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. 2004 Jul;13(7):1823–1831. doi: 10.1110/ps.04652804

Protein simulations: The absorption spectrum of barnase point mutants

Ken RF Somers 1, Peter Krüger 1, Sylwia Bucikiewicz 1, Marc De Maeyer 1, Yves Engelborghs 1, Arnout Ceulemans 1
PMCID: PMC2279920  PMID: 15215525

Abstract

The near-UV absorption spectra of barnase double-point mutants are calculated using a combination of molecular dynamics and ab initio techniques. The atoms of the fluorescent probes are placed in a cloud of point charges, generated by molecular dynamics simulations. Ab initio calculations (CASPT2) are performed on these systems. Three molecular dynamics packages are compared—Amber5.0, CHARMM-c27b1, and GROMOS96—using indole as the fluorescent probe. It was found that calculated absorption spectra reproduce experimental values very well, provided detailed charge cloud descriptions are included. These calculations further sustain the hypothesis that different tryptophan rotamers can be present in proteins. Molecular dynamics calculations of the double-point mutants also point to the structural effect of counter ions.

Keywords: barnase, absorption, molecular dynamics, force field, ab initio, CASPT2

The sensitivity of its fluorescence spectrum to the local environment (Konev 1967; Demchenko 1986) turns tryptophan (W) into a valuable probe tool in biochemistry. Indole is the chromophoric unit of tryptophan and has been studied extensively (Hollas 1963; Lami 1977; Callis 1991, 1997; Roos et al. 1996; Serrano-Andres and Roos 1996; Toptygin and Brand 2000). It mimics the behavior of tryptophan well, but its fluorescence maxima occur at considerably higher energies. A closer fit is obtained using 3-methyl-indole (3me-indole; Fig. 1 ▶; Strickland et al. 1970). The interaction of indole and 3me-indole with solvents results in similar spectral shifts (Strickland et al. 1970). One can therefore use either one of them to examine environmental effects. Callis and Burgess (1997) showed that there exists a relation between the fluorescence maximum and the electrostatic field of the protein over the indole subunits. They succeeded in predicting fluorescence maxima with fairly high accuracy using a combination of semiempirical (INDO/S-CIS) and molecular dynamics (CVFF force field) simulations.

Figure 1.

Figure 1.

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Optimized geometry of (3-methyl)-indole. 3-Methylindole geometry, without brackets; indole geometry, inside brackets.

Tryptophan exhibits a typical three-peak structure in absorption spectra (Valeur and Weber 1977). These absorption spectra are also sensitive to the local protein environment (Willaert et al. 1992), but much less than the fluorescence spectra.

In the present paper we investigate different computational methods to predict the valence absorption spectra (maxima) of tryptophan in proteins, using barnase as a working protein. This protein contains three tryptophan residues, and has been studied extensively (Bycroft et al. 1990; Loewenthal et al. 1991; Horovitz and Fersht 1992; Arcus et al. 1995; De Beuckeleer 1998; De Beuckeleer et al. 1999). Single and double-point mutants, replacing tryptophans, have been produced. From the spectroscopic data on these single tryptophan mutants absorption spectra can be obtained containing electronic fine structures (Willaert et al. 1992). The absorption maxima of the single tryptophan containing mutants (Willaert et al. 1992) that are used as reference for the theoretical work are displayed in Figure 2 ▶. The spectra were obtained by taking differences between the spectrum of the wild type, and spectra where one of the tryptophans was replaced. The same mutants were the subject of an extensive fluorescence study applying both steady-state and time-resolved fluorescence (De Beuckeleer et al. 1999).

Figure 2.

Figure 2.

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Absorption and emission spectra of individual tryptophan residues, in the absence of energy transfer. Spectra were obtained by taking difference spectra between wild type and point mutants. Mutants are identified by the remaining tryptophan: 35 = W71YW94F, 71 = W35FW94F, 94 = W35FW71Y. Reprinted with permission from Willaert et al. 1992, © 1992 American Chemical Society.

The geometries of the mutants are obtained by replacing the tryptophans, and using molecular mechanics (MM) and molecular dynamics (MD) techniques to optimize the structures. An important goal of the present paper is a critical assessment of the principal current force field methods. Three methods are compared: Amber 5.0 (Case et al. 1997), CHARMM-c27b1 (Brooks et al. 1983), and GROMOS96 (Gunsteren et al. 1996). Both charges and positions are obtained from the force fields, and are used to calculate the electric field over the chromophore of mutant W35FW94F. Different charge-geometry combinations are compared to evaluate the performance of various methods in calculating the absorption maxima.

The combination of MD (Amber) to generate the electric field with CASPT2 (complete active space self-consisting field with a second-order perturbation formalism), MOLCAS4.0 (Andersson et al. 1997), and MOLCAS5.4 (Andersson et al. 2002), to calculate the absorption maxima of 3me-indole (the chromophore) using the optimal water approximations reproduces the experimental absorption results for all three mutants.

Results

Valence excitations of all simulations are presented in Tables 1 and 2. The results are divided into two classes: the experimental data (Strickland et al. 1970; Willaert et al. 1992; Demmer et al. 1994) combined with the indole W35FW94F calculations comparing the different packages, and the prediction of the W71YW94F, W35FW94F, and W35FW71Y absorption spectra.

Table 1.

