Protein design from in silico dynamic information: the emergence of the `turn–dock–lock' motif

Ariel Fernández,1

Max-Planck-Institut für Biochemie, Abteilung Strukturforschung, Am Klopferspitz, 82152 Martinsried (bei München), Germany


    Abstract
 Top
 Abstract
 Introduction
 Methods
 Results
 Discussion
 References
 
A protein design methodology based on ab initio folding simulations is described and illustrated. First, the time evolution of the chain topology is generated to identify a collapse-triggering nucleus. Then, a minimal spliced sequence of nuclear residues is created and systematically mutated in silico until it can sustain a stable conformation retaining the original nucleus topology. The mutations introduce a structural compensation for the deletions and eventually lead to the recovery of the native fold motif beyond topological identity. For ubiquitin, the systematically modified sequence is predicted to be a resilient folder, since it is 92% homologous to the hyperthermophile variant of B1-domain in streptococcal protein G. The methodology enabling us to identify the nucleus is independently validated vis-á-vis site-directed mutagenesis experiments on chymotrypsin inhibitor (CI2).

Keywords: protein design/protein folding/protein topology/Ramachandran map/ubiquitin


    Introduction
 Top
 Abstract
 Introduction
 Methods
 Results
 Discussion
 References
 
Protein design remains essentially an endeavor demanding serendipity and structural information (Dahiyat and Mayo, 1997Go; Malakauskas and Mayo, 1998Go; Arnold, 2001). Here we provide an alternative avenue, showing how to systematize this task making use of dynamical information provided by an ab initio protein-folding algorithm which coarsely reproduces the native fold and dominant expeditious pathways (Fernández and Berry, 2000Go; Fernández et al., 2000Go; Fernández, 2001Go). Our aim is to use this dynamic information to splice and mutate a natural sequence (Voigt et al., 2001Go) in order to design a minimal sequence able to sustain a stable conformation which retains the topology of the original fold. From an engineering perspective, a core question addressed in this work is: How can mutations compensate for deletions in the original sequence so as to recover the original folding motif beyond topological identity? The foldability of the spliced and mutationally optimized sequence is assessed and its high homology with unrelated proteins—wild-type or variant—sharing a common structural motif is established to validate our methodology.

Rather than simulating the detailed torsional dynamics at all times, our algorithm focuses on the evolution of torsional constraints of the chain, as determined by the basin (attractive paraboloid-like region) each residue is visiting within its Ramachandran ({Phi}, {psi}) map (Fernández and Berry, 2000Go; Fernández, 2001Go). Since, in order to reach a specific ({Phi}, {psi}) value, the residue must first find the basin which contains it, our algorithm makes use of the fact that folding is subordinated by a coarser process determined by interbasin hopping. The transition rate for this discretized process is modulated according to the extent of structural involvement of the residues at each time. The whole set of basin occupancies is specified by the so-called local topology matrix (LTM) whose time-evolution provides a description of the evolving torsional constraints that guide the folding process. Thus, the algorithm operates iteratively, by random basin search with modulated rates, generation of the most probable conformation realizing the LTM and, based on this geometry, attribution of new basin-transition rates needed to generate the next LTM. The basic operating premises and their experimental validation are given in Methods.

The ab initio treatment sketched above appears to be a suitable tool to identify the residues which must be in a specific Ramachandran basin (local topology) for the chain to be able to control or quench structural fluctuations, a clear signature that a nucleus has been formed beyond which structural development becomes an energetically downhill process (Krantz et al., 2000Go). Thus, the main thrust of this paper is to engineer a shortened sequence able to retain the nucleus topology of the wild-type sequence when mutated so that this topology can be realized by a concrete conformation representing a free energy minimum. This automated engineering procedure might be applicable to most if not all two-state folders for which a single folding transition state is experimentally discernible (Sosnick et al., 1996Go; Krantz et al., 2000Go) and computationally detectable by a sudden quenching of structural fluctuations (Fernández, 2001Go).


    Methods
 Top
 Abstract
 Introduction
 Methods
 Results
 Discussion
 References
 
According to recent research (Fernández et al., 2000Go; Fernández, 2001Go) we may digitally codify dynamic information on the folding process so as to combine local conformational constraints imposed by steric hindrances on ({Phi}, {psi}) motions with non-bonded energy terms responsible for large-scale organization to develop a coarse ab initio folding algorithm governed by the hopping of individual residues among its available Ramachandran basins. By sacrificing structural resolution and representing the backbone torsional dynamics modulo Ramachandran basins we are able to access the millisecond timescale relevant to folding. This dynamic coarse graining of the folding process finds justification in the vast separation of timescales between Ramachandran basin exploration and the more drastic conformational changes entailing interbasin hopping.

The attributed basin-hopping rate for this discretized process is modulated according to the extent of structural involvement of each residue at each time. In turn, the extent of structural involvement is evaluated in thermodynamic terms—and as such it requires an intramolecular semiempirical effective potential—as the gain in free energy which would occur if the (virtual) move consisting of changing the Ramachandran basin for the given residue would take place. This thermodynamic change adopts as reference state the lowest free energy structure associated with the previous set of Ramachandran basin assignments. This evaluation requires: (i) an effective intramolecular potential which introduces an implicit treatment of the solvent and therefore contains many body correlations to account for the environments that the chain itself is creating as it folds onto itself, and (ii) a computation of the microcanonical lake areas of Ramachandran basins in order to determine the destiny basin for each residue which changes basin (such a computation is given in Fernández, 2001Go).

Once the hopping rate or number of steps required to change basin has been computed, the most probable target basin becomes the one with the largest lake area or microcanonical entropy, as indicated in Fernández (Fernández, 2001Go). The whole set of basin occupancies is specified by the LTM whose time evolution provides a digital description of the evolving torsional constraints that guide the folding process. Thus, the algorithm operates iteratively, by random basin search with modulated rates, generation of the most probable conformation realizing the LTM and, based on this geometry, attribution of new basin-hopping rates needed to generate the next LTM. The basic operating premises and their experimental validation vis-á-vis existing mutational data on a specific protein are sketched below.

The algorithm has been designed with two purposes in mind:

(i) Make accessible considerably long timescales (milliseconds to seconds) at the expense of losing some structural and temporal resolution while retaining the inherent geometric constraints of the semiflexible peptide backbone.

(ii) Introduce a crude model for folding cooperativity by introducing three-body correlations which account for conformation-dependent environments. Such correlations determine a rescaling of the two-body interactions (pairwise energy contributions) depending on the proximity of a third body.

In view of this, the basic tenets of the model are:

(i) The backbone torsional motion is constrained by the basin of attraction in the Ramachandran map topography visited by each residue at a given time. Thus, local torsional constraints change only when residues perform interbasin hopping.

(ii) Interbasin hopping is slower than intrabasin exploration and the search for a particular target ({Phi}, {psi}) region is contingent on the residue first finding the basin that contains this region. Thus, an efficient exploration of conformation space is achieved by adopting a discretized `modulo basin' representation of torsional states.

(iii) A state of the chain within this description is specified as a `word' of basins, assigning one basin to each residue. Such words, known as LTMs need to be translated into geometries to be properly interpreted in terms of standard structural motifs. The conformational realization of each LTM is described in Fernández (Fernández, 2001Go) and requires: (1) choosing ({Phi}, {psi}) points for each residue from within the basin assigned to it in the LTM; (2) optimizing the resulting conformations by minimizing a semiempirical intramolecular potential.

(iv) The LTM evolution is determined by interbasin transitions whose rates are modulated according to the extent of structural involvement of the residues at the time. Interbasin hopping rates decrease as a pattern compatible with a structural motif is suddenly recognized in the LTM and increase if patterns are dismantled due to the formation of out-of-consensus bubbles.

Thus, the algorithm consists of pattern-recognition-and-feedback iterations in which residues change their rates of interbasin hopping according to the information encoded in the structural pattern recognized in the latest LTM generated. To `read' any such pattern in the LTM, an optimized torsional coordinate representation is needed in order to identify new non-bonded interactions. However, the structural detail does not participate per se in the dynamics: it is only retrieved intermittently in order to assess the hopping rates of the less structurally constrained residues.

A quantity directly accessible from such simulations is L(t) = number of residues performing interbasin hopping at time t (Fernández, 2001Go). This quantity enables us to estimate the extent of structural fluctuations at each time, and thereby characterize the nucleus by finding the LTM at the time (t*) which marks a sudden decrease in L(t). To validate this methodology, we show how to compute the Fersht's {Phi} values (Fersht, 2000Go) for the well studied chymotrypsin inhibitor (CI2; PDB accession number 1COA, N = 64; Jackson and Fersht, 1991Go; Muñoz and Eaton, 1999Go).

From the computationally accessible LTM(t) pattern for CI2 (compare with Figure 1Go) we get t* = 0.74 ms and determine the time {tau} ( = 1.16 ms) at which the coarsely-resolved structural fluctuations cease completely [L(t) = 0, t > {tau}]. Then we define the dynamic parameter F(n) = t(n) / {tau}. The F(n) plot for CI2 is displayed in Figure 6aGo. The thick line absissas in regions 14–17 and 47–48 correspond to regions where F(n) is closest to the critical value F* = t* / {tau} within the uncertainty in t* determination, represented by the band flanked by dashed lines.



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Fig. 1. Time evolution of the Ub chain topology represented with a four-color code along the most reproducible run at T = 330 K, pH 5. The pattern coarsely describes the entire folding process residue by residue. The detached row at the top gives the topology of the pdb.1ubi structure. The chain starts searching in conformation space concurrently with its own translation. The time resolution is 100 ps. The row at time t, LTM(t), determines a basin assignment for each residue at that time. The nucleus topology is read directly from LTM(t*), the row at time t*. Basin 1 contains the extended (ß-strand) conformations, basin 2 contains the R-{alpha}-helix and zero-pitch turn conformations, basin 3 contains the L-helix conformation and basin 4 is only present in glycine. Thus blue color indicates a locally extended conformation, while red and green denote local bending (in opposite directions). Relative basin areas, distributions and restrictions for different kinds of residues are given in Fernández (Fernández, 2001Go).

 


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Fig. 6. (a) F(n) plot for CI2 averaged over 22 successful runs at 305 K, pH 5, each made up of 2x107 iterations. (b) Predicted and experimental {Phi} values for CI2.

 
By intersecting the F(n) plot with the threshold F*-band we identify the residues involved in the formation of the nucleus: residue n belongs to the nucleus if F(n) << F* or F(n) = F*. Such residues are meant to have large {Phi} values since their organization is paramount to quench the fluctuations. Of such residues, those organized at F(n) = F* (thick-line abscissas in Figure 6aGo) are predicted to have {Phi} values near unity since they are the most difficult to get organized while being germane to trigger the hydrophobic collapse. The {Phi} values may be directly predicted from the dynamic information given in Figure 6aGo. This is shown in Figure 6bGo, where comparison is made with the experimental values (shaded circles) averaged over different drastic mutations (those causing free energy changes of at least 1 kcal/mol) (Jackson and Fersht, 1991Go; Muñoz and Eaton, 1999Go). Only those residues for which the Gaussian dispersion in its experimental {Phi} value over different drastic mutations at the same site was less than a threshold value of 0.20 were considered, otherwise the averaged {Phi} value for the site was considered not reliable and the site was disregarded for further analysis. The {Phi} plot may be derived from basic tenets of nucleation theory. The mapping is given by:

