Protein Engineering, Vol. 12, No. 9, 747-754,
September 1999
© 1999 Oxford University Press
Computational analysis of chain flexibility and fluctuations in Rhizomucor miehei lipase
Department of Chemistry, Technical University of Denmark, Building 206, DK-2800, Lyngby, Denmark and 1 Biostructure Group, Novo Nordisk A/S, Novo Nordisk Park, DK-2760 Måløv, Denmark
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Abstract |
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We have performed molecular dynamics simulation of Rhizomucor miehei lipase (Rml) with explicit water molecules present. The simulation was carried out in periodic boundary conditions and conducted for 1.2 ns in order to determine the concerted protein dynamics and to examine how well the essential motions are preserved along the trajectory. Protein motions are extracted by means of the essential dynamics analysis method for different lengths of the trajectory. Motions described by eigenvector 1 converge after approximately 200 ps and only small changes are observed with increasing simulation time. Protein dynamics along eigenvectors with larger indices, however, change with simulation time and generally, with increasing eigenvector index, longer simulation times are required for observing similar protein motions (along a particular eigenvector). Several regions in the protein show relatively large fluctuations and in particular motions in the active site lid and the segments Thr57–Asn63 and the active site hinge region Pro101–Gly104 are seen along several eigenvectors. These motions are generally associated with glycine residues, while no direct correlations are observed between these fluctuations and the positioning of prolines in the protein structure. The partial opening/closing of the lid is an example of induced fit mechanisms seen in other enzymes and could be a general mechanism for the activation of Rml.
Keywords: enzyme/essential dynamics/molecular modelling/protein stability/structure–function relationships/site-directed mutagenesis
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Introduction |
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TopAbstractIntroductionMaterials and methodsResults and discussionReferences |
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Widespread industrial and academic interest in lipases (acylglycerol acylhydrolases, EC 3.1.1.3) has led to numerous biophysical studies and to the detailed structural characterization of several mammalian, fungal and microbial lipases. For full activity, most lipases require the presence of an oil–water interface (Verger et al., 1984
; Piéroni et al., 1990), a phenomenon known as interfacial activation. The phenomenon of interfacial activation seen in lipases has generated much discussion over a long period of time about what determines lipase activity. Effective hydrolysis probably depends on structural changes in the enzyme upon activation and the physical state and structure of the lipid substrate. Theoretical approaches have been developed based on the conformational changes in the enzyme (`enzyme' theory) or based on the properties of the lipid interface (`substrate' theory). However, there is increasing evidence that these models are merely conceptual extremes and depending on the substrate are not mutually exclusive (Derewenda et al., 1994b; Muderhwa and Brockman, 1992).
The structural basis for interfacial activation has been revealed by X-ray crystallography of lipases in complex with inhibitors or co-crystallized with micelles. Three-dimensional lipase structures from Rhizomucor miehei (Brady et al., 1990; Derewenda et al., 1992a), human pancreatic (Winkler et al., 1990), Geotrichum candidum (Schrag and Cygler, 1993), Candida rugosa (Grochulski et al., 1993), Rhizopus delemar (Derewenda, 1994b), Pseudomonas glumae (Noble et al., 1993), Penicillium camembertii (Derewenda et al., 1994a) and Humicola lanuginosa (Lawson et al., 1994) have been determined to high resolution. These studies provide considerable insight into the structure–function relationships in lipases. The crystal structures indicated that these lipases all have a common 
/ß-hydrolase fold (Ollis et al., 1992; Cygler et al., 1993), a catalytic triad (Ser–His–Asp/Glu) similar to that found in serine proteases (Kraut, 1977) and a lid covering the active site making it inaccessible to the substrate. The lid, however, is not a ubiquitous feature and it has been found that some lipolytic enzymes have solvent accessible active sites (Martinez et al., 1992; Hjort et al., 1993; Uppenberg et al., 1994).
