimized potentials for liquid simulations (OPLS) force field developed by Jorgensen and co-workers.27 In this approach, special care is devoted to the fine balancing of solvent-solvent and solute-solvent interactions, better to represent the behavior of condensed phase molecular systems. The AMBER force field is described as “minimalist” in its functional form with bonding interactions defined by simple analytical expressions and electrostatics modeled by a Coulombic interaction of atomcentered point charges.
J. Phys. Chem. B, Vol. 113, No. 15, 2009 5235 Force Field Parametrization Procedure. The program for approximate parametrization from quantum mechanical data (PAPQMD) computer program29 permits the user to determine force parameters by fitting the quantum mechanical energy (EQM) obtained from either semiempirical or ab initio computations to the energy (EFF) derived from molecular mechanics calculations. In this study, the stretching (ks) and bending (kb) force parameters of three bonds and two angles corresponding to each molecule (Scheme 1) were computed using the standard PAPQMD computer program. According to this method, each bond and angle type was perturbed from its equilibrium geometry. The quantum mechanical energy (∆EQM)of these perturbed structures was computed and then used in eq 1
(∆EQM - ∆EEF)2 ) minimum
(1)
All the parameters are changed until the difference between the force field (∆EEF) and the quantum mechanical energy is minimal. Computational Methods Quantum Mechanical Calculations. The lowest energy conformations of the different dipeptide residues (Figure 1) were fully optimized at the HF level using a 6-31G* basis set. On the other hand the DFT calculations were carried out using the Becke’s30 three-parameter hybrid functional with gradient corrections provided by the Lee, Yang, and Parr31 functional (B3LYP) level and the 6-31G* basis set. All calculations have been carried out using the Gaussian 98 program.32 The optimized geometries were used to determine the equilibrium bond TABLE 1: (a) Relevant Bond Distances and Bond Angles Calculated at the B3LYP/6-31G* Level of Theory of the Three Cage Residues Shown in Figure 1a; (b) Values of the Stretching and Bending Parameters of the Selected Bond Lengths and Angles of Table 1a a equilibrium bond lengths/ Å N-CR CR-Cβ CR-C′
Ala
Aib
trishomo
norbonane
PCU Cage
1.449 1.543 1.536
1.462 1.545 1.553
1.473 1.559 1.556
1.481 1.559 1.561
1.485 1.575 1.588
equilibrium bond lengths/ Å N- CR-C′ CR-C′-N
Ala
Aib
trishomo
norbonane
PCU Cage
106.9 114.8
104.3 116.3
110.4 117.4
105.3 114.9
108.6 115.6
b stretching force parameters kcal/mol Å2 R
N-C CR-Cβ CR-C′
Ala
Aib
trishomo
norbonane
PCU Cage
AMBER
296 232 221
276 186 205
231 214 188
233 220 197
229 231 233
337 340 317
bending force parameters kcal/mol rad2 Ala Aib trishomo norbonane PCU Cage AMBER R
N-C -C′ CR-C′-N a
44 59
54 69
88 58
70 67
86 59
70 70
For comparison purposes, also listed are the values of a standard residue alanine and a CR,R-disubtituted amino acid (Aib).
5236 J. Phys. Chem. B, Vol. 113, No. 15, 2009
Bisetty and Perez
Figure 3. Ramachandran maps for Ac-PCU Cage-NHMe using the modified parm94 force field parameters
Figure 2. DFT calculations fitting to a parabola to obtain the different bond stretching and bending constants for the PCU cage residue. eq distances (req ij ) and the angles (θij ) reported in Table 1a. The electronic contributions were evaluated by carrying out singlepoint MP2/6-31G(d) calculations without geometry optimizations. Selected bond distances and bond angles perturbed from its equilibrium geometry were obtained by constraining either the bond distances or the bond angles, while allowing all other variables to optimize and are shown in Figure 2. Parametrization Procedure. PAPQMD was utilized to calculate the force constant for both the symmetric stretching and symmetric bending parameters of the molecular model across the energy spectrum. PAPQMD takes its input data from a set of Gaussian32 simulations via the G2P subroutine (see Supporting Information). The correspondence between the force constants and the bending and stretching parameters is enough information to populate the AMBER19 database with a molecular mechanical force field entry for the unnatural biomolecule. Validation Studies. As a means of assessing the conformational profile of the cage monopeptide, Ramachandran maps were computed in vacuo, with the AMBER 9.0 program using the newly computed force field parameters incorporated into the Parm94 database. See Figure 3. Two cross sections on the potential energy surface of the PCU cage were selected. Single-point energy calculations were performed using the AMBER force field, as well as at the HF and DFT levels, shown in Figure 4.
