Three-Dimensional Mapping of Microenvironmental Control of Methyl

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Three-Dimensional Mapping of Microenvironmental Control of Methyl Rotational Barriers William I. Hembree† and Jerome Baudry†,‡,* † ‡

UT/ORNL Center for Molecular Biophysics, Oak Ridge, Tennessee, 37831 United States Department of Biochemistry & Cellular and Molecular Biology, University of Tennessee, Knoxville, Tennessee, United States ABSTRACT: Sterical (van der Waals-induced) rotational barriers of methyl groups are investigated theoretically, using ab initio and empirical force field calculations, for various three-dimensional microenvironmental conditions around the methyl group rotator of a model neopentane molecule. The destabilization (reducing methyl rotational barriers) or stabilization (increasing methyl rotational barriers) of the staggered conformation of the methyl rotator depends on a combination of microenvironmental contributions from (i) the number of atoms around the rotator, (ii) the distance between the rotator and the microenvironmental atoms, and (iii) the dihedral angle between the stator, rotator, and molecular environment around the rotator. These geometrical criteria combine their respective effects in a linearly additive fashion, with no apparent cooperative effects, and their combination in space around a rotator may increase, decrease, or leave the rotator’s rotational barrier unmodified. This is exemplified in a geometrical analysis of the alanine dipeptide crystal where microenvironmental effects on methyl rotators’ barrier of rotation fit the geometrical mapping described in the neopentane model.

’ INTRODUCTION The rotational energetics and dynamics of methyl functional groups are important microenvironmental markers that pertain to both the local environment of the rotator in solid phase and the global properties of much larger molecules, such as polymers and proteins. For instance, NMR relaxation spectra of methyl groups provide information on side chain motions and dynamics1 and on functional aspects of proteins such as ligand binding and folding variations.2
4 Methyl rotational dynamics also play a central role in the onset of anharmonicity in proteins at low temperature.5,6 Variations in methyl groups’ rotational barriers are linked to electronic changes that extend beyond the rotator moiety onto the stator, as shown on solid phase crystalline peptides.7 It is therefore important to characterize how methyl groups’ rotational barriers and dynamics are controlled by their microenvironment. As one of the smaller molecular rotors in chemistry, methyl groups offer a chemically simple way to study the physics of larger molecular rotors that are extensively used in nanotechnology and crystal design.8
10 Our previous work11,12 has indicated that methyl groups’ rotational barriers may be significantly increased or decreased when atomic density is located at specific locations around the methyl rotator by either destabilizing (in the case of reduced methyl rotational barriers) or stabilizing (in the case of increased methyl rotational barriers) the hydrogen atoms of the rotating methyl in the staggered conformation through van der Waals repulsive interactions. As previously described,11,12 the barrier-reducing effect originates from the destabilization of the rotator methyl group’s staggered conformation through van der Waals interactions between the r 2011 American Chemical Society

satellite functional groups and the rotator’s hydrogen atoms in the geometry shown in Figure 1A-left, where the centers of mass of the satellite molecules are located between the stator’s C
C bonds. This destabilization decreases the energy difference between the staggered and eclipsed conformations of the rotator methyl group. On the other hand, the geometry described in Figure 1A-right further increases the rotational barrier of the stator through repulsive van der Waals interactions between the satellite molecules and the hydrogen of the rotator in its eclipsed conformation. This showed that variations of the microenvironment around methyl groups can either catalyze (reducing the transition state barrier between eclipsed and staggered conformers) or hinder their rotation, and suggested that the methyl rotational barrier is controlled by the geometry of the atomic density around the rotator. In the present work this analysis of microenvironmental control of methyl rotational barriers is extended to include the entire three-dimensional space around the methyl rotator. The methyl rotational barriers are first studied in model neopentane molecules surrounded by satellite methane or dioxygen molecules, mimicking microenvironment often experienced by methyl groups in biomolecules,11 and the conclusions obtained from these model systems are verified in a peptide crystal displaying a diversity of microenvironmental conditions that are among those investigated in the neopentane model system. Received: February 26, 2011 Revised: May 27, 2011 Published: June 02, 2011 8575

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The scanning of these geometrical variables in the neopentane models was performed with a number of satellite molecules (methane or dioxygen molecules) varying between one to three satellites. The microenvironment of the alanine dipeptide side chain’s methyl group was investigated using the alanine dipeptide LAANMA crystal structure16 and applying all symmetry operations in order to obtain a complete crystal environment using the program MOE.14 Heavy atoms located within 4 Å of the alanine dipeptide side chain methyl’s carbon atom were considered for analysis of the methyl group’s microenvironment in the crystal.

’ RESULTS Methyl Rotational Barrier as a Function of the Number of Satellite Molecules. The variation of the methyl group’s rota-

Figure 1. Geometrical variables used in the following calculations. A: left: neopentane with 3 methane satellite molecules in the barrierreducing geometry with respect to the neopentane carbon
carbon stator, top view. Center: Newman projection of the barrier-reducing geometry. Right: neopentane with 3 methane satellite molecules in the barrier-increasing geometry conformation with respect to the neopentane carbon
carbon stator (nonrotator hydrogen atoms omitted for clarity). The atoms of the rotator are indicated in blue, the satellite methane molecules are indicated in green. B: variation of the C(S)
C(N)
C(M) angle investigated in the present calculations. The C(S)
C(N)
C(M) is indicated in red dashed lines. C: variations of the C(N)
C(N)
C(N)
O dihedral angle investigated in the present calculations. The atoms defining the dihedral angle are indicated by a green star; left: top view; right: side view.

’ METHODS A model system consisting of neopentane surrounded by up to three satellite molecules was built to investigate the rotational potential of the neopentane’s rotating methyl group, illustrated in Figure 1, as a function of the methyl group’s microenvironment consisting of satellite methane or dioxygen molecules in various geometries. The programs Spartan13 and MOE14 were used to calculate empirical force field (MMFF9415) and ab initio RIMP2/6-31G* rotational energy barriers as a function of the methyl group’s microenvironment following the protocol described in.12 Empirical force field calculations were performed in the gas phase with no cutoff for nonbonded interactions. The microenvironment around the rotating neopentane’s methyl group was varied by scanning geometrical parameters that define the location of satellite molecules around the rotating methyl: (1) The carbon(methane)/carbon(neopentane) distances (or “C(M)
C(N) distance”), or the proximal oxygen (dioxygen)/ carbon(neopentane) distance (or “O
C(N) distance”), as illustrated in Figure 1A. (2) The angle (varied from 90° to 150°) between the methyl axis and the C(M)
C(N) (or O
C(N)) axis, as illustrated in Figure 1B. (3) The C(N)
C(N)
C(N)
O dihedral angle (varied between 0° and
120°), as illustrated in Figure 1C.

tional barrier as a function of the number of satellite methane molecules and as a function of the C(M)
C(N) distance (Å) is shown in Figure 2 for a C(s)
C(N)
C(M) angle of 90°. As previously described, when the center of mass of the satellite molecules are located along the stator’s C
C bonds (Figure 1Aright), the methyl rotational barrier is increased with respect to that of an isolated neopentane molecule. Conversely, locating the satellite molecules between the C
C
bonds of the stator (Figure 1A-left) leads to a decrease of the neopentane’s methyl rotational barrier. The ab initio (RI-MP2) and empirical (MMFF94) rotational barriers and geometries in Figure 2 are in close agreement, in particular in the satellite geometry described in Figure 1A-left, with the empirical force field values being within ∼0.6 kcal/mol (energetically) and ∼0.1 Å (geometrically) from the ab initio values. In the case of the satellite geometry that leads to an increase of the methyl rotational barriers (Figure 1A-right), the barrier increase correlates with the number of satellite groups at a given C(M)
C(N) distance. In the satellite geometry that decreases the methyl rotational barrier (as in Figure 1A-left), the C(M)
C(N) distance at which the barrier is most reduced increases with the number of satellite molecules (Table 1). These results indicate an additive effect of the satellite molecules on the decrease or increase of the methyl group’s rotational barrier, although the C(M)
C(N) distance at which the barrier is at a minimum increases with the number of satellite groups. Figure 3 shows the variation of empirical force field barriers as a function of the number of satellite for selected C(M)
C(N) distances from Figure 2. The data shown in Figure 3 indicates that the effect of increasing the number of satellite groups is essentially linear; that is, at a given distance the methyl barrier is modified by the same amount when going from 1 satellite to 2 satellites and when going from 2 satellites to 3 satellites. Methyl Rotational Barrier as a Function of the Angle between Satellite Methane Molecules and Neopentane (C(s)
C(N)
C(M) Angle). Table 2 shows the values of the C(M)
C(N) distances at which the MMFF rotational barrier is at a minimum, i.e., for a barrier-reducing geometry of the satellite methane molecules (Figure 1A-left), as well as the value of the MMFF rotational barrier as a function of the number of satellite methyl groups and as a function of the C(s)
C(N)
C(M) angle. The values in Table 2 show that the C(N)
C(M) distance that corresponds to a minimum methyl rotational barrier is independent of the C(s)
C(N)
C(M) angle up to a 120° angle. At C(s)
C(N)
C(M) angles of 130° or higher, the C(M)
C(N) distance is reduced, indicating that the satellite molecules must be closer to the rotating methyl group to achieve 8576

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Figure 2. Variation of the neopentane methyl rotational barrier as a function of the C(M)
C(N) distance, and of the number of methane satellite molecules for geometries of the methane satellite molecules as in Figure 1A-left or -right. MMFF: empirical force field calculations; RI-MP2: ab initio calculations. A negative barrier value indicates a phase inversion of the minimum barrier (staggered/eclipsed).

Table 1. Ab Initio (RI-MP2) C(M)
C(N) Distances for the Minimum of the Methyl Rotational Barrier and the Value of the Corresponding Rotational Energy Barrier for Neopentane with Various Numbers of Methane Satellite Functionalizationa number of

C(M)
C(N)

barrier (kcal/

angle (°)

satellites

distance (Å)

mol)

90

1

3.2

0.4

2

3.4

0.1

3

3.5

0.3

1

2.9

0.0

2

3.3

0.0

3

3.4

0.0

100

a

methyl rotational

C(s)
C(N)
C(M)

Refer to Figure 1 for a description of the geometrical variables.

a maximum reducing effect on the methyl rotational barrier. The corresponding minimum rotational barriers exhibit limited decrease with increasing values of the C(s)
C(N)
C(M) angle, staying within 0.3 kcal/mol of each other up to a 140° C(s)
C(N)
C(M) angle. At a 150° C(s)
C(N)
C(M) angle, the minimum methyl rotational barriers are found significantly higher than at lower C(s)
C(N)
C(M) angle values, indicating that the barrier-reducing effect of the satellite molecules is partially lost. Dioxygen Satellite Molecules. Tables 3 (ab initio calculations) and 4 (empirical force field calculations) list C(N)
C(O) distances at which the neopentane’s central methyl group is most reduced, as a function of the number of satellite dioxygen and of the C(s)
C(M)
C(O) angle. Both levels of calculations give similar O
C(N) distances and methyl rotational barriers, within 0.4 Å and kBT (kBT ∼ 0.6 kcal/mol at T = 300 K) of each other, respectively. The O
C(N) distances for a minimal methyl barrier

Figure 3. Neopentane methyl rotational barriers for selected C(S)
C(N)
C(M) angles and C(M)
C(N) distances as a function of the number of satellite methane molecules. Top: for methane satellites in the barrier-increasing geometry; bottom: for methane satellites in the barrier-reducing geometry. The color code indicates the angle in degree and the distance in angstroms. 8577