The functional consequences of the structural changes observed during lipase activation are pronounced. As revealed by the crystallographic studies of the enzyme–inhibitor complexes of Rhizomucor miehei lipase (Brzozowski et al., 1991; Derewenda et al., 1992b), the pancreatic lipase–procolipase complex crystallized in the presence of mixed micelles (van Tilbeurgh et al., 1993) and the structure of the Candida rugosa lipase which was crystallized in the open conformation (Grochulski et al., 1993), the conformational change observed during activation is governed by a rigid body hinge-type motion of single or multiple helices (Derewenda et al., 1994b). During activation, the lid covering the active site is displaced by several Ångströms. This lid movement opens up the binding pocket and the active site becomes accessible to the substrate. Additionally, the movement causes (i) polar residues on the helical lid to be buried, (ii) water molecules bound at the polar protein surface in the closed conformer to be displaced and (iii) a hydrophobic lipid-binding surface adjacent to the lid to become exposed (Derewenda, 1994c). All these contributions add favorable enthalpic and entropic terms to the stability of the activated enzyme (Dodson et al., 1992). Experimental and computational studies have shown that electrostatic interactions mediate the contact between the active site lid and the protein surface in the activated lipases (Derewenda et al., 1992b; van Tilbeurgh et al., 1993; Peters et al., 1996a and 1997). One of the most convincing demonstrations of the functional importance of electrostatic interactions came from site-directed mutation of single titratable residues in the active site lid. Mutation of key residues in the lid decreases the catalytic activity of Rhizomucor miehei lipase (Rml) (Holmquist et al., 1993). Protein motions are complex in nature and depend inter alia on the nature of the amino acid residue side chains. It is anticipated that certain residue types will have a more significant effect on motion than others, e.g. glycines, due to their small size, and prolines, due to their cyclic structure. Indeed, single site mutations of glycines or of non-glycine residues at other sites to glycines can have remarkable effects on the biological function of enzymes and can be lethal. Mutations involving glycines invariably affect protein stability (Hecht et al., 1986; Matthews, 1987; Berndt et al., 1993), and have been stated to be the cause of reduced catalytic activity (Wilkinson et al., 1983; Jancso and Szent-Györgyi, 1994), and of changes in enzyme specificity (Vermersch et al., 1990). Moreover, such mutations have been implicated as being the etiological factor in diseases such as lipoprotein lipase deficiency (Henderson et al., 1992; Busca et al., 1996), haemolytic anaemia (Vulliamy et al., 1988), Alzheimer disease (Mann et al., 1992) or insulin resistance (Almind et al., 1996).
The alteration in the protein function could arise from a variety of sources involving changes in the tertiary structure, changes in the protein flexibility or disruption of hydrogen bonds (Subbiah, 1996). Of course, the effect of the mutation on the protein function will depend on the protein architecture and may involve destabilization of the enzyme–substrate or enzyme–transition-state complexes resulting in changes in binding and catalysis. If the enzyme–substrate complex is destabilized relative to the enzyme–transition-state complex a rate acceleration may ensue, while if the enzyme–transition-state complex is destabilized the catalysis will be impaired.
An important concept in considering substrate recognition and binding which has emerged from studies of many enzymes is that of induced fit (Koshland, 1958). We surmise that many of the fluctuations that we observe in this work fall into this category. In view of the importance of glycines and prolines in protein function we have investigated the protein dynamics of Rml and the extent of fluctuations around these residues. In particular, we are interested in the mobility of the active site lid and two loop regions, Gly35–Lys50 and Thr57–Asn63. In our previous study, we concluded that both loop regions are important for the function of lipases (Peters et al., 1996b) and their mobility is influenced by solvent polarity and bound inhibitor. Information about concerted atomic motions in the protein were extracted by applying the essential dynamics analysis technique (Amadei et al., 1993). This technique has previously been used (i) to correlate essential motions in lysozyme (Amadei et al., 1993), thermolysin (Van Aalten et al., 1995) and lipases (Peters et al., 1996b) to their biological function and (ii) to suggest point mutations in retinol-binding proteins (Van Aalten et al., 1997).
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Materials and methods |
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Molecular dynamics simulations were carried out using the parallelized C (charged) version of the GROMOS forcefield (Europort-D, van Gunsteren and Berendsen, 1987
) on an 18-processor SGI Challenge. The crystal structure of the native Rml solved to 1.9 Å resolution (Derewenda et al., 1992a) was used as the starting structure for the simulation. Coordinates were obtained from the Protein Data Bank at Brookhaven (Bernstein et al., 1977; entry code: 3tgl).
