Examination of the folding of E. coli CspA through tryptophan substitutions

Escherichia coli cold shock protein, CspA, folds very rapidly (time constant, tau = 4 msec) by an apparent two-state mechanism. However, recent time-resolved infrared (IR) temperature-jump experiments indicate that the folding trajectory of CspA may be more complicated. The sole tryptophan of wild-type CspA (Trp11), which is used to monitor the folding process by fluorescence spectroscopy, is located in an unusual aromatic cluster on the surface of CspA within the nucleic acid binding site. To gain a more global picture of the folding kinetics of CspA and to determine if there are any previously undetected intermediates, we have introduced a second tryptophan at three different surface locations in the protein. The three mutations did not significantly alter the tertiary structure of CspA, although two of the substitutions were found to be slightly stabilizing. Two-state folding, as detected by stopped-flow fluorescence spectroscopy, is preserved in all three mutants. These results indicate that the fast folding of CspA is driven by a concerted mechanism.     

The nature of the free energy barriers to two-state folding

We introduce a simple procedure to analyze the temperature dependence of the folding and unfolding rates of two-state proteins. We start from the simple transition-state-like rate expression: k = D(eff)exp(-DeltaG(TS)/RT), in which upper and lower bounds for the intra-chain effective diffusion coefficient (D(eff)) are obtained empirically using the timescales of elementary processes in protein folding. From the changes in DeltaG(TS) as a function of temperature, we calculate enthalpies and heat capacities of activation, together with the more elusive entropies of activation. We then estimate the conformational entropy of the transition state by extrapolation to the temperature at which the solvation entropy vanishes by cancellation between polar and apolar terms. This approach is based on the convergence temperatures for the entropy of solvating apolar (approximately 385 K) and polar groups (approximately 335 K), the assumption that the structural properties of the transition state are somewhere in between the unfolded and folded states, and the established relationship between observed heat capacity and solvent accessibility.1 To circumvent the lack of structural information about transition states, we use the empirically determined heat capacities of activation as constraints to identify the extreme values of the transition state conformational entropy that are consistent with experiment. The application of this simple approach to six two-state folding proteins for which there is temperature-dependent data available in the literature provides important clues about protein folding. For these six proteins, we obtain an average equilibrium cost in conformational entropy of -4.3 cal x mol(-1)K(-1)per residue, which is in close agreement to previous empirical and computational estimates of the same quantity. Furthermore, we find that all these proteins have a conformationally diverse transition state, with more than half of the conformational entropy of the unfolded state. In agreement with predictions from theory and computer simulations, the transition state signals the change from a regime dominated by loss in conformational entropy to one driven by the gain in stabilization free energy (i.e., including protein interactions and solvation effects). Moreover, the height of the barrier is determined by how much stabilization free energy is realized at that point, which is related to the relative contribution of local versus non-local interactions. A remarkable observation is that the fraction of conformational entropy per residue that is present in the transition state is very similar for the six proteins in this study. Based on this commonality, we propose that the observed change in thermodynamic regime is connected to a change in the pattern of structure formation: from one driven by formation of pairwise interactions to one dominated by coupling of the networks of interactions involved in forming the protein core. In this framework, the barrier to two-state folding is crossed when the folding protein reaches a "critical native density" that allows expulsion of remaining interstitial water and consolidation of the core. The principle of critical native density should be general for all two-state proteins, but can accommodate different folding mechanisms depending on the particularities of the structure and sequence.     

Local secondary structure content predicts folding rates for simple,two-state proteins

Many single-domain proteins exhibit two-state folding kinetics, with folding rates that span more than six orders of magnitude. A quantity of much recent interest for such proteins is their contact order, the average separation in sequence between contacting residue pairs. Numerous studies have reached the surprising conclusion that contact order is well-correlated with the logarithm of the folding rate for these small, well-characterized molecules. Here, we investigate the physico-chemical basis for this finding by asking whether contact order is actually a composite number that measures the fraction of local secondary structure in the protein; viz. turns, helices, and hairpins. To pursue this question, we calculated the secondary structure content for 24 two-state proteins and obtained coefficients that predict their folding rates. The predicted rates correlate strongly with experimentally determined rates, comparable to the correlation with contact order. Further, these predicted folding rates are correlated strongly with contact order. Our results suggest that the folding rate of two-state proteins is a function of their local secondary structure content, consistent with the hierarchic model of protein folding. Accordingly, it should be possible to utilize secondary structure prediction methods to predict folding rates from sequence alone.     

