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% Symbols
\newcommand{\dif}{\mathrm{d}}
\newcommand{\me}{\mathrm{e}}

% Specific
\addunit{\virion}{virions}
\addunit{\hpi}{hpi}
\addunit{\molar}{M}
\addunit{\virc}{[V]}
\newcommand{\adam}{NPI-5291\xspace}
\newcommand{\strain}{A/Albany/1/98 (H3N2)\xspace}
\newcommand{\AIC}{\ensuremath{\mathrm{AIC_C}}\xspace}
\newcommand{\real}{\ensuremath{R}\xspace}
\newcommand{\Vreal}{\ensuremath{V_\real}\xspace}
\newcommand{\breal}{\ensuremath{\beta_\real}\xspace}
\newcommand{\preal}{\ensuremath{p_\real}\xspace}
\newcommand{\ic}{\ensuremath{\mathrm{IC}_{50}}\xspace}
\newcommand{\emax}{\ensuremath{\epsilon_\mathrm{max}}\xspace}
\newcommand{\tmut}{\ensuremath{\tau_\mu}\xspace}

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\begin{document}
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\begin{titlebox}
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\textbf{\Huge Sample Phymbie \LaTeX\ Poster using pdflatex} \\[0.5em]
\noindent
\textsc{\Large Catherine A.A.\ Beauchemin$^{\ast,\dagger}$ and Phymbie$^\ast$} \\[0.5em]
\noindent
{\Large %
$^\ast$Department of Physics, Ryerson University, Toronto, ON\\
$^\dagger$Some other location somewhere
}
\end{center}
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\subsection*{\color{section0} Abstract}

Influenza A has become a growing concern for health authorities worldwide both in its seasonal and pandemic forms. The annual cost of influenza illness and the threat of an imminent pandemic make it necessary to revisit the treatment options currently available. Here, we show that using a controlled experimental system, the hollow fiber infection model (HFIM), it is possible to develop rigorous mathematical models of the course of influenza A infection and the effect of drug pressure. The current work reports on our preliminary experiments examining the effects of amantadine on flu A.

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\section*{\color{section0} Background}

\begin{item0}
\item Until recently, adamantane drugs were the primary prophylaxis and treatment method used to prevent and control influenza infection.
\item Resistance to adamantanes emerges rapidly during treatment. Resistant variants show no evidence of fitness impairment and are readily transmissible (Deyde et al., 2007).
\item There is now wide-spread resistance among circulating influenza strains worldwide with 90.5\% and 15.5\% resistance prevalence among H3N2 and H1N1 strains, respectively (Deyde et al., 2007).
\end{item0}

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\section*{\color{section0}Long-term objective}
\begin{item0}
\item To develop comprehensive models of influenza infection, its response to drugs, and emergence of drug resistance in multiple systems (tissue culture, animals, humans).
\end{item0} \vspace{-1em}

\section*{\color{section0}Approach}
\begin{item0}
\item Develop simple yet accurate mathematical models to fully capture influenza dynamics in vitro in the presence of drug.
\end{item0}

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\section*{\color{section0} The mathematical models}

\begin{minipage}[t]{0.45\textwidth}
Simple model
\noindent
\bea
\frac{\dif T}{\dif t}\es &=&\es - \mathbf{\color{magenta}(1-\epsilon)} \beta V T \\
\frac{\dif I}{\dif t}\es &=&\es \mathbf{\color{magenta}(1-\epsilon)} \beta V T  - \delta I \\
\frac{\dif V}{\dif t}\es &=&\es p I - \mathbf{\color{magenta}c} V - \mathbf{\color{magenta}\gamma} T V \\
\eea
\end{minipage}
\begin{minipage}[t]{0.46\textwidth}
Eclipse model
\bea
\frac{\dif T}{\dif t}\es &=&\es - \mathbf{\color{magenta}(1-\epsilon)} \beta V T \\
\frac{\dif E}{\dif t}\es &=&\es \mathbf{\color{magenta}(1-\epsilon)} \beta V T  - k E \\
\frac{\dif I}{\dif t}\es &=&\es k E  - \delta I \\
\frac{\dif V}{\dif t}\es &=&\es p I - \mathbf{\color{magenta}c} V - \mathbf{\color{magenta}\gamma} T V\\
\eea
\end{minipage}

