• One Site Saturation

This equation is used to fit specific binding data (y) as a function of ligand concentration (x).

• Variable Range Definition Units x >= 0 concentration of free ligand* concentration, M y >= 0 specific binding (=total - nonspecific) cpm, sites/cell, fmol of receptor/mg of tissue Bmax >0 maximum number of binding sites same as y Kd >0 concentration of ligand to reach half maximal binding concentration

  
  
  
• Two Site Saturation

This equation accounts for two receptor binding sites with two different affinities.

• One Site Saturation + Nonspecific

This equation is used to fit total binding concentration (y) as a function of ligand concentration (x). The extra parameter (from the one site saturation equation) N accounts for the nonspecific binding. You will need additional data points to get good estimates of the three parameters.

Variable Range Definition Units x >= 0 concentration of free ligand concentration, M y >= 0 total binding cpm, sites/cell, fmol of receptor/mg of tissue Bmax1 >0 maximum number of binding sites for receptor 1 same as y Bmax2 >0 maximum number of binding sites for receptor 2 same as y Kd1 >0 equilibrium dissociation constant for receptor 1 concentration Kd2 >0 equilibrium dissociation constant for receptor 2 concentration

• Two Site Saturation + Nonspecific

This equation is used to fit total binding concentration (y) as a function of the ligand concentration (x) when the data supports the existence of two receptor binding sites. This equation has five parameters and will require a considerable number of data points to accurately estimate these parameters.

Variable Range Definition Units x >= 0 concentration of free ligand concentration, M y >= 0 total binding cpm, sites/cell, fmol of receptor/mg of tissue Bmax1 >0 maximum number of binding sites for receptor 1 same as y Bmax2 >0 maximum number of binding sites for receptor 2 same as y Kd1 >0 equilibrium dissociation constant for receptor 1 concentration Kd2 >0 equilibrium dissociation constant for receptor 2 concentration N >0 slope of nonspecific binding line y units / x units

• Sigmoidal Dose Response

This equation describes a typical dose-response relationship. The drug data x is entered in logarithmic form. The y variable is the response. EC50 is the drug concentration for y halfway between min and max.

Variable Range Definition Units x >0 log concentration of drug log concentration, log(M) y >= 0 response response units min >0 minimum response plateau same as y max >0 minimum response plateau same as y LogEC50 >0 log of EC50 or IC50 log concentration

 

• Sigmoidal Dose Response (Variable Slope)

This equation describes a typical dose-response relationship but includes an additional parameter, Hillslope, which characterizes the slope of the curve at its midpoint. The drug data x is entered in logarithmic form. This equation is identical to the sigmoidal dose response curve when Hillslope = 1.0. It is also identical to the four-parameter logistic function except the slope parameters have opposite sign.

Variable Range Definition Units x >= 0 response response units y >0 minimum response plateau same as y min >0 minimum response plateau same as y max >0 log of EC50 or IC50 log concentration Hillslope all related to slope of curve. When > 0 curve increases with x. unitless

 

• One Site Competition

In a competition study a ligand is added which competes for another ligand (both ligands may be the same) already attached to a receptor. As ligand is added the amount of existing ligand bound decreases. The one site competition equation characterizes this decrease with added ligand. The drug data x is entered in logarithmic form. This equation is identical to the sigmoidal dose-response equation except for the sign change in the exponent (the sigmoidal dose-response equation increases with x whereas the one site competition decreases).

Variable Range Definition Units x >0 log concentration of cold liganda log concentration, log(M) y >= 0 total or specific bindingb,c cpm, % specific binding, sites/cell, fmol of receptor/mg of tissue min >0 nonspecific binding same as y max >0 maximum binding in absence of cold ligand same as y LogEC50 >0 log of EC50 or IC50 log concentration

a .enter x values in log units so that confidence limits for EC50 are > 0.

b .if use total then min is the nonspecific binding

c .if use % specific then the user might want to constrain min to 0 and max to 100

• Two Site Competition

This equation is used for competition studies where the ligand binds to two receptors. The drug data x is entered in logarithmic form.

Variable Range Definition Units x >0 log concentration of cold ligand log concentration, log(M) y >= 0 total or specific binding cpm, % specific binding, sites/cell, mol of receptor/mg of tissue min >0 nonspecific binding same as y max >0 maximum binding in absence of cold ligand same as y F1 >0 Fraction of receptors with affinity logEC501 unitless LogEC501 >0 log of EC501 or IC501 log concentration LogEC5 >0   log concentration

• Four-Parameter Logistic Function

This function is most frequently used for standard curves, radioimmunoassays and dose-response curves. It is included here only for the standard A, B, C, D parameter terminology that is commonly used in these fields. The drug data x is entered in logarithmic form. Except for a sign difference in the slope parameters it is exactly the same as the sigmoidal dose-response (variable slope) equation.

Variable Range Definition Units x >0 log concentration of drug, dose log concentration, log(M) y       D >0 maximum response plateau same as y A >0 maximum response plateau same as y logC >0 log of EC50 or IC50 log concentration B all related to slope of curve. When > 0 curve increases with x. unitless

• Four-Parameter Logistic Function (Linear)

This is identical to the four-parameter logistic equation except that the linear form of dose concentration (x data) is entered into the worksheet. This equation and the four-parameter logistic equation will yield exactly the same numerical curve fit results. The only reason to use this equation is if you want a graph with a linear X-axis scale. Fitting the four-parameter logistic equation using log(x) data and then changing the X-axis scale to linear will result in a fit line with poor resolution. Using this equation solves this problem.

Variable Range Definition Units x >0 concentration of drug, dose log concentration, log(M) y >= 0 response response units D >0 minimum response plateau   A >0 minimum response plateau   logC >0 log of EC50 or IC50 log concentration B all related to slope of curve. When > 0 curve increases with x. unitless

• One Site Competion, max=100
  
  
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