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Biophys J. Jan 1, 2006; 90(1): 112–123.
Published online Sep 23, 2005. doi:  10.1529/biophysj.105.059329
PMCID: PMC1367011

The Influence of Amino Acid Protonation States on Molecular Dynamics Simulations of the Bacterial Porin OmpF

Sameer Varma,*§ See-Wing Chiu,§ and Eric Jakobsson*§

Abstract

Several groups, including our own, have found molecular dynamics (MD) calculations to result in the size of the pore of an outer membrane bacterial porin, OmpF, to be reduced relative to its size in the x-ray crystal structure. At the narrowest portion of its pore, loop L3 was found to move toward the opposite face of the pore, resulting in decreasing the cross-section area by a factor of ~2. In an earlier work, we computed the protonation states of titratable residues for this system and obtained values different from those that had been used in previous MD simulations. Here, we show that MD simulations carried out with these recently computed protonation states accurately reproduce the cross-sectional area profile of the channel lumen in agreement with the x-ray structure. Our calculations include the investigation of the effect of assigning different protonation states to the one residue, D127, whose protonation state could not be modeled in our earlier calculation. We found that both assumptions of charge states for D127 reproduced the lumen size profile of the x-ray structure. We also found that the charged state of D127 had a higher degree of hydration and it induced greater mobility of polar side chains in its vicinity, indicating that the apparent polarizability of the D127 microenvironment is a function of the D127 protonation state.

INTRODUCTION

OmpF, located in the outer membrane of Gram-negative bacteria, belongs to a family of channel proteins that facilitate uptake of nutrients. Under normal conditions, it associates with other OmpFs in the membrane and exists as homotrimers (for reviews, refer to (18)). Each monomer folds into a rigid 16-stranded β-barrel with eight turns at the periplasmic side and eight loops (L1–L8) that narrow the structure at the cell surface and channel interior (9). Loop L3 in particular folds inside the barrel and creates a narrow region halfway through the membrane. This region, also called the “constriction zone”, gives the pore an hourglass-like shape.

OmpF allows diffusion of ions and even larger molecules of the size of several hundred daltons. It is moderately selective toward cations and has also been found to be voltage sensitive. Although several theoretical and experimental studies have been conducted to elucidate the origins of these observed behaviors, they are still not clearly understood. Molecular dynamics (MD) provides for an excellent tool to investigate these channel properties at the microscopic level. However, all the MD trajectories reported previously (1012) have resulted in producing large deviations of the trimer from its x-ray crystal structure, specifically at the constriction zone of the channel. In the constriction zone, loop L3 was found to move into the permeation pathway of the channel and toward the opposite face of the pore. In all these simulations, this movement of loop L3 was to an extent that it had decreased the cross-sectional area of the constriction zone to ~½ its magnitude in the x-ray structure. The low temperature (77 K) crystal structure indicates the dimensions of the constriction zone to be 7 × 11 Å, which corresponds to a solvent accessible area of ~32 Å2 (9). In the trajectory generated by Im and Roux (11), this area had decreased to ~15 Å2, and in the trajectory generated by our group (12), this area had decreased to ~19 Å2. Such a decrease in the size of the narrowest region of the pore can have substantial effects on permeation properties inferred from these simulations, especially since this region of the pore is exposed to several charged residues. The assumption here, that the size of the constriction zone as inferred from the low temperature crystal structure indeed corresponds to the size of the functional channel in its open state, has been validated by several experimental studies (1,13,14).

We had previously hypothesized (15) that the structural deviation in the constriction zone of the channel seen in MD simulations may have been due to protonation states assigned to some specific titratable residues lining the lumen of the channel and had therefore remodeled the protonation states of these titratable residues using Poisson-Boltzmann theory and taking into account the interactions of charged residues. Our results suggested a different set of protonation states from all of the previous assumptions (10,11,16) and left one ambiguity. Residue D127 was found to have a higher probability of being protonated if electrostatic pKa calculations were performed using a protein dielectric constant <12. On the other hand, if we assumed a protein dielectric constant of 12 or higher, as also used by Alcaraz et al. (17), this residue was found to have a higher probability of being fully charged. The results of the protonation calculations on D127 raise the following issues: Which protonation state assignment is the correct one? Conversely, which assignment of dielectric constant for the protein is the correct one?

In the crystal structure, the side chain of D127 interacts with two resolved water molecules that are contiguous with bulk water and also with several other residues, notably V130, R167, Q200, Q213, and A237 (see Fig. 6). It could be termed partially buried in a polar environment. In that context, the issue of the D127 protonation state is related to the issue of the energetic cost of burying a charged residue, or of charging a buried residue. Experimental pKa shifts associated with burying charged residues seem more consistent with treating such cases by assuming a higher polarizability (1821), which may be either due to increased penetration of water in the cavity or the intrinsic ability of the local environment of the protein to respond to changes in protonation state via disorder or rearrangement. Recent experimental work designed to distinguish between these two phenomena (local disordering or increased water penetration) in nonpolar cavities suggests local disordering as the actual mechanism, at least in the particular systems explored (2224).

