INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSION REFERENCES

Lipases (triacylglycerol hydrolases, EC 3.1.1.3) are enzymes, catalyzing both the hydrolysis and the synthesis of esters formed from glycerol and long-chain fatty acids. In addition to triglycerides, lipases are also able to catalyze hydrolysis and synthesis of a wide range of soluble and insoluble organic compounds making them potential catalysts for a wide variety of applications in chemical industries, biomedical sciences, and food technology.

The activation mechanism of these lipases has partly been revealed by their crystal structures (Derewenda et al., 1994; Brzozowski et al., 1991). The first lipase, resolved in the open (active) and inactive (closed) conformation, was the Rhizomucor miehei lipase (Brady et al., 1990; Derewenda et al., 1992). The crystal structures of this lipase indicate that the conformational change during activation is a rigid body hinge-type motion of a single helix. This type of motion is more complex for other lipases, involving hinge-type motions of multiple helices (Derewenda et al., 1994).

In the present study, we focus on the Thermomyces lanuginosa lipase (Tll) formerly named Humicola lanuginosa, crystallized in the open and closed conformation (Derewenda et al., 1994, 1992; Brzozowski et al., 1992, 2000). Tll shares, with other lipases, the characteristic structural / hydrolase fold (Grochulski et al., 1993) and possesses a trypsin-like triad consisting of a Ser/His/acidic residue active site region and a neighboring oxyanion hole. The Ser residue in the sequence G-X-S-X-G (X denotes any residue) forms the nucleophilic center, and His acts as a general acid/base. The acidic residue in the triad mediates the protonation of His during catalysis. The oxyanion hole stabilizes the incipient carbonyl of the ester group during turnover. As other lipases, Tll requires a lipid-water interface to exert full catalytic activity; i.e., the substrate concentration must exceed the critical micelle concentration (Panaiotov et al., 1997). The lipid interface triggers a conformational change in the enzyme that, as observed for the related R. miehei lipase, involves displacement of an -helical lid shielding the active site in aqueous solution. This displacement is essential for providing access of the substrate to the active site and, at the same time, exposes a hydrophobic part of the lid toward the lipid, thereby mediating binding of the lipase to the interface (Derewenda et al., 1994). Interactions between the lipid interface and hydrophobic residues of the lid contribute to the stabilization of the open conformation and the conformational rearrangements of the enzyme at the lipid interface correlate intimately with the phenomenon of interfacial activation (Derewenda et al., 1994).

A central issue in relating the conformational changes of lipases to their biological function is to understand to what extent these enzymes bind to, react with, or become catalytically activated by lipid-water interfaces (Rubingh, 1996). The presence of a structured lipid interface with subtle physical properties adds another complexity to the problem of explaining the response of the enzyme when in contact with the interface. Different mechanisms of interfacial activation, which can be classified in two extremes, have been proposed (Thuren, 1988; Derewenda et al., 1994; Peters et al., 1995). One is based on a substrate-mediated mechanism (Thuren, 1988), suggesting that changes in the physical properties of the lipid substrate such as hydration, fluidity, curvature, charge, and composition trigger the activation, whereas the other proposed mechanism involves conformational changes in the enzyme upon adsorption to the lipid interface (Derewenda et al., 1994). It should be noted that these schemes are not mutually exclusive (Peters et al., 1995), and refined kinetic models involving both of them have been suggested (Brzozowski et al., 1991; van Tilbeurgh et al., 1993; Verger et al., 1984; Ransac et al., 1990, 1991). These include a two-step mechanism initialized by adsorption of the enzyme at the interface followed by formation of an enzyme/substrate complex (Brzozowski et al., 1991; van Tilbeurgh et al., 1993; Verger et al., 1984).

A detailed insight into the mechanism of lipolytic hydrolysis requires that the binding of the lipase to the lipid interface, its subsequent/simultaneous activation, and ultimately, the catalytic reaction all can be investigated independently with respect to the physical properties of the lipid interface. One approach is to study the adsorption of lipases to different lipids using lipid monolayers (Panaiotov et al., 1997) or liposomes (Cajal et al., 2000; Jutila et al., 2000; Peters et al., 1998). The most detailed insight into interfacial binding of lipases at the molecular level has, however, been obtained by ESR experiments (Ball et al., 1999). Frequently used techniques such as Langmuir monolayer methods (Verger and de Haas, 1973) and fluorescence spectroscopy (Kinnunen et al., 1993; Millar, 1996) have yet to provide such information, although nanosecond dynamics of the lid movement have been monitored by time-resolved fluorescence spectroscopy (Jutila et al., 2000). Nevertheless, information about the orientation and conformation of the lipase at the interface as well as complete description of the triggering mechanism associated with interfacial activation are still lacking.

