ENH integrate new appendices

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Nathan Dwarshuis 2021-08-03 19:05:34 -04:00
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1 changed files with 24 additions and 17 deletions

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@ -1558,16 +1558,15 @@ 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}:
with a fixed number of `\gls{stp} binding sites' equal to the number of
\gls{stp} molecules experimentally determined to bind to the microcarriers.
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
@ -1598,15 +1597,23 @@ diffusion coefficient of \gls{stp} in water. This model was given by
The diffusion rate of \gls{stp} was assumed to be
\SI{6.2e-7}{\cm\squared\per\second}\cite{Kamholz2001}. 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. These equations were then used analogously to describe the reaction profile of
\inlinecode{ode45} in MATLAB and least squares as the fitting error. 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}. These same coefficients
\SI{4.8e-7}{\cm\squared\per\second}\cite{Sherwood1992}.
These same coefficients
were used in determining the kinetics of the washing steps, and
\SI{5.0e-6}{\cm\squared\per\second}\cite{Niether2020} was used as the diffusion
coefficient for free biotin (which should be the only species left in solution
after all the \gls{snb} has hydrolyzed). All diffusion coefficients were taken
to be valid at \gls{rt} and in \gls{di} water, which is a safe assumption given
that our reaction medium was 1X \gls{pbs}.
after all the \gls{snb} has hydrolyzed).
All diffusion coefficients were taken to be valid at \gls{rt} and in \gls{di}
water, which is a safe assumption given that our reaction medium was 1X
\gls{pbs}.
See \cref{sec:appendix_binding} and \cref{sec:appendix_washing} for the MATLAB
code (and output in the case of the washing steps) used.
% METHOD add the equation governing the washing steps
@ -4471,7 +4478,7 @@ hosted using \gls{aws} using their proprietary Aurora implementation.
The code is available here: \url{https://github.gatech.edu/ndwarshuis3/mdma}.
\chapter{binding kinetics code}
\chapter{binding kinetics code}\label{sec:appendix_binding}
The \gls{stp} binding kinetic profile was fit and calculated using the following
MATLAB code. Note that the \inlinecode{geometry} parameter was varied so as to
@ -4486,7 +4493,7 @@ reflect the \gls{mab} coating process.
\lstinputlisting{../code/diffusion_mab.m}
\chapter{washing kinetics code}
\chapter{washing kinetics code}\label{sec:appendix_washing}
The wash steps for the \gls{dms} were modeled using the following code: