The influence of the morphology of nuclei from hippocampal neurons on signal processing in nuclei [Elektronische Ressource] / presented by Sean Gillian Queisser

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INAUGURAL DISSERTATIONsubmitted to theFaculty for Mathematicsof the Ruperto-Carola University of Heidelberg, Germanyfor the degree ofDoctor of Natural Sciencespresented byDiplom-MathematikerSean Gillian Queisserborn in HannoverOral examination: ...............................April 30, 2008The In uence of the Morphology ofNuclei from Hippocampal Neuronson Signal Processing in NucleiGutachter: Prof. Dr. Gabriel WittumSummaryCalcium signaling in neurons is a key regulator of gene expression and plays an im-portant role in memory formation, learning and survival. One major route on whichsynapses and the nucleus of the neuron communicate, is through calcium waves thatpropagate from NMDA receptors { either synaptic or extra-synaptic { to the nucleuswhere they activate the transcription factor CREB.Novel mechanisms were recently unveiled at the IZN in Heidelberg, that are respon-sible for nuclear plasticity. The morphology of nuclei undergoes changes in time,regulated by calcium in ux through NMDA receptors. Changes in the nuclear mor-phology could a ect the communication pathway between synapse and nucleus.This thesis presents a novel inertia-based image processing lter that allows us toreconstruct the geometry of hippocampal nuclei from raw confocal microscopy data.

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INAUGURAL DISSERTATION
submitted to the
Faculty for Mathematics
of the Ruperto-Carola University of Heidelberg, Germany
for the degree of
Doctor of Natural Sciences
presented by
Diplom-Mathematiker
Sean Gillian Queisser
born in Hannover
Oral examination: ...............................
April 30, 2008The In uence of the Morphology of
Nuclei from Hippocampal Neurons
on Signal Processing in Nuclei
Gutachter: Prof. Dr. Gabriel WittumSummary
Calcium signaling in neurons is a key regulator of gene expression and plays an im-
portant role in memory formation, learning and survival. One major route on which
synapses and the nucleus of the neuron communicate, is through calcium waves that
propagate from NMDA receptors { either synaptic or extra-synaptic { to the nucleus
where they activate the transcription factor CREB.
Novel mechanisms were recently unveiled at the IZN in Heidelberg, that are respon-
sible for nuclear plasticity. The morphology of nuclei undergoes changes in time,
regulated by calcium in ux through NMDA receptors. Changes in the nuclear mor-
phology could a ect the communication pathway between synapse and nucleus.
This thesis presents a novel inertia-based image processing lter that allows us to
reconstruct the geometry of hippocampal nuclei from raw confocal microscopy data.
A data base of reconstructed nuclei shows, that cell nuclei from hippocampal neu-
rons contain deep infoldings of the nuclear envelope which increase nuclear surface
size, minimize di usion distances for calcium ions in the nucleus and form structural
micro domains inside the nucleus.
In order to mathematically assess the function of these complex nuclear structures,
a three dimensional model for calcium signaling in the nucleus, based on the recon-
structed nuclear geometries, was developed. This model was fully implemented in
the simulation environment UG, which o ers multi-grid solvers for the model equa-
tions. Simulation results show, that the nuclear morphology in fact in uences the
way calcium signals propagate inside the nucleus. The infoldings of the membrane
shorten di usion distances, therefore calcium can reach more distal sites faster.
Furthermore, infolded nuclei show higher levels of activity and are more adept at
resolving signals at high frequencies.
In addition to the three dimensional model for calcium signaling a method for es-
timating the di usion coe cient of nuclear calcium was developed. This method
makes use of numerical optimization techniques with data from laser-assisted cal-
cium uncaging experiments. Data driven simulations describe nuclear calcium to be
in a bu ered state, which is represented by an active di usion coe cient of approx-
2imately 36 m =s.
iiiZusammenfassung
Kalziumsignale in Neuronen sind ein zentraler Regulator fur Genexpression und
spielen bei der Ged achtnisformation, dem Lernen und dem Uberleben einer Zelle
eine wesentliche Rolle. Ein bedeutender Kommunikationsweg zwischen Synapse
und Zellkern basiert auf dem Transport von Kalziumionen, von synaptischen oder
extra-synaptischen NMDA Rezeptoren zum Kern, wo diese den Transkriptionsfaktor
CREB aktivieren.
Am IZN (Heidelberg) neu entdeckte Mechanismen sind verantwortlich fur Zell-
kernplastizit at. Die Morphologie von Zellkernen unterl auft zeitliche Ver anderungen,
die von Anderungen der zellul aren Kalziumkonzentration durch NMDA Rezeptoren
reguliert werden. Es besteht die M oglichkeit, dass die Kernmorphologie den Kom-
munikationsweg zwischen Synapse und Kern beein usst.
Diese Arbeit pr asentiert einen neu entwickelten Tagheits-basiertenr Bild lter, der es
uns erm oglicht die Zellkerngeometrie von Neuronen aus dem Hippocampus aus kon-
fokalen Mikroskopiedaten zu rekonstruieren. Eine Datenbank von rekonstruierten
Zellkernen zeigt, dass diese Zellkerne tiefe Einfaltungen der Kernhulle aufweisen,
welche die Kernobeacr he vergr o ern, Di usionsstrecken fur Kalziumionen im Kern
minimieren und strukturelle Micro-Domanen im Kern bilden.
Um die Funktion dieser komplexen Kernstrukturen mathematisch zu untersuchen
wurde ein dreidimensionales Model zur Beschreibung der Kalziumsignalverarbeitung
in Zellkernen entwickelt, basierend auf den rekonstruierten Kerngeometrien. Dieses
Modell wurde vollst andig in die Simulationsumgebung UG implementiert, welche
Mehrgitter-L oser fur die Modellgleichungen zur Verfugung stellt. Die Simulations-
ergebnisse zeigen, dass die Morphologie der Zellkerne in der Tat die in den Kern ein-
dringenden Kalziumsignale beein usst. Einfaltungen der Kernmembran verringern
Di usionsstrecken, wodurch Kalziumionen entferntere Stellen im Kern schneller er-
reichen k onnen. Zudem weisen eingefaltete Kerne h ohere Aktivit at auf und sind
besser in der Lage hochfrequente Signale aufzul osen.
Zus atzlich zu dem dreidimensionalen Modell der Kalziumsignalverarbeitung wurde
eine Methode zur Sch atzung des Di usionskoe zienten von Kernkalzium entwick-
elt. Diese Methode verwendet Techniken der numerischen Optimierung zusammen
mit experimentellen Daten, welche aus laserunterstutz en Kalzium-uncaging Experi-
menten stammen. Diese datenunterstutzten Simulationen beschreiben Kernkalzium
in einem gepu erten Zustand, der von einem aktiven Di usionskoe zienten von ca.
236 m =s beschrieben werden kann.
vContents
Introduction 1
1 The Neurobiology of Hippocampal Neurons 3
1.1 The Hippocampal Neuron Nucleus . . . . . . . . . . . . . . . . . . . 5
1.2 Signaling Cascades through NMDA Receptors . . . . . . . . . . . . . 5
1.2.1 The Glutamate Receptor NMDA . . . . . . . . . . . . . . . . 5
1.2.2 Cell Death or Cell Survival? . . . . . . . . . . . . . . . . . . . 6
1.3 Information Processing via Calcium Oscillations . . . . . . . . . . . . 7
1.3.1 Calcium Waves: From Synapse to Nucleus . . . . . . . . . . . 7
1.3.2 Protein Synthesis in the Nucleus . . . . . . . . . . . . . . . . . 7
1.3.3 Governing Parameters of the Calcium Code . . . . . . . . . . 8
1.4 The Nuclear Morphology: A Lot More than Just a Sphere . . . . . . 9
1.4.1 First, there was EM . . . . . . . . . . . . . . . . . . . . . . . 9
1.4.2 Image Recordings for Reconstructions . . . . . . . . . . . . . . 10
1.5 Evaluation of Experimental Data . . . . . . . . . . . . . . . . . . . . 11
1.5.1 Evaluating Single Nuclei and their Microdomains . . . . . . . 11
1.5.2 Measuring Nuclear Calcium Activity . . . . . . . . . . . . . . 12
2 Image Processing 15
2.1 Processing Data for Reconstruction of Hippocampal Nuclei . . . . . . 17
2.1.1 Filtering with Nonlinear Anisotropic Di usion Filters . . . . . 17
2.1.2 Adding More Structure Detection to the Filter . . . . . . . . . 19
