New insight into models of cardiac caveolae and arrhythmia

170 Pages·2016·4.58 MB·English

University of Iowa
Iowa Research Online
Theses and Dissertations
Summer 2015
New insight into models of cardiac caveolae and
arrhythmia
Chenhong Zhu
University of Iowa
Copyright 2015 Chenhong Zhu
This dissertation is available at Iowa Research Online: http://ir.uiowa.edu/etd/1945
Recommended Citation
Zhu, Chenhong. "New insight into models of cardiac caveolae and arrhythmia." PhD (Doctor of Philosophy) thesis, University of
Iowa, 2015.
http://ir.uiowa.edu/etd/1945.
Follow this and additional works at:http://ir.uiowa.edu/etd
Part of theApplied Mathematics Commons
NEW INSIGHT INTO MODELS OF CARDIAC CAVEOLAE AND
ARRHYTHMIA
by
Chenhong Zhu
A thesis submitted in partial fulfillment of the
requirements for the Doctor of Philosophy
degree in Applied Mathematical and Computational Sciences
in the Graduate College of
The University of Iowa
August 2015
Thesis Supervisor: Associate Professor Colleen Mitchell
Graduate College
The University of Iowa
Iowa City, Iowa
CERTIFICATE OF APPROVAL
PH.D. THESIS
This is to certify that the Ph.D. thesis of
Chenhong Zhu
has been approved by the Examining Committee for the
thesis requirement for the Doctor of Philosophy degree
in Applied Mathematical and Computational Sciences at
the August 2015 graduation.
Thesis committee:
Colleen Mitchell, Thesis Supervisor
Bruce Ayati
Keith Stroyan
Suely Oliveira
Surjit Khurana
To my family
ii
ACKNOWLEDGEMENTS
I would like to express my sincerely thanks to my advisor Professor Colleen
Mitchell for her enormous support and guidance through my graduate study. I truly
appreciate unlimited patience which she devoted to discussion with me. My very
great thanks to Professor Rodica Curtu for introducing me to the wonderful world of
computational modeling in biomedical topics and teaching a complete series of ODE
courses in a inspiring way. I am thankful to the rest of my Committee, Professors
Keith Stroyan, Bruce Ayati, Surjit Khurana and Suely Oliveira for their invaluable
assistance. I would also like to thank Professor Weimin Han, Long-sheng Song, Lihe
Wang, Hantao Zhang and Jianfeng Cai for their support and encouragement in my
research projects. Many thanks to Lulu Chu and Zhimao Liu for sharing ideas and
collaborating with me.
Thanks to all my friends, I enjoy your company. Many thanks to Xiayi Wang,
Boshi Yang, and Ling Du for sharing the ups and downs of my life. To my friends
Zhen Wu, Yan Wang and Ping Yang for always being here for me. To my fellow
graduate students: Tianyi Zhang, Colin Swaney, Paul Savala, Fan Yang, Bin Li,
Jeannine Abiva, Jonathan Ho, David Meyer and Qiwei Sheng for their friendship.
I am grateful to my parents, Yulan and Chuanlin for encouraging me and
believing in my work all the time. My great thanks to my husband Kai, who is always
supportive. AndmysonYesenalwaysmakesmefeelstrong. Noneofmyachievements
during these years would have been accomplished without their support.
iii
ABSTRACT
Recent studies suggest that cardiomyocyte membrane microdomains, caveolae
and transverse tubules, play a key role in cardiac arrhythmia. Mutation of caveolin-
encodinggenesCAV3, co-expressedwithgenesofcaveolaeionchannels, leadstoalate
persistent sodium currents and delayed repolarization stage, called LQT9 disease. A
simplified three-current model is created to largely reduce the well-known Pandit rat
ventricular myocyte model. The mathematical tractability of the three-current model
allows us to conduct asymptotic analysis and efficiently estimate action potential du-
ration. Improvement in the description of the mechanism for caveolae sodium current
is incorporated into the three-current model utilizing a probability density approach
for the four-state caveolae neck-channel coupling. The prolongation of action poten-
tials and the formation of potential arrhythmia are shown to arise if caveolae neck
open probability varies. A minimal model of the Ca2+ spatial distribution of CICR
units illustrates the transverse tubule remodeling in failing myocyte causes dysfunc-
tion in the Ca2+ profile. With regards to discrimination of protein localization, which
is widely used in biological experiments, the bagging pruned decision tree algorithm
is tested to be one of the algorithms with best performance on the large data set,
and it succeeds in extracting information to be highly predictive on test data. Par-
allel computation technique is applied to accelerate the speed of implementation in
K-nearest neighbor learning algorithms on big data sets.
iv
PUBLIC ABSTRACT
Heart diseases become the leading causes of sudden death in United States.
