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Copyright © 2007 The Biophysical Society. All rights reserved.
Biophysical Journal, Volume 92, Issue 10, 3474-3491, 15 May 2007

doi:10.1529/biophysj.106.100669

Biophysical Theory and Modeling

Lactose Permease H⁺-Lactose Symporter: Mechanical Switch or Brownian Ratchet?

Richard J. Naftalin^*, ,  , Nicholas Green^† and Philip Cunningham^‡

^* King's College London, Physiology Division, Franklin-Wilkins Building, London, United Kingdom
^† Department of Chemistry, Central Chemistry Laboratory, Oxford, United Kingdom
^‡ King's College London, Bioinformatics, Franklin-Wilkins Building, London, United Kingdom

Address reprint requests to R. J. Naftalin, King's College London, Physiology Division, Franklin-Wilkins Bldg., London SE1 9NH, UK. Tel.: 0207-848-4646; Fax: 0207-848-4500.

The crystallographic description of Escherichia coli lactose permease, a member of the major facilitator superfamily of membrane transport proteins, has added significantly to our understanding of the structure of membrane transporters 1,2,3,4,5. Nevertheless, the mechanism of lactose-proton cotransport remains ambiguous. Although arguments supporting an alternating mechanical “rocker switch” mechanism have been deduced from various kinds of mutation study, other findings are inconsistent with this mechanically coupled device, but more in harmony with an alternative stochastic model, to be discussed here.

A mechanical rocker switch mechanism for the Escherichia coli lactose permease (LacY) cotransport cycle has been inferred from kinetic, mutation, cross-linking, and, most recently, x-ray studies of the crystallized transporter protein 2,6,7. The model proposes that inward- and outward-facing conformations alternately expose the centrally bound disaccharide and proton to the adjacent cytosolic and external (periplasmic) solutions. This requires large-scale, precise, cyclic, coordinated conformational changes in transmembrane helices II, IV, and V in the N-terminal domain and VII, X, and XI in the C- terminal domain.

Recent x-ray comparisons of the crystallized LacY permease structure liganded to the high-affinity disaccharide β-D-galactopyranosyl-1-thio−β-galactopyranoside (TDG) with the unliganded LacY permease show small conformational differences resulting from TDG binding around Arg-144, Glu-126, and Glu-269 7. The TDG-induced disruption of a salt bridge between Arg-144 and Glu-126 is thought to promote movement of Glu-269 from a shielded hydrophobic environment into an exposed hydrophilic region, thereby altering its pK_a and hypothetically permitting proton transference via a bridging water molecule to the imidazole group of H322 7. This is believed to activate large-scale conformational changes leading to inversion of the locations of lactose and H-ligand binding sites to the trans side.

The position of TDG, the high-affinity disaccharide ligand, localized by x-ray crystallography within the central pore, is taken to be consistent with the rocker mechanism 4,7,8. However, this singular positioning of the ligand within the central pore does not readily explain how it is transported along the length of the pore, or how mutation of a single residue, e.g., H322 to F322 converts the H⁺-lactose (D-galactose-β1-4-D-glucose) symporter to a lactose/melibiose uniporter 9,10,11,12. Similar models in which a proton transfer reaction is activated by lactose have been proposed 13,14. As will be seen, none account for the finding that when the charged amino acids surrounding H322 are substituted by neutral replacements, downhill flow of lactose, or melibiose (D-galactopyranosyl-α1-6-D-glucose), and protons is recovered after mutation at any of five other “suppressor” sites with charged or uncharged amino acids 15.

Salt bridges provide a more energetically favorable environment to accommodate charged residues, particularly where the dielectric constant is low 16. It is proposed additionally that the oppositely charged amino acid pairs, Lys-319 with Asp-240 and Asp-237 with Lys-358, form salt bridges that “stabilize the H-bond network” 16,17,18,19. A problem with this scheme is that interchange of Lys-319 with Asp-240 with the double mutant K319D, D240K, although preserving the salt bridge, abolishes transport activity. However, this is not considered sufficient grounds for rejecting the view that both salt bridges are required to maintain the transport cycle, although the role of the K319/D240 salt bridge in proton translocation remains equivocal 18,20.

Another shortcoming of the mechanical rocker model of LacY permease activity is its lack of specific guidance regarding the relationship between the combined pH and electrical potential gradients, the proton motive force (PMF) across the symporter, and the kinetics of lactose transport in wild-type and uncoupled transporter mutants.

Loss of PMF, or uncoupling of the H⁺ gradient from lactose flow decreases lactose accumulation and increases both lactose efflux and its apparent affinity, as measured kinetically, for the export site 21,22,23,24,25,26,27. However, the affinities of right-side-out, or inside-out membrane vesicles containing LacY to lactose or TDG, measured by ligand binding, are symmetrical in the presence or absence of a PMF 28. This suggests that the apparent difference in affinity between inside and outside sites, like that with the GLUT1 transporter in human erythrocytes, is only observed when net ligand transport occurs, but not when measured by direct binding assays 29,30,31,32.