where g(n)=[F(n)(F* – F(n))]–1 for F(n) < F* and results from typical input–output relations from pattern recognition theory of critical nucleation (Fernández and Berry, 2000Go) with a single `organizational susceptibility' 1 / F(n) (the larger 1 / F, the easier for a residue to get organized), and fluctuation-measuring temperature for residue n given by F* – F(n) for F(n) < F*. Thus, the extent of influence on the folding process of a single mutation as measured by the {Phi} value depends on the point in time when the residue becomes organized in relation to the point of critical quenching of structural fluctuations. The relatively good agreement of our predictions with the site-directed mutagenesis results (Jackson and Fersht, 1991Go; Muñoz and Eaton, 1999Go) given in Figure 6bGo for CI2 validates this statement and supports our methodology.


    Results
 Top
 Abstract
 Introduction
 Methods
 Results
 Discussion
 References
 
A piece of information directly accessible from our algorithm and paramount to the design technique is the time-dependence of the LTM, represented as a two-dimensional pattern providing a description of the entire folding process. This picture contains all the dynamic information residue by residue, resolved at the topological level. One such plot for a chain which initially searches in conformation space as it is being sequentially generated (translated) is displayed in Figure 1Go. The sequential search is started with an N-terminus peptide five amino acids long. The algorithm used to generate the dynamic pattern is a modification to the one described in Fernández (Fernández, 2001Go) in order to incorporate chain-growth events that mimic translational steps. The process is meant to reproduce the sequential folding concurrent with translation: units are added at a rate comparable with ribosomal synthetic rates and thereafter, the chain is allowed to search in conformation space subject to the initial biases introduced by local propensities which played a dominant role during the early stages of the sequential process.

The pattern [LTM = LTM(t), 0 < t < 7 ms] displayed in Figure 1Go corresponds to the most reproducible successful run consisting of 7x107 iterations for mammalian ubiquitin (Ub, PDB accession number 1ubi) (Sosnick et al., 1996Go; Krantz et al., 2000Go). The simulation was perfomed at T = 316 K, a temperature demanding cooperativity and concertedness for structure survival. This feature is apparent in Figure 1Go: periods of overall stasis are flanked by periods of extensive large-scale fluctuations engaging up to 79% of the chain. The target stationary LTM at 7 ms is virtually identical to that of the crystallographic structure displayed in the last detached row in Figure 1Go. Only the local topology of a single internal residue is different, while the local topologies of the residues at both N- and C-terminii are crystal artifacts. On the other hand, the Hamming distance between the contact map associated with the LTM at 7 ms (Figure 2Go; Fernández, 2001Go) and that of the native fold is 1.02%, marking the success of the simulation. The contact maps are directly obtained from conformations realizing specific LTMs. The optimization of such conformations is governed by the semiempirical intramolecular potential given in Fernández (Fernández, 2001Go).



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Fig. 2. Contact matrix for the optimized conformation within the stationary topology dictated by the t = 7 ms row (LTM(7 ms)) in Figure 1Go. A black (i, j) entry denotes an {alpha}-carbon distance <7.2 Å, while a gray entry indicates a distance between 7.2 and 8 Å. Both abscissas and ordinates represent residue number as indicated in the figure.

 
Figure 1Go reveals that a dramatic quenching of structural fluctuations, marked by a sudden decrease in the number of residues performing interbasin hopping, takes place at t = t* = 5.61 ms. Beyond this critical time, fluctuations are reduced by 80% and become localized. The drastic drop in fluctuations signals the formation of a nucleus or collapse-inducing topology dictated by LTM(t*). This nucleus protects harnessing H-bonds and buttresses budding secondary structure (Sosnick et al., 1996Go; Schonbrunner et al., 1997Go; Fernández, 2001Go). The nucleus residues are identified as those whose basin assignment at t = t* prevails for t > t* in spite of occasional fluctuations. Thus, the nucleus excludes regions (18–21), (34–43), (46–47) and (73–76), which are belated organizers or remain flickering. Denoting by t(n) the time it takes for residue n to find its prevailing basin (directly accessible from Figure 1Go), we may state that n belongs to the nucleus if and only if t(n) < t*.

