ࡱ> KMJyM >bjbj== WW!-l T RRRRll 66z(>)= I/K/K/K/4/?24$r8 :#5A III#5#  d6###I R I/#II/#B # .` " .*  |R!& . .<z606 .H;=#H; .#     Contribution of a Pyrene Fluorescence Probe to the Aggregation Propensity of Polypeptides (Supporting Information) Guilford Jones, II* and Valentine I. Vullev Department of Chemistry and Photonics Center, Boston University, Boston, Massachusetts 02215  HYPERLINK "mailto:jones@chem.bu.edu" jones@chem.bu.edu Received Date (will be automatically inserted after manuscript is accepted) Experimental. Preparation and characterization of the polypeptides is described elsewhere.5 Phosphate buffer (pH 8, 50 mM) was purchased from Fisher Scientific. For all experiments Milli-Q water was used. The emission data were recorded on a PTI Fluorescence System with FeliX software (Windows 95 workstation), using 1-cm quartz cells. The CD spectra were measured using AVIV 62DS spectrophotometer, and employing 1-cm and/or 1-mm quartz cells depending on sample concentrations. The polypeptide samples were prepared by multiple dilutions from concentrated stock solutions. The concentrations for samples above ~ 1 mM were confirmed by measurements of optical densities (Beckman DU 640B spectrophotometer) at 346 nm for TT1p and at 280 nm for TT1b. The data analysis was performed using IgorPro software, version 3.14 (WaveMetrics, Inc.). The deconvolution of the emission spectra was performed by conducting a data fit for two-parameter function, i.e.,  EMBED Equation.3 , where F is the total emission, a and b are weighting coefficients, and Fm and Fd are the alkylpyrene monomer and aggregate emission spectra, respectively (Figure 3). For the monomer emission function, Fm, the fluorescence spectrum of 10 mM PA in aqueous media (pH 8) was used, while aggregate emission was approximated to a sum of two Gaussians, i.e.,  EMBED Equation.3 . Consequently, the integrated fluorescence parameters, Sm and Sd, were obtained from numerical integration of the deconvoluted functions: i.e.,  EMBED Equation.3  and  EMBED Equation.3 .  Figure 3. An example of deconvolution of an emission spectrum of TT1p (500 nM). Concentration dependence of the emission properties. From the expression for the ratio between emission quantum yields, integrated emission properties can be related to the corresponding chromophore concentrations:  EMBED Equation.3  (7) where Fm and Fd are the fluorescence quantum yields for the chromophore monomer and dimer, respectively,  EMBED Equation.3 , Am(lex) and Ad(lex) are the monomer and dimer absorptions at the excitation wavelength, which are directly proportional to the molar extinction coefficients and the concentrations of the monomer and the dimer. Substituting equation 7 into equation 1 yields an expression for the monomer equilibrium concentration:  EMBED Equation.3  (8) Expressing [(pyrene)2] from equation 2, i.e.,  EMBED Equation.3 , and with substitution in equation 7, another expression for the monomer equilibrium concentration is obtained:  EMBED Equation.3  (9) Equalizing the right sides of equations 8 and 9, followed by rearrangement results in the following quadratic equation,  EMBED Equation.3 , which has only one plausible solution:  EMBED Equation.3  (3) where  EMBED Equation.3 ,  EMBED Equation.3  and  EMBED Equation.3 . In the data analysis, K1,2(TT1p) and f(lex) were the two fitting parameters. Furthermore, in order to achieve equal distribution of the data points and wider parameter space, the sample concentration and the dimerization constant were introduced as logarithmic quantities (Figure 1, inset). Concentration dependence of the CD spectra. For this analysis, the additive property of the molar ellipticity is used; i.e., the total molar ellipticity at a wavelength, l, is equal to the weighted sum of all molar ellipticities at the same wavelength, which for a mixture of a monomer and an aggregate (n-mer) in an one-step aggregation equilibrium is:  EMBED Equation.3  (10) where ql is the observed molar ellipticity, ql (1) and ql (n) are the molar ellipticities of the monomer and the aggregate, respectively, Cres is the total residue concentration, and [res(1)] and [res(n)] are the concentrations of the residues in the monomer and the aggregate, respectively. Since TT1b contains 24 residues, the total and equilibrium polypeptide concentrations are  EMBED Equation.3 ,  EMBED Equation.3  and  EMBED Equation.3 . Hence, equation 10 can be transformed into:  EMBED Equation.3  (11) In addition, similar to equation 2, the total polypeptide concentration can be expressed as:  EMBED Equation.3  (12) For quantitative studies the ratio, Rq, between the ellipticities at 222 and 208 nm was used rather than their absolute values (Figure 2b).10, Equations 