Reconstructive Quantitation of Neuron Morphology: Potential Insights into Development, Synaptic Organization, and Disease

Master’s Thesis

Presented to

The Faculty of the Graduate School of Arts and Sciences Brandeis University Interdepartmental Program in Neuroscience Eve Marder, Advisor

In Partial Fulfillment of the Requirements for the Degree

Master of Science in Neuroscience

by Matthew Stenerson

May 2019

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Copyright by Matthew Stenerson

© 2019

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ACKNOWLEDGEMENTS

I would like to express my deep gratitude to everyone who supported this effort. This includes, but is not limited to, the following:

The faculty and staff of Brandeis University, for providing me a world-class education; and the Abraham and Sarah Kaplan Scholarship Fund, without which this spectacular privilege would never have been possible.

Fellow members of the Marder Lab, past and present, for making it the welcoming, diverse, challenging place it is:

Philipp Rosenbaum, PhD, for preparing double-neuron dye-fills;

Jason Pipkin, PhD, for his guidance with confocal microscopy and analysis;

Adriane Otopalik, PhD; Dirk Bucher, PhD; Marie Goeritz, PhD; Matt Bowers, PhD; Adam Taylor, PhD; and Roger Yang, MD, for preparing single-neuron dye-fills;

Alec Hoyland, MS; Alexander Sutton, PhD; Cosmo Guerini; Daniel Shin, BS; Dave Hampton, BS; Jessica Haley, MS; Katelyn Wadland, MS; Lily He; Noah Guzman; Srinivas Gorur Shandilya, PhD; and Ted Brookings, PhD.

Thesis committee members, Prof. Don Katz and Prof. Irv Epstein.

My advisor, Eve Marder, who has always given me her most honest, constructive advice—even when it was not easy to hear—and who has never stopped believing in me—even when others probably would have.

My family, including the Lorusso family (especially Jarred, Casey, and Collin Smith); my fiancé, Griffin Phenegar, who assisted in the design and execution of some analytical programs; my in-laws-to-be, Christine, Gibb, Chase, Ryan, and Graham Phenegar; my father, Richard Stenerson; and my late mother, Jean Stenerson.

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ABSTRACT

Reconstructive Quantitation of Neuron Morphology: Potential Insights into Development, Synaptic Organization, and Disease

A thesis presented to the Interdepartmental Program in Neuroscience

Graduate School of Arts and Sciences Brandeis University Waltham, Massachusetts

By Matthew Stenerson

From the inception of the neuron doctrine (i.e., the understanding that nervous systems are composed of individual cells), the morphology of neurons has been a predictable focus in the study of their physiology.1,2,3,4 After all, a practical understanding of the development, maintenance, and functional robustness of a neuron’s geometry is prerequisite to a full appreciation of the organization and adaptability (i.e., plasticity) of neural networks. In addition, a variety of neuromorphological abnormalities, which are often conspicuous, have been implicated in human diseases such as neurodegeneration, neuropsychiatric disorders (e.g., Autism Spectrum Disorder,

Major Depressive Disorder), cerebrovascular pathology, and neurotrauma.5,6,7 However, the sheer

1 Deiters & Guillery, 2013 2 Ramón y Cajal, 1928/1959 3 Revel & Karnovsky, 1967 4 Brightman & Reese, 1969 5 Rajkowska et al., 1999 6 Arvidsson et al., 2002 7 Shankar et al., 2008 iv complexity of neuron morphologies precludes consistent, objective analysis without the aid of computers. Automated methods of reconstructing entire neuron “skeletons” continue to improve; but for the time being, manual reconstruction in three dimensions remains the most reliable way of analyzing the structure of the entire neuropil. Two species that have been useful for neuromorphology analysis are the Jonah crab (Cancer borealis) and the American lobster

(Homarus americanus), both of which possess elegant and physiologically analogous stomatogastric ganglia (STG).8,9,10 This thesis reports on forty-eight manually-reconstructed STG neurons from these two species, including five electrophysiologically-characterized cell types and two developmental stages. Quantitative analyses reveal remarkable variability across all the considered parameters. No obvious morphological differences between STG cell types can be identified; however, branching complexity, soma size, and the space occupied by the neuropil are all shown to increase significantly between juvenile and adult developmental stages. Furthermore, branching patterns in these cells—specifically tortuosity, path length, and branch order—are not well-predicted by a leading computational algorithm. Finally, double-neuron reconstructions of synaptically-related neurons can readily identify candidate synaptic appositions. Ultimately, these efforts present a promising collection of quantitative tools which may be used to characterize fine structures within neuropils. As global repositories of neuronal reconstructions† grow—and as automated methods of reconstruction continue to improve—such quantitative approaches are likely to improve our understanding of how neuronal structure relates to functionality, development, and even disease.11,12