2.1.3 Segmentation . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2 Generating Grids from Processed Microscopy Data . . . . . . . . . . 22
2.2.1 Surface Grids . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.2.2 Volume Grids . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.3 Measuring Hippocampal Nuclei . . . . . . . . . . . . . . . . . . . . . 24
2.4 Visualizing 3D-Reconstructions . . . . . . . . . . . . . . . . . . . . . 24
3 Modeling Calcium Signaling in Hippocampal Neurons 27
3.1 Modeling Nuclear Calcium Signaling . . . . . . . . . . . . . . . . . . 29
3.1.1 Signal Transduction in the Nucleus . . . . . . . . . . . . . . . 29
3.1.2 Di usion Coe cients in Hippocampal Neuron Nuclei . . . . . 31
viiviii Contents
3.2 Numerical Methods for Nuclear Signaling . . . . . . . . . . . . . . . . 33
3.2.1 Introduction to Partial Di erential Equations . . . . . . . . . 33
3.2.2 Discretization of the Signaling Equation . . . . . . . . . . . . 35
3.2.3 Solving the Discrete Model Equation . . . . . . . . . . . . . . 38
3.3 The Simulation Software UG . . . . . . . . . . . . . . . . . . . . . . 41
3.3.1 The UG Concept . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.3.2 Implementing the Nucleus Model . . . . . . . . . . . . . . . . 41
3.3.3 Grid Integration for Modeling . . . . . . . . . . . . . . . . . . 43
3.4 Cytosolic Calcium Transients as Boundary Conditions for PDE . . . . 48
3.4.1 Single CCT Bursts . . . . . . . . . . . . . . . . . . . . . . . . 48
3.4.2 Multiple CCT Bursts . . . . . . . . . . . . . . . . . . . . . . . 50
3.4.3 Importing Experimentally Recorded CCTs . . . . . . . . . . . 50
3.5 Several Evaluation Tools for Nuclear Information Processing . . . . . 54
3.5.1 General Implementation . . . . . . . . . . . . . . . . . . . . . 54
3.5.2 Calcium Load . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.5.3 Activity . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.5.4 Concentration Minimum and Nuclear Center . . . . . . . . . . 58
3.5.5 Splitting the Nucleus Into Micro-Domains and Measuring Com-
partments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.5.6 Adaptability to Experimental Measuring Techniques . . . . . 61
3.6 Di usion Models on Test Geometries . . . . . . . . . . . . . . . . . . 66
3.6.1 2D-Test Models . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.6.2 3D-Test Models . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4 Parameter Estimation for Nuclear Calcium Di usion 71
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.1.1 Numerical Optimization . . . . . . . . . . . . . . . . . . . . . 73
4.1.2 Biological Context . . . . . . . . . . . . . . . . . . . . . . . . 74
4.2 The Fundamentals of Parameter Estimation in PDE . . . . . . . . . . 75
4.3 The Least Squares Problem . . . . . . . . . . . . . . . . . . . . . . . 78
4.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4.3.2 De nition of the Optimization Objective . . . . . . . . . . . . 79
4.3.3 A Steepest Descent Algorithm for the Di usion Model . . . . 80
4.3.4 Calculating Simulation Data . . . . . . . . . . . . . . . . . . . 82
4.3.5 Derivatives . . . . . . . . . . . . . . . . . . . . . . 82
4.3.6 Data from Local Uncaging Experiments . . . . . . . . . . . . 83
4.4 Implementing the Least Squares Problem in UG . . . . . . . . . . . . 85
4.4.1 General De nition of a Boundary Value Problem in UG . . . 85
4.4.2 Setting up a One-Way Coupled System . . . . . . . . . . . . . 86
4.4.3 Modifying the BVP Structure for the Least Squares Problem . 87