Context Navigation

source: liacs/pnbm/project/report.tex@ 19

Last change on this file since 19 was 18, checked in by Rick van der Zwet, 15 years ago
Revised model
File size: 6.2 KB

Rev	Line
[11]	1	%
	2	% $Id: report.tex 571 2008-04-20 17:31:04Z rick $
	3	%
	4
	5	\documentclass[12pt,a4paper]{article}
	6
	7	\frenchspacing
[12]	8	\usepackage[english]{babel}
	9	\selectlanguage{english}
[11]	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}
	26	Planar signaling is the process in which cells accumulate proteins based on the
	27	saturation of nearby cells. If one cell produces n ammount of proteins, it will
	28	initiate a transfering cascade to cells in the vicinity. This dissemination of
	29	proteins will eventually cease, considering that n is a finite variable. There
	30	is a gradation in the ammount of proteins transfered, meaning that neighbouring
	31	cells get n/2 the ammount of proteins of the most saturated cell.
	32
	33	XXX: Citing to the Bio Papers
	34	XXX: Small introductions Petri-nets
	35
	36	\section{Approch}
	37	First a PetriNet model will be defined textually and using graphs next the
	38	modeling will be taking into practice using the modeling tool\emph{CPNTools}.
	39
	40	\section{Modeling}
[12]	41	To 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
	43	solution that can be applied to any configuration of cells. We start with a
	44	bulding block that is an abstraction of a cell (figure: circle), which can then
	45	be coupled to other cells (figure: arrows). The abstraction contains two
	46	different types. First the proteins are modelled (figure: red), secondly the
	47	proteins (figure: blue) are leading in a second process of the creation of
	48	gradients which also needs modeling. We assume a 1:1 mapping between the amount
[18]	49	of proteins and gradients -this taken into consideration- ones an \texttt{INITIAL}
	50	protein is 'used' (e.g. has on posterisation counterpart) in this process it
	51	get called \texttt{ACTIVATED}. We assume that the proteins to posterisation
	52	process is taking place at the same time as the proteins distribution. And in a
	53	special format (figure: object B). It tries to matches the posterisation to the
	54	same level as the proteins present. But the moment the protein level lowers,
	55	the posterisation will remain the same. In pseudo-code:
	56	\begin{verbatim}
	57	if numPos < numProteins then
	58	numPos = numPos + 1
	59	endif
	60	\end{verbatim}
	61	\texttt{numProteins} is the proteins available and \texttt{numPos} is the
	62	posterisation present.
[11]	63
	64	The connectors between the cells (the membrams) has a special properly. One
	65	can see them as pressure valves others as sighons (see Fig~\ref{fig:pressure}).
	66	The moment the 'volume' at complies with the following properly $A / 2 < B$
[18]	67	then the pressure closes, else it passes volume from A to B at an certain rate
	68	(\texttt{flowSpeed}). This rate could depend on the difference, actual value present
	69	or something else.
	70
[11]	71	For the case there exists no standard PetriNet 'component', hence this require
[12]	72	the creation of a new property (figure: $2:1$), with the following properties:
[11]	73
[12]	74	\begin{verbatim}
[18]	75	flowSpeed = n
[12]	76	if A > 2 * B then
	77	A = A - flowSpeed
	78	B = B + flowSpeed
	79	else if B > 2 * A then
	80	B = B - flowSpeed
	81	A = A + flowSpeed
	82	endif
	83	\end{verbatim}
	84
[11]	85	Planar signaling could theoretically start in every cell, by
	86	inserting some amount of protiens. In our model represented as a bunch of
[18]	87	\texttt{INITIAL} tokens beeing put in a random cell.
[11]	88
[12]	89	\begin{figure}[htp]
	90	\centering
	91	\caption{Planar signaling model}
[18]	92	\includegraphics[width=100mm]{planar-signaling-model.eps}
[12]	93	\label{fig:model}
	94	\end{figure}
[11]	95
	96	\begin{figure}[htp]
	97	\centering
	98	\caption{Pressure valve example}
	99	\includegraphics[height=60mm]{pressure-valve.eps}
	100	\label{fig:pressure}
	101	\end{figure}
	102
	103	\section{CPNTools 'implementation'}
	104	CPNTools has quite some shortcomings when it comes to modeling (higher level
[12]	105	developmental) biology.
[11]	106
[12]	107	One it the shortcoming of the 'balancing'. It does not allow reading of how
	108	many tokens are present in a certain state and base action uppon them. As
	109	workaround for this (see Fig~\ref{fig:CPNplanar}) we used a 'dump' gradation
	110	function. In our case it simply take 3 tokens and pushes 1 forward and
[18]	111	converting 2 directly to \texttt{ACTIVATED}. This does not take in
	112	consideration if the amount get changed in 'further-up', by some external
	113	source.
[12]	114
[11]	115	Secondly it is missing a possibility to for easy random initialisation for
	116	modeling purposes. As a dirty quirk we 'hacked' it to choose between starting
	117	at the head or the tail.
	118
[12]	119	In this implementation the protiens to gradiants process is taking place at
	120	cell $A$ at the same time that the proteins get transfered from cell $A$ to
	121	$B$.
[11]	122
[12]	123	Also it should be noted that it missing a notion of timed firing sequences;
	124	meaning firing sequences which will occur at an certain time. This could for
[18]	125	example used to 'trigger' a timmed activation of the \texttt{INITIAL} to
	126	\texttt{ACTIVATED} process as modeled in fig~\ref{fig:model}. An initial idea
	127	is shown at fig\ref{fig:time-idea} in appendix 1.
[12]	128
[18]	129
[11]	130	\begin{figure}[htp]
	131	\centering
	132	\caption{CPNTools implementation}
	133	\advance\leftskip-2cm
	134	\advance\rightskip+2cm
	135	\includegraphics[width=1.3\textwidth]{planer-signaling.eps}
	136	\label{fig:CPNplanar}
	137	\end{figure}
	138
	139	\section{Conclusion}
	140	Using PetriNets for modeling biology processes is a powerful framework, which
	141	could be well extendable. The Proof Of Concept implementations and
	142	visualisations how-ever are lacking. \emph{CPNTools} for example does not
	143	provide a powerfull enough toolset for the modeling purposes.
	144
	145	\begin{thebibliography}{10}
	146	% sing Petri Nets in Higher Level Developmental Biology:
	147	% A case study on the AP axis development in Xenopus laevis
	148	% Extended Abstract
	149	% http://www.liacs.nl/~csbpn/COURSE%20DOCUMENTS/extended%20abstract%20Bertens%20Jansen%20Kleijn%20Koutny%20Verbeek.pdf
	150	% Laura M.F. Bertens
	151
	152	% http://www.liacs.nl/~csbpn/
	153	%
	154	%
	155
	156	\end{thebibliography}
[18]	157	\section{*Appendix}
	158
	159	\begin{figure}[htp]
	160	\centering
	161	\caption{Timed transition idea}
	162	\includegraphics[width=0.5\textwidth]{timer-proposal.eps}
	163	\label{fig:time-idea}
	164	\end{figure}
[11]	165	\end{document}

Note: See TracBrowser for help on using the repository browser.

Download in other formats: