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S5.tex
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\documentclass[a4paper, 12pt]{book}
\usepackage[utf8x]{inputenc}
\usepackage{amssymb,amsmath}
\usepackage{mathtools}
\usepackage{titlesec}
\usepackage{graphicx}
\usepackage{float}
\usepackage{lipsum}
\usepackage{pdfpages}
\usepackage{caption}
\usepackage{xcolor}
\usepackage{nicefrac}
\usepackage[ % page layout modifications
paper=a4paper, % - use A4 paper size
%scale={0.86,0.94}, % - total body size (h,v)
%scale={0.86,0.94}, % - total body size (h,v)
nohead, % - no header
%includefoot, % - include footer space
includemp, % - include side note space
bindingoffset=0.5cm, % - binding correction
top=2.5cm, % - total body: top margin
left=2.4cm, % - total body: left margin (odd pages)
right=0.05cm, % - total body: right margin (odd pages)
bottom=1.25cm, % - total body: bottom margin
%marginparwidth=1.75cm, % - width for side note
%marginparsep=10pt, % - space between notes and body text (content)
footskip=2cm, % - footer skip size
]{geometry}
\begin{document}
\pagestyle{empty}
\section*{Deterministic model (DM)}
The DM is equivalent to the Invergo 2014 model [21] with the following changes:
\begin{table}[H]
\centering
\caption{Reaction equation changes in the DM.}
\label{tab_det_model}
\begin{tabular}{l | l | l}
Reaction & Former rate & New rate\\
\hline
\hline
$\rightarrow {\rm cGMP}$ & $v_{\rm f} = \frac{\alpha_{\rm max}}{1 + \bigl( \frac{{\rm Ca}^{2+}_{\rm free}}{K_{\rm C1}} \bigr)^{m_1} } + \frac{\alpha_{\rm max}}{1 + \bigl( \frac{{\rm Ca}^{2+}_{\rm free}}{K_{\rm C2}} \bigr)^{m_2} } $ & $v_{\rm f} = f_1 \cdot \frac{\alpha_{\rm max}}{1+\bigl( \frac{{\rm Ca}^{2+}_{\rm free}}{K_{\rm C1}}\bigr)^{m_1}} + f_{\rm 1m} \cdot \frac{\alpha_{\rm max}}{1+\bigl( \frac{{\rm Ca}^{2+}_{\rm free}}{K_{\rm C1m}}\bigr)^{m_{\rm 1m}}} + ...$\\
& & $ + f_2 \cdot \frac{\alpha_{\rm max}}{1+\bigl( \frac{{\rm Ca}^{2+}_{\rm free}}{K_{\rm C2}}\bigr)^{m_2}}$
\end{tabular}
\end{table}
\begin{table}[H]
\centering
\caption{Parameter changes and new parameters in the DM.}
\label{tab_det_model}
\begin{tabular}{l | l | l | l}
Parameter & Former Value & New Value & Significance\\
\hline
\hline
$k_{\rm G3}$ & $8500/\mathrm{s}$ & $250/\mathrm{s}$ & Coupling rhodopsin - G-protein\\
\hline
$\beta_{\rm sub}$ & $2.1826 \cdot 10^{-3}/\mathrm{s}$ & $0.019/\mathrm{s}$ & cGMP hydrolysis by the effector\\
\hline
$\alpha_{\rm max}$ & $60 \mu {\rm M}/s$ & $120 \mu {\rm M}/s$ & Maximal rate of cGMP synthesis by the GCs\\
\hline
$K_{\rm C1m}$ & N/A & $ 0.171\,\mu\mathrm{M}$ & Calcium concentration at which cGMP synthesis is\\
& & & half-maximal for potential mutant\\
\hline
$m_{\rm 1m}$ & N/A & $3$ & Hill coefficient for cGMP synthesis for potential mutant\\
\hline
$f_1$ & N/A & $0.5$ & Fraction of the cGMP synthesis regulated by wild type\\
& & & GCAP1\\
\hline
$f_{\rm 1m}$ & N/A & $0$ & Fraction of the cGMP synthesis regulated by potential\\
& & & mutant GCAP1\\
\hline
$f_2$ & N/A & $0.5$ & Fraction of the cGMP synthesis regulated by wild type\\
& & & GCAP2\\
\end{tabular}
\end{table}
Please note: there is an option to include a GCAP1 mutant in the model, but in this case the parameters for the mutant were set to wild type values.