The necessity for histidine H322 participation in the LacY symport pump cycle has been questioned 11,33. Mutation of H322 to asparagine, H322N, permits a low level of H⁺-gradient-induced uphill lactose transport to ∼5% of wild-type accumulation and passive downhill lactose movement with accompanying proton movements (downhill symport). However, when H322 is replaced by arginine or phenylalanine (H322R or H322F), only downhill lactose flow without protons (uniport) is observed 21,34. Since the conversion of the symporter to a uniporter can occur by substituting a nonionizing benzyl for an imidazole group, loss of symporter function may be considered to be due to loss of an essential intermediate site in the proton transport chain without concurrent loss of the lactose-binding site. Nevertheless, as protonation of H322 imidazole is thought to induce inversion of the symporter 7,19, it is surprising that the F322 mutant lacks a strong inhibitory effect on either the net or exchange lactose/melibiose uniport process 6,10,33,35. Moreover, the observation that symport process is partially retained when asparagine is substituted for H322, even though its amide residue is not protonatable, suggests that an alternative mechanism to the rocker model for H⁺-lactose symport may exist. It is evident that proton transfer at H322, or its substitute cannot be the trigger for inversion of the ligand-binding site of LacY. As the uniport mechanism is also considered to be an alternating carrier process lacking H⁺ coupling, the conformational changes determining the inversion process at the central sugar binding site in the uniporter mode should be similar, or identical, to those of the symporter 36.

Another problem in reconciling H322 with its assigned role in the cyclic process leading to H⁺-lactose symport is that its proton turnover rate should match the turnover rate of the symporter, i.e., 20–50Hz 37,38. Nachliel and Gutman 39,40 have shown that protons diffuse rapidly within the large, water-filled central cavity of LacY, and protonation rates of H322, over a wide pH range, are two orders of magnitude faster than the turnover rate of the symporter in the presence or absence of lactose. This is discordant with a symport model, which requires synchronized mechanical linkages between the various stages of proton-lactose transit and the conformational changes they evoke. It would seem that the rapid rate of Brownian motion within the central cavity militates against such a precise clockwork model.

The inwardly directed PMF across the LacY symporter is thought to hasten return of the negatively charged empty carrier to the exofacial side of the transporter, thereby reducing the rate of ligand export while reciprocally increasing the ligand import rate 22,23,25. Two negatively charged amino acids might fulfill the role of PMF responsive elements. However, replacement of any five of the six charged amino acids most associated with symport—D240, E269, and E325, along with R302, K319, and H322—by nonionizable amino acids still permits downhill proton and lactose flow. Replacement of all six amino acids with nonionizable substitutes permits a limited degree of lactose uniport 15,41. These findings indicate that no amino acid can be individually assigned to the role of a proton conductor, or be responsible for PMF-evoked acceleration of the empty carrier. However, it is evident that K319, H322, and E325 all play important roles in H⁺-coupled lactose flow.

An additional problem is that the specificity of LacY toward various transported sugar ligands varies with different mutations or inhibitors 5,33,35,41,42,43,44,45,46. This is difficult to reconcile with a single site for sugar ligand binding as envisaged by the carrier model for symport 20,41,43.

To rationalize some of these problems we have applied the molecular docking program Autodock 3 to TDG-liganded LacY (Protein Data Bank (PDB) entry, 1PV7) and its unliganded forms at pH 6.5 and 5.5 (2CFP and 2CFQ). Many available mutation studies give valuable qualitative information about the effects of electrostatic potential changes within the central cavity. When combined with the three-dimensional (3D) crystal structure of LacY, these can now be accommodated with an alternative model for lactose symport.

Docking studies have been performed using Autodock 3 (http://autodock.scripps.edu) 47 on the published crystal structure of the mutant lactose symporter LacY (PDB entry, 1PV7) and the unliganded forms of the transporter (2CFP and 2CFQ). The 3-D structures of TDG, β-D lactose, melibiose, maltose, β-D-glucose, α- and β-D-galactose, and several other oligosaccharides, among which is the tetrasaccharide stachyose α−D-Gal-[1-6]-α−D-Gal-[1-6]-α−D-Glc-[1-2]-β-D-Fru, known to have minimal cotransport activity in LacY48,49, were obtained from Sweet II (The German Cancer research Centre DFKZ, http://www.dkfz.de/spec/sweet/) and used as docking ligands. Docking utilized a 3D grid with a spacing of 0.375Å, centered on the LacY molecule, with 100 points in each dimension.

DeepView/Swiss-PDBViewer (http://www.expasy.ord/spdbv) was used both to construct the 3D mutant protein forms of LacY (1PV7) and to view the mutant proteins and the ligands. After mutation in silico, the altered structures were subjected to an energy minimization routine using the GROMOS96 implementation within Deepview, before observing the effects of lactose-docking with Autodock 47.

The electrostatic potential maps were prepared using the routines for the solution of the Coulomb equation in Swiss PDB Viewer, or using the routines in the Voidoo software package (University of Uppsala Software Factory http://alpha2.bmc.uu.se/usf/voidoo.html). The Nottingham Algorithms Group (NAG) routine, E01TGF, was used to derive 2D grids of interpolated electrostatic values at 1-Å intervals (http://www.nag.com/numeric/fl/manual20/pdf/E01/e01tgf) within selected planes. The electrostatic potential gradients in the x and y directions within each plane were estimated using vector addition of the local potential differences of the eight nearest neighbor cells surrounding each cell. The gradients of the differences in the computed electrostatic potential distributions in the region around H322 in the control and some multiple mutants were also obtained by vector addition.

Hydration of both unliganded and docked-lactose forms of LacY was simulated using “Flood”, part of the Voidoo package. This necessitated constructing a cage around the protein structure so that the software “sees” “cavities” rather than “invaginations”.

