Charge sequence coding in statistical modeling of unfolded proteins

In silico modeling of pH-optimum of protein-protein binding

Protein-protein association is a pH-dependent process and thus the binding affinity depends on the local pH. In vivo the association occurs in a particular cellular compartment, where the individual monomers are supposed to meet and form a complex. Since the monomers and the complex exist in the same micro environment, it is plausible that they coevolved toward its properties, in particular, toward the characteristic subcellular pH. Here we show that the pH at which the monomers are most stable (pH-optimum) or the pH at which stability is almost pH-independent (pH-flat) of monomers are correlated with the pH-optimum of maximal affinity (pH-optimum of binding) or pH interval at which affinity is almost pH-independent (pH-flat of binding) of the complexes made of the corresponding monomers. The analysis of interfacial properties of protein complexes demonstrates that pH-dependent properties can be roughly estimated using the interface charge alone. In addition, we introduce a parameter beta, proportional to the square root of the absolute product of the net charges of monomers, and show that protein complexes characterized with small or very large beta tend to have neutral pH-optimum. Further more, protein complexes made of monomers carrying the same polarity net charge at neutral pH have either very low or very high pH-optimum of binding. These findings are used to propose empirical rule for predicting pH-optimum of binding provided that the amino acid compositions of the corresponding monomers are available.

Defining the role of salt bridges in protein stability

Although the energetic balance of forces stabilizing proteins has been established qualitatively over the last decades, quantification of the energetic contribution of particular interactions still poses serious problems. The reasons are the strong cooperativity and the interdependence ofnoncovalent interactions. Salt bridges are a typical example. One expects that ionizable side chains frequently form ion pairs in innumerable crystal structures. Since electrostatic attraction between opposite charges is strong per se, salt bridges can intuitively be regarded as an important factor stabilizing the native structure. Is that really so? In this chapter we critically reassess the available methods to delineate the role ofelectrostatic interactions and salt bridges to protein stability, and discuss the progress and the obstacles in this endeavor. The basic problem is that formation of salt bridges depends on the ionization properties of the participating groups, which is significantly influenced by the protein environment. Furthermore, salt bridges experience thermal fluctuations, continuously break and re-form, and their lifespan in solution is governed by the flexibility of the protein. Finally, electrostatic interactions are long-range and might be significant in the unfolded state, thus seriously influencing the energetic profile. Elimination of salt bridges by protonation/deprotonation at extreme pH or by mutation provides only rough energetic estimates, since there is no way to account for the nonadditive response of the protein moiety. From what we know so far, the strength of electrostatic interactions is strongly context-dependent, yet it is unlikely that salt bridges are dominant factors governing protein stability. Nevertheless, proteins from thermophiles and hyperthermophiles exhibit more, and frequently networked, salt bridges than proteins from the mesophilic counterparts. Increasing the thermal (not the thermodynamic) stability of proteins by optimization of charge-charge interactions is a good example for an evolutionary solution utilizing physical factors.

Electrostatic contribution to the thermodynamic and kinetic stability of the homotrimeric coiled coil Lpp-56: A computational study

The protein moiety of the Braun's E. coli outer membrane lipoprotein (Lpp-56) is an attractive object of biophysical investigation in several aspects. It is a homotrimeric, parallel coiled coil, a class of coiled coils whose stability and folding have been studied only occasionally. Lpp-56 possesses unique structural properties and exhibits extremely low rates of folding and unfolding. It is natural to ask how the specificity of the structure determines the extraordinary physical chemical properties of this protein. Recently, a seemingly controversial data on the stability and unfolding rate of Lpp-56 have been published (Dragan et al., Biochemistry 2004;43: 14891-14900; Bjelic et al., Biochemistry 2006;45:8931-8939). The unfolding rate constant measured using GdmCl as the denaturing agent, though extremely low, was substantially higher than that obtained on the basis of thermal unfolding. If this large difference arises from the effect of screening of electrostatic interactions induced by GdmCl, electrostatic interactions would appear to be an important factor determining the unusual properties of Lpp-56. We present here a computational analysis of the electrostatic properties of Lpp-56 combining molecular dynamics simulations and continuum pK calculations. The pH-dependence of the unfolding free energy is predicted in good agreement with the experimental data: the change in DeltaG between pH 3 and pH 7 is approximately 60 kJ mol(-1). The results suggest that the difference in the stability of the protein observed using different experimental methods is mainly because of the effect of the reduction of electrostatic interactions when the salt (GdmCl) concentration increases. We also find that the occupancy of the interhelical salt bridges is unusually high. We hypothesize that electrostatic interactions, and the interhelical salt bridges in particular, are an important factor determining the low unfolding rate of Lpp-56.

Electrostatic effects in unfolded staphylococcal nuclease

Structure-based calculations of pKa values and electrostatic free energies of proteins assume that electrostatic effects in the unfolded state are negligible. In light of experimental evidence showing that this assumption is invalid for many proteins, and with increasing awareness that the unfolded state is more structured and compact than previously thought, a detailed examination of electrostatic effects in unfolded proteins is warranted. Here we address this issue with structure-based calculations of electrostatic interactions in unfolded staphylococcal nuclease. The approach involves the generation of ensembles of structures representing the unfolded state, and calculation of Coulomb energies to Boltzmann weight the unfolded state ensembles. Four different structural models of the unfolded state were tested. Experimental proton binding data measured with a variant of nuclease that is unfolded under native conditions were used to establish the validity of the calculations. These calculations suggest that weak Coulomb interactions are an unavoidable property of unfolded proteins. At neutral pH, the interactions are too weak to organize the unfolded state; however, at extreme pH values, where the protein has a significant net charge, the combined action of a large number of weak repulsive interactions can lead to the expansion of the unfolded state. The calculated pKa values of ionizable groups in the unfolded state are similar but not identical to the values in small peptides in water. These studies suggest that the accuracy of structure-based calculations of electrostatic contributions to stability cannot be improved unless electrostatic effects in the unfolded state are calculated explicitly.

Statistical Studies of Flexible Nonhomogeneous Polypeptide Chains

Unfolded proteins attract increasing attention nowadays because of the accumulation of experimental evidence that they play an important role in different biological processes. Therefore, studies of various statistical properties of flexible protein-like polypeptide chains are becoming increasingly important as well. This paper presents distributions (histograms) of distances between atoms of titratable residues for flexible polypeptide chains with various residue compositions and with the hard-spheres potential taken into consideration. The factors influencing the parameters of the obtained histograms have been identified and analyzed. It was found that the sensitivity of the distributions with respect to the internal structure of intermediate residues increases with the number of residues between the considered charged residues. It was shown that branching at C(beta) atoms of the side chains of the intermediate residues is among the most considerable factors influencing the shape of the distance distribution and the average distance between atoms in flexible chains. Despite the model simplicity, the results of the calculations can be applied for systems with other types of interactions presented, and this was demonstrated for the charge-charge interactions. In particular, it was shown that those interactions have a significant effect on distances between the unlike charges, while such an effect for the like charges is much less pronounced. The comparison of predictions made on the basis of the presented calculations to some experimental data is also given, and possible applications of the theoretical concept described in the paper are discussed.