4, 11, and 12 were employed to develop a linear functional dependence of the ellipticity ratio, Rq, and the total peptide concentration, CTT1b; i.e.,  EMBED Equation.3   EMBED Equation.3 , where a and b are concentration independent constants. From equation 11, the ratio can be expressed as:  EMBED Equation.3  (13) Therefore,  EMBED Equation.3  (14) Using equation 12 to express [P] and substituting in equation 14 yields:  EMBED Equation.3  (15) From here [Pn] can be expressed as:  EMBED Equation.3  (16) where  EMBED Equation.3  and  EMBED Equation.3 . Identically, similar expression can be obtained for [P]:  EMBED Equation.3  (17) Substituting equations 16 and 17 in equation 4 (i.e.,  EMBED Equation.3  ), gives a function of nth order:  EMBED Equation.3  (18) Applying a natural logarithm to both sides of equation 18, yields:  EMBED Equation.3  (5) which is a linear function of  EMBED Equation.3  vs.  EMBED Equation.3  with a slope equal to the state of aggregation and the intercept minus the logarithm of the slope, yielding the natural logarithm of the equilibrium constant. This approach deviates from previously developed methods for concentration-dependent CD analysis11 that have been successfully applied to other polypeptide aggregation systems,10 in having no assumptions for the state of aggregation: i.e., the state of aggregation, n, is allowed to flow as one of the fitting parameters. Interpretation of additivity of binding free energy. The data fits yielded logarithmic values for the three dimerization constants (Table 1). The exponentials of these values are the equilibrium constants themselves, i.e., Ki = exp(ln(Ki)), and when multiplied by RT they give the Gibbs free energies of the corresponding aggregation process, i.e., DGi =  RT ln(Ki), where R = 8.31451 J K 1 mol 1 = 1.98722 cal K 1 mol 1, and T = 293.15 K. The results of the calculations, with various numbers of significant figures used, are shown in Table 1. (Note that the error limits range between ~ 2 and 11 %.) Reducing the number of significant figures used for the calculations can alter the overall sense of the results. Although, the fluctuations in the free energy values do not exceed 8 %, the values for the equilibrium constants fluctuate noticeably (Table 1). The latter spread is reflected in the reported variance in DG (S) (equation 6). Table 1. Calculated dimerization free energies and the corresponding equilibrium constants for TT1p, TT1b and PB. number of significant figures  values obtained from the data fits  dimerization constants [ M 1 ] calculated free energies [ kcal / mol ] DG (S) * [ kcal / mol ] 4  ln(K1,2(TT1p)) = 18.46 ( 0.31 ln(K1,2(TT1b)) = 11.75 ( 1.22 ln(K1,2(PB)) = 4.991 ( 0.570 K1,2(TT1p) = 1.040 ( 108 K1,2(TT1b) = 1.268 ( 105 K1,2(PB) = 147.1 DGP C =  10.75 ( 0.18 DGPep =  6.845 ( 0.711 DGChrm =  2.908 ( 0.332 0.9970 ( 0.8051 3  ln(K1,2(TT1p)) = 18.5 ( 0.3 ln(K1,2(TT1b)) = 11.7 ( 1.2 ln(K1,2(PB)) = 4.99 ( 0.57 K1,2(TT1p) = 1.08 ( 108 K1,2(TT1b) = 1.21 ( 105 K1,2(PB) = 147 DGP C =  10.8 ( 0.2 DGPep =  6.82 ( 0.70 DGChrm =  2.91 ( 0.33 1.07 ( 0.80 2  ln(K1,2(TT1p)) = 18 ( 0.3 ln(K1,2(TT1b)) = 12 ( 1.2 ln(K1,2(PB)) = 5.0 ( 0.6 K1,2(TT1p) = 6.6 ( 107 K1,2(TT1b) = 1.6 ( 105 K1,2(PB) = 150 DGP C =  10 ( 0.2 DGPep =  7.0 ( 0.7 DGChrm =  2.9 ( 0.3 0.1 ( 0.8 _________________________________________ * The reported error bar is of the smallest possible value since it was calculated with the assumption that there is no correlation between the measured quantities: i.e., s2 = Ssi2. In case of a positive correlation, additional terms should be added to this sum. () A more complicated model was also developed and applied to the CD data: e.g., n P  EMBED ChemDraw.Document.5.0  n/2 P2  EMBED ChemDraw.Document.5.0  Pn.13 However, the fitting results using such a model did not carry statistical significance because: (1) most of the CD spectra were taken at concentrations where, according to sedimentation equilibrium, the polypeptide monomer and dimer are the predominant species;5 (2) there is no reliable way to predict ql(2), which is the molar ellipticity of the dimer and necessary for an equation equivalent to equation 11 (letting ql(2) float as a fitting parameter, decreases the chances for finding an unique fit with relatively large statistical significance); (3) the most significant change in the molar ellipticity occurs at the monomer-dimer transition, and any further level of aggregation does not seem to bring detectable change in the CD spectroscopic properties of the peptide. () The ellipticity ratio of the two minima in the far UV CD spectra has been extensively used to characterize a-helical content in peptides and proteins. 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