ENH add diffusion method section

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Nathan Dwarshuis 2021-07-28 13:43:03 -04:00
parent 395efa6657
commit 4994343432
2 changed files with 70 additions and 1 deletions

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@ -1167,6 +1167,19 @@ CONCLUSIONS: We developed a simplified, semi-closed system for the initial selec
publisher = {Public Library of Science ({PLoS})}, publisher = {Public Library of Science ({PLoS})},
} }
@Article{Sherwood1992,
author = {Jill K. Sherwood and Richard B. Dause and W. Mark Saltzman},
journal = {Nature Biotechnology},
title = {Controlled Antibody Delivery Systems},
year = {1992},
month = {nov},
number = {11},
pages = {1446--1449},
volume = {10},
doi = {10.1038/nbt1192-1446},
publisher = {Springer Science and Business Media {LLC}},
}
@Comment{jabref-meta: databaseType:bibtex;} @Comment{jabref-meta: databaseType:bibtex;}
@Comment{jabref-meta: grouping: @Comment{jabref-meta: grouping:

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@ -975,7 +975,63 @@ at \SI{260}{\nm} were taken every minute for \SI{2}{\hour}.
\subsection{reaction kinetics quantification} \subsection{reaction kinetics quantification}
% METHOD add reaction kinetics diffusion mathy stuff The diffusion of \gls{stp} into biotin-coated microcarriers was determined
experimentally. \SI{40}{\ug\per\ml} \gls{stp} was added to multiple batches of
biotin-coated microcarriers, and supernatents were taken at fixed intervals and
quantified for \gls{stp} protein using the \gls{bca} assay.
% TODO defend why the microcarriers were saturated with stp
The effective diffusivity of the microcarriers was determined using a
pseudo-steady-state model. Each microcarrier was assumed to be a porous sphere
with a fixed number of `\gls{stp} binding sites' equal to the maximum number of
\gls{stp} molecules that could binding to the surface per area (eg, we assumed
the surface was fully covered by \gls{stp}). Because the reaction rate between
biotin and \gls{stp} was so fast, we assumed that the interface of free biotin
shrunk as a function of \gls{stp} bound until the center of the microcarriers
was reached. We also assumed that the pores in the microcarriers were large
enough that the interactions between the \gls{stp} and surfaces would be small,
thus the apparent diffusivity could be represented as a fraction of the
diffusion coefficient of \gls{stp} in water. This model was given by
\cref{eqn:stp_diffision_1,eqn:stp_diffision_2}:
% TODO actually derive these equations, eg state the initial conditions and
% governing equation
\begin{equation}
\label{eqn:stp_diffision_1}
\frac{dr}{dt} = \frac{-D_{app}C}{Br(1-r/R)}
\end{equation}
\begin{equation}
\label{eqn:stp_diffision_2}
\frac{dC}{dt} = \frac{-4 \pi n D_{app} C}{V(1/r-1/R)}
\end{equation}
\noindent where
\begin{itemize}[label={}]
\item $D_{app}$ is the apparent diffusion rate which is equal to $D_{STP}\beta$
\item $D_{STP}$ the diffusion rate of \gls{stp} in water
\item $\beta$ a fractional parameter representing the tortuousity and void
fraction of the microcarriers.
\item $r$ is the interfatial radius of the unbound biotin within a microcarrier
\item $t$ is the reaction time
\item $C$ is the concentration of \gls{stp} in the bulk solution
\item $V$ is the volume of the bulk medium
\item $R$ is the average radius of the microcarriers
\item $n$ is the number of microcarriers in the reaction volume
\end{itemize}
% TODO cite the diffusion rate of stp
The diffusion rate of \gls{stp} was assumed to be
\SI{3.89e-7}{\cm\squared\per\second} {\#}{diffusion rate citation}. Since all
but $\beta$ was known, the experimental data was fit using these equations using
\inlinecode{ode45} in MATLAB and least squares as the fitting error.
% TODO this diffusion rate isn't actually reflected in the code
These equations were then used analogously to describe the reaction profile of
\glspl{mab} assuming a diffusion rate of
\SI{4.8e-7}{\cm\squared\per\second}\cite{Sherwood1992}.
% METHOD add the equation governing the washing steps
\subsection{Luminex Analysis} \subsection{Luminex Analysis}