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Growth Cone Dynamics and Vesicle Trafficking in Developing Neurons in Vitro Jurjen Hendrik Pieter Broeke

ISBN: 978-94-6182-006-8 Layout and printing: Off Page, www.offpage.nl Copyright © 2011 by J. Broeke. All rights reserved. No part of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, without prior permission of the author.

VRIJE UNIVERSITEIT

Growth Cone Dynamics and Vesicle Trafficking in Developing Neurons in Vitro

ACADEMISCH PROEFSCHRIFT

ter verkrijging van de graad Doctor aan de Vrije Universiteit Amsterdam, op gezag van de rector magnificus prof.dr. L.M. Bouter, in het openbaar te verdedigen ten overstaan van de promotiecommissie van de faculteit der Aard- en Levenswetenschappen op donderdag 22 september 2011 om 13.45 uur in de aula van de universiteit, De Boelelaan 1105

door

Jurjen Hendrik Pieter Broeke geboren te Papendrecht

promotor: copromotor:

prof.dr. M. Verhage dr. R.F.G. Toonen

Contents Chapter 1

General introduction

7

Chapter 2

Early neurite outgrowth in release–deficient neurons

31

Chapter 3

Effect of glutamate auto–feedback on neurite outgrowth  in development

49

Chapter 4

Automated quantification of cellular traffic in living cells

67

Chapter 5

Transport and fusion of Corticotropin Releasing Factor  Binding Protein is distinct from previously described dense core vesicle cargoes

83

Chapter 6

Optical tools for studying vesicle dynamics

105

Chapter 7

Conclusions

123

Appendix A

Mathematical framework for a recursive bayesian estimation  algorithm

137

Appendix B

Nederlandse samenvatting

153

Appendix C

Dankwoord Curriculum Vitae

159 161

CHAPTER 1 General introduction

development of the brain In order to form a fully functional brain, several developmental steps are required to achieve the complex and intricate network of interconnected neurons and the supporting astrocytes. Neurons and astrocytes are derived from the ectoderm, a group of pluripotent stem cells that develop into both the central and the peripheral nervous system. During embryonic development, the ectoderm forms a tube-like structure, the neural tube. The rostral and medial part of the neural tube will develop into the spinal cord and the peripheral nerves. At the caudal side, three vesicles arise: the prosencephalon, mesencephalon and the rhombencephalon. These vesicles will develop into the cerebral cortex, the midbrain and the cerebellum and brain stem, respectively. Cells in the prosencephalon will rapidly divide and differentiate into neurons and glia. After differentiation, the newly formed neurons begin to migrate in order to form the different nuclei of the brain (Gilbert, 2010). In the cerebral cortex of mammals, neurons form a layered structure in an inside-out fashion (Guillemot et al., 2006; Rakic, 1971). This was discovered when mutations were found in two genes, LIS–1(Reiner et al., 1993) and doublecortin (des Portes et al., 1998; Gleeson et al., 1998), both resulting in abnormal morphology of the layers in the cortex. During embryonic development, stem cells will differentiate and migrate to their final position in the brain. When they have arrived in their proper location, they are ready to form neurites that will become the dendrites and the axon, allowing the neurons to establish connections.

neurite development After migration, the next step in brain development is for neurons to develop neurites. There are five different stages in neurite development described in cultured cells (see Dotti, Sullivan and Banker (Dotti et al., 1988)). A neuron has a very specific compartmentalization of its processes: there are multiple dendrites but only a single axon. Dendrites serve a different purpose compared to axons: dendrites receive signals from other cells and relay them to the soma, while axons send the signal to the next cell. Control over the formation of the axon is therefore important in order to prevent a situation where neurons generate more than one axon. The formation of the axon gives rise to polarization of the neuron, which has major consequences for the further development for the neurites. Axons are in general very long processes, which can extend over several millimeters up to centimeters in the mouse brain. Their growth rate and internal composition is different from the much shorter but more elaborately branched dendrites. But before dendrites and axons can be formed, the round cell first needs to extend process and subsequently polarity has to be established. Formation of neural polarity The first stage of neurite formation involves the formation of ruffles along the perimeter of the neuron called lamellipodia, and these are the sites where the neurites will form Introduction

9

(Dotti et al., 1988). Several studies have examined what determines which of the early neurites will develop into an axon. There are indications that the microtubule organizing center (MTOC), an organelle involved in mitosis, is an indicator for where the axon will form. In neurons, the axon was found in close proximity to the MTOC as well as the Golgi and the endosome (de Anda et al., 2005). Furthermore, it was also demonstrated that interfering with microtubule polymerization or ablating the MTOC interfered with polarization (de Anda et al., 2005). As soon as the axon has been established, it develops a specialized structure called the initial segment (or axon hillock), which was found to act as a barrier for free diffusion of phospholipids (Nakada et al., 2003). This barrier function would than aid in specific targeting the resources for outgrowth and development of the axon. Another theory about establishment of polarity is the competition for resources between developing neurites (Goslin and Banker, 1989). This would result in preferential trafficking of resources to on e process, which will become the axon, while the remaining processes will develop into dendrites. After polarization has been established via selective targeting of resources, structures at the tips of the growing processes called growth cones allow the process to move forward (Dotti et al., 1988) and steer in the right direction to the right target area based on signals from the environment. There are three processes that influence the rate and direction of outgrowth in the growth cones. Firstly, actin dynamics regulate the motility and morphology of the growth cone. Secondly, signals from the environment provide guidance cues leading the growth cone towards or away from specific regions. Finally, synaptic vesicle release in growth cones influence the outgrowth of processes. Actin dynamics in growth cones The growth cone is a specialized structure consisting of three distinct domains: the shaft, the central domain and the peripheral domain (Landis, 1983; Dent and Gertler, 2003; Bridgman and Dailey, 1989) (Figure 1). The shaft contains microtubules and neurofilaments which function as tracks for the transport of organelles required for outgrowth (Rogers and Gelfand, 2000). The central domain lacks the structured microtubule skeleton of the shaft and contains organelles such as large dense core vesicles, endoplasmatic reticulum and mitochondria (Bridgman et al., 1989). These are necessary for signaling, protein synthesis and energy metabolism within the growth cone. The peripheral domain consists of actin-rich lamellipodia and filopodia. These structures function similar to antennae, sampling the surrounding area for cues. These dynamic structures are involved in selectively reshaping and steering growth cones toward their target (Buettner et al., 1994; Schaefer et al., 2008). Actin dynamics control the shape changes of growth cones while microtubuli are responsible for directed motion (Schaefer et al., 2008; Tanaka et al., 1995). Actin dynamics consists of polymerization and depolymerization of actin subunits. Globular actin (G–actin) is a small molecule that in the ATP-bound form can readily polymerize into filamentous actin (F–actin). Two prominent features of growth cones, filopodia and lamellipodia (Figure 1), are dependent on the formation and regulation 10

Chapter 1

Actin filament

}

}

C

T

Filopodium

Lamellipodium

Microtubule P

Central domain (C)

Transition domain (T)

Peripheral domain (P)

Figure 1: Growth cone morphology. The growth cone consists of three domains: the central domain (C) which is rich in microtubules (green), LDCVs (red circles), synaptic vesicles (purple circles), mitochondria and endoplasmatic reticulum (yellow). The transition domain (T) consists of a filamentous actin ring (red filaments) and some microtubules together with some SVs and LDCVs. The peripheral domain (P) contains mostly actin filaments, either in a cross-linked bundle as in the filopodia, or as a branched meshwork in the lamellipodia. In this domain, vesicles are also present which can be ready for release docked at the membrane (dark orange).

of actin dynamics. In order to form a filopodium, nucleation of actin is initiated by Arp2/3 (Mattila and Lappalainen, 2008). Arp2/3 allows the formation of a new filament at an angle from an existing filament, which is extended by polymerization at the plus–end directed towards the membrane (Mattila et al., 2008). The membranebound protein Dia2 forms an attachment that allows the actin filaments to push the membrane outwards, and is essential in the formation of filopodia (Schirenbeck et al., 2005). The protein ENA/VASP cross-links several parallel filaments in the shaft of the filopodium, generating a strong core inside the filopodium (Schirenbeck et al., 2006; Introduction

11

Co et al., 2007). This process is aided by myosin–X motor proteins that can exert force on the membrane by moving along the filaments (Sousa and Cheney, 2005). For lamellipodia formation, Arp2/3 is necessary to crosslink several filaments, thereby creating a meshwork of F–actin (Small et al., 2002). Proteins that bind actin filaments and the monomers regulate the length of the filaments. Cofilin binds to the minus-end and induces depolymerization, shortening the filaments (Chen et al., 2000). Profilin enhances the amount of ATP-bound G–actin, thereby enhancing the polymerization of actin filaments by proteins such as formin and WASP (Chen et al., 2000). An important class of molecules in actin dynamics are the GTPases: Rho, Rac and Cdc42. GTPases are molecular switches that can be switched on by proteins called guanine nucleotide exchange factor (GEF) and deactivated by activating the GTPase activity by GTPase activating proteins (GAP). GEFs displace GDP from the GTPase, allowing GTP to bind to the GTPase, thereby activating it. GAPs on the other hand activate the inherent GTPase activity, causing the hydrolysis of the GTP and deactivating the GTPase. The different GTPases have opposite effects, and together they regulate the actin cytoskeleton (Luo, 2000; Kozma et al., 1997). Rho was found to induce actin depolymerization in fibroblasts (Nobes and Hall, 1995). In growth cones, this induces smaller lamellipodia and shorter filopodia (Kozma et al., 1997). Rac and Cdc42 were found to induce an increase in stress fibers in fibroblasts (Nobes et al., 1995). In growth cones, this translates to a larger lamellipodia and longer filopodia (Kozma et al., 1997). Besides there direct role in actin dynamics, they are also implicated in other important developmental processes, such as polarity, vesicle trafficking and gene transcription (Bustelo et al., 2007). In conclusion, growth cones consist of a highly dynamic cytoskeleton that allows for rapid formation and retraction of filopodia. These dynamics serve to move the growth cone forward or steer it. In order for the growth cone to reach a target, several cues in the environment provide guidance by influencing the actin dynamics. Guidance cues and growth cones In the third stage of neural development, one of the outgrowing processes will differentiate into an axon, while the other processes will become dendrites (Dotti et al., 1988). The axon will start to extend faster than the dendrites in order to reach its target area, which can be several millimeters to centimeters away. This fast outgrowth of the axon needs to be regulated both in space and time in order for the right areas to connect to each other and form a functional pathway. Many signaling molecules have been described that guide the outgrowing neurite towards its target (Chilton, 2006). These can be split into two classes of guidance molecules that together regulate this process: one group is repulsive while the other is attractive (Chilton, 2006). One of these repulsive cues is Collapsin/Semaphorin3A, which was found to induce growth cone collapse in dorsal root ganglion neurons (Luo et al., 1993). Semaphorin3A is a secreted guidance cue that binds to the semaphorin receptor neuropilin-plexin complex (Pasterkamp and Kolodkin, 2003). Activated neuropilin-plexin activates the tyrosine kinases Cdk5 and Fyn, which regulate the actin filaments via phosphorylation of cofilin by LIMK (Aizawa et al., 2001; Guan and Rao, 2003).

