Protein Engineering, Vol. 16, No. 4, 279-286,
April 2003
© 2003 Oxford University Press
A simple electrostatic criterion for predicting the thermal stability of proteins
1 Departament de Ciències Mèdiques Bàsiques, Facultat de Medicina, Universitat de Lleida, Avda. Rovira Roure 44, 25198 Lleida and 3 Institut de Biotecnologia i Biomedicina, Departament de Bioquímica i Biologia Molecular, Universitat Autònoma de Barcelona, Bellaterra, Barcelona, Spain
2 To whom correspondence should be addressed. E-mail: angel.mozo{at}cmb.udl.es
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Abstract |
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The enhancement of protein thermostability is an important issue for both basic science and biotechnology purposes. We have developed a thermostability criterion for a protein in terms of a quasi-electric dipole moment (contributed by its charged residues) defined for an electric charge distribution whose total charge is not zero. It was found that minimization of the modulus of this dipole moment increased its thermal stability, as demonstrated by surveying these values in pairs of mesostable–thermostable homologous proteins and in mutations described in the literature. The analysis of these observations provides criteria for thermostabilization of a protein, by computing its dipole profile. This profile is obtained by direct substitution of each amino acid of the sequence by either a positive, negative or neutral amino acid, followed by a recalculation of the dipole moment. As an experimental example, these criteria were applied to a ß-glucanase to enhance its thermal stability.
Keywords: electric dipole moment/electrostatic interactions/hydrophobicity/thermostability
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Introduction |
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In recent years, there has been increasing interest in unraveling the specific mechanisms used by Nature to render proteins stable in the face of thermal inactivation. The interest in this issue involves questions that range from basic science to the design and manufacture of more efficient enzymes for industrial processes. At present, when confronted with the need to determine which amino acid is to be changed in order to enhance the thermal stability of a protein, most researchers still tend to opt for mainly casuistic criteria, since it is still difficult to follow definitive rules (Querol et al., 1996
).
Of all the interactions that take place within proteins, electrostatic and hydrophobic are the ones that have probably captured the attention of most researchers (Querol et al., 1996; Mozo-Villarías and Querol, 2000; Sterner and Liebl, 2001; Vieille and Zeikus, 2001). As far as electrostatic forces are concerned, an increasing number of papers have established the enormous importance (both in number and constitution) of ion pair networks in maintaining thermal stability (Bashford, 1991; Honig and Nicholls, 1995; Vogt et al., 1997; Chin et al., 1999; Xiao and Honig, 1999). The idea that emerges from these observations is that of a protein which works as an electric network, mostly at the surface and around a hydrophobic core. The stronger and more complex the net is, the most resistant the protein is to destabilization. A large number of computer software tools based on different numerical approximations analyzing electrical interactions have demonstrated their utility for computing and establishing electrical characteristics, such as the distributions of electric field and electric potential in proteins (Honig and Nicholls, 1995). The present work suggests the use of magnitudes that characterize electrical properties of a protein in order to help determine which points of the protein are most sensitive in maintaining its 3D structure.
In this paper, we describe common traits shown by studies of protein thermostabilization involving electrical interactions. It must be noted that when extracting protein thermal information from the literature, it is difficult to choose interesting cases in a coherent manner, owing to the different criteria used by different researchers when reporting their results in terms of the thermal characteristics of the protein under study. The transition temperature, Tm, is considered to be the standard parameter for describing the thermal stability of a protein, yet many researchers prefer to present their results in terms of thermoresistance, which is the half-life of residual activity at a given temperature and therefore not necessarily related to Tm. This is a frequent case in studies involving enzymes for biotechnological purposes. Other authors simply provide information about optimal temperatures at which original organisms live, while there are those who directly provide values for 
G, that is, the change in free energy associated with thermostabilization.
The analysis presented in this paper provides an approximate but very simple way to monitor the outcome of any prediction of thermostabilization when a given mutation involving charged residues is proposed.