FIGURE 6
Local environment of residue D127 as revealed by the x-ray structure (9). Residue names are indicated in black, and the atom names are indicated in gray. Carboxylate oxygen atoms OD1 and OD2 of D127 are labeled as 1 and 2, respectively. Distances from ...

In this work, we generate and analyze data from two separate 9-ns-long MD trajectories of the trimer (embedded in explicit POPE bilayers and 1 M KCl salt solutions) differing only in the protonation state of residue D127. This work has two aims: a), to test our hypothesis that assignments of protonation states to specific titratable residues was the problem in earlier MD simulations, and b), to explore the consequences of varying the protonation state of D127.

METHODS

Under Methods we present three sections: “Assigning protonation states to titratable residues”, “Molecular dynamics”, and “Calculating solvent accessible cross-sectional areas”. All simulations for this work were conducted on the IA-32 Linux cluster provided by the National Center for Supercomputing Applications, University of Illinois, Urbana-Champaign.

Assigning protonation states to titratable residues

Protonation states of all titratable residues lining the lumen of the channel were assigned values based on our earlier work (15). Residues E296 and D312 were assigned protonation states to conform to the hydrogen bond network indicated by Fig. 4 c in that publication. All other residues were assigned protonation states corresponding to their default values at neutral pH.

FIGURE 4
Variation of SAXA along the axis of four OmpF monomers: crystal structure, monomer representing the MD trajectory generated with a neutral D127, monomer representing the MD trajectory generated with a charged D127, and monomer representing the MD trajectory ...

Molecular dynamics

All energy minimizations and MD simulations were carried out using the GROMACS (Ver. 3.1.4) modeling software (25).

Initially, a small POPE lipid bilayer containing 128 lipid molecules and 28 waters per lipid molecule was constructed and equilibrated at 310 K for 10 ns. A larger POPE bilayer (1152 POPE + 32,256 waters) was then constructed by multiplying the last snapshot of the MD trajectory using the GROMACS utility program — genconf. This large POPE bilayer was then subjected to an equilibration for 1 ns at the same temperature. The last snapshot of this MD trajectory was then used for solvating the two OmpF trimers. In a separate setup, each trimer was rotated to orient its central axis parallel to that of the bilayer normal (z axis). The coordinates of the trimer were then translated to the center of a box that had XY dimensions the same as that of the lipid bilayer system (18 nm × 18 nm). Each of the trimers was then embedded in separate equilibrated lipid bilayer systems by using the GROMACS utility program — genbox. The z coordinates of the geometric centers of the trimers and their respective bilayers were then manually superimposed. The entire system, now comprising the lipid bilayer, water, and protein, was then energy minimized with position restraints on all protein atoms. The system was then translated to the center of a larger box (dimensions, 18 nm × 18 nm × 10 nm) and then solvated with more water. To generate a KCl solvent having a 1 M ionic strength, 2 out of every 57 water molecules were randomly selected and replaced by a set of K+ and Cl ions. To obtain charge neutrality in the two trimer systems, one containing the residue D127 in its protonated state and the other containing the same residue in its deprotonated state, an additional 30 and 33 water molecules were respectively replaced by K+ ions. Thus finally, the protonated D127 trimer system ended up embedded in a lipid bilayer having 787 POPE molecules, 59,707 water molecules, 1104 K+ ions, and 1074 Cl ions, and the deprotonated D127 trimer system ended up embedded in a lipid bilayer with the same number of lipid molecules and Cl ions but 3 extra K+ ions in place of 3 water molecules. Each of the OmpF trimer systems was then once again energy minimized with position restraints on all protein atoms. The MD trajectory was then initiated with harmonic restraints (force constant, 1000 kJ molnm−2) on all protein heavy atoms. These harmonic restraints were maintained for the first 500 ps, after which they were gradually reduced in steps of 100 kJ mol−1 nm−2/50 ps. As a result, the first nanosecond trajectory was generated with harmonic restraints. Thereafter, the two systems were simulated without any restraints for another 8 ns. The system size was continuously monitored to obtain the optimal point in time for data analysis. We found that the simulation box sizes stabilized near the 3 ns mark. Thus, all the data for this manuscript were collected and analyzed after the 3 ns mark.