Surface sensitive synchrotron x-ray scattering has proven useful for investigation of biological systems assembled as thin films at the air-water interface (Alonso, et al., 2001; Rapaport et al., 2000; Jensen et al., 2001). To gain structural insight into the orientation and conformation of Tll at a hydrophobic-hydrophilic interface, we have measured the x-ray reflectivity of lipases adsorbed at an air-water interface. This interface is the simplest representation of a hydrophobic-hydrophilic interface and is a first step towards studying Tll at more complex interfaces (lipid-water). Although electron density profiles can be extracted from the reflectivity curve, the profiles are not uniquely determined due to the crystallographic phase problem (Jensen and Kjaer, 2001). Furthermore, the interpretation of the reflectivity data in terms of enzyme conformation and orientation is not trivial. In the present work, we demonstrate that molecular dynamics (MD) simulations can be used in interpreting the experimental electron density profiles in terms of enzyme conformation, orientation, and surface concentration.

Several MD simulations of triacylglyceride lipases have been reported (Peters et al., 1995, 1996a, 1996b, 1998; Brzozowski, 2000), but to our knowledge, no study addresses the question of enzyme orientation and conformation at an interface. Here, we outline a computational scheme by which one can extract electron density profiles from an MD trajectory that refers to an average enzyme orientation relative to an implicit interface. The computed profiles can be compared with profiles extracted from our x-ray reflectivity measurements to provide the most probable orientation and conformation of Tll at the interface.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSION REFERENCES

In the following we briefly describe the MD simulations and the x-ray reflectivity experiments. We then outline the method for extraction of multiple electron density profiles from a single trajectory along with the procedure for comparing calculated and experimental electron density profiles.

Modeling and simulation

We carried out MD simulations on both the closed and open conformations of Tll in cubic simulation boxes with explicit water. These two conformations are the two extremes of possible Tll conformations. We carried out simulations without an explicit air-water interface, because the reflectivity data indicate that the major part of each adsorbed lipase molecule is embedded in the water phase. Furthermore, the part of the experimental electron density profile providing structural information refers manifestly to the water phase (see Results and Discussion). For purposes of analysis, we incorporated an implicit interface (see below).

Starting coordinates for the open conformation were obtained from the Protein Data Bank (Bernstein et al., 1977), entry code 1TIC. The coordinates for the closed conformation were kindly provided by Prof. M. Brzozowski. These structures are resolved to 2.5 Å (closed) and 2.6 Å (open). Enzymes of either conformation were initially placed in simulation boxes of volume 59 × 59 × 59 Å³ with the active site lid pointing along the normal to the interface, i.e., in the direction of n_z (Fig. 1).

View larger version (49K): [in this window] [in a new window]   FIGURE 1   Superposition of open (blue) and closed (red) conformation of Tll: (a) active site lid aligned along the outgoing interfacial normal nz and (b) view towards active site. In the experiment z = 0 is defined as the location of the interface, here coinciding with the origin of nz. RMSD between the C carbons of the x-ray structures is 1.6 Å. The lid residues 83 to 96 of the semiopen conformation taken after 10 ns of simulation are shown in yellow. The C atoms of residues Gly-144 and Ser-146, which are shown for the open conformation only, are rendered as van der Waals spheres in green and ochre, respectively. During the transition from the closed to the open conformation an additional turn in the -helical lid is formed involving residues 91 to 94. A similar mechanism has been observed for Candida rugosa (Grochulski et al., 1993).

To saturate the enzyme interior with water, water molecules were initially inserted into sufficiently large protein cavities in the open conformation of Tll using the program QUANTA97 (MSI, 1997). Insertion was possible in a few (14) hydrophilic pockets. No additional water molecules were inserted inside the closed conformation. The enzymes were solvated using an equilibrated configuration of ~5000 SPC water molecules. The net negative charges of the enzymes were in both systems neutralized by replacing seven water molecules by Na⁺ ions at positions of lowest Coulomb potential. The total system sizes were ~20,000 atoms.

