Appraisal of blob-Based Approaches in the Prediction of Protein Folding Times.

A series of reports published in the last 3 years has illustrated that a blob-based model (BBM) can predict the folding time of proteins from their primary amino acid (aa) sequence based on three simple rules established to characterize the long-range backbone dynamics (LRBD) of racemic polypeptides. The sole use of LRBD to predict protein folding times with the BBM represents a radical departure from all other prediction methods currently applied to determine protein folding times, which rely instead on parameters such as the structure content, folding kinetics, chain length, amino acid properties, or contact topography of proteins. Furthermore, the built-in modularity of the BBM enables the parametrization and inclusion of new phenomena affecting the LRBD of polypeptides, while its conceptual simplicity makes it an interesting new mathematical tool for studying protein folding. However, its novelty implies that its relationship with many other methods used to predict protein folding times has not been well researched. Consequently, the purpose of this report is to uncover the physical phenomena encountered during protein folding that are best described by the BBM through the identification of parameters that have been recognized over the years as being strong predictors for protein folding, such as protein size, topology, structural class, and folding kinetics. This was accomplished by determining the parameters most strongly correlated with the folding times predicted by the BBM. While the BBM in its present form appears to be a good indicator of the folding times of the vast majority of the 195 proteins considered so far, this report finds that it excels for moderately large proteins that are primarily composed of locally formed structural motifs such as α-helices or for proteins that fold in multiple steps. Altogether, these observations based on the use of the BBM support the notion that proteins fold the way they do because the LRBD of polypeptides is mostly driven by the local interactions experienced between aa's within reach of one another.

Synergetic Effects of Alanine and Glycine in Blob-Based Methods for Predicting Protein Folding Times.

The polypeptide PGlyAlaGlu was prepared with 20 mol % glycine (Gly), 36 mol % d,l-alanine (Ala), and 44 mol % d,l-glutamic acid (Glu) and labeled with the dye 1-pyrenemethylamine to yield a series of Py-PGlyAlaGlu samples. The fluorescence decays of the Py-PGlyAlaGlu samples were analyzed according to the fluorescence blob model (FBM) to obtain the number Nblobexp of amino acids (aa's) encompassed inside the subvolume Vblob of the polypeptide probed by an excited pyrene. An Nblobexp value of 29 (±2) was retrieved for Py-PGlyAlaGlu, which was much larger than for any of the copolypeptide PGlyGlu or PAlaGlu prepared with either Gly and Glu or Ala and Glu, respectively. The continuous increase in Nblobexp with decreasing side chain size (SCS) from 10 aa's for PGlu to 16 aa's for PAlaGlu and 22 aa's for PGlyGlu was used earlier to define the reach of an aa and determine the groups of aa's that could interact with each other along a polypeptide backbone according to their SCS. These groups of aa's, referred to as blobs, led to the implementation of blob-based models (BBM) to predict the folding time τFtheo,BBM of 145 proteins, which was found to match their experimental folding time τFexp with a relatively high 0.71 correlation coefficient. Nevertheless, the much higher Nblobexp value found for Py-PGlyAlaGlu compared to all other pyrene-labeled polypeptides studied to date indicates that the reach of aa's along a polypeptide sequence is affected not only by SCS but also by synergetic effects between different aa's. Following this new insight, a revised BBM was implemented to predict τFtheo,BBM for 195 proteins assuming the existence or absence of synergies to control the interactions between aa's along a polypeptide sequence. Similarly good correlation coefficients of 0.71 and 0.74 were obtained for a direct 1:1 comparison of τFexp and τFtheo,BBM for the 195 proteins without and with synergies, respectively. This result suggests that synergetic effects between different aa's have little effect on τFtheo,BBM predicted from BBM underlying the robustness of this methodology.

Pyrene Excimer Formation (PEF) and Its Application to the Study of Polypeptide Dynamics.

This Perspective describes how the fluorescence blob model (FBM) has been developed and applied over the past 30 years to characterize the long-range backbone dynamics (LRBD) of polymers in solution. In these experiments, the polymers are randomly labeled with the dye pyrene, which forms an excimer upon the encounter between an excited and a ground-state pyrenyl label inside a finite subvolume of the polymer coil referred to as a blob representing the volume probed by the excited pyrene. By compartmentalizing the polymer coil into a cluster of identical blobs, FBM analysis of the fluorescence decays acquired with the polymers yields the number Nblob of structural units inside a blob. Since a flexible or rigid backbone will result in an Nblob that is either large or small, Nblob can be used as a measure of the flexibility of a given polymer. After having established that these experiments based on pyrene excimer formation (PEF) yielded quantitative information about the LRBD of a variety of polymers in solution, control experiments were carried out to characterize the effects that different molecular variables, such as the side-chain size (SCS) of a structural unit or the length of the linker connecting pyrene to the polymeric backbone, had on the parameters retrieved with the FBM. At this point, the FBM was applied to study the LRBD of polypeptides prepared from racemic mixtures of amino acids (aa's). These studies led to the establishment of simple rules that could be developed into mathematical equations to describe the LRBD of polypeptides. The Nblob values retrieved from the FBM analysis of the fluorescence decays acquired with the pyrene-labeled polypeptides could then be employed to predict the total conformational search time (τtcs) of any polypeptide based on their sequence. Strong correlations were found between the predicted τtcs and the experimental folding times of 145 proteins. The good quality of these correlations suggests that the blob-based approach described in this report might represent an interesting mathematical means for studying protein folding.

Unfolding of Helical Poly(L-Glutamic Acid) in N,N-Dimethylformamide Probed by Pyrene Excimer Fluorescence (PEF).

The denaturation undergone by α-helical poly(L-glutamic acid) (PLGA) in N,N-dimethylformamide upon addition of guanidine hydrochloride (GdHCl) was characterized by comparing the fluorescence of a series of PLGA constructs randomly labeled with the dye pyrene (Py-PLGA) to that of a series of Py-PDLGA samples prepared from a racemic mixture of D,L-glutamic acid. The process of pyrene excimer formation (PEF) was taken advantage of to probe changes in the conformation of α-helical Py-PLGA. Fluorescence Blob Model (FBM) analysis of the fluorescence decays of the Py-PLGA and Py-PDLGA constructs yielded the average number () of glutamic acids located inside a blob, which represented the volume probed by an excited pyrenyl label. remained constant for randomly coiled Py-PDLGA but decreased from ~20 to ~10 glutamic acids for the Py-PLGA samples as GdHCl was added to the solution. The decrease in reflected the decrease in the local density of PLGA as the α-helix unraveled in solution. The changes in with GdHCl concentration was used to determine the change in Gibbs energy required to denature the PLGA α-helix in DMF. The relationship between and the local density of macromolecules can now be applied to characterize the conformation of macromolecules in solution.

Effect of Structure on Polypeptide Blobs: A Model Study Using Poly(l-lysine).

The conformation of a series of pyrene-labeled poly(l-lysine)s (Py-PLLs) in 60:40 and 90:10 (v/v) acetonitrile:water mixtures was determined by comparing the results obtained from the fluorescence blob model (FBM) analysis of their fluorescence decays with those obtained from molecular mechanics optimizations (MMOs). PLL aggregates formed in both solutions as demonstrated by FRET experiments between naphthalene- and pyrene-labeled PLLs. Addition of an excess of unlabeled PLL allowed the conformational study of isolated Py-PLL embedded in a matrix of unlabeled PLLs. By varying the acetonitrile (ACN) content of the solution from 60 to 90 vol % ACN, Py-PLL was found to undergo a conformational change from a random coil to an α-helix. The conformational change induced an increase in the maximum number of lysines (Nblob) separating two pyrene-labeled lysines that could still form an excimer between an excited- and a ground-state pyrene. Nblob obtained from the FBM analysis increased from 15.2 ± 2.1 to 25.2 ± 1.2 lysines as PLL changed its conformation from a random coil to an α-helix. AFM revealed that the α-helical PLLs organized themselves into structured bundles ∼22 nm in diameter. The FBM analysis of the decays acquired with a solution of aggregated Py-PLLs in a 90:10 ACN:water mixture yielded a larger Nblob value of 36.6 ± 3.4. The increase in Nblob indicated that the Py-PLL constructs could now interact with one another in the helical bundles. This increase in Nblob was then used in conjunction with MMOs to determine an interhelical spacing of 2.9 ± 0.1 nm for Py-PLLs in a bundle. This interhelical spacing resulted in a local density of 0.25 ± 0.01 g·cm-3 for the bundles of PLL α-helices, which was a reasonable density for a protein in solution. This study describes an experimental means to probe the number of amino acids that interact with each other as the conformation of a polypeptide evolves from that of a random coil to that of an α-helix to finally that of a bundle of α-helices.