\section*{Hybrid stochastic-deterministic model}
\label{sec_appendix_small}
Please note that the number of available phosphorylation sites was reduced to three in this model, and therefore rhodopsin's phosphorylation state $n$ goes from zero to three.\\
\newgeometry{left=0.5cm,right=0.5cm}
\begin{table}[H]
\centering
\caption{Reaction equations in the HSDM frontend.}
\begin{tabular}{c | l | l}
Nr. & Reaction equation & Rate \\
\hline
\hline
1 & ${\rm R}_n + {\rm RK} \leftrightarrow {\rm R}_n\_{\rm RK}_{\rm pre}$ & $v_{\rm f} = k_{{\rm RK1,}n} \cdot {\rm RK} \cdot {\rm R}_n$\\
& & $v_{\rm r} = k_{\rm RK2} \cdot {\rm R}_n\_{\rm RK}_{\rm pre} $\\
\hline
2 & ${\rm R}_n\_{\rm RK}_{\rm pre} \rightarrow {\rm R}_{n+1}\_{\rm RK}_{\rm post}$ & $v_{\rm f} = k_{\rm RK3,ATP} \cdot {\rm R}_n\_{\rm RK}_{\rm pre} $\\
\hline
3 & ${\rm R}_{n+1}\_{\rm RK}_{\rm post} \rightarrow {\rm R}_{n+1} + {\rm RK}$ & $v_{\rm f} = k_{\rm RK4} \cdot {\rm R}_{n+1}\_{\rm RK}_{\rm post} $\\
\hline
4 & ${\rm Arr} + {\rm R}_n \leftrightarrow {\rm R}_n\_{\rm Arr}$ & $v_{\rm f} = k_{{\rm A1,}n} \cdot {\rm Arr} \cdot {\rm R}_n $\\
& & $v_{\rm r} = k_{\rm A2} \cdot {\rm R}_n\_{\rm Arr} $\\
\hline
5 & ${\rm R}_n\_{\rm Arr} \rightarrow {\rm Arr}$ & $v_{\rm f} = k_{\rm A3} \cdot {\rm R}_n\_{\rm Arr} $\\
\hline
6 & ${\rm R}\_{\rm Gt} \rightarrow {\rm Gt} + {\rm R}$ & $v_{\rm f} = k_{\rm Gpre2} \cdot {\rm R}\_{\rm Gt} - k_{\rm Gpre1} \cdot {\rm R} \cdot {\rm Gt} $\\
\hline
7 & ${\rm Gt} + {\rm R}_n \leftrightarrow {\rm R}_n\_{\rm Gt}$ & $v_{\rm f} = k_{{\rm G1,}n} \cdot {\rm Gt} \cdot {\rm R}_n $\\
& & $v_{\rm r} = k_{\rm G2} \cdot {\rm R}_n\_{\rm Gt}$\\
\hline
8 & ${\rm R}_n\_{\rm Gt} \leftrightarrow {\rm R}_n\_{\rm G}$ & $v_{\rm f} = k_{\rm G3} \cdot {\rm R}_n\_{\rm Gt}$\\
& & $v_{\rm r} = k_{\rm G4,GDP} \cdot {\rm R}_n\_{\rm G} $\\
\hline
9 & ${\rm R}_n\_{\rm G} \rightarrow {\rm R}_n\_{\rm G}_{\rm GTP}$ & $v_{\rm f} = k_{\rm G5,GTP} \cdot {\rm R}_n\_{\rm G}$\\
\hline
10 & ${\rm R}_n\_{\rm G}_{\rm GTP} \rightarrow {\rm R}_n + {\rm G}_{GTP}$ & $v_{\rm f} = k_{\rm G6} \cdot {\rm R}_n\_{\rm G}_{\rm GTP}$\\
\hline
11 & ${\rm G}_{\rm GTP} \rightarrow {\rm G}_{\alpha{\rm GTP}} + {\rm G}_{\beta\gamma}$ & $v_{\rm f} = k_{\rm G7} \cdot {\rm G}_{\rm GTP}$\\