The program Gromacs (Berendsen and van der Spoel, 1995) was used with the Gromos 87 force field (van Gunsteren and Berendsen, 1987) for the simulations. The simulations were conducted in the NPT ensemble at 300 K (temperature-coupling constant 0.1 ps) with the Berendsen pressure-coupling scheme (pressure-coupling constant 1.0 ps) (Berendsen et al., 1984). A 2-fs time-step was used throughout, and van der Waals and Coulomb interactions were computed within cutoffs of 10 and 14 Å, respectively. Periodic boundary conditions were imposed in all directions. Initially, both systems were minimized followed by 10 ps of dynamics where all heavy atoms were harmonically restrained to their initial positions. Subsequently, the restraints were removed, and the simulations were conducted for 10 and 12 ns for the open and closed conformation, respectively.

Synchrotron x-ray scattering

Surface-sensitive synchrotron x-ray scattering of lipase monolayers assembled at the air-water interface was performed at the undulator beamline BW1 at the synchrotron radiation facility HASYLAB (Hamburg, Germany), using a liquid surface diffractometer developed at Risø National Laboratory, Denmark (Als-Nielsen et al., 1994; Weissbuch et al., 1997). The sample cell is a Teflon-made Langmuir film balance placed in a gas-tight container with windows transparent to the x-rays. A glass plate is placed in the trough under the x-ray footprint area to reduce the subphase depth to ~0.3 mm, thereby suppressing mechanically excited long-wavelength waves on the liquid surface (Braslau et al., 1985). The x-ray beam illuminates an area of ~2 × 50 mm² equivalent to ~10¹³ molecules of Tll. The microbial lipase Tll was provided by Novozymes, Inc. (Bagsvaerd, Denmark). Tll is a monomer of 269 amino acids (Fig. 1) with a molecular weight of 2.947 × 10⁴ g/mol. Tll was dissolved in water giving transparent solutions of ~1.1 mg/mL, spread on a MilliQ purified subphase of water (T = 293 K) and compressed to a surface pressure,  = 15 mN/m. An inactive mutant with Ser-146 mutated to Ala (denoted S146A) was also investigated.

To obtain information about the vertical (laterally averaged) structure of an interface, a purely vertical scattering vector is required (Jensen and Kjaer, 2001). This can be achieved using specular x-ray reflectivity with equal angles between the surface and the incident and reflected x-rays; _i = _f  . The scattering vector q_z then becomes

(1)

The so-called "master formula for reflectivity" relates the measured reflectivity, R(q_z), (kinematically) to the electron density profile along the normal n_z (Als-Nielsen et al., 1994; Als-Nielsen and McMorrow, 2001; Kjaer, 1994)

(2)

The Fresnel reflectivity, R_F(q_z), is calculated from standard optics (Born and Wolf, 1984) for a perfectly sharp interface between air and a pure subphase of average electron density . The root-mean-square roughness, , for a pure water surface caused by thermally excited microscopic capillary waves is 3 Å (Braslau et al., 1985).

The master formula, Eq. 2, gives raise to the phase problem of x-ray crystallography, because the ratio R(q_z)/R_F(q_z) equals the absolute square of the Fourier transform of the normalized gradient of the electron density across the interface. The measured (normalized) reflectivity, R(q_z)/R_F(q_z), can be inverted to yield the laterally averaged electron density, (z); i.e., the density as a function of the vertical z coordinate. However, the phase problem can in some cases give raise to more than one solution for (z).

In the following we denote the experimental profiles obtained from x-ray reflectivity measurements _e(z), and likewise, the electron density profiles calculated from MD, _c(z). _e(z) and _c(z) are further classified by superscripts used to specify whenever the density refers specifically to wild-type (wt) Tll or S146A in the experiment, or to the open or closed conformation of wt Tll in the simulations.

The electron density profile

To interpret _e(z) in terms of enzyme orientation and conformation, we will compare _c(z) obtained for both Tll conformations in different orientations directly with _e(z). However, to accomplish this, two issues must be resolved. The first relates to the discrete nature of the charge representation in the MD force field. The second relates to the computation of _c(z) in a way that uniquely characterizes the enzyme orientation relative to an (implicit) interface.

The discrete charge representation implies that only an inherently discontinuous _c(z) can be extracted from the MD trajectory. The atomic partial electronic charge (q) may be Gaussian distributed with a root-mean-square  using Gaussian convolution, which transforms q of the nth atom at position z_n into a Gaussian. For the N-particle system we obtain the continuous electron density profile as

(3)

in which  ·  denotes a time average. A universal smearing factor (_n = ) applied for all n atoms is the only physical parameter to be specified in Eq. 3. The maximal value for  used here is 3 Å, which fully takes into account the roughness of the experimental water surface (Braslau et al., 1985; Jensen and Kjaer, 2001). Assignment of individual  for different atoms is superfluous, because  = 3.0 Å suppresses the different individual Gaussians.

