Question

Calculate LC50 if the equation MTT trend line was y =-50,000ln(x) +400,000 and the cell density in the control treatment was 500,000 cells/mL.

Answer 1

Calculation of LC50 value for MTT assay.

LC50 is the concentration of the drug molecule at which 50% of the microbial population dies/survive.

Given the trend line is y =-50,000*ln(x) +400,000. Clearly this is a downward sloping sigmoidal curve. So, the percent survival has been plotted on the y-axis. This is an equation of the form y=mx + c. where x and y are variables and m is the slope with c as intercept.

The question does not give details about underlying data, rather a trend line has been given. So, directly substituting y=50% in the above equation we can solve for x.

After substituting y=50% we have,

50/100 = 50,000*ln(x) +400,000

or, 50,000*ln(x) = 50/100 - 400,000

or, ln(x) = -399999.5/50000

or, ln(x) = -7.9

or, x = e^-7.9

or, x = 1/ e^-7.9

or, x = 3.707 * 10^-4 concentration units of the drug/ ml.

The estimation of LC50 concentration of a drug molecule has application in toxicity studies and routinely used in drug discovery and clinical trials.