For each of these simulations we used normal pressure temperature conditions with semiisotropic pressure coupling; particle mesh Ewald with Fourier spacing of 0.15 nm, a sixth-order interpolation, and a 1.0 nm cutoff in direct space for long-range electrostatic corrections; a twin-range cutoff (1.0/1.6) for van der Waal interactions; a time step size of 2 fs; five step intervals for neighbor pair list updates; the LINCS algorithm (26) to constrain all bond lengths; the SETTLE algorithm (27) for constraining bond lengths in water molecules (SPC/E); a Nosé-Hoover algorithm (28) with a coupling constant of 0.2 ps to maintain temperature at 310 K; a Parrinello-Rahman method (29) with a coupling constant of 1 ps to maintain semiisotropic boundary pressure conditions; the GROMOS96 43A1 force field (30) for protein; and a recently revised force field parameter set for POPE lipid molecules (S. W. Chiu, E. Jakobsson, and H. L. Scott, unpublished). The newly calculated POPE force field parameter set is available as supplementary information to this work.

Calculating solvent accessible cross-sectional areas

The program HOLE (32) determines the dimensions of a pore running through a structural model of an ion channel. It does so by finding the best route for a sphere with variable radius that can squeeze through a channel. HOLE defines the axis of the channel as a series of points in which each point is the center of the largest sphere that can fit into the channel at each depth into the channel. HOLE, in its original form, also defines the channel cross-sectional area as the area of a circle whose radius is the same as the radius of the largest sphere. In a later HOLE refinement for the purpose of dealing with irregular channel shapes (33), the points on the channel axis are expanded into lines and the channel cross-sectional area is defined as the cross section in the plane perpendicular to the channel protein axis (also corresponding to the mean membrane plane) of spherocylindrical capsules expanded from the lines. In our methodology we use the spherical HOLE routine of the channel to define a set of points, which we call equation M1 (where each point equation M2 is the center of the pore at some position along the path of the pore). But to most accurately characterize the cross section for channels of highly irregular geometry, we use the following angular-sweep methodology in conjugation with the HOLE (33) algorithm:

From each point equation M3 at the center of the channel as defined by HOLE, we send out a set of “rays” in the plane perpendicular to the long axis of the protein. Each ray terminates when it arrives at a point 1.4 Å (the radius of a water molecule) from the van der Waals surface of any protein atom, defining a vector. Each vector has a length equation M4 where the superscript i denotes the depth of the plane into the channel and the subscript θ denotes the angular direction of the ray. If the rays are sent out at radial intervals of equation M5 radians, then for sufficiently small equation M6 the cross-sectional area of the channel at the depth i is given very accurately by the assumption that the cross section is tiled with equation M7 “pie-wedges”, each with an area of equation M8 Thus the solvent accessible cross-sectional area at depth i (SAXAi) is given by

equation M9
(1)

The method is shown graphically in Fig. 1. In our calculations for this work, we chose equation M10 to be 0.02 radians.

FIGURE 1
Schematic of the angular-sweep methodology that was used in conjugation with the HOLE (33) algorithm to determine accurate descriptions of SAXA of channel pores. See the “Calculating solvent accessible cross-sectional areas” section for ...

RESULTS AND DISCUSSIONS

We generated two separate 9-ns-long MD trajectories of the trimer embedded in explicit POPE bilayers and 1 M KCl salt solutions, each containing approximately a quarter of a million atoms. The first 3 ns of each trajectory were considered equilibration and excluded from data analysis. The starting conditions of these trajectories essentially differ from each other only in the assignment of the protonation state of residue D127. We present and discuss results in three sections below: “Backbone structure and dynamics”, “Side-chain configurations and hydrogen-bonding patterns”, and “Ion permeation”.

Backbone structure and dynamics

The backbone structure of each monomer of OmpF can be described (10) as a 16-stranded antiparallel β-barrel enclosing an aqueous pore. The β-strands are connected via eight β-hairpin turns (T1–T8) at the periplasmic side and eight loops (L1–L8) at the extracellular side of the channel. All the periplasmic turns are short and comprise 2–4 residues with the exception of turn T4, which comprises nine residues. In contrast, the loops are longer and their lengths vary from 7 residues (L7) to 35 residues (L3). Six of these loops, L1 and L4–L8, extend toward the axis of the β-barrel and decrease the size of the pore at the extracellular end. Loop L2, also called the latching loop, extends away from the axis of its pore and folds into the channel of an adjacent monomer. Loop L3 folds into the channel pore and packs against the channel wall, decreasing the size of the pore halfway through the length of the channel. This gives the pore an hourglass-like shape, with the narrowest region of the pore (also referred to as the constriction zone) having a solvent accessible cross-sectional area (SAXA) of ~32 Å2.

