Hello,
I fit a classical dose response curve
Y=Bottom + (Top-Bottom)/(1+10^((LogEC-X)*HillSlope))
to my data (not related to inhibitors etc). The model I use is purely qualitative but it fits the data well. I have a few (trivial) questions.
1. Does the EC50 value depend on the Hill slope? Or alternatively: Can two EC50 values with different hill slopes be compared?
2. Is the conversion of the x-axis values to logarithmic scale a requirement for an adequate fit?
Kind regards
I don't think they are trivial questions.
1. Consider the meaning of the Hill slope in your system. If it differs between two EC50 values, it may be telling you something important. I'll give you an example from enzyme inhibitor studies. For an enzyme that has no active site cooperativity, the EC50 (we would say IC50) curve of the inhibitor (% inhibition versus inhibitor concentration) should have a Hill slope of 1. If the curve has a Hill slope that is very different from 1 (e.g. 0.5 or 2), it usually means there is a problem with the measurement, such as insolubility of the inhibitor, a non-specific mechanism of inhibition, interference by the inhibitor with the readout, or the IC50 is too close to the enzyme concentration.
2. If you are using an equation for the curve that features the logarithm of the EC50, it is proper to use the logarithm of the values on the x axis. However, it is not necessary to use logarithms to do the curve fitting. You can use a non-logarithmic equation and the arithmetic values of the x-axis parameter, but plot the curve on a logarithmic axis if desired by choosing that setting in the graphing program. It's up to you. A non-logarithmic Hill equation is:
y = bottom + (top-bottom)*Xn/( EC50n + Xn), where n is the Hill coefficient.
I don't think they are trivial questions.
1. Consider the meaning of the Hill slope in your system. If it differs between two EC50 values, it may be telling you something important. I'll give you an example from enzyme inhibitor studies. For an enzyme that has no active site cooperativity, the EC50 (we would say IC50) curve of the inhibitor (% inhibition versus inhibitor concentration) should have a Hill slope of 1. If the curve has a Hill slope that is very different from 1 (e.g. 0.5 or 2), it usually means there is a problem with the measurement, such as insolubility of the inhibitor, a non-specific mechanism of inhibition, interference by the inhibitor with the readout, or the IC50 is too close to the enzyme concentration.
2. If you are using an equation for the curve that features the logarithm of the EC50, it is proper to use the logarithm of the values on the x axis. However, it is not necessary to use logarithms to do the curve fitting. You can use a non-logarithmic equation and the arithmetic values of the x-axis parameter, but plot the curve on a logarithmic axis if desired by choosing that setting in the graphing program. It's up to you. A non-logarithmic Hill equation is:
y = bottom + (top-bottom)*Xn/( EC50n + Xn), where n is the Hill coefficient.
Kindly check https://fisbio.biof.ufrj.br/restrito/bioEstatistica/90_top_especiais/fitting_dose_response_curves.pdf
Also check https://www.sciencedirect.com/science/article/pii/S1056871914002470
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