Calculating the Free Energy of Association of Transmembrane Helices

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Presentation transcript:

Calculating the Free Energy of Association of Transmembrane Helices Jinming Zhang, Themis Lazaridis Biophysical Journal Volume 91, Issue 5, Pages 1710-1723 (September 2006) DOI: 10.1529/biophysj.106.081224 Copyright © 2006 The Biophysical Society Terms and Conditions

Figure 1 Polar coordinate system on the x, y plane of the membrane. The two helices in a dimer are presented as two cylinders. Points A and B are the center of the reference helix A and the center of the moving helix B, respectively. Point C represents a specific Cα atom on the reference helix. r is the distance between points A and B, and θ is the angle between AB and AC. Biophysical Journal 2006 91, 1710-1723DOI: (10.1529/biophysj.106.081224) Copyright © 2006 The Biophysical Society Terms and Conditions

Figure 2 Three Euler angles (A) and the reference state (B) in the rotational entropy calculations. The reference state is defined as follows: a), the center of 21 α-carbon atoms on residues from Thr-74 to Gly-94 (from CA 5 to 25) is at the origin (0, 0, 0); b), the center of seven α-carbon atoms on residues from Thr-74 to Val-80 (from CA 5 to 11) is on the +x axis; and c), the α-carbon atom on residue Val-84 (CA 15) is on the x, y plane and its coordinate on the positive y axis. Biophysical Journal 2006 91, 1710-1723DOI: (10.1529/biophysj.106.081224) Copyright © 2006 The Biophysical Society Terms and Conditions

Figure 3 Difference in GpA association in a lipid bilayer (A) and detergent micelles (B). Biophysical Journal 2006 91, 1710-1723DOI: (10.1529/biophysj.106.081224) Copyright © 2006 The Biophysical Society Terms and Conditions

Figure 4 Translation of GpA monomer inside a micelle. To simplify the problem, a GpA helix and the hydrophobic core of a detergent micelle are presented as a cylinder and a sphere, respectively, and the helical axis is parallel to the z axis (only the cross section is shown). Points O and C are the origin of the coordinate system, and the center of the helix, respectively. Points B1 and B2 are the crossing points of the helical axis and the micelle surface. Points D, A1, and A2 are projections of points C, B1, and B2 on the z axis, respectively. CD equals the distance of the center of a GpA monomer to the origin on the x, y plane, rm. OB1 and OB2 denote the radius of the micelle sphere. The radius of the hydrophobic core of the spherical micelle is arbitrarily defined as 11.5Å since we are using the IMM1 with thickness of 23Å to mimic the hydrophobic environment of micelles. The thickness of the hydrophobic phase (T) at a distance of rm is A1A2 (A1A2=OA1+OA2=2OA1=2OA2), thus T=2(11.5)2−(rm)2. Biophysical Journal 2006 91, 1710-1723DOI: (10.1529/biophysj.106.081224) Copyright © 2006 The Biophysical Society Terms and Conditions

Figure 5 RMSD of GpA monomers (the gray and solid line for monomer A and the gray and dashed line for monomer B) and dimer (the black and solid line) during 1ns MD simulations for run No. 1. Biophysical Journal 2006 91, 1710-1723DOI: (10.1529/biophysj.106.081224) Copyright © 2006 The Biophysical Society Terms and Conditions

Figure 6 Change in configuration of GpA upon association. Biophysical Journal 2006 91, 1710-1723DOI: (10.1529/biophysj.106.081224) Copyright © 2006 The Biophysical Society Terms and Conditions

Figure 7 Joint probability distribution of the relative distance r between two helices and the angle θ in a dimer on the x, y plane (A) and joint probability distribution of the z coordinates of helix A and helix B in a dimer (B). The bin size for distance or z is 0.4Å and the bin size for θ angle is 10°. Biophysical Journal 2006 91, 1710-1723DOI: (10.1529/biophysj.106.081224) Copyright © 2006 The Biophysical Society Terms and Conditions

Figure 8 Probability distribution of the γ-angle (the difference between helix A and B in a dimer). The bin size is 18°. Biophysical Journal 2006 91, 1710-1723DOI: (10.1529/biophysj.106.081224) Copyright © 2006 The Biophysical Society Terms and Conditions

Figure 9 Joint probability distribution of α-angle and β-angle of helix A as a monomer (A) and in a dimer (B). The bin size is 18° and 5° for α-angle and β-angle, respectively. Biophysical Journal 2006 91, 1710-1723DOI: (10.1529/biophysj.106.081224) Copyright © 2006 The Biophysical Society Terms and Conditions