598 PJ

Homework 3

BIOE 498/598 PJ, Spring 2020

Due Wednesday, April 8th by 5pm CDT.

Your goal is to optimize production of acetoin, a byproduct secreted by an engineered strain of the Gram positive bacterium Lactococcus lactis. A previous screening experiment identified five factors that affect the titers of acetoin. You will vary these factors over the following ranges:

Factor | Coded Variable | Low Level (-1) | High Level (+1) | Units -------|----------------|----------------|-----------------|------ pH | x1 | 6.0 | 7.2 | stirring rate | x2 | 40 | 60 | RPM [lactose] | x3 | 80 | 120 | mM [casamino acids] | x4 | 0.4 | 0.6 | g/L [nisin] | x5 | 0.2 | 0.4 | mM

Lactose is the preferred carbon source for L. lactis.
Casamino acids are a nitrogen source made from digested soy protein.
Nisin is a peptide that induces expression of the acetoin production pathway.
The units of the response variable (acetoin titer) are mg/L.

Rather than run the experiments yourself, you will add the response data using this R package. If you haven't already, install the devtools package:

install.packages("devtools")

If you have a Windows machine you may need to install the Rtools package before installing devtools

Next, install and load this package:

devtools::install_github("bioe498/bioe498pj.hw3")
library("bioe498pj.hw3")

This package includes a function run_experiments that adds the responses to your design object. The function returns a new design object with the titer column filled in. If your CCD is stored in a variable named design, then

design <- run_experiments(design, block=1)

will add the responses for the first block of runs (the factorial points).

Using the rsm package, set up a full-factorial, rotatable CCD. Do not randomize the run order. Set the variable codings using the names in the above table and name the response variable titer. Make sure your design includes a blocking factor so you can perform the factorial and axial runs separately.
Use the run_experiments function with block=1 to add the responses for the factorial experiments.
Build a RSM model using FO and TWI terms. Does the FO and TWI surface fit the data well? Does this model have a reasonable stationary point? If so, is it a minimum, maximum, or a saddle point?
Use the run_experiments function with block=2 to add the responses for the axial experiments.
Build an SO RSM model. Do the second-order terms improve the model? Does this model have a reasonable stationary point? If so, is it a minimum, maximum, or a saddle point?
Use the steepest function to find the conditions with the maximum acetoin titer within the design space. What are the optimal operating conditions?
Repeat the above steps using a CCD with a 2^5-1 Fractional Factorial Design.