Assignment 2 You are encouraged to work in groups (maximum 3) on homework. For each part below, please provide the MATLAB code you implemented. Do not submit the homework solutions from previous years (The data are different). Dose-Response Modeling (100 points) Suppose that you work for a pharmaceutical company and you are supposed to assess the efficacy and potency of two drugs (Agent A and Agent B) before allowing the agents to proceed to clinical trials. You performed a preliminary experiment to get an overall idea and obtained the following data. Dose(mg/kg) % Response % Response (Agent A) (Agent B) 1 GO 9 10 49 31 60 82 60 100 88 74 200 92 77 450 94 78 600 96 80 850 96 79 1000 98 85 You decided to model the dose-response relationship using a three-parameter Hill Model taking a value of 1 for the Hill coefficient as given below. ECC) =Emex EC50 + a) Using the MATLAB function fitnlm (or Isqcurvefit) perform a nonlinear regression. What are the optimal values for Emax and ECso for each drug? b) Linearize the Hill Equation using Lineweaver-Burk method. Using the linearized form of the function and the data given above compute the EC50 value and the maximum effect (Emax) for each drug. Are the values exactly the same as those you computed in (a)? Explain. c) Plot separately the fitted curve and the fitted line that you computed in (a) and (b), together with the data used. What do you observe? d) Compute R2 for both (a) and (b). Which fit seems to be better? e) Considering the definitions below, compare the efficacy and potency of the drugs. Which one would you prefer and why? Efficacy: maximum effect that a drug can produce regardless of dose. Potency: amount of a drug that is needed to produce a given effect (e.g, for instance EC50)