Ignore:
Timestamp:
Dec 20, 2009, 8:23:54 PM (15 years ago)
Author:
Rick van der Zwet
Message:

Final version of report

File:
1 edited

Legend:

Unmodified
Added
Removed
  • liacs/pnbm/project/report.tex

    r25 r52  
    2424\maketitle
    2525\section{Abstract}
    26 Planar signaling is the process within the development of the AP axis
    27 development of the \emph{Xenopus laevis} \cite{Bertens09} in which cells
    28 accumulate proteins based on the saturation of nearby cells. If one cell
    29 produces n amount of proteins, it will initiate a transferring cascade to cells
    30 in the vicinity.  This dissemination of proteins will eventually cease,
    31 considering that n is a finite variable. There is a gradation in the amount of
    32 proteins transferred, meaning that neighbouring cells get n/2 the amount of
    33 proteins of the most saturated cell.
     26Planar signaling is a process that is part of the development of the AP axis in
     27\emph{Xenopus laevis} \cite{Bertens09}, in which cells accumulate proteins
     28based on the saturation of nearby cells. If one cell produces n amount of
     29proteins, it will initiate a transferring cascade to cells in the vicinity.
     30This dissemination of proteins will eventually cease, considering that n is a
     31finite variable. There is a gradation in the amount of proteins transferred,
     32meaning that neighboring cells get n/2 the amount of proteins of the most
     33saturated cell.
    3434
    35 We are going to model this into Petri-Nets beeing a mathematical modeling
    36 language, which suit well for this purpose as we could nicely model the process
    37 in graphical interactive representation and could also be used for automated
    38 model tracking and analyze.
     35We are going to model this into Petri-Nets, since it supports a mathematical
     36modeling language as well as a graphical interactive representation, which is
     37well suited for this purpose, as we could model the process based on algorithms
     38and also used it for automated model tracking and analysis, while having a
     39visual representation of the process.
    3940
    40 \section{Approach}
    41 First a Petri-Net model will be defined textually and using graphs next the
    42 modeling will be taking into practice using the modeling tool\emph{CPNTools}
    43 \footnote{http://wiki.daimi.au.dk/cpntools/cpntools.wiki}.
     41\section{Method}
     42Our approach to modeling Planar signaling is firstly construct a biological
     43model of the process, one that illustrates the phenomenon taking place (shown
     44at figure~\ref{fig:ab-model}). Next we decided to create a conceptual model,
     45one that abstracts from the biological model and contains some mathematical
     46equations that describe the processes occurring in nature.
     47
     48\begin{figure}[htp]
     49\centering
     50\caption{Conceptual abstract model}
     51\includegraphics[width=\textwidth]{frog-model.eps}
     52\label{fig:ab-model}
     53\end{figure}
     54
     55Finally we are going to construct a Petri-Net model using the software
     56\emph{CPNTools} \footnote{http://wiki.daimi.au.dk/cpntools/cpntools.wiki}.
    4457
    4558\section{Modeling}
    46 To model this process we will take a modular approach using coloured Petri-Nets
    47 (see Fig~\ref{fig:model}), since the goal of this assignment is to have a
    48 solution that can be applied to any configuration of cells. We start with a
    49 building block that is an abstraction of a cell (figure: circle), which can then
    50 be coupled to other cells (figure: arrows). The abstraction contains two
    51 different types. First the proteins are modelled (figure: red), secondly the
    52 proteins (figure: blue) are leading in a second process of the creation of
    53 posterisation which also needs modeling. We assume a 1:1 mapping between the amount
    54 of proteins and the posterisation -this taken into consideration- ones an
    55 \texttt{INITIAL} protein is 'used' (e.g. has on posterisation counterpart) in
    56 this process it
    57 get called \texttt{ACTIVATED}. We assume that the proteins to posterisation
    58 process is taking place at the same time as the proteins distribution. And in a
    59 special format (figure: object B). It tries to matches the posterisation to the
    60 same level as the proteins present. But the moment the protein level lowers,
    61 the posterisation will remain the same. In pseudo-code:
     59\begin{figure}[htp]
     60\centering
     61\caption{Planar signaling model}
     62\includegraphics[width=100mm]{planar-signaling-model.eps}
     63\label{fig:model}
     64\end{figure}
     65
     66For the conceptual model (Fig.~\ref{fig:model}) we start with a building block
     67that is an abstraction of a cell (figure: circle), which can then be coupled to
     68other cells (figure: arrows). The abstraction contains two different token
     69types. For one the proteins are modeled through red tokens, and secondly the
     70proteins generate a second process, the level of posterisation (blue tokens)
     71which is also required in the model. We assume a 1:1 mapping between the amount
     72of proteins and the posterisation, taking into consideration that when an
     73\texttt{INITIAL} protein is ’used’ (e.g. has a posterisation counterpart) in
     74this process is called \texttt{ACTIVATED}. We assume that the “proteins to
     75posterisation” process is taking place at the same time as the proteins
     76distribution. This is represented in a special format, represented by the
     77square B in the figure. It tries to match the posterisation to the same level
     78as the proteins present. The moment the protein level lowers, the posterisation
     79will remain the same. In pseudo-code:
    6280\begin{verbatim}
    6381if numPos < numProteins then
    64     numPos = numPos + 1
     82  numPos = numPos + 1
    6583endif
    6684\end{verbatim}
     85
    6786\texttt{numProteins} is the proteins available and \texttt{numPos} is the
    6887posterisation present.
    6988
    70 The connectors between the cells (the membranes) has a special properly. One
    71 can see them as pressure valves others as siphons (see Fig~\ref{fig:pressure}).
    72 The moment the 'volume' at complies with the following properly $A / 2 < B$
    73 then the pressure closes, else it passes volume from A to B at an certain rate
    74 (\texttt{flowSpeed}). This rate could depend on the difference, actual value present
    75 or something else. Please do mind that negative values could ever appear hence
    76 the checking whether the source is bigger or equal then the flowSpeed.
     89The connectors between the cells (the membranes) have a special property. One
     90can see them as pressure valves (like figure~\ref{fig:pressure}) that close
     91when the ’volume’ in the containers (cells) complies with the following
     92property $A/2 < B$, or siphons when the property before is not achieved,
     93passing volume from $A$ to $B$ at a certain rate (\texttt{flowSpeed}). This
     94rate could depend on the difference, actual value present or something else.
     95Please keep in mind that negative values could sometimes appear, hence there is
     96a need to check whether the source is bigger or equal than the
     97\texttt{flowSpeed}.
    7798
    78 For the case there exists no standard Petri-Net 'component', hence  this require
    79 the creation of a new property (figure: $2:1$), with the following properties:
     99\begin{figure}[htp]
     100\centering
     101\caption{Pressure valve example}
     102\includegraphics[height=60mm]{pressure-valve.eps}
     103\label{fig:pressure}
     104\end{figure}
    80105
     106For this case there exists no standard Petri-Net ’component’, hence this
     107requires the creation of a new property, which is described in pseudo-code
     108below:
    81109\begin{verbatim}
    82110flowSpeed = n
     
