This report provides evidence that the blobs characterized through the application of the fluorescence blob model (FBM) to the analysis of the fluorescence decays acquired with pyrene-labeled polypeptides are equivalent to the foldons used in the study of protein folding. The FBM was applied to characterize the length and time scale over which pyrene excimer formation (PEF) took place between pyrene labels covalently attached onto α-helical and partially helical poly(L-glutamic acid) (Py-PLGA) in DMF and DMSO, respectively, and unfolded poly(DL-glutamic acid) (Py-PDLGA) in both DMF and DMSO. The blob size obtained for α-helical Py-PLGA in DMF and the characteristic time determined for the backbone dynamics of unfolded Py-PDLGA matched very closely the expected size of foldons and their characteristic folding times, respectively. In particular, the blob size was confirmed by conducting molecular mechanics optimizations (MMOs) with HyperChem. Furthermore, the level of pyrene clustering along the polypeptides correlated nicely with their expected conformation, either coiled or helical for the Py-PDLGA or Py-PLGA constructs in DMF, respectively. Consequently, these results suggest that PEF experiments conducted on pyrene-labeled polypeptides provide valuable information on the time and length scales experienced by the amino acids located inside a polypeptide blob and that if polypeptide blobs and foldons present similar length and time scales, both entities must be equivalent. Since dynamic or spatial information on foldons is usually retrieved by conducting NMR or hydrogen exchange mass spectrometry experiments, PEF might thus provide an alternative, possibly simpler, route toward the characterization of polypeptide foldons in solution.

The response of the internal dynamics of a polypeptide to changes in its amino acid (aa) composition was investigated by applying the florescence blob model (FBM) to a series of pyrene-labeled poly(D,L-alanine-co-D,L-glutamic acid)s (PAlaGAs) and poly(D,L-glutamic acid) (PGA). The alanine content of the PAlaGA samples was varied between 24 and 58 mol % by using PGA (containing 0 mol % alanine) for comparison purposes. The FBM yielded the number N blob of aa's that could diffusively encounter one another in a blob, which is the volume probed by an excited pyrenyl label covalently attached to the polypeptide. The incorporation of 24 mol % of alanine was found to significantly increase N blob from 11 ± 1 for PGA to 16 ± 1 for the Pala 24 GA 76 sample in DMSO due to the enhanced conformational freedom provided by alanine to the polypeptide. Interestingly, further increases in the alanine content of the PAlaGA samples from 24 to 58 mol % did not change the N blob value, implying that only a few flexible aa's in the backbone of a polypeptide are required to disrupt its rigid conformation. The N blob values of 16 for PAlaGA and 23 found earlier for poly(glycine-co-D,Lglutamic acid) (PGlyGA) were then used to estimate an average N blob value of 19 aa's for proteins based on their average aa composition, which should include at least one glycine or one alanine residue for a blob of this size. The N blob value of 19 aa's was then used to estimate the folding times of 145 different proteins by applying a simple hierarchical conformational search method to determine the number of conformations that could be adopted by the oligopeptide segment of a protein located inside a blob. Surprisingly for such a crude and simple approach, the method provided folding time (τ F ) estimates that were in good agreement with experimentally measured values, resulting in a correlation coefficient of 0.73. The good agreement found between the calculated and experimentally determined τ F 's supports the notion that the folding of proteins occurs in and among localized subdomains which happen to be well represented by a FBM analysis of the fluorescence decays of pyrene-labeled polypeptides.

The fluorescence blob model (FBM) was applied to analyze the fluorescence decays of a series of pyrene-labeled polypeptides to better understand how the amino acid (aa) composition of a polypeptide affected its dynamics. Three pyrene-labeled polypeptides were prepared by copolymerizing racemic (D,L) mixtures of different aa's, namely, glycine (Gly), alanine (Ala), and carbobenzyloxylysine (Lys(Z)) with glutamic acid (Glu) to yield Py-PGlyGlu, Py-PAlaGlu, and Py-PLys(Z)Glu, respectively. All polypeptides contained 44 (± 3) mol % Glu for fluorescence labeling with 1-pyrenemethylamine. The behavior of these three polypeptides was characterized in N,N-dimethylformamide (DMF) and dimethyl sulfoxide (DMSO) by fluorescence. It was then compared with the behavior of pyrene-labeled poly(D,L-glutamic acid) (Py-PGlu) to assess the effect that each comonomer had on the backbone dynamics of the polypeptides. The FBM analysis of the fluorescence decays yielded the maximum number (N blob ) of residues separating two Glu's bearing a pyrenyl group while still allowing excimer formation between an excited and a ground-state pyrene. Py-PLys(Z)Glu yielded the same blob size (N blob = 11) as for the Py-PGlu samples. In contrast, the incorporation of ∼56 mol % Ala and Gly resulted in an increase in N blob from 11 for Py-PGlu and Py-PLys(Z)Glu to 16 for Py-PAlaGlu and 23 for Py-PGlyGlu in DMSO. Considering that the internal dynamics of a polymer depend strongly on the size of its structural units and keeping proline aside, whose cyclic structure prevents backbone motion, this result implied that N blob for the 17 largest aa's of the 20 most common aa's with two or more atoms in their side chain must take a value between 11 for PGlu and 16 for PAlaGlu. This rather narrow range of N blob values suggests that the internal dynamics of polypeptides should be much simpler to predict than their structure since only two aa's, namely, Gly and Ala, out of the 20 most common aa's, appear to contribute differently to the internal dynamics of polypeptides.

Three series of pyrene-labeled polypeptides, namely, poly­(l-lysine) (Py-PLL), poly­(l-glutamic acid) (Py-PLGA), and poly­(d,l-glutamic acid) (Py-PDLGA), were studied in dimethyl sulfoxide (DMSO) by monitoring their ability to form an excimer between an excited and a ground-state pyrene. The effect that the charges of protonated Py-PLL (Py-PLL·HCl) and deprotonated Py-PLGA (Py-PLGNa) and Py-PDLGA (Py-PDLGNa) had on their conformation and dynamics was assessed by monitoring their fluorescence. The fluorescence decays were analyzed according to the fluorescence blob model (FBM) to determine N blob, which is the number of structural units in a blob, and k blob, which is the rate constant for diffusive encounters between structural units and their side chains inside a blob. FBM analysis indicated that the blob size for Py-PLGA and Py-PDLGA was unaffected by the presence of anionic charges, yielding N blob values of 10.3 ± 1.7 and 18.2 ± 1.1 glutamic acid units, respectively. These N blob values matched the values found for their uncharged counterparts. Molecular mechanics optimizations (MMOs) were then applied to determine the theoretical N blob th value that could be obtained if Py-PLGA adopted the conformation of a random coil, a polyproline type II helix, a 310-helix, or an α-helix. The agreement found between the N blob value of 17.9 ± 1.1 for protonated PLGA and deprotonated PLGNa and the N blob th of 19 found for 310-helical conformation suggested that this was the conformation adopted by the PLGAs in DMSO. Py-PLL·HCl was studied in a similar manner, yielding an N blob value of 14.3 ± 1.3 lysines, which suggested a coiled conformation according to MMOs. Comparison of k blob between charged and neutral polypeptides demonstrated that the presence of charges slowed the dynamics experienced by the amino acids. Because the polypeptide blobs appeared to have features in terms of their size and dynamics that were similar to those of foldons, this study further supports the notion that blobs and foldons might be identical objects.

A combination of fluorescence blob model and molecular mechanics optimizations was applied to determine the number (N blob ) of amino acids (aa's) located in the volume probed by an excited pyrene for poly(L-lysine) labeled with 1-pyrenebutyric acid (PyBu-PLL), as it adopted an extended conformation in DMSO. The N blob value of PyBu-PLL was then compared to those of other pyrene-labeled polypeptides adopting a similarly extended conformation over the length scale of a blob to quantify the contribution of the pyrenyl label to N blob . After subtracting the pyrene contribution, the plot of the corrected N blob as a function of aa side chain reach (SCR) led to the conclusion that, for a polypeptide in an extended conformation, increasing the SCR of an aa by one bond resulted in an ∼1.8 aa increase in N blob . This information could then be applied to predict the intrinsic N blob value (N(SCR)) of any aa based on its SCR as long as this aa was part of an aa sequence in an extended conformation. The increase in N blob resulting from the conformational freedom imparted by smaller aa's to a polypeptide backbone was accounted for by multiplying N(SCR) with the bending function f b (SCS), which was determined experimentally for the different side chain sizes (SCS) of aa's. By scanning the sequence of a protein, an N blob value was calculated for each aa from its N(SCR) and f b (SCS) values. The N blob values were then sorted from largest to lowest and averaged to yield ⟨N blob ⟩. Renormalization group theory was applied to determine the number (Ω) of conformations that would be available to a protein based on its ⟨N blob ⟩ value and the number of blobs found in the protein sequence. Multiplying Ω by the time required by an aa to adopt its possible conformations yielded the protein folding time (τ F ). A correlation coefficient of 0.73 was obtained from the comparison of the calculated and experimentally determined τ F values, demonstrating the ability of this blobbased approach to predict the protein folding times within ±1.4 orders of magnitude from the experimentally determined value.