Unlike glucose docking on GLUT1 30,50, neither lactose, TDG, nor melibiose dock at clearly defined cluster sites on LacY; instead, the docking sites cover the walls of the endofacial and central cavity regions. The docked positions of disaccharides TDG and β-D-lactose on LacY have affinities in the range 0.02–0.5mM, as determined by Autodock 3 (average for lactose=0.4mM) (Table 1). Also, in contrast to the docking studies on GLUT1 30,50, there is no evidence of a continuous pathway for sugar movement across LacY, as no lactose, melibiose, or TDG (not shown) docking is observed in the exofacial vestibule (Figure 1A). This absence probably results from a narrowing of the exofacial vestibule in the crystallized form of LacY (PDB 1PV7), which is a thermostable LacY mutant, C154G lacking any transport activity. This distortion of the basic major facilitator superfamily structure has been removed in the templated form of GLUT1 (PDB 1SUK) 50, and thereby permits four clusters of glucose docking sites in the exofacial vestibule of GLUT1 30. However, even in the C154G LacY mutant, there are isolated clusters docking sites of D-galactose in the exofacial vestibule (Figure 1A).

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Figure 1

(A) Slab view of LacY centered on the central pore, showing all the lactose (yellow), melibiose (green), and galactose (purple) docking sites on LacY. Superimposed numbers show the positions of mutations, which alter the sugar specificity of the transporter (Table 4). (B) The orange colored molecule shows TDG in the assigned position by crystallography 1 and two additional docked lactose molecules H-bonded to lactose H322 within the central cavity of LacY.

Surprisingly, none of the TDG molecules docked with Autodock 3 coincides exactly with the position of TDG assigned by crystallography (Figure 1B, orange molecule). The current version of the rocker mechanism requires that TDG should initially dock to Arg-144, Glu-269, and Trp-151 7. Autodock assigns four possible TDG docking positions to within 3Å of the OH group of W151, so these findings are consistent with the recent finding that TDG binds close to this central tryptophan residue 51. Nevertheless, none has the coordinates assigned by crystallography. The nearest docked TDG molecule, shown in the CPK color scheme, is within 1.5Å of the galactopyranosyl ring, which crystallography indicates binds to W151, but deviates by >3Å from the other galactose ring. The TDG molecule with the highest affinity assigned by Autodock docks >10Å from the crystal-assigned TDG position (not shown).

The ligand binding site for TDG as identified by crystallography is absent from unliganded LacY 7. Nevertheless, around H322, there are no significant differences between lactose docking positions assigned by Autodock 3 in the liganded (PDB 1PV7) and unliganded form of LacY (PDB 2CFQ, at pH 5.5), although substantial differences are observed in lactose docking positions at other sites on the endofacial cavity walls (not shown). Similar lack of agreement with the crystal docking assignments for TDG has been reported using molecular dynamic simulation 14.

Computerized molecular docking studies on a crystal structure of a protein such as LacY have a clear advantage over such studies on a templated model structure, as with GLUT1, as the postulated templated structure may be less dependable and so must be “authenticated” in as many ways as possible 14,30,52,52,53. Nevertheless, such corroborating procedures should also be applied to any predicted conformational changes deviating from the existing x-ray structure.

Although the x-ray structure is taken as a benchmark of reliability, the prediction of mechanism based on results from x-ray data should not be viewed uncritically. According to Horsefield et al. 53, there are several possible reasons for differences between ligand docking positions in silico and crystallographic assignments. Some of the interactions could be affected by the crystallization process itself, or x-irradiation could shift the docking position of the ligand. Additionally, ligand binding to low-affinity sites is not stable enough to give satisfactory x-ray diffraction images, and thus is not revealed by crystallography. These explanations are used to account for the 2.8-Å root mean-square deviations between the positions of ubiquinone in the native structure of succinate/ubiquinone oxidoreductase (Q₁-site) assigned by x-ray crystallography and the position of ubiquinone when docked by the molecular recognition program GOLD (Q₂ site). Similar arguments hold for the lack of conjunction between lactose binding to LacY assigned by crystallography—by the same laboratory—and those predicted with Autodock, as observed here.

Another possibility is that Autodock incorrectly assigns TDG and lactose docking positions. However, this is an unlikely explanation for the many observed differences between in silico and crystal docking of TDG on lactose permease. Autodock examines an extremely large number of potential docking sites on the basis of the van der Waals, electrostatic, and ligand torsional forces 47, and generates similar docking positions for a number of different sugar ligands for lactose permease. The following sugars generated similar docking patterns: lactose, melibiose (Figure 1A), maltose, TDG, and stachyose (Figure 2C) in that there was no evident clustering of the docked sugars. Nevertheless, both melibiose and maltose have similar docking patterns within the central cavity of LacY and both dock at separate sites from lactose in the region between Asp-240 and Asp-237 and Glu-325 (average K_i of 27 docked melibiose molecules in this region, as obtained by Autodock 3, 0.29±0.05mM) (Figure 1AB).

When Arg, Phe, Gln, or Tyr is substituted for H322 in LacY, LacY H⁺-lactose symporter becomes a uniporter (Table 2) 33,34. However, when asparagine replaces histidine 322 (H322N), uphill H-lactose symport is still observed, albeit at only a twentieth of the rate and extent of lactose accumulation seen in the wild-type 11,33,34. On this basis, it has been argued that H322 is inessential for symporter function.

