Changeset 52 for liacs/pnbm/project/report.tex

Timestamp:

Dec 20, 2009, 8:23:54 PM (15 years ago)

Author:

Rick van der Zwet

Message:

Final version of report

File:

• liacs/pnbm/project/report.tex (modified) (4 diffs)

liacs/pnbm/project/report.tex

@@ -24 +24 @@
 \maketitle
 \section{Abstract}
-Planar signaling is the process within the development of the AP axis
-development of the \emph{Xenopus laevis} \cite{Bertens09} in which cells
-accumulate proteins based on the saturation of nearby cells. If one cell
-produces n amount of proteins, it will initiate a transferring cascade to cells
-in the vicinity.  This dissemination of proteins will eventually cease,
-considering that n is a finite variable. There is a gradation in the amount of
-proteins transferred, meaning that neighbouring cells get n/2 the amount of
-proteins of the most saturated cell.
+Planar signaling is a process that is part of the development of the AP axis in
+\emph{Xenopus laevis} \cite{Bertens09}, in which cells accumulate proteins
+based on the saturation of nearby cells. If one cell produces n amount of
+proteins, it will initiate a transferring cascade to cells in the vicinity.
+This dissemination of proteins will eventually cease, considering that n is a
+finite variable. There is a gradation in the amount of proteins transferred,
+meaning that neighboring cells get n/2 the amount of proteins of the most
+saturated cell.
 
-We are going to model this into Petri-Nets beeing a mathematical modeling
-language, which suit well for this purpose as we could nicely model the process
-in graphical interactive representation and could also be used for automated
-model tracking and analyze.
+We are going to model this into Petri-Nets, since it supports a mathematical
+modeling language as well as a graphical interactive representation, which is
+well suited for this purpose, as we could model the process based on algorithms
+and also used it for automated model tracking and analysis, while having a
+visual representation of the process.
 
-\section{Approach}
-First a Petri-Net model will be defined textually and using graphs next the
-modeling will be taking into practice using the modeling tool\emph{CPNTools}
-\footnote{http://wiki.daimi.au.dk/cpntools/cpntools.wiki}.
+\section{Method}
+Our approach to modeling Planar signaling is firstly construct a biological
+model of the process, one that illustrates the phenomenon taking place (shown
+at figure~\ref{fig:ab-model}). Next we decided to create a conceptual model,
+one that abstracts from the biological model and contains some mathematical
+equations that describe the processes occurring in nature.
+
+\begin{figure}[htp]
+\centering
+\caption{Conceptual abstract model}
+\includegraphics[width=\textwidth]{frog-model.eps}
+\label{fig:ab-model}
+\end{figure}
+
+Finally we are going to construct a Petri-Net model using the software
+\emph{CPNTools} \footnote{http://wiki.daimi.au.dk/cpntools/cpntools.wiki}.
 
 \section{Modeling}
-To model this process we will take a modular approach using coloured Petri-Nets
-(see Fig~\ref{fig:model}), since the goal of this assignment is to have a
-solution that can be applied to any configuration of cells. We start with a
-building block that is an abstraction of a cell (figure: circle), which can then
-be coupled to other cells (figure: arrows). The abstraction contains two
-different types. First the proteins are modelled (figure: red), secondly the
-proteins (figure: blue) are leading in a second process of the creation of
-posterisation which also needs modeling. We assume a 1:1 mapping between the amount
-of proteins and the posterisation -this taken into consideration- ones an
-\texttt{INITIAL} protein is 'used' (e.g. has on posterisation counterpart) in
-this process it
-get called \texttt{ACTIVATED}. We assume that the proteins to posterisation
-process is taking place at the same time as the proteins distribution. And in a
-special format (figure: object B). It tries to matches the posterisation to the
-same level as the proteins present. But the moment the protein level lowers,
-the posterisation will remain the same. In pseudo-code:
+\begin{figure}[htp]
+\centering
+\caption{Planar signaling model}
+\includegraphics[width=100mm]{planar-signaling-model.eps}
+\label{fig:model}
+\end{figure}
+
+For the conceptual model (Fig.~\ref{fig:model}) we start with a building block
+that is an abstraction of a cell (figure: circle), which can then be coupled to
+other cells (figure: arrows). The abstraction contains two different token
+types. For one the proteins are modeled through red tokens, and secondly the
+proteins generate a second process, the level of posterisation (blue tokens)
+which is also required in the model. We assume a 1:1 mapping between the amount
+of proteins and the posterisation, taking into consideration that when an
+\texttt{INITIAL} protein is ’used’ (e.g. has a posterisation counterpart) in
+this process is called \texttt{ACTIVATED}. We assume that the “proteins to
+posterisation” process is taking place at the same time as the proteins
+distribution. This is represented in a special format, represented by the
+square B in the figure. It tries to match the posterisation to the same level
+as the proteins present. The moment the protein level lowers, the posterisation
+will remain the same. In pseudo-code:
 \begin{verbatim}
 if numPos < numProteins then
-    numPos = numPos + 1
+  numPos = numPos + 1
 endif
 \end{verbatim}
+
 \texttt{numProteins} is the proteins available and \texttt{numPos} is the
 posterisation present.
 
