PEDS Advance Access originally published online on August 23, 2004
Protein Engineering Design and Selection 2004 17(7):557-563; doi:10.1093/protein/gzh066
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COMMUNICATION |
Altered ionization of the B13 Glu in insulin B9 and B10 mutants: a computational analysis
1Department of Biology and 4Structural Biology Laboratory, Department of Chemistry, University of York, York YO10 5YW, 2Department of Biomolecular Sciences, UMIST, P.O. Box 88, Manchester M60 1QD, 5Protein Structure Division, NIMR, The Ridgeway, Mill Hill, London NW7 1AA, UK and 6Bioinformatics Institute, 30 Biopolis Way, #07-01 Matrix, Singapore 138671
3 To whom correspondence should be addressed (at the UMIST address for R.B.G.). E-mail: r.greaves{at}umist.ac.uk or chandra{at}bill.a-star.edu.sg
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Abstract |
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An experimentally determined pKa change of +2.50 units has been reported for the B13 Glu residue in a dimeric B9 Ser
Asp insulin mutant relative to the native dimer. Poisson–Boltzmann electrostatics-based pKa calculations were performed to probe the effect of the B9 Ser Asp and B10 His Asp mutations on aggregation and the ionization behaviour of the B13 carboxylate. The method produced shifts of +2.64 and +2.45 units for the pKa shift of the two B13 residues in the B9 mutant dimer relative to the wild-type dimer, which is in good agreement with the experimental value (<6% error). The calculations also suggest that the reason neither mutant insulin can aggregate into hexamers is the resultant crowding of negatively charged groups in the central solvent channel on hexamer formation. In the wild-type insulin, binding of zinc ions by B10 His overcomes this problem, whereas in the B10 mutant this possibility is ruled out by the absence of the zinc binding site. A series of mutations are predicted to stabilize the medically relevant, monomeric form of insulin.
Keywords: B13 Glu/insulin/mutants/pKa/Poisson–Boltzmann electrostatics
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Introduction |
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In the crystal structure of 2Zn insulin (Baker et al., 1988
), it can be seen that the side chain of B13 Glu lies on the surface of the monomer and is solvent exposed (Figure 1a). During aggregation to the dimeric state, the two large hydrophobic faces of the monomers come together (Figure 1b) in an entropically favourable association (Tidor and Karplus, 1994). This dimerization is strengthened by the formation of four hydrogen bonds between the ß-strands of the monomers. Dimerization also brings the two ionizable B13 Glu residues of the associated monomers into close proximity. Aggregation of dimers to form hexamers occurs by burial of further hydrophobic regions and through the binding of metal ions (Figure 1c). In 2Zn insulin, two zinc ions bind on the threefold axis which runs down the central solvent channel of the hexamer. The binding sites are formed by three symmetry-related B10 His side chains, the octahedral coordination at each site being completed by solvent molecules. The binding of zinc ions in this manner compensates the crowding of the six charged B13 Glu residues in the hexamer centre. Zinc-free hexamers are not known to exist for insulins with an acidic group at residue B13. However, zinc-free hexamers have been crystallized for a B13 Glu Gln mutant insulin (Bentley et al., 1992). The solvent-exposed surface areas of residues B9, B10 and B13 are as follows: 78.2, 120.1 and 99.1 Å2 in monomer, 30.8, 81.2 and 46.5 Å2 in dimer and 11.2, 42.2 and 38.8 Å2 in hexamer; the decreases of up to 7-fold clearly reflect the gradual shielding from solvent as the aggregation state increases.
