• Aucun résultat trouvé

Acknowledgments iv

N/A
N/A
Info
Télécharger
Protected

Academic year: 2021

Partager "Acknowledgments iv"

Copied!
3
0
0

Chargement.... (Voir le texte intégral maintenant)

Texte intégral

(1)

Contents

Contents i

Acknowledgments iv

Abstract – R´ esum´ e vi

1 Introduction 1

1.1 Context . . . . 1

1.2 Modelling strategy . . . . 3

1.2.1 Generalities . . . . 3

1.2.2 The mesoscopic approach . . . . 4

1.3 Objectives . . . . 9

I Effects of compartmentalisation on nonlinear chem- ical reactions 13 2 Nonlinear behaviour and fluctuation-induced dynamics in the photosensitive BZ reaction 14 2.1 Reaction mechanism and models . . . . 15

2.1.1 The Field-K¨ or¨ os-Noyes model . . . . 15

2.1.2 Modelling of the compartmentalised BZ reaction . . . . 17

2.2 Deterministic analysis . . . . 19

2.2.1 The non-photosensitive BZ reaction . . . . 20

2.2.2 The photosensitive BZ reaction . . . . 24

2.3 Stochastic simulations . . . . 27

2.3.1 The non-photosensitive case . . . . 29

2.3.2 The photosensitive case . . . . 34

2.4 Discussion . . . . 37

i

(2)

Contents 3 Emergence of chaos in a spatially confined reactive system 39

3.1 Introduction . . . . 39

3.2 The amended Willamowski-R¨ ossler model . . . . 41

3.3 Deterministic behaviour . . . . 44

3.4 Stochastic dynamics . . . . 48

3.4.1 Fluctuations in a homogeneous system . . . . 48

3.4.2 Inhomogeneous fluctuations . . . . 51

3.5 Discussion . . . . 58

II Calcium release from IP

3

Rs clusters : from local to global signals 60 4 Introduction to calcium signalling 61 4.1 Compartmentalisation of the cell and calcium fluxes . . . . 62

4.2 Interactions between IP

3

Rs . . . . 65

4.2.1 Blips and puffs . . . . 66

4.2.2 Spikes and waves . . . . 68

4.3 Statistical properties of puffs and spikes . . . . 70

4.4 Models . . . . 72

4.4.1 Puff models . . . . 72

4.4.2 Modelling of spikes and waves . . . . 73

4.4.3 An effective cluster model . . . . 77

5 Emergence of global signals from clusters dynamics: a deter- ministic approach 80 5.1 Spatially homogeneous model . . . . 81

5.1.1 Governing equations and properties of the model . . . 81

5.1.2 Bistable regime . . . . 83

5.1.3 Oscillatory regime . . . . 89

5.2 Reaction-diffusion model . . . . 97

5.2.1 Governing equations and properties of the model . . . 97

5.2.2 Nucleation phenomena in the bistable regime . . . . . 99

5.2.3 Spatiotemporal patterns in the oscillatory regime . . . 102

5.3 Discussion . . . 105

6 Fully stochastic modelling of global spikes 108 6.1 The fully stochastic model . . . 109

6.1.1 Problem formulation and numerical code . . . 109

6.1.2 Macroscopic limit . . . 113

6.1.3 Comparison with the model by Calabrese et al. . . . . 117

ii

(3)

Contents

6.2 Stochastic bistable regime . . . 119

6.2.1 Influence of ρ

c

on the global Ca

2+

dynamics . . . 120

6.2.2 Influence of the local σ on Ca

2+

dynamics . . . 125

6.3 Coupling strength between the clusters . . . 128

6.3.1 Influence of D . . . 128

6.3.2 Influence of v

p

. . . 132

6.4 Stochastic oscillatory regime . . . 135

6.5 Conclusions . . . 137

General conclusions and outlook 139

A Fluorescence measurements of concentrations in cells: cali-

bration of fluorescence signals 145

Bibliography 147

iii

Références

Télécharger maintenant ( PDF - 3 Page - 170.16 KB )

Documents relatifs

Internal and External Fluid Sources for Eclogite-facies Veins in the Monviso Meta-ophiolite, Western Alps: Implications for Fluid Flow in Subduction Zones

Most of the vein minerals have major and trace element compositions that are comparable with the host-rock minerals, and vein and host-rock zircons have similar Hf

Flux analysis of the Trypanosoma brucei glycolysis based on a multi-objective criteria bioinformatic approach, Advances in Bioinfromatics, 2012, in press. International conference with published acts

brucei metabolic flexibility when constraining the system by five different constraints known from experi- mental data or assumed from the literature, that is, (i) the topology of

Convex optimization and machine learning for scalable verification and control

In the context of stability analysis for LTI systems, the compositional idea is.. typically materialized as the search of block-diagonal Lyapunov matrices. Various necessary

Snow loads on roofs 1958-59: third progress report

- Although Kingston's snowfall for the 1958-59 winter was 91 inches (60 per cent above normal), the maximum average load remained less than 30 and 40 per cent of the }ffiC design

Médecine régénératrice du disque intervertébral : De la physiopathologie à l’application clinique

timents cellulaires altérés, associées ou non à un biomatériau, la médecine régénératrice du DIV a pour objectif de restaurer la MEC discale afin de rétablir ses propriétés

Rapport annuel 1974-1975 - CSE

Comme complément de ses audiences, le Comité catholique a voulu attein dre un public plus large en multipliant ses contacts avec différents organismes provinciaux dont les

Les transactions lors de ruptures de contrats de travail

Si l’on peut invoquer le fait que le motif de « mésen- tente » apparaît plus approprié par la proximité hiérarchique et sociale qui existe entre certains cadres supérieurs et