Validation of previous computer models and MD simulations of discoidal HDL by a recent crystal structure of apoA-I.

HDL is a population of apoA-I-containing particles inversely correlated with heart disease. Because HDL is a soft form of matter deformable by thermal fluctuations, structure determination has been difficult. Here, we compare the recently published crystal structure of lipid-free (Δ185-243)apoA-I with apoA-I structure from models and molecular dynamics (MD) simulations of discoidal HDL. These analyses validate four of our previous structural findings for apoA-I: i) a baseline double belt diameter of 105 Å ii) central α helixes with an 11/3 pitch; iii) a “presentation tunnel” gap between pairwise helix 5 repeats hypothesized to move acyl chains and unesterified cholesterol from the lipid bilayer to the active sites of LCAT; and iv) interchain salt bridges hypothesized to stabilize the LL5/5 chain registry. These analyses are also consistent with our finding that multiple salt bridge-forming residues in the N-terminus of apoA-I render that conserved domain “sticky.” Additionally, our crystal MD comparisons led to two new hypotheses: i) the interchain leucine-zippers previously reported between the pair-wise helix 5 repeats drive lipid-free apoA-I registration; ii) lipidation induces rotations of helix 5 to allow formation of interchain salt bridges, creating the LCAT presentation tunnel and “zip-locking” apoA-I into its full LL5/5 registration.

that involves the use of temperature jumps to 500 K and unrestrained simulated annealing, approaches generally frowned upon by the MD community. Why did we think that MD combined with temperature jumps and/or unrestrained simulated annealing, generally considered to be inadequate for determination of globular protein structure, was capable of determining HDL structure? The answer, we hypothesized, was in the constraints noted above imposed by lipid on conformations of lipid-associated proteins ( 16,25 ), constraints that are lacking in globular proteins.
At the time that our various models were published (25)(26)(27)(28)(29)(30)(31), no high-resolution structural information on apoA-I was available for comparison. This situation changed with the recent publication of a high-resolution crystal structure of C-terminally truncated lipid-free apoA-I by Mei and Atkinson ( 32 ). Examination of this structure confi rms many of the conformational features of apoA-I discoidal HDL previously proposed by us using modeling and MD simulations. These conformational features include structural details of the geometry of the double-belt model ( 16,26,28,31 ), the existence of the ␣ 11/3 helix structural motif ( 16 ), and three of our previously reported key MD fi ndings with biological relevance for the double-belt model for discoidal HDL, the LCAT presentation tunnel ( 26 ), the importance of interchain salt bridges in doublehelix registration ( 16,25,28,33 ), and the presence of a "sticky" N-terminus ( 26,30 ).

METHODS
The all-atom MD and molecular dynamics-simulated annealing (MDSA) protocol were performed using NAMD ( 34 ) as described ( 25,27 ). Each system was solvated with the solvate plug-in of Visual Molecular Dynamics (VMD) ( 35 ).The TIP3P water model was used ( 36 ). Each system was also ionized and charge-neutralized with NaCl to 0.15 M with the autoionize plug-in of VMD. The CHARMM 22 ( 37,38 ) and 27 ( 39,40 ) force fi elds were used for protein and lipid molecules, respectively. For simulations at a fi xed temperature, velocity reassignments occurred every 1 ns to prevent the "fl ying ice cube" effect ( 41 ). The MDSA protocol consisted of 10 ns equilibration at 500 K, 10 ns nonlinearly cooling to 310 K, and 10 ns equilibration at 310 K (26)(27)(28)(29)(30). The initial MD at 310 K followed by the MDSA protocol was replicated to give an ensemble of 16 trajectories and fi nal structures of discoidal HDL particles with POPC and unesterifi ed cholesterol (UC) with stoichiometries of POPC:UC:apoA-I of 160:24:2 ( 26,28,30 ).
Other simulations previously published and used in this paper are: i ) an ensemble of six discoidal particles with POPC:( ⌬ 1-40)apoA-I stoichiometry of 100:2 subjected to temperature jump MD (500 K), which expanded the disc diameter to a size comparable to 160:2 ( 25,27 ); ii ) an ensemble of two discoidal particles with POPC: UC:apoA-I stoichiometry of 240:32:2 subjected to temperature jump MD (500 K) ( 26,28,30 ); and iii ) an ensemble of four discoidal particles with the same stoichiometry as the ensemble of sixteen but simulated prior to that larger set ( 26,28,30 ). These two sets are also referred to as an ensemble of twenty 160:24:2 particles ( 26,28,30 ).

RESULTS
Comparison of apoA-I in the crystal structure of the C-terminally truncated lipid-free apoA-I to apoA-I in our 44-243 of lipid-free apoA-I reported by Borhani et al. in 1997 ( 14 ) that suggested an antiparallel double-belt model. In the fi rst experimental test of the belt model, Koppaka et al. ( 15 ) used polarized attenuated total internal refl ection Fourier-transform infrared spectroscopy to conclude that the result unambiguously supported a belt model. Theoretical considerations of the geometric and physical chemical nature of the apoA-I double-belt model resulted in the publication by our lab of an atomic resolution antiparallel double-belt amphipathic helical model for discoidal HDL ( 16 ) with a helix-helix registry termed LL5/5 (implying juxtaposition of pairwise helix 5 antiparallel repeats) surrounding the edge of a bilayer disc. This model provided sound theoretical rationale for use of the lipid-free X-ray crystal structure as a valid model for lipid-associated apoA-I. Five laboratories subsequently have studied reconstituted discoidal HDL using a variety of physical chemical methods, and the results have been consistent with our double-belt model (17)(18)(19)(20)(21).
One approach to coping with the dynamic nature of HDL is the use of molecular dynamics (MD) that produces a computer simulation of physical movements of atoms and molecules. The atoms and molecules are allowed to interact for a period of time, giving a view of the motion of the atoms. MD uses high-performance computing to predict successive atomic positions and velocities of a molecule or molecular assembly by numerically solving Newton's laws of motion (F = ma). The hydrophobic effect results naturally from the statistical thermodyamics of the probability of ordering of water molecules at nonpolar interaces versus the much higher probability of water forming hydrogen bonds in every direction. A number of computer alogrithms have been developed [e.g., NAMD ( 22 ) and GROMACS ( 23 )] that generate a trajectory of atomic motion over time that acts upon atoms and bonds. Forces between the particles and potential energy are defi ned by molecular mechanics force fi elds. Temperature is simulated by random assignment of a Boltzmann velocity distribution, equivalent to the desired temperature, to all of the atoms of the simulation. Because electrostatic interactions are accounted for by using fi xed partial charges, chemical reactions involving chemical bonds being created or broken cannot be simulated (for a review, see Ref. 24 ).
Although conventional wisdom has been that time constraints and potential energy barriers are major obstacles to the use of MD simulations for determining protein conformations, we hypothesized that four profound constraints would be imposed on the conformations of lipid-associated apolipoproteins by lipid: the low dielectric environment, the hydrophobic effect, the amphipathic helix, and the planar bilayer environment ( 16,25 ), such that MD simulations of HDL would produce useful structural information. Accordingly, by application of MD simulations to our detailed antiparallel double-belt model for discoidal HDL ( 16 ), we developed atomistic models of the dynamic interactions of apoA-I with itself and the "soft" lipid components of discoidal HDL (25)(26)(27)(28)(29)(30)(31).
To increase exploration of conformational space of these HDL particles through all-atom MD, we developed a protocol by GGE of 105.5 Å ( 28,33 ). For POPC, assuming a molecular surface area of 65 Å 2 ( 28 ), a bilayer disc containing 160 POPC has a diameter of 81.4 Å. Adding the thickness of an ␣ helix (10 Å) on each side, the full POPC discoidal HDL particle has a diameter of 101.4 Å, also close to the diameter measured by GGE of 102 Å ( 28 ).

Modifi ed ideal ␣ helix with a pitch of three turns per 11 residues ( ␣ 11/3 helix)
In 1999, we introduced the concept of the ␣ 11/3 amphipathic helix. We proposed this slight conformational variation on the ideal ␣ 18/5 helical motif as a mechanism to create an amphipathic helical ring with a continuous hydrophobic edge on the inside of the ring, ideal for encirclement of the hydrophobic edge of a bilayer disc ( 16 ). We further suggested that only the central residues of the lipid-associating domain, helixes 2-9, residues 66-220, formed an ␣ 11/3 amphipathic helical conformation ( 16 ).
