Figure 1.
Membrane model of hydrophobic moments.
Left: Cartoon representation of the hydrophobic moment vector, H (yellow arrow) formed in a single phospholipid within a membrane. Its modulus is defined as the product of the total hydrophobicity of the phospholipid tail, times the distance between the hydrophobic centroid (somewhere in the tail) and the hydrophilic centroid (in the polar head). Right: Schematic representation of the transmembrane protein Chloroplast ATP synthase c-ring (PDBid 3V3C) inserted in a membrane. Blue and red arrows represent hydrophobic (H) and electric dipole moment (D) vectors respectively. Small yellow arrows represent the hydrophobic moment of each layer constituting the membrane. All hydrophobic moments of the phospholipids are quasi-parallel and perpendicular to the plane of the membrane.
Figure 2.
Variation of the moduli of the hydrophobic, (H, green) and electric dipole, (D, red) moment vectors as new monomers are added to the polymer. A) Variation of the moduli of both D (left vertical axis) and H (right vertical axis) with number of monomers within the polymer, n. The initial dimer formation suggests a decrease in the value of D as compared to those of the monomers. B) Variation of the angles formed by the hydrophobic, H∧H and dipole moments, D∧D, formed by the polymer and the new monomer. Note that in both cases the value of the angles decrease to steady state values. In the hydrophobic case this is a little above 20°, whereas in the dipole case, it lies between 80° and 90°, implying virtually no electric interaction. D values in debyes. H values in rhu (see methods). Error bars are from averages using the different series mentioned in the text.
Figure 3.
First four actin monomers from PDBid: 1M8Q, numbered from 0 to 3, following the notation given in [21]. a) View along the polymer axis: arrows are D vectors (colors of the arrows correspond with their actin subunits). Note the rotating pattern of these vectors as more monomers are added. b) Side view of the polymer. Hydrophobic moments keep a relatively small angle around the elongation axis.
Figure 4.
Representation of two groups of six amyloid Aß1–40 peptides, each obtained from PDBid: 2LMN [26]. a) Profile view of the two sets (2LMN1 and 2LMN2, see text). The two dark blue arrows represent the sum of the individual H vectors of the respective set. The two dark green arrows represent the sum of the individual H vectors of the mutated sets (Q15L). In this view, the total hydrophobic moment is near zero in both native and mutated species. b) The same complexes rotated 90° towards the reader. In this position, the hydrophobic moments of both sets of native (2LMN, blue) and mutated (Q15L, green) add to those represented vertically by both the purple and light green arrows in the direction of growth. For clarity, dipole moments have not been drawn since they are very small and directed almost vertically, making the total D in the same direction as H.
Figure 5.
Two views of the SOD1 dimer: a) front plane; b) rotated 90° towards the viewer. Red (D) and green (H): native dimer, PDBid: 2C9V. Magenta (D) and purple (H): depletion of metal ions (PDBid: 3ECU). Orange (D) and dark blue (H): G93A mutation (PDBid: 3GZO). Yellow (D) and pale blue (H): both depletion of metal ions plus G93A mutation (PDBid: 3GZP). For clarity, in b) hydrophobic vectors have not been drawn.
Figure 6.
a) Front and side views of one turn of HIV capsid (PDBid: 3J4F). Blue and red arrows represent the individual hydrophobic and dipole moments of each of the 12 hexamers in each turn of the microtubule. Green and yellow arrows are for the first hexamer of the next turn. In the side view (right), the slight leaning of the vectors toward the axis on the ensemble can be appreciated. b) Front and side views of one of the hexamers. Components of the H and D vectors of each of the six monomers within the hexamer are not symmetrical and are the cause of the deviation of both H and D vectors of the hexamer in respect to its own axis. As new hexamers are incorporated into the complex, the resulting Htot vector describes a helical trajectory around the axis of the tubule.
Figure 7.
Whole Brome Mosaic Virus capsid.
One of the lateral pentamers has been drawn as a ribbon and colored. Blue and red arrows represent the individual H and D vectors respectively of each of the five components constituting the pentamer. Projections of the five individual Hi vectors on the plane of the pentamer cancel each other out, whereas projections on the pentamer axis leave a net H vector radiating away from the centre of the capsid (long horizontal green arrow). Analogously, there is a net D vector pointing to the centre.
Figure 8.
Protein cage from PDBid: 3VCD, as viewed perpendicularly to the plane defined by the electric dipole moment vectors (red arrows) and the hydrophobic moment vectors (blue arrows) of the three octamers.
In this plane the total H and the total D are negligible due to the almost perfect 120° rotation symmetry.
Figure 9.
Front (a) and side (b) views of the eight monomers that compose the Ebola virus matrix protein VP40. Blue arrows represent the individual H vectors of the ensemble. Red arrows are the individual D vectors. The green arrow in the centre is the net H vector. The net D vector is virtually zero.
Figure 10.
a) A view of four parallel NNQNTF peptides [30] and their respective H vectors. These simple peptides associate side-by-side in arrays in opposite directions. b) Assembly of the doublet of cross-ß peptides (YTIAALLSPYS) [31], PDBid: 2M5K. Dark blue arrows represent the individual hydrophobic moments of each component of the doublet. Notice that the doublet is formed by two lobes of four peptides each. The components of the hydrophobic moments in the plane of the doublet cancel each other out leaving a negligible perpendicular component (not shown). Similar results are found in the triplet and quadruplet configurations. This association is somewhat more elaborate than that shown in a) since the distribution of H vectors combines opposite directions alternatively.
Figure 11.
Postulated antiparallel arrangement of arrays of SOD1, as proposed in the text, in which two pairs of dimers form two different arrays.
Red arrows represent electric dipole moments and blue arrows represent hydrophobic moments. Pale yellow arrows indicate the polarity of each linear association. This arrangement is both electrically and hydrophobically favorable for for a continuous growth: the individual D vectors lay at almost 90° of each other thus minimizing their interaction energy, whereas the H vectors align laterally. This disposition is in agreement with that given in [25].
Figure 12.
Structural heterogeneity of monomers in HIV capsid hexamers.
Superposition of the six monomers that comprise the first hexamer of PDBid 3J4F. The variability in both moduli and direction of all six D (red) and H (blue) moments can be observed.
Table 1.
Summary of angles of hydrophobic and electric dipole moments in compounds studied in this article.