12

Chapter 1

An example of an attractive guidance cue is netrin, which binds to its receptor DCC (Chan et al., 1996; Keino-Masu et al., 1996). Upon binding its ligand, DCC activates Rac GTPase, which increases actin polymerization (Li et al., 2002; Shekarabi and Kennedy, 2002). Depending on the presence of receptors for these secreted molecules on the surface of the extending process, the growth cone will turn towards, away or ignore the gradient, guiding it to its target (Chilton, 2006). Previous studies have shown that activation of the netrin-pathway involves elevation of calcium via cyclic AMP (Ming et al., 1997; Song et al., 1997). Using local uncaging of calcium, it has been shown that growth cone turning and vesicle translocation are directed towards the site of calcium elevation (Tojima et al., 2007; Zheng, 2000). Guidance cues allow growth cones to navigate through the brain in order to reach their target. Of course the main function of neurons is to provide neurotransmission, and synaptic vesicle release during early development also influences the outgrowth of neurites (see also Box 1). Neurotransmitter release in early development The major content of SVs in the brain is glutamate, an excitatory neurotransmitter that binds to AMPA, kainate and NMDA receptors. The role of glutamate secretion and receptor activation in neurotransmission has been well studied. However, in developing neurons, AMPA receptors (AMPA–R) are also present both post- and presynaptically (Fabian-Fine et al., 2000; Lee et al., 2002; Lu et al., 2002), and are thought to regulate development by signaling cascades in the growth cone (Schenk et al., 2005). Staining of AMPA receptors showed surface expression of GluR2/3 receptors (Schenk et al., 2003), and addition of AMPA to a growth cone induced growth cone stalling and vesicle dispersion (Schenk et al., 2003). Growth cone stalling was also found in growth cones when stimulated with kainate (Ibarretxe et al., 2007). Growth cone stalling during development can affect the outgrowth of neurites, resulting in altered connectivity. Stimulation of AMPA receptors was also found to increase AMPA receptor surface presence in a SNARE-dependent manner (Schenk et al., 2003). Addition of AMPA was also found to increase phosphorylation of MAPK in hippocampal growth cones (Schenk et al., 2005). This phosphorylation could be blocked by a Src family tyrosine kinase inhibitor, but not a Trk family kinase inhibitor (Schenk et al., 2005). MAP kinase is part of an important signaling cascade that influences gene transcription (Cobb et al., 1991), synaptic plasticity (Di Cristo et al., 2001), cell migration (Pullikuth and Catling, 2010) and growth cone resensitization for guidance cues (Ming et al., 2002). Besides the well known role of neurotransmitter release in the mature brain, it is now clear that neurotransmitter release is also important during the early stages of neurite development. After the axon has extended a considerable distance, the dendrites are now ready to start elongating and branching.

Introduction

13

BOX 1: INVESTIGATING THE ROLE OF THE FUSION MACHINERY In order to study the effect of vesicle release on development, several transgenic animal models are available and have been studied with regard to vesicle release. The core components in the vesicle fusion machinery are synaptosomal-associated protein 25kD (SNAP25), Synaptobrevin/VAMP2 and Syntaxin–1, which form a four α-helical bundle. Transgenic animals which lack SNAP25 were not capable of vesicle release and die shortly after birth. Their brains and neuromuscular junctions were however morphologically normal (Washbourne et al., 2002). In knockout animals of SNAP–25 or in wild type neurons treated with Botilinum neurotoxin, vesicle fusion is abolished, indicating that the formation of the complex is essential for vesicle fusion (Sørensen et al., 2003; Gonelle-Gispert et al., 1999). Synaptobrevin knockout animals have a similar phenotype (Schoch et al., 2001). Syntaxin-1A deficient mice on the other hand have severe developmental problems (McRory et al., 2008). This demonstrates that the core machinery for vesicle fusion is not essential in brain development, but still may play a role in the fine structure of the brain. Binding partners for the core complex include munc18 and munc13, which bind the N– terminal domain of syntaxin (Betz et al., 1997; Johnson et al., 2009). These proteins are involved in vesicle docking (munc18) and vesicle priming (munc13). Another syntaxin binding protein is Tomosyn-1, which was found to influence neurite outgrowth by inducing neurite retraction (Gracheva et al., 2006). Knockout animals of munc18-1 lack spontaneous and evoked vesicle release (Verhage et al., 2000), yet develop brains with structurally complete synapses connected over long distances (Verhage et al., 2000). In chromaffin cells, it was shown that over–expression of munc18–1 resulted in an increase of docked vesicles, as well as an increase in the thickness of the actin cytoskeleton (de Wit et al., 2006a; Toonen et al., 2006). The munc13-1/2 double null mutant (M13) also lacks spontaneous and evoked release (Varoqueaux et al., 2002). Munc13 can bind the fully assembled SNARE complex (Guan et al., 2008), thereby priming the vesicle for calcium–dependent fusion and lowering the fusion barrier (Richmond et al., 2001; Basu et al., 2005; Basu et al., 2007). Both transgenic models die at birth due to failures in breathing, but neurons can be cultured from embryonic day (E)18 pups. However, mun18–1 null (M18) neurons die after DIV7 (Heeroma et al., 2004), unlike munc13–1/2 double null neurons. The loss of munc18 and munc13 affects synaptic vesicle release, but not large dense core vesicles (LCDVs). Synaptic vesicles (SVs) contain neurotransmitters, which is essential for neurotransmission in the nervous system. LCDVs contain peptides and neuro-amines, which function as modulators of synaptic transmission as well as trophic support. Both types of vesicles are important in development. For the two types of release recognized for synaptic vesicles, spontaneous and evoked release, only the evoked release is dependent on the opening of voltagesensitive calcium channels. For evoked release, Rab3a and RIM associate the

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Chapter 1

docked vesicle with a calcium channel (Kiyonaka et al., 2007), and were found to influence the dynamics of vesicle fusion during long term potentiation (Schoch et al., 2002). The influx of calcium is registered by a calcium sensor on the vesicle. One of the main calcium sensors in the brain is synaptotagmin, which is attached to the synaptic vesicle, and upon binding of calcium interacts with the SNARE complex (Ullrich et al., 1994). A protein involved in spontaneous release is Doc2b, which was found to be a calcium sensor for spontaneous release (Groffen et al., 2010). All mentioned mutants of the vesicle fusion machinery are lethal at birth, indicating that this process is essential for postnatal functioning but not for embryonic development of the brain. So in order to study the effect of the vesicle fusion machinery on early development, in vitro assays are the only viable option to examine these processes live. There are some advantages to these types of assays; most importantly they allow a large amount of possible manipulations. Among the manipulations is specific stimulation of receptors or local activation of cells. By using the organotypic slice cultures as described before (Gähwiler, 1981; Stoppini et al., 1991), an environment more comparable to the in vivo situation can be created. In order to over-express or knock down different proteins, a dissociated culture system is more convenient. Dissociated cultures also allow for clear staining of surface proteins, something that is not possible in slice cultures or in vivo. Using time lapse microscopy, these in vitro systems allow visualization and quantification of both motility and outgrowth dynamics, giving more information than taking snapshots from fixed tissue at different time points during development. Also, the fact that all these mutants develop a morphologically normal appearing brain suggests that the effect of the functionality of the machinery is probably very subtle, and could be compensated for over time. So in order to investigate the role of the vesicle fusion machinery during early development, organotypic slice cultures and dissociated cell cultures derived from mutants are a valuable way to examine these effects. Late neurite development In the fourth stage, the axon has grown substantially and the dendrites start to develop (Dotti et al., 1988). This process is mediated by similar mechanisms as the axonal outgrowth. One important factor in outgrowth is the expansion of the plasma membrane. Between the first and the fourth stage of development, the extent of plasma membrane surface area may have increased from ~1200µm2 (20µm–diameter spherical cell) to more than 250,000µm2: a 200–fold increase of membrane (Pfenninger, 2009). There are different pathways for expanding the membrane: vesicle fusion, protein insertion and lipid rafts. Changing the amount of secretion taking place in neurons would therefore be expected to result in altered outgrowth, thereby influencing brain morphology. Vesicle fusion can supply lipids to the expanding membrane (for a review, see Pfenninger et al. (Pfenninger, 2009)). Previous work on proteins involved in the vesicle fusion machinery (SNARE, see Introduction

15

Box 1) have shown that reducing or abolishing vesicle fusion affects outgrowth. It was shown that a cleavage of SNAP25 by Botulinum neurotoxin (BoNT) decreased neurite outgrowth (Grosse et al., 1999; Morihara et al., 1999). It was found that upon release of calcium in the growth cone, vesicles translocated to the site of calcium influx, leading to turning of the growth cone towards the side of stimulation (Tojima et al., 2007). Before vesicles can fuse, they first have to be brought close to the membrane (docking; see Box 2) after which they are primed (priming; see Box 2) and ready for fusion upon entry of calcium. Two important proteins in these two steps are munc18 and the two isoforms of munc13 (see Box 1 and Box 2 for their roles). During the late development, dendrites also start to develop a highly branched morphology. The function of this highly branched morphology are not fully understood, but it has been implicated that plays a role in regulation of neurotransmission and plasticity in the brain (Gidon and Segev, 2009; van Elburg and van Ooyen, 2010). There is also evidence that dendritic branches can function as computational units (Branco et al., 2008; Rudolph and Destexhe, 2003), thereby processing the input before it is send to the soma. What factors control the branching of dendrites is poorly understood,

BOX 2: THE SYNAPTIC VESICLE CYCLE In order for neurons to fire repeatedly and at high rates, vesicles in a synaptic terminal undergo a repeated cycle of exocytosis and endocytosis. Vesicles in synaptic terminals are filled with neurotransmitter and translocate towards the active zone. The vesicles dock at the active zone and are primed for release. Upon entry of calcium into the terminal, the primed vesicle fuses with the plasma membrane and release its cargo into the synaptic cleft. The vesicle is then recycled via one of several routes: immediate reuse, fast recycling and clathrin–mediated endocytosis (Sudhof, 2004). Immediate reuse means the vesicle stays docked and is refilled with neurotransmitter and re-acidified, ready to fuse again. In fast recycling, the vesicle undocks and is refilled and re-acidified. The clathrin–mediated endocytosis involves the formation of a clathrin-coated pit, after which the vesicle is refilled directly or via an endosome intermediate step. Vesicle pools Vesicles seem to reside in one of several pools: based on EM pictures and functional measurements, it was found that only a small proportion of the total number of vesicles in a terminal is ready for immediate fusion (Rosenmund and Stevens, 1996; Sätzler et al., 2002; Schikorski and Stevens, 2001). This pool, termed the readily releasable pool, can be emptied by high frequency stimulation and sucrose application (Rosenmund et al., 1996). After high frequency stimulation, a slower and stable release rate is an indication for another vesicle pool: the reserve pool. Together, they form the recycling pool. Using FM dye it was found that using high

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Chapter 1

frequency stimulation labels the recycling pool, but that there still is a pool of vesicles in the terminal that does not participate in this cycle (the resting pool) (Sudhof, 2004; Südhof, 2000). Vesicle pools are not linked to presynaptic boutons, but are shared by neighboring boutons (Darcy et al., 2006). Proteins involved in docking Munc18–1 was found to have a role in docking of vesicles: fewer vesicles were docked to the membrane when EM pictures of WT and Munc18–1 null chromaffin cells were examined (Toonen et al., 2006). This could be rescued by munc18–1 expression (Toonen et al., 2006). Over-expression of Munc18–1 in wild type cells resulted in an increase in docked vesicles, as well as an increase in release rate (Toonen et al., 2006). Secreting cells expressing fluorescently labeled SNAP25 show patches of protein on the membrane that co-localize with syntaxin–1 (OharaImaizumi et al., 2004). The presence of SNAP25 was correlated with docking and secretion (Ohara-Imaizumi et al., 2004). When syntaxin–1 was deleted, less vesicles were docked but the total number of vesicles remained equal (de Wit et al., 2006a). Taken together, the patches of syntaxin–1 and SNAP25 could form docking platforms for vesicles. Proteins involved in priming Munc13 was found to be important for vesicle priming: an increase in the rate of calcium-induced vesicle release was found in chromaffin cells over-expressing munc13–1 (Ashery et al., 2000; Augustin et al., 1999). Rab3 interacting molecules (RIMs) were found to be associated with vesicles and influence tethering and docking of vesicles to presynaptic calcium channels, priming them for release (Kiyonaka et al., 2007). Another factor in priming is Ca2+-dependent activator protein for secretion (CAPS), which was found to be essential for priming synaptic vesicles (Jockusch et al., 2007). Proteins involved in endocytosis Several proteins were found important for endocytosis, with the earliest discovered component clathrin as the major player (Slepnev and De Camilli, 2000; Heuser and Reese, 1973). Adapter-binding proteins attach to the plasma membrane, and recruit clathrin resulting in a cage around the vesicle (Slepnev et al., 2000). In neurons, the adapter protein AP–180 is enriched in synaptic terminals and mediates clathrindependent endocytosis (Ahle and Ungewickell, 1986). Dynamin was found to be important in facilitating the final step of endocytosis, forming a collar around the neck of the budding vesicle (Koenig and Ikeda, 1989). It has been proposed that this facilitates the severing of the neck (Hinshaw and Schmid, 1995; Takei et al., 1995), thereby completing endocytosis. Although other evidence shows that dynamin is not necessary for endocytosis (Sever et al., 1999).

Introduction

17

although transgenic animals lacking semaphorin3A were found to have a reduction in dendritic branching (Fenstermaker et al., 2004). Also, a role for the secretory pathway was suggested: when the Golgi apparatus and their outposts were reduced, both branching and the total dendritic length was reduced (Ye et al., 2007). Late development calls for a great amount of expansion of membrane, which requires the vesicle fusion machinery and the secretory pathway. Furthermore, branching of dendrites increases the complexity of the neuron, preparing the neuron for the final stage: the formation of synaptic contacts.

Synaptogenesis In the fifth and final stage, the neurons mature and begin forming synaptic contacts (Dotti et al., 1988). Synaptogenesis requires several steps; firstly, the pre- and postsynaptic sites have to contact each other, secondly the recruitment of pre- and postsynaptic proteins and finally the stabilization of the synaptic contact (see for a review, Gerrow & El-Husseini (Gerrow and El-Husseini, 2006)). After the synaptic contact has been established and becomes functional, maintenance of the synaptic contact and regulation of its strength is determined by factors such as vesicle release (Katz and Shatz, 1996; Zito and Svoboda, 2002). This has been described extensively in the visual system, where release of neurotransmitter during the critical period shapes the topography of the brain (Weliky, 2000; Wiesel and Hubel, 1963; 1965). Furthermore, several trophic factors have been identified that influence synapse formation and maintenance, such as BDNF (Hu et al., 2005; Sanchez et al., 2006) and Semaphorins (Fenstermaker et al., 2004; Morita et al., 2006; Tran et al., 2009). It has also been postulated that during early synapse formation, neurons form many connections, which eventually are not all needed for functional neurotransmission. A process called pruning is thought to take place, which eliminates a subset of synaptic contacts (Katz et al., 1996; Hashimoto et al., 2009; Hensch, 2004; Purves and Lichtman, 1980). During synaptogenesis, three steps take place to form a synaptic contact. Adhesion molecules provide a means of initiating the contact, while secreted factors from both synaptic vesicles and large dense core vesicles influence the formation and maintenance of synaptic contacts. Adhesion molecules and synapse formation Initiating contact between the pre-and postsynaptic element involves a class of molecules called adhesion molecules and their receptors. Once the cell adhesion molecules bind to their receptor, they initiate the recruitment of proteins necessary for neurotransmission, as well as vesicles and other organelles. Several molecules were found that could induce synaptic specialization. When expressed in non-neuronal cells, these molecules were capable of inducing synaptic vesicle clustering in presynaptic terminals contacting the non-neuronal cells (Scheiffele et al., 2000). Evidence suggests 18

Chapter 1

that there are separate classes of adhesion molecules and receptors for inhibitory and excitatory synapses, allowing specificity in the initiation of synapse formation (de Wit, Sylwestrak, et al., 2009). There are also findings suggesting that these adhesion molecules are involved in the later stages of synaptogenesis by linking the pre- and postsynaptic terminal, thereby stabilizing them (Mendez et al., 2010). Once the adhesion molecules have initiated synapse formation, synaptic vesicle dynamics will allow neurotransmission and modulation of the number and the strength of synapses. Synaptic vesicle dynamics during synaptogenesis During formation of synapses, activity was found to be important in regulating the number of synapses in release-deficient munc18–1 null mice (Bouwman et al., 2004). The morphology of the synapses that were formed were comparable to control synapses (Verhage et al., 2000; Bouwman et al., 2004). However, no effect on synapse numbers was seen in munc13-1/2 double null neurons, and the synapses were morphologically similar to controls (Varoqueaux et al., 2002). The normal vesicle cycle entails vesicles being transported to the membrane, fuse and then endocytosed to be re-used in the next round of vesicle release (Südhof, 2000; Sudhof, 2004). Interestingly, synaptic vesicles are not restricted to a synaptic bouton, but are exchanged actively between neighboring synapses (Darcy et al., 2006; Staras et al., 2010). This dynamic exchange has not been fully studied, but might influence homeostatic plasticity in the brain (Branco and Staras, 2009; Branco, Marra, et al., 2009). Homeostatic plasticity ensures that synaptic transmission can occur without saturation: by regulating synaptic properties such as release-probability (Branco and Staras, 2009; Branco, Marra, et al., 2009) and post-synaptic receptor density (Ehlers, 2003; O’Brien et al., 1998), neurotransmission can be kept stable over a broad range of inputs during development (see the review by Turrigiano & Nelson (Turrigiano and Nelson, 2004)). Although neural activity was thought to be critical in synapse formation, several transgenic animal models have shown that it is actually not essential for synapse formation. Synapse formation might therefore rely on LDCV fusion as well. Large dense core vesicle dynamics during synaptogenesis The difference between synaptic vesicles and large dense core vesicles is found in the vesicle content and its synthesis. Neuropeptides are synthesized as a large precursor peptide, which is processed by cleavage and glycosilation into a functional peptide fragment. An example of such a precursor is POMC, which is the precursor for six different peptides (Chang et al., 1980). The precursor peptide is transcribed in the endoplasmatic reticulum (ER) and transported to the Golgi apparatus. It is first cleaved into different peptides by the subtilisin-like enzymes (Eipper and Mains, 1980). POMC can be cleaved into different neuropeptides such as adrenocorticotropic hormone (ACTH) (Chrétien et al., 1979). ACTH can be further processed into yet more active peptides such as β-endorphin (Chrétien et al., 1979), showing that one peptide can be used to generate a whole range of related signaling peptides which function Introduction

19

within a similar pathway in different roles. Many of these peptides influence activity of the brain and change the levels of other neuropeptides. Among these peptides are neuropeptide Y (NPY) and corticotropin releasing factor (CRF), which play a role in energy homeostasis (White, 1993) and addiction and stress (Hauger et al., 2009; Koob and Heinrichs, 1999; Navarro-Zaragoza et al., 2010), respectively. Both trophic factors and neuropeptides are produced in the neural soma and transported along microtubules in LDCVs towards their target. Availability of these peptides depends on their production rate and the rate of transport towards the periphery of the branched neurites. The distance from the soma to the periphery can reach distances of more than 200µm in dendrites and several millimeters in axons. Transporting these vesicles is done by several motor proteins that bind to LDCVs and transport them along the microtubules towards or away from the soma. In the axon, where microtubuli are oriented with the plus–end away from the soma (Baas et al., 1988; Jaworski et al., 2008), kinesin motor proteins such as Kinesin-I transport organelles anterogradely (Varadi et al., 2003; Hirokawa et al., 2009), while dynein motor proteins transport organelles retrogradely (Holzbaur and Vallee, 1994; Varadi et al., 2003). Motor proteins are attached to their cargo via an adapter protein, which could provide a means of linking a specific cargo to a specific motor protein, thereby influencing the direction of transport (Hirokawa et al., 2009; Schlager and Hoogenraad, 2009). For example, mitochondria transported in the axon are linked to the kinesin Kif5 via the adapter protein Milton (Hirokawa et al., 2009; Wang and Schwarz, 2009). Transport of LDCVs will affect the availability of secreted cues involved in synaptogenesis and synapse stabilization. Trafficking of the guidance cue semaphorin3A was shown to be different in axons versus dendrites (de Wit et al., 2006b) and vesicle stalling occurred on electrical activity (de Wit et al., 2006b; Shakiryanova et al., 2006). For many other LDCV cargoes, the characterization of transport has not been established. Once transported, release of these signaling molecules is regulated and calcium–dependent (Mansvelder and Kits, 2000; Park et al., 2006; Voets, 2000), and occurs at the growth cone and along neuronal processes (de Wit et al., 2006b). For LDCVs there are different types of fusion: transient release and stable deposits. It was found that certain LDCV cargoes prefer release as stable deposits such as Semaphorin3A, tissue plasminogen activator (tPA) and BDNF (de Wit, Toonen, et al., 2009). These secreted peptides influence synapse formation and stabilization as was shown before (Pasterkamp et al., 2003; Hu et al., 2005; Sanchez et al., 2006; Tran et al., 2009), indicating that LDCV release is important for network formation and stability. It is therefore important to investigate the transport and release to understand the availability of peptides involved in synapse formation. Besides their role in neurite outgrowth, a great body of work also supports the role of LDCV cargo secretion in synapse formation. Most of these cargoes are secreted and likely work over a relatively large distance, which allows synaptic partners to get close to each other. The next step is then for adhesion molecules to stabilize and initiate specialization of the pre-and postsynaptic element by recruiting vesicles and proteins to the synaptic site. When these proteins are in place, a functional synapse is formed

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that is capable of processing inputs and generating an output. Depending on the level of activity, these synapses can then be regulated to increase or decrease their efficiency.

aim and outline of this thesis In order to investigate the role of vesicle release in developing neurons, we cultured cells from release-deficient mutants and compared them with wild type controls. First, we investigated the role of vesicle release on outgrowth and motility, and looked at the role of secreted neurotransmitter on outgrowth and motility (stage 3/4 from Dotti et al. (Dotti et al., 1988)). We found a 40% reduction, but not abolishment in neurite outgrowth during the first week. However, this did not result in an impaired morphology at the synaptogenesis stage at 2 or 3 weeks in culture (Chapter 2). Using organotypic slice cultures of release-deficient and control animals, we examined the effect of chronic activation or inhibition on outgrowth during development. We found that chronic AMPA application resulted in increased outgrowth for WT and M18 neurons, but a decrease in M13 deficient neurons. Growth cone motility was reduced when AMPA was applied, but only after 3 days in culture (Chapter 3). Secondly, I investigated the transport and release of large dense core vesicles during the final stage of development (stage 5 from Dotti et al. (Dotti et al., 1988)). Using methods in image segmentation and Bayesian statistics (Appendix A), we developed a method to automatically quantify the trafficking of labeled vesicles (Chapter 4). We then applied this method to study the trafficking and release of a yet uncharacterized LDCV-cargo: CRFBP. We found that CRFBP is localized in a specific subset of LDCVs, and behaves differently than previously characterized LDCV-cargoes. Most importantly, fusion occurred only with stationary vesicles, where the entire cargo was released into the extracellular environment (Chapter 5). Then, I describe some optical tools that allow us to manipulate key factors in vesicle release such as calcium using local photolysis and to image these events using a label-free method called interference reflection microscopy (Chapter 6). Finally, I will discuss the main findings of the role of vesicle release during development and the role of vesicle dynamics during synaptogenesis. I will also provide some insights for future research into the field of development and vesicle dynamics (Chapter 7).

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Schirenbeck, A., Arasada, R., Bretschneider, T., Stradal, T. E. B., Schleicher, M., and Faix, J. (2006). The bundling activity of vasodilator-stimulated phosphoprotein is required for filopodium formation. Proc Natl Acad Sci U S A 103, 7694-7699. Schirenbeck, A., Bretschneider, T., Arasada, R., Schleicher, M., and Faix, J. (2005). The Diaphanous-related formin dDia2 is required for the formation and maintenance of filopodia. Nat Cell Biol 7, 619-625. Schlager, M. A., and Hoogenraad, C. C. (2009). Basic mechanisms for recognition and transport of synaptic cargos. Mol Brain 2, 25-25. Schoch, S., Deák, F., Königstorfer, A., Mozhayeva, M., Sara, Y., Südhof, T. C., and Kavalali, E. T. (2001). SNARE function analyzed in synaptobrevin/VAMP knockout mice. Science 294, 1117-1122. Schoch, S., Castillo, P. E., Jo, T., Mukherjee, K., Geppert, M., Wang, Y., Schmitz, F., Malenka, R. C., and Sudhof, T. C. (2002). RIM1[alpha] forms a protein scaffold for regulating neurotransmitter release at the active zone. Nature 415, 321-326. Sever, S., Muhlberg, A. B., and Schmid, S. L. (1999). Impairment of dynamin’s GAP domain stimulates receptor-mediated endocytosis. Nature 398, 481-486. Shakiryanova, D., Tully, A., and Levitan, E. S. (2006). Activity-dependent synaptic capture of transiting peptidergic vesicles. Nat Neurosci 9, 896-900. Shekarabi, M., and Kennedy, T. E. (2002). The Netrin-1 receptor DCC promotes filopodia formation and cell spreading by activating Cdc42 and Rac1. Mol Cell Neurosci 19, 1-17. Slepnev, V. I., and De Camilli, P. (2000). Accessory factors in clathrin-dependent synaptic vesicle endocytosis. Nat Rev Neurosci 1, 161-172. Small, J. V., Stradal, T., Vignal, E., and Rottner, K. (2002). The lamellipodium: where motility begins. Trends Cell Biol 12, 112-120. Song, H. J., Ming, G. L., and Poo, M. M. (1997). cAMP-induced switching in turning direction of nerve growth cones. Nature 388, 275-279.

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Introduction

27

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CHAPTER 2 Early neurite outgrowth in release–deficient neurons

Abstract Background information: During development, growth cones of outgrowing neurons express proteins involved in vesicular secretion, such as soluble n-ethyl maleimide sensitive attachment protein receptor (SNARE) proteins, Munc13 and Munc18. Vesicles are known to fuse in growth cones prior to synapse formation, which may contribute to outgrowth. Results: We tested this possibility in dissociated cell cultures and organotypic slice cultures of two release-deficient mice (munc18–1 null and munc13–1/2 double null). Both types of release-deficient neurons have a decreased outgrowth speed and therefore have a smaller total neurite length during early development (DIV1-4). In addition, more filopodia per growth cone were observed in Munc18–1 null, but not wild type (WT) or Munc13–1/2 double null neurons. The smaller total neurite length during early development was no longer observed after synaptogenesis (DIV14-23). Conclusion: These data suggest that the inability of vesicle fusion in the growth cone affects outgrowth during the initial phases when outgrowth speed is high, but not during/after synaptogenesis. Overall, outgrowth speed is probably not rate limiting during neuronal network formation at least in vitro. In addition, Munc18, but not Munc13, regulates growth cone filopodia, potentially via its previously observed effect on filamentous actin.

32

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introduction During early development, neurons form various indifferent processes, neurites, each bearing a growth cone at its tip (Goslin and Banker, 1989). In order to extend these neurites, the insertion of plasma membrane proteins and phospholipids is necessary (Goslin et al., 1989) to expand the plasma membrane. Phospholipids can reach the outgrowing neurite via either lateral diffusion of lipids incorporated at the soma or via lipid droplets and vesicles, thereby contributing to the necessary membrane expansion for outgrowth (Vance et al., 2000). The vesicle release machinery that operates in mature neurons is already present in developing neurons at the tip of the growth cone (Kimura et al., 2003; Igarashi et al., 1996). This machinery is used for the release of synaptic vesicles containing neurotransmitter, which is thought to depend on SNARE proteins (Igarashi et al., 1996) and to be distributed along the whole axonal surface (Hua et al., 2005). These vesicles are thought to mature by repetitive recycling throughout axons (Krueger et al., 2003). From these vesicles, a plethora of molecules is released that have a role in neurite guidance and trophic support. In addition, vesicular fusion is considered to add lipids to the outgrowing neurites (Futerman and Banker, 1996). Another source of lipids that may contribute to the outgrowing neurites is lipid droplets. These lipid droplets are trafficked in both directions along microtubules (Pol et al., 2004) and consist of lipids coated with a single phospholipid leaflet. The SNAREdependent release machinery has previously been found to be associated with lipid droplets in fibroblasts (Bostrom et al., 2007). As SNARE-dependent membrane fusion has been implicated in the supply of membrane and proteins to developing neurites, loss of this function is expected result in abnormalities in long distance projections and synaptogenesis. However, this does not seem to be true in two cases where expression of proteins essential for SNAREdependent membrane fusion were genetically deleted: knockout mice of Munc18–1 (M18 null (Verhage et al., 2000)), and of Munc13–1 and Munc13–2 (M13 null (Varoqueaux et al., 2002)). Both these mutants lack spontaneous and evoked vesicle release but develop long distance projections and contain many synapses at birth (Varoqueaux et al., 2002; Bouwman et al., 2004). In order to investigate this apparent discrepancy, we examined the effect of SNARE-dependent membrane fusion on initial neurite outgrowth in two reduced systems in a quantitative manner, primary and organotypic slice cultures during early development. Our data indicate that initial outgrowth in vitro is indeed impaired in fusion defective mutant neurons when neurites grow out at maximal speed and that the morphology of growth cones is abnormal in the case of M18 null neurons. However, this impaired outgrowth apparently is not rate limiting and does not prevent the eventual formation of normal neuronal networks in more mature primary and organotypic cultures, in line with previous observations in vivo (Varoqueaux et al., 2002; Bouwman et al., 2004).

Vesicle release during outgrowth

33

Materials and methods Laboratory animals Munc18–1 null, Munc13–1/2 double null and EGFP–tKras mice have been described before (Verhage et al., 2000; Varoqueaux et al., 2002; Roelandse et al., 2003). Mouse embryos were obtained by caesarian section of pregnant females from timed heterozygous matings of EGFP–tKras with WT, with Munc18–1 heterozygous or with Munc13–1 heterozygous/munc13–2 null animals (C57/Bl6 background). Animals were housed and bred according to institutional, Dutch and U.S. governmental guidelines. Dissociated cultures Cortices or hippocampi were dissected from embryonic day 18 (E18) mice and collected in Hanks Buffered Salts Solution (HBSS – Sigma, St. Louis, USA), buffered with 7 mM HEPES. After removal of the meninges, the cortices were minced and incubated for 20 minutes in trypsinated HBSS at 37 ºC. After washing the neurons were triturated with fire polished Pasteur pipettes, counted with a hemacytometer and plated in Neurobasal medium (Invitrogen, Carlsbad, CA) supplemented with 2% B-27 (Invitrogen), 1.8% Hepes, 1% glutamax (Invitrogen), 1% Pen/Strep (Invitrogen) and 0.2% β-mercaptoethanol (Sigma). Low density cultures were plated on poly-Llysine (Sigma) coated glass cover slips at 25,000/cm2. For the analysis of early neurite outgrowth (DIV0 – 4), random images were taken of the cultures using a 40x lens on a Leica MZ12 microscope. Cultures were fixed on DIV14 and DIV23 with 2% paraformaldehyde (PFA; Invitrogen) and 2% sucrose for 20 minutes, and then 10 minutes in 4% PFA. After washing with PBS, the cultures were stained with a monoclonal α-MAP2 antibody (Millipore, Billerica, MA) in order to analyze the neurite length. Synapses were stained with α-Synapsin1. Localization of Munc18-1 in growth cones was done by staining with α-Munc18-1 and α-Bassoon antibodies. Quantification of actin and tubulin was done by incubating cultures with phalloidin-Alexa488 and poststaining with an α-tubulin antibody. Organotypic slice cultures Organotypic slice cultures from E18 hippocampus were prepared as follows. Mouse embryos were obtained by caesarean section of pregnant females from timed heterozygous mating. GFP-expressing animals were identified by direct inspection using a Leica MZ12 dissection microscope fitted with fluorescence optics. Hippocampi were dissected from brains in ice-cold dissection Gey’s balanced salt solution (dGBSS, consisting of GBSS (BioConcept, Allschwill Switzerland) with 0.65g glucose and 1mM kynurenic acid, pH 7.4) and cut into 400 µm thick slices using a McIlwain tissue chopper (Mickle Engineering, Gomshall UK). These hippocampal slices were kept at 4°C in dGBSS for 60 min to recuperate. All subsequent procedures were identical to those described for organotypic slice cultures from P8 mice (de Wit et al., 2006; Toonen et al., 2006). Briefly, Poly-D-Lysine coated cover slips were covered with chicken plasma, and 34

Chapter 2

a tissue slice was placed in the center. An equal amount of thrombin was added to the plasma to form a plasma cloth. The organotypic slice cultures were left to recuperate for 1 hour at room temperature and then placed in a roller tube at 37ºC. Live cell imaging For confocal imaging slices were mounted in purpose-built chambers (Life Imaging Services, Olten Switzerland) and observed in slice imaging medium containing 1 part HBSS with 7mM HEPES and 1 part Liebovitz L15 medium with supplements (1.8% HEPES, 0.2% β-mercaptoethanol, 2% B27 supplement and 1% GlutaMAX) using a Yokogawa microlens Nipkow confocal system (Perkin Elmer, Life Science Resources, Cambridge UK). Images were acquired using a cooled CCD camera (Hamamatsu photonics) every minute for 20 minutes using a 60× water lens (NA 1.20). Overview pictures were made using a 40× oil objective (NA 1.20) or a 10× air objective (NA 0.40) on a LSM510 microscope (Karl Zeiss, Jena, Germany). FM dye uptake experiment Dissociated cultures were cultured on glass cover slips coated with PDL and imaged on DIV3 on a Zeiss confocal using a 40× Oil objective (NA 1.20) at 37ºC using perfusion of Tyrode’s solution (containing, in mM: 115 NaCl; 2.5 KCl; 2 CaCl2; MgSO4; Glucose). FM4-64 (Invitrogen) was diluted in high potassium Tyrode’s solution (regular Tyrode’s, but with: 61.5mM NaCl; 60mM KCl;) and added to the cells for 1 minute. After washing for 10 minutes with Tyrode’s solution, brightfield and fluorescence images were taken. Data analysis Analysis of neurite length was done by manually tracing the neurites using Metamorph software (Universal Imaging Corp., West Chester PA). For the analysis of neurite outgrowth in 3 DIV hippocampal slice cultures various parameters were analyzed using MetaMorph software using the ‘Track Points’ function. Growth cone velocity and accumulated distance were calculated from this tracking of growth cones that extended into the surrounding matrix outside the slice. For the growth cone morphology, growth cones in the first frame of a 20 minute time-lapse were analyzed using ImageJ software (NIH, Bethesda MD). The growth cone area was determined by drawing a polygon around the palm of the growth cone and filopodia length by drawing lines. Visualization of growth cone morphology was done by flattening a one hour timelapse series and combining it with the first frame of the original time-lapse series. Before overlaying these pictures, the flattened time-lapse series was made green, while the first frame was made red. Statistical testing was done using SPSS software (SPSS Inc., Chicago IL) and Excel, using the Student’s t-test and a significance level of 0.05.

Vesicle release during outgrowth

35

Results We set out to study the effect of SNARE–dependent synaptic vesicle release on early neurite development using low-density cultures of cortical or hippocampal neurons. We took advantage of two transgenic mouse lines that lack protein(s) involved in vesicle release, Munc18–1 (Verhage et al., 2000) and Munc13–1/2 (Varoqueaux et al., 2002). Genetic deletion of Munc18–1 (M18 null) or of Munc13–1 and Munc13–2 (M13 null) in mice completely abolishes spontaneous and evoked neurotransmitter release in neurons. Both mutations result in neonatal lethality. However, tissue derived from either of these lines can be cultured for a period of time (Varoqueaux et al., 2002; Heeroma et al., 2004). We crossed these mice with mice bearing EGFP tagged to their membrane (EGFP– tKras (Roelandse et al., 2003)) in order to visualize morphological alterations in fine neuronal structure. We focused on neurite extension and growth cone morphology during the first week in culture using dissociated cultures. Outgrowth is decreased in release–deficient Munc18-1 null neurons from DIV3 onwards As was shown before in Munc13-1/2 null neurons, there is no vesicle cycle as measured by FM dye uptake (Varoqueaux et al., 2002). To test whether this also holds true for munc18-1 null neurons, we examined FM dye uptake in WT and Munc18-1 null neurons. For these first experiments, neurons were grown on glass without astrocyte feeder layer to reduce background signal of FM-dye taken up by astrocytes. Under these culture conditions, the morphology of growth cones is slightly different from growth cones in glia-supported or organotypic slice cultures (see below) We found that munc18-1 null neurons indeed lacked FM dye uptake, indicating that there was no vesicle cycle (Figure 1, M18 null). Because the incorporation of lipids is a necessary component for the expansion of the membrane in outgrowing neurites, we examined whether the loss of lipids from synaptic vesicles decreased neurite outgrowth (for review, see Vance et al. (Vance et al., 2000)). To this end, we used dissociated cortical neurons at DIV1 through DIV4 and measured total neurite length of WT and releasedeficient Munc18-1 null neurons. Examples of traced neurons show that the initiation of neurite outgrowth occurred in all genotypes (Fig. 2A). However, release-deficient neurons lagged behind in length as compared to WT neurons (Fig. 2A,B, Munc18 and Munc13). This effect became apparent after 3 days in culture (19.6% reduction in length for Munc18-1 null neurons and 51.4% for Munc13-1/2 null neurons) and increased significantly on the fourth day (40.0% reduction in M18 and 61.1% in M13; Fig. 2B). We therefore examined the speed of outgrowth at DIV3, as release-deficient neurons start to lag behind the WT neurons from this moment onwards.

