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* Laboratory of Biomolecular Dynamics, Catholic University of Leuven, Heverlee, Belgium;
Laboratory of Biomolecular Modelling, Catholic University of Leuven, Heverlee, Belgium;
Institute of Biosciences and Technology, Texas A&M University, System Health Sciences Center, Houston, Texas;
Department of Molecular Biotechnology, University of Ghent, Ghent, Belgium; and ¶ Laboratory of Phytopathology and Plant Protection, Catholic University of Leuven, Heverlee, Belgium
Correspondence: Address reprint requests to Dr. Yves Engelborghs, Katholieke Universiteit Leuven, Laboratory of Biomolecular Dynamics, Celestijnenlaan 200D, 3001 Heverlee, Belgium. Tel.: 321-632-7160; Fax: 321-632-7974; E-mail: yves.engelborghs{at}fys.kuleuven.ac.be; or Dr. Marc De Maeyer, Katholieke Universiteit Leuven, Laboratory of Biomolecular Modelling, Celestijnenlaan 200D, 3001 Heverlee, Belgium. Tel.: 321-632-7521; Fax: 321-632-7974; E-mail: Marc.DeMaeyer{at}fys.kuleuven.ac.be.
| ABSTRACT |
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3 atom to the carbonyl carbon of the peptide bond. Therefore it is expected that a shorter [C
3-C=O] distance leads to a shorter lifetime as observed for these ten rotamers. Applying the same rule to the other 30 lifetimes, a link with their corresponding rotameric state could also be made. In agreement with the theory of Marcus and Sutin, the nonradiative rate constant shows an exponential relationship with the [C
3-C=O] distance for the 40 datapoints. | INTRODUCTION |
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3 atom of tryptophan as donor (Sillen et al., 2000
Sillen et al. (2000)
presented a method that allowed the calculation of the lifetimes of tryptophan residues on the basis of spectral and structural data. In their article the authors determined an exponential relation between the nonradiative rate constant knr and the distance between the indole C
3 atom and the carbonyl carbon of the peptide bond. This suggests a mechanism of electron transfer as the main determinant for the value of the nonradiative rate constant. This relation was based on the equation derived for electron transfer by Marcus and Sutin (1985)
. The authors used a molecular dynamics simulation map to identify the different rotamers of tryptophan. Further exploration of this method has to be done.
Here we report a new method to identify the different microconformations of tryptophan together with a method to link the rotamers with their respective lifetime on the basis of the correlation between the values of the rate constants for quenching with an external quencher (kq) and the rotamer surface exposed to the solvent. In this study we use the dead-end elimination (DEE) method to determine the possible rotamers of tryptophan. This method is able to find the global optimal arrangement of a collection of side chains attached to a fixed main-chain structure (De Maeyer et al., 2000
). The DEE method detects and eliminates iteratively those rotamers that cannot be members of the Global Minimum Energy Conformation (GMEC; Desmet et al., 1992
). The rotamer elimination occurs on the basis of energy criteria balancing rotamers against each other by comparing their main-chain interaction energy and a lower or higher limit for their interactions with the other side chains of the protein (De Maeyer et al., 2000
). In this study the DEE method is applied on eight different proteins, whose single tryptophan mutants are available. The fact that the tryptophans of the eight proteins are buried inside the molecule strengthens the use of the DEE method to determine the possible rotamers of the Trp-residue. Indeed, it has been proven that the DEE method is quite accurate for buried residues (De Maeyer et al., 1997
). The time-resolved fluorescence properties of the single tryptophan mutants of seven of these proteins have already been extensively investigated. These proteins, their tryptophan residues and the reference that describes them are listed in Table 1.
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| MATERIALS AND METHODS |
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Protein purification
Trichosanthin was essentially purified as described previously (Zhang et al., 1993
). The purity of the protein was examined by SDS-PAGE. The activity of the protein was determined by the method of Endo et al. (1987)
by running the targeted RNA on a 1,2% agarose gel.
Multifrequency phase fluorometry
Fluorescence lifetimes were measured using automatic multifrequency phase fluorometry between 1.6 MHz and 1 GHz as described previously (Sillen et al., 2000
). NATA in ddH2O with a fluorescence lifetime of 3.059 ns (at 22°C) was used as reference. Data analysis was performed using a nonlinear least-squares algorithm (Bevington, 1969
). Measurements performed at different emission wavelengths (320380 nm) were analyzed simultaneously with global analysis to improve the recovery of lifetimes and amplitude fractions (Beechem et al., 1983
). The data were fitted using the modified Levenberg-Marquardt algorithm (More and Sorensen, 1983
) assuming that the fluorescence lifetimes are independent of the wavelength. This procedure allows the recovery of the fractional intensities with good accuracy.
Fluorescence quenching
The quenching of trichosanthin with increasing amounts of quencher was performed by adding aliquots of a freshly prepared 1-M acrylamide stock solution to the cuvette after which the changes in the fluorescence lifetimes and corresponding amplitude fractions were monitored. Fluorescence lifetime as function of quencher concentration [Q] was fitted by the classical Stern-Volmer equation,
![]() | (1) |
0 (
) is the lifetime in absence (presence) of quencher.
Starting structures
For each protein a full hydrogen model and energy minimized x-ray structure was used as the starting structure. For each structure only the monomer is taken into account. Some residues like Cys, HisH+, Tyr, and Cystine are able to strongly quench fluorescence (Vos and Engelborghs, 1994
; Chen and Barkley, 1998
). Fluorescence data are available for single Trp-mutants of the eight proteins in which the neighboring quenching residues are mutated in nonquenching residues. Because we only take electron transfer to the peptide carbonyl into account, it is necessary to mutate in silico these neighboring quenching residues in the starting structures, so that it is possible to link the modeled structures with the experimental data. Table 1 shows the PDB:IDs of the starting structures and the mutations that have been made.
Dead-end elimination (DEE) method
To determine the possible conformations of tryptophan we used the dead-end elimination method. This method allows the determination of the GMEC of a side-chain collection in a fixed backbone configuration, using a side-chain rotamer library (Desmet et al., 1992
). Tryptophan was placed in 1296 different starting values (for each
-angle every 10°). Throughout this article,
1 is defined by the internal rotation around bond C
-Cß and
2 by the bond Cß-C
. Within a shell of 8 Å around the fixed tryptophan, all side-chain residues were allowed to evolve. For each of the starting structures the GMEC was calculated with DEE. The backbone is kept fixed during the calculation. The rotamer library we used was an enhanced version of the libraries of De Maeyer et al. (1997)
. The energy parameters are based on the CHARMM force field (Brooks et al., 1983
) but with reduced Van der Waals radii to account for small backbone movement (Gordon et al., 1999
). For each GMEC, the nonbonded energy of tryptophan (ETrpnb) in relation to the remaining structure of the protein and the total nonbonded energy (Etotnb) of the whole modeled protein was computed. The distance between the indole C
3 atom and the carbonyl carbon of the peptide bond is also determined. The DEE algorithm has been implemented in the Brugel package (Delhaise et al., 1984
). All calculations were performed on a single processor of a 4-processor Silicon Graphics Origin 2100 (R10000, 250 MHz).
Solvent-accessible area calculation
The solvent-accessible surfaces were calculated with the Survol option in the Brugel software package (Delhaise et al., 1984
), using a probe sphere with a standard radius of 1.4 Å (Alard et and Wodak, 1991
).
Determination of the radiative rate constant
Quantum yields were determined relative to tryptophan in water according to the method of Parker and Rees (1960)
:
![]() | (2) |
I is the integrated intensity over the wavelength region 300450 nm. A is the absorbance at 295 nm, and the quantum yield QTrp for tryptophan in water is taken as 0.14 (Kirby and Steiner, 1970
The average radiative rate constant is calculated by dividing the quantum yield by a wavelength-independent amplitude average lifetime (Sillen and Engelborghs, 1998
),
![]() | (3) |

i
i the average lifetime,
i is a wavelength-independent amplitude fraction and is defined as (Sillen and Engelborghs, 1998
![]() | (4) |
) of each lifetime is integrated over the wavelength region 300450 nm and then normalized.
Calculation of the nonradiative rate constant
The nonradiative rate constant (knr) is calculated as
![]() | (5) |
is the fluorescence lifetime. | RESULTS |
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3 atom and the C atom of the peptide carbonyl is calculated. Table 2 shows the number and range of the rotamer clusters found for each modeled structure together with their mean distance between the indole C
3 atom and the carbonyl carbon of the peptide bond. In most cases we find for tryptophan an equal number of rotamer clusters and fluorescence lifetimes.
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1 and
2, respectively. The value of kq for the short lifetime component is 10-fold larger than that of the longer one, indicating that the short lifetime component is more solvent-accessible. For a fully exposed tryptophan residue (e.g., free Trp in water), kq can be as high as 6.4 M-1 ns-1 (Vos et al., 1995
1 and
2 is shown in Table 4 and remains practically constant during the quenching experiment.
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| DISCUSSION |
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![]() | (6) |
![]() |
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![]() | (7) |
When we fill in the results of the fluorescence lifetime measurements of trichosanthin with no acrylamide present, we find a value of 0.2926 for (kA0 + kAB). If Hudson's model would be applicable on TCS, then adding an external quencher Qext, e.g., acrylamide would change the ratio of the amplitudes, as in
![]() | (8) |
The quenching experiments we performed provide us with values for k1, k2, and kqA. Together with the value of 0.2926 for (kA0 + kAB), we can calculate the ratio of the amplitudes for each concentration of acrylamide, in which case Hudson's model would be valid for TCS. These values are shown in Table 4. We clearly see that the ratio of the amplitudes should raise upon addition of acrylamide. However, in our experiments the ratio of the amplitudes remains practically constant (see Table 4). We therefore can exclude reversible electron transfer in this case. We can explain the results by the existence of different rotamers of Trp, where the amplitudes reflect populations of different rotamers. These ground-state rotamers are the result from rotations about the C
-Cß and Cß-C
bonds. Each rotamer has a specific local environment with different distances and/or orientations to quencher groups, yielding distinct nonradiative decay rates. Since the Trp fluorescence is not damaged upon radiation, electron transfer has to be reversible. The fact that the Hudson model is not applicable for this protein indicates that the reverse reaction is much slower than the nanosecond timescale. Usually reverse electron transfer reactions are orders-of-magnitude smaller than forward reactions (Mataga et al., 1988a
,b
; Paddon-Row et al.,1988
). For the other proteins we did not eliminate the possibility of fast reversible electron transfer, but on the basis of the reasoning above we think it is very unlikely.