The topology and kinetics of formation of the Ub nucleus, accessible from Figure 1Go, have eluded proton-exchange and other kinetic probes (Sosnick et al., 1996Go; Krantz et al., 2000Go), suggesting a backbone H-bond pattern vulnerable to solvation, typical of a ß-sheet system (Schonbrunner et al., 1997Go). The contact map for the optimized conformation realizing the nucleus topology LTM(t*) is displayed in Figure 3Go. This nucleus involves the antiparallel (1–15) ß-sheet, a displaced (1–5)–(58–63) parallel ß-sheet and part of the native context-dependent (22–33) helix, a motif which cannot be inferred based solely on local propensities (Lacroix et al., 1998Go). Comparison between Figures 2 and 3GoGo reveals that the nucleus contains about 64% of the native structure.



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Fig. 3. Contact matrix for the optimized geometry of the Ub nucleus whose topology is dictated by LTM(t*). Both abscissas and ordinates represent residue number, as given in the figure.

 
We may splice the Ub sequence by deleting the non-nuclear residues and pasting the nuclear regions. This process leads to the spliced sequence Ub* shown in Figure 4Go. The optimized Ub* conformation retaining the nucleus topology is obtained following Fernández (Fernández, 2001Go) according to two prescriptions: (i) restrict the ({Phi}, {psi}) search by fixing the nuclear residues at the basins indicated by the LTM(t*); (ii) pick ({Phi}, {psi}) coordinates within the fixed basins according to the PROCHECK probability distribution (Laskowski et al., 1993Go). This leads to a marginally stable (~0.9 kcal/mol below random coil) conformation shown in Figure 5aGo. This fold lacks the native parallel ß-sheet that engaged the two extremities of the molecule: deletions precluded the spliced sequence from reproducing the native fold motif since the complex long (45–60) loop, responsible for the C-terminus ß-strand docking in Ub, has been mutilated.



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Fig. 4. Spliced Ub sequence (Ub*), spliced-mutated Ub sequence (Ub**) and sequence for hyperthermophile variant of streptococcal protein G (B1 domain) (pdb.1gb4) (Malakauskas and Mayo, 1998Go). Regions marked with dashed underlining are invariant along the Ub*–Ub** mutational pathway and conserved across all three sequences. Regions marked with solid underlining are the most actively mutated in Ub*.

 


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Fig. 5. (a) Optimized conformation of Ub* retaining the Ub nucleus topology but differing geometrically from the native Ub fold motif. The most actively mutated residues (G39, G42 and W44 in Ub**) are marked with an asterisk. (b) Optimized conformation of Ub** sharing the Ub nucleus topology. The Ub-like parallel ß-sheet system has been reconstituted by introducing suitable mutations at the locations indicated with an asterisk. The two backbone hydrogen bonds protected by W44 are represented as thin black segments.

 
We now show how systematic mutations on Ub* leading to a stable fold produce a compensatory effect with recovery of the native Ub fold motif. Mutations are performed concertedly according to individual schedules and each block of mutations is accepted or rejected according to the Metropolis-like tenets indicated below:

(i) The topology of the chain remains invariant throughout the entire mutational pathway: the basin assigned to residue n is fixed according to the nth entry in the LTM(t*) given in Figure 1Go.

(ii) The nuclear residues most difficult to get organized will mutate at the slowest rate: the number of mutations, M(n), which nuclear residue n undergoes every 100 iterations of the topologically-restricted Metropolis-like simulation is M(n) = 100 x [(t* – t(n)) / t*], where the brackets indicate closest integer.

(iii) For each new block of mutations, a single most probable chain conformation is generated by chosing ({Phi}, {psi}) values within the pre-assigned basins according to the PROCHECK distribution (Laskowski et al., 1993Go). Once a particular residue has been chosen to occupy a specific position in the chain, the ({Phi}, {psi}) coordinates at that location are chosen to be the most probable for that residue in the fixed basin.