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The use of insulin as a treatment against insulin-dependent diabetes mellitus has led to the search for faster acting insulins. Since the active form of the hormone is the monomer, this has led to protein engineering insulins with a tendency to overcome sluggish absorption (arising mainly from a tendency to aggregate) and at the same time preserving stability in the therapeutic preparations. Two strategies commonly employed to produce insulins with reduced association are (a) abolition of metal binding at the hexamer centre and (b) charge repulsion at the monomer–monomer interface (Brange et al., 1990
). Two target residues B9 Ser and B10 His lie approximately one turn of helix away from B13 at the molecular interface. Mutation of B10 His Asp abolishes metal binding at this site and the mutant insulin is essentially dimeric at physiological concentrations. However, metal binding can occur at a new site, B5 His, and at high insulin concentrations dodecamers can form (Turkenberg, 1992). Mutation at B9 Ser Asp was aimed at reducing association due to charge repulsions because in a dimer, two B9 and two B13 are in close proximity and in a hexamer 12 negatively charged groups would be brought together. This insulin has been reported as monomeric at moderately high concentrations and is possibly monomeric at physiological concentrations (Brange et al., 1988; Kaarsholm et al., 1990). The structure of B9 Ser Asp insulin in solution has been reported to be very like that of the wild-type insulin crystal (Kristensen et al., 1991; Jorgenssen et al., 1992). Potentiometric titration studies have indicated that the mutation at B9 Ser causes an increase of 2.47 units in the pKa of B13 Glu relative to the value observed for the wild-type insulin in a dimeric aggregation state (Kaarsholm et al., 1990).
This paper sets out to examine this experimental observation using Poisson–Boltzmann electrostatics calculations and also to probe the effect of the two mutations in different aggregation states on B13 Glu ionization. Our intention is to reproduce an experimentally observed shift and then to use the ‘benchmarked’ parameters to assess mutants that have been experimentally characterized; we then hope to predict mutations that will be useful in the design of therapeutically useful insulins. We have found such calculations to be very useful in computing a subset of protein properties, notably relative binding energetics and shifts in titration characteristics (Plou et al., 1996; Gibas et al., 2000; Hussain et al., 2003). Of course, it has to be borne in mind that no one method of computing pKa values in proteins can claim to reproduce all the titration characteristics of proteins simultaneously with accuracy and such approaches are fraught with difficulties and limitations (see, for example, Schutz and Warshel, 2001); however, limited success can be achieved with careful model building (Plou et al., 1996; Mehler et al., 2002).
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Methods |
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All the models prepared were based on the X-ray crystal structure of 2Zn insulin (RCSB entry 4ins; Baker et al., 1988
). The wild-type insulin dimer model was taken directly from these coordinates with the solvent and zinc ions removed. The starting structure was prepared according to methods outlined elsewhere (Plou et al., 1996). The monomer model was then simply the A and B chains of molecule 2 in the dimer. The hexamer model was prepared by generating symmetry copies of the dimer around the threefold axis using the CCP4 program GENSYM (CCP4, 1994). The zinc atoms were still missing and a second hexamer model was constructed with zinc ions present. Acidic residues (Asp and Glu) were treated as negatively charged and the basic groups (Arg and Lys) as positively charged. The ionization behaviour of all the titratable groups in each model (a total of 16 titratable sites in each monomer) was computed.
Models for the mutant insulins were created by mutating the appropriate residues in each monomer using Quanta (Accelrys, San Diego, CA). The conformations of the mutated side chains were investigated using a rigid body mapping. The 
1 ands 2 conformations were set at the low-energy conformations determined from the mapping. The mutated residues were all modelled as charged aspartate groups. All models were then briefly energy minimized to relieve any close contacts present in the structure.