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Materials and methods |
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Theory
Hydrophobic density calculations. The center-of-mass of each protein was determined using the coordinates provided by the Protein Data Bank (PDB). The coordinates for each atom were re-calculated and used for subsequent calculations. In this way, the center-of-mass of the protein was the origin of coordinates for all subsequent computations.
Hydrophobic tensors equivalent to the inertia tensor were calculated for positive hydrophobicities (h+i) and negative hydrophobicities (h-i), according to the Eisenberg hydrophobicity scale (Eisenberg et al., 1982). On this scale, positive values indicate hydrophobicity and negative values indicate hydrophylicity. These tensors were subsequently diagonalized: 
. The radii of the equivalent ellipsoids were calculated from their respective diagonal elements. Thus, the radii of the ellipsoid corresponding to the positive hydrophobicity amino acids were calculated as
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where 
are the diagonal elements of the negative electric charge distribution and 
is the sum of all the positive hydrophobicity amino acids in the protein. Subscript i denotes the three dimensions of space x, y, z. Similarly, 
for negative hydrophobicity were calculated.
The positive hydrophobicity ellipsoid is of particular interest in this study, since it provides a measure equivalent to the density of the hydrophobic packing of a protein, 
. This density is computed as 
Dipole moment vectors. The classical definition of the electric dipole moment vector or first-order electric moment is given
by 
, where 
is the position vector of residue j with charge qj. Unless the total charge of the protein is zero, 
is not independent of the origin of coordinates. Since in most proteins the total charge is not zero, it is useful to define two quasi-dipole moments, 
and 
, as 
and 
, where 
and 
are the total negative and positive charges (
is the total charge) and
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are the positive and negative centroids of the charge distributions, respectively.
Note that 
and 
differ, as 
, and when
.
Both and are independent of the origin of coordinates and therefore they are intrinsic parameters of the protein. As a consequence, these quasi-dipole moments provide a useful characterization of the dipolar nature of the charge distribution of a protein. Since the information provided by is essentially
the same as that of , in what follows is used to characterize the charge distribution in a protein and its modulus is designed as P and expressed in debye. We prefer to use these quasi-moments rather than the origin-dependent true moment 
since the purpose of this study was to compare moments among proteins with different thermal properties as described below and the use of D could give rise to meaningless conclusions.
All these magnitudes were easily calculated for the proteins described below using a desktop computer and employing a very simple function written in Mathematica.
Mesostable–thermostable protein pairs. Coordinates for mesostable–thermostable pairs of proteins, whose thermal properties are described in the literature, were obtained from the PDB. These proteins are listed in Table I. Here we report only those proteins whose sequences are complete. In some cases, proteins in their native state are complexes of several monomers, but only the coordinates of the monomers are reported in the PDB. In such cases, the oligomers were reconstructed by means of the Swiss-PDBViewer software, using their oligomeric homologues as templates. Proteins which lacked important fragments are not reported. In a few cases, mesostable–thermostable pairs also included a hyperthermostable member whose parameters were also calculated for comparison.
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Sets of mutants. Table II
shows significant cases of mutations that were collected according to the same criteria used for thermostable-mesostable pairs, in which Tm 
1°C. This collection of mutations was obtained from a previously reported mutant database (Querol et al., 1996), together with later reports on mutations that have appeared in the literature in recent years. When reporting, we tried to give preference to cases in which mutations resulted in crystallized proteins whose 3D structure could be resolved and thus have a PDB entry code. If not, the position of the mutant amino acid was taken to be the same as that of the mutated and an energy minimization was performed using the Swiss-PDBViewer software.
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Most of the mutations reported in the literature and referred to in this paper provide a wealth of mutants for each protein. Owing to space restrictions we report only the most significant mutants here. A complete list of all the mutants identified is available from the authors upon request.