Except for the case of the two tryptophans in NSCP, the number of rotamer clusters found for a tryptophan residue is equal to the number of Trp fluorescence lifetimes. The challenge is to find a procedure to link the rotamer clusters with their respective lifetimes. In this case we are able to link 10 lifetimes with 10 rotamers. To link to the rotamer clusters with their fluorescence lifetimes, we calculated the accessible surface area of the clusters and compared them with the values of the bimolecular quenching constants. In the case of trichosanthin, we find two rotamer clusters, one with an ASA of 13.5 Å2 and another with an ASA of 3.0 Å2, as shown in Table 6. The quenching experiments with acrylamide yield two bimolecular quenching constants and indicate that the short lifetime is more solvent-accessible. According to these results the cluster with the highest ASA should be linked with the short fluorescence lifetime of tryptophan. If we compare the accessible areas of the tryptophans of Colicin A (Table 6) with the bimolecular quenching constants found in quenching experiments with acrylamide of these tryptophans (Table 3, Vos et al., 1995
) we see the same similarity as in the case of trichosanthin. In this set of 10 rotamers we also observed that the short lifetimes correlate with a short distance between C
3 and the peptide carbonyl C atom, in agreement with the mechanism of electron transfer proposed by Marcus and Sutin. Because of this observed relation, we linked the 40 found rotamer clusters for Trp of the eight proteins with their respectable lifetimes in the same way. In the future, additional quenching experiments of those proteins where up to now no acrylamide quenching has been performed, can further confirm the match between both methods.
Recently, the quantum yield was correlated to the environment of the tryptophan in the protein, i.e., the electric field, by using quantum mechanical calculations (Callis and Vivian, 2003
). Although these calculations provide the most general answer, we try here to find out if the exponential relation for electron transfer, as proposed by Marcus and Sutin (1985)
, and as attempted before (Sillen et al., 2000
), can be applied. It should be noted that the tryptophan residues we study in this sample are selected for the absence of special features like quenching groups, charge, stacked, or perpendicular aromatic groups.
The radiative rate constant is experimentally determined for all the proteins from the quantum yield and the average fluorescence lifetime. The knowledge of both the fluorescence lifetime and radiative rate constant for each rotamer cluster makes it possible to calculate the nonradiative rate constant for each rotamer cluster with Eq. 5.
These nonradiative rate constants are fitted to their respective distance between C
3 of Trp and the carbonyl carbon of the peptide bond by the following equation, derived for electron transfer by Marcus and Sutin:
![]() | (9) |
![]() | (10) |
![]() | (11) |
the standard deviation of the fluorescence lifetime
and Skr the standard deviation of the radiative rate constant kr. This fit yields a value of 5.046 ± 0.335 ns-1 for k0 and a value of 1.497 ± 0.074 Å-1 for ß and is shown in Fig. 4.
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1.9 Å-1 in agreement with Sillen et al. (2000)
3.7 ns-1. Adams et al. (2002)
For Ribonuclease T1, using molecular mechanics (Ababou and Bombarda, 2001
) only identified one tryptophan rotamer and therefore these authors rejected the rotamer model. This in contrast with the two rotamers revealed here by the DEE method. Contrary to other methods like energy minimization, molecular mechanics, or molecular dynamics, the DEE method explores the complete conformational space and detects the GMEC. The classic method of an energy map cannot explore all possible rotamer combinations by brute force. As an example, a Trp in contact with six other residues (having only two rotatable
-angles) and allowing
-angle deviations in steps of 10° explodes into 6.1021 possible conformations. If one rotamer calculation takes 1 ms, the total exploration of the conformational space would require 2.1011 years. In addition, molecular dynamics runs are in general too short to be sure that all possible energy minima are visited. If we compare the energy minima we find with DEE for Trp57 in NSCP with those determined by a molecular dynamics simulation performed by Sillen et al. (2000)
, we can see that the two most populated conformations are found with both techniques.
| CONCLUSION |
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3-C=O distance, suggesting the electron transfer mechanism. Therefore the same correlation was used to identify the rotamers of 30 additional lifetimes. The whole set of 40 datapoints allows us to determine a good average of k0 and ß. Only for the tryptophans of NSCP is an additional lifetime found, which might be an indication for additional sources of heterogeneity. | ACKNOWLEDGEMENTS |
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Submitted on November 17, 2002; accepted for publication May 30, 2003.
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