In both the MD trajectories generated here, we find that the secondary structure of each monomer, as revealed by the x-ray structure, is maintained. We also find that in both simulations, the backbones of all the extracellular loops and the periplasmic turns are more flexible than the transmembrane β-barrel. This can be seen in Fig. 2, which compares the averages of the backbone root mean-square (RMS) fluctuations of the three monomers computed from these MD trajectories and those derived from Debye-Waller B-factors. We find that the computed RMS fluctuations of all the loops and extracellular turns in both simulations are either in accord with, or slightly greater than, those derived from the experimental B-factors. The larger fluctuations of some of these loops and turns may be due to the differences between the crystallization and simulation conditions. OmpF was crystallized at a temperature of 77 K and in the absence of any salt (34), whereas these simulations were performed at temperatures of 310 K and in the presence of 1 M salt solutions.

FIGURE 2
MD backbone RMS fluctuations of OmpF simulated with D127 in its charged and neutral states are compared with RMS fluctuations derived from Debye-Waller B-factors. The RMS fluctuations were calculated for all three monomers of each trimer and then averaged ...

Residue D127 is located near the extracellular end of the pore in loop L3 and interacts with residues belonging to three other loops: R167 in L4, Q200 and Q213 in L5, and A237 in L6. A comparison of the RMS fluctuation profiles computed from the two present simulations, which essentially differ from each other only in the protonation state of D127, indicates no systematic effects of the protonation state of residue D127 on backbone fluctuations of loops L4 and L5. For loop L6, we find that the RMS fluctuations are larger when D127 is set neutral. Based on the crystal structure, the carboxylate side chain of D127 in loop L3 is expected to interact with the backbone carbonyl group of residue A237 in loop L6. We show later (in Fig. 11) that the distance between the carboxylate side chain of D127 and the carbonyl oxygen of A237 undergoes lesser fluctuations if D127 is set neutral. Therefore, the larger RMS fluctuations of loop L6 seen in the case of a neutral D127 are not likely to be due to the protonation state assigned to D127.

FIGURE 11
Evolution of the local environment of D127 in all the six monomers of the two trajectories. The distances of all potential proton donors and acceptors relative to the two carboxylate oxygen atoms of D127, as indicated in Fig. 6, are shown as a function ...

Table 1 lists the average RMS deviations for the backbone atoms of all the eight loops and the longest turn (T4) for each of the three monomers simulated in the two trajectories. We see that there are no systematic effects of the protonation state of D127 on the RMS deviations of these loops. We also find that some loops, notably loop L1 in monomer M1 and loop L8 in monomer M3 of trajectory generated with a charged D127, have exceptionally much higher RMS deviations than all the other loops. These are, however, sporadic events but indicate that loops L1 and L8 are flexible and can adopt multiple conformations, especially since they are all made up of several polar residues. The time-averaged MD structures of these two loops are shown superimposed on the crystal structure in Fig. 3.

FIGURE 3
Superimposed backbone structures of OmpF. The time-averaged MD structures of the trajectories generated with a charged D127 (magenta) and with a neutral D127 (green) are shown superimposed on the x-ray structure. Most of the loops have been clipped to ...
TABLE 1
Comparison of average RMS deviations of backbone atoms of different residue fragments of each monomer (M1, M2, and M3) in the two trimers simulated using different protonation states for residue D127

Together, we find that the assignment of a protonation state to residue D127 does not have any systematic effects on the structure or the dynamics of the protein backbone. We also find that irrespective of the assignment of the protonation state to residue D127, the protein backbone does not undergo any major systematic conformational changes during the simulation. This result is, however, different from that obtained from any of the previously reported MD simulations (1012), mainly with respect to the average structure of the PEFGGD fragment of loop L3. The PEFGGD fragment of loop L3, which comprises residues P116, E117, F118, G119, G120, and D121 at the tip of the loop, is the signature sequence of enterobactrial porins (35). It is shown in Fig. 3, highlighted orange in the x-ray structure. In Fig. 3, we also see that in the current two simulations, there are no systematic differences between the average structures of these fragments in any of the monomers of the two trimers. However, in all previous MD simulations, this fragment was consistently found to move into the permeation pathway and toward the opposite face of the pore, decreasing the SAXA of the narrowest region of the constriction zone to almost one-half the corresponding magnitude in the x-ray structure. In the trajectory generated by Im and Roux (11), the SAXA of the narrowest portion of the constriction zone had decreased from ~32 Å2 to ~15 Å2, and in the trajectory generated by our group (12), this area had decreased to ~19 Å2. In this simulation, we do not see such a decrease in the size of the constriction zone. This is more evident from Fig. 4, which shows the variation of SAXA along the axes of the pores in the time-averaged MD structures of each of these simulations in comparison with the variation of the SAXA along the axis of the pore in the x-ray structure (refer to the Methods section for calculation details). In this figure, we also show for comparison the SAXA profile for the mean structure from our own previous MD simulation (12). Clearly in the current two simulations, we find that size of the constriction zone does not decrease dramatically, in contrast to previous simulations.