The second issue arises due to translational and rotational motion of the enzyme (Fig. 2). After the completion of the simulations and prior to the calculations of _c(z), we aligned the unit vector ((t)_Ser146:C  (t)_Gly144:C) (Fig. 1) so it coincides with the surface normal, n_z, thereby leading to a well-defined enzyme orientation. From the aligned enzyme coordinates we generated additional coordinate sets by consecutive rotations that allows for calculation of multiple orientation-specific forms (relative to n_z) of _c(z). Only Tll and the nearest neighboring water molecules located within a radial cutoff of half of the shortest box-length, r_cut(t) (centered on Gly-144:C), were aligned. Because the simulations were performed at a constant ambient pressure, r_cut(t) is time dependent but sufficiently large to capture the whole enzyme. The alignment was accomplished by requiring that the aligning matrix R((t), (t), (t)) at all t fulfills

(4)

in which ((t),(t),(t)) are the Euler angles defining the matrix at t. The rotation aligning the enzyme and the nearby water molecules (altogether N' of the N atoms in total) provides the aligned coordinates {r'_i(t)}. These coordinates are subject to the rotation R'(', ', ') × r'_i(t) = r_i(t) using /6 intervals between consecutive (', ', '). We calculate the orientation-specific forms of _c(z) from the resulting coordinates {r_i(t)}. The values ' = 0, ' = {m/6} and ' = {n/6} are used in R'(', ', '). _c(z) is invariant to rotations about the z axis (involving ') and due to symmetry, _c(z, ', ', ') and _c(z,',',') are identical as are _c(z, ', 0, ') and _c(z, ', , '). All remaining _c(z) are distinct and these we fit to _e(z) to deduce the most probable interfacial orientation and conformation of wt Tll and S146A.

View larger version (32K): [in this window] [in a new window]   FIGURE 2   (Upper panels) Distances |rCOM  rGly144:C| (thin) and|rGly144:C  rSer146:C| (bold) for the two conformations of Tll as a function of time. (Lower panels) Autocorrelation function for the interfacial alignment vector as a function of time. Gly-144 is located in the hydrophobic core of Tll close to the center of mass (COM) and Ser-146 is the active site residue (Fig. 1). As evident from the upper panels, both of these sites are located at positions generally undergoing minor fluctuations. Therefore, the unit vector ((t)Ser146:C  (t)Gly144:C) was used in the alignment procedure (see text for details). The need for the alignment is evident from c(t). In particular the open conformation is seen to rotate significantly during the simulation.

By applying the spherical cutoff r_cut(t) we ignore more distant water molecules in the rotations above, implying that the total amount of water in the simulation box with volume V₁ is not conserved. To correct for this, water with density , calculated as an average over the outermost water in the box, are added to fill the volume difference V₁  V₂ (V₂ is the sphere volume being determined by r_cut(t)). From the electron density profile in the sphere of the time-averaged volume V₂ and from , the time-averaged orientation specific form of _c(z) in the cubic box of volume V₁ is therefore obtained as

(5)

f(z) is the ratio between the sphere and square slab volumes

(6)

ensuring normalization of _c(z) with the square box volume V₁ = L_x × L_y × L_z (omitting time dependencies for clarity). In Eq. 5, N and N are the number of electrons in Tll and in the water, which is part of the sphere. In Eq. 6, z_low and z_up are the lower and upper values of z, respectively, defining the slice of the sphere of width dz. Finally, by applying periodic boundary conditions we ensure charge conservation during the convolution of _c(z) and that the water density approaches  = 0.333 Å³ at the box boundaries.

Least squares fitting

Eqs. 5 and 6 are also used in the least squares fit. V₁(z) = V₁ then refers to the experimental volume perpendicular to n_z and V₂(z) = V₂ refers to the simulation box volume. We applied and f = f(z) as two fitting parameters. Using (= 0.325 Å³) as a parameter permits correction for an offset between and (amounting to 2%). Setting L₂(z)  L₁(z) ( = L_c(z)  L_e(z)) we find f = A_c/A_e and note that the experimental (lateral) area per molecule, A_e, is independent of z. A_e can then be deduced from linear variation of the calculated lateral box area. Keeping L_z constant, we have A_e = A_c/f = (L_x × L_y)/f. Consequently, we renormalize _c(z) through iterative variation of f while approaching the experimental area per molecule, i.e., the surface concentration. We varied f using intervals of 0.1. Because the interface only appears implicit in the simulations, the origin for _c(z) along the z axis (equivalent to the position of the interface, z₀, in the experiment; Fig. 1) is arbitrarily defined. To translate _c(z) discretely along the z axis with intervals of 0.01 Å, a parameter, z, was introduced.