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Table 2. Empirical Force Field C(M)
C(N) Distances for the Minimum of the Methyl Rotational Barrier and the Value of the Corresponding Rotational Energy Barrier for Neopentane with Various Numbers of Methane Satellite Functionalizationa C(s)
C(N)
C(M) number of of C(M)
C(N)

methyl rotational

C(s)
C(M)
O

number of

O
C(N)

methyl rotational barrier

angle (°)

satellites

distance(Å)

barrier (kcal/mol)

angle (°)

satellites

distance (Å)

(kcal/mol)

90

1 2

3.3 3.5

0.4 0.5

90

1 2

2.7 3.1

0.1 0.3

3

3.6

0.5

3

3.3

0.5

1

3.3

0.6

1

2.9

0.2

2

3.5

0.5

2

3.2

0.3

3

3.6

0.6

3

3.4

0.5

1

3.3

0.6

1

3.0

0.2

2

3.5

0.5

2

3.3

0.4

3 1

3.6 3.3

0.5 0.5

3 1

3.4 3.0

0.7 0.3

2

3.5

0.4

2

3.3

0.3

3

3.6

0.4

3

3.4

0.5

1

3.3

0.4

1

3.0

0.4

2

3.5

0.4

2

3.3

0.3

3

3.6

0.4

3

3.4

0.5

1

3.3

0.4

1

3.0

0.4

2 3

3.5 3.6

0.3 0.4

2 3

3.3 3.4

0.3 0.4

100

105

110

115

120

130

140

150 a

1

3.2

0.3

2

3.4

0.2

3

3.5

0.3

1

2.9

0.2

2

3.2

0.1

3

3.4

0.4

1 2

2.7 3.0

2.7 3.3

Refer to Figure 1 for description of the geometrical variables.

Table 3. Ab Initio (RI-MP2) O
C(N) Distances for the Minimum of the Methyl Rotational Barrier and the Value of the Corresponding Rotational Energy Barrier for Neopentane with Various Numbers of Dioxygen Satellite Functionalizationa C(s)
C(M)
O

number of

O
C(N)

methyl rotational barrier

angle (°)

satellites

distance (Å)

(kcal/mol)

90

1

2.5

0.0

2

3.0

0.3

3 1

3.2 2.9

0.0 0.7

2

3.1

0.8

3

3.2

0.1

100

a

Table 4. Empirical Force Field O
C(N)) Distances for the Minimum of the Methyl Rotational Barrier and Value of the Corresponding Rotational Energy Barrier for Neopentane with Various Numbers of Dioxygen Satellite Functionalizationa

Refer to Figure 1 for description of the geometrical variables.

are shorter than the C(M)
C(N) distances obtained in the case of methane satellite functionalization. This is due, in the case of the empirical force field calculations, to the smaller van der Waals radius parameters for sp2 oxygen (1.77907 Å) than for sp3 carbon (1.96887 Å) in the MMFF94s force field, as well as to the presence

100

105

110

115

120

130

140

150 a

1

3.0

0.3

2

3.2

0.2

3

3.3

0.1

1

2.8

0.2

2

3.0

0.0

3

3.1

0.1

1 2

2.4 2.6

0.2 0.2

Refer to Figure 1 for description of the geometrical variables.