\hline
12 & ${\rm PDE} + {\rm G}_{\alpha{\rm GTP}} \leftrightarrow {\rm PDE}\_{\rm G}_{\alpha{\rm GTP}}$ & $v_{\rm f} = k_{\rm P1} \cdot {\rm PDE} \cdot {\rm G}_{\alpha{\rm GTP}}$\\
& & $v_{\rm r} = k_{\rm P1_{rev}} \cdot {\rm PDE}\_{\rm G}_{\alpha{\rm GTP}} $\\
\hline
13 & $ {\rm PDE}\_{\rm G}_{\alpha{\rm GTP}} \rightarrow {\rm PDE}^{*}\_{\rm G}_{\alpha{\rm GTP}} $ & $v_{\rm f} = k_{\rm P2} \cdot {\rm PDE}\_{\rm G}_{\alpha{\rm GTP}}$\\
\hline
14 & $ {\rm PDE}^{*}\_{\rm G}_{\alpha{\rm GTP}} + {\rm G}_{\alpha{\rm GTP}} \leftrightarrow {\rm G}_{\alpha{\rm GTP}}\_{\rm PDE}^{*}\_{\rm G}_{\alpha{\rm GTP}}$ & $v_{\rm f} = k_{\rm P3} \cdot {\rm PDE}^{*}\_{\rm G}_{\alpha{\rm GTP}} \cdot {\rm G}_{\alpha{\rm GTP}} $\\
& & $v_{\rm r} = k_{\rm P3_{rev}} \cdot {\rm G}_{\alpha{\rm GTP}}\_{\rm PDE}^{*}\_{\rm G}_{\alpha{\rm GTP}} $\\
\hline
15 & $ {\rm G}_{\alpha{\rm GTP}}\_{\rm PDE}^{*}\_{\rm G}_{\alpha{\rm GTP}} \rightarrow {\rm G}_{\alpha{\rm GTP}}\_{\rm {}^{*} PDE}^{*}\_{\rm G}_{\alpha{\rm GTP}}$ & $v_{\rm f} = k_{\rm P4} \cdot {\rm G}_{\alpha{\rm GTP}}\_{\rm PDE}^{*}\_{\rm G}_{\alpha{\rm GTP}} $\\
\hline
16 & ${\rm G}_{\alpha{\rm GTP}}\_{\rm {}^{*} PDE}^{*}\_{\rm G}_{\alpha{\rm GTP}} + {\rm RGS} \rightarrow {\rm RGS}\_{\rm G}_{\alpha{\rm GTP}}\_{\rm {}^{*} PDE}^{*}\_{\rm G}_{\alpha{\rm GTP}}$ & $v_{\rm f} = k_{\rm RGS1} \cdot {\rm RGS} \cdot {\rm G}_{\alpha{\rm GTP}}\_{\rm {}^{*} PDE}^{*}\_{\rm G}_{\alpha{\rm GTP}} $\\
\hline
17 & ${\rm RGS}\_{\rm G}_{\alpha{\rm GTP}}\_{\rm {}^{*} PDE}^{*}\_{\rm G}_{\alpha{\rm GTP}} \rightarrow {\rm PDE}^{*}\_{\rm G}_{\alpha{\rm GTP}} + {\rm G}_{\alpha{\rm GDP}} + {\rm RGS} $ & $v_{\rm f} = k_{\rm RGS2} \cdot {\rm RGS}\_{\rm G}_{\alpha{\rm GTP}}\_{\rm {}^{*} PDE}^{*}\_{\rm G}_{\alpha{\rm GTP}} $\\
\hline
18 & ${\rm PDE}^{*}\_{\rm G}_{\alpha{\rm GTP}} + {\rm RGS} \rightarrow {\rm RGS}\_{\rm PDE}^{*}\_{\rm G}_{\alpha{\rm GTP}}$ & $v_{\rm f} = k_{\rm RGS1} \cdot {\rm RGS} \cdot {\rm PDE}^{*}\_{\rm G}_{\alpha{\rm GTP}} $\\
\hline
19 & ${\rm RGS}\_{\rm PDE}^{*}\_{\rm G}_{\alpha{\rm GTP}} \rightarrow {\rm PDE} + {\rm G}_{\alpha{\rm GDP}} + {\rm RGS} $ & $v_{\rm f} = k_{\rm RGS2} \cdot {\rm RGS}\_{\rm PDE}^{*}\_{\rm G}_{\alpha{\rm GTP}} $\\