	RESULTS AND DISCUSSION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSION REFERENCES

In the following we present and discuss the calculated electron density profiles, _c(z) followed by a comparison of these with the experimental data, _e(z) derived from x-ray reflectivity. Equilibration of the simulations was monitored by thermodynamic and geometric quantities. Radius of gyration and the root mean square displacement (RMSD) of the protein backbone atoms are shown in Fig. 3. RMSD stabilizes at 2 Å after 1 to 2 ns. The radius of gyration is constant over the full time scale. Together with the RMSDs, this indicates that both conformations are stable in the simulations.

View larger version (29K): [in this window] [in a new window]   FIGURE 3   RMSD of backbone atoms calculated along the trajectories with respect to the two initial (x-ray) structures for the open and closed conformation of Tll (left panels) and total radius, R, of gyration (right panels).

Properties of calculated electron density profiles

Raw and convoluted _c(z) are shown in Fig. 4, in which  values of 0.5, 1.0, 2.0, and 3.0 Å are used to demonstrate the dependence of the fine structure in the electron density profile on this parameter. The intrinsic noise in _c(z) is efficiently removed by the convolution. At the 3-Å level, however, where  fully includes the effect of surface roughness (Braslau et al., 1985), the fine structure almost vanishes. The _c(z) shown are calculated for both the open and the closed conformation of Tll in the orientation (0, 0, 0). In this orientation the active site lid points towards the direction of decreasing z; i.e., towards the interface (Fig. 1).

View larger version (32K): [in this window] [in a new window]   FIGURE 4   Orientation-specific electron density profiles of Tll shown in the (0, 0, 0) orientation: (A) closed conformation and (B) open conformation. The total profiles are decomposed into contributions from Tll and from water. Raw (noisy) electron density profiles ( = 0 Å) appear in all panels and are compared with smeared profiles using various values of  (respective -values are indicated at the top right of each panel). The profiles were averaged over 3 ns.

Equilibration of the water density profile is displayed in Fig. 5 at various time instants. The value of that will be added as background density in Eq. 5 to obtain the total _c(z) can be recognized at the box boundaries. This value is consistently found to be below one implying that is not completely recovered in the simulations. The discrepancy is within 2%. The determination of is subject to large fluctuations close to the boundaries due to the small slab volumes of the (spherical) slices at the box boundaries (slab width < 0.03 Å) used in Eqs. 5 and 6. This effect vanishes as  approaches 3 Å. For  = 1.0 Å, the fine structural features of the water electron density profile clearly evolve with time reflecting (re-) distribution of water inside the enzyme and/or relatively small conformational changes of the enzyme. It cannot be distinguished how water equilibration and conformational fluctuations individually affects the fine structure of _c(z), but the dependence on these parameters demonstrates why _c(z) cannot straightforwardly be calculated from a static x-ray structure.

View larger version (16K): [in this window] [in a new window]   FIGURE 5   Equilibration of the water electron density. The profiles are shown for  = 1.0 Å and are averages over 0 to 1 ns (dashed line), over 1 to 2 ns (long dashed line), over 2 to 3 ns (dash-dotted) line, and over 3 to 4 ns (solid line). A density of one corresponds to the electron density of bulk water at 300 K (0.333 Å3).

To further illustrate the information that is provided by _c(z), Fig. 6 displays (z) and (z) in selected orientations relative to n_z. Despite a 3-Å smearing, fine structure persists in all representations and the two conformations in the same orientation lead unambiguously to different profiles. Hence, we conclude that _c(z) can be used for unique characterization of the orientation and conformation of the enzyme.

View larger version (177K): [in this window] [in a new window]   FIGURE 6   Orientation specific electron density profiles for selected orientations of the closed (solid lines) and open (dashed lines) conformation of Tll are shown in A to C. Values for (', ', ') given in all panels indicate the enzyme orientation relative to nz (Fig. 1). Only (', ') vary (see text for details), because c(z) is invariant to rotations around the z axis (i.e., to the '-value). Snapshots of Tll taken after 2 ns of simulation of the open and closed conformation are shown in orientations referring to the particular electron density profile. The active site lid residues are displayed as a black tube.