Recent studies suggest that cardiomyocyte membrane microdomains, caveolae and
transverse tubules, play a key role in cardiac arrhythmia. Mutation of caveolin-
encoding genes CAV3, co-expressed with genes of caveolae ion channels, leads to a
latepersistent sodiumcurrents anddelayed repolarizationstage, calledLQT9 disease.
A simplified three-current model is created to largely reduce the well-known Pandit
rat ventricular myocyte model. The mathematical tractability of the three-current
model allows us to conduct asymptotic analysis and efficiently estimate action poten-
tial duration. Improvement in the description of the mechanism for caveolae sodium
currentisincorporatedintothethree-currentmodelutilizingaprobabilitydensityap-
proach for the four-state caveolae neck-channel coupling. The prolongation of action
potentials and the formation of potential arrhythmia are shown to arise if caveolae
neck open probability varies. A minimal model of the Ca2+ spatial distribution of
CICR units illustratesthe transverse tubule remodeling infailing myocyte causes dys-
function in the Ca2+ profile. With regards to discrimination of protein localization,
which is widely used in biological experiments, the bagging pruned decision tree al-
gorithm is tested to be one of the algorithms with best performance on the large data
set, and it succeeds in extracting information to be highly predictive on test data.
Parallel computation technique is applied to accelerate the speed of implementation
in K-nearest neighbor learning algorithms on big data sets.
v
TABLE OF CONTENTS
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x
CHAPTER
1 INTRODUCTION TO CARDIAC CAVEOLAE AND ARRHTHMIA 1
1.1 Significance and Background . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Heart Disease and Cardiac Microdomains . . . . . . . . . 1
1.1.2 Cardiac Caveolae . . . . . . . . . . . . . . . . . . . . . . 3
1.1.3 Transverse Tubule . . . . . . . . . . . . . . . . . . . . . . 10
1.1.4 Electriphysiology . . . . . . . . . . . . . . . . . . . . . . . 11
1.2 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2 REDUCED THREE-CURRENT MODEL . . . . . . . . . . . . . . . . 15
2.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1.0.1 Previous models . . . . . . . . . . . . . . . . . . 16
2.2 Formulation of Three-Current Model . . . . . . . . . . . . . . . . 18
2.2.0.2 Equations . . . . . . . . . . . . . . . . . . . . . 19
2.2.0.3 Currents . . . . . . . . . . . . . . . . . . . . . . 20
2.2.1 Parameter Estimation and Simulation . . . . . . . . . . . 21
2.2.1.1 Numerical Simulation . . . . . . . . . . . . . . . 21
2.2.1.2 Parameter Estimation . . . . . . . . . . . . . . . 23
2.2.1.3 Genetic Algorithm . . . . . . . . . . . . . . . . . 24
2.2.1.4 Parameter Values . . . . . . . . . . . . . . . . . 26
2.2.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.2.2.1 Comparison with Pandit Model . . . . . . . . . 27
2.2.2.2 Caveolar-Inclusive Three-Current Model . . . . . 29
2.3 Asymptotic analysis . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.3.1 Phase 4s . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.3.2 Phase 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.3.2.1 Asymptotic Approach . . . . . . . . . . . . . . . 37
2.3.2.2 Approximation vs Numerical Result . . . . . . . 39
2.3.2.3 Bifurcation Analysis . . . . . . . . . . . . . . . 39
2.3.3 Phase 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.3.3.1 Asymptotic approach . . . . . . . . . . . . . . . 42
2.3.3.2 Approximation vs Numerical Result . . . . . . . 43
2.3.3.3 Alternative Method . . . . . . . . . . . . . . . . 44
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2.3.4 Phase 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.3.4.1 Asymptotic Approach . . . . . . . . . . . . . . . 45
2.3.4.2 Bifurcation . . . . . . . . . . . . . . . . . . . . . 45
2.3.5 Phase 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
2.3.5.1 Asymptotic Approach . . . . . . . . . . . . . . . 46