The x-ray structure (9) indicates that the PEFGGD fragment of loop L3 is expected to interact with the wall of the β-barrel via a hydrogen bond network involving the backbone nitrogen atom of residue E117 and two other titratable residues, E296 and D312. This is shown in Fig. 5. The differences between the current MD data and data from all previous MD simulations, therefore, appear to arise from differences in the assignments of the protonation states of residues D312 and E296. In two of the previous simulations (10,11), both residues were set protonated. In the other simulation (12), both residues were set partially charged. The spatial proximity of residues D312 and E296 in this structure suggests that at least one of the two acidic groups should be protonated. If D312 is protonated, the hydrogen bonding between the carboxylate group of D312 and the backbone nitrogen of E117 is weakened. This seems likely to have caused the large-scale deviations of the loop from the crystal structure in two of the previous simulations (10,11). This interpretation of the significance of the charged state of D312 is supported by the work of Liu and Delcour (36), who mutated residue D315 in OmpC (which corresponds to aspartate D312 in OmpF) to an uncharged alanine. This mutation essentially mimics a scenario in which residue D312 is assumed protonated and thereby incapable of forming a hydrogen bond with the backbone nitrogen atom of residue E117. They found that such a mutation resulted in a significant increase in the frequency of pore closures in patch clamp studies, clearly demonstrating the significance of the charged state of residue D312 in maintaining both the structural and functional properties of the channel. It should be noted that although this correlation between a particular experimental condition and a previous computational setup neatly demonstrates the effect of discharging residue D312, it does not necessarily imply that a change in the charged state of D312 is a trigger for voltage gating in the native channel. The involvement of loop L3 in voltage gating via its movement into the permeation pathway was ruled out by a cysteine-scanning mutagenesis investigation (37).

FIGURE 5
Partial view of the x-ray structure (9). Titratable residues E117, E296, and D312, which are involved in the interaction of the PEFGGD fragment of loop L3 with the wall of the β-barrel, are shown as stick models. The solid lines on the backbone ...

On the other hand, setting E296 simultaneously charged along with D312, as our group previously did (12), creates a strong electrostatic repulsion between the two acidic side chains triggering a coordinated movement of D312 along with the PEFGGD segment of loop L3 into the permeation pathway of the channel, essentially the same structural result as the other previous simulations but for a slightly different underlying reason. In the current simulation, D312 was set fully charged and E296 was set protonated based on our recent protonation state calculations (15). In this scenario, D312 acts as a proton acceptor from both residues, E117 and E296, which keeps the segment tethered to the wall of the β-barrel in accord with the x-ray structure. In these simulations, we also note that the χ-angles of the side chain of residues E296 in the different monomers undergo rotations that result in minor coordinated movements of the side chains of their respective D312 residues either toward or away from the wall of the β-barrel. These side-chain movements result in positioning PEFGGD fragments of loops L3 either slightly away from (monomers M2 of both trimers in Fig. 3) or slightly closer to (monomer M1 of the trimer simulated with a charged D127) the wall of the β-barrel. However, such movements had no noticeable effect on the average SAXA profiles of the constriction zone.

In summary, a comparison of backbone RMS fluctuations and the backbone RMS deviations between the two trajectories showed no significant dissimilarities. This implies that the assignment of a protonation state to D127 does not have a large-scale effect on the structural dynamics of the trimer. In the following section, we explore the side-chain configurations and hydrogen-bonding patterns in the vicinity of D127 for both assumptions of protonation states.

Side-chain configurations and hydrogen-bonding patterns

Fig. 6 shows the local environment of residue D127 as revealed by the x-ray structure (9). There are two carbonyl oxygen atoms, A237.O and Q213.OE1 that are within 3.5 Å of the carboxylate group of D127, indicating that they may be able to contribute to stabilization of D127 in its neutral (protonated) state. However, there are two crystallographically resolved water oxygens at distances 3.7 Å and 2.9 Å, respectively, from the OD1 and OD2 atoms of D127, indicating that they may be able to stabilize D127 in its charged state. Furthermore, there are four amine groups, two belonging to R167 and one each belonging to residues Q200 and Q213, that are close to ~6 Å from the carboxylate side chain of D127, indicating that they may be able to further stabilize the charged state of D127. Thus, the x-ray data do not provide unambiguous guidance to model the protonation state of D127. Moreover, our previous electrostatics-based pKa calculations (15) predicted a protonation state of D127 that was dependent on the choice of the protein dielectric constant, further indicating a close balance between factors tending toward a neutral state and those tending toward a charged state. In essence, the presence of a charged arginine and several other protein dipoles and two water dipoles combine to put residue D127 in the center of a hydrogen bond network with a complicated balance of forces that on the face of it are consistent with either a charged or uncharged state for D127.