Experimental and calculated electron densities

We investigated both the wt Tll and the S146A mutant adsorbed at the air-water interface by x-ray reflectivity (Fig. 7 a). The corresponding electron density profiles, (z) and (z) obtained through Eq. 2 are shown in Fig. 7 b and both profiles show distinct features. The fine structure featured in _e(z) is independent of the methods used to invert the data (compare Eq. 2), and no modulations occur in the profile of pure water using any of these methods. Hence, (z) and (z) provide distinct molecular fingerprints of the two enzymes at the interface. The different fine structures featured in (z) and (z) suggest that the spatial resolution of _e(z) could be sufficient to differentiate experimentally between conformations and/or orientations of Tll at the interface. X-ray diffraction from S146A adsorbed at an air-water interface was measured using a liquid surface diffractometer (Kjaer, 1994; Jensen et al., 2001b). For wt Tll no diffraction was observed. The diffraction data of S146A correspond either to a hexagonal or to a rectangular unit cell (Kjaer, 1994) with areas of 2400 Å² or 1200 Å² per Tll, respectively (further details will be published elsewhere).

View larger version (20K): [in this window] [in a new window]   FIGURE 7   (A) Measured reflectivity curves with standard deviations for wt Tll and S146A (upper panels) and least squares fits to the measured curves (lower panels; measured curves included for comparison). The background was determined experimentally by offsetting the detector from the specular position (out of the scattering plane). The normalization was determined experimentally by measuring the direct beam intensity. Thus, neither background nor normalization introduces any adjustable parameters. The inversion of R(qz)/RF(qz) was performed by a model-independent method, writing e(z) as a weighted sum of cubic-spline functions (Pedersen, 1992; Pedersen and Hamley, 1994; Hamley and Pedersen, 1994). The reflectivity is then calculated for such a model. Least-squares fitting to the measured data, with a smoothness constraint on the model for stabilization, results in the final e(z) (Pedersen and Hamley, 1994). Due to the so-called phase problem of x-ray scattering the data inversion is not in general unique. As seen from Fig. a the Fourier cutoff is approximately qz  0.85 Å1. (B) Experimental electron density profiles for wt Tll and S146A (upper panels) and calculated electron density profiles for wt Tll in open and closed conformation in the (0, 0, 0) orientation (lower panels). All profiles are normalized with the electron density of bulk water. In the upper panels, the solid region indicates the part of the electron density that is used in comparison with the calculated profiles. The standard deviation within this region is included for the wt Tll profile (similar values apply to the S146A profile). The calculated profiles in the lower panels, averaged over 3 ns, are for  = 1.0 Å (dotted lines) and for  = 3.0 Å (solid lines). Average standard deviations (along z) are shown next to the profiles.

The x-ray reflectivity data inversion in Eq. 2 is hampered by the crystallographic phase problem and multiple (z) and (z) resulted from the respective reflectivity curves. By comparison of the experimental electron density profiles (z) and (z) with (z) and (z), as done in Fig. 6, the profiles that were not physically meaningful were easily discarded. Recall that (z) and (z) result from lateral averages over an area of 2 × 50 mm² corresponding to contributions from ~10¹³ enzymes. In this respect, _e(z) is determined fundamentally different from _c(z), which is calculated as an average over a number of enzyme conformations that is several orders of magnitude smaller than 10¹³.

As discussed earlier, comparison between _e(z) and _c(z) is only appropriate for  = 3.0 Å (Braslau et al., 1985). For  = 1.0 Å, (z) and (z) obtained for the two conformations of Tll in the same orientation are clearly different (Fig. 6) and display more fine structure than (z) and (z). The superposition of the two conformations presented in Fig. 1 indicates that the structural differences between the two conformations mainly amount to the lid region. In contrast, _c(z) indicates that there are differences in the whole protein due to the different conformations sampled during the simulations. Even for  = 3.0 Å, fine structural features persist suggesting that molecular information of the adsorbed enzyme can be deduced from fitting _c(z) ( = 3.0 Å) to _e(z). According to Fig. 7, structural information over an interval of ~25 Å can be taken into account when fitting the profiles.

Quantitative comparison

To quantify the comparison of _c(z) with _e(z) we carried out least squares fits of _c(z) to both (z) and to (z) using Eqs. 5 and 6. Although we did not carry out simulations on S146A we know from our earlier simulations of S146A (Peters et al., 1998) that structural differences between S146A and wt Tll are restricted to a few local regions in the protein. We therefore consider (z) as a reasonable approximation for (z). There is experimental evidences that wt Tll and S146A bind differently to hydrophobic-hydrophilic interfaces (Peters et al., 1998), which is in accord with the characteristic differences featured by (z) and (z) in Fig. 7.