    90118\end{verbatim}
    91119
    92 Planar signaling could theoretically start in every cell, by
    93 inserting some amount of proteins. In our model represented as a bunch of
    94 \texttt{INITIAL} tokens being put in a random cell.
     120Planar signaling could theoretically start in every cell, by inserting some
     121amount of proteins. In our model this is represented as $n$ \texttt{INITIAL}
     122tokens being put in a cell chosen at random.
    95123
    96 \begin{figure}[htp]
    97 \centering
    98 \caption{Planar signaling model}
    99 \includegraphics[width=100mm]{planar-signaling-model.eps}
    100 \label{fig:model}
    101 \end{figure}
    102124
    103 \begin{figure}[htp]
    104 \centering
    105 \caption{Pressure valve example}
    106 \includegraphics[height=60mm]{pressure-valve.eps}
    107 \label{fig:pressure}
    108 \end{figure}
     125\section{CPNTools implementation}
     126CPNTools has some shortcomings when it comes to modeling higher level
     127developmental biology. One is the shortcoming of ’balancing’. It does not allow
     128the reading of how many tokens are present in a certain state and base action
     129upon them.
    109130
    110 \section{CPNTools 'implementation'}
    111 CPNTools has quite some shortcomings when it comes to modeling (higher level
    112 developmental) biology.
     131As workaround for this (see Fig~\ref{fig:CPNplanar}) we used a ’dump’ gradation
     132function.  In our case it simply takes 3 tokens and pushes 1 forward while
     133converting 2 directly to \texttt{ACTIVATED}. This does not take into
     134consideration if some external source changes the amount further up.
    113135
    114 One it the shortcoming of the 'balancing'. It does not allow reading of how
    115 many tokens are present in a certain state and base action upon them. As
    116 workaround for this (see Fig~\ref{fig:CPNplanar}) we used a 'dump' gradation
    117 function. In our case it simply take 3 tokens and pushes 1 forward and
    118 converting 2 directly to \texttt{ACTIVATED}. This does not take in
    119 consideration if the amount get changed in 'further-up', by some external
    120 source.
    121 
    122 Secondly it is missing a possibility to for easy random initialisation for
    123 modeling purposes. As a dirty quirk we 'hacked' it to choose between starting
    124 at the head or the tail.
    125 
    126 In this implementation the proteins to gradients  process is taking place at
    127 cell $A$ at the same time that the proteins get transferred from cell $A$ to
    128 $B$.
    129 
    130 Also it should be noted that it missing a notion of timed firing sequences;
    131 meaning firing sequences which will occur at an certain time. This could for
    132 example used to 'trigger' a timed activation of the \texttt{INITIAL} to
    133 \texttt{ACTIVATED} process as modeled in fig~\ref{fig:model}. An initial idea
    134 is shown at fig~\ref{fig:time-idea} in appendix~\ref{sec:timer-idea}.
    135 
     136Secondly it misses the possibility to easily randomize the initialization. As a
     137quick fix we ’hacked’ it to choose between starting at the head or the tail. In
     138this implementation the protein to gradient process is taking place at cell $A$
     139at the same time that the proteins get transferred from cell $A$ to $B$. It
     140should be noted that the model avoids the notion of timed firing sequences;
     141meaning that the firing sequences will not occur at pre-determined times. This
     142could be changed in the future to ‘trigger’ a timed activation of the
     143\texttt{INITIAL} to \texttt{ACTIVATED} process as modeled in
     144figure~\ref{fig:model}.
    136145
    137146\begin{figure}[htp]
     
