The sarcosine effect on protein stability: a case of nonadditivity?

We have used differential scanning calorimetry to determine the effect of low concentrations (C = 0-2 M) of the osmolyte sarcosine on the Gibbs energy changes (deltaG) for the unfolding of hen-egg-white lysozyme, ribonuclease A, and ubiquitin, under the same buffer and pH conditions. We have also computed this effect on the basis of the additivity assumption and using published values of the transfer Gibbs energies for the amino acid side chains and the peptide backbone unit. The values thus predicted for the slope delta deltaG/deltaC agree with the experimental ones, but only if the unfolded state is assumed to be compact (that is, if the accessibility to solvent of the unfolded state is modeled using segments excised from native structures). The additivity-based calculations predict similar delta deltaG/deltaC values for the three proteins studied. We point out that, to the extent that this approximate constancy of delta deltaG/deltaC holds, osmolyte-induced increases in denaturation temperature will be larger for proteins with low unfolding enthalpy (small proteins that bury a large proportion of apolar surface). The experimental results reported here are consistent with this hypothesis.

An osmolyte effect on the heat capacity change for protein folding.

We have carried out a differential scanning calorimetry study into the pH effect on the thermal denaturation of ribonuclease A at several concentrations of the osmolyte sarcosine. In order to properly analyze these data, we have elaborated the thermodynamic theory of the linkage between temperature, cosolvent, and pH effects. The denaturation heat capacity increases with sarcosine concentration. The effects of temperature and sarcosine concentration on the denaturation enthalpy and entropy values are well described by convergence equations, with convergence temperatures of around 100 degrees C for the enthalpy and around 112 degrees C for the entropy; we suggest that these effects might be related to a solvent-induced alteration of the apolar-group-hydration contribution to the folding thermodynamics. From our data, we estimate that about 70 extra molecules of water are thermodynamically bound upon ribonuclease denaturation in diluted aqueous solutions of sarcosine; this number is 6-9 times smaller than that predicted on the basis of the following two premises: (a) the osmolyte is strongly excluded from the surface of both the native and the denatured protein and (b) the denatured state is a fully solvated chain. We suggest that at least one of these two premises does not hold. We briefly comment on the potential use of cosolvent effects on thermal denaturation to evaluate the degree of hydration of denatured proteins (thus providing an independent measure of the consequence of their possible residual structure) and, also, on the possibility of finding substances that are more efficient protein stabilizers than known osmolytes are.

Temperature and guanidine hydrochloride dependence of the structural stability of ribonuclease T1.

The thermal unfolding of ribonuclease T1 has been studied by high-sensitivity differential scanning calorimetry as a function of temperature, [GuHCl], and scanning rate. The destabilizing effect of GuHCl has revealed that the kinetics of the unfolding transition become extremely slow as the transition temperature decreases. At pH 5.3 and zero GuHCl, the unfolding transition is centered at 59.1 degrees C; upon increasing the GuHCl concentration, the transition occurs at lower temperatures and exhibits progressively slower kinetics; so, for example, at 3 M GuHCl, the transition temperature is 40.6 degrees C and is characterized by a time constant close to 10 min. Under all conditions studied (pH 5.3, pH 7.0, [GuHCl] < 3 M), the transition is thermodynamically reversible. The slow kinetics of the transition induce significant distortions in the shape of the transition profiles that can be mistakenly interpreted as deviations from a two-state mechanism. Determination of the thermodynamic parameters from the calorimetric data has required the development of an analytical formalism that explicitly includes the thermodynamics as well as the kinetics of the transition. Using this formalism, it is shown that a two-state slow-kinetics model is capable of accurately describing the structural stability of ribonuclease T1 as a function of temperature, GuHCl concentration, and scanning rate. Multidimensional analysis of the calorimetric data has been used to estimate the intrinsic thermodynamic parameters for protein stability, the interaction parameters with GuHCl, and the time constant for the unfolding transition and its temperature dependence.

Maximum entropy, analysis of kinetic processes involving chemical and folding-unfolding changes in proteins.

