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ADD link to appendix for derivations

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Nathan Dwarshuis 2021-09-07 16:02:52 -04:00
parent 2c120c95c7
commit fbb09a07cf
1 changed files with 4 additions and 7 deletions
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@ -1669,8 +1669,8 @@ quantified for \gls{stp} protein using the \gls{bca} assay.
The geometric diffusivity of the microcarriers was determined using a The geometric diffusivity of the microcarriers was determined using a
pseudo-steady-state model. Each microcarrier was assumed to be a porous sphere pseudo-steady-state model. Each microcarrier was assumed to be a porous sphere
with a fixed number of uniformly distributed `\gls{stp} binding sites' equal to with a fixed number of uniformly distributed ``\gls{stp} binding sites'' equal
the number of \gls{stp} molecules experimentally determined to bind to the to the number of \gls{stp} molecules experimentally determined to bind to the
microcarriers. Because the reaction rate between biotin and \gls{stp} is so fast microcarriers. Because the reaction rate between biotin and \gls{stp} is so fast
(it is the strongest non-covalent bond in known existence), we assumed that the (it is the strongest non-covalent bond in known existence), we assumed that the
interface of free biotin shrunk as a function of \gls{stp} diffusing to the interface of free biotin shrunk as a function of \gls{stp} diffusing to the
@ -1679,10 +1679,9 @@ 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 interactions between the \gls{stp} and surfaces would be small, thus the
geometric diffusivity could be represented as a fraction of the diffusion geometric diffusivity could be represented as a fraction of the diffusion
coefficient of \gls{stp} in water. This model was given by coefficient of \gls{stp} in water. This model was given by
\cref{eqn:stp_diffusion_1,eqn:stp_diffusion_2}: \cref{eqn:stp_diffusion_1,eqn:stp_diffusion_2} (see \cref{sec:appendix_binding}
for derivations):
% TODO actually derive these equations, eg state the initial conditions and
% governing equation
\begin{equation} \begin{equation}
\label{eqn:stp_diffusion_1} \label{eqn:stp_diffusion_1}
\frac{dr}{dt} = \frac{-D_{app}C_b}{Br(1-r/R)} \frac{dr}{dt} = \frac{-D_{app}C_b}{Br(1-r/R)}
@ -3717,7 +3716,6 @@ group, while the \gls{colb} group visibly lowered CD62L and CD4, indicating
partial enzymatic cleavage (\cref{fig:collagenase_fx}). Based on this result, we partial enzymatic cleavage (\cref{fig:collagenase_fx}). Based on this result, we
used \gls{cold} moving forward. used \gls{cold} moving forward.
% FIGURE this figure is tall and skinny like me
\begin{figure*}[ht!] \begin{figure*}[ht!]
\begingroup \begingroup
@ -4867,7 +4865,6 @@ Python, with a subprocess running R in a Docker container to handle the flow
cytometry data (\cref{fig:meta_overview}). The Postgres database itself was cytometry data (\cref{fig:meta_overview}). The Postgres database itself was
hosted using \gls{aws} using their proprietary Aurora implementation. hosted using \gls{aws} using their proprietary Aurora implementation.
% FIGURE explain what the colors mean
\begin{figure*}[ht!] \begin{figure*}[ht!]
\begingroup \begingroup