The method used for calculating pKa shifts has been outlined by several groups (see, for example, Bashford and Karplus, 1990; Yang et al., 1993; Antosiewicz et al., 1994; Demchuk and Wade, 1996; Schutz and Warshel, 2001) and hence will not be mentioned here. For our work, the point charges and van der Waals radii used in the models are those of the AMBER/OPLS parameter set (Weiner et al., 1984). Parameters for the Zn2+ ion were derived from the CHARMM22 parameter set (Brooks et al., 1983; Neria et al., 1996). The solvent dielectric was set to 78 and the protein dielectric was taken to be 8.5; the reason for this choice of the protein dielectric is outlined later. Calculations were performed at 293 K using the methodology of Yang et al. (1993). The interaction energies used to design the mutants were computed by calculating the interactions between the charges on each atom of one monomer (of the dimer) by the potential generated at that site from the charge distribution on the other monomer (of the dimer). The program UHBD (version 6.1) (Davis et al., 1991; Madura et al., 1995; Accelrys, San Diego, CA) was used to perform these calculations using protocols employed previously (Plou et al., 1996) and the ZRF methodology of Demchuk and Wade (1996). The ZRF methodology utilizes a modified OPLS parameter set which is calculated so as to eliminate the need to construct theoretical hydrogen atom positions which are a source of potential inaccuracy in such calculations. Therefore, hydrogen bond network optimization such as that performed by Nielsen and Vriend (2001) was not performed. However, the rotameric states of Asn, His and Gln residues were assessed visually using Quanta in each model and subsequently assessed as being the minimum energy rotamer (Plou et al., 1996) prior to performing the calculations. The pKa calculations employed the multiple titratable site cluster methodology that is implemented in UHBD, this being the method of Gilson (Gilson, 1993; Antosiewicz et al., 1994) in order to calculate the titration curves for the model systems.
To examine the influence of protein fluctuations/conformational flexibility on the computed pKa shifts, several calculations were performed at set time points in a molecular dynamics trajectory. Each model used for the calculation of pKas was subjected to a 50 ps equilibration followed by 100 ps of restrained Langevin molecular dynamics. The production trajectory was sampled at 10 ps intervals and the structures derived were briefly minimized using harmonic restraints on heavy atoms prior to being used as the starting point for subsequent pKa calculations. Statistics were collected for each trajectory and the percentage variance for each ionizable group was calculated.
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Results and discussion |
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The computed pKa shifts for each B13 side chain are shown in Table I.
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In the monomeric form, the distances between the B9 and B13 of opposing monomers and between B10 and B13 are 6.7 and 7.4 Å, respectively. Additionally, this region is well exposed to solvent and the charge screening is reflected in the small influence of the mutations at the two sites (B9 and B10) on the shift in pKa of B13. In contrast, in the dimer, the computed pKa shift of the B13 in B9 Asp relative to the wild-type is +2.64 units, which is within 6% of the experimental value of 2.5 units (Kaarlsholm et al., 1990
). This large shift is not surprising since in the dimer, the separation between B9 and B13 of the two different molecules is only 4.2 Å and additionally a negative charge is being introduced at B9. In contrast, B10 is 7.8 Å away from B13 of the adjacent monomer and hence mutation at B10 unsurprisingly causes a more modest shift in pKa.
The theoretical cases of a zinc-free and a 2Zn hexamer for each mutant insulin (B9 Ser Asp, B10 His Asp) illustrate the role of the Zn2+ ion in dissipating the concentration of negative electrostatic charge in the central solvent channel. Very large shifts in pKa are predicted for B13 in the B9 mutant hexamer, presumably because of the very high charge concentration that this would entail (12 charged groups within the solvent channel). The lower shift for B13 pKa in the putative B10 mutant hexamer would presumably be due to the fact that B10 is further away from B13 than is B9. Adding Zn2+ to the hexamer models appears to make B13 ionization in the wild-type hexamer more favourable than in the mutant species.
The influence of conformational flexibility is most apparent in the case of the monomer where the variance is the highest. A progressive decrease in the variance as the aggregation state increases reflects the increasingly constrained environment and hence a relative reduction in the flexibility of the residues. Apart from the wild-type monomer, which displays a large variance of about 20%, the other states are mostly within 10%.
Solutions to the Poisson–Boltzmann equation have been successfully used to compute pKa shifts for B13 Glu in a mutant form of the insulin dimer, B9 Asp; the computed value is within 6% of the experimental value. It is clear that the proximity of B9 to B13 has the largest influence on the titration behaviour of B13. The shift in pKa for B13 is dependent on the rotameric state of the B13 side chain under consideration (data not shown).