By contrast with D127, the reasons our previous electrostatics-based pKa calculations predicted R167 to be fully charged are evident by inspection from its local environment. First, the side chain of R167 is not straight but bent toward its own backbone, such that its side-chain amine group is at hydrogen bonding distance from its own backbone oxygen atom. Second, there are two other carbonyl oxygens, one belonging to residue S125 and the other belonging to residue D126, that are within hydrogen-accepting distances from R167 (also shown in Fig. 6). And third, R167 is not completely buried in the low dielectric environment of the protein, implying that associating a charge with R167 is electrostatically not expensive.

To investigate local effects of assigning a protonation state to residue D127, we first computed the average center of mass deviations of all the residues involved in its hydrogen bond network, namely, D127, V130, R167, Q213, and A237 in both trajectories. The computed values of these deviations in all the six monomers are listed in Table 2. We find that R167 is a special case, because its center of mass deviation is exceptionally higher than all the other residues. Since the backbone atoms of R167 remain within 0.03 Å of the crystal structure, it follows that the relatively large center-of-mass deviation is entirely due to a side-chain configuration that is different from the crystal structure. Fig. 7 compares the time-dependent center-of-mass deviations of residue R167 for all monomers in the two trajectories. In the MD trajectory, when D127 was neutral, we find that the side chains of R167 of all monomers consistently move away from D127 and into the permeation pathway of the channel. We find that this side-chain movement occurs within the first 0.3 ns of the simulation conducted without any harmonic restraints. On the other hand, in the MD trajectory when D127 is charged, we did not find R167 to move away from D127 until the 3 ns mark. We found the same deviation in two out of the three monomers, M1 and M2, but only after 3 ns and 6 ns, respectively. Together, we find that the charged state of D127 shows a stronger tendency to hold the side chain of R167 out of the permeation pathway. This is illustrated in Fig. 8, where we compare the conformational space sampled by residues D127 and R167 in each of the three monomers of the two simulated trajectories. The side-chain configuration of R167 in monomer M3 with charged D127 is in agreement with the crystal structure.

FIGURE 7
Time-dependent center of mass deviation from x-ray crystal structure of residue R167 belonging to each of the three monomers (M1, M2, and M3) of the trajectories generated with (a) a charged D127 and (b) a neutral D127. These deviations were first computed ...
FIGURE 8
Conformational space sampled by residues D127 and R167 in each monomer (M1, M2, and M3) of the trajectory generated with D127 in its (a) charged state and (b) neutral state. The carbon atoms are shown in green, oxygen atoms in red, nitrogen atoms in blue, ...
TABLE 2
Comparison of average center of mass deviations of all residues involved in the hydrogen bond network of residue D127

Fig. 9, a and b, shows the radial distribution function of water oxygens around each of the carboxylate oxygens of residue D127 for the charged and neutral states, respectively. In the crystal structure, there are crystallographically resolved water molecules within hydrogen bonding distance from both the OD1 and OD2 atoms of D127. In these simulations, it is seen that irrespective of the protonation state of residue D127, a water molecule is consistently present at hydrogen bonding distance from the OD2 atom of D127, consistent with the x-ray data. However, we find that a water molecule is present close to atom OD1 only when residue D127 is fully charged. We find that the water molecule that was crystallographically resolved near atom OD1 is missing in the trajectory of all the three monomers when residue D127 is neutral.

FIGURE 9
Radial distribution of water around the two carboxylate oxygen atoms of residue D127 calculated for the last nanosecond trajectory of both simulations: (a) around OD1 atom and (b) around OD2 atom. Radial distributions were first calculated separately ...

Recent work of Denisov et al. (23) suggests that water molecules resolved in nonpolar cavities using low temperature x-ray crystallography are not likely to be immobilized (with dwell times <10 ns) under physiological conditions. Our simulations suggest the same in polar cavities, since we see multiple water molecules interacting with D127 during the course of the simulation for both of the assumed charged states. For instance, we find in the case of monomer M3 of the trimer simulated with a charged D127 six separate water molecules that move in and out of this cavity and interact with D127 at some point of their respective trajectories. This is illustrated in Fig. 10, which shows the positions visited over a 5 ns interval of each of the six water molecules that adopted the nearest neighbor position to the OD1 atom of D127 at any time during the 5 ns. This figure shows the water molecule positions at 50 ps intervals, so there are in principle 100 positions plotted for each water (although not all are visible, because some are hidden behind others). Interestingly, one of these water molecules (coded yellow) also translocated the channel between the periplasmic and extracellular ends.