Characterization of the Distribution of Pyrene Molecules in Confined Geometries with the Model Free Analysis.

Evidence is provided showing that global Model Free Analysis (MFA) of monomer and excimer fluorescence decays of pyrene dissolved in aqueous solutions of sodium dodecyl sulfate (SDS) provides the same structural and dynamic information on SDS micelles as the well-established Micelle Model (MM) does. Both MFA and MM were employed to characterize the quenching kinetics between dyes and quenchers located in surfactant micelles and the aggregation number of surfactant micelles. However, contrary to the MM, which assumes that dyes and quenchers distribute themselves among SDS micelles according to a Poisson distribution and react with a rate constant that is proportional to the number of reactants in a micelle, the MFA accomplishes this task without making any assumption about the process of pyrene excimer formation in SDS micelles. The ability of the MFA to retrieve accurately the molar fraction of pyrene molecules that are isolated in SDS micelles and do not form excimers was taken advantage of to establish that it equaled the Poisson probability of exciting micelles that contained a single pyrene. The molar fraction of isolated pyrenes could then be utilized to determine the aggregation number of the SDS micelles, and the rate constant of excimer formation between one excited- and one ground-state pyrene located inside a same micelle. Within experimental error, both the MFA and MM yielded the same micelle aggregation number and rate constant of excimer formation, with the MFA making no prior assumptions about the physical principles underlying the process of excimer formation contrary to the MM. The ability of the MFA to retrieve quantitative parameters providing structural and dynamic information about macromolecular systems with no prior knowledge about their architecture or labeling scheme implies that it can be applied to characterize a wide range of macromolecular architectures in solution.

DiPyMe in SDS Micelles: Artifacts and Their Implications in the Interpretation of Micellar Properties.

This study provides experimental evidence that di(1-pyrenylmethyl) ether or DiPyMe, a well-known fluorescent probe employed to determine the microviscosity of surfactant or polymeric micelles, is being hydrolyzed in the presence of water upon UV irradiation. This effect was established from a careful analysis of the fluorescence spectra and decays acquired with aqueous solutions of DiPyMe dissolved in micelles of sodium dodecyl sulfate (SDS). The size of the SDS micelles could be adjusted from an aggregation number (N(agg)) of 70 to 172 by increasing the ionic strength of the aqueous solution from 0.0 to 0.5 M NaCl. The hydrolysis of DiPyMe was much reduced in the larger SDS micelles. While the degradation of DiPyMe in aqueous solutions of SDS micelles affected the analysis of the fluorescence spectra, model-free analysis (MFA) of the fluorescence decays of DiPyMe could reliably retrieve the rate constant ⟨k⟩ of excimer formation for DiPyMe. After calibration with mixtures of organic solvents of known macroscopic viscosity, the ⟨k⟩ values obtained for DiPyMe yielded the microviscosity (µÎ·) of the SDS micelles as a function of salt concentration. The µÎ· was found to increase from 4.0 to 8.8 mPa·s as the salt concentration increased from 0.0 to 0.5 M. This study demonstrated that, regardless of the problem of its hydrolysis that jeopardizes its use in steady-state fluorescence experiments, DiPyMe remains an extremely valuable probe for describing the microviscosity of hydrophobic domains in aqueous solution as long as its decays are analyzed with a model that accounts for the presence of degradation products as the MFA does.