pKD: re-designing protein pKa values.

The pK(a) values in proteins govern the pH-dependence of protein stability and enzymatic activity. A large number of mutagenesis experiments have been carried out in the last three decades to re-engineer the pH-activity and pH-stability profile of enzymes and proteins. We have developed the pKD webserver (http://polymerase.ucd.ie/pKa_Design), which predicts sets of point mutations that will change the pK(a) values of a set of target residues in a given direction, thus allowing for targeted re-design of the pH-dependent characteristics of proteins. The server provides the user with an interactive experience for re-designing pK(a) values by pre-calculating DeltapK(a) values from all feasible point mutations. Design solutions are found in less than 10 min for a typical design job for a medium-sized protein. Mutant DeltapK(a) values calculated by the pKD web server are in close agreement with those produced by comparing results from full-fledged pK(a) calculation methods.

INTRODUCTION

The pH-dependence of enzymatic activity and protein stability is of major importance for the biological function and industrial application of enzymes and proteins. pH-dependent protein characteristics have therefore been the subject of significant research efforts over the last two decades [e.g. (1–8)]. The pH-dependence of protein characteristics is determined by the pKa values of amino acid residues in the unfolded and folded state of a protein. Consequently a growing number of theoretical methods have been constructed for calculating the pKa values of protein titratable groups (9–20), and presently the best pKa calculation methods are accurate to within 0.5 pKa units when benchmarked against experimentally determined pKa values. The application of pKa calculation methods in biology is limited to a relatively small number of studies on catalytic mechanisms and ligand binding [e.g. (2–4,13,21–27)], and there is thus much scope for a wider application of pKa calculation methodology to biological problems. To our knowledge pKa calculations have yet to be used for designing proteins with novel pH-dependent properties, although methods have been developed for dissecting the contribution of charged groups to protein pKa values (25) (J. E. Nielsen, manuscript submitted). These methods can, in principle, be used for targeted re-design of protein pKa values.

To motivate research into designing proteins with novel pH-dependent properties we have developed the pKD web server (), which interfaces with a novel algorithm (B. M. Tynan-Connolly and J. E. Nielsen, manuscript submitted) for re-designing protein pKa values. The web server allows the user to specify a set of design criteria (target residues, desired Δ pKa values, maximum number of mutations and minimum distance between target residue and any mutation) that specifies how the user want to change the pKa values of the protein. The pKD web server subsequently calculates a number of design solutions consisting of sets of point mutations predicted to change the target pKa values as specified by the design criteria. In addition to reporting the design solutions, the server produces 3D structural models of the proposed solutions and allows the user to inspect the pKa values calculated from the wild-type structure. The results and inputs of the pKD server can be analysed with a novel graphical interface (pKaTool) that facilitates the analysis of protein pKa calculations and titration curves. pKatool is freely available to academic researchers at .

MATERIALS AND METHODS

The pKD server combines the functionality of a number of software packages using Python scripts. Figure 1 shows an overview of the functionality of the server and indicates where other software packages are employed. The parameters for the pKD pKa calculations are described in detail below. The pKD server software is freely available to academic researchers by contacting pka@ucd.ie, or in some cases by download from .

Figure 1

The workflow of the pKD server. The server incorporates the functionality of the WHAT IF pKa calculation package (WIpKa), construction of point mutations (WHAT IF) and the pKa_Design algorithm.

Preparation of PDB files

PDB files are prepared for a pKD design by deleting all water molecules and non-protein atoms. Missing protein atoms are rebuilt using the position-specific rotamer libraries (28) in WHAT IF (29).

Calculation of pKa values of the wild-type structure

The pKa values of the wild-type structure are calculated with the WHAT IF pKa calculation package as described elsewhere (19), except that a uniform dielectric constant of eight is used for the protein, and that the neutral–charged, charged–neutral and neutral–neutral interaction energies are calculated only for residue pairs with an interaction energy greater than 10 kT. The latter approximation is employed to speed up the pKa calculation step for large structures and can introduce errors in the reported pKa values for tightly coupled titratable groups. Users that find this to be a problem for a particular structure should request a full pKa calculation to be carried out by emailing pka@ucd.ie.

Modelling point mutations

Point mutations are modelled using position-specific rotamer libraries as implemented in WHAT IF (28). We mutate only residues that are at least 30% solvent exposed and fit well in the wild-type structure as deemed by automatic inspection of the rotamer library population. In addition we allow the mutation of buried charged residues to neutral residues of a similar size.

Finally we allow the user to exclude mutations at sites less than a certain distance (user adjustable but recommended to be at least 5 Å) from the residue whose pKa value is being redesigned.

Calculation of interaction energies for single point mutations

The interaction energies between a point mutation and all other residues are calculated using the WHAT IF pKa calculation package as described above.