FIGURE 10
Superimposed trajectories of six separate water molecules (colored spheres) that were found to adopt the nearest neighbor position to the OD1 atom of residue D127 (drawn as a stick model) during any time of their respective trajectories. Residue D127 ...

The panels of Fig. 11 show the time evolution of the relative interatomic distances shown in Fig. 6 that are not considered in Figs. 7–9.. Overall, Fig. 11 reveals distinct differences in side-chain behavior as a function of whether or not D127 is protonated. In the neutral state, the interatomic distances move to distinctly larger values than seen in the crystal structure and then mostly remain near the same values for the rest of the duration of the simulation. In the charged state, the interatomic distances remain relatively closer to the crystal structure values than for the protonated state but continue to undergo transitions during the rest of the duration of the simulation. Note that these changes are all side chain changes. Note also that the simulations are done at 310 K and the x-ray structure was determined at 77 K. It appears that at physiological temperatures the side chains in the vicinity of D127 find conformations that tend to increase the interatomic distance of electrostatically interacting side chain atoms, as compared to the crystal structure. This tendency is especially pronounced when D127 is in its neutral state. For both the neutral and charged states, this “expansionist” tendency of the side chains occurs in the context of a mean backbone structure that remains essentially fixed at the crystal structure. Presumably such an “expansion” in the context of an unchanging backbone structure can only occur near the surface of a protein, since in the core there would be no room to expand.

The increased frequency of side-chain transitions in the vicinity of the charged D127 suggests that the apparent polarizability of the protein in the vicinity of the charged D127 is higher than in the vicinity of the uncharged D127. Interestingly, this was also seen in the experimental work of Denisov et al. (23) in nonpolar cavities.

Together, if we use the crystal data as a reference to determine the protonation state of residue D127, as is normally done in electrostatics-based titration models, a comparison of data between the two trajectories suggests that residue D127 is more likely to be charged in the crystal. This is mainly supported by the observations that a), the charged state of D127 has a higher tendency to prevent residue R167 from moving away from D127 and into the channel lumen, and b), the charged state of D127 does better at holding water in the positions of the crystallographically resolved waters. However, since we find that the local environment of D127 as revealed by the low temperature x-ray structure is not precisely maintained in either trajectory, it seems plausible that under physiological conditions D127 might be in either state.

Ion permeation

We observed that cations and anions permeated the channel along different pathways in a screw-like fashion, similar to that observed in several other previous investigations (11,3840). Fig. 12 shows the time-averaged number of ions at different positions along the length of the pore in both MD trajectories. In both cases, we find cations to have a moderately higher tendency to occupy the pore than anions, corresponding to the known moderate preference of cation-over-anion conduction through the channel (for the most recent review, see Nikaido (8)). In both cases, we find that the bulk of the difference between potassium and chloride ion occupancy is at and around the constriction zone of the channel. The most distinctive difference in the curves for the different protonation states is that for the charged D127, there are two distinct preferred occupancy sites that appear selective for potassium. Before doing the simulations, we wondered if the potassium selectivity might depend on whether D127 was charged, but Fig. 12 shows that this is not the case; the selectivity is maintained in either case. However, this dependency of ion distribution profiles on charges of single residues suggests a basis for changes seen in reversal potentials when charge altering point mutations are introduced (for example, see Phale et al. (40), Van Gelder et al. (41), Samartzidou and Delcour (42), Bredin et al. (43), and Nestorovich et al. (44)), a subject we anticipate will be explored in future studies.

FIGURE 12
Average number of ions along the axis of the two trimers: (a) charged D127 and (b) neutral D127. Positions of the constriction zone and residue D127 along the axis of the channel are shown. Irrespective of the protonation state of residue D127, there ...

SUMMARY AND CONCLUSIONS

The specific conclusions we draw about the system studied in this work are:

  1. Results of the MD simulations and their analysis presented in this work confirmed the hypothesis that use of protonation states computed by Varma and Jakobsson (15) result in agreement between the cross-sectional areas of the constriction zone in the crystal structure of OmpF and unconstrained MD, with residue D127 either charged or neutral.
  2. Both protonation states of residue D127, charged or neutral, predict moderate selectivity of potassium over chloride in agreement with experiment.
  3. In the 310 K simulations presented in this work, there were no systematic dependencies of the backbone structure dynamics of OmpF on the protonation state of residue D127. The side-chain configurations, hydrogen bonding patterns, and hydration patterns seen in the local environment of residue D127 were somewhat different from the corresponding configurations and pattern seen in the crystal structure at 77 K. For the neutral D127, the interatomic distances remained essentially unchanged during the simulation after equilibration, whereas for the charged D127, the side chain conformations continued to undergo transitions throughout the simulation. Water radial distribution functions showed that the neutral D127 had close interactions with just one water molecule, whereas the charged D127 was usually interacting closely with two water molecules. Conclusions about the detailed interaction network of the side chains and water are subject to two caveats: a), It has recently been shown that classical force fields do not give accurate results for the hydration of carboxylate groups (45). Therefore conclusions based in part on simulating this type of interaction should be reconsidered in the future with better force fields. b), And the model we use for protonation states of residues is static. For residues such as D127 in OmpF, where there is a close balance between influences tending toward protonation and deprotonation, it would be more realistic to construct a dynamical model for protonation, where a proton could exchange between a residue and water in the course of a simulation.
  4. Based primarily on our finding shown in Fig. 8 that the uncharged D127 cannot keep the R167 side chain from swinging out into the channel lumen, we conclude that D127 is probably charged in the low temperature crystal structure. However, under physiological conditions, it seems plausible that D127 can exist in both the charged and the uncharged states, and thus switch dynamically between the two states. This hypothesis is reinforced by the results in Fig. 10, which demonstrate that there is frequent exchange of waters in the vicinity of D127, and hence ample opportunity for protonation-deprotonation reactions.
  5. These simulations point out a limitation of electrostatics-based titration models in which the dielectric constant of the protein is set at a fixed value. (For a similar point with respect to permeation models, see Allen et al. (46)). Indeed, it is hard to see how any continuum dielectric model, even one that allows for anisotropy and spatial variation, can capture the behavior of polarizable groups in the vicinity of D127, as shown in Fig. 11. We see by the increased mobility of the polar groups in the vicinity of the charged D127 that the local apparent polarizability of the channel protein is variable in response to the protonation state of D127. Furthermore, we also see by the increased hydration of charged D127 that the polarizability of the cavity associated with penetration of water is also a function of the protonation state of D127. However, we find that the changes in the hydration number of D127 are coupled to the changes in interaction of D127 with the protein. We see from Fig. 8 b that when D127 is neutral, its protonated side-chain carboxylate is closely coordinated with the backbone carbonyl of R167. In essence, we see in this polar cavity that the polarizability of the local protein charge groups, the degree of penetration of water, and the protonation state of D127 all seem to be very tightly coupled to each other. This is somewhat different from what was seen for the case of introducing a charged residue into a nonpolar cavity (23), where the increase in the local polarizability was essentially exclusively due to increased protein disorder.

The more general inferences we draw from these conclusions are:

  1. When considering a situation where multiple charged residues interact with each other, it is important to consider exhaustively the combinatorics of possible interactions, and the range of plausible parameters in Poisson-Boltzmann calculations, when assigning protonation states.
  2. Side chain configurations and hydration patterns seen in low-temperature crystals may not reflect the array of configurations experienced in physiological-temperature dynamics.
  3. To fully understand the protonation states of titratable residues in proteins, it is necessary to modify the view that the protonation state is determined by the protein dielectric properties. One may consider instead that the protonation state of a residue and the protein dielectric properties near the residue each affect the other.

Future work suggested by the results of this work include:

  1. Similar calculations on the numerous mutants of OmpF for which structures are known to validate the capability of describing in atomistic detail the functional changes associated with mutations. In the longer term, the ultimate goal would be to combine the very compute-intensive MD simulations of the sort described in this work with a more coarse-grained and a less compute-intensive simulation technique. Candidate coarse-grained approaches include transport Monte Carlo (12,47), continuum Poisson-Nernst-Planck theory (48), or Brownian dynamics (4952). In this strategy, the MD simulations would be used to validate the detailed description of the system. The detailed description of the system would be used to parameterize the much less compute-intensive Brownian dynamics or transport Monte Carlo, which in turn could be used to do sufficiently long simulations that the physiology of the channel could be predicted. Such a capability could be used to develop a computer-aided design capability for reengineering β-barrel channel proteins as conducting components of nano-devices, as postulated by Bayley and Jayasinghe (53).
  2. Work on force field improvement to more confidently characterize hydrogen bonding and hydration patterns in side chains.
  3. Development of a dynamical protonation/deprotonation model to more confidently characterize this aspect of protein-water interactions.
  4. Experimental comparison between side-chain configurations in OmpF at low and physiological temperatures.

SUPPLEMENTARY MATERIAL

An online supplement to this article can be found by visiting BJ Online at http://www.biophysj.org.

Supplementary Material

[Supplement]

Acknowledgments

We gratefully acknowledge computational time from the National Computational Science Alliance. We also thank all our lab members for their helpful comments and discussions.

This work was supported by National Institutes of Health grant R01GM054651-08 and by the U.S. Dept. of Energy's Genomics: GTL program (www.doegenomestolife.org) under project “Carbon Sequestration in Synechococcus Sp.: from Molecular Machines to Hierarchical Modeling” (www.genomes-to-life.org).

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