\hline
20 & ${\rm PDE}^{*}\_{\rm G}_{\alpha{\rm GTP}} \rightarrow {\rm PDE} + {\rm G}_{\alpha{\rm GDP}} $ & $v_{\rm f} = k_{\rm PDE_{shutoff}} \cdot {\rm PDE}^{*}\_{\rm G}_{\alpha{\rm GTP}} $\\
\hline
21 & ${\rm G}_{\alpha{\rm GTP}}\_{\rm {}^{*} PDE}^{*}\_{\rm G}_{\alpha{\rm GTP}} \rightarrow {\rm PDE}^{*}\_{\rm G}_{\alpha{\rm GTP}} + {\rm G}_{\alpha{\rm GDP}} $ & $v_{\rm f} = k_{\rm PDE_{shutoff}} \cdot {\rm G}_{\alpha{\rm GTP}}\_{\rm {}^{*} PDE}^{*}\_{\rm G}_{\alpha{\rm GTP}} $\\
\hline
22 & ${\rm G}_{\alpha{\rm GTP}} \rightarrow {\rm G}_{\alpha{\rm GDP}}$ & $v_{\rm f} = k_{\rm G_{shutoff}} \cdot {\rm G}_{\alpha{\rm GTP}}$\\
\hline
23 & $ {\rm G}_{\beta\gamma} + {\rm G}_{\alpha{\rm GDP}} \rightarrow {\rm Gt}$ & $v_{\rm f} = k_{\rm G_{recyc}} \cdot {\rm G}_{\beta\gamma} \cdot {\rm G}_{\alpha{\rm GDP}} $\\
\hline
\end{tabular}
\end{table}
\restoregeometry
In the following table, parameters that have been changed with respect to the Invergo model (and not only scaled) are marked in red.
\begin{table}[H]
\centering
\caption{Parameters in the HSDM frontend.}
\begin{tabular}{l | l | l | l}
Name & Unscaled value & Scaling & Scaled value \\
\hline
\hline
$k_{{\rm RK1,}n}$ &
$\begin{cases}
k_{{\rm RK1},0} \cdot e^{-\omega \cdot n} & n < 3 \\
0 & n=3
\end{cases}$ & N/A &
$\begin{cases}
k_{{\rm RK1},0} \cdot e^{-\omega \cdot n} & n < 3 \\
0 & n=3
\end{cases}$\\
\hline
\textcolor{red}{$k_{{\rm RK1},0}$} & 0.03103 & $\cdot 580$ & $18/\mathrm{s}$\\
\hline
$\omega$ & $2.5$ & N/A & 2.5\\
\hline
$k_{\rm RK2}$ & $250/\mathrm{s}$ & N/A & $250/\mathrm{s}$\\
\hline
$k_{\rm RK3,ATP}$ & $4000/\mathrm{s}$ & N/A & $4000/\mathrm{s}$\\
\hline
$k_{\rm RK4}$ & $250/\mathrm{s}$ & N/A & $250/\mathrm{s}$\\
\hline
$k_{{\rm A1,}n}$ & $k_{\rm Arr} + (n-1) m_{\rm Arr}$ & N/A & $k_{\rm Arr} + (n-1) m_{\rm Arr}$\\
\hline
$k_{\rm Arr}$ & $9.9147\cdot 10^{-6}/\mathrm{s}$ & $\cdot 580$ & $5.751\cdot 10^{-3}/\mathrm{s}$ \\
\hline
$m_{\rm Arr}$ & $9.5475\cdot 10^{-6}$ & $\cdot 580$ & $5.538\cdot 10^{-3}/\mathrm{s}$\\
\hline
$k_{\rm A2}$ & $0.026/\mathrm{s}$ & N/A & $0.026/\mathrm{s}$\\
\hline
