Calcium dynamics in astrocytes: from oscillations to Alzheimer's

191 Pages·2011·12.29 MB·English

UC San Diego
UC San Diego Electronic Theses and Dissertations
Title
Calcium dynamics in astrocytes : from oscillations to Alzheimer's
Permalink
https://escholarship.org/uc/item/60k4x659
Author
MacDonald, Christopher Lloyd
Publication Date
2011

Peer reviewed|Thesis/dissertation
eScholarship.org Powered by the California Digital Library
University of California
UNIVERSITY OF CALIFORNIA, SAN DIEGO
Calcium Dynamics in Astrocytes: From Oscillations to Alzheimer’s
A dissertation submitted in partial satisfaction of the
requirements for the degree
Doctor of Philosophy
in
Bioengineering with Specialization in Multi-scale Biology
by
Christopher Lloyd MacDonald
Committee in charge:
Professor Gabriel Silva, Chair
Professor Henry Abarbanel
Professor Anna Devor
Professor Herbert Levine
Professor Kun Zhang
2011
Copyright
Christopher Lloyd MacDonald, 2011
All rights reserved.
The dissertation of Christopher Lloyd MacDonald is ap-
proved, and it is acceptable in quality and form for pub-
lication on microfilm and electronically:
Chair
University of California, San Diego
2011
iii
DEDICATION
To two, the loneliest number since the number one.
iv
EPIGRAPH
A careful quotation
conveys brilliance.
—Smarty Pants
v
TABLE OF CONTENTS
Signature Page . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
Dedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
Epigraph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv
Vita and Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv
Abstract of the Dissertation . . . . . . . . . . . . . . . . . . . . . . . . . . . xvi
Chapter 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Astrocyte intercellular calcium waves . . . . . . . . . . . 5
1.2.1 Are intercellular calcium waves regenerative? . . . 7
1.2.2 Minimal network signaling model of astrocyte sig-
naling . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2.3 Alzheimer’s Disease, amyloid beta, and astrocytes 9
1.2.4 Why does Aβ cause spontaneous calcium waves,
and how can we prevent it? . . . . . . . . . . . . 11
1.3 Fractional calculus . . . . . . . . . . . . . . . . . . . . . 11
1.3.1 Mathematical introduction to fractional calculus . 12
1.3.2 Applications of fractional calculus . . . . . . . . . 15
1.3.3 Developing useful numerical algorithms . . . . . . 15
Chapter 2 Diffusion modeling of ATP signaling suggests a partially re-
generative mechanism underlies astrocyte intercellular calcium
waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3 Materials and Methods . . . . . . . . . . . . . . . . . . . 22
2.3.1 Reagents and Cell Cultures . . . . . . . . . . . . 22
2.3.2 Calcium Imaging . . . . . . . . . . . . . . . . . . 22
2.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.4.1 Model Description . . . . . . . . . . . . . . . . . . 23
vi
2.4.2 A fully regenerative diffusion model cannot repro-
duce experimentally measured data . . . . . . . . 26
2.4.3 A partially regenerative diffusion model produced
spatiotemporally realistic propagating waves . . . 30
2.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 36
Chapter 3 Amyloid-β directly induces spontaneous calcium transients,
delayed intercellular calcium waves, and gliosis in rat cortical
astrocytes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.3 Materials and Methods . . . . . . . . . . . . . . . . . . . 45
3.3.1 Astrocyte Cell Culture . . . . . . . . . . . . . . . 45
3.3.2 Calcium Imaging . . . . . . . . . . . . . . . . . . 46
3.3.3 Quantification of Ca2+ Transients . . . . . . . . . 47
3.3.4 GFAP and S100B Immunocytochemistry . . . . . 48
3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.4.1 Aβ increases the frequency of intracellular cal-
cium transients and the number of activated as-
trocytes . . . . . . . . . . . . . . . . . . . . . . . 49
3.4.2 Aβ induces spontaneous time-delayed intercellu-
lar calcium waves in astrocytes . . . . . . . . . . . 51
3.4.3 Aβ induces changes in S100B and GFAP expres-
sion in astrocytes by 12h . . . . . . . . . . . . . . 52
3.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 56
Chapter 4 A nucleation phenomenon can theoretically explain the dy-
namics of intrercellular calcium waves in astrocytes under nor-