We show that numerical inversion of the Laplace transform by using the maximum entropy method can be successfully applied to the analysis of complex kinetic processes involving chemical and folding-unfolding changes in proteins. First, we present analyses of simulated data which support that: (i) the maximum entropy calculation of rate distributions, combined with Monte Carlo analyses of the associated uncertainties, yields results consistent with the information actually supplied by the data, thus preventing their over-interpretation; (ii) maximum entropy analysis may be used to extract discrete rates (corresponding to individual exponential contributions), as well as broad rate distributions (provided, of course, that the adequate information is supplied by the data). We further illustrate the applicability of the maximum entropy analysis with experimental data corresponding to two nontrivial model processes: (a) the kinetics of chemical modification of sulfhydryl groups in glycogen synthase by reaction with Ellman's reagent; (b) the kinetics of folding of ribonuclease a under strongly folding conditions, as monitored by fluorescence and optical absorption. Finally, we discuss that the maximum entropy approach should be particularly useful in studies on protein folding kinetics, which generally involve the comparison between several complex kinetic profiles obtained by using different physical probes. Thus, protein folding kinetics is usually interpreted in terms of kinetic mechanisms involving a comparatively small number of kinetic steps between well-defined protein states. According to this picture, rate distributions derived from experimental kinetic profiles by maximum entropy analysis are expected to show a small number of comparatively narrow peaks, from which we can determine, without a priori assumptions, the number of exponential contributions required to describe each experimental kinetic profile (the number of peaks), together with their amplitudes (from the peak areas), time constant values (from the peak positions), and associated Monte Carlo uncertainties. On the other hand, recent theoretical studies describe protein folding kinetics in terms of the protein energy landscape (the multidimensional surface of energy versus conformational degrees of freedom), emphasize the difficulty in defining a single reaction coordinate for folding, and point out that individual chains may fold by multiple pathways. This indicates that, in some cases at least, folding kinetics might have to be described in terms of broad rate distributions (rather than in terms of a small number of discrete exponential contributions related to kinetic steps between well-defined protein states). We suggest that the maximum entropy procedures described in this work may provide a method to detect this situation and to derive such broad rate distributions from experimental data.

Lower kinetic limit to protein thermal stability: a proposal regarding protein stability in vivo and its relation with misfolding diseases.

In vitro thermal denaturation experiments suggest that, because of the possibility of irreversible alterations, thermodynamic stability (i.e., a positive value for the unfolding Gibbs energy) does not guarantee that a protein will remain in the native state during a given timescale. Furthermore, irreversible alterations are more likely to occur in vivo than in vitro because (a) some irreversible processes (e.g., aggregation, "undesirable" interactions with other macromolecular components, and proteolysis) are expected to be fast in the "crowded" cellular environment and (b) in many cases, the relevant timescale in vivo (probably related to the half-life for protein degradation) is expected to be longer than the timescale of the usual in vitro experiments (of the order of minutes). We propose, therefore, that many proteins (in particular, thermophilic proteins and "complex" proteins systems) are designed (by evolution) to have significant kinetic stability when confronted with the destabilizing effect of irreversible alterations. We show that, as long as these alterations occur mainly from non-native states (a Lumry-Eyring scenario), the required kinetic stability may be achieved through the design of a sufficiently high activation barrier for unfolding, which we define as the Gibbs energy barrier that separates the native state from the non-native ensemble (unfolded, partially folded, and misfolded states) in the following generalized Lumry-Eyring model: Native State <--> Non-Native Ensemble --> Irreversibly Denatured Protein. Finally, using familial amyloid polyneuropathy (FAP) as an illustrative example, we discuss the relation between stability and amyloid fibril formation in terms of the above viewpoint, which leads us to the two following tentative suggestions: (a) the hot spot defined by the FAP-associated amyloidogenic mutations of transthyretin reflects the structure of the transition state for unfolding and (b) substances that decrease the in vitro rate of transthyretin unfolding could also be inhibitors of amyloid fibril formation.