of hydrogen atoms attached to the carbon in the methane molecule that may be closer to the rotating methyl than the methane’s carbon atom. Table 4 shows that the O
C(N) distances and minimal rotational barriers increase more with increasing C(s)
C(M)
C(O) angle values than in the case of methane satellite functionalization. At C(s)
C(M)
C(O) angle values above 130°, the O
C(N) distances for a minimum barrier decrease, as was the case for methane satellites, although in the case of dioxygen satellites the methyl rotational barrier remains low. In the case of dioxygen satellite molecules, the methyl rotational barriers as a function of the number of satellite molecules fluctuates in the case of the ab initio calculations, but appear to increase in the case of the force-field calculations. The force field calculations may overestimate the methyl rotational barriers, exemplifying the limits of the force field parametrization, although the ab-inito and empirical values are still within kBT from each other. Mixed Geometries of the Satellite Molecules. Figure 4 shows the variation of the empirical force field neopentane’s methyl rotational barrier as a function of the C(C)
C(C)
C(M)
O dihedral angle defined in Figure 1C. In these calculations, the satellite dioxygen molecule goes from a barrier-increasing geometry (as in Figure 1A-right) to a barrier-reducing conformation at a 8578

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The Journal of Physical Chemistry B C(N)
C(N)
C(N)
O dihedral angle value of (
60°), and to another barrier-increasing conformation at (
120°). Figure 4 shows that when a satellite molecule is located between the barrier-increasing and barrier-reducing geometries, the reducing and increasing effect of the satellite molecule cancel each other out, and the methyl rotational barrier is essentially similar to its in vacuo value. Methyl Rotational Barriers in the Alanine Dipeptide Crystal. The alanine dipeptide (N-methyl-L-alanyl-N-methylamide) crystal contains two alanine dipeptide molecules in its asymmetric unit. The rotational barriers of the methyl groups on the two alanine side chains differ from each other because of differences in their crystal microenvironment: one of the methyl rotational barriers exhibits a decreased value with respect to its value in vacuo, and the rotational barrier of the other alanine dipeptide’s side chain is increased with respect to its in vacuo value.11 Figure 5 shows the alanine dipeptide side chain’s microenvironment, i.e., heavy atoms within 4 Å of the alanine

Figure 4. Neopentane methyl rotational barriers as a function of the C(N)
C(N)
C(N)
O dihedral angle, for selected O
C(N) distances, given in angstroms in the color code.

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side chain’s carbon atom, in the case of the reduced methyl rotational barrier (Figure 5A) and in the case of the increased methyl rotational barrier (Figure 5B). In the case of a reduced methyl rotational barrier (Figure 5A), the methyl group’s microenvironment exhibits two carbon atoms in the barrier-reducing geometry with respect to the alanine dipeptide stator, one oxygen atom close to a barrier-increasing geometry, and one oxygen atom between the barrier-reducing and barrier-increasing geometries. Based on the above calculations for the neopentane model system with satellite groups, the microenvironment of this alanine dipeptide side chain methyl does indeed reduce the methyl’s rotational barrier; that is, the atomic density around the methyl group is richer in barrier-reducing geometries than in barrier-increasing geometries. On the other hand, Figure 5B shows that in the case of the other alanine dipeptide molecule in the asymmetric unit (with increased side chain methyl rotational barrier) the microenvironment of the methyl side chain consists of a carbon atom in a barrier-increasing geometry, and one oxygen atom between the barrier-increasing and barrier-reducing geometries. This corresponds to a microenvironment rich in the barrier-increasing geometry that leads to an increase of the methyl rotational barrier.

’ DISCUSSION AND CONCLUSIONS The present work maps in three dimensions the microenvironmental control of methyl groups’ rotational barriers. Our previous results were obtained considering only what is in the present study the case of a C(s)
C(N)
C(M) angle of 90° and C(N)
C(N)
C(N)
C(methane) dihedral angles values of either 0° or 120°. In the present work the description of microenvironmental geometries was extended to describe the entire three-dimensional space around the methyl rotator. The results indicate that the methyl rotational barrier is not significantly affected by the C(s)
C(N)
C(M) or C(s)
C(N)
C(O) angle, i.e., by how far above the methyl “plane” the

Figure 5. Microenvironment of the alanine dipeptide’s side chain methyl in crystal. A: methyl with reduced rotational barrier; B: methyl with increased rotational barriers. Interactomic distances are in angstroms. 8579