The lactose transport system of Streptococcus thermophilus Lac S permease has structural similarity around H376 to the sequence adjacent to H322 in E. Coli LacY. Lac S E379 is an analog of LacY E325 in E. coli. In Lac S permease the mutant H376Q has reduced lactose symporter activity and zero melibiose and methyl-D-thiogalactopyranoside symport activity 27,33.

Our docking studies show that only histidine or asparagine in LacY at position 322 can H-bond to an oxygen atom of closely docked lactose. Lactose H-bonds to H322, only at its Nɛ4 position (Figure 2AC, and Table 1).

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Figure 2

Slab view showing the central pore of LacY with the docked positions of lactose close to position 322. (A) Lactose H-bonds to H322 and B) N322 not at Q, F or K 322. (C) Stachyose also H-bonds between a glycosidic oxygen and H322. (D–F) Positions of lactose docked to glutamine, phenylalanine, and lysine mutations of H322. None of these has any lactose H-bonded at position 322.

H322 imidazole also H-bonds between its Nδ1 position and Tyr-236 OH, which retards rotation of the imidazole ring and raises the pK_a of the imidazole base. Lactose can H-bond to both oxy residues of the asparagine mutation, H322N (Figure 2B). However, no H-bonding to lactose is observed with R322, Q322, Y322, or F322 mutants (Figure 2DF). A possible inference is that amino acids at position 322 permitting H-bonding to sugar oxygen electrons are required for H-lactose symport activity.

Six charged amino acid side chains at the vertices of two intersecting planar trapezoids, positioned edge to face, are equidistant (4.8–6.25Å) to H322 (Figure 3A and Figure 4A). H322 imidazole lies at the centroid of the Lys-319/Arg-302/Glu-325/Glu-269 plane (KREE) and the Lys-319/Asp-237/Asp-240/Glu-325 plane (KDDE), which is normal and on the diagonal joining Glu-325 and Lys-319 of the KREE plane (Figure 3A and Figure 4A). Evidently, the charge state of H322 has a pivotal role in electrostatic charge balance within the space between the other six local charged groups close to the roof of the central cavity. The central cavity is open to the cytoplasmic solution and can be filled with several hundred water molecules 14, as we confirmed using Flood (University of Uppsala Software Factory http://alpha2.bmc.uu.se/usf/voidoo.html) (not shown). It is therefore likely that the local dielectric constant surrounding H322 is closer to that of the external solution than it would be in the center of a nonpolar globular protein (∼20–80vs. 4) 39,40. Electrostatic potential maps of the central docking zone within the hydrated endofacial cavity (see Methods) disclose a uniform charge distribution in a band between Arg-302 and Lys-319 of ∼1.0eV on the KREE plane when H322 is protonated (Fig. 5, panel 2). This electropositive region projects toward H322 in the KDDE plane (Fig. 5, panel 6) and decreases sharply in a band between Glu-269 and Glu-325 (KREE), extending in the KDDE plane toward Asp-237. Protonation of H322 imidazole generates an increase in local potential difference of 0.5–1.0 eV/Å in a 2- to 3-Å-wide band stretching between H322 and Glu-269 and Glu-325 in the KREE plane (Fig. 5, panels 1 and 2). The region most affected by protonation of H322 imidazole coincides with where docked lactose H-bonds to H322 (Figure 2AAB and Figure 3AAB and Figure 4AAB). The electrostatic potential gradients of Lac Y in KREE and KDDE planes with protonated H322 are illustrated in Fig. 5, panels 10 and 16, respectively. Twin parallel tracks with a continuous gradient of 0.5–1.0eV/Å cross the field (Fig. 5, panel 10). The upper track lies between Arg-302 and Glu-325 and the lower between Lys-319 and Glu-269. There is a shallow gradient (0.25–0.5 eV/Å) between Lys-319, Glu-325, and Asp-237 in the KDDE plane (Fig. 5, panel 16).

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Figure 3

Scale diagram showing the relationship of the six fixed-charge amino acids close to H322 within the central cavity of LacY. Also shown are the single mutations at each of these positions and their effects on LacY transport function. NS, no symport; U, uniport; NU, no uniport; UL, lactose uniport; DS, downhill H⁺ -lactose symport. The shaded areas delineate the planar trapezoids between K319/R302/E325/E269 KREE en face and K319/D240/D237/E325 KDDE perpendicular.

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Figure 4

Two views of the quadrilateral planes centered on H322. (A) The KREE plane is facing and the KDDE plane is seen on edge; the positions of two lactose molecules H-bonded to H322 are shown. (B) Docking positions of galactose (purple), melibiose (green), and lactose (yellow) within 3Å of H322.