2.3.5.2 Rough Approximation . . . . . . . . . . . . . . . 47
2.3.5.3 Taylor Expansion . . . . . . . . . . . . . . . . . 48
2.3.5.4 Bifurcation . . . . . . . . . . . . . . . . . . . . . 49
2.3.6 Phase 4r . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.4 Action Potential Duration Approximation . . . . . . . . . . . . . 51
2.4.1 APD Approximation . . . . . . . . . . . . . . . . . . . . . 51
2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3 PROBABILITY DENSITY MODEL FOR CARDIAC CAVEOLAE . 54
3.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.2 Model formulation . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.2.1 ProbabilityDensityApproachtoGatingFunctionforCave-
olar Sodium Current . . . . . . . . . . . . . . . . . . . . . 56
3.2.1.1 StateCC:BothNa+ InactivationGateandCave-
olae Neck are Closed . . . . . . . . . . . . . . . 58
3.2.1.2 State OC: Na+ Inactivation Gate is Open, and
Caveolae Neck is Closed . . . . . . . . . . . . . 59
3.2.1.3 State CO: Na+ Inactivation Gate is Closed, and
Caveolae Neck is Open . . . . . . . . . . . . . . 60
3.2.1.4 StateOO:BothNa+ InactivationGateandCave-
olae Neck are Open . . . . . . . . . . . . . . . . 61
3.2.2 Dynamic Systems for the Whole Cell . . . . . . . . . . . . 62
3.2.2.1 System Variations . . . . . . . . . . . . . . . . . 63
3.2.3 Numerical Simulation . . . . . . . . . . . . . . . . . . . . 67
3.2.3.1 Numerical Scheme . . . . . . . . . . . . . . . . . 67
3.3 Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.3.1 Physiological Influence of Caveolae Currents . . . . . . . 73
3.3.2 LQT9 Disease . . . . . . . . . . . . . . . . . . . . . . . . 78
3.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4 CALCIUMDYNAMICWITHTRASVERSETUBULEDYSFUNCTION 83
4.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.2 Minimal Calcium Dynamic Models and Its Bifurcation . . . . . . 84
4.2.1 Bifurcation Analysis . . . . . . . . . . . . . . . . . . . . . 86
4.3 1D Ca2+ Propagation Model . . . . . . . . . . . . . . . . . . . . 93
4.3.1 Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
4.3.2 TTs Remodeling . . . . . . . . . . . . . . . . . . . . . . . 98
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4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
5 MINING PROTEIN LOCALIZATION DATA . . . . . . . . . . . . . . 102
5.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
5.2 Mining Yeast Protein Data Set . . . . . . . . . . . . . . . . . . . 103
5.2.1 Background and Preprocessing . . . . . . . . . . . . . . . 103
5.2.1.1 Background . . . . . . . . . . . . . . . . . . . . 103
5.2.1.2 Preprocessing . . . . . . . . . . . . . . . . . . . 106
5.2.2 Implementation with Well-Known Mining Algorithms . . 108
5.2.2.1 Probabilistic Classifiers . . . . . . . . . . . . . . 109
5.2.2.2 Non-Probabilistic Classifiers . . . . . . . . . . . 111
5.2.2.3 Comparison and Biological Implication . . . . . 117
5.2.3 Proposed Method . . . . . . . . . . . . . . . . . . . . . . 118
5.2.3.1 Feature Selection . . . . . . . . . . . . . . . . . 118
5.2.3.2 Ensemble . . . . . . . . . . . . . . . . . . . . . . 120
5.3 Parallel K-Nearest Neighbor Method . . . . . . . . . . . . . . . . 123
5.3.1 K-Nearest Neighbor Method . . . . . . . . . . . . . . . . 123
5.3.1.1 Technical Approach . . . . . . . . . . . . . . . . 125
5.3.1.2 Sorting Algorithms . . . . . . . . . . . . . . . . 128
5.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
APPENDIX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
A.1 Three-Current Model . . . . . . . . . . . . . . . . . . . . . . . . 131
A.1.1 Genetic Algorithm for Parameter Fitting . . . . . . . . . 131
A.1.2 Three-Current Model . . . . . . . . . . . . . . . . . . . . 134
A.2 Probability Density Model . . . . . . . . . . . . . . . . . . . . . 136
A.2.1 Implementation of Reduced System . . . . . . . . . . . . 136
A.3 Original Classes Distribution of the Protein Data Set . . . . . . . 142
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