8 Stenerson et al., 2016 9 Otopalik et al., 2017a,b 10 Stenerson & Marder, 2017 11 Ascoli et al., 2007 12 George Mason Univ., 2018 † 107,395 collected by NeuroMorpho.Org as of April 25, 2019 v

TABLE OF CONTENTS

(PAGE)

1. Introduction 1

Section I: Historical foundations 1 Section II: Putative morphological bases of disease 8 Section III: Three-dimensional reconstruction and quantitation 9 Section IV: Computational modeling 16 Section V: Multi-cell reconstruction and synaptic mapping 19 Section VI: The stomatogastric nervous system 20

2. Methods 26

Section I: Dissection of the stomatogastric nervous system 26 Section II: Electrophysiological subtyping of STG neurons 28 Section III: Neuron dye-fills, amplification, and immunohistochemistry 28 Section IV: Confocal microscopy and image processing 31 Section V: Manual reconstruction 33 Section VI: Post-reconstruction analysis 34

3. Results 37 Section I: Macroscopic features 37 Section II: Qualitative features 42 Section III: Geometry of somata 47 Section IV: Neurite diameter 48 Section V: Neuropil space-filling 51 Section VI: Branching patterns 54 Section VII: Double-neuron reconstructions 60

4. Conclusion 67 5. Appendices 70 6. Bibliography 75

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LIST OF TABLES (PAGE)

Table 1 Cell sample composition 37 Appendix B1 Catalog of reconstructions 71 Appendix B2 Catalog of reconstructions (continued) 72 Appendix C Voxel configurations 73 Appendix D Tracing history 74

LIST OF EQUATIONS (PAGE)

Equation 1 Time constant 3 Equation 2 Length constant 3 Equation 3 Passive decay transients in a multipolar neuron 4 Equation 4 Equalizing time constants 4 Equation 5 Electrotonic length 4 Equation 6 Morphometric model of membrane resistance 5 Equation 7 Cable-to-soma conductance ratio 5 Equation 8 Branching constant 5 Equation 9 Balancing factor 17 Equation 10 General tortuosity 22 Equation 11 Branch angle triangulation 35 Equation 12 Rall power 35 Equation 13 Triangulation-based estimation of polyhedron volume 36 Equation 14 Absolute tortuosity 54 Equation 15 Path tortuosity 54 Equation 16 Branch tortuosity 54 Equation 17 Euclidian distance 64

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LIST OF FIGURES (PAGE)

Figure 1 Cat cerebellar Purkinje neuron by Ramón y Cajal 2 Figure 2 Neuron skeletonization 15 Figure 3 Stomatogastric ganglion connectivity diagram in C. borealis 21 Figure 4A Stomatogastric ganglion neurons in H. americanus 23 Figure 4B Stomatogastric ganglion neurons neurons in H. americanus (continued) 24 Figure 5 Schematic of the stomatogastric nervous systems 27 Figure 6 Schematic of procedural workflow 27 Figure 7 Electrophysiological signatures of the stomatogastric nervous system 29 Figure 8 Schematic of confocal z-stack stitching 31 Figure 9 Schematic of confocal z-stack stitching (continued) 32 Figure 10 Schematic of confocal z-stack stitching (continued) 32 Figure 11 Manual reconstruction process in KNOSSOS 34 Figure 12 Computed polyhedron model of neuropil space 36 Figure 13 Number of distal projections 38 Figure 14 Number of distal projections (continued) 39 Figure 15 Schematic of H. americanus carapace size 39 Figure 16 Skeleton complexity as a function of objective power 40 Figure 17 Number of nodes 41 Figure 18 Number of nodes (continued) 41 Figure 19 Comparison of C. borealis and H. americanus PD neurons 42 Figure 20 “Hand-like” neurite features 43 Figure 21 Adult H. americanus PD neurons 45 Figure 22 Juvenile H. americanus PD neurons 46 Figure 23 Soma area and volume 47 Figure 24 Soma area (continued) 48 Figure 25 Neurite diameter as a function of branch order 49

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LIST OF FIGURES (continued) (PAGE)