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Figure 5

Effects of protonation of H322 on the electrostatic charge distribution on the KREE and KDDE planes. A comparison of panels 2 and 6 with panels 1 and 5 shows the effects of protonation of His-322 in the KREE and KDDE planes, respectively. The color chart shows the potential scale: highest potential, 1.25eV, lowest potential, 0.5eV. Comparison of the electrostatic potential maps of control (protonated His-322) (panels 2 and 6), double mutant D240K/K319D (panels 3 and 7), and treble mutant K319N/H322/E325Q (panels 4 and 8). (Panels 1–4) KREE plane or equivalent. (Panels 5–8) KDDE or equivalent plane. (Panels 9–11, 13, 14–17, and 19) The electrostatic potential gradient maps are derived from the contour maps in panels 1–8, respectively, i.e., the potentials in the KREE and KDDE planes of the control and D240K/K319D double mutant and K319N/H322Q/E325Q triple mutant. (Panels 12 and 18) Differences obtained by subtraction of electrostatic potential gradient between control and D240K/K319D double mutant in the KREE and KDDE planes, respectively. (Panels 14 and 18) Difference maps between control gradients and triple mutant K319N/H322′/E325Q gradients in the KREE and KDDE planes, respectively, i.e., the gradient of the difference between panels 2 and 4 shown in panel 14 and the gradient of the difference between panels 5 and 8 shown in panel 20. The areas of white space in these difference maps indicate that there is no difference in the electrostatic potential gradients between control and mutant gradients.

An alternative symport mechanism to the mechanical rocker model is one in which a proton is transferred from H322 imidazole Nɛ4 via the N-H⁺-OH H-bond to lactose (Table 1) to form a short-lived protonated alcohol hydroxonium group H⁺OH on lactose (Fig. 6). Hydroxonium ions are short lived (t_1/2≈2.0ns) and have a very low pKa of∼−2.0 54,55,56. Consequently, lactose alcohol hydroxonium forms in significant amounts only when the lactose acceptor and imidazolium proton donor make close contact, by H-bonding. However, among many disaccharides, lactose has been shown to be particularly amenable to complex formation with proton donating amino acids in vacuo 70. Sugar hydroxyl groups also make good proton donors for imidazole pK_a ∼12.0 and the proton transfer rate is relatively fast in solution (10,000s⁻¹) 57,58,59. The lactose hydroxonium proton will dissociate to either form a hydroxonium ion on one of the adjacent caging water molecules or restore the imidazolium by geminate recombination.

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Figure 6

Mechanism of proton transfer between His-322 and lactose by (a) H-bonding between NH and OH followed by (b) proton transference between imidazolium and OH, and (c) reprotonation of imidazolium with protonated lactose adjacent.

After H322 imidazolium proton transference to lactose, the imidazole base is free to reassociate with another proton (Figure 6c). If this event occurs during the ∼2.0-ns interval when protonated lactose is present in the primary water shell surrounding the lactose-histidine complex, it will increase the overall energy of charge repulsion between the electropositive charges emanating from Arg-302 and Lys-319 and the still-protonated lactose, raising the net repulsive energy from 5 to ∼25kJmole⁻¹. This repulsive force prevents geminate recombination of the lactose proton with H322 (with a dielectric constant of 20, the recombination rate is typically reduced by a factor of 10⁵) and greatly increases the probability that lactose and its associated proton will be expelled from the primary hydration shell of polarized water surrounding the lactose-histidine complex. During the time the sugar remains charged and thereafter, its dissociation product, protonated water (H₃O⁺) drifts in a direction controlled by the anisotropic electrostatic charge distribution on the pore wall toward the electronegative endofacial surface. This process is analogous to the way an electrospray ionizer first ionizes then drives the ionized products in a mass spectrometer 60. A similar principle is adopted to activate movement in several Brownian synthetic machines 61,62,63.

The kinetics of proton movements within the central cavity of LacY are critically important to this model of H⁺-lactose symport. In free solution the rate coefficient for imidazole protonation is 1.5×10¹⁰M⁻¹s⁻¹, and the rate coefficient for imidazolium dissociation is 1700s⁻¹. Hence, the pK_a for imidazolium is 6.94 57,58.

The pK_a of LacY H322 in situ is 7.3, a factor of 2 less than that of imidazolium in water 39,40. This increased basicity is probably a consequence of its H-bonding interaction with neighboring Tyr-236 (Figure 1B). As the protonation rate of imidazole within the cavity remains close to the diffusion control rate k_ass=1.5×10¹⁰M⁻¹s⁻¹, the proton dissociation rate k_βdiss=750s⁻¹ is evidently reduced (Fig. 6).

Given that k_D=2.5×10¹⁰M⁻¹s⁻¹, then inversion of formulas and yields the microscopic boundary rate constants in the radiation boundary condition k_a=3.8×10¹⁰M⁻¹s⁻¹ and k_diss=4300s⁻¹ (Fig. 7).

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Figure 7

Diagram showing the relationships between the rate constants for proton dissociation within the central cavity of LacY.

However, the rate coefficient of protonation of LacY H322 measured directly is much smaller, k_ass=1×10⁹M⁻¹s⁻¹ than the free solution value 39,40. With the pK_a of His-322 at 7.3, the corresponding dissociation rate coefficient k_γdiss=50s⁻¹ (Fig. 6). Assuming that the real microscopic dissociation rate of the histidine is the same as in free solution, then only 1.2% of its dissociations result in net loss of protons from the central cavity; the remainder recombine with H322 imidazole.

The average rate for proton recombination with H322 can be estimated as follows. First, let us assume that the central cavity of LacY is a closed sphere of radius b with a H322 imidazole-H-bonded lactose reactive site at its center. If the imidazole-lactose complex has a radius a, then the mean reaction time, of a reactive particle generated at some point in the sphere b, a distance r from the center, can be obtained. This is achieved by solution of the backward diffusion equation using a reflecting boundary at the surface of the cavity and a radiation boundary condition at the reactive site. The boundary rate constant for reassociation k_a=3.8×10¹⁰M⁻¹s⁻¹. The equation used to solve for the mean reaction time is:

(A10)

Taking the radius of the central cavity of LacY to be 1.5nm and that of the imidazole-lactose reaction center to be 3Å gives a mean recombination time of 0.23ns. Because of their similar pK_a values, the recombination rates for protonated lactose and hydroxonium ions will be similar. If the H322 imidazole is protonated from a source other than protonated lactose, then recombination with the protonated lactose is blocked by strong Coulombic repulsion until either the imidazole deprotonates again (average time ∼240ns), or until the protonated lactose deprotonates (∼2ns).