This conformation was used to create all our starting discoidal HDL models for MD simulations. However, this slight variation on the ␣ helix structure is almost indistinguishable from an idealized ␣ helix and has been diffi cult to confi rm, even in the fi nal MD-simulated discoidal structures, because of the curvature of the helical segments around the disc.
We examined the high-resolution crystal structure of ( ⌬ 185-243)apoA-I ( 32 ) for evidence of the ␣ 11/3 helix. In Fig. 2A , we present two molecular graphic views of a straight 12 residue ␣ helical segment (residues 144-155; Fig. 1 ) of helix 6 for comparison with plots of the sequence in the form of ␣ 11/3 and ␣ 18/5 helical wheel diagrams ( Fig. 2B, C , respectively). We avoided inclusion of P143 because of the obvious helix bends induced in the double belt by prolines ( Fig. 1 ). Although there are slight irregularities in the ␣ helicity of residues 144-155, this 12-residue segment clearly has an ␣ 11/3-helical pitch; note that residues 1 and 12 lie in the same plane along the long axis of the helix.

Presentation tunnel hypothesis
Our MD simulations of discoidal HDL consistently result in a gap forming between the pairwise helix 5 repeats ( 26,31 ) of the antiparallel molecular double-belt structure ( 16 ), a gap not present in the idealized starting structure with extended side chains ( Fig. 3 ). The unique and consistent conformation of the residues forming the gap suggested to us a molecular basis for the activation by lipid-associated apoA-I of the plasma enzyme LCAT: after attachment of LCAT to discoidal HDL, the pairwise helix 5 repeats in apoA-I create an amphipathic "presentation" tunnel for migration of hydrophobic acyl chains and amphipathic UC from the bilayer to the phospholipase A2-like and esterifi cation active sites of LCAT, respectively ( 26,31 ). Examination of our ensemble of 16 MDSA simulations ( 26,30,43 ) shows that, in 14 of the 16, the methyl ends of POPC acyl chains (POPC-Me) from the bilayer center are inserted into the presentation tunnel and exposed to solvent ( Fig. 4A ). In the other two examples of the ensemble, the hydroxyl moiety of UC (UC-OH) is inserted into the presentation tunnel and exposed to solvent ( Fig. 4B ). discoidal HDL models and simulations demonstrates certain similar or identical conformational features of both crystal and simulated antiparallel apoA-I dimers, several that were observed originally in our MD simulations and proposed to have important biological functions ( 16,25,26,28 ).

Double-belt model for apoA-I in discoidal HDL
Although multiple laboratories (17)(18)(19)(20)(21) have used a variety of physical chemical methods that support our original detailed double-belt model for discoidal HDL, no direct structural data, other than the low-resolution X-ray crystal structure for ( ⌬ 1-43)apoA-I published by Borhani et al. ( 14 ), have been available to provide atomic resolution information about specifi c features of the double belt. The Mei and Atkinson structure ( 32 ) provides highresolution atomic resolution information applicable for half of the double-belt model discoidal HDL model ( 16 ). As shown in Fig. 1 , residues 79-178 in the unit cell dimer AB create a hemi circle of continuous antiparallel double helical domains. This portion of the crystal structure represents the complete pairwise antiparallel helix 4/6, 5/5, and 6/4 repeats and portions of the antiparallel helix 2-3/7 and 7/3-2 pairs. The diameter of this half circle is 105-106 Å, a value very close to diameters of the major reconstituted discoidal HDL particle created by disc formation from dimyristoylphospha-tidylcholine (DMPC) and POPC.