Protein folding: defining a "standard" set of experimental conditions and a preliminary kinetic data set of two-state proteins

Recent years have seen the publication of both empirical and theoretical relationships predicting the rates with which proteins fold. Our ability to test and refine these relationships has been limited, however, by a variety of difficulties associated with the comparison of folding and unfolding rates, thermodynamics, and structure across diverse sets of proteins. These difficulties include the wide, potentially confounding range of experimental conditions and methods employed to date and the difficulty of obtaining correct and complete sequence and structural details for the characterized constructs. The lack of a single approach to data analysis and error estimation, or even of a common set of units and reporting standards, further hinders comparative studies of folding. In an effort to overcome these problems, we define here a "consensus" set of experimental conditions (25 degrees C at pH 7.0, 50 mM buffer), data analysis methods, and data reporting standards that we hope will provide a benchmark for experimental studies. We take the first step in this initiative by describing the folding kinetics of 30 apparently two-state proteins or protein domains under the consensus conditions. The goal of our efforts is to set uniform standards for the experimental community and to initiate an accumulating, self-consistent data set that will aid ongoing efforts to understand the folding process.     

Microscopic stability of cold shock protein A examined by NMR native state hydrogen exchange as a function of urea and trimethylamine N-oxide

Native state hydrogen exchange of cold shock protein A (CspA) has been characterized as a function of the denaturant urea and of the stabilizing agent trimethylamine N-oxide (TMAO). The structure of CspA has five strands of beta-sheet. Strands beta1-beta4 have strongly protected amide protons that, based on experiments as a function of urea, exchange through a simple all-or-none global unfolding mechanism. By contrast, the protection of amide protons from strand beta5 is too weak to measure in water. Strand beta5 is hydrogen bonded to strands beta3 and beta4, both of which afford strong protection from solvent exchange. Gaussian network model (GNM) simulations, which assume that the degree of protection depends on tertiary contact density in the native structure, accurately predict the strong protection observed in strands beta1-beta4 but fail to account for the weak protection in strand beta5. The most conspicuous feature of strand beta5 is its low sequence hydrophobicity. In the presence of TMAO, there is an increase in the protection of strands beta1-beta4, and protection extends to amide protons in more hydrophilic segments of the protein, including strand beta5 and the loops connecting the beta-strands. TMAO stabilizes proteins by raising the free energy of the denatured state, due to highly unfavorable interactions between TMAO and the exposed peptide backbone. As such, the stabilizing effects of TMAO are expected to be relatively independent of sequence hydrophobicity. The present results suggest that the magnitude of solvent exchange protection depends more on solvent accessibility in the ensemble of exchange susceptible conformations than on the strength of hydrogen-bonding interactions in the native structure.     

Two-state vs. multistate protein unfolding studied by optical melting and hydrogen exchange

A direct conflict between the stabilization free energy parameters of cytochrome c determined by optical methods and by hydrogen exchange (HX) is quantitatively explained when the partially folded intermediates seen by HX are taken into account. The results support the previous HX measurements of intermediate populations, show how intermediates can elude the standard melting analysis, and illustrate how they confuse the analysis when they are significantly populated within the melting transition region.     

Protein folding rates estimated from contact predictions

Folding rates of small single-domain proteins that fold through simple two-state kinetics can be estimated from details of the three-dimensional protein structure. Previously, predictions of secondary structure had been exploited to predict folding rates from sequence. Here, we estimate two-state folding rates from predictions of internal residue-residue contacts in proteins of unknown structure. Our estimate is based on the correlation between the folding rate and the number of predicted long-range contacts normalized by the square of the protein length. It is well known that long-range order derived from known structures correlates with folding rates. The surprise was that estimates based on very noisy contact predictions were almost as accurate as the estimates based on known contacts. On average, our estimates were similar to those previously published from secondary structure predictions. The combination of these methods that exploit different sources of information improved performance. It appeared that the combined method reliably distinguished fast from slow two-state folders.     

Calculation of static hyperpolarisabilities of donor-acceptor systems using a desktop molecular modelling package

A method for calculating the first static hyperpolarisability (₀) values of donor-acceptor molecules using a desktop molecular modelling package is presented. The ₀ values are deduced from a two-state model using geometries from AM1 and dipole moments from ZINDO/s calculations. The estimated ₀ values are in reasonable agreement with reported EFISH values. This method involves the use of a conventional PC and a molecular modelling package and does not require powerful workstations or long computational times.     

Investigation into the experimental kinetic support of the two-state model of the cell cycle

Five previously published cell generation-time distribution functions have been examined in an effort to elucidate the parameters of the two-state model of the cell cycle. These parameters are the fractional number of cells that bypass the G₀ state, the probability of exit from G₀ and the distribution of traversal times through the active state. To explain observed β-curve behavior of cell populations, it is necessary to define the parameters in terms of pairwise behavior of newborn sister cells. From the β-curve, we demonstrate that at least 50% of the cells must pass through the G₀ state. The α-curve is consistent with any positive fraction of newborn cells passing through the G₀ state, and provides no further information. We explore a possible method for resolving the remaining indeterminacy regarding the number of cells bypassing the G₀ state, namely, examination of the generation-time distribution functions of fast sister cells only. Such an approach, although theoretically attractive, presents formidable experimental difficulties, however. If it should turn out that indeed only 50% of the cells are apparently passing through a randomexiting phase of the cell cycle, then an alternative plausible biological mechanism for the observed variability in generation times is supplied by Prescott's hypothesis: variability is a consequence of the inequality in the metabolic content of sister cells at birth.