Experimental
ß-Glucanase and its mutant N207D were obtained and purified by using experimental procedures described elsewhere (Pons et al., 1997). Transition temperatures (Tm) upon heating were measured spectrofluorimetrically on ß-glucanase wild-type and N207D mutant. Experiments were carried out with a Shimadzu RF2000 spectrofluorimeter.
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Results |
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Mesostable–thermostable pairs
Sets of mesostable–thermostable pairs of proteins were obtained by pooling all cases recently reported in the literature (Vogt et al., 1997; Karshikoff and Ladenstein, 1998; Xiao and Honig, 1999; Knochel et al., 2000; Kumar et al., 2000; Sterner and Liebl, 2001; Vieille and Zeikus, 2001; Klein et al., 2002; Nicholson et al., 2002; Robic et al., 2002). In the cases reported here, we did not take into account particular atomic or structural considerations. The only condition imposed was that the proteins reported should not lack any fragments or elements that could be of importance in the interpretation of electrical results. The electrical parameters described in the Materials and methods section were calculated for 37 groups of mesostable–thermostable (and/or hyperthermostable) proteins and are shown in Table I
, together with their thermal and mechanical characteristics. For the computation of the electrical parameters, the charged amino acids were used [+1 for arginines and lysines, -1 for aspartates and glutamates and +0.5 for histidines (Spassov et al., 1997)]. Regardless of the thermal properties of each protein, it was found that the sizes of the equivalent electric ellipsoids (both positive and negative) were, as expected, somewhat larger than those of the inertia ellipsoids, since most charged amino acids tend to be located in the surface of the protein. Of the 37 pairs of proteins reported, 27 (73%) had their quasi-dipole moment value (P) lower than that of their mesostable counterpart. It was also observed that many cases also show an increase in 
+ concomitant with higher thermostability. Only two families (CheY and methionine aminopeptidase) showed both opposite effects simultaneously: increase in P and decrease in + for higher thermostability.
We estimated the error in these parameters from observed differences in values obtained in different subunits of polymeric crystals. For example, we found that in glutamate dehydrogenase, the variability was of the order of 2% for these calculated parameters.
Point mutations
The considerations explained in the preceding section also apply for the proteins reported in Table II and their respective point mutations (Dao-Pin et al., 1991; Meiering et al., 1992; Zhang et al., 1992; Kanaya et al., 1996; Predki et al., 1996; White et al., 1996; Malakauskas and Mayo, 1998; Grimsley et al., 1999; Lebbnik et al., 1999; Mikami et al., 1999; Peterson et al., 1999; Wray et al., 1999; Zhu et al., 1999; Arrizubieta and Polaina, 2000; Chen et al., 2000; González-Blasco et al., 2000; Ha et al., 2000; Hasegawa et al., 2000; Tchan et al., 2000; Martin et al., 2001; Ohmura et al., 2001; Pedone et al., 2001; Perl and Schmid, 2001; Shaw et al., 2001; Stewart et al., 2001; Sung et al., 2001; Trejo et al., 2001; Almog et al., 2002; Pokkuluri et al., 2002). This table reports 55 mutations carried out in 30 proteins involving electric changes. In 43 of the cases reported (78%) mutations showed a decrease in P when thermostability increased or, conversely, an increase in P when thermostability decreased, which is common among reported mutations.
Relative electric dipole moment versus transition temperature
In order to illustrate the sensitivity of the thermal stability of a protein with respect to its quasi-dipole moment, the relative change of P was plotted against the increase in Tm, Tm. This relative change, P/Pmeso, is calculated by taking the value of P of the mesostable protein as reference, in cases dealing with meso–thermostable pairs or the value of the wild-type when dealing with point mutations. Figure 1 shows this relative change in P vs Tm for those cases whose variations of thermal properties are reported in terms of Tm, for both meso–thermostable pairs of proteins and point mutations. Both plots show linear correlations between both increments, P/Pmeso and Tm. The linear fit characteristics of both populations are displayed in Table III. It should be noted that both fits show similar slope values around -0.011. The level of significance for both sets of proteins is p < 0.05 for meso–thermo pairs (n = 18) and p < 0.01 for mutated proteins (n = 39).