A key question is whether there is a significant probability of reprotonating H322 imidazole with another proton before recombination with the geminate proton in lactose hydroxonium. These other protons must arise either from a source outside the central cavity, i.e., periplasm, possibly by traversing a proton wire to the central cavity through the protein 39,64, or from additional protons in the cavity.

Once both lactose and imidazolium protonations occur, the mean time for protonated lactose to reach the surface of the cavity, including the effects of both diffusion and Coulombic repulsion, can be calculated by solving the appropriate backward Debye-Smoluchowski equation using the Green's function method, which is given by

(A16)

If the lifetime of the imidazole with respect to reprotonation is1ns, then the probability of its reprotonation before geminate recombination with the proton from protonated lactose is 0.18.

Given that the proton ionic diffusion coefficient is 1×10⁻⁹m²s⁻¹ (ionic mobility ∼4×10⁻⁸m²s⁻¹V⁻¹) 39, and a local dielectric constant of 20, the initial electrostatic repulsion of protonated lactose at the point of contact with imidazolium generates a drift velocity out of the cavity of ∼30ms⁻¹. This reduces to ∼1ms⁻¹ at the edge of the cavity. A very crude estimate of the average exit time is 0.4ns. This is ∼50 times faster than the random diffusive escape rate. Thus, the escape time, assisted by the Coulombic repulsion, is substantially less than the time for either the histidine or the lactose to deprotonate. This shows that the suggested mechanism for cotransport of lactose is a possible option.

The relatively slow rate of proton pumping of LacY permease (turnover rate ∼20–50s⁻¹) 37,38 is consistent with the low probability of proton escape from the central cavity. However, as seen above, this does not correlate with the microscopic rates of deprotonation of H322 within the central cavity.

Assuming that the electrostatic fields generated by the charged amino acids within 5–7Å of H322 are the most proximal force determinants of symport, then mutations of these amino acids affecting any charge sign or position will influence the force vectors within the enclosed space. A number of mutation studies can be reinterpreted in terms of the above mechanism.

Replacement of either of the two basic amino acids close to H322 inhibits symport activity. Replacement of Arg-302 by either Leu, Ser, His, or Lys inhibits both symport and uniport activity (Figure 3 and Figure 4 and Table 2), 41,66,67,68,69. Replacement of Lys-319 with either electroneutral Cys or Ala also leads to inactivation of symport 18,41,70. Similarly, replacement of acid residue Asp-240 with neutral residues Cys or Ala inactivates the symport 16,41,45,66,70,71. Replacement of Glu-269 with Asp, E269D, permits both limited uphill H⁺-symport of lactose and lactose uniport, however replacements with neutral Gly or Ala, E269G or E269A, respectively, are devoid of both H⁺-lactose symport or uniport. However, surprisingly, TDG and other galactosides, e.g., melibiose, can induce downhill H⁺-symport in these mutants.

The importance of Glu-325 and its relationship with H322 was demonstrated by Carrasco et al. 77. The E325A mutant has no symport activity, but is as effective at uniport as Gln, His, Val, Cys, or Trp substitutions at position 325 77.

Thus, it is evident that replacement of any single charged residue within the near vicinity of H322 with a neutral residue abolishes symport and often uniport also, whereas mutations conserving charge tend to conserve some residual transport function.

Although single charge replacements can only cause distortions of the electrostatic fields, multiple replacements either exaggerate, or sometimes may induce, compensatory changes, which reduce the net deformation. Such revertant mutants can produce some recovery of the transport function.

Double replacement of both Lys-319 and Asp-240 by Ala or Cys leaves symport activity unchanged, as it conserves the electrostatic potential gradients across the KREE plane between Arg-302 and Glu-269 and Glu-325 16,78. Similarly, when Asp-237 and Lys-358 are both replaced with the neutral amino acids cysteine or alanine, symporter activity remains intact. However, when only one of these amino acids is replaced, symport activity is lost. Switching of Asp for Lys between positions 237 and 358 with the double mutant D237K/K358D also preserves full transport activity and contrasts with the effects of double mutant D240K/K319D, where symport activity remains at zero. As K358 is almost twice as far from H322 as K319 (13.8Å vs. 7.5Å) and its electrostatic potential vector does not intersect with either the KREE or KDDE planes (Figure 3A and Figure 4A), transposition of the ion pair K358/D237 has a negligible effect on the charge distribution close to H322. It is therefore unsurprising that this double mutation is without effect on symport and contrasts with the large effect of transposition of the K319/D240 pair on the potential field around H322 (Table 3) 16,18,20,78.