Simple geometric calculations using the formula for the area of a circle, A = r 2 , support these two particle sizes. For DMPC, assuming a molecular surface area of 63 Å 2 ( 42 ), a bilayer disc containing 180 DMPC has a diameter of 85.0 Å. Adding the thickness of an ␣ helix (10 Å) on each side, the full DMPC discoidal HDL particle has a diameter of 105.0 Å., close to the diameter measured between the two clusters of salt bridges enlarge the gap or tunnel in the pairwise helix 5 repeats; larger residues would obstruct the gap; iii ) the resulting tunnel is lined on its long edges by K133 and E125 and on its narrow edges by G129 and A130; G129 faces the solvent, A130 the lipid; iv ) in essentially every simulation of discoidal HDL, either one ( Our earlier MD simulations of discoidal HDL composed of POPC without UC show that the presentation tunnel forms even in the absence of UC ( 27 ). The representative example shown in Fig. 4C of a presentation tunnel formed in discoidal HDL particles containing POPC without UC illustrates the key conformational features of the presentation tunnel ( 26,31 ): i ) two clusters of salt bridges form between residues E125, K133, E136, and K140 that pull the two K133 acyl chains away from the center of the pairwise helix 5 repeats to create a gap; ii ) the low-bulk residues G129 and A130, located    Fig. 5D, E ); ii ) E125, K133, E136, and K140 on antiparallel helixes rotate toward one another ( Fig. 6 ), allowing E125 to form interchain salt bridges with K133; iii ) L126 (starred residues in Fig. 5A ) rotates out of the gap and faces the lipid; this consensus conformation, two salt bridge clusters separated by low-bulk residues, that creates and stabilizes the tunnel is convincingly illustrated by molecular alignment of the pairwise helix 5 domains of the 16 simulations of the MD ensemble shown in Fig. 7 .

Stabilization of LL5/5 chain registry by salt bridges
Another fi nding from our MD simulations of discoidal HDL confi rmed by the crystal structure is formation of wp 2 ↔ wp 2 ( wp refers to ␣ 11/3 wheel positions within each 11-mer tandem repeat) interchain "solvent-inaccessible" salt bridges ( 16,25,28 ), bonds strengthened by the low dielectric environment ( 45 ) of the lipid matrix of the bilayer disc that we suggested represented stabilizing elements for the LL5/5 double-belt registry. Comparison of side views of the crystal and MD structures ( Fig. 8A, B , respectively) shows that two of the three pairs of "solvent-inaccessible" MD structure of discoidal HDL in Fig. 5B, C and 5E, F shows that both structures form salt bridges between residues K133, E136, and K140, and in both structures, the lowbulk residues G129 and A130 ( 26 ) are arranged between the salt bridges to create a gap or tunnel between the pairwise helix 5 repeats; this similarity was noted by Mei and Atkinson ( 32 ).
There is one pronounced difference between the protein crystal and the discoidal HDL simulation structures regarding pairwise helix 5 interactions: E125 in the crystal structure forms no interchain salt bridges with K133, whereas E125-K133 interchain salt bridges are generally formed in the discoidal HDL simulation structures (compare Fig. 5A, B ). The reason is simple: in the antiparallel double helical protein-alone crystal structure, the hydrophobic faces of interchain pairwise helix 5 repeats remove themselves from solvent by associating with one another ( Fig. 6A ), but they rotate ‫ف‬ 50° around the long axis of each helix to associate with the edges of the discoidal lipid bilayer ( Fig. 6B ). This rotation has several effects: i ) A130, located in wheel position 10 in the center of the hydrophobic face ( 16,44 ), rotates out of the tunnel gap to point directly at the lipid, and G129 rotates into the gap (compare  It is clear from examination of the salt bridge cluster, E169 ↔ K96, R173 ↔ D92, and E78 ↔ H177, present in both the crystal and the MD simulations shown in Fig. 8A, B , that E78 ↔ H177 is behind the cluster E169 ↔ K96 and R173 ↔ D92 and thus less accessible to solvent. A reasonable question, however, is whether "solvent-inaccessible" salt bridges should be considered "solvent-inaccessible" or simply "lesssolvent-accessible" than those we term "solvent accessible." Because we have shown that the pairwise helix 5 repeats in the MD-simulated discoidal HDL relative to the crystal structure are rotated ‫ف‬ 50° toward the discoidal bilayer, we looked at the rotational positioning of the "solventinaccessible" salt bridges in the crystal structure versus those in MD-simulated discoidal HDL ( Fig. 9 ). Surprisingly, in the helix pairwise helix 4/6 repeats, there is very little difference between the rotational alignments of the helical pairs in the crystal structure versus the MD-simulated discoidal HDL. In Fig. 9 , the C ␣ atoms of wp 10 are indicated by magenta spheres. The rotation of helix 6 is slightly different between the crystal and the simulation; in the simulation, helix 6 is rotated 15-20° toward the discoidal bilayer compared with helix 6 in the crystal. In any case, the relative rotations of the "solvent-inaccessible" salt bridge (E111 ↔ H155) in the crystal structure versus that in the MD-simulated discoidal HDL are similar ( Fig. 9 ).