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The Journal of Physical Chemistry B microenvironmental atomic density is located, as variations of these angles do not significantly affect the satellite/rotator distances. However, the number of satellite molecules is found to be linearly additive in their effect on the rotational barrier: the more the atomic density around the rotator, the more the rotator’s barrier will be lowered or increased, depending on the geometry. No cooperative effect of atomic density increase around the rotator was found; that is, adding satellite molecules around the rotator does not affect the reduction (or increase depending on the geometry) of the methyl rotational barrier other than just adding individual satellite’s effect on the barrier. Atomic density located between the barrier-reducing and barrierincreasing geometries around the rotator does not affect the methyl’s rotational barrier, as the barrier-increasing and -reducing effects cancel each other out, and the methyl rotational barrier is then equivalent to that of a rotator in vacuo, experiencing only interactions with the stator. The conclusions drawn from these model systems are in agreement with observation of the alanine dipeptide crystal’s structure: the methyl groups that have a low rotational barrier in the alanine dipeptide crystal have indeed satellite atomic densities that are richer in barrier-reducing geometries with respect to the stator, while those methyl groups that have a high rotational barrier in the alanine dipeptide are found to have atomic densities that are richer in barrier-increasing geometries. This has potentially useful applications in the prediction of rotators’ rotational barriers and crystal design. For instance, examination of the geometry of the atomic density around a rotator could be used to predict whether those rotational dynamics of the rotator will be facilitated or hindered. To the extent that the microenvironmental structure around a rotator remains essentially unchanged at room temperature (which is more likely the case in crystals than in solvated proteins11,12), this increasing or reducing effect of the rotator’s microenvironment can mostly be understood and predicted on the basis of structural observation of the rotator’s three-dimensional environment.

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(9) Garcia-Garibay, M. A. Proc. Natl. Acd. Sci. U.S.A 2005, 102, 10771. (10) Ben Shir, I.; Sasmal, S.; Mejuch, T.; Sinha, M. K.; Kapon, M.; Keinan, E. J. Org. Chem. 2008, 73, 8772. (11) Baudry, J.; Smith, J. C. J. Phys. Chem. B. 2005, 109, 20572– 20578. (12) Baudry J. Am. Chem. Soc. 2006, 128, 11088–11093. (13) Spartan version 08; Wavefunction, Inc.: Irvine, CA. (14) MOE, version 2009; The Chemical Computing Group: Montreal, Canada. (15) Halgren, T. A. J. Comput. Chem. 1999, 20, 720. (16) Harada, Y.; Iitaka, Y. Acta Crystallogr. 1974, 30, 1452.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. Tel.: þ1 865 574 6308. Fax.: þ1 865 576 7651.

’ ACKNOWLEDGMENT We thank the University of Tennessee’s department of Biochemistry & Cellular and Molecular Biology for its support and members of the UT/ORNL Center for Molecular Biophysics for useful discussions. ’ REFERENCES (1) Krishnan, M.; Smith, J. C. J. Am. Chem. Soc. 2009, 131, 10083. (2) Ishima, R.; Louis, J.; Torchia, D. J. Mol. Biol. 2001, 305, 515. (3) Frederick, K. K.; Marlow, M. S.; Valentine, K. G.; Wand, A. J. Nature 2007, 448, 325. (4) Lee, A.; Wand, A. Nature 2001, 411, 501. (5) Roh, J.; Novikov, V.; Gregory, R.; Curtis, J.; Chowdhuri, Z.; Sokolov, A. Phys. Rev. Lett. 2005, 95, 038101. (6) Krishnan, M.; Kurkal-Siebert, V.; Smith, J. J. Phys. Chem. B 2008, 112, 5522. (7) Hayward, J.; Smith, J. C. Biophys. J. 2002, 82, 1216. (8) Jarowski, P. D.; Houk, K. N.; Garcia-Garibay, M. A. J. Am. Chem. Soc. 2007, 129, 3110. 8580

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