Calculation of Δ pKa values resulting from point mutations

ΔpKa values are calculated using a Monte Carlo sampling method (30) implemented as a C++ class, which is imported into a python script. ΔpKa values arising from single mutations are calculated by modifying the site–site interaction energy matrix using energies derived from an explicit model of the mutant protein structure. ΔpKa values arising from multiple point mutations are calculated by modifying the site–site interaction energy matrix using energies calculated from single point mutation models. Thus no explicit 3D modelling of multiple point mutations takes place until the final solutions are found. Nevertheless we have shown (B. M. Tynan-Connolly and J. E. Nielsen, manuscript submitted) that ΔpKa values calculated in this way are in excellent agreement with the ΔpKa values found by comparing the results of full-fledged pKa calculations on wild-type and mutant protein structures, provided that only a small fraction of protein residues are mutated.

Finding the optimal set of point mutations

The search for sets of point mutations that fulfil the design criteria is initiated by selecting 20 sets of combinations of single point mutations, whose cumulative ΔpKa values are closest to the design criteria. Since ΔpKa values only sometimes can be combined linearly (B. M. Tynan-Connolly and J. E. Nielsen, manuscript submitted), we calculate a more realistic set of ΔpKa values for each solution as described above. Finally we perform a short Monte Carlo sampling to find solutions that do cannot be found from a linear combination of individual ΔpKa values.

Scoring of design solutions

We apply a scoring function of the form to identify the design solutions in agreement with the design criteria. The sum in equation 1 is calculated over all pKa criteria specified in the design setup phase. The function is optimized to identify a specific pKa change rather than identifying the largest possible pKa change. Therefore, if one is interested in a maximum pKa change then one should specify design criteria of ±20 to obtain solutions that yield the maximum pKa shift possible for the residue in question.

RESULTS AND CONCLUSIONS

We have constructed a the pKD web server, which allows for the re-design of protein pKa values by site-directed mutagenesis. Proteins with redesigned pKa values will display a change in their pH-dependent characteristics, such as ligand binding, stability and, for enzymes, catalytic rate, and the pKD server is thus aimed at researchers who aim to understand or change the pH-dependent properties of proteins.

The pKD webserver asks the user to select one or more titratable groups for pKa value re-design. It must specify how many mutations one is willing to construct and how close these mutations can be to the titratable groups of interest. Subsequently the pKD server predicts a set of point mutations that will change the pKa values of the selected titratable groups in the given direction, by the desired amount. Furthermore the user is presented with a set of modelled 3D structures containing the proposed mutations, which can be analysed using pKaTool (J. E. Nielsen, manuscript submitted).

It is thus possible for the user to achieve an interactive, in-depth understanding of the titrational behaviour of any given protein using these two freely available software tools. Future work will focus on integrating pKaTool and the pKD server directly to allow for a desktop-based, convenient, interactive analysis facility of the titrational behaviour of wild-type and mutant proteins.

Table 1 and Figure 2 show a typical design solution from the pKD server, and illustrates that good agreement is obtained between the ΔpKa values reported by the pKD server and those predicted by a full-fledged pKa calculation packages. The pKD server uses a full physical model of the pH-dependent behaviour of titratable groups, which ensures that effects arising from differences in intrinsic pKa values and complicated pair-wise electrostatic interaction networks are calculated as accurately as possible. Therefore, the solutions calculated with the pKD server are more physically realistic than solutions obtained using the classic relation (8), which is known to break down when multiple strong electrostatic interactions are present and when dealing with titratable groups with perturbed intrinsic pKa values.

Table 1

Example design solutions and predicted ΔpKa values from pKD, the WHAT IF pKa calculation package (19) and the H++ webserver (12) for a re-design of the pKa of Glu 35 in HEWL (PDBID 2lzt)

Design criteria	Minimum distance to target	Mutations	pKD ΔpKa	WI ΔpKa	H++ ΔpKa
Glu35 +2.0	5.0 Å	R112E+R114Q+N37E+W62D	1.2	0.9	1.0
Glu35 −2.0	10.0 Å	N103H+D48R+T43K	−0.6	−0.6	−0.7

The maximum number of mutations allowed was set to 5, WI pKa calculations were carried out as described in Materials and Methods, and H++ calculations were carried out with the default settings on the website. The results illustrate that it often is not possible to achieve the desired pKa change with the parameters and the structure in question.

Figure 2

A 3D molecular representation of HEWL with the sites of mutations suggested by the pKD server in Table 1 highlighted in yellow. The proton donor (Glu 35) is shown in blue, whereas the catalytic nucleophile (Asp 52) is shown in red. Figure produced with the Yasara () and Pov-ray () packages.

We have calculated design solutions for a large number of protein structures and examined the dependence of the results on the algorithm parameters, and we have found the algorithm to reliably identify mutations that will change the pKa values of target residues as judged by theoretical methods. We are currently verifying these pKa shifts in the lab, and simultaneously continuing our theoretical studies on factors that influence the pH-dependent properties of proteins.

We believe that the pKD server will be of great benefit to researchers that are interested in re-designing and understanding the pH-dependent characteristics of proteins, and we furthermore hope that the server will encourage more experiments aimed at understanding the complex links between protein structures and their pH-dependent characteristics.