The lack of transport function of the double mutant D240K/K319D is discordant with the view that these amino acids behave as a reversible salt bridge. Reversal of the positions of residues K319/D240 causes large alterations in the electrostatic potential field around H322. The predicted electrostatic potential and potential gradient maps of the double mutant D240K/K319D shown in Fig. 5 (panels 3 and 7) and the electrostatic gradients in the equivalent KREE and KDDE planes of the D240K/K319D double mutant are shown in Fig. 5, panels 11 and 17. As expected, large decreases in the electrostatic potential gradients occur near positions 319 and 240 when Lys and Asp at positions 319 and 240 are exchanged. Comparison of the mutant gradient in the KREE plane with control (Fig. 5, panels 11 and 12, and 17 and 18) shows that the continuous positive potential gradient between 319 and 269 is abolished in the mutant (cf. Fig. 5, panels 10 and 11). This is apparent as a loss of electropositive gradient around position 325, seen in the lower left corner of Fig. 5, panel 11, and in the difference map between control and mutant potentials (Fig. 5, panel 12).

The loss of the electrostatic potential gradient between Lys-319, His-322, and Glu-269 elucidates why this double mutant disrupts symporter activity so effectively. The proton drift rate within the central cavity driven by the normal fixed potential is abrogated despite conservation of net charge and the potential for salt bridge formation.

It is evident that rescue of poorly functioning uniport mutants can be attained by multiple selective neutral substitutions at positions 319, 322, and 325. None of these single mutants permits H⁺-lactose symport, and they have only low rates of lactose uniport (Table 2). However, the double mutant K319N/E325Q permits more rapid downhill coupled proton and lactose flow 13,66 and the triple mutant K319N/H322Q/E325Q allows downhill H⁺-TDG symport, but not H⁺-lactose symport (Table 3) 79.

Examination of the electrostatic map of the triple mutant K319N/H322Q/E325Q around H322 shows that despite loss of three charged groups (Fig. 5, panels 4 and 8), the electrostatic potential gradients in both the KREE and KDDE planes are similar to those of the wild-type LacY. This is shown quantatively in Fig. 5, panels 13, 14, 19, and 20). The positive potential gradient between the central region and Glu-269 is conserved, as demonstrated by the large area of white space in the central region of the KREE plane, Fig. 5, panel 14). White space in the difference maps signifies an absence of difference in the potential gradients between the triple mutant and control. A similar lack of gradient difference between the triple mutant and control exists in the KDDE plane in the sector bounded by Gln-322, Gln-325, and Asp-237 (Fig. 5, panel 20).

Mimicry by the triple mutant of the wild-type electrostatic gradients could be an explanation for the preservation of the capacity to transport lactose, albeit only in the uniport mode. The mutant suppressor, by restoring the electrostatic potential gradients within the field that are introduced by single mutations, could reduce major residue displacements and thereby rehabilitate the transport function along the pathway.

Several LacY mutations lose their capacity for growth on lactose media, without concurrent loss of their capacity to grow on melibiose, or galactose-enriched media. The position numbers in Fig. 1 A signify the mutation sites that alter LacY specificity. Two are in the outer vestibule (29 and 33); four in the central cavity close to H322 (265, 321, 322, and 325), and another in a side pocket (177). Lactose, melibiose, and galactose all dock close to H322, although melibiose, unlike lactose, docks close to E325. Positions 177 and 319 are close to galactose clusters and not near either lactose or melibiose sites. Mutations (Table 4) causing major selectivity changes are localized at three main loci, A122, C148, and H322. When the mutation A122C is alkylated with N-ethylmaleimide (NEM), active lactose symport is abolished. Lactose, melibiose, and TDG protect against inactivation of C122 by NEM, but galactose does not protect against NEM inactivation. Galactose transport is also unaffected by NEM reaction with C122 5,79. Mutations at 122 with large side chains, e.g., F122 or Y122, also inhibit lactose, but not galactose transport (Table 4).

Consistent with altered relative capacities for transport of lactose, melibiose, and galactose by single or multiple mutations is the finding that the docking profiles of these sugars differs substantially on LacY (Figure 1AB and Figure 2AB and Figure 3AB and Figure 4AB). It seems likely that there are several possible tracks for passive sugar permeation across the LacY. Selective blockade will alter the relative capacity to transport these sugars (Figure 8AB). Similar multiple tracks discriminating between quercetin and D-glucose have been previously inferred from kinetic and docking studies using transport in human erythrocyte GLUT1 30 and for Cl⁻ and H⁺ in CIC channels 80.

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Figure 8

(A and B) Diagram showing how mutations can alter LacY selectivity for lactose and melibiose transport by preventing lactose binding to secondary sites within the transporter, thereby affecting lactose but not melibiose transit. (C) Diagram showing the condition for accelerated exchange or counterflow. Labeled lactose enters the LacY from the outside (periplasmic side). In contrast to the situation in A, it is prevented from binding to secondary binding sites within the central cavity by unlabeled lactose entering from the cytoplasmic side. This prevents labeled lactose reflux to the periplasmic side and consequently increases the apparent rate of labeled uptake. This will result in countertransport if the cytoplasmic lactose concentration is higher than the periplasmic concentration.

A seemingly compelling reason for accepting a unique sugar-binding site within LacY is the corroborating evidence advanced from mutation studies 20. Only a few amino acids are absolutely required for active transport. However, indispensability for symport implies only that the particular amino acid is an essential component in the matrix of interactions necessary for ligand binding and/or transport. Cysteine mutagenesis and site-directed labeling studies have shown that ∼70 of the total 417 amino acids in LacY have their reactivity to alkylating agents either activated or inhibited by ligand (TDG) binding 81,82,83,84,85,86. Nearly all of the TDG-sensitive sites on the periplasmic side have increased reactivity, whereas 16 of the 24 sites on the cytoplasmic side have decreased reactivity. This pattern of reactivity is consistent with the separate inward and outward facing conformations of the rocker model 84. However, another interpretation is that the reactivity of most groups lining the pore cavity is reduced by the high TDG concentrations accumulated within the cavity, whereas the exofacial sites are exposed only to dilute ligand concentrations.