The simulations were performed using periodic boundary conditions with a truncated octahedron central cell at a temperature of 300 K. SPC water taken from a liquid equilibrium configuration (Berendsen et al., 1987) were added to the box. Ten water molecules at the lowest electrostatic potential were replaced by sodium ions to neutralize the simulation cell of Rml/water systems. Details of the molecular dynamics protocol and the effect of the force field on the motions of Rml are presented elsewhere (Peters et al., 1996b). Examinations of the molecular structures and analyses of the trajectories were carried out using the WHAT IF modeling program (Vriend, 1990) and the essential dynamics routines supplied therein. Simulations were run for more than 1 ns and 600 ps trajectories were used for the essential dynamics and structural analyses. The essential dynamics method has been described several times in the literature and the reader is referred to Amadei et al. (1993), van Aalten et al. (1995, 1996a) and Peters et al. (1996b). Briefly, the method is based on the diagonalization of the covariance matrix of the atomic displacements (Ichiye and Karplus, 1991), which yields a set of eigenvectors and eigenvalues. The eigenvectors represent a direction in a high-dimensional space, describing concerted displacements of atoms. The eigenvalues represent the mean square fluctuation of the total displacement along these eigenvectors. Motion within the subspace can be studied by projecting the trajectory onto the individual eigenvectors. This dot product provides information about the time dependence of the conformational changes. The reported eigenvalues are ordered for convenience by decreasing value; i.e. the first eigenvector is the vector with the largest eigenvalue. The central hypothesis of essential dynamics is that only the directions indicated by eigenvectors with sufficiently high eigenvalues are important for the description of the protein dynamics. It has been observed that these motions can be linked to the biological function of proteins (Amadei et al., 1993; van Aalten et al., 1995, 1996a). In many proteins, the positional fluctuations are concentrated in correlated motions in a subspace of only a few degrees of freedom (<10% of the original configurational space), while the other degrees of freedom represent small, independent Gaussian fluctuations.
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Results and discussion |
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TopAbstractIntroductionMaterials and methodsResults and discussionReferences |
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In the present study, we have focused on examining the protein dynamics in Rml and have investigated the motions close to glycine and proline residues. Rml belongs to the family of fungal lipases and is classified according to SCOP (http://scop.mrc-lmb.cam.ac.uk/scop/data/scop.1.html) as
and ß. The CATH (http://www.biochem.ucl.ac.uk/bsm/cath/CATH.html) class is C:3 A:40 T:50 H:480. The enzyme has a typical /ß-hydrolase fold, which is composed of a central ß-sheet system of nine strands. The middle five strands are all parallel, while the pairs flanking the C- and N-termini are antiparallel to the others. The nine strands form a concave surface, across which runs the N-terminal helix filling the shallow cavity generated by the central ß-sheet system. The sheets are connected by a series of segments and helices, where the helices run approximately parallel to the strand direction. Rml is stabilized by three disulfide bridges, two of which are conserved within the family of lipases. One is located in the loop connecting the N-terminal helix with the first ß-strand. The second cross-links the C-terminus to the N-terminal helix effectively reducing the mobility of the C-terminus. The remaining bridge, which is not conserved in other lipases, links the start of the extended C-terminus to the central ß sheet. There are 18 glycines in Rml (see Table I). Due to the fact that glycine residues have to side chain, which has consequences for both rotational flexibility at a glycine site and packing of the side chains of other residues near a glycine site, this residue type very often has a structurally important function. We shall see that some of the glycines in the Rml structure play a critical role in dictating the flexibility of the lipase.
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Another important residue in protein structures is proline (Yutani et al., 1991
; von der Osten et al., 1992; Hardy et al., 1993; Masul et al., 1994). Due to the imido bond isomerization (Vermersch et al., 1990), prolines do not contain a peptide NH group for hydrogen bond donation. The side chain is cyclic, alkylating the peptide nitrogen. This effectively freezes the 
torsion angle of the residue and confers a low backbone configurational entropy at that site. Prolines effectively restrict backbone flexibility and cause a decrease in the entropy change of unfolding. There are 13 prolines in Rml (see Table I
).
In order to obtain detail structural and dynamic properties, we have performed molecular dynamics simulation of the wild-type structure of Rml in water using explicit SPC water molecules. The stability of the simulation was checked by computing several geometrical properties. Root mean square displacement (r.m.s.d.'s) calculated with respect to the initial structure, number of hydrogen bonds and radius of gyration as a function of simulation time are displayed in Figure 1. R.m.s.d. data indicate that extensive equilibration times were necessary (in the order of 200–300 ps) before reaching a constant r.m.s.d.