The computed results clearly show that the wild-type monomer protein environment does not significantly shift the pKa of B13 beyond its solution pKa. The two mutant monomers show slight increases in the pKa of B13 relative to its solution value owing to the introduction of nearby charged groups. The wild-type dimer environment again only slightly perturbed the ionization of B13 Glu. The B9 Ser Asp mutation, however, caused this shift to be somewhat larger, at +2.64 and +2.45 units relative to the solution pKa of glutamic acid. Thus a maximum shift of +2.64 units has occurred relative to the pKa in the wild-type dimer, in good accord with the experimental value of +2.50 units. The effect of the B10 His Asp mutation in the dimer was less marked, with an increase of only +0.90 units relative to solution being recorded. In the mutant B10Asp zinc-free hexamer models, ionized B13 was found to be extremely disfavoured. Inclusion of the zinc ions in the hexamer models reduced the pka of B13 groups in all the model systems studied as compared with the zinc-free models. However, B10 His Asp hexamers cannot form because of the loss of zinc binding capability at B10 His. The charge build-up in the central hexamer channel is seen to be prohibitively large towards ionization of B13 groups in a model B9 Ser Asp hexamer.
Design of mutants
Having successfully reproduced the experimental pKa shift in our calculations, we used this protocol to examine the influence of electrostatics in predicting mutations that would enhance the therapeutic efficacy of engineered insulin. In general, the mutational spectrum of insulin has been examined fairly exhaustively (see, for example, http://pmd.ddbj.nig.ac.jp; Nishikawa et al., 1994; or http://pmr.sdsc.edu/; Krebs and Bourne, 2003). In an attempt to predict mutations from our computations, we examined the interactions that are made between the monomers that form a dimer. There are two aspects on which one needs to focus while suggesting a medically relevant mutation: (a) reduce the tendency to aggregate or ideally, completely abolish aggregation and (b) maintain or even enhance receptor binding. The interactions that will destabilize dimer formation were examined with the idea that any site of one monomer (say B) that has a destabilizing interaction energy with the other monomer will lead to decreased dimerization (for example, relative to the B13 Glu, the site with the strongest interactions is B9 Ser). Several studies have been devoted to engineering mutants of insulin based on residues located either in the dimer-forming or the hexamer-forming or the receptor binding surfaces (Shoelson et al., 1992; Kaarlsholm et al., 1993; Hua et al., 1996) and indeed there are several factors that seem to control the structure–function relationships of insulins (Pittman et al., 1997; Guo et al., 2001). Although mutations of Pro have been found to be useful (Shoelson et al., 1992), we deliberately left them out of this study. We are interested in examining this problem from a purely electrostatic point of view; this offers the advantage of including long-range and more complex effects that would not be evident from a cursory visual examination of the structures. Our study can only suggest mutations that result in switching off a charge or changing a charge or charging an uncharged side chain. They do not take into account any conformational rearrangements or structural couplings that may be induced as a result (Zeng et al., 2000).
