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Mathematics and Biosciences in Interaction Managing Editor Wolfgang Alt Division of Theoretical Biology Botanical Institute University of Bonn Kirschallee 1 D-53115 Bonn e-mail: SINGLE-CELL- BASED MODELS IN BIOLOGY AND MEDICINE Alexander R.A. Anderson Mark A.J. Chaplain Katarzyna A. Rejniak Editors Birkhäuser Basel • Boston • Berlin Editors: Dr. Alexander R.A. Anderson Dr. Katarzyna A. Rejniak Division of Mathematics Division of Mathematics University of Dundee University of Dundee 23 Perth Road 23 Perth Road Dundee DD1 4HN Dundee DD1 4HN UK UK Prof. Mark A.J. Chaplain Division of Mathematics University of Dundee 23 Perth Road Dundee DD1 4HN UK Library of Congress Control Number: 2007923086 Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at <http://dnb.ddb.de>. The use of registered names, trademarks etc. in this publication, even if not identified as such, does not imply that they are exempt from the relevant protective laws and regulations or free for general use. ISBN 978-3-7643-8101-1 Birkhäuser Verlag AG, Basel - Boston - Berlin This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. For any kind of use permission of the copyright owner must be obtained. © 2007 Birkhäuser Verlag AG, P.O. Box 133, CH-4001 Basel, Switzerland Part of Springer Science+Business Media Printed on acid-free paper produced from chlorine-free pulp. TFC ∞ Cover design: Armando Losa, graphic designer Cover illustration: The cover image is constructed from the 3-D simulation of a growing tumour by Alexander R.A. Anderson, the 2-D simulation of an epithelial acinus by Katarzyna A. Rejniak and from a real picture of an epithelial cell by David Russell, Division of Cell and Developmental Biology, School of Life Sciences, University of Dundee. Printed in Germany ISBN 978-3-7643-8101-1 e-ISBN 978-3-7643-8123-3 9 8 7 6 5 4 3 2 1 www.birkhauser.ch 53E `> FD[-D[U L\ ,02?*F 4 !D01 F+-A>D; _A[>&-AA_A T [T_&[_T-U U>D; [<- _#&-AA_A T A-B-D[ F+-A L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L L GG6 L 3 ?1 3E?5HE.53 7!// 1 ?,;;B! ;*!// 1 21! /!$ 1 (2D!: :! ;2 01F 32:?,21; 2$ 0??!: 1 ,? ,; ,1 2! ,!1! ?2 ?*! /D; 2$ 3*F;,; ?*? ?*!,: 3:?,/!; *C! !!1 02C! 02B/ ! 1 21$2:0! 4 *!F :! 12 !E!3?,21; ?2 ?*! :B/! ?*? 2 /+ DF; )!20!?:,G!;4 *!,: 3:2/!0; 2$ $2:0 :! ,1 ?*! 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D*2 ;!!.; $2: 0!?*2 ; D,?*2B? *C,1) !'1,?! 3:2/!0 ,1 0,1 ;!!.; ,1 ?*! 02;? 3:? ,1 C,14 *! $B:?*!: 0?*!0?,/ ?*!2:F ,; !C!/23! ?*! 02:! *:+ 021,2B;/F 1 B1,$2:0/F 2!; ,?; 21;?:B?,21 3:2!! 1 B1;B;3!?! :!/?,21; :! ,;/2;! !?D!!1 *,?*!:?2 ;!3:?! :1*!; 2$ ?*! ;,!1!48 >[< T-; T+ [F [<- UH-&>7& &FD[-D[ F3 [<>U # -D-T AD[TF+_&[>FD >b < [ >U &-T[ >D [ [<- HT-U-D[ [>B-* D+ 3FT [<- 3FT-U-- #A- 3_[_T-* >U [< [ >D= [-T+>U&>HA>D Tc &[>`>[c #-[a--D #>FAF;c D+ B [<-B [>&U* a>[< ;-D_>D- +> AF;_- #-[a--D [<- H T[>&>H [>D; H T[D-TU* B c #- `>-a-+ U [<- BFU[ 3T_>[3_A a c [F += ` D&- U&>-D[>7& _D+-TU[ D+>D; >D #F[< U_#?-&[UL <-U- T- ;-D_>D-Ac -b&>[>D; [>B-U [F #- >D`FA`-+ >D [<- U_#?-&[L `-T &-D[_Tc A [-T* [<- aFT+U F3 `>+ >A#-T[ T- H T[>&_A TAc HHFU>[- D+ < `- HFa-T3_A T-UFD D&- 3FT [<- HHA>& [>FD F3 +>U&T-[- BF+-AA>D; [-&<D>N_-U >D [<- T- F3 &-AA #>FAF;c) 7*2 2$ B; D2B/ 12? ! )/ ?2 /,$? ?*! C!,/ !*,1 D*,* ?*! $B?B:! /,!; *, !1< ?2 ;? )/1! ? ?*! 1!E? C1!; 2$ 2B: ;,!1! 1 ? ?*! ;!:!?; 2$ ,?; !C!/230!1? 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