Results and Discussion Aimed at studying the conformational profile of the PCU residue, in a previous study we carried out different ab initio calculations of the PCU dipeptide in the gas phase12 that permitted us to characterize four different minima (see Tables 2 and 3). Moreover, it was demonstrated that the use of different
basis sets and even the inclusion of the correlation energy at the MP2 level do not change the relative order of energies or geometries found. In the present work, we performed new calculations at the DFT level using the B3LYP/6-31G* functional (Tables 2 and 3), corroborating previous findings. In contrast, molecular mechanics calculations using AMBER with the standard set of parameters parm9433 and parm9634 yields systematically the reverse in order of the two C7 conformations for about 2 kcal/mol. On the other hand, although the parm9935 set provides a qualitative correct rank order of the minima, the energy differences are not qualitatively well reproduced. Selected distances and angles involving backbone atoms of the different residues studied in the present study in its C7ax conformation and computed from the B3LYP/6-31G* calculations are listed in Table 1a. A close look at the table suggests a few significant differences that can be associated with the different nature of the side chain. As can been seen, backbone bond distances of the cage residues differ considerably in regard to those of alanine and even to those of the aminoisobutiric acid (Aib). Specifically, there is a clear trend in the distances N-CR and CR-Cβ being longer for the cage molecules. The distance CR-C′ is longer in PCU but similar to that of the Aib residue for the other two cage residues and longer that the one found in alanine. Bond angles differ up to five degrees, but clear trends cannot be observed. It is well documented that bond distances and to a lesser extend bond angles depend on the conformation adopted by the residue. Accordingly, it could be thought that backbone distances constrained by the nature of the side chain may be critical in forcing a residue to favor specific conformations. In order to test this hypothesis, we proceeded to get a new set of parameters for the stretching and bending atoms of the backbone to perform molecular mechanics calculations. As explained in Computational Methods, parameters consistent with the AMBER force field were obtained from DFT calculations. Figure 2 shows as an example the parabolas used to obtain the force constants of the stretching parameters. Table 1b lists the stretching and bending parameters for the different residues. Regarding the stretching N-CR constants, those for the cage residues are much smaller than those of the alanine and R-aminoisobutyric acid, being the latter smaller than
Force-Field Parametrization of PCU Cage Peptides
J. Phys. Chem. B, Vol. 113, No. 15, 2009 5237
Figure 4. Horizontal and vertical cross sections of the Ramachandran plot of the PCU dipeptdide computed at the DFT level and AMBER force fields with the new parametrization.
TABLE 2: Geometries of the Low Energy Conformations of Ac-PCU Cage-NHMe Computed with Different Methods torsional angles/degrees C7ax
C7eq method ab initio DFT AMBER AMBER AMBER
φ
HF/6-31G* B3LYP/6-31G* Parm94 Parm99 this work
-79.8 -77.5 -61.1 -77 -79.6
Ψ
φ
79.6 74.1 74.9 80 80.5
80.2 77.3 69.2 80 80.5
RL
310
Ψ
Ψ
φ
-69.8 -66.0 -68.8 -70 -70.6
-66.5 -65.9 -50.3 -66 -66.5
-39.9 -37.5 -28.6 -37 -41.9
Ψ
φ 65.8 65.3 44.8 66 65.8
43.6 41.5 54.3 41 46.8
TABLE 3: Relative Energies for the Low Energy Conformations of Ac-PCU Cage-NHMe relative energies/kcal mol-1 (old parameters) ab initio DFT AMBER AMBER AMBER
method
C7eq
C7ax
310
RL
HF/6-31G* MP2/6-31G* B3LYP/6-31G* Parm94 Parm99 this work
0.86 0.93 0.75 0.0 0.52 1.03
0.0 0.0 0.0 2.65 0.0 0.0
3.81 4.13 4.74 5.17 0.79 1.30
6.32 6.68 6.69 4.99 2.16 2.67
the former. The CR-C′ parameter is close for all the residues with the difference of the Aib residue slightly smaller. Finally, for the CR-CR parameter the results are also smaller for the cage residues. As can be seen, the standard parameters of AMBER are higher than any of the parameters found. However, they may be adequate for alanine and Aib. However, the cage residues require much softer parameters, and this might be crucial for an adequate behavior of the force field in this case. In regard to the bending parameters, they are similar among the different residues and close to the standard parameters of AMBER. These new parameters were embedded in the parma94 set of parameters and used to compute the conformational profile of
