A Monte Carlo Study of the Self-Assembly of Bacteriorhodopsin Kamakshi Jagannathan, Rakwoo Chang, Arun Yethiraj  Biophysical Journal  Volume 83, Issue 4, Pages 1902-1916 (October 2002) DOI: 10.1016/S0006-3495(02)73954-4 Copyright © 2002 The Biophysical Society Terms and Conditions

Figure 1 The 120° sector model used for the protein. The points b and b′ represent the helices on the protein, p represents the internal lipids, and a and a′ represent the external lipids. The trimeric unit formed by three monomers is represented by a circle formed by three sectors in this model. Biophysical Journal 2002 83, 1902-1916DOI: (10.1016/S0006-3495(02)73954-4) Copyright © 2002 The Biophysical Society Terms and Conditions

Figure 2 Conditions for overlap between two sectors. When the apexes are at distances less than σ, the sectors can overlap for certain values of the relative orientation. Biophysical Journal 2002 83, 1902-1916DOI: (10.1016/S0006-3495(02)73954-4) Copyright © 2002 The Biophysical Society Terms and Conditions

Figure 3 Structural properties of the systems with p-p interactions. The main figure shows the apex-apex pair correlation function, gpp(r), plotted against r/σ. One of the inset plots shows the fraction of the total number of sectors, Nf, plotted against the number of nearest sectors, nb, and the other inset plot shows the contour plot of the structure factor, Spp(k), plotted against kx and ky. The four parts are for: (A) ϵ*pp=1 and ϕ=0.63; (B) ϵ*pp=2.5 and ϕ=0.66; (C) ϵ*pp=4 and ϕ=0.64; and (D) ϵ*pp=4 and ϕ=0.68. Biophysical Journal 2002 83, 1902-1916DOI: (10.1016/S0006-3495(02)73954-4) Copyright © 2002 The Biophysical Society Terms and Conditions

Figure 4 Snapshots of the final configurations for the four cases shown in Fig. 3, i.e., (A) ϵ*pp=1 and ϕ=0.63; (B) ϵ*pp=2.5 and ϕ=0.66; (C) ϵ*pp=4 and ϕ=0.64; and (D) ϵ*pp=4 and ϕ=0.68. Biophysical Journal 2002 83, 1902-1916DOI: (10.1016/S0006-3495(02)73954-4) Copyright © 2002 The Biophysical Society Terms and Conditions

Figure 5 The fraction of trimers, f, plotted against the area fraction, ϕ, for different values of the attractive well depth, ϵ*pp, ranging from 1 to 8. Biophysical Journal 2002 83, 1902-1916DOI: (10.1016/S0006-3495(02)73954-4) Copyright © 2002 The Biophysical Society Terms and Conditions

Figure 6 The specific heat per sector, Cv/〈N〉kB, plotted against the area fraction, ϕ, for ϵ*pp=2.5 and ϵ*pp=4. Biophysical Journal 2002 83, 1902-1916DOI: (10.1016/S0006-3495(02)73954-4) Copyright © 2002 The Biophysical Society Terms and Conditions

Figure 7 The parameter Smax plotted against the area fraction, ϕ, for different values of the attractive well depth, ϵ*pp, ranging from 1 to 8. The arrows indicate the transition points from the disordered trimer phase to the hexagonal lattice for ϵ*pp=4, ϵ*pp=5, and ϵ*pp=8. Biophysical Journal 2002 83, 1902-1916DOI: (10.1016/S0006-3495(02)73954-4) Copyright © 2002 The Biophysical Society Terms and Conditions

Figure 8 The phase diagram for the case of the p-p attractions with 1/ϵ*pp plotted against the area fraction, ϕ. The three phases indicated are the disordered monomer phase, a predominantly trimer phase, and the hexagonal lattice assembly. The lines drawn through the points are merely to guide the eye. Biophysical Journal 2002 83, 1902-1916DOI: (10.1016/S0006-3495(02)73954-4) Copyright © 2002 The Biophysical Society Terms and Conditions

Figure 9 The specific heat per sector, Cv/〈N〉kB, plotted against the area fraction, ϕ, for ϵ*bb′=2.5 and ϵ*bb′=4. Biophysical Journal 2002 83, 1902-1916DOI: (10.1016/S0006-3495(02)73954-4) Copyright © 2002 The Biophysical Society Terms and Conditions

Figure 10 Structural properties of the system for ϵ*aa′=1, ϵ*pp=4, and ϕ=0.68. The main figure depicts the radial distribution function, gpp(r), plotted against r/σ. The inset plot shows the fraction of the total number of sectors, Nf, plotted against the number of nearest sectors, nb. Note the similarity between this figure and Fig. 3 D. Biophysical Journal 2002 83, 1902-1916DOI: (10.1016/S0006-3495(02)73954-4) Copyright © 2002 The Biophysical Society Terms and Conditions

Figure 11 Probability distribution, P(θ), for the angle, θ, between the bisectors of any two sectors for ϵ*pp=4 and ϕ=0.68 with ϵ*aa′=0 and 1. Note that the a-a′ interaction causes the trimers to orient in a specific direction. Biophysical Journal 2002 83, 1902-1916DOI: (10.1016/S0006-3495(02)73954-4) Copyright © 2002 The Biophysical Society Terms and Conditions

Figure 12 Snapshot of the final configuration of the system for ϵ*aa′=1, ϵ*pp=4, and ϕ=0.68 showing the hexagonal order and the specific orientation of the trimers. Biophysical Journal 2002 83, 1902-1916DOI: (10.1016/S0006-3495(02)73954-4) Copyright © 2002 The Biophysical Society Terms and Conditions