Ignore:
Timestamp:
Dec 1, 2009, 11:07:43 AM (15 years ago)
Author:
Rick van der Zwet
Message:

For peer-review

File:
1 edited

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  • liacs/pnbm/project/report.tex

    r11 r12  
    66
    77\frenchspacing
    8 \usepackage[english,dutch]{babel}
    9 \selectlanguage{dutch}
     8\usepackage[english]{babel}
     9\selectlanguage{english}
    1010\usepackage{graphicx}
    1111\usepackage{url}
    … …  
    3939
    4040\section{Modeling}
    41 To model this process we will take a modular approach, since the goal of this
    42 assignment is to have a solution that can be applied to any configuration of
    43 cells. We start with a bulding block that is an abstraction of a cell,
    44 which can then be coupled to other cells. The abstraction contains two
    45 different types. First the proteins are modelled, secondly the proteins are leading
    46 in a second process of the creation of gradients which also needs modeling. We
    47 assume a 1:1 mapping between the amount of proteins and gradients -this taken
    48 into consideration- ones an $INITIAL$ protein is used in this process it get
    49 called $ACTIVATED$. We assume that this process is taking place at cell $A$ at
    50 the same time that the proteins get transfered from cell $A$ to $B$.
     41To model this process we will take a modular approach using coloured PetriNets
     42(see Fig~\ref{fig:model}), since the goal of this assignment is to have a
     43solution that can be applied to any configuration of cells. We start with a
     44bulding block that is an abstraction of a cell (figure: circle), which can then
     45be coupled to other cells (figure: arrows). The abstraction contains two
     46different types. First the proteins are modelled (figure: red), secondly the
     47proteins (figure: blue) are leading in a second process of the creation of
     48gradients which also needs modeling. We assume a 1:1 mapping between the amount
     49of proteins and gradients -this taken into consideration- ones an $INITIAL$
     50protein is used in this process it get called $ACTIVATED$. We assume that the
     51proteins to gradients process is starting at an certain time from the start of
     52the process.
    5153
    5254The connectors between the cells (the membrams) has a special properly. One
    … …  
    5557then the pressure closes, else it passes volume from A to B at an certain rate.
    5658For the case there exists no standard PetriNet 'component', hence  this require
    57 the creation of a new property.
     59the creation of a new property (figure: $2:1$), with the following properties:
     60
     61\begin{verbatim}
     62flowSpeed = 2
     63if A > 2 * B then
     64  A = A - flowSpeed
     65  B = B + flowSpeed
     66else if B > 2 * A then
     67  B = B - flowSpeed
     68  A = A + flowSpeed
     69endif
     70\end{verbatim}
    5871
    5972Planar signaling could theoretically start in every cell, by
    … …  
    6174$INITIAL$ tokens beeing put in a random cell.
    6275
     76\begin{figure}[htp]
     77\centering
     78\caption{Planar signaling model}
     79\includegraphics[width=60mm]{planar-signaling-model.eps}
     80\label{fig:model}
     81\end{figure}
    6382
    6483\begin{figure}[htp]
    … …  
    7190\section{CPNTools 'implementation'}
    7291CPNTools has quite some shortcomings when it comes to modeling (higher level
    73 developmental) biology. One it the shortcoming of the 'balancing'. It does not
    74 allow reading of how many tokens are present in a certain state and base action
    75 uppon them. As workaround for this (see Fig~\ref{fig:CPNplanar}) we used a
    76 'dump' gradation function. In our case it simply take 3 tokens and pushes 1
    77 forward and converting 2 directly to $ACTIVATED$. This does not take in
    78 consideration if the amount get changed in 'further-up', by some external source.
     92developmental) biology.
     93
     94One it the shortcoming of the 'balancing'. It does not allow reading of how
     95many tokens are present in a certain state and base action uppon them. As
     96workaround for this (see Fig~\ref{fig:CPNplanar}) we used a 'dump' gradation
     97function. In our case it simply take 3 tokens and pushes 1 forward and
     98converting 2 directly to $ACTIVATED$. This does not take in consideration if
     99the amount get changed in 'further-up', by some external source.
    79100
    80101Secondly it is missing a possibility to for easy random initialisation for
    … …  
    82103at the head or the tail.
    83104
    84 Not very important for our case, but also it should be noted that it missing a
    85 notion of timed firing sequences; meaning firing sequences which will occur at
    86 an certain time. This could for example used to 'trigger' a timmed activation
    87 of the $INITIAL$ to $ACTIVATED$ process.
     105In this implementation the protiens to gradiants  process is taking place at
     106cell $A$ at the same time that the proteins get transfered from cell $A$ to
     107$B$.
     108
     109Also it should be noted that it missing a notion of timed firing sequences;
     110meaning firing sequences which will occur at an certain time. This could for
     111example used to 'trigger' a timmed activation of the $INITIAL$ to $ACTIVATED$
     112process as modeled in fig~\ref{fig:model}.
    88113
    89114\begin{figure}[htp]
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