source: liacs/pnbm/project/report.tex@ 11

Last change on this file since 11 was 11, checked in by Rick van der Zwet, 15 years ago

Save my ass from deleting stuff if I don't want to

File size: 4.7 KB
Line 
1%
2% $Id: report.tex 571 2008-04-20 17:31:04Z rick $
3%
4
5\documentclass[12pt,a4paper]{article}
6
7\frenchspacing
8\usepackage[english,dutch]{babel}
9\selectlanguage{dutch}
10\usepackage{graphicx}
11\usepackage{url}
12\usepackage{multicol}
13\usepackage{fancybox}
14\usepackage{amssymb,amsmath}
15
16\title{DRAFT: Modeling planar signalling in AP axis development in \emph{Xenopus laevis}\\
17\large{using Petri Nets in Higher Level Developmental Biology}}
18\author{Rick van der Zwet, Tiago Borges Coelho \\
19 \texttt{<hvdzwet@liacs.nl>,<borges.coelho@gmail.com>}\\
20 LIACS - Leiden University, The Netherlands}
21\date{\today}
22
23\begin{document}
24\maketitle
25\section{Abstract}
26Planar signaling is the process in which cells accumulate proteins based on the
27saturation of nearby cells. If one cell produces n ammount of proteins, it will
28initiate a transfering cascade to cells in the vicinity. This dissemination of
29proteins will eventually cease, considering that n is a finite variable. There
30is a gradation in the ammount of proteins transfered, meaning that neighbouring
31cells get n/2 the ammount of proteins of the most saturated cell.
32
33XXX: Citing to the Bio Papers
34XXX: Small introductions Petri-nets
35
36\section{Approch}
37First a PetriNet model will be defined textually and using graphs next the
38modeling will be taking into practice using the modeling tool\emph{CPNTools}.
39
40\section{Modeling}
41To model this process we will take a modular approach, since the goal of this
42assignment is to have a solution that can be applied to any configuration of
43cells. We start with a bulding block that is an abstraction of a cell,
44which can then be coupled to other cells. The abstraction contains two
45different types. First the proteins are modelled, secondly the proteins are leading
46in a second process of the creation of gradients which also needs modeling. We
47assume a 1:1 mapping between the amount of proteins and gradients -this taken
48into consideration- ones an $INITIAL$ protein is used in this process it get
49called $ACTIVATED$. We assume that this process is taking place at cell $A$ at
50the same time that the proteins get transfered from cell $A$ to $B$.
51
52The connectors between the cells (the membrams) has a special properly. One
53can see them as pressure valves others as sighons (see Fig~\ref{fig:pressure}).
54The moment the 'volume' at complies with the following properly $A / 2 < B$
55then the pressure closes, else it passes volume from A to B at an certain rate.
56For the case there exists no standard PetriNet 'component', hence this require
57the creation of a new property.
58
59Planar signaling could theoretically start in every cell, by
60inserting some amount of protiens. In our model represented as a bunch of
61$INITIAL$ tokens beeing put in a random cell.
62
63
64\begin{figure}[htp]
65\centering
66\caption{Pressure valve example}
67\includegraphics[height=60mm]{pressure-valve.eps}
68\label{fig:pressure}
69\end{figure}
70
71\section{CPNTools 'implementation'}
72CPNTools has quite some shortcomings when it comes to modeling (higher level
73developmental) biology. One it the shortcoming of the 'balancing'. It does not
74allow reading of how many tokens are present in a certain state and base action
75uppon 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
77forward and converting 2 directly to $ACTIVATED$. This does not take in
78consideration if the amount get changed in 'further-up', by some external source.
79
80Secondly it is missing a possibility to for easy random initialisation for
81modeling purposes. As a dirty quirk we 'hacked' it to choose between starting
82at the head or the tail.
83
84Not very important for our case, but also it should be noted that it missing a
85notion of timed firing sequences; meaning firing sequences which will occur at
86an certain time. This could for example used to 'trigger' a timmed activation
87of the $INITIAL$ to $ACTIVATED$ process.
88
89\begin{figure}[htp]
90\centering
91\caption{CPNTools implementation}
92\advance\leftskip-2cm
93\advance\rightskip+2cm
94\includegraphics[width=1.3\textwidth]{planer-signaling.eps}
95\label{fig:CPNplanar}
96\end{figure}
97
98\section{Conclusion}
99Using PetriNets for modeling biology processes is a powerful framework, which
100could be well extendable. The Proof Of Concept implementations and
101visualisations how-ever are lacking. \emph{CPNTools} for example does not
102provide a powerfull enough toolset for the modeling purposes.
103
104\begin{thebibliography}{10}
105% sing Petri Nets in Higher Level Developmental Biology:
106% A case study on the AP axis development in Xenopus laevis
107% Extended Abstract
108% http://www.liacs.nl/~csbpn/COURSE%20DOCUMENTS/extended%20abstract%20Bertens%20Jansen%20Kleijn%20Koutny%20Verbeek.pdf
109% Laura M.F. Bertens
110
111% http://www.liacs.nl/~csbpn/
112%
113%
114
115\end{thebibliography}
116\end{document}
Note: See TracBrowser for help on using the repository browser.