36

Chapter 2

WT M18 null

Figure 1: Developmental time course shows lagging of release-deficient neurites. In order to investigate the endocytosis of release-deficient Munc18-1 null neurons, an FM4-64 dye uptake experiment was done. After loading the cells using stimulation with 60mM potassium and washing for 10 minutes with Tyrode’s solution, WT neurons show punctuate staining in the growth cone (top row), which is not the case for the M18 null growth cone (bottom row). Scale bar represents 5µm.

Decreased outgrowth in release-deficient neurons is not caused by cell death The early onset of cell death in dissociated cultures of Munc18-1 null – starting around DIV4 – may explain the decreased outgrowth. We therefore switched to organotypic hippocampal slice cultures where Munc18-1 null neuron survival exceeds DIV7. We cross-bred WT and Munc18-1 null mice with mice expressing EGFP tagged to their membrane (EGFP–tKras (Roelandse et al., 2003)) in order to visualize morphological alterations in fine neuronal structure. In these organotypic cultures, neurons extend long neurites – most likely axons originating from the CA1 area of the hippocampus (Frotscher and Heimrich, 1993) – that reach far into the surrounding matrix, which is permissive for neurite outgrowth as shown previously (McKinney et al., 1999). We then measured speed of outgrowth into the surrounding matrix, as total neurite length could not be established in the densely packed network of outgrowing processes and somata in the slice itself. We also included Munc13-1/2 null animals (Fig. 3A, M13 null) to further exclude cell death as a confounding effect in the changes in outgrowth speed. The outgrowth during the time-lapse series was reduced in the release-deficient cultures (Munc18-1 null and Munc13-1/2 null in Fig. 3A; red line indicates starting point). Quantification showed a 42% and 46% (p 1

(6)

by assigning smaller weights to pixels farther from the object centroid, it increases the reliability of distribution estimates since the boundary pixels are often believed to be affected by occlusions or background (Comaniciu et al., 2003). But, when a object has a very small size, we suggest a flat kernel to avoid participating pixels in the estimation too few: 1 𝐾𝐾(𝑟𝑟) = � 0

if ‖𝑟𝑟‖ ≤ 1 if ‖𝑟𝑟‖ > 1

(7)

3.2 A framework for optimal tracking

As an example, Figure 4 shows the complications of object tracking. During the process, the following events may occur: » Update: an existing object is evolved from one frame to the next » Birth: a new object is added. » Death: an existing object disappears in the next frame. » Merge: several existing objects are merged into a single object in the next frame. » Split: an existing object is divided into several objects in the next frame. Therefore by state representation of an object as in Eq. (4), the established object tracks in each frame 𝑘𝑘 is a finite random set 𝑋𝑋𝑘𝑘 = {x𝑘𝑘,1 , … , x𝑘𝑘,𝑛𝑛(𝑘𝑘) } where 𝑛𝑛(𝑘𝑘) is the varying number of objects and x𝑘𝑘,𝑖𝑖 , 𝑖𝑖 = 1, … , 𝑛𝑛(𝑘𝑘) are individual object states. The evolution of the set is characterized by the motion model 𝑋𝑋𝑘𝑘 = 𝑆𝑆𝑘𝑘 (𝑋𝑋𝑘𝑘𝑘𝑘 ) ∪ Γ𝑘𝑘 (𝑋𝑋𝑘𝑘𝑘𝑘 ) ∪ Ψ𝑘𝑘 (𝑋𝑋𝑘𝑘𝑘𝑘 ) ∪ 𝐵𝐵𝑘𝑘

(8)

which states that the set 𝑋𝑋𝑘𝑘 of object tracks in current frame 𝑘𝑘 consists of the set 𝑆𝑆𝑘𝑘 of tracks updated from the previous frame 𝑘𝑘 𝑘 1, the sets Γ𝑘𝑘 and Ψ𝑘𝑘 of new objects that are formed by merge and split of (part of) objects 𝑋𝑋𝑘𝑘𝑘𝑘 in previous frame 𝑘𝑘 𝑘 1, and the set 𝐵𝐵𝑘𝑘 of new objects which appear spontaneously in frame 𝑘𝑘. As shown in Figure 4, due to limitation of the imaging and detection, measured objects may include false alarms or clutters. In addition, some objects may have their measurements overlapped (data not shown), while some others may not be detected. As a result, the set of measurements 𝐼𝐼𝑘𝑘 = �z𝑘𝑘,1 , … , z𝑘𝑘,𝑚𝑚(𝑘𝑘) � is also random, where 𝑚𝑚(𝑘𝑘) is the number of measurements and z𝑘𝑘,𝑖𝑖 , 𝑖𝑖 = 1, … , 𝑚𝑚(𝑘𝑘) is the single object measurement state z𝑘𝑘,1 = {𝑧𝑧𝑘𝑘,𝑖𝑖 , 𝐴𝐴∗𝑘𝑘,𝑖𝑖 } in which 𝑧𝑧𝑘𝑘𝑘𝑘 gives the detected object location and 𝐴𝐴∗𝑘𝑘,𝑖𝑖 the associated appearance computed using Eq. (5). The presence of uncertainty prompts a probabilistic tracking. Using to denote the object tracks over the sequence of images, to denote the corresponding measurements, tracking can be formulated as computing the posterior density 𝑝𝑝(𝑋𝑋1:𝐾𝐾 |𝐼𝐼1:𝐾𝐾 ) that fits naturally into a Bayesian recursion (Mahler, 2003), for 2 ≤ 𝑘𝑘 𝑘𝑘𝑘, 144

Appendix A

𝑝𝑝(𝑋𝑋𝑘𝑘 |𝐼𝐼1:𝑘𝑘−1 ) = � 𝑝𝑝(𝑋𝑋𝑘𝑘 |𝑋𝑋𝑘𝑘−1 )𝑝𝑝(𝑋𝑋𝑘𝑘−1 |𝐼𝐼1:𝑘𝑘−1 )𝛿𝛿𝑋𝑋𝑘𝑘−1 𝑝𝑝(𝑋𝑋𝑘𝑘 |𝐼𝐼1:𝑘𝑘 ) ∝ 𝑝𝑝(𝐼𝐼𝑘𝑘 |𝑋𝑋𝑘𝑘 )𝑝𝑝(𝑋𝑋𝑘𝑘 |𝐼𝐼1:𝑘𝑘−1 )

(9) (10)

where ∫∙ 𝛿𝛿𝛿𝛿 is the set integral, 𝑝𝑝(𝑋𝑋𝑘𝑘 |𝑋𝑋𝑘𝑘𝑘𝑘 ) is the transition density. The density form of the motion model (Eq. (8)), which incorporates our knowledge about the internal dynamics of the objects and predicts the object tracks at current frame 𝑘𝑘 given the previous track set 𝑋𝑋𝑘𝑘𝑘𝑘 . 𝑝𝑝(𝐼𝐼𝑘𝑘 |𝑋𝑋𝑘𝑘 ) is the density form of the measurement model, which serves as the likelihood function and expresses the probability we would have measured objects 𝐼𝐼𝑘𝑘 given the track set 𝑋𝑋𝑘𝑘 in frame 𝑘𝑘. The recursive equations (9) and (10) provide a theoretically rigorous approach to optimally track a variable number of objects over an image sequence. However, computation of the joint posterior density 𝑝𝑝(𝑋𝑋𝑘𝑘 |𝐼𝐼1:𝑘𝑘 ) over object states is in general an intractable problem, for it requires solving a combinatorial sum of integrals of high dimensions with a prohibitively large number of combinations even for medium number of targets. There are some methods that have been proposed to ease the computational complexity. One class of methods is based on the probability hypothesis density (PHD (Mahler, 2002; Vo et al., 2005)), the first moment of joint distribution whose integral over any sub-area in state space is the expected number of objects in that area. The PHD method brings the recursion into a computationally feasible form by propagating the first moment in the place of the posterior distribution itself. In general, this method does not maintain the identities of objects †, while our tracking problem requires the temporal association of estimated object states over time so that individual object track can be established. Another class of methods relies on the disassembly of the joint state estimation into a collection of conditional independent single object tracking. The representative methods of this kind include the multiple hypothesis tracking (MHT (Reid, 1979)), the joint probabilistic data association (JPDA (Shalom and Fortmann, 1988)) and their variations (Blackman and Popoli, 1999). The core of these methods is to form the most likely model-data association. Our implementation of the object tracking is based on the idea of MHT. 3.3 Multiple hypothesis tracking (MHT) In our representation of the set of objects in each frame (Figure. 4) by 𝑋𝑋𝑘𝑘 , 𝑘𝑘 = 1, … , 𝐾𝐾, it is implicitly assumed that the state x𝑘𝑘,𝑖𝑖 of each object has a unique identifier 𝜏𝜏𝑘𝑘,𝑖𝑖 attached to it, i.e., (x𝑘𝑘,𝑖𝑖 , 𝜏𝜏𝑘𝑘,𝑖𝑖 ). 𝜏𝜏𝑘𝑘,𝑖𝑖 is called the object track ID. Suppose there are in total 𝑁𝑁𝐾𝐾 objects in the sequence of 𝐾𝐾 images, each object track is assigned a unique ID ranging from 1 to 𝑁𝑁𝐾𝐾 , then 𝜏𝜏𝑘𝑘,𝑖𝑖 ∈ {1, … , 𝑁𝑁𝐾𝐾 }. Writing explicitly, for each set 𝑋𝑋𝐾𝐾 , there is a corresponding object ID set 𝒯𝒯𝑘𝑘 . Likewise, each measurement set 𝐼𝐼𝑘𝑘 has an associated index set ℳ𝑘𝑘 , which is the subset of {1, … , 𝑀𝑀𝑘𝑘 } where 𝑀𝑀𝑘𝑘 is the total number of †

For linear Gaussian multi-target models, a closed-form solution to the PHD recursion may be derived to include object identity (Clark et al., 2006).

Appendix A

145

measurements. For each frame, we introduce an association hypothesis ℎ𝑘𝑘 as a relation on the set ({0} ∪ 𝒯𝒯𝑘𝑘𝑘𝑘 ) × ({0} ∪ ℳ𝑘𝑘 ): ℎ𝑘𝑘 = {(𝑛𝑛, 𝑚𝑚)|𝑛𝑛 ∈ {0} ∪ 𝒯𝒯𝑘𝑘−1 , 𝑚𝑚 ∈ {0} ∪ ℳ𝑘𝑘 }

(11)

The ℎ𝑘𝑘 links the existing object tracks to newly received measurements. By ℎ𝑘𝑘 (𝑛𝑛, 𝑚𝑚), 𝑛𝑛 𝑛 0 and 𝑚𝑚 𝑚 0, it means that measurement 𝑚𝑚 is associated to object 𝑛𝑛. By ℎ𝑘𝑘 (𝑛𝑛, 0), 𝑛𝑛 𝑛 0, it means that object track 𝑛𝑛 is not detected and generates no measurement, and by ℎ𝑘𝑘 (0, 𝑚𝑚), 𝑚𝑚 𝑚 0, it means that measurement 𝑚𝑚 is not associated with any object track. With the introduction of ℎ𝑘𝑘 , the representation of set of objects in frame 𝑘𝑘 is augmented from 𝑋𝑋𝑘𝑘 to (𝑋𝑋𝑘𝑘 , ℎ𝑘𝑘 ). Correspondingly, the Markov transition density 𝑝𝑝(𝑋𝑋𝑘𝑘 |𝑋𝑋𝑘𝑘𝑘𝑘 ) that characterizes the dynamics of the object set becomes 𝑝𝑝(𝑋𝑋𝑘𝑘 , ℎ𝑘𝑘 |𝑋𝑋𝑘𝑘𝑘𝑘 , ℎ𝑘𝑘𝑘𝑘 ); the likelihood function 𝑝𝑝(𝐼𝐼𝑘𝑘 |𝑋𝑋𝑘𝑘 ) characterizing the measurement process becomes 𝑝𝑝(𝐼𝐼𝑘𝑘 |𝑋𝑋𝑘𝑘 , ℎ𝑘𝑘 ). Tracking of objects over the image sequence can therefore be formulated as to estimate 𝑝𝑝(𝑋𝑋𝑘𝑘 , ℎ𝑘𝑘 |𝐼𝐼1:𝑘𝑘 ) recursively: 𝑝𝑝(𝑋𝑋𝑘𝑘 , ℎ𝑘𝑘 |𝐼𝐼1:𝑘𝑘−1 ) � � 𝑝𝑝(𝑋𝑋𝑘𝑘 , ℎ𝑘𝑘 |𝑋𝑋𝑘𝑘−1 , ℎ𝑘𝑘−1 )𝑝𝑝(𝑋𝑋𝑘𝑘−1 , ℎ𝑘𝑘−1 |𝐼𝐼1:𝑘𝑘−1 )𝑑𝑑𝑋𝑋𝑘𝑘−1 ℎ