Singlet-valence-excitations: Evaluation of molecular dynamics packages using mutant W35FW94F

Class Name E1 (eV) E2 (eV) 3E (eV)
Experiment
    indolea 4.37 4.77 0.40
    W35FW94F 4.26 4.36 0.10
Evaluation of molecular dynamics packages (indole-based)
    indoleb 4.36 4.80 0.44
    GGs 4.16 ± 0.18 4.73 ± 0.30 0.57 ± 0.28
    GGp c c
    GAs 4.36 ± 0.01 4.75 ± 0.07 0.40 ± 0.06
    GAp 4.27 ± 0.02 4.74 ± 0.07 0.47 ± 0.13
    GCs 4.37 ± 0.01 4.82 ± 0.07 0.45 ± 0.06
    GCp 4.37 ± 0.02 4.82 ± 0.07 0.46 ± 0.06
    AAs 4.35 ± 0.01 4.85 ± 0.25 0.50 ± 0.24
    AAp 4.33 ± 0.02 4.77 ± 0.05 0.44 ± 0.05
    ACs 4.36 ± 0.01 4.80 ± 0.04 0.44 ± 0.05
    ACp 4.35 ± 0.02 4.87 ± 0.09 0.52 ± 0.10
    AlAs 4.32 ± 0.02 4.75 ± 0.01 0.43 ± 0.02
    AlAp 4.32 ± 0.01 4.73 ± 0.03 0.40 ± 0.02
    CCs 4.36 ± 0.01 5.13 ± 0.17 0.78 ± 0.17
    CCp 4.38 ± 0.04 5.17 ± 0.17 0.79 ± 0.06
    CAs 4.33 ± 0.02 5.02 ± 0.12 0.70 ± 0.11
    CAp 4.34 ± 0.02 5.06 ± 0.08 0.72 ± 0.06
    ClCs 4.33 ± 0.01 4.76 ± 0.03 0.43 ± 0.02
    ClCp 4.34 ± 0.01 4.78 ± 0.01 0.44 ± 0.01
    ClAs 4.31 ± 0.02 4.67 ± 0.04 0.36 ± 0.03
    ClAp 4.31 ± 0.01 4.68 ± 0.01 0.37 ± 0.01
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a Results from Strickland et al. (1970).

b Results from Somers et al. (2004).

c No results due to unstable CASSCF active space.

Table 2.

Singlet-valence-excitations: Absorption of mutants

Class Name E1 (eV) E2 (eV) 3E (eV)
Experiment
    3me-indolea 4.32 4.59 0.27
    W71YW94F 4.26 4.40 0.14
    W35FW94F 4.26 4.36 0.10
    W35FW71Y 4.24 4.36 0.12
Calculation of mutant spectra (3me-indole-based)
    3mc-indoleb 4.30 4.59 0.29
    W71YW94Fc 4.24 ± 0.02 4.31 ± 0.05 0.10 ± 0.01
    W71YW94Fd 4.29 ± 0.02 4.53 ± 0.04 0.24 ± 0.05
    W35FW94Fc 4.22 ± 0.07 4.34 ± 0.13 0.13 ± 0.08
    W35FW94Fd 4.27 ± 0.02 4.40 ± 0.06 0.13 ± 0.06
    W35FW94Fe 4.30 ± 0.01 4.56 ± 0.08 0.26 ± 0.08
    W35FW71Yc 4.27 ± 0.04 4.45 ± 0.08 0.18 ± 0.07
    W35FW71Yd 4.29 ± 0.01 4.60 ± 0.05 0.31 ± 0.05
    W35FW71Yf 4.32 ± 0.03 4.47 ± 0.08 0.15 ± 0.08
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a Result from Strickland et al. (1970).

b Results from K.R.F. Somers and A. Ceulemans, in prep.

c Charge cloud built from the protein and two chloride counterions.

d Charge cloud built from the protein, two chloride counterions, and all simulated water molecules.

e Charge cloud from d but the protein and the two chloride counterions are removed.

f Charge cloud as in d, but the chromophore is rotated 180° around χ2.

Evaluation of molecular dynamics packages

A ribbon representation of barnase is shown in Figure 3 ▶. The result of different MD packages is presented by a set of test calculations on mutant W35FW94F, combining indole as chromophore with Amber (A), CHARMM (C), and GROMOS (G) MD results. In Table 1 the combinations are specified by a three-letter code: the first letter refers to the force field used to determine the geometry (G, A, or Al, C or Cl, where l refers to the use of long-range electrostatics); the second indicates the MD package that provides the point charges; and the third indicates whether the excitation calculations are performed on a set of snapshots, property sampling (p), or on averaged positions, structure sampling (s; Fig. 4 ▶). The difference between the first and second excitation energy is always included to facilitate the comparison of the different force field calculations. Table 1 is visualized in Figure 5 ▶.

Figure 3.

Figure 3.

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Ribbon representation of barnase (1BNR). 2D-NMR based structure by Bycroft et al. (1991).

Figure 4.

Figure 4.

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Representation of the sampling procedure. The top part represents property sampling, the bottom part represents structure sampling.

Figure 5.

Figure 5.

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Shifts in excitation energies and the difference between them, relative to the calculated indole properties. All energies are in eV.

The shifts of the excitation energies are compared with the original indole values. Bars to the left indicate a lowering of the value compared to indoles value. The same identification is used for both Table 1 and Figure 5 ▶.

Calculation of mutant absorption spectra

For the purpose of the actual calculation of the absorption spectra we turn to 3me-indole as the chromophore, which is a better model for tryptophan. The results for the three double-point mutants, including counter ions in the MD simulation, are presented in Table 2, together with the calculation that also fully incorporates the water box. An extra set of calculations simulating the reaction field of the surrounding water molecules is also performed. The table also contains the results of the χ2 + 180° (for notation, see Discussion/Calculation of mutant absorption spectra) rotamer of W35FW71Y, using all-inclusive charge clouds. The RMS values, comparing the backbone of barnase with that of the mutants, are obtained for all MD calculations. All values are close to 3 Å. The domain structure is preserved in all MD calculations, but there exists some flexibility in the loops. Mutant W71YW94F is sensitive to fold opening. Simulating this mutant, in the absence of counter ions, results in folding of the loop between the second and the third α-helix and in the disturbance of the protein core. This fold opening is discussed and visualized in Discussion/Calculation of mutant absorption spectra. Placing counter ions stabilizes the protein and prevents the opening.