The tertiary structure of the crystal dimer can explain the difference in relative rotational alignments of the pairwise helix 5 and helix 4/6 repeats. Only the helix 5 repeats are completely exposed to solvent; the helix 4/6 repeats form a "four-helix" bundle with the N-terminal domains ( 32 ), indicated by two circles in Fig. 9A, that partially mimic the effects of a lipid bilayer. Figure 9 also provides evidence of the existence of the ␣ 11/3 helical pitch in the simulation as well as the crystal structures. In Fig. 9 , the wp 2 residue pairs present in helix 4 (Y100 and E111) and helix 6 (L144 and H155) are indicated by arrows. In both helixes, in both the crystal and simulation structures, the wp 2 C ␣ atoms lie on a plane through the long axis of the helix, unequivocally supporting the existence of the ␣ 11/3 in these two tandem helical segments in both crystal and simulation structures.

Molecular stickiness of the N-terminal domain
Finally we showed from MD simulations ( 27,28,30 ) that the N-terminal domains (residues 1-22) act as a form of molecular "Velcro" to avidly stick to their N-terminal companions in the double belt ( Fig. 5E ) as well as other portions of apoA-I ( 30 ), a property that we hypothesize stabilizes multiple conformations of apoA-I on HDL ( 30 ). The stickiness of N-terminal pairs during MD simulations salt bridges (E111 ↔ H155, D89 ↔ R177) seen in MD simulations are also seen in the crystal structure, noted by Mei and Atkinson ( 32 ). The third pair, E78 ↔ R188, is not present in the crystal structure because of C-terminal truncation at residue N184 ( 32 ). The high frequency of formation of the fi rst two pairs of "solvent-inaccessible" salt bridges is indicated by alignment of the 16 simulations of the MD ensemble between residues 78-120 and 143-188 ( Fig. 8C ). The third salt bridge pair, E78 ↔ R188, in a more-mobile region of the double belt, forms less frequently (for example, it has not formed in Fig. 8B ). As noted elsewhere ( 27,28 ), this terminal pair of "solvent-inaccessible" salt bridges, E78 ↔ R188, unlike the two more-central ones, are not only often broken during MD simulations but are poorly conserved evolutionarily ( 44 ).
We have also proposed that wp 5 ↔ wp 9 interchain solventaccessible salt bridges play a role in interchain stability ( 16,25,28 ). Residues putatively involved in formation of solvent-accessible salt bridges are also shown in Fig. 8A, B . Moving circumferentially from the central pairwise helix 5 repeats, no wp 5 ↔ wp 9 interchain salt bridges are found in the crystal structure until E169 ↔ K96 and R173 ↔ D92 at the beginning of the pairwise helix 7/3 junctions. We have found that solvent-accessible interchain salt bridges form less readily ( 16,25,28 ) than "solvent-inaccessible" salt bridges during MD simulations (for example, E162 ↔ K103 has not formed in the example shown in Fig. 8B ).
cross-eyed stereo views of apoA-I double belt from a representative example of 16 all-atom MDSA simulations of discoidal HDL ( 26,28,30 ) viewed from the lipid-bound or nonpolar face of the pairwise helix ( 26 ) domain of the protein alone or associated with the bilayer disc, respectively. Residues key to formation of the tunnel (E125, G129, A130, K133, E136, and K140) are indicated in A and D, along with the conserved residue W8 in E and F postulated to hold the N-terminal domains to the lipid surface. Key residue color code: basic, blue; acidic, red; W8, turquoise; L126, L134, L137, L141, gold; G129, magenta; A130, white; prolines, yellow; remaining residues, green; lipid in C and F, gray. Created with the PyMOL Molecular Graphics System, Version 1.3, Schrödinger, LLC. highly conserved, as are many of the fi rst 22 residues of the N-terminal domain ( 44 ).