(iv) A block of mutations is accepted if and only if its associated ({Phi}, {psi}) conformation is lower in energy than that resulting from the previous iteration. The semiempirical intramolecular potential adopted is the one successfully used to fold Ub (Fernández, 2001Go).

Starting with Ub*, and after 8.2x107 topologically-restricted Metropolis-like block mutational iterations, we obtain the sequence Ub** (Figure 4Go). The associated optimized conformation of Ub** is displayed in Figure 5bGo: it reproduces the native Ub fold motif with an r.m.s. displacement of 1.7 Å in the conserved nucleus region and lies 7.43 kcal/mol below that for Ub*. The invariant regions in the transition Ub*–Ub** are the `belated' nuclear residues with t(n) closest to t* (indicated in dashed underlining in Figure 4Go), while the most actively mutated regions are precisely those needed to recover the native parallel ß-sheet lost in Ub*. These residues, responsible for the turning, docking and locking of the terminal ß-sheet, are marked by solid underlining in Figure 4Go and indicated with an asterisk in Figure 5Go.

Essentially, the mutational process has produced a sequence able to sustain a stable fold retaining the nucleus topology along the entire mutational pathway and, in so doing, the mutational process lead to the reconstruction of the Ub native fold motif.

To reach a stable conformation, the mutational process produced a short highly flexible turn engaging residues G39, G42 and W44. The latter acts as a hydrophobic seal for the turn: Since water is organized around W44, the adjacent H-bonds which buttress the new parallel and antiparallel ß-sheets (Figure 5bGo) become effectively desolvated and thereby stabilized. This `locking of the ß-strand docking' induced by W44 is probably a kinetic inhibitory mechanism (Fernández, 2001Go): water organized around W44 would have to be disrupted if it were to solvate the exposed backbone resulting from the dismantling of the buttressing H-bonds shown in Figure 5bGo. Thus, facing diminished competition from surrounding water molecules, the harnessing H-bonds are effectively protected.

This primitive flexible turn motif is detectable in immunoglobulin-binding proteins such as PDB.1igd (Derrick and Wigley, 1994Go), in which the region G43-V44-D45-G46-V47-W48 performs the docking and locking of the terminal ß-strands.

The extensive mutation of Ub* leaves the first 33 units qualitatively unchanged and produces a new `turn–dock–lock' motif by increasing flexibility in the (38–43) region while protecting the recovered native motif. Significantly, the first 33 units in Ub* and Ub** have 38% homology with the hyperthermophile variant of streptococcus protein G B1 domain (pdb.1gb4; Malakauskas and Mayo, 1998Go; Cregut and Serrano, 1999Go), including identity within the regions conserved between Ub* and Ub** (Figure 4Go). The rest of the Ub* sequence shows virtually no homology with pdb.1gb4.

On the other hand, the Ub** recovery of the native fold motif (Spector et al., 1999Go), required forming a new `turn–dock–lock motif' demanding extensive mutation of the non-conserved (34–56) portion of the molecule. Significantly, Ub** is 92% homologous (modulo equivalent residues, such as L, I) to the hyperthermophile protein (Figure 4Go), while the r.m.s. displacement between their respective folds is 2.02 Å. This suggests that the Ub** fold shown in Figure 5bGo is a more `primitive' design of the Ub nuclear motif in which the finely tuned (38–60) complex Ub loop has been replaced with the highly flexible and harnessing (39–44) region.

Hence, a mutational pathway retaining the Ub basic topology and with implications for protein engineering (Cordes et al., 1999Go) has been elucidated using dynamical information on the wild-type folding history.