-The connectors between the cells (the membranes) has a special properly. One
-can see them as pressure valves others as siphons (see Fig~\ref{fig:pressure}).
-The moment the 'volume' at complies with the following properly $A / 2 < B$
-then the pressure closes, else it passes volume from A to B at an certain rate
-(\texttt{flowSpeed}). This rate could depend on the difference, actual value present
-or something else. Please do mind that negative values could ever appear hence
-the checking whether the source is bigger or equal then the flowSpeed.
+The connectors between the cells (the membranes) have a special property. One
+can see them as pressure valves (like figure~\ref{fig:pressure}) that close
+when the ’volume’ in the containers (cells) complies with the following
+property $A/2 < B$, or siphons when the property before is not achieved,
+passing volume from $A$ to $B$ at a certain rate (\texttt{flowSpeed}). This
+rate could depend on the difference, actual value present or something else.
+Please keep in mind that negative values could sometimes appear, hence there is
+a need to check whether the source is bigger or equal than the
+\texttt{flowSpeed}. 
 
-For the case there exists no standard Petri-Net 'component', hence  this require
-the creation of a new property (figure: $2:1$), with the following properties:
+\begin{figure}[htp]
+\centering
+\caption{Pressure valve example}
+\includegraphics[height=60mm]{pressure-valve.eps}
+\label{fig:pressure}
+\end{figure}
 
+For this case there exists no standard Petri-Net ’component’, hence this
+requires the creation of a new property, which is described in pseudo-code
+below:
 \begin{verbatim}
 flowSpeed = n
@@ -90 +118 @@
 \end{verbatim}
 
-Planar signaling could theoretically start in every cell, by
-inserting some amount of proteins. In our model represented as a bunch of
-\texttt{INITIAL} tokens being put in a random cell.
+Planar signaling could theoretically start in every cell, by inserting some
+amount of proteins. In our model this is represented as $n$ \texttt{INITIAL}
+tokens being put in a cell chosen at random.
 
-\begin{figure}[htp]
-\centering
-\caption{Planar signaling model}
-\includegraphics[width=100mm]{planar-signaling-model.eps}
-\label{fig:model}
-\end{figure}
 
-\begin{figure}[htp]
-\centering
-\caption{Pressure valve example}
-\includegraphics[height=60mm]{pressure-valve.eps}
-\label{fig:pressure}
-\end{figure}
+\section{CPNTools implementation}
+CPNTools has some shortcomings when it comes to modeling higher level
+developmental biology. One is the shortcoming of ’balancing’. It does not allow
+the reading of how many tokens are present in a certain state and base action
+upon them.
 
-\section{CPNTools 'implementation'}
-CPNTools has quite some shortcomings when it comes to modeling (higher level
-developmental) biology.
+As workaround for this (see Fig~\ref{fig:CPNplanar}) we used a ’dump’ gradation
+function.  In our case it simply takes 3 tokens and pushes 1 forward while
+converting 2 directly to \texttt{ACTIVATED}. This does not take into
+consideration if some external source changes the amount further up. 
 
-One it the shortcoming of the 'balancing'. It does not allow reading of how
-many tokens are present in a certain state and base action upon them. As
-workaround for this (see Fig~\ref{fig:CPNplanar}) we used a 'dump' gradation
-function. In our case it simply take 3 tokens and pushes 1 forward and
-converting 2 directly to \texttt{ACTIVATED}. This does not take in
-consideration if the amount get changed in 'further-up', by some external
-source.
-
-Secondly it is missing a possibility to for easy random initialisation for
-modeling purposes. As a dirty quirk we 'hacked' it to choose between starting
-at the head or the tail.
-
-In this implementation the proteins to gradients  process is taking place at
-cell $A$ at the same time that the proteins get transferred from cell $A$ to
-$B$. 
-
-Also it should be noted that it missing a notion of timed firing sequences;
-meaning firing sequences which will occur at an certain time. This could for
-example used to 'trigger' a timed activation of the \texttt{INITIAL} to
-\texttt{ACTIVATED} process as modeled in fig~\ref{fig:model}. An initial idea
-is shown at fig~\ref{fig:time-idea} in appendix~\ref{sec:timer-idea}.
-
+Secondly it misses the possibility to easily randomize the initialization. As a
+quick fix we ’hacked’ it to choose between starting at the head or the tail. In
+this implementation the protein to gradient process is taking place at cell $A$
+at the same time that the proteins get transferred from cell $A$ to $B$. It
+should be noted that the model avoids the notion of timed firing sequences;
+meaning that the firing sequences will not occur at pre-determined times. This
+could be changed in the future to ‘trigger’ a timed activation of the
+\texttt{INITIAL} to \texttt{ACTIVATED} process as modeled in
+figure~\ref{fig:model}.
 
 \begin{figure}[htp]
@@ -140 +149 @@
 \advance\leftskip-2cm
 \advance\rightskip+2cm
-\includegraphics[width=1.3\textwidth]{planer-signaling.eps}
+\includegraphics[width=1.3\textwidth]{planar-signaling.eps}
 \label{fig:CPNplanar}
 \end{figure}
 
 \section{Conclusion}
-Using Petri-Nets for modeling biology processes is a powerful framework, which
-could be well expandable. The Proof Of Concept implementations and
-visualisations how-ever are lacking. \emph{CPNTools} for example does not
-provide a powerful enough tool-set for the modeling purposes.
+Using Petri-Nets for modeling biology processes is a powerful framework, one
+which could be well expandable. The proof of concept implementation and
+visualization however is lacking. \emph{CPNTools} does not currently provide a
+powerful enough tool-set for the modeling purposes. This could be improved with
+the support of a programming language that can produce algorithms that can
+replace the mathematical functions of arcs.
+
+
 
 \bibliographystyle{amsalpha}
@@ -156 +169 @@
 laevis Extended Abstract, 2009
 \end{thebibliography}
-\appendix
-\section{Timer Idea}
-\label{sec:timer-idea}
-
-\begin{figure}[htp]
-\centering
-\caption{Timed transition idea}
-\includegraphics[width=0.5\textwidth]{timer-proposal.eps}
-\label{fig:time-idea}
-\end{figure}
 \end{document}