$k_{\rm A3}$ & $1.1651/\mathrm{s}$ & N/A & $1.1651/\mathrm{s}$\\
\hline
$k_{Gpre1}$ & $1.6\cdot 10^{-3}$ & $\cdot 580^2$ & $538.4/\mathrm{s}$\\
\hline
$k_{Gpre2}$ & $6.93\cdot 10^5$ & $\cdot 580$ & $4.019\cdot 10^8/\mathrm{s}$\\
\hline
$k_{{\rm G1},n}$ & $k_{{\rm G1},0} \cdot e^{-\omega_{\rm G} \cdot n}$ & N/A & $k_{{\rm G1},0} \cdot e^{-\omega_{\rm G} \cdot n}$\\
\hline
\textcolor{red}{$k_{{\rm G1},0}$} & $2.5862\cdot 10^{-3}$ & $\cdot 580$ & $1.5/\mathrm{s}$\\
\hline
$\omega_{\rm G}$ & 0.6 & N/A & 0.6\\
\hline
\textcolor{red}{$k_{\rm G2}$} & $2600/\mathrm{s}$ & N/A & $2600/\mathrm{s}$\\
\hline
\textcolor{red}{$k_{\rm G3}$} & $85000/\mathrm{s}$ & N/A & $85000/\mathrm{s}$\\
\hline
$k_{\rm G4}$ & $400/\mathrm{s}$ & N/A & $400/\mathrm{s}$\\
\hline
\textcolor{red}{$k_{\rm G5,GTP}$} & $ 12000/\mathrm{s}$ & N/A & $ 12000/\mathrm{s}$\\
\hline
\textcolor{red}{$k_{\rm G6}$} & $ 85000/\mathrm{s}$ & N/A & $ 85000/\mathrm{s}$\\
\hline
$k_{\rm G7}$ & $ 200/\mathrm{s}$ & N/A & $200/\mathrm{s}$\\
\hline
$k_{\rm P1}$ & $0.05497/\mathrm{s}$ & $\cdot 580$ & $ 31.8826/\mathrm{s}$ \\
\hline
\textcolor{red}{$k_{\rm P1_{rev}}$} & $ 100/\mathrm{s}$ & N/A & $ 100/\mathrm{s}$\\
\hline
$k_{\rm P2}$ & $ 940.7/\mathrm{s}$ & N/A & $ 940.7/\mathrm{s}$\\
\hline
\textcolor{red}{$k_{\rm P3}$} & $ 0.05497/\mathrm{s}$ & $\cdot 580$ & $31.8826/\mathrm{s}$ \\
\hline
\textcolor{red}{$k_{\rm P3_{rev}}$} & $ 3000/\mathrm{s}$ & N/A & $ 3000/\mathrm{s}$\\
\hline
\textcolor{red}{$k_{\rm P4}$} & $ 940.7/\mathrm{s}$ & N/A & $ 940.7/\mathrm{s}$ \\
\hline
\textcolor{red}{$k_{\rm RGS1}$} & $ 1.0344 \cdot 10^{-4}/\mathrm{s}$ & $\cdot 580$ & $0.06/\mathrm{s}$ \\
\hline
\textcolor{red}{$k_{\rm RGS2}$} & $ 140/\mathrm{s}$ & N/A & $ 140/\mathrm{s}$ \\
\hline
$k_{\rm PDE_{shutoff}}$ & $ 0.1/\mathrm{s}$ & N/A & $ 0.1/\mathrm{s}$\\
\hline
$k_{\rm G_{shutoff}}$ & $ 0.05/\mathrm{s}$ & N/A & $ 0.05/\mathrm{s}$ \\
\hline
$k_{\rm G_{recyc}}$ & $ 2/\mathrm{s}$ & N/A & $ 2/\mathrm{s}$\\
\hline
\end{tabular}
\end{table}
\newpage
All initial conditions have been reduced by a scaling factor of $1/580$, as given below, except for the activated rhodopsin (${\rm R0}(0)$ or the precoupled ${\rm R0}\_{\rm Gt}(0)$).