Discussion

Evaluation of molecular dynamics packages

Our principal criterium to judge the quality of the simulation methods is how well the computed transition energies match the experimental values. The transitions are calculated for ground-state geometries, and therefore correspond to so-called vertical transition energies to the maximum of the Franck-Condon envelope of the absorption band. For chromophores such as indole in the gas-phase, such theoretical predictions of absorption maxima give excellent results (Somers et al. 2004). However, in the protein environment the determination of the experimental absorption maximum is less reliable, because the band envelope can have a natural width of several 1000 cm-1, and its shape and even its maximum can depend on the actual resolution (Callis 1997). There is thus an important caveat that the spectral comparison of protein data be subject to uncertainties of perhaps 0.1 eV, as far as absolute transition energies are concerned.

If we compare the spectrum of 3me-indole with the spectra of the tryptophans in the protein environment, it is clear that for the tryptophans, transitions are at slightly longer wavelengths, and that the gap between the excitation energies is smaller in the tryptophans. The downshift of the first excitation is approximately 0.05 eV, and that of the second excitation is 0.20 eV. Even more pronounced bathochromic shifts of respectively 0.11 and 0.40 eV are observed if one relates tryptophan absorptions to the indole spectrum. The charge clouds placed around indole should therefore perform the job of lowering the excitation energies and diminishing the difference between the excitation energies. We use this requirement to evaluate the performance of the different MD methods we have investigated.

Five sets are discerned based on the source of the geometry of the charge cloud: G, A, Al, C, and Cl. The first set is based on the GROMOS geometries. Combining the GROMOS geometry with GROMOS point charges leads only to results when applying structure sampling (GGs). These structure sampling results have lower excitation energies, but increase the separation between the two transitions. Using the charge cloud determined by property sampling (GGp) in the CASSCF-calculation results in an unstable active space. It is therefore impossible to determine the excitation energies for this combination. Replacement of the GROMOS point charges by Amber point charges gives rise to one set of results that fulfill all three requirements: GAs. The GAp settings do not fulfill the energy difference criterion. In contrast, the GAs combination is acceptable, as it has downshifts in both the second excitation and the energy difference, while the first excitation remains unshifted. The apparent insensitivity of the first excitation is not problematic because the electric field is known only to have a small effect on the first excitation due to the small change of dipole moment upon excitation (Callis 1991). Usage of CHARMM point charges gives higher excitation energies and larger energy differences. This behavior is rather unexpected, as CHARMM and Amber have the same building philosophy based on quantum mechanical calculations, and should therefore have similar effects on the spectra.

The second and third set consist of all Amber-based geometries. The combination of Amber point charges with geometries obtained using long-range electrostatics creates two well-suited candidates. Omitting the long-range electrostatics as a time saving measure reveals one more acceptable candidate: AAp. Replacing the Amber point charges by CHARMM point charges when forming the charge cloud generates energy shifts that are opposite to the required shift.

CHARMM geometries are applied in the construction of the fourth and fifth set. Only the geometries obtained by simulations using long-range electrostatics fulfill the energy shift requirements. The use of Amber point charges in both sets tends to downshift the energies even more.

A comparison of the different packages with the afore mentioned requirements shows that only one combination without long-range electrostatics creates an electric field that slightly lowers the excitation energies, without enlarging the difference between the excitation energies: AAp. The AAp spectrum has a difference of 0.44 eV, which is similar to the indole spectrum, but both excitations are downshifted. Thus, the AAp formalism is capable of reproducing the necessary shifts without long-range electrostatics in the geometry determination. This result can be attributed to both the small size of the protein and the use of group based cutoffs. The cutoff radius used in the simulation is already half the radius of the protein; most of the proteins electrostatic interactions are therefore incorporated when the residues with atoms inside the cutoff radius are added to the set of electrostatically interacting atoms. Using Amber on a small protein therefore results in good geometries, even when the long-range electrostatics are omitted. This is in marked contrast with the atom-based cutoff used in the CHARMM calculation, which produces erroneous geometries, as too few electrostatic interactions are present.

Evaluation of the five sets shows that—provided long-range electrostatics are included—good results are obtained in all cases except for some of the GROMOS geometry-based combinations. The only GROMOS combination that downshifts both excitation energies is GAs. This result is inherent to the building philosophy behind both the GROMOS geometry and the Amber point charges. The quality of the Amber point charges resides in their construction principle. All Amber building blocks are based on QM calculations using RESP (Restrained ElectroStatic Potential; Bayly et al. 1993) charges on different conformations (Cieplak et al. 1995); consequently, they do form a good approximation of the real charges. The GROMOS point charges are engaged in the force field optimization, and have therefore less physical meaning (Gunsteren et al. 1996). The GROMOS force field is parametrized to bear resemblance to the average behavior of the system, while the Amber force field is built to resemble more closely the molecular properties of the amino acids. The GROMOS package therefore performs well when looking at averages, whereas the Amber package requires snapshots. The deficiency of the GROMOS building principle, concerning geometry and point charges, is especially manifest when calculating the GGp excitation energies, as the unphysical nature of the electric field makes it impossible to construct a coherent active space.

