From 75b1b9e5881e4a7ed638ddd78414bec315226bb1 Mon Sep 17 00:00:00 2001 From: ndwarshuis Date: Tue, 3 Aug 2021 19:05:34 -0400 Subject: [PATCH] ENH integrate new appendices --- tex/thesis.tex | 41 ++++++++++++++++++++++++----------------- 1 file changed, 24 insertions(+), 17 deletions(-) diff --git a/tex/thesis.tex b/tex/thesis.tex index 1680040..e42dfac 100644 --- a/tex/thesis.tex +++ b/tex/thesis.tex @@ -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: