The goal of this problem is

to examine the process data for a protein refolding operation and determine the suitability

of a third order relationship of the rate data.

Problem Statement : The following data were obtained for the concentration, C$,$ of a soluble,

monomeric recombinant pharmaceutical protein as a function of time, t$,$ during a refolding

operation:

Process time, t $($minutes$)$ soluble protein concentration, C $($g$/$L$)$

$114\mathrm{.}76$

$751\mathrm{.}17$

$1390\mathrm{.}67$

$1880\mathrm{.}51$

Based on a review of the biotechnology and bioprocessing literature, it is suspected that the

soluble protein is consumed by a third$-$order aggregation reaction during this refolding operation:

if this were indeed the case, the relationship between C and t for this third order reaction would

be C $=(1/($Co$)2+2$kt$)^-1/2$ where Co and k are constants.

Use linear regression to determine the constants Co and k from the given data and compute the

corresponding correlation coefficient $($R$2).$ How good is the fit? Be sure to give due regard to

significant figures and dimensions. What conclusion can you draw from your fit?