The three best fitting orientations for the applied value of (= 0.325 Å³) and the parameter f are compiled in Table 1 [fit of _c(z) to (z)] and Table 2 [fit of _c(z) to (z)]. The corresponding electron density profiles are displayed in Figs. 8 and 9 together with snapshots of the two best fitting enzyme orientations of each conformation. To further quantify the quality of the fits, we calculated the resulting variances between _c(z) and _e(z) denoted _ec on the fitted interval.

View this table: [in this window] [in a new window]   TABLE 1   Quantitative comparison of calculated and experimental electron density profiles of wt Tll extracted from X-ray reflectivity data [fit of c(z) to (z)]

View this table: [in this window] [in a new window]   TABLE 2   Quantitative comparison of calculated wt Tll electron density profiles with the experimental S146A electron density profile extracted from x-ray reflectivity data (fit of c(z) to (z), see caption to Table 1 for more details)

View larger version (39K): [in this window] [in a new window]   FIGURE 8   Three best fitting orientation specific profiles resulting from a fit of the calculated electron density profile to the experimental electron density profile for wt Tll; (A) closed conformation and (B) open conformation. Only the fitted parts of the best (dotted lines), second best (dashed lines), and third best (thin solid lines) are shown together with the fitted part of the experimental profile (bold solid lines). The deduced area per lipase molecule (in Å2) appears in each panel. See caption to Table 1 and text for more details. A snapshot taken after 2 ns of simulation of Tll in the two best fitting, different orientations according to Table 1 appears below the electron density profiles. The active site lid residues are displayed as a black tube. Standard deviations for experimental and calculated data are indicated by solid and dashed error bars, respectively.

View larger version (39K): [in this window] [in a new window]   FIGURE 9   Three best fitting orientation specific profiles resulting from a fit of the calculated electron density profile to the experimental electron density profile for S146A; (A) closed conformation and (B) open conformation. See caption to Fig. 8 for more details. Dashed error bars indicate standard deviations of the calculated data.

To deduce the experimental area, A_e, we used the time averaged simulation box area, A_c, (perpendicular to n_z), which is 3387 Å² (3400 Ų) and 3469 Å² (3450 Ų) for the simulation box containing the closed and open conformation of Tll, respectively. Because V_c/V_e ~ A_c/A_e using L_z,c = L_z,e  59 Å we have A_e = A_c/f. We solved iteratively for A_e by varying f using the above values for A_c. This leads to the different areas per molecule listed in Tables 1 and 2 and in Figs. 8 and 9. For instance an f value above 1.0 implies that A_e is smaller than A_c.

For the fit of _c(z) to (z) we find, according to the variances _ec in Table 1, that the orientation (0, 4/6, /6) of the open conformation fits (z) best. The corresponding value for A_e is 2300 Ų. For the closed conformation the orientation, which furnishes the best fit to _e^wt(z) is (0, /6, 2/6) with A_e 1900 Ų. However, _ec is significantly larger and identical to the value for the second best fitting orientation of the open conformation (0, 4/6, 9/6) with A_e 2300 Ų. For the fit of _c(z) to _e^S146A(z) we find significantly lower variances (Table 2) for several orientations with areas between 2300 Ų and 2800 Ų. The best fitting orientation is (0, 4/6, 9/6) with A_e 2300 Ų. All deduced areas conform best to the diffraction result obtained for S146A of 2400 Å² per molecule (hexagonal unit cell), whereas A_e 1200 Ų (rectangular unit cell) seems unlikely. Simple calculations based on the enzyme dimension also support an area of 2400 Å². A neutron diffraction study of wt Tll at a surfactant-water interface deduced the volume fraction of interfacially bound enzyme. However, this could not be translated into an area per molecule (Lee et al., 1999). In the fit of _c(z) to (z) and of _c(z) to _e^S146A(z) the end point of the region fitted is z 40 Å, which agrees well with the normal dimension of Tll (45 Å). The 40-Å region therefore captures the relevant normal dimension of the enzyme and confirms the presence of an adsorbed monolayer of both wt Tll and S146A in the two experiments.