the PCU dipeptide. Table 2 shows the values of the relative energies using the ab initio calculations, the standard AMBER parm94 set of parameters, and those generated in the present work. As can be seen, the standard set of force field parameters are unable to reproduce the right ordering of the minima. In contrast, the modifications made for the stretching and bending parameters are enough to yield the right relative energy to the minima of the residue. In order to further assess the performance of the new parameters, Figure 3 shows a comparison between the energy computed with the new set of parameters and the DFT calculations along cross sections at constant values of φ of the Ramachandran plot. As can be seen, force field calcula-
5238 J. Phys. Chem. B, Vol. 113, No. 15, 2009 tions now reproduce at least qualitatively the behavior of the DFT calculations. Conclusions The results reported in this work represent an interesting example where the nature of the side chain constrains the peptide’s backbone geometry in such a way that it represents a major force of the conformational profile of the residue. This can be seen in the molecular mechanics representation of the residue where small changes in the stretching and bending parameters can produce dramatic effects of the topology of the Ramachandran plot. Further investigation needs to be carried out to understand this process. Acknowledgment. Authors would like to express their gratitude for the financial support provided by the Joint Research Grant under the South African-Spain Research Partnership Programme Bilateral Agreement, through Grant 2075517 (HS2006-00022), and Professor Carlos Aleman, UPC, Barcelona, for providing us with the PAPQMD software. Supporting Information Available: This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Noren, C. J.; Anthoney-Cahill, S. J.; Griffith, M. C.; Schultz, P. G. A general-method for site-specific incorporation of unnatural amino-acids into proteins. Science 1989, 224, 182–188. (2) Roesser, J. R.; Chorghade, M. S.; Hecht, S. M. Ribosomecatalyzed formation of an abnormal peptide analogue. Biochemistry 1986, 25, 6361– 6365. (3) Hanessian, S.; McNaughton-Smith, G.; Lombart, H. G.; Lubell, W. D. Design and synthesis of conformationally constrained amino acids as versatile scaffolds and peptide mimetics. Tetrahedron 1997, 53, 12789– 12854. (4) Marchand, A. P. Chem. ReV. 1989, 89, 1011–1033. (5) Griffin, G. W.; Marchand, A. P. Chem. ReV. 1989, 89, 997–1010. (6) Marchand, A. P. In AdVances in Theoretically Interesting Molecules; Thummel, R. P., Ed.; JAI Press: Greenwich, 1989; Vol. 1, pp 357-399. (7) Ranganathan, D.; Haridas, V.; Madhusudanan, K. P.; Roy, R.; Nagaraj, R.; John, G. B.; Sukhaswami, M. B. Angew. Chem., Int. Ed. Engl. 1996, 35, 1105–1107. (8) Brookes, K. B.; Hickmott, P. W.; Jutle, K. K.; Schreyer, C. A. S. Afr. J. Chem. 1992, 45, 8–11. (9) Oliver, D. W.; Dekker, D. G.; Snykers, F. O. Pentacyclo[5.4.0.02.6.03.10.05.9undeccylamine- Synthesis and Pharmacology. Eur. J. Med. Chem. 1991, 26 (4), 375–379. (10) Oliver, D. W.; Dekker, D. G.; Snykers, F. O. Synthesis and biological activity of D3-trishomocubyl-4-amines. J. Med. Chem. 1991, 34 (2), 851–854. (11) Geldenhuys, W. J.; Malan, S. F.; Bloomquist, J. R.; Marchand, A. P.; Van der Schyf, C. J. Pharmacology and structure-activity relationships of bioactive polycyclic cage compounds: A focus on pentacycloundecane derivatives. Med. Res. ReV. 2005, 25 (1), 21–48. (12) Bisetty, K.; Gomez-Catalan, J.; Aleman, C.; Giralt, E.; Kruger, H. G.; Perez, J. J. J. Pept. Sci. 2004, 10, 274–284. (13) Bisetty, K.; Corcho, F. J.; Canto, J.; Kruger, H. G.; Perez, J. J. J. Mol. Struct. (Theochem) 2005, 731, 127–137. (14) Bisetty, K.; Govender, P.; Kruger, H. G. Biopolymers 2006, 81, 339–349. (15) Aigami, K.; Inamoto, Y.; Takaishi, N.; Fujikura, Y. J.; Takatsuki, A.; Tamura, G. J. Med. Chem. 1976, 19, 536–550.
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