Explanation of flux asymmetry in the context of this new cotransport model is relatively straightforward. The electrostatic potential across the polarized KREE plane between the positively charged band between R302 and K315 and the negatively charged belt between E325 and E269 supplies a steady-state driving force (Fig. 5, panels 1, 2, 9, and 10, and Fig. 6). This can be exploited by injection of mobile protonated species, e.g., protonated lactose and protons, into the field after H322 imidazolium dissociation. The steady-state electrostatic potential gradients within the LacY cavity are maintained by the transmembrane potential in the living cell, which is regulated at ∼80–120mV over pH range 5–8 by independent ion pumps 38,85. The anisotropic electrostatic field across H322 determines the probability that protonated lactose and dissociated protons will drift toward the endofacial pole of the transporter rather than the periplasmic pole. The limiting accumulation ratio, C_in/C_out, by this mechanism, as with the carrier mechanism, is controlled by the energy transduced from the membrane potential in pH range 5–8, ∼80–120mV 23,85.

Thus, at 310°K, C_in/C_out=exp(zFΔPD/RT)=90; where z is the charge, F the Faraday constant, ΔPD the membrane potential (V), R the gas constant, and T the temperature (°K).

As mentioned in the Introduction, the apparent difference in affinity between inside and outside sites, like that with the GLUT1 transporter in human erythrocytes, is only observed when net ligand transport occurs, but not when measured by direct binding assays 29,30,31,32.

As with GLUT130, asymmetry between influx and efflux can be ascribed to the imported labeled (cis) ligand binding to sites within the central cavity, with partially occluded access to the trans surface of the transporter. Reflux of labeled ligand from this cavity reduces net “unidirectional” flow (Figure 8C). However, when a competing unlabeled ligand is present in the trans solution, as in the exchange condition, it prevents labeled ligand binding from the cis solution to the low-affinity binding sites in the central cavity. The resulting retardation of reflux of labeled ligand generates an apparent acceleration of unidirectional influx of labeled ligand. Uphill counterflow into the cytosol can also be induced by this mechanism.

Additionally, during net exit of lactose across the LacY symporter from a high intracellular concentration (zero trans efflux), lactose has to diffuse upstream against the inward drift of lactose and water hydroxonium ions induced by the electrostatic gradients in the center of the protein. This upstream movement may retard uncharged lactose efflux and further reduce the apparent affinity for export 21,25,26,36.

LacY has a similar large endofacial vestibule to GLUT1, into which lactose or melibiose from the periplasmic solution will accumulate and bind (Figure 1A). Furthermore, disaccharide accumulation here will be exaggerated by symport. It is proposed that ligand accumulation within this internal cavity is the precondition for generation of both accelerated exchange and counterflow in LacY as in GLUT1. Any mutation that substantially alters the fixed or fluctuating potential close to H322 will both slow symport and simultaneously increase the apparent affinity and rate of lactose export, because competition for export “sites” will be reduced by lack of accumulation of ligand from the external solution within the central cavity.

Similar principles have been demonstrated experimentally by spectroscopy of photolytic dissociation of carbon monoxide from myoglobin. At 250°K, CO binds in microcavities within myoglobin after photodissociation from heme at low temperatures 86. Geminate recombination of this bound CO slows the net rate of CO dissociation from the protein. Xenon, which can also fill the microcavities, competes with CO binding here, but not on heme. Xenon, by preventing local accumulation of CO, prevents its geminate recombination with heme and thereby increases the net dissociation rate of CO by 50% at this temperature.

This new model for H⁺-lactose symport has several features in common with Brownian motors 62,87,88, namely, a source of randomly fluctuating kT energy emanating from a stabilized molecule that is transferable to a contiguous mobile molecule. Brownian models of active transport and motility apply potential energy to the transported molecule, which is guided thereafter via a route statistically favoring either forward or backward escape. In this case, the energy comes from electrostatic repulsion between imidazolium anchored within a protein chain conjoined via an H-bond and mobile protonated lactose. Similar force is used to motivate translation in molecular shuttles 61,62. The scalar force generated by electrostatic repulsion is channelled by the anisotropic electrostatic field and thereby converted to a vector force. This is a necessary condition for any form of chemically induced active transport 89.

By definition, a ratchet prevents reversal of positional displacement. The low probability of protonated lactose reentering the water cage surrounding His-322, after ejection by electrostatic repulsion, accounts for the molecular ratcheting effect here. “Resetting” of the “imidazolium pump” has to come from a fresh proton, possibly supplied via a proton-wire connecting the central cavity with the periplasmic solution, similar to that proposed for cytochrome c oxidase 39,40,64,90. The electrostatic potential within the protein cavity is maintained by independent pumps in the bacterial membranes requiring an exogenous energy source 85. These essential processes for maintenance and resetting of the symporter pump are otherwise described as “escapement”, “balance”, and “linkage” processes 62,91. In the absence of these energy-requiring housekeeping processes, protons and other counterions will accumu