The other methods using long-range electrostatics fulfill all requirements. All of them have similar standard deviations and only small shifts for the first valence excitation. This small shift is expected, because the first excitation is characterized by a small permanent dipole difference. The second excitation induces a larger change of dipole moment, and therefore interacts more with the electric field. This increased sensitivity is visible in the second valence excitation of the Amber results, which show a small yet distinct improvement due to the enclosure of long-range electrostatics in the geometry simulation. The effects of this enclosure are more profound on the CHARMM geometries. All CHARMM geometry-based spectra, without long-range electrostatics, have large errors on the second excitation. Even the use of Amber point charges, shown to be more appropriate by the Amber geometry calculations, is unable to correct for the large deviation in the second excitation energy. This shift towards higher excitation energies when using CHARMM point charges has been reported previously (Short et al. 1999), but results from the combination of CHARMM geometries with CHARMM point charges are not available. The introduction of long-range electrostatics rehabilitates the code in accordance with earlier findings on the molten protein problem (York et al. 1993). The largest downshifts are present in the combination of CHARMM geometries, obtained with long-range electrostatics, with Amber point charges.

Although inclusion of the long-range electrostatics improves the calculations, a strong disadvantage shows up: the time-consuming nature of these calculations. It is therefore preferable to use the AAp method in the further research. Not only does this method use the same force field for both geometry and point charges, but it also reproduces the downshifts of the valence excitation energies. Analogous reasoning explains why the ClAp method is not chosen, although its results are more promising. All further calculations in Table 2 are therefore performed with the AAp formalism.

Calculation of mutant absorption spectra

Comparison of the all-inclusive with the no-water valence excitation energies of the three mutants shows large water effects for the water accessible tryptophans (W71YW94F and W35FW71Y) and small effects for the buried tryptophan (W35FW94F). This result is supported by the water-only values of mutant W35FW94F that show only, on average, a small 0.03-eV downshift from the gas phase result for the second excitation. The corresponding spread of 0.08 eV points out that the electric field created by the water molecules is strong enough to shift the second excitation substantially, but that the orientational polarization of the water layers around the protein is too low to induce a permanent shift of the excitation. The W35FW94F results are also an indication of the complexity of the electric field effects: both the no-water calculation and the water-only calculation obtain downshifted second excitation energies, but the all-inclusive calculation, combing both electric fields, downshifts this excitation less than the no-water calculation. This suggest that there exist an interaction between the water and the protein that is responsible for the specific shift of the all-inclusive results. This interaction is probably electrostatic in nature: the electric field of the protein polarizes the nearby water layers, which creates a reaction field. This reaction field opposes the electric field of the protein, which explains the smaller downshifts in the all-inclusive calculation. Similar effects of the reaction field of water have been noted recently for protein fluorescence spectra (Vivian and Callis 2001). The all-inclusive results of mutants W71YW94F and W35FW94F are close to the experimental values. The differences between experiment and theory are, respectively, 0.03 eV and 0.04 eV for the first excitation and 0.13 eV and 0.04 eV for the second excitation. These differences are within the 0.2-eV error margin of the CASPT2 technique. The absorption prediction apparently meets difficulties for mutant W35FW71Y that differs, respectively, 0.05 eV and 0.24 eV from the experimental first and second valence excitation, and therefore falls outside the CASPT2 error margin.

A visual inspection of W35FW71Y’s protein structure reveals that tryptophan W94 is located in a cleft, and that two conformers can exist. Both conformers were manually generated and simulated with molecular dynamics calculations. The last 100 ps of these 600-ps runs are depicted in Figure 6 ▶). Each of the calculations clearly converged to a different zone (The χ1 and χ2 values of the original mutant are depicted in the upper part of the figure, labeled A). This analysis is supported by dead-end elimination calculations (Smet et al. 1992) on the rotamers of barnase (Hellings et al. 2003), which suggested the existence of four different ro-tamers for the tryptophan at position 94 (Szabo and Rayner 1980). Molecular dynamic runs of these rotamers converged to two different rotamer manifolds, which coincide with the visually generated rotamer zones. The second excitation of the W35FW71Y rotamer differs 0.11 eV from the experimental value, an error that is comparable to the W71YW94F result. The theoretical results depicted in Figure 6 ▶ suggest that the tryptophan at position 94 in barnase may be rotated 180° around χ2. It is therefore possible that two rotameric manifolds of mutant W35FW71Y exist, a hypothesis that is also supported by the life time measurements of this mutant (De Beuckeleer et al. 1999). Two clearly different fluorescence maxima appear in the life-time measurements—one at 3.59 eV and one at 3.76 eV—whereas the steady-state measurements only show one maximum at 3.59 eV. It is hence noteworthy that the absorption difference between the calculated second excitation energies of W35FW71Y and its rotamer is 0.13 eV, which resembles the difference of 0.17 eV between the two fluorescence maxima of W35FW71Y.

Figure 6.

Figure 6.

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Predicted rotamers of tryptophan W94 in mutant W35FW71Y using Dead-End Elimination and Molecular Dynamics. In the MD calculations one identifies two rotamers A and B, as depicted below. The molecular dynamics calculations using dead-end elimination rotamers as starting structures also converge to these two structures.

The molecular dynamics calculations an sich also provided interesting results concerning the structural role of the counter ion. Indeed, when trying to simulate the W71YW94F mutant without counter ions an opening of the structure was observed (see Fig. 7 ▶). Adjustment of heating speed, coupling constants, and time steps did not lead to an increase in folding stability. This opening may potentially be interesting in its own right because it bears a resemblance to the open form of barnase, which is observed in the trimer (Zegers et al. 1999). The barnase monomers fold open using the loop between the second and third α-helix as a hinge to form the building blocks of the trimer. The combination of the first and second α-helix of the first opened monomer with the remaining α-helix and β-sheets of the second opened monomer results in a globular structure that bears close resemblance to the unopened monomer. Repeating this operation three times chains together the monomers into a trimer with C3-symmetry. The fold opening observed in our simulation could give a clue with respect to the initial steps in the trimer formation.

Figure 7.

Figure 7.

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Ribbon representation of barnase mutant W71YW94F and the trimer (1YVS) subunit. From left to right: barnase mutant W71YW94F; opened barnase mutant W71YW94F; the trimer subunit taken from Zegers et al. (1999).

Conclusions

In this paper we have presented a hybrid approach of molecular dynamics and ab initio techniques to calculate the absorption spectra of tryptophan in barnase. Two aspects were investigated.

First of all, the groundwork was laid by comparing the ability of three different MD packages to predict the electric field at the tryptophan sites, using unsubstituted indole as a probe. Both Amber and CHARMM yield reliable results when long-range electrostatics are included. The GROMOS package can be used to simulate the spectra, but only when the average geometries are combined with the Amber point charges: GAs. The local electric field created by adding Amber point charges on the snapshot Amber geometries generated in the absence of long-range electrostatics forms a good and time-saving approximation: AAp.

Second, calculations on 3me-indole in an electric field generated by the protein environment were shown to yield very reliable results for the positions of the lowest two near-UV absorption bands. There is a clear influence of the electric field on the higher of the two, which is related to the excited state dipole reached in this transition. Variations between the different tryptophan sites are, however, very small, and below the level of accuracy of the calculations. This confirms the experimental finding that the absorption maxima are, in this case, insensitive to the protein environment. Our absorption results also suggest that there might exist different rotameric manifolds of the tryptophan residues in barnase.

In addition, we have found that in one mutant counterions play a crucial role to prevent the protein from unfolding. Further investigation of the implied mechanism and its relation to trimer formation is required.

Materials and methods

Before calculating the spectra of the double-point mutants the most suitable MD package is selected, using indole as the chromophore. The results of this investigation are then used to calculate the tryptophan absorption spectra of three barnase double-point mutants. Small adjustments are necessary to complete this task.

Experimental results

Barnase is a small (110 AA; radius of 15 Å), single-domain protein with three α-helices and one β-sheet (Fig. 3 ▶). Single- (W35F, W71Y, W94F) and double-point mutants (W71YW94F, W35FW94F, W35FW71Y) were previously prepared and examined, providing detailed absorption spectra (Willaert et al. 1992; Fig. 2 ▶), and showing that the mutants stability and activity remained. These detailed spectra can only be obtained by making difference spectra between the double- and single-point mutant spectra, as difference spectra remove all but the required absorption/fluorescence features. Double- and single-point mutants are used to remove the effects of interacting tryptophans. The absorption maxima are determined using the automatic digitization option of the Ungraph 4.0 package (Biosoft) on the scanned spectra, as no digitized data were available. This package enables the user to introduce the digitized axes to a scanned spectrum, thus calibrating the scanned points to their original values.

Computational procedures

Quantum mechanical computations

Geometry optimizations of indole and 3me-indole are executed using Gaussian98 (Frisch et al. 1998), applying the DFT-formalism (Density Functional Theory; Hohenberg and Kohn 1964; Kohn and Sham 1965). The B3LYP (Becke 1993) functional is used in combination with a 6-31+G(d) basis set. Frequencies are determined at the same level of calculation, and are applied to determine transition structures and local minima. Both structures are depicted in Figure 1 ▶. Indole and 3me-indole are calculated (MOLCAS5.4; Andersson et al. 2002) at the complete active space self-consisting-field (CASSCF; Roos 1992) level of theory, employing an atomic natural orbital (ANO-S; Serrano-Andres and Roos 1996)-type basis set, contracted to (C,N 3s2p1d/H 2s1p). The basis set is supplemented with a 3s3p3d set of Rydberg-type functions (contracted from eight primitives of each angular momentum type), which are built following the standard procedure (Roos et al. 1996). The Rydberg function is placed at the charge centroid of the indole cation in its A″ ground state. The active space is built with 10 orbitals of a′ symmetry (nine valence π and one Rydberg) and no orbitals of a″ symmetry. Inclusion of one Rydberg function is necessary for the correct prediction of the first two valence excitation energies of both indole and 3me-indole. The use of more Rydberg functions is needed for the calculation of the first Ryd-berg excitation energy (the highest energy peak of the absorption spectrum; Serrano-Andres and Roos 1996). Because of the relative insensitivity of this peak to the local environment and the time-consuming nature of this extension we have not pursued this option.

A second-order perturbation formalism (CASPT2; Andersson et al. 1990) is applied to the wave function, obtained by averaging the first 10 roots from the CASSCF calculation, resulting in the first and second valence excitation energies. A more thorough quantum mechanical study of indole and 3me-indole is presented by Somers et al. (2004) and K.R.F Somers and A. Ceulemans (in prep.).

The effect of the protein environment on the chromophore spectrum is incorporated by adding point charges in the CASPT2 calculation. Charge and position of the point charges are provided by MD simulations, only using protein atoms as source. Point charges that are associated with the chromophore atoms are removed, as they are already represented by atoms in the CASPT2 calculation. The total charge is made neutral by placing the appropriate counter charges at the edges of a brick with 1.5 times the dimensions of the protein. The chromophore geometry is slightly different in both MD and QM techniques. Relocation of the chromophore, moving from MD to QM, is executed by placing atom C8 at a common position, by making atom C8−C9 a common axis, and by constructing atom C3−C8−C9 as a common plane.