𝑝𝑝(𝑋𝑋𝑘𝑘 , ℎ𝑘𝑘 |𝐼𝐼1:𝑘𝑘 ) ∝ 𝑝𝑝(𝐼𝐼𝑘𝑘 |𝑋𝑋𝑘𝑘 , ℎ𝑘𝑘 )𝑝𝑝(𝑋𝑋𝑘𝑘 , ℎ𝑘𝑘 |𝐼𝐼1:𝑘𝑘−1 )

(12)

(13)

Given the previous object states and association hypotheses at frame 𝑘𝑘 𝑘 1, the first equation predicts the states one step forward. The operation of this stage can be seen more clearly if we further factor the motion density:

Frame k-1

Frame k

1 Update

1

2

2

7

Merge

7

8

3

3

Frame k+1

Split 8

4

9

5

5 6

9

4

6

10

Death Birth

Clutter

11 10

Xk-1 ={1,2,3,4,5,6}

Xk ={1,5,7,8,9,10}

I k-1 ={1,2,3,4,5,6}

I k ={7,8,9,10,11}

Established vesicle track x k,i Measured vesicle z k,i

Figure 4: Vesicle tracking. An illustration of vesicle tracking over time. Several events can occur that change the number of tracks, such as merges and splits or birth and death of a vesicle track. Numbers in red indicate vesicle tracks, while numbers in blue represent the measured vesicles in each frame.

146

Appendix A

𝑝𝑝(𝑋𝑋𝑘𝑘 , ℎ𝑘𝑘 |𝑋𝑋𝑘𝑘−1 , ℎ𝑘𝑘−1 ) = 𝑝𝑝(𝑋𝑋𝑘𝑘 |ℎ𝑘𝑘 , 𝑋𝑋𝑘𝑘−1 , ℎ𝑘𝑘−1 )𝑝𝑝(ℎ𝑘𝑘 |𝑋𝑋𝑘𝑘−1 , ℎ𝑘𝑘−1 )

(14)

As shown the conditional state transition 𝑝𝑝(𝑋𝑋𝑘𝑘 |ℎ𝑘𝑘 , 𝑋𝑋𝑘𝑘𝑘𝑘 , ℎ𝑘𝑘𝑘𝑘 ) is following the evolution of the hypothesis 𝑝𝑝(ℎ𝑘𝑘 |𝑋𝑋𝑘𝑘𝑘𝑘 , ℎ𝑘𝑘𝑘𝑘 ). Based on the reasoning of the motion model (Eq. (8)) and random measurements in the previous section, the hypothesis ℎ𝑘𝑘 helps to partition the objects and measurements into the different sets (Table 1). With this partitioning, each object track evolves independently, leading to the following joint probability density 𝑝𝑝(𝑋𝑋𝑘𝑘 , ℎ𝑘𝑘 |𝑋𝑋𝑘𝑘−1 , ℎ𝑘𝑘−1 ) =

� 𝑝𝑝𝑠𝑠 �x𝑘𝑘−1,𝑖𝑖 � 𝑝𝑝(x𝑘𝑘,𝑖𝑖 |x𝑘𝑘−1,𝑖𝑖 ) � 𝑝𝑝𝑏𝑏 (x𝑘𝑘,𝑖𝑖 )

x𝑘𝑘 1 𝑖𝑖 ∈Φ

(15)

x𝑘𝑘 𝑖𝑖 ∈𝐵𝐵

where Φ = 𝑆𝑆1 ∪ 𝑆𝑆2 ∪ Γ ∪ Ψ ∪ 𝐷𝐷, 𝑝𝑝𝑠𝑠 is the probability that the object track will survive and 𝑝𝑝𝑏𝑏 is the probability density of a new born object. Similarly, the measurements, conditioned on ℎ𝑘𝑘 , are statistically independent. Further assuming a state independent clutter model, the likelihood function (measurement density) can be obtained by: 𝑝𝑝(𝐼𝐼𝑘𝑘 |𝑋𝑋𝑘𝑘 , ℎ𝑘𝑘 ) = ×

×



x𝑘𝑘|𝑘𝑘𝑘𝑘,𝑖𝑖 ∈𝑆𝑆1



x𝑘𝑘|𝑘𝑘𝑘𝑘,𝑖𝑖 ∈𝑆𝑆2



𝑝𝑝𝑑𝑑 �x𝑘𝑘|𝑘𝑘−1,𝑖𝑖 � 𝑝𝑝�z𝑘𝑘,𝑚𝑚 �x𝑘𝑘|𝑘𝑘−1,𝑖𝑖 �

�1 − 𝑝𝑝𝑑𝑑 �x𝑘𝑘|𝑘𝑘𝑘𝑘,𝑖𝑖 ��

x𝑘𝑘|𝑘𝑘−1,𝑖𝑖 �x �∈Γ 𝑘𝑘|𝑘𝑘−1,𝑗𝑗



x𝑘𝑘|𝑘𝑘𝑘𝑘,𝑖𝑖 ∈Ψ

𝑝𝑝Ψ �x𝑘𝑘|𝑘𝑘𝑘𝑘,𝑖𝑖 �

(16)

𝑝𝑝Γ (x𝑘𝑘|𝑘𝑘𝑘𝑘,𝑖𝑖 , x𝑘𝑘|𝑘𝑘𝑘𝑘,𝑗𝑗 ) � 𝑝𝑝𝐶𝐶 z𝑘𝑘,𝑖𝑖 ∈𝐶𝐶

where 𝑝𝑝𝑑𝑑 (x𝑘𝑘,𝑖𝑖 ) is the state dependent probability of detection, 𝑝𝑝Γ (x𝑘𝑘,𝑖𝑖 , x𝑘𝑘,𝑗𝑗 ) is the object tracks merge density, 𝑝𝑝Ψ = (x𝑘𝑘,𝑖𝑖 ) is the object track split density, and 𝑝𝑝𝐶𝐶 is the clutter density. As in Eq. (13), the likelihood is used to modify the predicted states 𝑝𝑝(𝑋𝑋𝑘𝑘 , ℎ𝑘𝑘 |𝑋𝑋𝑘𝑘𝑘𝑘 , ℎ𝑘𝑘𝑘𝑘 ). Table 1: Vesicle track hypothesis. Each hypothesis is a measurement-to-track association, which defines a set of compatible vesicle tracks.

𝑆𝑆1 (update)

𝑆𝑆2 (update) Γ (merge) Ψ (split) 𝐵𝐵 (birth)

Object in frame 𝑘𝑘 − 1

Prediction 𝑘𝑘 | 𝑘𝑘 − 1

Object in frame 𝑘𝑘

Measurement in frame 𝑘𝑘

x𝑘𝑘−1,𝑖𝑖

x𝑘𝑘|𝑘𝑘−1,𝑖𝑖

x𝑘𝑘,𝑖𝑖

𝜙𝜙

x𝑘𝑘−1,𝑖𝑖

x𝑘𝑘|𝑘𝑘−1,𝑖𝑖

x𝑘𝑘−1,𝑖𝑖 �x � 𝑘𝑘−1,𝑗𝑗

x𝑘𝑘|𝑘𝑘−1,𝑖𝑖 �x � 𝑘𝑘|𝑘𝑘−1,𝑗𝑗

x𝑘𝑘−1,𝑖𝑖

x𝑘𝑘|𝑘𝑘−1,𝑖𝑖

𝜙𝜙

𝜙𝜙

𝐷𝐷 (death)

x𝑘𝑘−1,𝑖𝑖

x𝑘𝑘|𝑘𝑘−1,𝑖𝑖

Unions

𝑋𝑋𝑘𝑘−1

𝑋𝑋𝑘𝑘|𝑘𝑘−1,𝑖𝑖

𝐶𝐶 (clutter)

𝜙𝜙

𝜙𝜙

x𝑘𝑘,𝑖𝑖

z𝑘𝑘,𝑚𝑚

x𝑘𝑘,𝑚𝑚

z𝑘𝑘,𝑚𝑚

x𝑘𝑘,𝑚𝑚 �x �

z𝑘𝑘,𝑚𝑚 �z �

𝜙𝜙

𝜙𝜙

𝑘𝑘,𝑛𝑛

x𝑘𝑘,𝑖𝑖 𝜙𝜙

𝑋𝑋𝑘𝑘

𝑘𝑘,𝑛𝑛

z𝑘𝑘,𝑖𝑖 z𝑘𝑘,𝑖𝑖 𝑍𝑍𝑘𝑘

Hypothesis ℎ𝑘𝑘

Object x𝑘𝑘−1,𝑖𝑖 is associated with exactly one measurement Object x𝑘𝑘−1,𝑖𝑖 does not associate with any measurement If two objects x𝑘𝑘−1,𝑖𝑖 and x𝑘𝑘−1,𝑗𝑗 are associated with the same measurement z𝑘𝑘,𝑚𝑚 , they merge into a new object x𝑘𝑘,𝑚𝑚 If object x𝑘𝑘−1,𝑖𝑖 is associated with two different measurements z𝑘𝑘,𝑚𝑚 and z𝑘𝑘,𝑛𝑛 , it may split into two objects x𝑘𝑘,𝑚𝑚 and x𝑘𝑘,𝑛𝑛 If measurement z𝑘𝑘,𝑖𝑖 is not associated with an existing object, it may represent a born object Object x𝑘𝑘−1,𝑖𝑖 does not associate with any measurement If measurement z𝑘𝑘,𝑖𝑖 is not associated with an existing object, it may represent a clutter

Appendix A

147

Next, we look at the model's ingredients. The transition density 𝑝𝑝(x𝑘𝑘,𝑖𝑖 , x𝑘𝑘,𝑗𝑗 ) in Eq. (15) expresses a single object motion model, which is object type dependent corresponding to different motion patterns. Currently we use a first order discrete time linear statistics model (Bar-Shalom and Li, 1993): 𝑥𝑥𝑘𝑘 = 𝐹𝐹𝑘𝑘 x𝑘𝑘−1 + v𝑘𝑘

(17)

to describe the vesicle’s position and velocity, where 𝐹𝐹𝑘𝑘 is the state transition matrix defining the deterministic component of the model and v𝑘𝑘 is a multivariate Gaussian random variable. Note that the vesicle index 𝑖𝑖 has been omitted for simplification. Adopting this general model partially reflects our lack of knowledge about the dynamics of cell constituents, but exchange of the model into other forms is straightforward. The likelihood function 𝑝𝑝𝑝z𝑘𝑘,𝑚𝑚 �x𝑘𝑘|𝑘𝑘𝑘𝑘,𝑖𝑖 � for individual objects in Eq. (16) incorporates both location and appearance information of the object. For simplicity we omit the time index, the measurement likelihood is defined as: (𝑧𝑧𝑚𝑚 − 𝑥𝑥𝑖𝑖 )2 (1 − 𝜌𝜌[𝐴𝐴𝑖𝑖 , 𝐴𝐴∗𝑚𝑚 ]) 𝑝𝑝(z𝑚𝑚 |x𝑖𝑖 ) ∝ exp �− � exp �− � (18) 𝜎𝜎𝑑𝑑2 𝜎𝜎𝐴𝐴2

where the first term is the distance part, 𝑥𝑥𝑖𝑖 is the object's predicted position (using Eq. (17)) and 𝑧𝑧𝑚𝑚 the measured position, 𝜎𝜎𝑑𝑑 accounts for the measurement noise. However, considering that an object may suddenly change its motion and that the dynamic model is only an approximation of the vesicle’s dynamics, the distance measure along can be inadequate. It is therefore introduced into the likelihood the second term: a measure of the similarity between the known vesicle in track 𝑖𝑖 and measurement 𝑚𝑚. 𝐴𝐴𝑖𝑖 and 𝐴𝐴∗𝑚𝑚 are appearance model as defined by Eq. (5), 𝜎𝜎𝐴𝐴 is the noise term and 𝜌𝜌 is the Bhattacharyya distance (Kailath, 1967) which measures the similarity of two discrete probability distributions. 𝜌𝜌[𝐴𝐴𝑖𝑖 , 𝐴𝐴∗𝑚𝑚 ] = � �𝑝𝑝𝑢𝑢 𝑝𝑝𝑢𝑢∗