The electrostatic interaction free energy between the native monomers is –3.6 kcal/mol. As a method of benchmarking, we focus our attention on some mutant form of insulin that is known to exist as a monomer. The double mutant B9 Ser Asp/B27 Thr Glu is known to be monomeric (Ray et al., 1990) and our calculations of the electrostatic interaction free energies between the monomers in a double mutant derived from the wild-type dimer show a 37% destabilization (–2.3 kcal/mol) relative to the wild-type. Additionally, the quadruple mutant B1 Phe Glu/B10 His Glu/B16 Tyr Glu/B27 Thr Glu, which is an engineered monomer (Olsen et al., 1998), severely destabilizes the electrostatic interactions between the monomers (the electrostatic interaction energy is +360 kcal/mol). However, this value is probably too high and illustrates the complexities of such analyses, pointing towards the need for additional considerations such as structural/energetic optimizations to relieve the strain that ensues on modelling based upon the wild-type dimer structure. In Figure 2A are shown the electrostatic potentials (the electrostatic interaction energy in kcal/mol is shown and is computed as the electrostatic potential at the site multiplied by a unit charge) generated at all the side chain positions of one monomer due to the charge changes in the other monomer in the wild-type dimer (the sequence at the top of Figure 2A lists the residues along the insulin monomer and also shows residues that are implicated in residue binding). Of course, this does not take into account any structural relaxations that will result from the incurred electrostatic changes. We list a set of mutations and the destabilization they will cause to the dimerization in Table II. Owing to the lack of consensus information on the nature of the ‘unfolded state’ (Oliveberg and Fersht, 1996), we hypothesize brief discussions of the potential effects of each proposed mutation on the stability of the monomer with respect to its unfolded state (Table III). It is clear that the A-chain residues do not contribute significantly to the electrostatic interactions between the dimers. Only the residue Asn at the C-terminal end of chain A makes a contribution. This residue incidentally is known to be conserved across all species and is thought to be dynamically coupled to B25 Phe (Zeng et al., 2000). From this table, B9 Ser Asp is known to be monomeric (see Introduction). B15 Leu is buried and hence introduction of a charge in this hydrophobic core may not yield a stable monomer. Only a few of these residues are conserved (somewhat) across insulins from different sources (Pierce et al., 2001) (these are B12 Val, B15 Leu and B18 Val which, tend to be hydrophobic; B20 Gly is conserved to some degree although in some species it appears as charged). In addition, if multiple mutants are made from some combinations of these mutations (Table II), then we see destabilizations to various degrees including evidence of cooperativity. It is interesting that while the single site mutations we suggest seem stable (Table III), the multiple mutations suggest that there may be instability favouring the unfolded state. However, as pointed out earlier, careful considerations of structural relaxations need to be taken into account before any firm conclusions can be arrived for the multiple mutants. Of course, until a clear picture emerges of the conformational coordinates that characterize the states of insulin prior to binding its receptor, a cursory glance at data, such as those presented by Kaarsholm et al. (1993), show how complex the relationship is between designing a stable folded mutant and engineering high potency; for example, a neutral mutation (B26 Thr) is marginally more stable than the wild-type and yet is only half as potent while the triple mutant A8 His–B10 Asp–B25 His is destabilized by about 3 kcal/mol relative to the wild-type and yet is twice as potent. Similarly, a recent study has reported some progress in the interactions that mediate insulin–receptor interactions (Huang et al., 2004). They report that B12 Val is an important mediator of receptor interactions and that mutation to larger side chains in general impairs activity. However, this is confounded by the fact that mutation to Glu coupled to deletion of B30 (Brange et al., 1988) retains activity similar to that of the wild-type, once again pointing to the complexities that characterize biomolecular dynamics and functions.
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Finally, the particular choice of a protein dielectric of 8.5 was arrived at in line with the philosophy we have outlined elsewhere and found extremely useful in examining experimental observables which have then led on to predictions that have been confirmed by experiments (Plou et al., 1996
; Hussain et al., 2003). This value gave us the closest match with experiment and is also close to estimates made elsewhere (Garcia-Moreno et al., 1997). We evaluated the results by varying the dielectric and in almost all cases the results were invariant when the dielectric was varied between the popular values of 4 and 20 (Schutz and Warshel, 2001). However, in the case of the B9 Ser Asp mutation, the value did vary somewhat (by up to 20%), a value normally within the expected margins of error. A more detailed study that takes into account structural relaxations is currently being carried out. In conclusion, we have computed and successfully reproduced the experimental pKa shift of a mutant insulin; using the parameters that we have established for the computations, we have identified residues that could potentially, upon mutation, lead to the formation of more stable monomeric insulins that might be therapeutically beneficial.
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Acknowledgments |
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We thank the BBSRC for support and Dr Rebecca Wade for her kind help and advice in setting up the pKa calculations in UHBD. The Bioinformatics Institute is a research institute funded by A-STAR. All the work presented here was carried out a York.
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Received April 8, 2004; revised July 28, 2004; accepted August 1, 2004.
Edited by Bruce Tidor
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