Although the two N-terminal residues D1 and E2, because of excess motion, are not resolved in the crystal structure appears to be largely driven by strategically placed moieties primed to form salt bridges ( 27,28,30 ), particularly the acidic D1 and E2 and the basic R10 and N-terminal Ϫ NH3 + ( Fig. 10 ). The three residues, D1, E2, and R10 are  ( 30 ). A: View of polar (solvent exposed) face of aligned pairwise helix 5 domains. B: View of nonpolar (lipid exposed) face of aligned pairwise helix 5 domains (residues 121-143). Color code: prolines, yellow; key basic residues, blue; key acidic residues, red; G129, magenta; A130, white; leucines, gold; remainder of helix 5, green. Alignments were created by the VMD ( 35 ) align command in the root mean squared deviation (RMSD) trajectory tool as described ( 30 ).  A and B were created with the PyMOL Molecular Graphics System, Version 1.3, Schrödinger, LLC. Alignments in C were created by the VMD align command in the RMSD trajectory tool as described ( 30 ). illustrated in Fig. 11C indicates that consistent with alternate salt bridge pairing and the sticky N-terminal hypothesis, Q5 is more mobile (yellow) than adjacent residues P4 and S6 (both green), whereas P3 is more mobile than all three (red).

DISCUSSION
At present, no direct experimental methods exist for determining atomic resolution structures of biologically important nanoscale particles of soft condensed matter, such as intact HDL and other lipoproteins. The similarity reported here between key conformational elements from the crystal structure of lipid-free apoA-I and apoA-I in an ensemble of discoidal HDL subjected to MD simulation ( 25,28 ) supports the proposition that virtual experimentation by MD simulation provides a reasonably robust method for determining details of the structure of soft protein-lipid assemblies such as discoidal HDL particles. Our simulations of discoidal HDL were successful because we developed a detailed model for the starting protein registry of the antiparallel apoA-I chains, the detailed antiparallel double-belt model ( 16 ). The studies reported here confi rm two elements of that starting model: i ) a lowest-free-energy particle diameter of 105-106 Å; and ii ) an ␣ 11/3 helical pitch. If we had started with a random registry and an ideal ␣ 18/5 helical pitch, convergence to the LL5/5 registry would have been beyond current computational capabilities. It is likely that biosynthesis of nascent discoidal HDL particles will depend critically upon self-registry of the lipid-free apoA-I ( 46 ). If this is true, the C-terminally truncated crystal structure of Mei and Atkinson ( 32 ) will prove useful in elucidating the structure of circulating lipid-free/lipid-poor (pre-␤ -HDL) apoA-I.
In the crystal structure, residues 79-178 in the independent dimer AB create essentially a perfect half circle of continuous antiparallel double helical domains with a diameter of 105-106 Å ( Fig. 1 ). This is the portion of the apoA-I double belt in discoidal HDL that remains relatively immobile during MD simulations ( 30 ) and is largely responsible for determining the diameter of the discoidal particle. This feature: i ) supports the relevance of the crystal structure for discoidal HDL; ii ) supports our MD simulation results; and iii ) suggests that the conformation of residues 78-178 in the Mei-Atkinson crystal refl ects the lowest-free-energy state for apoA-I in a reconstituted discoidal HDL structure. Supporting the lowest-freeenergy concept, the diameter of this most-prevalent particle varies only 3 Å between reconstituted discoidal HDL made from two very different phospholipids, DMPC and POPC ( 28 ).