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To further elucidate the origin of protein motions in Rml, we applied essential dynamics analysis. The basic results of an essential dynamics analysis on lipase have been described elsewhere (Peters et al., 1996b
), where we have shown that there is pronounced motion in the active site lid and that, as also found for other proteins, there are only a few essential eigenvectors describing the protein dynamics (Amadei et al., 1993; van Aalten et al., 1995). Motions along these eigenvectors are mainly large anharmonic fluctuations. The harmonicity of the motion along an eigenvector can be estimated by comparing the probability distribution for the displacements along that eigenvector with an ideal Gaussian distribution derived from the eigenvalue of the corresponding eigenvector (Amadei et al., 1993). The correlation coefficients resulting from this comparison and the eigenvalues as a function of eigenvector index are displayed in Figures 2a and b, respectively. As shown in Figure 2, approximately 80% of the total positional fluctuations are described by the first 40 eigenvectors. The number of significant eigenvectors is considerable larger than observed for other proteins; e.g. for thermolysin it has been shown that taking the first 10 eigenvectors represents about 95% of the total motion of the protein (Amadei et al., 1993; van Aalten et al., 1995). This indicates that the fluctuations in lipases are more complex and consequently more eigenvectors are needed to describe the motions in lipases. Generally, it may be surmised that the number of significant eigenvectors will correlate with the complexity of the function of a protein, which ranges from structural proteins to binding proteins then enzymes and, very likely, receptors have even more complex functions than that. Within the family of enzymes there will be differing degrees of complexity, depending on a variety of factors including the type of substrate, the environment in which the enzyme operates and the way in which the enzyme is regulated. Many enzymes in addition to the lipases undergo appreciable changes in conformation upon substrate binding, a phenomenon known as `induced fit' (Koshlands, 1958). Examples of such induced fit, some of which have also been studied by molecular dynamics, are adenylate kinase (Kern et al., 1994), CD4 protein (Ptaszek et al., 1994), HIV reverse transcriptase (Filipowsky et al., 1996), tRNA synthetase (Ribas de Pouplana et al., 1996), ricin (Olson, 1997), serine protease PB92 (Martin et al., 1997), -adrenoceptor (De Benedetti et al., 1997), antibodies (Miyazaki et al., 1997) and phosphoglycerate kinase (Bernstein et al., 1997). We would expect such proteins also to exhibit a larger number of significant eigenvectors than enzymes of comparable size but lacking the induced-fit behavior.
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Even if the number of eigenvectors is large, as is the case for lipases, this number is still much smaller than the original 3N-dimensional configurational space formed by the C
coordinates (3N C; N = 265 for Rml). This shows that most of the information concerning internal motion of lipases is confined within a subspace of relatively very small dimension. This is also reflected in the correlation coefficients shown in Figure 2b. Of the first 40 eigenvectors describing approximately 80% of the total positional fluctuations, 15 eigenvectors describe non-harmonic (non-Gaussian) fluctuations. Non-harmonic fluctuations are often found to be correlated to the biological function of proteins and therefore are of particular interest. The remaining fluctuations can be described by Gaussian distributions (i.e. independent and harmonic motions) and in terms of understanding the function of the enzyme are generally of less importance than non-harmonic fluctuations.
An important issue in any computational study is the duration of the simulation. To investigate the effect of the duration of the simulation on the results of the essential dynamics (ED) analysis, we have further analyzed the 1.2 ns trajectory of the Rml simulation. The initial 400 ps trajectories were used as equilibration of the systems and were not considered in the analysis. The remaining 800 ps trajectory was divided in two equal parts. Essential dynamics analysis was separately performed on both trajectory parts, and additionally on the first part using different time slices of the trajectory (100, 200, 300 and 400 ps). The average cumulative square inner vector products calculated between the eigenvectors of the time intervals of the first trajectory part and eigenvectors of the second trajectory part are shown in Figure 3. The inner product is normalized so that for two sets of identical eigenvectors the value is 1. As shown in Figure 3a, the inner vector product slowly converges with the number of eigenvectors. The inner product computed with 100 eigenvectors is approximately 0.65. This is lower than determined for the histidine-containing phosphocarrier protein from Escherichia coli (HPr) (de Groot et al., 1996). The difference is again probably caused by the more complex motion in lipase. HPr consists of 85 residues, whereas for instance Rml consists of 265 amino acids. As shown in Figure 3b, the inner vector converges more rapidly with simulation time and after 300 ps only small changes are observed (Figure 3b). Though slow divergence of the inner product is observed, the total positional fluctuations are similar for different time intervals (see Figure 4); i.e. the total fluctuations (root mean square deviations) are similar. In Figure 5, the absolute values of the first three eigenvectors are displayed as a function of residue number. The essential dynamics analysis was performed on trajectories with different length ranging from 100–800 ps in steps of 100 ps (picoseconds are given to the right of the curves). One would expect that with increasing simulation time the curves should converge and should show the same features. Overall the fluctuations are similar and constant over distinct time intervals. However, deviations are observed indicating that the protein explores different parts of the configurational space and even an approximately 1 ns trajectory does not cover the full configurational space (Clarage et al., 1995; Hodel et al., 1995; Balsera et al., 1996). Generally, longer simulation times are required for increasing eigenvector indices to obtain convergence of protein motions observed along individual eigenvectors. Fastest convergence of fluctuations is observed along eigenvector 1, where similar motions are found after 200 ps. Relatively large fluctuations are seen for the active site lid and the segments Thr57–Asn63, Pro101–Gly104, Ala154–Phe170, Glu221–Leu239 and Ser247–Leu255. These regions are shown in Figure 6, which shows the position of glycine and proline residues (Figure 6a). As indicated in Figures 5b and c, motions along eigenvectors 2 and 3 vary with simulation time. However, some of the fluctuations are conserved with simulation time and similar characteristics in the absolute value of the vector as a function of time are observed.