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Similar calculations were also carried out using P
n instead
of Pp and very similar results were obtained in terms of P/Pmeso.
Detailed analysis and profiles of some examples
Cold shock protein. In order to illustrate the use of these electric dipole moments in predicting thermostabilizing mutations, profiles of P were calculated throughout the cold shock protein sequence. Figure 2 shows profiles of computed P for the mesostable–thermostable pair, when each amino acid is replaced by either a negative charge, a neutral amino acid or a positive charge throughout its sequences. Those substitutions in which wild-type P values were reduced should, in principle, be considered as candidates for stabilizing mutations. For example, mutations E3R and E66L produced a decrease in P. Perl and Schmidt performed these mutations on the mesostable cold shock protein 1csp with a resulting increase in Tm (Perl and Schmidt, 2001). A corresponding decrease in Tm was observed when reversed mutations were carried out on the thermostable cold shock protein 1c90. An increase in P was observed for R3E and L66E mutations.
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Glucanase. It is clear that not all of the substitutions suggested by the P profile should be regarded as mutation candidates, as many of these amino acids may be important for protein functions. In the case of ß-glucanase, the resulting profile shows several minima corresponding to residues/stretches in positions 9–10, 50, 55, 80, 99, 104–109, 128–130, 145, 178 and 207 (Figure 3
). Careful analysis of the protein structure by Rasmol and previous work on ß-glucanase mutants carried out in our laboratories (Juncosa et al., 1994; Pons et al., 1997) enabled us to exclude some potential substitutions as potential targets for replacement by a charged residue. These deductions were reached on the basis of structural/functional conservation: (a) positive/negative charged residues electrostaticaly interacting with a neighboring negative/positive charged residues/ions: Lys80 with Glu46; Lys155 with Asp150; Glu9 with Ca2+; Asp50 with Ca2+; Asp99 with Lys178; (b) residues belonging to the active site (general acid and base catalysts, nucleophiles or residues from the active site cleft), which we prefer not to replace or which lie on a key secondary structure: 104–109, 128–130 and 178–180 (Juncosa et al., 1994; Pons et al., 1997); (c) the remaining amino acids contain two putative targets: His148 and Asn207. Asp was chosen as a substitute for Asn207, because they are isosteric. For this mutation N207D, the value of P was found to change from 12.3 (wild-type) to 10.9 D, whereas Tm increased from 71.4 to 75.3°C.
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It should also be noted that, upon profiling and as shown empirically in our previous work, most of the positions initially considered as good candidates for mutations lay in external regions of the protein structure (Querol et al., 1996
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Discussion |
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It is important to stress that the electrical characteristics of a protein, especially in terms of its dipolar nature, are determined not only by its charged amino acids, but also by its peptide bonds and secondary structures. However, we found that for any given protein, the total dipole moment contributed by these elements (excluding the charged amino acids) has a much lower value than that contributed by the charged amino acids and, what is most important in this study, its value does not change substantially among the mesostable and thermostable varieties or between the wild-type protein and the mutant.
We found an inverse linear correlation between the relative change in dipole moment and transition temperature increase. Such a correlation should be expected since the attractive Coulomb force, which is a cohesive force, exerted by both positive and negative centroids depends on the inverse square distance between them. This finding is in good agreement with current ideas about the role played by the electrostatic networks of ion pairs and their optimization in thermostable proteins, as pointed out by several investigators (Spassov et al., 1994; Vogt et al., 1997; Xiao and Honig, 1999). According to these authors, such a clustering of opposite charges brings the centers of positive and negative charges close in space and thus reduces the magnitude of the electrostatic dipole moment of the protein. A similar correlation is found when the mesostable–thermostable pairs of Table I are used to compute dipole moments according to the method described by Felder et al.(1998) by means of the true concept of dipole moment taking the precaution of being systematic with the choice of the origin of coordinates. However, the correlation coefficient found with their dipole moments was lower than those reported in Table III.