\vspace{-1em}
\begin{minipage}[t]{0.45\textwidth}
Delay model
\noindent
\bea
\frac{\dif T}{\dif t}\es &=&\es - \mathbf{\color{magenta}(1-\epsilon)} \beta V T \\
\frac{\dif I}{\dif t}\es &=&\es \mathbf{\color{magenta}(1-\epsilon)} \beta V(t - \tau) T(t-\tau)  - \delta I \\
\frac{\dif V}{\dif t}\es &=&\es p I - \mathbf{\color{magenta}c} V - \mathbf{\color{magenta}\gamma} T V \\
\eea
\end{minipage}

\begin{minipage}[t]{\textwidth}
where the free virions (V) are absorbed by target cells (T) which can then become infected (I). The effect of amantadine, $\mathbf{\color{magenta}(1-\epsilon)}$, is such that it will reduce the rate at which virus (V) successfully infect target cells (T).
\end{minipage}

\vspace{1em}
\begin{minipage}[t]{0.45\textwidth}
Drug is modeled by:
\be
\epsilon(t) = \frac{\emax D(t)}{D(t) + \ic}
\ee
\end{minipage}
\begin{minipage}[t]{0.54\textwidth}
\vspace{0.5em}
where $D(t)$ is the amantadine concentration and $\emax$ is its maximum effect.
\end{minipage}

\vspace{1em}
\begin{minipage}[t]{1.0\textwidth}
The basic reproductive number is given by \\
\be
R_0 = \underbrace{\frac{p}{\delta}}_{\mathrm{virion/cell}} \cdot \underbrace{\frac{\beta T_0}{c + \gamma T_0}}_{\mathrm{infection\ rate}}
\ee
\end{minipage}

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\section*{\color{section0} The HFIM experimental model}
\vspace{-0.7em}

\begin{center}
	\resizebox{0.4\linewidth}{!}{\includegraphics{images/hf-system}}
\end{center}

\vspace{-1.5em}
\begin{item0}
\item HFIM loaded with $10^8$ MDCK cells in growth medium + 100 cells pre-infected with A/Albany/1/98 (H3N2) and kept at cst amantadine concentration.
\item At $t = \unit{22}{\hour}$, \unit{28}{\hour}, \unit{46}{\hour}, \unit{72}{\hour}, \unit{96}{\hour}, and \unit{144}{\hour}, \unit{3}{\milli\liter} of the \unit{15}{\milli\liter} of the HFIM are harvested for analysis.
\end{item0}

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\section*{\color{section0} Clearance in the HFIM}

\resizebox{0.65\linewidth}{!}{\includegraphics{images/clearance}}

\vspace{-12em}
\begin{flushright}
\begin{minipage}[t]{0.34\textwidth}
Using the model \vspace{-0.7em}
\be
\frac{\dif V}{\dif t} = - c V \vspace{-0.7em}
\ee
which integrates to \vspace{-0.7em}
\be
V(t) = V(0)\,\me^{-c t} \vspace{-0.7em}
\ee
\hspace{3em} or \vspace{-0.7em}
\be
\ln(V) = \ln(V) - c t
\ee
\end{minipage}
\end{flushright}
\vspace{0.5em}

\begin{item0}
\item Deposited virus + drug $\rightarrow$ plaque assays at various time to obtain rate of loss of infectivity.
\item Linear least square fit: $c = \unit{0.105\pm0.003}{\hour^{-1}}$: half-life of \unit{6.6\pm0.2}{\hour} for influenza virions in HF.
\end{item0}

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\section*{\color{section0}Fitting models to experiments}

\resizebox{0.95\linewidth}{!}{\includegraphics{images/entry_pfu}}

Fit of the simple (--), eclipse (- -), and delay ({\color{red}--}) models against the experimental viral titer.

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\section*{\color{section0}A first stab at drug resistance}
\vspace{-0.7em}

We investigated the effect of fixing \emax = 95\% with
\begin{minipage}[t]{0.5\textwidth}
\be
\ic =
\begin{cases}
\unit{0.40}{\micro\molar} & t \le \tmut \\
\unit{33}{\micro\molar} & t > \tmut
\end{cases}
\ee
\end{minipage}

\vspace{-5.5em}
\begin{flushright}
\begin{minipage}[t]{0.5\textwidth}
\footnotesize
\begin{tabular}{cc}
\hline
Drug concentration & \tmut \\
(\micro\molar) & (\hour) \\
\hline
0.0 & 144 \\
0.05 & 120 \\
0.5 & 13 \\
5.3 & 15 \\
16 & 9.2 \\
53.3 & 0 \\
\hline
\end{tabular}
\end{minipage}
\end{flushright}

\vspace{-0.7em}
\resizebox{0.95\linewidth}{!}{\includegraphics{images/switch_ic50}}

Viral titer when drug resistance is ignored (---) or included in an implicit way ({\color{red}---}).

