Does anyone have a good resource to share on describing the colorimetric signal in sandwich ELISA mathematically as a function of antibody- and antigen concentration and other variables?
In order to better understand what's actually happening in the microplate, I am looking for something to start from that represents the current knowledge. A recent paper, review or textbook paper would be fine.
Dear Wolfgang,
ELISA binding is often described by 4-parameter logistic fit models or a simplified equlibrium model (basically Michaelis Menten). An approximation which better reflects the real equilibrium situation is given by the formula below. It is deduced from the law of mass action. Bmax is the saturation signal, x: antibody concentrtaion, c: antigen conc., KD. dissociation constant. However, even this model does only apply for monovalent binding (i.e. Fab fragments). Moreover mass transport limitations, re-binding, washing effects, etc. is not taken into account. Actually, there is no mathematical model which really can describe what is going on in a simple ELISA plate.
1:1 Binding Model according to the law of mass action:
Y=Bmax/(2*c)*(x+c+KD-sqrt((x+c+KD)*(x+c+KD)-4*x*c))
More details about the formula above are described by Abraham et al., J. Mol. Recogn. 9 (1996), 456-461.
Dear Wolfgang,
ELISA binding is often described by 4-parameter logistic fit models or a simplified equlibrium model (basically Michaelis Menten). An approximation which better reflects the real equilibrium situation is given by the formula below. It is deduced from the law of mass action. Bmax is the saturation signal, x: antibody concentrtaion, c: antigen conc., KD. dissociation constant. However, even this model does only apply for monovalent binding (i.e. Fab fragments). Moreover mass transport limitations, re-binding, washing effects, etc. is not taken into account. Actually, there is no mathematical model which really can describe what is going on in a simple ELISA plate.
1:1 Binding Model according to the law of mass action:
Y=Bmax/(2*c)*(x+c+KD-sqrt((x+c+KD)*(x+c+KD)-4*x*c))
More details about the formula above are described by Abraham et al., J. Mol. Recogn. 9 (1996), 456-461.
I agree with Bodo.....it's complicated. You might look in to some work out of Rick Zangar's laboratory. His laboratory is interested in ELISA microarrays and fitting those data to determine protein concentration. Perhaps this reference will help:
Daly DS, KK Anderson, AM White, RM Gonzalez, SM Varnum, and RC Zangar. 2008. "Predicting protein concentrations with ELISA microarray assays, monotonic splines and Monte Carlo simulation." Statistical Applications in Genetics and Molecular Biology 7(1):Article 21.
Dear Wolfgang,
the best model describing the law of mass action in a second order ist the Rodbard function.
http://rsb.info.nih.gov/ij/docs/menus/analyze.html#cal
Other function are adpting the calibration curve also well but are somtimes to adaptive. The Rodbard function is able to overcome some minor mistakes in the measurement much better than others.
We have recently modeled extraction/sorption of analytes onto a surface using Comsol Multiphysics. We studied both the effect of mass transport and binding to surface (with Langmuir model). In addition, the effect of any other binding compenents present in the sample is also studied. I am also interested in learning if there are other available models. Thanks.
http://pubs.acs.org/doi/10.1021/acs.analchem.5b02239
Hi Wolfgang,
I found the following publication by Zhang et al., 2014 insightful (attached). It helped me to understand what factors affect the limit of detection in a Sandwich ELISA. I used it as a base to script a simple ELISA model in Wavemetrics Igor software to see how different hydrodynamic radii, Kds, coating surface areas etc can affect the observed signal.
Article Predicting detection limits of enzyme-linked immunosorbent a...
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