ENH integrate new appendices
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@ -1558,16 +1558,15 @@ quantified for \gls{stp} protein using the \gls{bca} assay.
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% TODO defend why the microcarriers were saturated with stp
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The effective diffusivity of the microcarriers was determined using a
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pseudo-steady-state model. Each microcarrier was assumed to be a porous sphere
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with a fixed number of `\gls{stp} binding sites' equal to the maximum number of
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\gls{stp} molecules that could binding to the surface per area (eg, we assumed
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the surface was fully covered by \gls{stp}). Because the reaction rate between
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biotin and \gls{stp} was so fast, we assumed that the interface of free biotin
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shrunk as a function of \gls{stp} bound until the center of the microcarriers
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was reached. We also assumed that the pores in the microcarriers were large
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enough that the interactions between the \gls{stp} and surfaces would be small,
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thus the apparent diffusivity could be represented as a fraction of the
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diffusion coefficient of \gls{stp} in water. This model was given by
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\cref{eqn:stp_diffision_1,eqn:stp_diffision_2}:
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with a fixed number of `\gls{stp} binding sites' equal to the number of
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\gls{stp} molecules experimentally determined to bind to the microcarriers.
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Because the reaction rate between biotin and \gls{stp} was so fast, we assumed
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that the interface of free biotin shrunk as a function of \gls{stp} bound until
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the center of the microcarriers was reached. We also assumed that the pores in
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the microcarriers were large enough that the interactions between the \gls{stp}
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and surfaces would be small, thus the apparent diffusivity could be represented
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as a fraction of the diffusion coefficient of \gls{stp} in water. This model was
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given by \cref{eqn:stp_diffision_1,eqn:stp_diffision_2}:
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% TODO actually derive these equations, eg state the initial conditions and
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% governing equation
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@ -1598,15 +1597,23 @@ diffusion coefficient of \gls{stp} in water. This model was given by
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The diffusion rate of \gls{stp} was assumed to be
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\SI{6.2e-7}{\cm\squared\per\second}\cite{Kamholz2001}. Since all but $\beta$ was
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known, the experimental data was fit using these equations using
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\inlinecode{ode45} in MATLAB and least squares as the fitting error. These equations were then used analogously to describe the reaction profile of
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\inlinecode{ode45} in MATLAB and least squares as the fitting error. These
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equations were then used analogously to describe the reaction profile of
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\glspl{mab} assuming a diffusion rate of
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\SI{4.8e-7}{\cm\squared\per\second}\cite{Sherwood1992}. These same coefficients
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\SI{4.8e-7}{\cm\squared\per\second}\cite{Sherwood1992}.
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These same coefficients
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were used in determining the kinetics of the washing steps, and
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\SI{5.0e-6}{\cm\squared\per\second}\cite{Niether2020} was used as the diffusion
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coefficient for free biotin (which should be the only species left in solution
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after all the \gls{snb} has hydrolyzed). All diffusion coefficients were taken
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to be valid at \gls{rt} and in \gls{di} water, which is a safe assumption given
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that our reaction medium was 1X \gls{pbs}.
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after all the \gls{snb} has hydrolyzed).
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All diffusion coefficients were taken to be valid at \gls{rt} and in \gls{di}
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water, which is a safe assumption given that our reaction medium was 1X
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\gls{pbs}.
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See \cref{sec:appendix_binding} and \cref{sec:appendix_washing} for the MATLAB
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code (and output in the case of the washing steps) used.
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% METHOD add the equation governing the washing steps
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@ -4471,7 +4478,7 @@ hosted using \gls{aws} using their proprietary Aurora implementation.
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The code is available here: \url{https://github.gatech.edu/ndwarshuis3/mdma}.
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\chapter{binding kinetics code}
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\chapter{binding kinetics code}\label{sec:appendix_binding}
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The \gls{stp} binding kinetic profile was fit and calculated using the following
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MATLAB code. Note that the \inlinecode{geometry} parameter was varied so as to
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@ -4486,7 +4493,7 @@ reflect the \gls{mab} coating process.
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\lstinputlisting{../code/diffusion_mab.m}
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\chapter{washing kinetics code}
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\chapter{washing kinetics code}\label{sec:appendix_washing}
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The wash steps for the \gls{dms} were modeled using the following code:
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