Molecular dynamics computations

All calculations are performed on barnase double-point mutants. The barnase coordinates are obtained from the Protein Data Bank (1BNR; Bernstein et al. 1977). They are based on 2D-NMR measurements with water as a solvent (Bycroft et al. 1991). Simulated annealing was carried out during this structure determination using the CHARMM energy function. A total of 20 geometries was determined, which differ only in the terminal residues position, so only one geometry is chosen. Residues are replaced to create the mutants. All simulations are performed with the protein solvated in a slightly basic solution with neutral histidine residues.

In all cases the protein is solvated in a periodic box with explicit solvent (water). Shake is used in all packages, keeping the water molecule internal coordinates fixed and restraining the hydrogen atom bonds in the protein. The system is kept at a constant pressure of 1013 hPa, and at a constant temperature of 300 K. The pairlist is updated every 20 steps. The solvent is relaxed using MM, while the protein is kept frozen (10,000 steps). Next, the protein is relaxed with the solvent being frozen (10,000 steps). The solvent and solute are allowed to relax during 50,000 steps. After this relaxation the MD calculations are started. The system is heated from 0 K to 300 K in 10 ps, using a 2-fs time step, followed by a 200-ps equilibration, using 2-fs time steps. After this preparation the system runs for another 500 ps (2-fs time steps). Snapshots and averaged positions are taken every 10 ps, starting 200 ps after the preparation of the system. Data are collected over 100 ps to 200 ps, and are used to calculate the properties. The sampling procedure is depicted in Figure 4 ▶. Structure sampling uses the average geometry over a 10-ps time interval to calculate the desired properties, whereas property sampling uses the geometry at a specific time.

Evaluation of molecular dynamics packages

The ability to reproduce the maxima of the absorption spectra of proteins is examined for three MD packages using the absorption spectrum of indole in mutant W35FW94F as a reference: Am-ber5.0 (topology 96; Case et al. 1997), CHARMM-c27b1 (topology 22; Brooks et al. 1983), and GROMOS96 (force field 43A1; Gunsteren et al. 1996). Atom positions and point charges are used as provided by the packages. Combinations of atom positions and point charges from different packages are examined to compare the interchangeability of the geometries. Standard parameters are used with all three packages, and no counter ions are placed.

The Amber solvation box is a brick (55 × 61 × 69 Å) containing 5550 TIP3P (Transferable Intermolecular Potential 3 points; Jorgensen et al. 1983) water molecules. A first set of Amber calculations uses a group based cutoff of 8 Å without long-range electrostatics, whereas a second set uses the Particle Mesh Ewald method with a grid space of 1 Å, a spline order of 4, and a forced neutralization of the charge. The two sets of calculations are denoted as A and Al, respectively.

In CHARMM 3818 TIP3P, water molecules are placed in a cube-shaped box with dimension of 52 Å. As with Amber, two sets of calculations are performed, C and Cl. The first batch uses an atom-based cutoff of 8 Å without long-range electrostatics. The second set uses the extended electrostatics option, with the standard parameters to generate the long-range electrostatics (short distance cutoff of 8 Å, long-distance cutoff of 12 Å).

The GROMOS solvation box, on the contrary, is a truncated octahedron with dimension 62 Å, containing 3529 water molecules of the SPC (Simple Point Charge; Berendsen et al. 1981) type. The long-range electrostatics are mimicked using a Poison-Boltzmann reaction field, as described in the manual (short-distance cutoff of 8 Å, long-distance cutoff of 14 Å; Gunsteren et al. 1996).

Charge models for water molecules

Amber is selected for the further calculations on the barnase double-point mutants. The simulation scheme is kept identical, except for some minor parameter adjustments and the inclusion of counterions in the MD simulation (using the addions routine as implemented in Amber). The counterions are used to neutralize the total charge of the system and to form some necessary salt bridges. An improved stability of the system is reached by including two chlorine anions. Exclusion of counterions leads to the unfolding of mutant W71YW94F. Some other small adjustments include the changing of the time constant for the heat bath coupling to 2 ps, and the introduction of a 2-ps time interval for the pressure relaxation. These adjustments are necessary to maintain the globular shape of the mutants, which is predicted by the experiment (Willaert et al. 1992). The use of the group-based cutoff made it possible to leave out long-range electrostatics as shown by the evaluation of the molecular dynamic packages. This approximation is necessary to reduce the calculation time.

Point charges and positions are obtained from these simulations to form the charge cloud that is placed around the 3me-indole chromophore.

The charge of the counterions is included in the calculation of the mutants’ excitation spectra. The accessibility of the solvent to the chromophore (Loewenthal et al. 1991) in mutant W35FW71Y and W71YW94F made it necessary to include water in all the excitation calculations. Calculations without the water molecules are also included to investigate the extent of the water presence. The effect of the inclusion of water on the buried chromophore of mutant W35FW94F is studied with a specific set of point charges. These point charges are derived from the previous “all-inclusive” (containing water molecules, counterions, and the protein) charge clouds, but the protein representing charges are removed.

Acknowledgments

Financial support from the Flemish Government through the Concerted Action Scheme (Ministerie van het Wetenschapsbeleid) and from the National Science Foundation (FWO) is gratefully acknowledged. Ken Somers is indebted to the Flemish institute for the promotion of science-technology research in industry (IWT) for a specialization grant.

The publication costs of this article were defrayed in part by payment of page charges. This article must therefore be hereby marked “advertisement” in accordance with 18 USC section 1734 solely to indicate this fact.

Article and publication are at http://www.proteinscience.org/cgi/doi/10.1110/ps.04652804.

Supplemental material: see www.proteinscience.org

References

  1. Andersson, K., Malmqvist, P.-Å., Roos, B.O., Sadlej, A.J., and Wolinski, K. 1990. Second-order perturbation-theory with a CASSCF reference function. J. Phys. Chem. 94 5483–5488. [Google Scholar]
  2. Andersson, K., Blomberg., M.R.A., Fülscher, M.P., Karlström, G., Lindh, R., Malmqvist, P.-Å., Neogrády, P., Olsen, J., Roos, B.O., Sadlej, A.J., et al. 1997. Molcas version 4. Lund University, Sweden.
  3. Andersson, K., Barysz, M., Bernhardsson, A., Blomberg, M.R.A., Cooper, D.L., Fülscher, M.P., de Graaf, C., Hess, B.A., Karlström, G., Lindh, R., et al. 2002. Molcas version 5.4. Lund University, Sweden.
  4. Arcus, V.L., Vuilleumier, S., Freund, S.M.V., Bycroft, M., and Fersht, A.R. 1995. A comparison of the pH, urea and temperature-denatured states of barnase by heteronuclear nmr: Implications for the initiation of protein folding. J. Mol. Biol. 254 305–321. [DOI] [PubMed] [Google Scholar]
  5. Bayly, C.I., Cieplak, P., Cornell, W.D., and Kollman, P.A. 1993. A well-behaved electrostatic potential based method using charge restraints for deriving atomic charges: The RESP model. J. Phys. Chem. 97 10269–10280. [Google Scholar]
  6. Becke, A.D. 1993. Density-functional thermochemistry. 3. The role of exact exchange. J. Chem. Phys. 98 5648–5652. [Google Scholar]
  7. Berendsen, H.J.C., Postma, J.P.M., van Gunsteren, W.F., and Hermans, J. 1981. Interaction models for water in relation to protein hydration. In Intermolecular forces (ed. B. Pullman) pp. 331–342. Reidel, Dordrecht, The Netherlands.
  8. Bernstein, F.C., Koetzle, T.F., Williams, G.J., Meyer Jr., E.E., Brice, M.D., Rodgers, J.R., Kennard, O., Shimanouchi, T., and Tasumi, M. 1977. The protein data bank: A computer-based archival file for macromolecular structures. J. Mol. Biol. 112 535–542. [DOI] [PubMed] [Google Scholar]
  9. Brooks, B.R., Bruccoleri, R.E., Olafson, B.D., States, D.J., Swaminathan, S., and Karplus, M. 1983. CHARMM: A program for macromolecular energy, minimization, and dynamics calculations. J. Comp. Chem. 4 187–217. [Google Scholar]
  10. Bycroft, M., Sheppard, R.N., Tat-Kwong Lau, F., and Fersht, A.R. 1990. Sequential assignment of the 1H nuclear magnetic resonance spectrum of barnase. Biochemistry 29 7425–7432. [DOI] [PubMed] [Google Scholar]
  11. Bycroft, M., Ludvingen, S., Fersht, A.R., and Poulsen, F.M. 1991. Determination of the three-dimensional solution structure of barnase using nmr spectroscopy. Biochemistry 30 8697–8701. [DOI] [PubMed] [Google Scholar]
  12. Callis, P.R. 1991. Molecular orbital theory of the 1Lb and 1La states of indole. J. Chem. Phys. 95 4320–4240. [Google Scholar]
  13. ———. 1997. 1La and 1Lb transitions of tryptophan: Applications of theory and experimental observations to fluorescence of proteins. Methods Enzymol. 278 113–150. [DOI] [PubMed] [Google Scholar]
  14. Callis, P.R. and Burgess, B.K. 1997. Tryptophan fluorescence shifts in proteins from hybrid simulations: An electrostatic approach. J. Phys. Chem. 101 9429–9432. [Google Scholar]
  15. Case, D.A., Pearlman, D.A., Caldwell, J.W., Cheatham, T.E.I., Ross, W.S., Simmerling, C.L., Darden, T.A., Merz, K.M., Stanton, R.V., Cheng, A.L., et al. 1997. Amber 5. University of California, San Francisco, CA.
  16. Cieplak, P., Cornell, W.D., Bayly, C., and Kollman, P.A. 1995. Application of the multimolecule and multiconformational RESP methodology to biopolymers: Charge derivation for DNA, RNA, and proteins. J. Comp. Chem. 16 1357–1377. [Google Scholar]
  17. De Beuckeleer, K. 1998. “Physicochemical study of barnase and its tryptophane mutants.” Ph.D. thesis, Katholieke Universiteit Leuven, Leuven, Belgium.
  18. De Beuckeleer, K., Volckaert, G., and Engelborghs, Y. 1999. Time resolved fluorescence and phosphorescence properties of the individual tryptophan residues of barnase: Evidence for protein–protein interactions. Proteins 36 42–53. [PubMed] [Google Scholar]
  19. De Smet, J., De Maeyer, M., Hazes, B., and Lasters, I. 1992. The dead-end elimination theorem and its use in protein side-chain positioning. Nature 356 539–542. [DOI] [PubMed] [Google Scholar]
  20. Demchenko, A.P. 1986. Ultraviolet spectroscopy of proteins. Springer, Berlin.
  21. Demmer, D.R., Leach, G.W., and Wallace, S.C. 1994. 1La-1Lb coupling in the excited state of 3-methylindole and its polar clusters. J. Phys. Chem. 98 12834–12843. [Google Scholar]
  22. Frisch, M.J., Trucks, G.W., Schlegel, H.B., Scuseria, G.E., Robb, M.A., Cheeseman, J.R., Zakrzewski, V.G., Montgomery, J.A., Stratmann, R.E., Burant, J.C., et al. 1998. Gaussian 98 (revision a.9). Gaussian, Inc., Pittsburgh, PA.
  23. Hellings, M., De Maeyer, M., Verheyden, S., Hao, Q., Van Damme, E.J.M., Peumans, W.J., and Engelborghs, Y. 2003. The dead-end elimination method, trytophan rotamers and fluorescence lifetimes. Biophys. J. 85 1894–1902. [DOI] [PMC free article] [PubMed] [Google Scholar]
  24. Hohenberg, P. and Kohn, W. 1964. Inhomogenous electron gas. Phys. Rev. 136 B864. [Google Scholar]
  25. Hollas, J.M. 1963. Vapour-phase ultra-violet absorption spectra of indene, indole, coumarone and thionaphthene. Spectrochim. Acta 19 753–767. [Google Scholar]
  26. Horovitz, A. and Fersht, A.R. 1992. Co-operative interactions during protein folding. J. Mol. Biol. 224 733–740. [DOI] [PubMed] [Google Scholar]
  27. Jorgensen, W.L., Chandrasekhar, J., Madura, J., Impey, R.W., and Klein, M.L. 1983. Comparison of simple potential functions for simulating liquid water. J. Chem. Phys. 79 926–935. [Google Scholar]
  28. Kohn, W. and Sham, L.J. 1965. Self-consistent equations including exchange and correlation effects. Phys. Rev. 140 A1133. [Google Scholar]
  29. Konev, S.V. 1967. Fluorescence and phosphorescence of proteins and nucleic acids. Plenum Press, New York.
  30. Lami, H. 1977. Presence of a low-lying “Rydberg” band in the vapour phase absorption spectra of indole and 1-methylindole. Chem. Phys. Lett. 48 447–450. [Google Scholar]
  31. Loewenthal, R., Sancho, J., and Fersht, A.R. 1991. Fluorescence spectrum of barnase: Contributions of three tryptophan residues and a histidine related pH dependence. Biochemistry 30 6775–6779. [DOI] [PubMed] [Google Scholar]
  32. Roos, B.O. 1992. Lecture notes in chemistry 58. In European summerschool in quantum chemistry (ed. B.O. Roos). Springer-Verlag, Berlin.
  33. Roos, B.O., Andersson, K., Fülscher, M.P., Malmqvist, P.-A., Serrano-Andrés, L., Pierloot, K., and Merchán, M. 1996. Multiconfigurational perturbation theory: Applications in electronic spectroscopy (eds. I. Prigogine and S.A. Rice). Adv. Chem. Phys. 93 219–331. [Google Scholar]
  34. Serrano-Andrés, L. and Roos, B.O. 1996. Theoretical study of the absorption and emission spectra of indole in the gas phase and in a solvent. J. Am. Chem. Soc. 118 185–195. [Google Scholar]
  35. Short, K.W., Wagner, V., and Callis, P.R. 1999. Simulations of tryptophan fluorescence in proteins. II. Comparison of CHARMM and CVFF force fields. Biophys. J. 76 A261. [Google Scholar]
  36. Somers, K.R.F., Kryachko, E.S., and Ceulemans, A. 2004. Theoretical study of indole: Protonation, indolyl radical, tautomerism of indole, and its interaction with water. Chem. Phys. 301 61–79. [Google Scholar]
  37. Strickland, E.H., Horwitz, J., and Billups, C. 1970. Near-ultraviolet absorption bands of tryptophan. Studies using indole and 3-methylindole as models. Biochemistry 9 4914–4921. [DOI] [PubMed] [Google Scholar]
  38. Szabo, A.G. and Rayner, D.M. 1980. Fluorescence decay of tryptophan conformers in aqueous solution. J. Am. Chem. Soc. 102 554–563. [Google Scholar]
  39. Toptygin, D. and Brand, L. 2000. Spectrally- and time-resolved fluorescence emission of indole during solvent relaxation: A quantative model. Chem. Phys. Lett. 322 496–502. [Google Scholar]
  40. Valeur, B. and Weber, G. 1977. Resolution of the fluorescence excitation spectrum of indole into the 1La and 1Lb excitation bands. Photochem. Photobiol. 25 441–444. [DOI] [PubMed] [Google Scholar]
  41. van Gunsteren, W.F., Billeter, S.R., Eising, A.A., Hünenberger, P.H., Krüger, P., Mark, A.E., Scott, W.R.P., and Tironi, I.G. 1996. Biomolecular simulation: The GROMOS96 manual and user guide. Vdf Hochschulverlag AG an der ETH Zürich, Zürich.
  42. Vivian, J.T. and Callis, P.R. 2001. Mechanism of tryptophan fluorescence shifts in proteins. Biophys. J. 80 2093–2109. [DOI] [PMC free article] [PubMed] [Google Scholar]
  43. Willaert, K., Loewenthal, R., Sancho, J., Froeyen, M., Fersht, A., and Engelborghs, Y. 1992. Determination of the excited-state lifetimes of the tryptophan residues in barnase via multifrequency phase fluometry of tryptophan mutants. Biochemistry 31 711–716. [DOI] [PubMed] [Google Scholar]
  44. York, D.M., Darden, T.A., and Pedersen, L.G. 1993. The effect of long-range electrostatic interactions in simulations of macromolecular crystals: A comparison of Ewald and truncated list methods. J. Chem. Phys. 99 8345–8348. [Google Scholar]
  45. Zegers, I., Deswarte, J., and Wyns, L. 1999. Trimeric domain-swapped barnase. Proc. Natl. Acad. Sci. 96 818–822. [DOI] [PMC free article] [PubMed] [Google Scholar]

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