Light Sheet Microscopy and Image Analysis of Neural Development and Programmed Cell Death in C. Elegans Embryos

The positioning of neuronal cell bodies and neurites is critical for intact functioning of the nervous system. Mapping the positions of the soma and neurites in the brains of developing embryos as important central nervous system structures are being created may yield novel insight into the role of distinct cell groups in creating these structures. New developments in microscopy have made this an excellent time to study neural development in the C. elegans embryo. In the past decade, implementations of highly light efficient methods such as single plane illumination microscopy have rendered it possible to follow development of embryonic structures in 3D with excellent temporal resolution (Huisken et al., 2004) and low phototoxicity. Recent work has resulted in quantitative characterization of the outgrowth of a single neurite in the late, rapidly moving three-fold stage of the C. elegans embryo for the first time (Christensen et al., 2015). In this thesis, I first describe the construction and programming of a single plane illumination microscope (SPIM) based on a design from Hari Shroff\u27s lab (Wu et al., 2011). The microscope is developed especially for use with C. elegans embryos and permits fast image acquisition without excessive photodamage, compared to other forms of microscopy. Second, I describe the use of the SPIM microscope to image the development of a subset of sublateral neurons, the earliest known entrants to the nerve ring (Rapti et al, in preparation), into which they grow in the 1.5-fold stage. I describe an algorithm for automatically aligning developing embryos onto one another until the beginning of the rapid embryonic movements known as twitching, which begin at the start of the twofold stage. I employ my algorithm to align a group of identically imaged embryos onto one another and deduce information about the positioning of the nerve ring in an approximately uniform coordinate system. I determine that nerve rings are precisely positioned in the embryo to within about a micrometer while the cell bodies that grow into the nerve ring are positioned over a much wider distance. My work suggests that the nerve ring grows out towards the ALA neuron as an anchor, and that twitching may begin when the developing nerve ring reaches the ALA. I additionally describe observation of new phenotypes related to the cam-1 mutation, which was previously identified as a regulator of anterior-posterior placement of the nerve ring (Kennerdell et al., 2009). Third, I describe an application of the SPIM microscope for imaging the death of the tail spike cell, a complex, multi-compartment differentiated cell which dies over a period of hours during the three-fold stage, when the animal is rapidly moving in its shell, and cannot be imaged otherwise than with a rapid, light efficient microscope such as the one described here. I determined the time course and confirmed the sequence of events of wild type tail spike cell death. Additionally, I report stronger phenotypes for some known tail spike cell death genes when imaged in the embryo, suggesting that eff-1 plays a stronger role than previously known in clearance of the distal part of the tail spike cell process, and additionally that ced-5 has a strong role in clearance of the same compartment (in addition to its known role in soma clearance). In an appendix I describe work beginning on an extension of the microscope, which will hopefully see the microscope used as a tool for selectively inducing fluorescence in individual cells and following the development of those cells in time. My results demonstrate the utility of single plane illumination microscopy for study of C. elegans embryogenesis and establish fundamental facts about the variability of the C. elegans central nervous system by making direct comparisons between animals. This work contributes to our understanding of the C. elegans nervous system by establishing fundamental bounds on the range of nerve ring positioning between individuals

CLIMATE GAMES: WHO’S ON FIRST? WHAT’S ON SECOND?

We study four different climate change games and compare with the outcome of choices by a Social Planner. In a dynamic setting, two players choose levels of carbon emissions. Rising atmospheric carbon stocks increase average global temperature which damages player utilities. Temperature is modelled as a stochastic differential equation. We contrast the results of a Stackelberg game with a game in which both players act as leaders (a Leader-Leader, or Trumpian game). We also examine an Interleaved game where there is a significant time interval between player decisions. Finally we examine a game where a Nash equilibrium is chosen if it exists, and otherwise a Stackelberg game is played. One or both players may be better off in these alternative games compared to the Stackelberg game, depending on state variables. We conclude that it is important to consider alternate game structures in examining strategic interactions in pollution games. We also demonstrate that the Stackelberg game is the limit of the Interleaved game as the time between decisions goes to zero.Nous étudions quatre jeux différents sur le changement climatique et les comparons aux résultats des choix d’un Planificateur Social. Dans un contexte dynamique, deux joueurs choisissent des niveaux d’émissions de carbone. L’augmentation des stocks de carbone dans l’atmosphère augmente la température moyenne mondiale, ce qui nuit aux services publics des joueurs. La température est modélisée comme une équation différentielle stochastique. Nous contrastons les résultats d’un jeu à la Stackelberg avec un jeu dans lequel les deux joueurs jouent le rôle de meneur (un jeu Leader-Leader, ou Trumpian). Nous examinons également un jeu Entrelacé dans lequel il existe un intervalle de temps important entre les décisions des joueurs. Enfin, nous examinons un jeu dans lequel un équilibre de Nash est choisi s’il existe, et un jeu de Stackelberg est joué dans le cas contraire. Un seul ou les deux joueurs peuvent terminer dans une meilleure position avec ces jeux alternatifs par rapport au jeu à la Stackelberg, dépendamment des variables d’état. Nous concluons qu’il est important d’envisager d’autres structures de jeu lors de l’examen des interactions stratégiques dans les jeux portant sur pollution. Nous démontrons également que le jeu de Stackelberg constitue une limite du jeu Entrelacé lorsque le temps entre les décisions tend vers zéro

Automated <i>C</i>. <i>elegans</i> embryo alignments reveal brain neuropil position invariance despite lax cell body placement

<div><p>The <i>Caenorhabditis elegans</i> cell lineage is nearly invariant. Whether this stereotyped cell-division pattern promotes reproducibility in cell shapes/positions is not generally known, as manual spatiotemporal cell-shape/position alignments are labor-intensive, and fully-automated methods are not described. Here, we report automated algorithms for spatiotemporal alignments of <i>C</i>. <i>elegans</i> embryos from pre-morphogenesis to motor-activity initiation. We use sparsely-labeled green-fluorescent nuclei and a pan-nuclear red-fluorescent reporter to register consecutive imaging time points and compare embryos. Using our method, we monitor early assembly of the nerve-ring (NR) brain neuropil. While NR pioneer neurons exhibit reproducible growth kinetics and axon positions, cell-body placements are variable. Thus, pioneer-neuron axon locations, but not cell-body positions, are under selection. We also show that anterior NR displacement in <i>cam-1</i>/ROR Wnt-receptor mutants is not an early NR assembly defect. Our results demonstrate the utility of automated spatiotemporal alignments of <i>C</i>. <i>elegans</i> embryos, and uncover key principles guiding nervous-system development in this animal.</p></div

Quantitative measures of alignment accuracy.

<p>Quantitative measure of overlap between test and reference embryos, The proportion given is labeled pixels in the test/reference stack which are within 1 micrometer of a labeled pixel in the reference/test (<b>A, B</b>), respectively, averaged across test embryos. Image stacks are compared to reference at the last time point that could be matched prior to twitching. Overlap is calculated for four states: no transformation; long axis (AP) aligned; indirect alignment, all alignment steps except for final 3D refinement; full alignment, 3D refinement added. Error bars are S.E.M., calculated across embryos.</p

Correcting internal embryo rotations.

<p>Internal coordinate systems are established for individual embryos by correcting rotations about the AP-axis throughout development, by point-matching segmented nuclei against one another between time points. <b>A</b>,<b>B</b>) Segmentation of an embryo before (<b>A</b>) and after (<b>B</b>) an internal rotation (and concurrent neurite outgrowth). <b>C</b>) Summed degrees of internal rotations, calculated using the rotation correction method described in the text, in degrees counterclockwise about the embryo long axis. Each point represents a single embryo. Embryos display a preference for counterclockwise rotation (p = 0.001), but magnitude of rotation varies. <b>D,E</b>) Example of rotational correction between adjacent time points. <b>D,E</b>) Overlay of two <i>unc-130</i>::GFP nuclear segmentation channels (light, dark blue) from successive time points, before (<b>D</b>), and after (<b>E</b>) correction.</p

Temporal alignments of embryos.

<p><b>A,B</b>) Bold green curve: reference embryo. Other curves, individual test embryos. <b>A</b>) Raw nuclear counts over time. <b>B</b>) Nuclear counts over time after implementation of temporal correction algorithm. <b>C,D</b>) Onset of twitching, relative to reference embryo without (<b>C</b>) and with temporal alignment (<b>D</b>). Mean and SD of data are indicated.</p

Defining a universal coordinate system for alignment of test and reference embryos.

<p>Green, <i>unc-130</i>::GFP segmentation. Red, mCherry segmentation. <b>A</b>) Raw segmented test embryo. <b>B</b>) Axes of the embryo determined using convex hull of mCherry segmentation. Long axis, orange. <b>C</b>) Using information in <b>B</b>, embryo is centered, aligned to the camera axis, and rescaled. <b>D-F</b>) An axis perpendicular to the long axis is defined by generating a vector (yellow arrow) pointing between clusters of <i>unc-130</i>::GFP expression (<b>D</b>), and projecting onto a plane perpendicular to the long axis (<b>E</b>). Solid olive-green arrow, perpendicularly projected vector. Dashed arrow, direction of projection. <b>F</b>) Raw overlays of <i>unc-130</i>::GFP segmentation of a test embryo (gray) and the reference (green), prior to establishing axes perpendicular to the long axis. This step uses a relaxed segmentation threshold. <b>G</b>) Overlay of same segmentation as in <b>F</b>, after rotation to align the projection vectors found in <b>E</b>. <b>H-I</b>) Fine correction for rotation transform in <b>G</b>. <b>H</b>) Segmentation as in <b>G</b>, with a tighter segmentation threshold, at a time point twenty minutes earlier. <b>I</b>) Point clouds from <b>H</b> are matched using CPD-register, to provide fine corrections.</p

Hatching rates of <i>cam-1(gm122)</i> animals.

<p>Hatching rates of <i>cam-1(gm122)</i> animals.</p

Quantitative measurements of wild-type nerve ring and cell body positions.

<p><b>A</b>) Sublateral and ALA cell bodies in the reference embryo. NR, nerve ring. <b>B</b>) Overlap of a test embryo with the reference. Cell bodies in test embryos are identified with corresponding cell bodies in reference based on overlap at earlier time points in the fully aligned 4D sequences. <b>C</b>) Individual sublateral neuron cell body centers are measured by hand (Methods) at the last time point before twitching, and absolute value of distance from the mean position is reported. <b>D</b>) Nerve rings, NR, were traced out with a semi-automatic method in FIJI (Methods) and their centers measured by averaging over the traces, while ALA neuron center positions were measured by hand as with the sublateral neurons. Reported are deviations from the mean. <b>E</b>) The angle of the vector through the nerve ring was measured by fitting the nerve ring to a plane with a linear cost function. Deviations from the mean are reported.</p

Imaging strain reporters and GFP segmentation.

<p><b>A-C)</b> Embryo, just before twitching, expressing indicated fluorescent reporters for alignments and for visualization of the nerve ring and sublateral neuron cell bodies. <b>A</b>) Cyan arrowhead, <i>unc-130</i>::GFP-labeled nucleus. Yellow arrowhead, sublateral neuron cell body. Brown arrowhead, nerve ring. Magenta arrowhead, ALA neuron. <b>B)</b> mCherry channel of same embryo. <b>C</b>) Merge of <b>A</b> and <b>B</b>. <b>D-F</b>) Segmentation of GFP signals on a test embryo not used for training the classifier. <b>D</b>) Raw image. <b>E</b>) Blue, segmented <i>unc-130</i>::GFP nuclei. Segmentation is restricted to anterior half of embryo outside a central cylinder surrounding the nerve ring. White arrowhead, false negative. <b>F</b>) Blue, <i>ceh-17</i>::GFP sublateral neuron cell body segmentation. Orange arrowhead, false positive.</p