In the calculations of the electrostatic dipole moment, it was assumed that all ionizable groups are fully charged except for histidines that were considered to have +0.5 charge. Given the large set of proteins being considered, we propose that this assumption is acceptable in the light of recent results on the possibility that a point mutation might not change the net charge of the protein. Alexov et al.(2000), working with replacements of a neutral group with ionizable in the reaction centers of several species of Rhodobacter, found that the replacements might not change the charge of the protein simply because the ionizable group could be uncharged owing to the specific environment in the protein or it might alter the charge of its neighbor.
It is worth mentioning that the attractive electrostatic force also depends on the inverse of the dielectric constant of the protein, which is also likely to decrease upon increasing the hydrophobic density. The difficulty in obtaining values for the dielectric constant of a protein has already been pointed out (Pitera et al. 2001; Schutz and Warshel, 2001), being a function of the hydrophobic amino acid composition of the protein. The link between the electrical and hydrodynamic forces operating in a protein is certainly an unresolved complex issue and one in which determination of the distribution of the dielectric constant in the protein is crucial. It may not even be possible to propose general rules to describe their mutual influence, since they may depend on the context of each protein. It is necessary to rely on the opportunistic nature of this equilibrium in which other forces, like hydrogen bonding, solvation and others that have been excluded from this study, are also present. However, in a first approximation, an increase in positive hydrophobic density, +, should imply a decrease in the average dielectric constant of the core of the protein and this would contribute to an increase in the strength of the attractive electric force, even in cases in which dipole moment increases. There are some cases reported in this paper in which we see thermal stabilizations in spite of a relative increase in P. At this point we can only suggest that when the core is more densely packed (as expressed by an increase in the positive hydrophobicity density, +), the effect of increasing the separation between electric centroids (increase in P) may be compensated by an increase in the dielectric constant of the medium.
Another important aspect to be taken into account is the fact that the stabilization factors suggested here (minimization of P and maximization of +) are defined in a specific structural context involving relatively small structural variations within a protein. When major changes are to be considered, such as those simulated by Petrey and Honig (Petrey and Honig, 2000), where the sequence of a given protein was superimposed on a totally different fold, the effects described in this paper should not be expected necessarily to hold.
The interest in this analysis lies mostly in the way it effectively provides both electric and hydrophobic equivalent spheroids for the study protein, without the need for a detailed knowledge of atomic peculiarities such as steric constraints, the existence of water-filled or empty cavities, etc. This circumstance imposes certain limitations on the applicability of this analysis in the case of very asymmetric proteins, as exemplified in the case of aminotransferase (not reported here). In this protein, the association of an ellipsoid with such an irregular structure (‘S’-shaped) causes a considerable distortion of the model, which considers a protein as a spheroid possessing a compact hydrophobic nucleus, enclosed in an electrical layer.
Although the present state of knowledge does not allow a quantitative prediction of the degree of protein stability from its sequence and/or its 3D structure, or the amount of acquired stabilization (or destabilization) when a given mutation takes place, it is possible to check if putative specific replacements are likely to enhance the thermal stability of a protein.
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Acknowledgments |
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This research was supported by grants BIO2000-647 and BIO2001-2046 from the CICYT (Ministerio de Educación y Ciencia, Spain), by the Center de Refèrencia R+D de Biotecnologia de la Generalitrat de Catalunya and by La Paeria (Lleida City Hall). We thank Drs S.Marqusee and C.Klein for providing unpublished coordinates used in this study, Mr Malcolm Hayes for correcting the English and Mr Carmel Bonet for useful suggestions and comments.
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Received July 23, 2002; revised January 20, 2003; accepted February 5, 2003.
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