### Abstract

A new mathematical method of analyzing radioreceptor assay data is presented. When there are many binding classes with different affinities, the probability-density function B(p) is described by the equation B(p) = ∫_{-∞}
^{∞}q(k)f(p-k)dk, where q(k) is the affinity spectrum (density of a particular binding class as a function of affinity) and f(p-k) is a probability function (probability that dissociation constants will fall between k and p-k, where p is the free ligand concentration). This equation is solved for q(k) and evaluated explicitly by Fourier transformation, namely, q ̂(w) = b ̂(w) f ̂(w), where w is frequency. Since division by f ̂(w) can amplify any high frequency noise present in the experimental data, a Gaussian smoothing function is introduced thus: q ̂_{s}(w) = q ̂(w)e^{( -w W0)2}, where W_{0} is a constant. This produces an affinity spectrum defined as a plot of the number of binding sites, q_{s}(k), versus their respective dissociation constants, k. Using a FORTRAN computer program, we verify this algorithm using simulated data. We also apply the procedure to resolve heterogenous populations of estrogen binders in human endometrium using [^{3}H]estradiol as ligand. Two estrogen binder classes are revealed with dissociation constants approximately 2.5 natural logarithmic units apart. We identify one high-affinity (K_{d} = 0.18 nm)-low density (70 pm [or 72 fmol/mg protein]) subpopulation and one low affinity (K_{d} = 2.5 nm)-high density (101 pm [or 102 fmol/mg protein]) subpopulation of estradiol binders. The management of experimental error, sampling limitations, and nonspecific binding are discussed. This method directly transforms experimental data into an easily interpretable representation without mathematical modeling or statistical procedures.

Original language | English (US) |
---|---|

Pages (from-to) | 221-235 |

Number of pages | 15 |

Journal | Analytical Biochemistry |

Volume | 157 |

Issue number | 2 |

DOIs | |

State | Published - 1986 |

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### ASJC Scopus subject areas

- Biochemistry
- Biophysics
- Molecular Biology

### Cite this

*Analytical Biochemistry*,

*157*(2), 221-235. https://doi.org/10.1016/0003-2697(86)90619-6

**Resolution of steroid binding heterogeneity by fourier-derived affinity spectrum analysis (FASA).** / Mechanick, Jeffrey I.; Peskin, Charles.

Research output: Contribution to journal › Article

*Analytical Biochemistry*, vol. 157, no. 2, pp. 221-235. https://doi.org/10.1016/0003-2697(86)90619-6

}

TY - JOUR

T1 - Resolution of steroid binding heterogeneity by fourier-derived affinity spectrum analysis (FASA)

AU - Mechanick, Jeffrey I.

AU - Peskin, Charles

PY - 1986

Y1 - 1986

N2 - A new mathematical method of analyzing radioreceptor assay data is presented. When there are many binding classes with different affinities, the probability-density function B(p) is described by the equation B(p) = ∫-∞ ∞q(k)f(p-k)dk, where q(k) is the affinity spectrum (density of a particular binding class as a function of affinity) and f(p-k) is a probability function (probability that dissociation constants will fall between k and p-k, where p is the free ligand concentration). This equation is solved for q(k) and evaluated explicitly by Fourier transformation, namely, q ̂(w) = b ̂(w) f ̂(w), where w is frequency. Since division by f ̂(w) can amplify any high frequency noise present in the experimental data, a Gaussian smoothing function is introduced thus: q ̂s(w) = q ̂(w)e( -w W0)2, where W0 is a constant. This produces an affinity spectrum defined as a plot of the number of binding sites, qs(k), versus their respective dissociation constants, k. Using a FORTRAN computer program, we verify this algorithm using simulated data. We also apply the procedure to resolve heterogenous populations of estrogen binders in human endometrium using [3H]estradiol as ligand. Two estrogen binder classes are revealed with dissociation constants approximately 2.5 natural logarithmic units apart. We identify one high-affinity (Kd = 0.18 nm)-low density (70 pm [or 72 fmol/mg protein]) subpopulation and one low affinity (Kd = 2.5 nm)-high density (101 pm [or 102 fmol/mg protein]) subpopulation of estradiol binders. The management of experimental error, sampling limitations, and nonspecific binding are discussed. This method directly transforms experimental data into an easily interpretable representation without mathematical modeling or statistical procedures.

AB - A new mathematical method of analyzing radioreceptor assay data is presented. When there are many binding classes with different affinities, the probability-density function B(p) is described by the equation B(p) = ∫-∞ ∞q(k)f(p-k)dk, where q(k) is the affinity spectrum (density of a particular binding class as a function of affinity) and f(p-k) is a probability function (probability that dissociation constants will fall between k and p-k, where p is the free ligand concentration). This equation is solved for q(k) and evaluated explicitly by Fourier transformation, namely, q ̂(w) = b ̂(w) f ̂(w), where w is frequency. Since division by f ̂(w) can amplify any high frequency noise present in the experimental data, a Gaussian smoothing function is introduced thus: q ̂s(w) = q ̂(w)e( -w W0)2, where W0 is a constant. This produces an affinity spectrum defined as a plot of the number of binding sites, qs(k), versus their respective dissociation constants, k. Using a FORTRAN computer program, we verify this algorithm using simulated data. We also apply the procedure to resolve heterogenous populations of estrogen binders in human endometrium using [3H]estradiol as ligand. Two estrogen binder classes are revealed with dissociation constants approximately 2.5 natural logarithmic units apart. We identify one high-affinity (Kd = 0.18 nm)-low density (70 pm [or 72 fmol/mg protein]) subpopulation and one low affinity (Kd = 2.5 nm)-high density (101 pm [or 102 fmol/mg protein]) subpopulation of estradiol binders. The management of experimental error, sampling limitations, and nonspecific binding are discussed. This method directly transforms experimental data into an easily interpretable representation without mathematical modeling or statistical procedures.

UR - http://www.scopus.com/inward/record.url?scp=0022551004&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0022551004&partnerID=8YFLogxK

U2 - 10.1016/0003-2697(86)90619-6

DO - 10.1016/0003-2697(86)90619-6

M3 - Article

VL - 157

SP - 221

EP - 235

JO - Analytical Biochemistry

JF - Analytical Biochemistry

SN - 0003-2697

IS - 2

ER -