Differential spectral topographic analysis (DISTA)

A method of determining apparent free energy of a conversion reaction between a folded form and an unfolded form of a molecule in solution, comprising:

• (a) summing absolute differences in topographic values between each of two reference spectra representing a folded form and an unfolded form of the molecule of interest and a sample spectrum taken at different magnitudes of at least one perturbation parameter to obtain DISTA values;
• (b) proportionally scaling the DISTA values between known reference values for a folded form of the molecule and an unfolded form of the molecule to obtain an estimate of the fraction of the unfolded form of the molecule;
• and
• (c) converting the estimate of the fraction of the unfolded form of the molecule to an estimate of the free energy of unfolding.

A method of determining the respective fractions of a folded form A and unfolded form B of a molecule in solution, comprising the steps of:

• (a) recording two reference spectra for each of the forms A and B;
• (b) normalizing both reference spectra to a topographical space such that the values of the normalized spectra are substantially dependent on the molecular configuration of the molecule of interest;
• (c) recording test spectra periodically in response to variation in at least one perturbation parameter selected from a group including temperature, pressure, pH, presence of a stabilizer, presence of a ligand, electromagnetic radiation, magnetic field, gravitational field, and presence of a denaturant;
• (d) normalizing each spectrum to the appropriate topographical space;
• and
• (e) calculating a DISTA value for each test spectrum using the equation:
• [ ∑ λ ⁢ ⁢ i ⁢ [LeftBracketingBar] S λ ⁢ ⁢ ir - S λ ⁢ ⁢ it [RightBracketingBar] n ] 1 / n
• where n is a transform scaling exponent, Sλir is the normalized reference signal at wavelength λi, Sλit is the normalized test signal at λi and the sum is over all λi.

A method of determining the fraction of secondary structure lost in a molecule of interest in solution, comprising:

• (a) recording Far-UV CD reference spectra for a folded form and an unfolded form of the molecule;
• (b) recording Far-UV CD test spectra as at least one perturbing parameter is systematically varied;
• (c) normalizing each spectra by converting to ellipticity;
• (d) calculating DISTA values for the test spectra;
• and
• (e) calculating the fraction of secondary structure lost, Fu, using the equation:
• F u = D s - D r2 D r1 - D r2
• where Ds is the sample DISTA signal, Dr1 is the reference signal of greater magnitude, and Dr2 is the reference signal of lesser magnitude.

A method of measuring a change from a first configuration to a second configuration in a physical configuration of a system of interest, comprising:

• (a) calculating a DISTA value for each test spectrum using the equation:
• [ ∑ λ ⁢ ⁢ i ⁢ [LeftBracketingBar] S λ ⁢ ⁢ ir - S λ ⁢ ⁢ it [RightBracketingBar] n ] 1 / n
• where n is a transform scaling exponent, Sλir is the normalized reference signal at wavelength λi at the value r of the perturbing parameter, Sλit is the normalized test signal at λi at the value of the perturbing parameter and the sum is over all λi;
• (b) plotting at least one sum for a perturbation value t versus one perturbation parameter at value t to create a DISTA curve;
• and
• (c) proportionally scaling the DISTA values at a value of interest of the perturbation parameter between known reference values for the first and second configurations of the physical configuration of the system of interest to obtain an estimate of the fraction of conversion to the second configuration of the physical configuration of the system of interest.

A method of determining the respective fractions of a folded form A and unfolded form B of a molecule in solution, comprising the steps of:

• (a) recording reference spectra for the molecule in solution over a set of range(s) one for each of one or more perturbation parameters such that for each range the molecule is essentially entirely in form A.
• (b) normalizing reference spectra to a topographical space such that the values of the normalized spectra are substantially dependent on the molecular configuration of the molecule of interest;
• (c) characterizing, for each wavelength in the reference spectra, any remaining dependence of the normalized reference spectral values on the perturbation parameter(s) by fitting the reference spectral normalized intensity values to the following equation:
• Iλinormalized(P1,P2, . . . Pn)=(A1+A2*P1+A3*P12+ . . . +Am*P1m)*(B1+B2*P2B3*P22+ . . . +Bk*P2k)* . . .
• wherein the Pi are the values of the ith perturbation parameter, the Ai, Bi, etc. are fitting constants, and m, k, etc. are the smallest exponents such that the fit is within the accuracy of the noise of measurement, and I is the normalized intensity at the ith wavelength;
• (d) extrapolating the values of I throughout the full range of Pi at which experimental spectra will be recorded;
• (e) recording test spectra periodically in response to variation in at least one perturbation parameter selected from a group including temperature, pressure, pH, presence of a stabilizer, presence of a ligand, electromagnetic radiation, magnetic field, gravitational field, and presence of a denaturant;
• (f) normalizing each spectrum to the appropriate topographical space;
• (g) calculating a DISTA value for each test spectrum using the equation:
• [ ∑ λ ⁢ ⁢ i ⁢ [LeftBracketingBar] S λ ⁢ ⁢ ir - S λ ⁢ ⁢ it [RightBracketingBar] n ] 1 / n ,
• wherein n is a transform scaling exponent, Sλir is the normalized reference signal at wavelength λi taken from a spectrum extrapolated in step (d), Sλit is the normalized test signal at λi and the sum is over all λi;
• and
• (h) repeating, optionally, steps (a) through (g) using a set of ranges over which the unfolded form B is essentially the only form to generate a second set of extrapolated reference spectra.