    Discussion
 Top
 Abstract
 Introduction
 Methods
 Results
 Discussion
 References
 
The example studied in the Results illustrates a straightforward way to use our semiempirical algorithm to determine the topology of the collapse-triggering nucleus for two-state folders and identify the residues whose organization is required to form the nucleus. Once this dynamic information has been obtained, an automated way of mutating a shortened sequence can be easily implemented in order to determine the shortest subsequence that might retain the nucleus topology of the wild-type while folding into a stable conformation. The mutations on the shortened sequence are introduced iteratively and in parallel along the sequence with an individual schedule that depends on the time when the residue participated in the quenching of structural fluctuations of the wild type.


    Notes
 
1 Present address: Instituto de Matemática, Universidad Nacional del Sur—CONICET, Bahía Blanca 8000, Argentina E-mail: arifer{at}criba.edu.ar Back


    Acknowledgments
 
The author would like to thank Professors Robert Huber, R.Stephen Berry and Tobin R.Sosnick for enlightening discussions and encouragement. This research was partially supported by the Alexander von Humboldt Foundation.


    References
 Top
 Abstract
 Introduction
 Methods
 Results
 Discussion
 References
 
Arnold,F.H. (2001) Nature, 409, 253–257.[CrossRef][ISI][Medline]

Cordes,M.H., Walsh,N.P., McKnight,C.J. and Sauer,R.T. (1999) Science, 284, 325–328.[Abstract/Free Full Text]

Cregut,D. and Serrano,L. (1999) Protein Sci., 8, 271–2812[Abstract]

Dahiyat,B.I. and Mayo,S.L. (1997) Science, 278, 82–87.[Abstract/Free Full Text]

Derrick,J.P. and Wigley,D.B. (1994) J. Mol. Biol. , 243, 906–918.[CrossRef][ISI][Medline]

Fernández,A. (2001) J. Chem. Phys., 114, 2489–2502.[CrossRef][ISI]

Fernández,A. and Berry,R.S. (2000) J. Chem. Phys. , 112, 5212–5222.[CrossRef][ISI]

Fernández,A., Colubri,A. and Berry,R.S. (2000) Proc. Natl Acad. Sci. USA, 97, 14062–14066.[Abstract/Free Full Text]

Fersht,A. (2000) Proc. Natl Acad. Sci. USA, 97, 1525–1529.[Abstract/Free Full Text]

Jackson,S.E. and Fersht,A.R. (1991) Biochemistry, 30, 10428–10435.[ISI][Medline]

Krantz,B., Moran,L.B., Kentsis,A. and Sosnick,T.R. (2000) Nat. Struct. Biol., 7, 62–71.[CrossRef][ISI][Medline]

Lacroix,E., Viguera,A.R. and Serrano,L. (1998) J. Mol. Biol., 284, 173–188.[CrossRef][ISI][Medline]

Laskowski,P.A., MacArthur,M.W., Moss,D.J. and Thornton,J.M. (1993) J. Appl. Crystallogr., 26, 283–329.[CrossRef][ISI]

Malakauskas,S.M. and Mayo,S.L. (1998) Nat. Struct. Biol., 5, 470–475.[ISI][Medline]

Muñoz,V. and Eaton,W.A. (1999) Proc. Natl Acad. Sci. USA, 96, 11311–11316.[Abstract/Free Full Text]

Schonbrunner,N., Pappenberger,G., Scharf,M., Engels,J. and Kiefhaber,T. (1997) Biochemistry, 36, 9057–9065.[CrossRef][ISI][Medline]

Sosnick,T.R., Mayne,L. and Englander,S.W. (1996) Proteins: Struct. Func. Genet., 24, 413–426.[CrossRef][ISI]

Spector,S., Young,P. and Raleigh,D.P. (1999) Biochemistry, 38, 4128–4136.[CrossRef][ISI][Medline]

Voigt,C.A., Mayo,S.L., Arnold,F.H. and Wang,Z.G. (2001) Proc. Natl Acad. Sci. USA, 98, 3778–3783.[Abstract/Free Full Text]

Received May 16, 2001; revised July 28, 2001; accepted September 25, 2001.





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