For the best fitting wt Tll orientation [(z) to _e^wt(z)], the lid is positioned ~120 degrees away from n_z (see also Fig. 1). According to _ec, the fit of (z) to (z) was better than the fit of (z) to (z). For S146A, the orientations (0, /6, 6/6), (0, /6, 7/6), (0, /6, 5/6), and (0, 4/6, 2/6) [fit of (z) to (z)] and (0, /6, 4/6), (0, 3/6, 10/6), and (0, 2/6, 3/6) [fit of (z) to (z)] cannot be discerned statistically considering the respective values of _ec and the standard deviation of _c(z) (Fig. 9). As indicated by the results in Tables 1 and 2, several orientations therefore fit the experimental profiles equally good. The general trend is that the open conformation, which in fact should be characterized as a partially open conformation (discussed in the next section), provides the best fits to both (z) and (z).

Partially open Tll conformation

A dynamic equilibrium between a so-called preactivated, yet closed, and a closed, activated (but catalytically inactive) conformation of Tll was reported by crystallographic trapping of these conformations (Brzozowski et al., 2000). The closed activated conformation should not be confused with the catalytic active, open conformation in the present study; the closed activated state is identical to our closed conformation (Brzozowski et al., 2000). These crystal structures suggest that the interfacial activation of Tll might well be a multistep process involving more than two conformational transitions before a fully active conformation is assumed.

One could speculate whether there exists a dynamic equilibrium between open and closed conformations at the interface, or the enzyme is adsorbed in a partially open/partially closed conformation. The presence of a dynamical equilibrium between the closed activated (our closed) and fully activated (our open) conformation remains to be confirmed experimentally. The simulations of Tll (open) showed that lid closed partially resulting in the conformation shown in Fig. 1. Focusing on the lid residues 84 to 95, the RMSD between the C atoms of these residues along the trajectory relative to the initial open (crystal) structure are found to be 3.5 Å (2 ns), 4.4 Å (4 ns), 3.9 Å (6 ns), 3.8 Å (8 ns), and 4.1 Å (10 ns). Accordingly, the lid does not close completely. The intermediate conformation should be characterized as slightly more open than closed, because the RMSD values of the C atoms of the same lid residues relative to the initial closed (crystal) structure are 5.5 Å (2 ns), 5.3 Å (4 ns), 5.4 Å (6 ns), 5.4 Å (8 ns), and 5.7 Å (10 ns). These RMSD values indicate that the observed lid closure is a significant conformational change that most likely occurs due to a shielding of the hydrophobic part of the lid from the aqueous solvent. The lid of the closed conformation remained essentially in the same conformation over the 12-ns simulation time.

	CONCLUSION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS RESULTS AND DISCUSSION CONCLUSION REFERENCES

Biomolecules can assemble at the air-water interface and form two-dimensional crystalline layers (Rapaport et al., 2000; Alonso et al., 2001). As demonstrated here protein layers can be investigated by using x-ray techniques. Specifically, we have investigated electron density profiles of wt Tll and a mutant of Tll in the case where these enzymes adsorb at the air-water interface. The interpretation of the resulting electron density profiles in terms of conformation and orientation of the enzyme relies on the amount of fine structure present as shown by the computation of the electron density profiles for the active and inactive conformation of wt Tll. Although the interpretation of such experiments on a molecular level in nontrivial, the experimental electron densities were interpreted using the corresponding profiles computed from MD trajectories. The analysis was accomplished by developing a computational scheme that allowed for extraction of several electron density profiles from a single trajectory, and by subsequently bringing these on the same scale as the experimental profiles. Convergence of the computed profiles and reduction of statistical noise were ensured by performing simulations for several ns. Our computational results indicate that there is in principle sufficient information in the electron density profiles to uniquely characterize the orientation and conformation of the adsorbed enzyme and even to differentiate between closely related enzymes. In fact, we performed similar calculations on the open and closed conformations of Rhizomucor meihei lipase and found that the resulting electron density profiles are different from those of Tll. The comparison of the calculated and measured profiles is predominantly limited by the intrinsic surface roughness in the experiment. We find that the experiment can hardly distinguish between open and closed conformation of Tll. A least squares fit of the calculated profiles to the experimental profile yields an area per adsorbed molecule between 2300 and 2800 Å for both wt and the mutant, which is in accordance with our x-ray diffraction result, thereby confirming the existence of an adsorbed monolayer. The best fitting orientation of wt Tll has the lid oriented at an angle of ~120 degrees away from the surface normal. The orientation of S146A has the lid oriented 30 to 120 degrees away from the surface normal. The simulations furthermore suggest that the conformation of the adsorbed enzym