mal and Alzheimer’s like conditions . . . . . . . . . . . . . . . 59
4.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.3 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.3.1 Calcium induces calcium release from the ER . . 64
4.3.2 IP is generated through metabotropic GPCR
3
cascades . . . . . . . . . . . . . . . . . . . . . . . 66
4.3.3 ATP diffuses through the media, degrades, and is
ejected by excited cells . . . . . . . . . . . . . . . 68
4.3.4 Parameters . . . . . . . . . . . . . . . . . . . . . 69
4.3.5 Model simulations . . . . . . . . . . . . . . . . . . 71
4.4 Results and discussion . . . . . . . . . . . . . . . . . . . 72
4.4.1 Nucleation of IP R activity at the whole cell level
3
leads to a critical threshold shift in calcium ex-
citability . . . . . . . . . . . . . . . . . . . . . . . 72
vii
4.4.2 Intracellular calcium transients and oscillations . . 73
4.4.3 Intercellular calcium waves . . . . . . . . . . . . . 74
4.4.4 Potential new targets in AD signaling cascades . . 78
4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . 82
Chapter 5 Computational efficiency of fractional diffusion using adaptive
time step memory . . . . . . . . . . . . . . . . . . . . . . . . . 83
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 84
5.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
5.2.1 Gru¨nwald-Letnikov formulation and simplification 85
5.2.2 Discretization . . . . . . . . . . . . . . . . . . . . 87
5.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.3.1 Diffusion simulation examples . . . . . . . . . . . 88
5.3.2 Adaptive Memory Method . . . . . . . . . . . . . 89
5.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 92
Chapter 6 Method for Decreasing the Memory Footprint of Fractional
Partial Differential Equations . . . . . . . . . . . . . . . . . . 97
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 98
6.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
6.2.1 Mathematical Implementation . . . . . . . . . . . 101
6.2.2 Computer implementation . . . . . . . . . . . . . 102
6.2.3 Linked List Implementation . . . . . . . . . . . . 104
6.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
Chapter 7 Using a Smart Adaptive History Mesh for Improving Compu-
tational Efficiency of Fractional Order Differential Equations . 106
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 107
7.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
7.2.1 Basic discretization . . . . . . . . . . . . . . . . . 108
7.2.2 Approximating the discrete Gru¨nwald-Letnikov
series as a continuous time integral . . . . . . . . 109
7.2.3 Extension of ψ(γ,m) to the positive real domain . 110
7.2.4 Choosing the adaptive history mesh and dropping
points in the history . . . . . . . . . . . . . . . . 116
7.2.5 Preliminary Results . . . . . . . . . . . . . . . . . 116
Appendix A AstroTracker - image segmentation software for in vivo astro-
cyte calcium imaging . . . . . . . . . . . . . . . . . . . . . . . 121
A.1 Description . . . . . . . . . . . . . . . . . . . . . . . . . 122
A.2 Source Code . . . . . . . . . . . . . . . . . . . . . . . . . 126
A.2.1 FollowAstCa.m . . . . . . . . . . . . . . . . . . . 126
A.2.2 astfind.m . . . . . . . . . . . . . . . . . . . . . . . 129
viii
A.2.3 Stack2compAVI.m . . . . . . . . . . . . . . . . . 133
Appendix B Future Studies on IP3RKO mouse . . . . . . . . . . . . . . . . 136
B.1 IP RKO mouse line . . . . . . . . . . . . . . . . . . . . . 137
3
Appendix C Issues in determining neuronal voltage from neuronal calcium 138
C.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . 139
C.1.1 Neuronal spiking is commonly defined as the fun-
damental information processing unit in the brain 139
C.1.2 Methods to observe neuronal activity . . . . . . . 140
C.1.3 Models . . . . . . . . . . . . . . . . . . . . . . . . 142
C.1.4 Testing the deconvolution algorithm . . . . . . . . 144
Appendix D Novel method for neuronal network patterning . . . . . . . . . 151
D.1 Protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
D.1.1 Surface preparation . . . . . . . . . . . . . . . . . 152
D.1.2 Astrocyte Cell Culture . . . . . . . . . . . . . . . 153
D.1.3 GFAP and S100B Immunocytochemistry . . . . . 154
D.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
ix