(19)

𝑝𝑝Ψ (x𝑖𝑖 ) = 𝐿𝐿(x𝑖𝑖 , z𝑚𝑚 )𝐿𝐿(x𝑖𝑖 , z𝑛𝑛 )𝑝𝑝𝑠𝑠𝑠𝑠𝑠𝑠 (𝐴𝐴∗𝑚𝑚 , 𝐴𝐴∗𝑛𝑛 )

(20)

The larger 𝜌𝜌 is the more similar between 𝐴𝐴𝑖𝑖 and 𝐴𝐴∗𝑚𝑚 . The vesicle split density 𝑝𝑝Ψ �x𝑘𝑘|𝑘𝑘𝑘𝑘,𝑖𝑖 � in Eq. (16) appears hard to define. We use the following equation: Where 𝐿𝐿(x𝑖𝑖 , z𝑚𝑚 ) = 𝑝𝑝𝑑𝑑 (x𝑖𝑖 )𝑝𝑝𝑑𝑑 (z𝑚𝑚 |x𝑖𝑖 ) is the likelihood that the measurement z𝑚𝑚 comes from the object track x𝑖𝑖 ,similarly for 𝐿𝐿(x𝑖𝑖 , z𝑛𝑛 ). 𝑝𝑝𝑠𝑠𝑠𝑠𝑠𝑠 expresses the criteria about the object track split, which is application and/or experimental dependent. Currently an object 𝑖𝑖 is considered to have split into two objects 𝑚𝑚 and 𝑛𝑛 if the appearance 𝐴𝐴∗𝑚𝑚 of 𝑚𝑚 and the appearance 𝐴𝐴∗𝑛𝑛 of 𝑛𝑛 are similar. Similarly, the object merge density is defined as 𝑝𝑝Γ �x𝑖𝑖 , x𝑗𝑗 � = 𝐿𝐿(x𝑖𝑖 , z𝑚𝑚 )𝐿𝐿�x𝑗𝑗 , z𝑚𝑚 �𝑝𝑝𝑚𝑚𝑚𝑚𝑚𝑚 148

Appendix A

(21)

Where 𝑝𝑝𝑚𝑚𝑚𝑚𝑚𝑚 is the weighting factor dependent on the criteria about the object track merge, currently we set this factor to 1. 3.4 An efficient implementation We have presented a method capable of tracking a variable number of vesicles in an optimal way, but for formation and maintenance of hypothesis the computational complexity increases rapidly with the number of objects. A sample scenario is shown in Figure 5. It is clear that to enumerate and keep all the hypotheses propagating over time would be infeasible. It is also shown how to resolve the problem of matching received measurements with established vesicle tracks is critical, because at each new frame, the new hypotheses are generated using the detected vesicles and the existing tracks. A proposed method in the literature for optimal asymmetric assignment is the auction algorithm (Bertsekas, 1989). Under its framework, the association problem (Eq. (11)) is formulated as arg max � � 𝐿𝐿(𝑛𝑛, 𝑚𝑚) ℎ(𝑛𝑛, 𝑚𝑚) ℎ

𝑛𝑛

(22)

𝑚𝑚

where 𝑚𝑚 𝑚 {0} ∪ ℳ𝑘𝑘 and 𝑛𝑛 𝑛 {0} ∪ 𝒯𝒯𝑘𝑘𝑘𝑘 are used to index the measurement set and the track set, 𝑚𝑚 = 0 indicates a missed detection, and 𝑛𝑛 = 0 represents a new source which could either be a new object track or a clutter. ℎ(𝑛𝑛, 𝑚𝑚) is an assignment indicator defined as 1 ℎ(𝑛𝑛, 𝑚𝑚) = � 0

if measurement 𝑚𝑚 is assigned to track 𝑛𝑛 otherwise

(23)

𝐿𝐿(𝑛𝑛, 𝑚𝑚)is the assignment weight, i.e. the likelihood of matching measurement 𝑚𝑚 with vesicle track 𝑛𝑛. Based on the discussion in the previous section, it is given by 𝑝𝑝𝑑𝑑 𝑝𝑝(z𝑚𝑚 |x𝑛𝑛 ) 𝑚𝑚 > 0, 𝑛𝑛 > 0 𝑚𝑚 > 0, 𝑛𝑛 = 0 𝐿𝐿(𝑛𝑛, 𝑚𝑚) = �𝑝𝑝𝑛𝑛𝑛𝑛𝑛𝑛 (24) 1 − 𝑝𝑝𝑑𝑑 𝑚𝑚 = 0, 𝑛𝑛 > 0

where 𝑝𝑝𝑑𝑑 is the probability of detecting a vesicle, 𝑝𝑝(z𝑚𝑚 |x𝑛𝑛 ) is the measurement likelihood defined in Eq. (18). 𝑝𝑝𝑛𝑛𝑛𝑛𝑛𝑛 is experiment specific and dependent on density new of clutter 𝑝𝑝𝐶𝐶 and new born object 𝑝𝑝𝑏𝑏 . In our current implementation, 𝑝𝑝𝑑𝑑 and 𝑝𝑝𝑛𝑛𝑛𝑛𝑤𝑤 are set to fixed values, but substitution into other expressions is straightforward. The auction algorithm solves Eq. (22) iteratively based on a one-to-one assignment, except for 𝑚𝑚 = 0 or 𝑛𝑛 = 0 which are allowed multiple assignments: �

ℎ(𝑛𝑛, 𝑚𝑚) = 1 for 𝑚𝑚 ∈ ℳ𝑘𝑘

(25)



ℎ(𝑛𝑛, 𝑚𝑚) = 1 for 𝑛𝑛 ∈ 𝒯𝒯𝑘𝑘−1

(26)

𝑛𝑛∈0∪𝒯𝒯𝑘𝑘−1

Constrains that each measurement can have only one source, and

𝑚𝑚∈0∪ℳ𝑘𝑘

constrains that each established track can associate with only one measurement. For our example scenario in Figure 5, the result of assignments made by the auction Appendix A

149

algorithm is shown in Figure 6A. The auction algorithm has assigned the established vesicle tracks and measurements into one of the four sets: track set 𝒯𝒯 1 , in which each track is associated with exactly one measurement of the measurement set ℳ 1 ; track set 𝒯𝒯 0 for tracks having no measurements assigned to it, and measurement set ℳ 0 for measurements not assigned to any existing tracks. In Figure 6A, 𝒯𝒯 1 = �x𝑘𝑘𝑘𝑘,1 , x𝑘𝑘𝑘𝑘,3 , x𝑘𝑘𝑘𝑘,4 �, ℳ 1 = {z𝑘𝑘,1 , z𝑘𝑘,2 , z𝑘𝑘,3 }, 𝒯𝒯 0 = {x𝑘𝑘𝑘𝑘,2 } and ℳ 0 = {z𝑘𝑘,4 }. The one-to-one auction algorithm appears inadequate for our problem. As discussed in the previous section, there are cases where two tracks may be associated with one measurement, e.g., when two vesicles are crossing, they may produce a single unresolved measurement; or when two vesicles merge, there will be only one measurement in the next frame. Similarly, one track may have two measurements assigned to it as a result of vesicle split. To compensate for “merged” and “split” measurements, we propose a second round assignment (Tsaknakis et al., 1991; Kirubarajan et al., 2001). The assignment is made between 𝒯𝒯 0 and ℳ 1 , 𝒯𝒯 1 and ℳ 0 (Figure 6B). Figure 6C shows seven tracks formed after two times application of the auction algorithm. Each track corresponds to a different data association hypothesis. For a track formed during 𝒯𝒯 1 and ℳ 0 assignment, its assignment weight (Eq. (24)) must be modified to reflect the split event (Eq. (20)). For example, the assignment weight for track 7 is changed to 𝑝𝑝𝑑𝑑 𝑝𝑝𝑝z𝑘𝑘,4 �x𝑘𝑘𝑘𝑘,4 �𝑝𝑝𝑠𝑠𝑠𝑠𝑠𝑠 (𝐴𝐴∗𝑘𝑘,3 , 𝐴𝐴∗𝑘𝑘,4 ). The tracks formed at frame 𝑘𝑘 are propagated to frame 𝑘𝑘 + 1 (Eq. (17)) and associated with measured objects through the two-round auction algorithm. In Figure 7A, nine tracks are formed. Because the tracks formed by branching in the second round auction assignment at time 𝑘𝑘 can represent at most one vesicle track, they are alternatives and incompatible. For example, referring to Figure 7A, the tracks 2,3,8 are incompatible, the same goes for the track 6,7,9. We rank each track using the sum of its assignment weights over two frames, and resolve the track clash by selecting the most likely hypothesis. In example of Figure 7A, this is accomplished by computing (𝐿𝐿2 + 𝐿𝐿4 ), (𝐿𝐿3 + 𝐿𝐿4 ) and (𝐿𝐿8 + 𝐿𝐿4 ), where 𝐿𝐿 is the track assignment weight. Suppose (𝐿𝐿8 + 𝐿𝐿4 ) is the maximum of the three, 𝐿𝐿 will be selected and the established vesicle track x𝑘𝑘𝑘𝑘,2 will be associated with measurement z𝑘𝑘,2 . Similarly, by computing and comparing (𝐿𝐿6 + 𝐿𝐿5 ), (𝐿𝐿7 + 𝐿𝐿5 ) and (𝐿𝐿9 + 𝐿𝐿5 ), the most likely hypothesis is chosen as to match measurement z𝑘𝑘,4 with vesicle track x𝑘𝑘𝑘𝑘,4 . The assignments after hypothesis selection are shown in Figure 7B. These assignments will be used to update established tracks forward (Eq. (13)) and assignment/selection process is repeated through the whole image sequence. If two established vesicle tracks share the same measurements for three consecutive frames, they will be considered as merged into a new single vesicle. Any measurement that is not assigned to an existing track will be used to initiate a new track, but any track will not be confirmed until it lasts for at least three frames. This condition is necessary to exclude false detection in noisy images. If a track does not have a measurement assigned to it for three consecutive frames, it will be consider dead.

150

Appendix A

Established tracks k-1

1

Measured vesicles k

Established tracks k-1 1

2

Measured vesicles k 2

Established tracks k-1

Measured vesicles k

1

3

3

2

4

4

3

5

4

5

Figure 5: Multiple Hypothesis Tracking. An example of vesicle track hypothesis options. Vesicles along an established track can be linked to measured vesicles in the next frame in several different ways. The three different hypotheses lead to a different number of tracks.

A

B

Established tracks k-1 x k-1,1

Measured vesicles k z k,1

x k-1,2 x k-1,3 x k-1,4

C

Established tracks k-1

z k,3

4

z k,4

5

Measured vesicles k

Established tracks k-1

x k-1,1

x k-1,1

x k-1,2

2 3

Established tracks k-1

z k,1

1

z k,2

Measured vesicles k

Measured vesicles k z k,1

x k-1,2 z k,2

6

z k,3

x k-1,3

x k-1,3

x k-1,4

x k-1,4 z k,4

7

Measured vesicles k+1

1 2

z k,2

6 3

z k,3

4

z k,4

7 5

Figure 6: Multi-assignment. Illustration of the multi-assignment by the auction algorithm. (a) First round assignment. (b) Second round assignment. Left: the assignment between and ; Right: the assignment between and . (c) Tracks formed through multiassignment auction algorithm contain incompatible hypotheses, but the evaluation of hypotheses will use information in the next frame.