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In our previous study, where we studied the dynamics of Rml in the presence of substrate molecules, a molecule entered the active site groove at the loop Val97–Gly110 (Peters et al., 1996b
). It is this loop where two conserved glycines are located. This may indicate that the glycines are important for allowing fluctuations to occur in that loop, which provide an `entering gate' for the substrate. The strategic location of glycines may well turn out to be a general mechanism for achieving an induced fit for an incoming substrate. This mechanism has been suggested for several other systems (Olah et al., 1993; Zheng et al., 1993; Teplyakov et al., 1996; Narayana et al., 1997).
To locate mobile regions in the enzyme a moving window superposition method was used (van Aalten et al., 1996b). Root mean square deviations (r.m.s.d.'s) calculated from the minimum and maximum structures of the eigenvector motion as a function of residue number are shown in Figure 7. There is apparently no direct correlation between the position of the prolines and the flexibility of Rml. Significant r.m.s.d. data are observed close to glycines. Gly81, which also conserved in Rml, Humicola lanuginosalipase, Rhizopus delemar and Penicillium camembertii is located in the hinge-bend region of the active site lid and provides a flexible link for the displacement of the lid (i.e. activation of the lipase). It is noticeable, that the loops Gly35–Lys50 and Thr57–Asn63 (Rml numbering), which have different flexibility, show low homology between the lipases, and that the glycines (35 and 69 in Rml) are not conserved in the different lipase structures. This may suggest that fluctuations in these loops may govern the biological function of the different lipases.
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Conclusion
Microbial lipases have attracted considerable attention, due to their capability of catalyzing a wide variety of reactions, which allows their widespread application in industrial areas, such as detergents, food processing, synthesis of oils or enantiomerically pure compounds (Wulfson, 1994). Many lipases show discrete substrate specificity, which is probably governed by distinct interactions between substrate and protein and/or conformational changes (flexibility) in the protein. It is generally recognized (Subbiah, 1996) that protein motions are dependent on the location of glycines (and maybe prolines) residues in the protein structure. These motions could be central to the biological function of lipases and could determine the activity and selectivity of these enzymes. These fluctuations constitute one of the most clearly defined examples of induced fit in enzymes.
To study the protein dynamics in Rml and to determine fluctuations close to glycine or proline residues, we have performed molecular dynamics simulations in periodic boundary conditions using explicit SPC water. The first 400 ps was discarded for equilibration and the remaining 800 ps trajectory was considered in the analyses. Flexible regions in the protein were determined using the essential dynamics analysis technique combined with the moving window position method. To study the effect of the length of the simulation on the protein motions, we divided the 1.2 ns trajectory in increasing time intervals. The essential dynamics analyses indicate that motions along different eigenvectors converge slowly with simulation time. Motions along eigenvectors with larger indices require longer simulation time to converge than those motions described by eigenvectors with smaller indices. Fluctuations in the active site as well as (for activation important) segments Thr57–Asn63 and Pro101–Gly104 are observed along several eigenvectors and are conserved along the trajectory. Other fluctuations (e.g. Ala154–Phe170, Glu221–Leu239 and Ser247–Leu255) occur but their extent/frequency vary with simulation time. We conclude that those fluctuations at or in close proximity to the active site can represent an induced fit mechanism. The observed fluctuations are associated with the location of glycines in the protein structure, while no clear correlation is observed between protein dynamics and the presence of proline residues.
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Acknowledgments |
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Computations were performed at Novo Nordisk A/S on an 18 processor SGI Challenge and the project was financially supported by the European Commission DG III within the EUROPORT-D project. The parallel version of GROMOS87 was developed by the Parallel Applications Centre, Southampton, England and installed on the SGI Challenge by Ken Meacham.
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2 To whom correspondence should be addressed
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Received January 12, 1999; revised June 4, 1999; accepted June 11, 1999.
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