\begin{table}[H]
\centering
\caption{Nonzero initial conditions in the HSDM frontend.}
\begin{tabular}{l | l}
Species & Molecules \\
\hline
\hline
${\rm R0}(0)$ & 0 or 1\\
\hline
${\rm R0}\_{\rm Gt}(0)$ & 0 or 1\\
\hline
${\rm R}(0)$ & 169228\\
\hline
${\rm Gt}(0)$ & 14056\\
\hline
${\rm R}\_{\rm Gt}(0)$ & 3185\\
\hline
${\rm PDE}(0)$ & 3448 \\
\hline
${\rm Arr}(0)$ & 2174\\
\hline
${\rm RK}(0)$ & 1\\
\hline
${\rm RGS}(0)$ & 172\\
\hline
\end{tabular}
\end{table}
\begin{table}[H]
\centering
\caption{Reaction equations in the HSDM backend.}
\label{tab_reacts_mouse}
\begin{tabular}{c | l | l}
Nr. & Reaction equation & Rate \\
\hline
\hline
24 & ${\rm Ca}^{2+}_{\rm free} \leftrightarrow {\rm Ca}^{2+}_{\rm buff}$ & $v_{\rm f} = k_1 \cdot \left( e_{\rm T} - {\rm Ca}^{2+}_{\rm buff} \right) \cdot {\rm Ca}^{2+}_{\rm free} $\\
& & $v_{\rm r} = k_2 \cdot {\rm Ca}^{2+}_{\rm buff}$\\
\hline
25 & ${\rm Ca}^{2+}_{\rm free} \rightarrow $ & $v_{\rm f} = \gamma_{\rm Ca} \cdot \left({\rm Ca}^{2+}_{\rm free} - {\rm Ca}^{2+}_{0} \right) $\\
\hline
26 & $ \rightarrow {\rm Ca}^{2+}_{\rm free}$ & $v_{\rm f} = \frac{10^6 \cdot f_{\rm Ca} \cdot J_{\rm dark}}{\left(2+f_{\rm Ca} \right)\cdot F \cdot V_{\rm cyto}} \cdot \left(\frac{{\rm cGMP}}{{\rm cGMP}_{\rm dark}}\right)^{n_{\rm CG}} $\\
\hline
27 & $\rightarrow {\rm cGMP}$ & $v_{\rm f} = f_1 \cdot \frac{\alpha_{\rm max}}{1+\bigl( \frac{{\rm Ca}^{2+}_{\rm free}}{K_{\rm C1}}\bigr)^{m_1}} + f_{\rm 1m} \cdot \frac{\alpha_{\rm max}}{1+\bigl( \frac{{\rm Ca}^{2+}_{\rm free}}{K_{\rm C1m}}\bigr)^{m_{\rm 1m}}} + ...$\\
& & $ + f_2 \cdot \frac{\alpha_{\rm max}}{1+\bigl( \frac{{\rm Ca}^{2+}_{\rm free}}{K_{\rm C2}}\bigr)^{m_2}}$\\
\hline
28 & ${\rm cGMP} \rightarrow $ & $v_{\rm f} = \left( \beta_{\rm dark} + \beta_{\rm sub} \cdot E \right) \cdot {\rm cGMP} $\\
\hline
\end{tabular}
\end{table}
\newpage
Parameters and variables that have changed with respect to the Invergo model are marked in red.
\begin{table}[H]
\centering
\caption{Parameters and variables in the HSDM backend.}
\label{tab_params_mouse}
\begin{tabular}{l | l}
Name & Value \\
\hline
\hline
$k_1$ & $ 9.37059/\mathrm{s}\mu\mathrm{M}$ \\
\hline
$e_{\rm T}$ & $ 400\,\mu\mathrm{M}$ \\
\hline
$k_2$ & $ 46.412/\mathrm{s}$ \\
\hline
$\gamma_{\rm Ca}$ & $ 981.356/\mathrm{s}$ \\
\hline
${\rm Ca}^{2+}_0$ & $ 0.023\,\mu\mathrm{M}$ \\
\hline
$f_{\rm Ca}$ & $ 0.12$ \\
\hline
$J_{\rm dark}$ & $ 14.87\,\mathrm{pA}$ \\
\hline
$F$ & $ 96485.3/\mathrm{cm}$ \\
\hline
$V_{\rm cyto}$ & $ 0.03916\,\mathrm{pL}$ \\
\hline
${\rm cGMP}_{\rm dark}$ & $ 6.4944\,\mu\mathrm{M}$ \\
\hline
$n_{\rm CG}$ & $ 3.8$ \\
\hline
\textcolor{red}{$\alpha_{\rm max}$} & $60\,\mu\mathrm{M}/s$ \\
\hline
$\beta_{\rm dark} $ & $ 3.19/\mathrm{s}$ \\
\hline
${\rm Ca}^{2+}_{\rm dark}$ & $ 0.25\,\mu\mathrm{M}$ \\
\hline
$K_{\rm C1}$ & $ 0.171\,\mu\mathrm{M}$ \\
\hline
\textcolor{red}{$K_{\rm C1m}$} & $ 0.171\,\mu\mathrm{M}$ \\
\hline
$K_{\rm C2}$ & $ 0.059\,\mu\mathrm{M}$ \\
\hline
$m_1$ & $3$\\
\hline
\textcolor{red}{$m_{\rm 1m}$} & $3$\\
\hline
$m_2$ & $1.5$\\
\hline
\textcolor{red}{$f_1$} & $0.5$\\
\hline
\textcolor{red}{$f_{\rm 1m}$} & $0$\\
\hline
\textcolor{red}{$f_2$} & $0.5$\\
\hline
\textcolor{red}{$\beta_{\rm sub}$} & $0.01/\mathrm{s}$\\
\hline
$E$ & ${\rm PDE}^{*}\_{\rm G}_{\alpha{\rm GTP}} + {\rm G}_{\alpha{\rm GTP}}\_{\rm PDE}^{*}\_{\rm G}_{\alpha{\rm GTP}} + 2\cdot {\rm G}_{\alpha{\rm GTP}}\_{\rm {}^{*} PDE}^{*}\_{\rm G}_{\alpha{\rm GTP}}$\\
\hline
$J$ & $\frac{2}{2 + f_{\rm Ca}} \cdot \left( \frac{{\rm cGMP}}{{\rm cGMP}_{\rm dark}} \right)^{n_{\rm CG}} \cdot J_{\rm dark} + \frac{f_{\rm Ca}}{f_{\rm Ca} + 2} \cdot \frac{{\rm Ca}^{2+}_{\rm free}-{\rm Ca}^{2+}_0}{{\rm Ca}^{2+}_{\rm dark}-{\rm Ca}^{2+}_0} \cdot J_{\rm dark}$ \\
\hline
$\Delta J$ & $J_{\rm dark} - J$\\
\hline
\end{tabular}
\end{table}
\begin{table}[H]
\centering
\caption{Nonzero initial conditions in the HSDM backend.}
\label{tab_init_mouse}
\begin{tabular}{l | l}
Species & Concentration \\
\hline
\hline
${\rm Ca}^{2+}_{\rm free}(0)$ & $0.25\,\mu\mathrm{M}$\\
\hline
${\rm Ca}^{2+}_{\rm buff}(0)$ & $19.2199\,\mu\mathrm{M}$\\
\hline
${\rm cGMP}(0)$ & $6.4944\,\mu\mathrm{M}$\\
\hline
\end{tabular}
\end{table}
\end{document}