    140149\advance\leftskip-2cm
    141150\advance\rightskip+2cm
    142 \includegraphics[width=1.3\textwidth]{planer-signaling.eps}
     151\includegraphics[width=1.3\textwidth]{planar-signaling.eps}
    143152\label{fig:CPNplanar}
    144153\end{figure}
    145154
    146155\section{Conclusion}
    147 Using Petri-Nets for modeling biology processes is a powerful framework, which
    148 could be well expandable. The Proof Of Concept implementations and
    149 visualisations how-ever are lacking. \emph{CPNTools} for example does not
    150 provide a powerful enough tool-set for the modeling purposes.
     156Using Petri-Nets for modeling biology processes is a powerful framework, one
     157which could be well expandable. The proof of concept implementation and
     158visualization however is lacking. \emph{CPNTools} does not currently provide a
     159powerful enough tool-set for the modeling purposes. This could be improved with
     160the support of a programming language that can produce algorithms that can
     161replace the mathematical functions of arcs.
     162
     163
    151164
    152165\bibliographystyle{amsalpha}
     
    156169laevis Extended Abstract, 2009
    157170\end{thebibliography}
    158 \appendix
    159 \section{Timer Idea}
    160 \label{sec:timer-idea}
    161 
    162 \begin{figure}[htp]
    163 \centering
    164 \caption{Timed transition idea}
    165 \includegraphics[width=0.5\textwidth]{timer-proposal.eps}
    166 \label{fig:time-idea}
    167 \end{figure}
    168171\end{document}
Note: See TracChangeset for help on using the changeset viewer.