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\section*{\color{section0}Parameter estimates from the fits}

\footnotesize
\begin{center}
\begin{tabular}{lccc}
\hline
\hline
Param.\ & Simple model & Eclipse model & Delay model \\
\hline
\hline
$1/k$ or $\tau$ ($\hour$)
	& --- & 3.2 & 0.22 \\
$1/\delta$ ($\hour$)
	& $13$ & $13$ & $13$ \\
$p/\delta$
	& 1.7 & 1.6 & 1.7 \\
$\beta/\gamma$
	& 6.9 & 29 & 8.8 \\
$R_0$
	& 11 & 36 & 13 \\
$\ic$ ($\micro\molar$)
	& $0.40$ & $0.30$ & $0.38$ \\
$\emax$
	& 0.56 & 0.74 & 0.60 \\
\hline
SSR & 3.6 & 3.7 & 3.6 \\
\AIC & -65 & -61 & -61 \\
\hline
\hline
\end{tabular}
\end{center}
\normalsize

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\section*{\color{section0}Parameter consistencies}

\footnotesize
\tabcolsep 3pt
\begin{center}
\begin{tabular}{ccccc}
& & \multicolumn{3}{c}{HFIM vs human primary infection} \\
\cline{3-5} \\
System & Model & eclipse phase & infect.\ cell lifespan & $R_0$ \\
\hline
	& simple & --- & \unit{6.0}{\hour} & 11 \\
\raisebox{1.5ex}[0pt]{Human}
	& eclipse & \unit{6.0}{\hour} & \unit{4.6}{\hour} & 22 \\
\hline
	& simple & --- & \unit{13}{\hour} & 11 \\
HFIM
	& eclipse & \unit{3.2}{\hour} & \unit{13}{\hour} & 36 \\
	& delay & 0.22 & \unit{13}{\hour} & 13 \\
\hline
\end{tabular}
\end{center}
\normalsize

\begin{item0}
\item Basic reproductive numbers, $R_0$, found for the HFIM data compared well with those found for an in vivo human infection (Baccam et al., 2006).
\item The longer infected cell lifespan and shorter eclipse phase found for the HFIM may reflect active killing of infected cells by the immune system in vivo or differences between MDCK and human lung epithelial cells.
\item $\ic\sim$0.3--\unit{0.4}{\micro\molar} for amantadine in good agreement with \unit{0.56}{\micro\molar} found for in vitro A/Panama/2007/99 (H3N2) infection of MDCK cells (Ilyushina et al., 2006).
\end{item0}

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\section*{\color{section0}Parameter inconsistencies}
\vspace{-0.7em}

\begin{item0}
\item The models predict an infected cell will produce $p/\delta \sim 1.7$ infectious virion over its lifespan.
\item Even though cells would be producing $\sim 1.7$ virion, the basic reproductive number, $R_0$, suggest they would infect $\sim 11$--36 cells over their infected lifespan.
\item $\beta > \gamma$ suggesting that less than one virion is lost for each cell becoming infected.
\end{item0}

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\section*{\color{section0}Conclusion}
\vspace{-0.7em}

\begin{item0}
\item The controlled experimental system allows the use of simple yet accurate mathematical models to quantify the dynamics of the experiments.
\item The parameter values found were consistent with those available for a human influenza infection.
\item The results indicated that experimental manipulations accounted for a loss of $\sim$ 90\% of infectious virions: a fact that was verified experimentally.
\item We showed that the rapid emergence of drug resistance over the course of a single treatment can account for the low efficacy ($\sim$ 56--74\%) found for amantadine.
\item This work constitutes a first step in developing a combination of experimental and theoretical tools to quantitate drug effects and the emergence of drug resistance over the course of an influenza infection.
\end{item0}

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\section*{\color{section0}Where to read more?}
\vspace{-0.7em}

\begin{item0}
\item blah blah blah
\item blih blih blih
\begin{item1}
	\item bloh, bloh, bloh
	\item bluh, bluh, bluh
\end{item1}
\item bleh, bleh, bleh
\item bleu, bleu, bleu
\item blau, blau, blau
\end{item0}

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\end{multicols}
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\end{document}
