1 Department of Physiology and Biophysics, Mount Sinai School of Medicine, One Gustave Levy Place, New York, NY 10029, USA
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Abstract |
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Keywords: proline kink/transmembrane proteins
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Introduction |
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The special local flexibility of the PK confers a dynamic behavior on the proline-containing helix that can be relevant in the conformational changes related to functional mechanisms of the protein. For example, the structural distortion of the -helix by a conserved proline has been shown to play a key role in the voltage-dependent gating mechanism of conexin32 (Ri et al., 1999
). By mediating the propagation of conformational changes from one domain in the protein to another, the prolines can acquire a dynamic role in the interconversion of different protein states, as has been proposed in the activation mechanisms of G-protein coupled receptors (Luo et al., 1994
; Ballesteros and Weinstein, 1995
; Gether et al., 1997
). Computational techniques attempting to simulate the dynamic behavior of proteins evaluate the conformational changes that can be related to such functional mechanisms of the proteins. An accurate quantification of the geometry of the distortion introduced in helices by prolines, recorded both on average and for individual `snapshots' along a molecular dynamics trajectory, can therefore provide a useful tool in determining and evaluating the role of proline-induced flexibility and distortions in protein function.
The PK has been defined previously in terms of a bend (Barlow and Thornton, 1988) and a twist (Ballesteros and Weinstein, 1992
; Sankararamakrishnan and Vishweshwara, 1992
). We describe here a practical geometric definition of helix distortions by the PK, and introduce an algorithm for numerical evaluation of the parameters describing the proline-kinked helix. This algorithm can be used to characterize the deviation from ideal helix geometry regardless of the reasons for the distortion.
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Methods |
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The method quantifies three aspects of the helix's coordinates that are referenced to the proline-kinked helix itself, the bend angle, the wobble angle and the face shift, defined as shown in Figures 1 and 2. The definition of the PK involves two parts in the helix: from the N-terminus to the proline, the segment constitutes the `pre-proline' helix; the segment from the proline to the C-terminus is the `post-proline' helix.
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Quantification
To quantify the change in the helix distortion parameters throughout the MD trajectory, the orientation must remain constant. This is accomplished by choosing common positions in the helices and placing them at similar positions in the coordinates systems by rotations and translations. As a starting point the proline -carbon is translated to the cartesian origin, as exemplified in Figure 1
for a transition between parts A and B. The unit vectors that define pre- and post-proline axes are defined at this origin. Rotations are performed so that the unit vector that defines the axis of the pre-proline helix is on the positive x-axis. (Figure 1B
). For practical purposes each segment should be chosen to contain complete turns of helix, preferably a minimum of two turns (seven residues) in order to make the calculation reliable.
Wobble angle.
The calculation of the wobble angle requires a reorientation of the system that translates the center of the pre-proline helix to the positive x-axis (with y and z values equal to zero) and the proline -carbon to the positive y-axis (with x and z values equal to zero) (Figure 1C
). With the pre-proline helix's axis on the x-axis and the pre-proline helix's center on the x-axis, a plane is defined that bisects this cylinder perpendicular to the x-axis. When this plane contains the point that defines the proline
-carbon, it is the y,z-plane. The point where the y,z-plane bisects the axis of the pre-proline helix is the origin.
As shown in Figure 1D, the wobble angle is calculated as the angle between the projection of the vector that defines the axis of the post-proline helix on the y,z-plane, with the vector that connects the origin with the proline
-carbon (this vector is in the y,z-plane). The measure ranges from 180 to 180°. The wobble angle is close to zero when the post-proline helix is bent so that its axis is moved towards the proline
-carbon. It is close to 180 or 180° when the axis of the post-proline helix is moved away from the proline. The wobble angle is negative when the post-proline helix axis has a negative z value and it is positive for positive values of z (see Figure 1D
).
Bend angle.
To calculate the bend angle, the coordinate system is rotated around the x-axis so that the axis of the post-proline helix is in the x,y-plane (Figure 1C). From this orientation, the angle between the axes of the two helices can be calculated. The bend angle ranges from 0 to 180°; the closer it is to 0°, the smaller is the bend in the helix.
Face shift.
To calculate the face shift, the pre-proline helix is left unaltered but the post-proline helix is rotated so that its axis is on the negative x-axis. For the purposes of this part of the analysis, the proline -carbon is included in the post-proline helix and undergoes this rotation. In this orientation, both portions of the helix, pre- and post-proline, have their axes on the x-axis.
The face shift is calculated as the angle illustrated in Figure 2: the angle is between the projection of the vector connecting the proline
-carbon with the origin in the y,z-plane and the projection of the average of the vectors connecting the
-carbons of the (i 3) and (i 4) amino acids with the origin in the y,z-plane (Figure 2
). The values of the face shift range from 180 to 180°. Values closer to zero mean that the (i 3) and (i 4) amino acids are on either side of the proline
-carbon. A negative face shift means that the helix is over-wound as a result of the proline kink, whereas positive values mean that the helix is under-wound (Figure 2
).
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Results |
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To obtain a set of reference values for the helix parameters, we calculated the bend, wobble angle and face shift of an -helix (
= 65,
= 40), a 310 helix (
= 60,
= 30) and a
-helix (
= 30,
= 90).
When the algorithm is applied to two sequential fragments of a perfect -helix, the calculated bend angle is 1° and the face shift is 13° (Figure 3
). When the helix is completely straight (the bend angle is 0°) the wobble angle cannot be calculated, since the post-proline helix axis does not have a projection in the y,z-plane. Even the smallest deviation from 0° allows a projection of the vector in the y,z-plane and yields a significant value for the wobble angle. Thus, wobble is a very sensitive measure of the position of the two axes, and becomes meaningful only when the bend angle is large enough. In practice, wobble angle values become meaningful for bend angles larger than 10°.
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Illustrations
The algorithm was applied to several crystal structures obtained from the Brookhaven Protein Databank (PDB) (Berman et al., 2000) with resolution
2 Å, containing apparently straight and bent helices. One example, the helix comprising residues 128140 in myoglobin [accession code 1MBC (Kuriyan et al., 1986
)], does not have a proline or other distortions of its helical character. The computed bend angle for this helix is 6° and the face shift 11.1°, both very close to the standard values calculated for an ideal
-helix. Similarly, the helix containing residues 104117 of subtilisin [1CSE (Bode et al., 1987
)] has a bend angle of 6° and a face shift of 12.4°.
To evaluate the distortions induced by prolines we selected helices in cytrate syntase [2CTS (Remington et al., 1982)] and thermolysin [8TLN (Holland et al., 1992
)]. Pro15 in 2CTS and Pro69 in 8TLN are in the middle of the
-helices. The bend angle associated with Pro15 in 2CTS is 23.3°, the face shift is 38.6° (indicating that the helix is slightly underwound in the region of the proline kink) and the wobble angle is 131°. The Pro69-containing helix in 8TLN has a bend angle of 27.7°, a face shift of 4.1° and a wobble angle of 125.5°. The wobble angle determines the direction of the kink and indicates that, in this case, the presence of the proline is associated with an overwind of the helix.
As an example of the calculation along a molecular dynamics simulation (MD), we applied the algorithm to the characterization of the distortion induced by proline in transmembrane (TM) helix 6 of the 5HT2C receptor during 350 ps of the production run of an MD simulation (Figure 4).
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The algorithm presented here fully characterizes the three-dimensional geometry of the distortion introduced by proline in a helix, and is also able to characterize any deviation from ideality in helices of various types.
The program is written in FORTRAN 77. The input required to run the program is described below.
The documentation of the program, source code and executable are available on-line at http://transport.physbio.mssm.edu/prokink/.
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Notes |
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Acknowledgments |
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References |
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Received April 14, 2000; revised July 10, 2000; accepted July 10, 2000.