A

B Established tracks k-1 x k-1,1

Measured vesicles k z k,1

x k-1,4

1 2 3

x k-1,2 x k-1,3

Measured vesicles k+1

8

Established tracks k-1 x k-1,1

z k,1

x k-1,2

4

x k-1,3

z k,3

5

x k-1,4

z k,4

6 9

z k,2

Measured vesicles k

Measured vesicles k+1

1

2 z k,2

6 3

z k,3

4

z k,4

7 5

7

Figure 7: Hypothesis maintenance. Example of hypothesis maintenance. (a) The hypothesis is selected based on the auction algorithm assignments over two consecutive frames, which allows evaluation to be performed on a more global level while avoids to keep track of a very large number of hypotheses. (b) Track update is based on the selected most likely hypothesis. Appendix A

151

references Bar-Shalom, Y., and Li, X.-R. (1993). Estimation and tracking: principles, techniques and software (Norwood, MA: Artech House, Inc) Bertsekas, D. P. (1989). The auction algorithm for assignment and other network flow problems. Interfaces, 133-149. Blackman, S., and Popoli, R. (1999). Design and analysis of modern tracking systems (Norwood, MA: Artech House) Cheng, Y. (1995). Mean shift, mode seeking, and clustering. IEEE Trans Pattern Anal Mach Intell 17, 790-799. Clark, D., Panta, K., and Vo, B. (2006). The GM-PHD filter multi-target tracker. In Proc. 8th International Conference on Information Fusion. Comaniciu, D., Ramesh, V., and Meer, P. (2003). Kernel-based object tracking. IEEE Trans Pattern Anal Mach Intell, 564-577. Comaniciu, D., Ramesh, V., and Meer, P. (2000). Real-time tracking of non-rigid objects using mean shift. In Proc IEEE Conf Comp Vis Patt Recogn 2000. Gonzalez, J., Rojas, H., Ortega, J., and Prieto, A. (2002). A new clustering technique for function approximation. IEEE Trans neural netw 13, 132-142. Kailath, T. (1967). The divergence and Bhattacharyya distance measures in signal selection. IEEE Trans Commun Techn 15, 52-60. Kirubarajan, T., Bar-Shalom, Y., and Pattipati, K. R. (2001). Multiassignment for tracking a large number of overlapping objects [and application to fibroblast cells]. IEEE Trans Aerosp and Electron Syst 37, 2-21.

152

Appendix A

Ku, T.-C., Huang, Y.-N., Huang, C.-C., Yang, D.-M., Kao, L.-S., Chiu, T.-Y., Hsieh, C.-F., Wu, P.-Y., Tsai, Y.-S., and Lin, C.-C. (2007). An automated tracking system to measure the dynamic properties of vesicles in living cells. Microsc Res Tech 70, 119-134. Mahler, R. P. S. (2003). Multitarget Bayes filtering via first-order multitarget moments. IEEE Trans Aerosp and Electron Syst 39, 1152- 1178. Mahler, R. P. S. (2002). A theoretical foundation for the Stein-Winter “probability hypothesis density (PHD)” multitarget tracking approach. MSS Nat’l Symp. on Sensor and Data Fusion. Otsu, N. (1979). A threshold selection method from gray-level histograms. IEEE Trans Syst Man Cybern 9, 62-66. Reid, D. (1979). An algorithm for tracking multiple targets. IEEE trans autom contr 24, 843-854. Sezgin, M., and Sankur, B. (2004). Survey over image thresholding techniques and quantitative performance evaluation. J electron imaging 13, 146-168. Shalom, Y. B., and Fortmann, T. E. (1988). Tracking and data association (Boston: Academic-Press). Tsaknakis, H., Buckley, M. D., and Washburn, R. B. (1991). Tracking closelyspaced objects using multi-assignment algorithms. Tri-Service Data Fusion Symposium. Vo, B.-N., Singh, S., and Doucet, A. (2005). Sequential Monte Carlo methods for multitarget filtering with random finite sets. IEEE Trans Aerosp and Electron Syst 41, 1224- 1245.

Appendix B Nederlandse samenvatting

Dynamiek van de groei conus en blaasjes transport in gekweekte neuronen tijdens de ontwikkeling. Samenvatting De ontwikkeling van de hersenen van gewervelden zoals de mens doorloopt verschillende stadia, waarbij cellen zich vermenigvuldigen, specialiseren en aanpassen aan hun omgeving. Cellen beginnen met delen waarna een gedeelte zich specialiseren in bijvoorbeeld zenuwcellen, terwijl andere cellen zich specialiseren tot astrocyten en ondersteuning bieden voor de zenuwcellen. Tijdens de ontwikkeling van de hersenen doorlopen dehersencellen verschillende stadia. Deze stadia zijn nauwkeurig bestudeerd door cellen uit embryonaal weefsel te isoleren en te kweken. Hieruit bleek dat de hersencellen 5 specifieke stadia doorlopen: eerst ontstaan er plooien in het membraan. Deze plooien worden lamellopodia genoemd. In het volgende stadium groeien verschillende processen vanuit het cellichaam (de neurieten). Zenuwcellen hebben een speciale compartimentalisatie: een zenuwcel heeft meerdere neurieten die opgedeeld kunnen worden in twee groepen: neurieten die signalen ontvangen (de dendrieten) en een neuriet die signalen verzend (het axon). Een zenuwcel heeft meerdere dendrieten, maar slechts een axon. Tijdens het volgende stadium zal het axon snel uitgroeien op zoek naar andere zenuwcellen. Dit uigroeien wordt gereguleerd door verschillende sensoren op het oppervlak van een speciaal compartiment aan het uiteinde van het axon (de groei-conus). Dit handvormige compartiment tast de omgeving af op zoek naar signalen die aangeven welke kant het axon op moet. Nadat het axon uitgegroeid is, gaan de dendrieten uitgroeien. De dendrieten leggen veel kortere afstanden af maar zijn vaak meer vertakt vergeleken met het axon. Het volgende en laatste stadium van de ontwikkeling is het vromen van contacten tussen axonen en dendrieten, de zogenaamde synapsen. Dit zijn de punten waarop signalen van de ene zenuwcel overgedragen worden aan de volgende zenuwcel enzovoort. Deze synapsen zijn belangrijk voor het functioneren van de hersenen en spelen een belangrijke rol in het verwerken van informatie en leren en geheugen. Synapsen worden gevormd door twee compartimenten die gescheiden worden door een kleine ruimte. Aan de ene zijde is de presynaps, die zich bevindt op het axon, en aan de andere kant zit de postsynapsop de dendriet. Signaaloverdracht vindt plaats doordat speciale blaasjes (synaptische vesicles) fuseren met de presynaptische membraan en hun lading van signaalstoffen (neurotransmitter) afgeven als de presynaps een elektrische puls ontvangt. Deze signaalstoffen binden aan receptoren op de postsynaptische membraan en wekken daar een elektrische puls op. Deze puls gaat naar het cellichaam en kan dan doorgegeven worden via het axon naar de volgende cel. Naast de synaptische vesicles bestaat er nog een tweede groep blaasjes die kunnen fuseren met het membraan en stoffen uitscheiden. Deze blaasjes bevatten kleine

Appendix B

155

eiwitten in een compacte matrix en laten onder een electronenmicroscoop een donkere kern zien en worden daarom dense core vesicles genoemd. Deze blaasjes zijn belangrijk voor de vorming van synapsen: de eiwitten die ze bevatten stimuleren het vormen van de synaptische elementen (pre- en postsynaps). Verder spelen ze ook een rol in het stabiliseren van de synaptische contacten. In dit proefschrift wordt de rol van deze twee type blaasjes bekeken op de ontwikkeling van de zenuwcellen. Met behulp van speciale muizen die specifieke genen missen die essentieel zijn voor het fuseren van synaptische blaasjes met de membraan, is het mogelijk om de rol van deze blaasjes in de beginstadia van de ontwikkeling van dezenuwcel te ontrafelen. Door de eiwitten die zich in de dense core vesicles bevinden te voorzien van een fluorescent label kan de dynamiek van deze blaasjes bestudeerd worden: zowel het transport door de neurieten als het fuseren met de membraan. Verder wordt hier ook nog een techniek beschreven om dit transport op een geautomatiseerde wijze te analyseren. Ook worden twee technieken beschreven die helpen om het proces van fuseren van blaasjes met het membraan te bestuderen. De ene techniek staat het toe om het fuseren van blaasjes te observeren zonder het toepassen van fluorescente labels. De andere techniek staat het toe om de benodigdheden voor vesicle fusie met behulp van licht nauwkeurig te manipuleren.

156

Appendix B

Appendix C Dankwoord Curriculum Vitae

Dankwoord De klus is geklaard: na vier lange jaren is dan eindelijk dit boekje tot stand gekomen. Hoewel er maar 1 naam op de omslag staat, ben ik toch veel mensen dankbaar voor het tot stand komen van dit werk. Dit is slechts een poging om die mensen te bedanken die me geholpen hebben en die bijgedragen hebben aan het volbrengen van dit werk. Als eerste wil ik graag mijn ouders bedanken voor de steun die ik gehad heb om te kunnen studeren in een ‘verre’ stad. Pa, als rasechte Rotterdammer was het misschien moeilijk te verkroppen dat ik juist in Amsterdam ging studeren, maar uiteindelijk is het toch nog goed gekomen met mij (ja toch?). Ma, je hebt me altijd gesteund in mijn keuze om te gaan studeren en me zelfs af en toe achter de veren gezeten om te zorgen dat alles goed kwam: hopelijk heb ik niet al te veel grijze haren veroorzaakt? Ik moet ook veel (oud)collega’s bedanken die me geholpen hebben met het werk zoals beschreven in dit boekje, of die gewoon gezorgd hebben voor een geweldige werksfeer (ook heel belangrijk). Ten eerste Matthijs en Ruud, die voor de prima begeleiding en de mogelijkheden hebben gezorgd om dit project te kunnen doen en blijven doen. Martijn, je was maar kort mijn begeleider, maar het was een nuttige en leuke tijd. Dan de collega’s die veel werk doen en onmisbaar zijn: de ‘technicians’. Boukje en Desiree, bedankt voor het uitzetten van de cellen nodig voor mijn onderzoek, jullie hulp was onmisbaar. Ook Joost en Robbie wil ik graag bedanken voor hun bijdrage. Verder wil ik graag de dierenverzorgers bedanken, Chris, Joke, Bert en Lieselotte, al die muizen kwamen niet uit het niets. De ‘inwoners’ van kamer A445, mijn kamer voor de afgelopen 5+ jaar: Tatiana, altijd druk met van alles en nog wat, bedankt voor de vele discussies over ontwikkeling en experimenten. Greg en Jens, als onderdeel van het After Work Movie Night™ committee hebben we heel wat lol gehad met het kiezen van films om onze collega’s mee lastig te vallen. Tony, ik heb genoten van de discussies en natuurlijk van het oplappen van de microscoop als er weer wat scheef stond (hoe komt dat toch?). Nog 1 klein puntje: niet alles is een systeem... En natuurlijk allemaal bedankt voor het dagelijkse ‘4 o’clock bull sh*t’ uurtje, het perfecte einde van een werkdag. Ook nog een bedankje aan het adres aan mijn mede-aquarianen, Rocio en Julia, voor het brengen van tropisch leven in de kamer. Iedereen die ik niet genoemd heb (een lange lijst), bedankt voor de geweldige sfeer en behulpzame gesprekken, en ik hoop dat ik jullie ook verder kan helpen.

Appendix C

159

Curriculum vitae 2000-2003: 2003-2006: 2006-2006: 2006-2010: 2010-present:

Bachelor Medical Biology at the Universiteit van Amsterdam Master Cognitive Science Universiteit van Amsterdam Internship at the Netherlands institute for Neuroscience about the role of Oligophrenin1 in neuronal morphology and development. PhD at the Vrije Universiteit Amsterdam on the topic of growth cone dynamics and vesicle dynamics in cultured neurons System developer at the Vrije Universiteit Amsterdam

Publications Broeke, Jurjen H P, Martijn Roelandse, Maartje J Luteijn, Tatiana Boiko, Andrew Matus, Ruud F Toonen, and Matthijs Verhage. “Munc18 and Munc13 Regulate Early Neurite Outgrowth.” Biology of the Cell 102, no. 8 (May 19, 2010): 479-488. Broeke, Jurjen H.P., Haifang Ge, Ineke M. Dijkstra, Ali Taylan Cemgil, Jürgen A. Riedl, L. Niels Cornelisse, Ruud F. Toonen, Matthijs Verhage, and William J. Fitzgerald. “Automated quantification of cellular traffic in living cells.” Journal of Neuroscience Methods 178, no. 2 (April 15, 2009): 378-384.

Appendix C

161