Many other laboratories call this most-prevalent of reconstituted discoidal HDL particles the 96 Å particle ( 19,47,48 ). Because this particle varies in diameter with both the lipid:protein molar ratio and the type of phospholipid , we prefer the less-ambiguous nomenclature R2-2 ( 30,33 ). We also believe that 96 Å is not the correct diameter of this particle, for reasons we have discussed elsewhere ( 33 ). ( 32 ), the Velcro hypothesis is consistent with analysis of the X-ray data ( Fig. 11 ). The N-terminal domains of each apoA-I dimer, e.g., chain A in unit cell AB, contact adjacent apoA-I dimers, e.g., chain D in unit cell CD, at the juncture of helixes 6 and 7 ( Fig. 11A ). Chain D contains two highly conserved basic residues, R160 and R171 ( 30 ), and one highly conserved acidic residue, D168 ( 30 ), that are extended toward and into close proximity with the last resolved N-terminal residue in chain A, P3 ( Fig. 11A, B ). Residues R160, R171, and D168 in chain D are 9.8 Å, 10.4 Å, and 6.8 Å from P3 in chain A, respectively. Based upon the geometry of Fig. 11 , this conformational proximity suggests that interaction of chain A with chain D in Fig. 11B involves interaction of the N-terminal region of chain A with residues R160, R171, and perhaps D168 of chain D. This interaction is almost certainly through salt bridge formation between the terminal two residues of D1 and E2 of chain A, and perhaps its N-terminal Ϫ NH3 + with residues R160, R171, and perhaps D168 of chain D. The lack of resolution of D1 and E2 in the crystal structure and the distances of R160 and R171 from P3 are consistent with alternate salt bridge pairing of D1/E2 with R160/R171 that would introduce what would appear to be motion in the terminal residues of chain A. Modeling (data not shown) shows that for D1 to salt bridge alternately with R160 and R171, residue Q5 must make a substantial rotation about its , bonds. The b-factor analysis of C ␣ atoms in chain A Fig. 9. Backbone cross-eyed stereo comparisons of the relative rotations of the pairwise helix 4/6 segments in the C-terminally truncated ( ⌬ 185-243)apoA-I dimeric crystal structure ( 32 ) and a representative example of discoidal HDL subjected to MDSA simulation ( 26,28,30 ) We proposed the ␣ 11/3 helical pitch, a slight variation on the ideal ␣ 18/5 helical motif, as a mechanism to create an amphipathic helical ring with a continuous hydrophobic edge on the inside of the ring, ideal for encirclement of the hydrophobic edge of a bilayer disc ( 16 ). The ␣ 11/3 helix was mentioned by Linus Pauling in his original description of the ␣ helix when he observed that the pitch of the ␣ helix could vary from 3.6 (18/5) to 3.67 (11/3) residues per turn without signifi cant energy penalty ( 50 ). The result presented in this paper unequivocally support the existence of the ␣ 11/3 helix in both crystal and simulation structures of apoA-I. The ␣ 11/3 amphipathic helix has been suggested for several lipid-associating proteins (apoA-I, apoA-IV, and ␣ -synuclein), but the results presented here are the fi rst solid structural evidence for this variant of the ideal ␣ 18/5 helix.
The results in this paper provide validation of the LCAT presentation tunnel hypothesis. Certainly both the crystal and MD simulation structures of apoA-I show that the pairwise helix 5 repeats are uniquely designed to create a gap that exposes both acyl chains and UC. This result of the N-terminally truncated apoA-I crystal structure fully validates the LCAT presentation tunnel hypothesis, has enormous biological implications for HDL function, and provides a powerful working model for confirmation by future in-solution experimental studies.
We show that the presence or absence of UC has no effect on the formation of the gap between the pairwise helix 5 repeats. The major difference between discoidal HDL with and without UC that we fi nd in our MD simulations The simple geometric calculations in the RESULTS section using the formula for the area of a circle, A = r 2 , giving a diameter of 102-111 Å, depending upon the phospholipid, also support this conclusion.
In none of our simulations do we see evidence for the Belt-Buckle model of Bhat et al. ( 47 ). Because of the unusual stickiness of the N-terminal domains of the doublebelt apoA-I to one another that we see in our MD simulations ( 30 ), except when particles are too large to maintain N-terminal/N-terminal salt bridge connections ( 30 ), we never see the kind of movement of the N-terminal domain that these authors suggest. It could, of course, be that we do not explore suffi cient conformational space in the time frame available to our MD simulations. However, we, are in favor of another explanation: attachment of a long cross-linking reagent to the N-terminal end of apoA-I on the discs creates serious artifacts: i ) attachment increases the fl exibility of the N-terminus, resulting in cross-linking to lysine residues outside the actual cross-linking distance; ii ) some of the cross-links are to the Ϫ NH 3 + moiety of the N-terminus itself, and because that basic moiety is part of the sticky salt bridge network, as is K12, N-terminal stickiness is destroyed, and that portion fl ops around to cross-linking to lysine residues outside the actual cross-linking distance; iii ) or both.
We would like to comment on the previously published crystal structure for untruncated apoA-I ( 49 ). There are substantial reasons to think that this is an invalid structure. For details, see http://main.uab.edu/Sites/ reporter/articles/71570/, "UAB's Statement on Protein Data Bank Issues." However, as noted by Mei and Atkinson ( 32 ), the pairwise helix 5 repeats form impressive leucine zipper motifs between opposing chains at both ends: L141/L122/L137/ L126 and perhaps L134 ( Fig. 12 ). These multiple residue leucine zipper motifs at opposite ends of the pairwise helix 5 repeats should be inconsequential once the domain is associated with lipid but seem highly likely to be the principal is discoidal bilayer fl exibility and stability; UC-containing discs are less fl exible and more stable than those without UC (data not shown).
The presence in the C-terminally truncated crystal structure of wp 2 ↔ wp 2 interchain "solvent-inaccessible" salt bridges supports our hypothesis that these represent stabilizing elements for the LL5/5 double-belt registry ( 16,25,28 ). Some portions of the crystal structure also show the presence of interchain solvent-accessible salt bridges, suggesting that they too may play a role in LL5/5 interchain stabilization. Based upon the analysis shown in Fig. 9 , in the future, we will refer to the wp 2 ↔ wp 2 interchain salt bridges as less-solvent-accessable and the wp 5 ↔ wp 9 interchain salt bridges as more-solvent-accessable.
Because a reasonable assumption is that helix 5 initiates the double-helix registry, the lack of any interchain salt bridges in the pairwise helix 5 repeats in the crystal structure requires discussion. We looked for other interchain interactions that could initiate the LL5/5 registry in the lipid-free apoA-I structure. We observed one pair of aromatic residues, Y100 and Y166, which might be close enough to forming -stacks, and juxtaposition of one pair of methionine residues, M112 and M148. None of these features of the crystal structure seemed necessary or suffi cient to induce registry of the pairwise helix 5 repeats in the lipid-free state. Fig. 11. Cross-eyed stereo images of the interaction of the N-terminus of 1 apoA-I in 1 U cell dimer (chain A) with the helix 6-helix 7 junction of another apoA-I in a second unit cell dimer (chain D) from the Cterminally truncated ( ⌬ 185-243)apoA-I dimeric crystal structure ( 32 ). A: Ribbons model emphasizing the juxtaposition of (space-fi lling) residues P3-P4-Q5 in chain A with R160, D168, and R171 in chain D. B: Space-fi lling model from a perspective identical to that in A highlighting the same residues. C: Stick model from a perspective identical to that in A with residues color-coded for motion or b-factor (temperature factor), blue → green → yellow → orange → red represents least → highest motion or temperature. The C ␣ atoms in chain A are represented as balls color-coded for motion or b-factor. Created with the PyMOL Molecular Graphics System, Version 1.3, Schrödinger, LLC. showing the presence of four-to fi ve-residue leucine zippers at both ends in the C-terminally truncated ( ⌬ 185-243)apoA-I dimeric crystal structure ( 32 ). Helix 5, cartoon green; prolines, space-fi lling yellow; L122, L126, L134, L137, and L141, space-fi lling gold. motif for aligning the pairwise antiparallel helix 5 repeats in the lipid-free state. Upon association with lipid, rotation of each pairwise helix 5 by ‫ف‬ 50° would induce interchain salt bridges, create the presentation tunnel, and "zip-lock" the double belt into the LL5/5 rotamer registration.
Finally, although MD simulations convince us of the likely importance of the N-terminal stickiness of apoA-I in stabilizing both discoidal and spheroidal HDL particles, because the most-important residues in induction of stickiness, D1 and E2, are not visible in the crystal structure, our arguments for evidence of stickiness are indirect and less than conclusive.
In conclusion, we have demonstrated that molecular modeling and MD simulations are able to provide accurate detailed structural information about soft protein-lipid assemblies such as HDL, even when high temperature jump MD simulated annealing is used to increase exploration of conformational space.