Figure 26 Axon Hillock diameter 50 Figure 27 Neuropil space occupation: juvenile versus adult 51 Figure 28 Neuropil space occupation: juvenile versus adult (continued) 52 Figure 29 Path length distributions: juvenile versus adult 53 Figure 30 Branch tortuosity 55 Figure 31 Branch tortuosity (continued) 56 Figure 32 Branch angles 57 Figure 33 Radial dendrograms of juvenile H. americanus PD neurons 58 Figure 34 Radial dendrograms of adult H. americanus PD neurons 59 Figure 35 Double-neuron dye-fill and reconstruction 61 Figure 36 Double-neuron dye-fill and reconstruction (continued) 62 Figure 37 Double-neuron dye-fill and reconstruction (continued) 63 Figure 38 Candidate synaptic appositions as a function of distance threshold 64 Figure 39 Visual corroboration of identified candidate synaptic appositions 65 Figure 40 Adjusted candidate synaptic appositions 66 Appendix A Emission and excitation properties of the major dyes 70

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INTRODUCTION

Section I: Historical foundations

Although the Spanish neuroanatomist Santiago Ramón y Cajal (1852–1934) is widely credited as the father of cellular neuroscience, microscopic descriptions of neural somata, axis cylinders (axons), and protoplasmic (dendritic) processes were first provided by German neuroanatomist Otto F. K. Deiters (1834–1863) (Deiters & Guillery, 2013). Nevertheless, Ramón y Cajal, in collaboration with Italian biologist Camillo Golgi (1843–1926), did indeed forge an enduring foundation for the inchoate field of neuromorphology (Kemp & Powell, 1971). Ramón y Cajal conducted experiments using a silver staining method developed by Golgi—a method still commonly performed today. His experiments afforded some of the earliest quantitative measurements of individual nerve cells (e.g., process length, process density, area of dendritic arbor, area of soma, etc.) (Ramón y Cajal, 1928/1959). For their contributions, Golgi and Ramón y Cajal shared the 1906 Nobel Prize in Physiology or Medicine (Bock, 2013). Ramón y Cajal’s experiments also produced the many beautifully detailed illustrations of neurons that remain iconic today (Fig. 1) (Newman et al., 2017)

As Deiters, Golgi, and Ramón y Cajal gradually unveiled the distinctive complexities of the neuronal form, questions of structure–function relationships were already at the forefront of the scientific conversation. In spite of limiting analytical technology, Ramón y Cajal boldly began hypothesizing about the driving forces on neurological organization. He proposed that the development of neurons and their constitutive systems was shaped by three laws of optimization:

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[1] el ahorro del espacio, or spatial optimization; [2] el ahorro del material, or resource optimization; and [3] el ahorro del tiempo, or temporal optimization (Llinás, 2003). These three principles intuitively addressed the functionality and inherent limitations of individual neurons.

For example, neurites, or any projection from a neuronal soma, must grow into their environments and establish up to several thousand synaptic connections; too few or too many connections may compromise network integrity (McCulloch & Pitts, 1943; Markram, 2006). Neurite space-filling regimes must therefore be shaped by the cell’s synaptic requirements—i.e., be spatially optimized.

One must also never forget that neurons—no matter how special—are cells that must manage all their complex duties with limited resources. Each neurite must be maintained with not only a continuous supply of systemic essential nutrients (e.g., oxygen, carbohydrates, ions, etc.), but also with the organelles and infrastructure necessary for local protein synthesis, autophagic mechanisms (disruptions of which have been implicated in axonal and dendritic degeneration),

intracellular transport, and a myriad of other processes

(Campbell & Holt, 2001; Yang et al., 2013). This

considerable investment of resources and energy is therefore

expected to shape neurite development. Finally, neurons are

distinguished by their capacity to rapidly transmit signals

from one cell to the next—a development with obvious

benefits to an organism’s fitness, such as agility in fight-or-

flight situations. Conduction time and electrotonic efficiency

are thus also ostensible morphogenic constraints.

Figure 1. An iconic illustration by Ramón y Cajal of a cat cerebellar Purkinje neuron. (Bock, 2013)

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In the 1940s and 1950s, many notable advances were made in formalizing the relationships between conduction time, neuron geometry, and biophysical properties. Intracellular electrophysiology experiments performed by Graham and Gerard in 1946 offered the first direct measurements of muscular membrane time constants (휏푚); and the same technique was later applied to mammalian spinal motoneurons in 1952 (ref. Equation 1) (Graham & Gerard, 1946;

Woodbury & Patton, 1952; Brock et al., 1952).

휏푚 = 푟푚푐푚

Equation 1. The passive time constant (휏푚) quantifies the decay of membrane voltage and is equal to the time elapsed when Vmax reaches 37% of its original value. The membrane capacitance (푐푚 (F)) quantifies the charge required for the membrane to induce current (and therefore affect Vm). Length and time constants are relevant to spatial and temporal summation, respectively.

푟푚 λ = √ 푟푖

Equation 2. The length (or space) constant, denoted by lambda (λ), quantifies the distance traveled via passive conduction by a graded electrical potential. Membrane resistance (푟푚 (Ω)) quantifies the hindrance to the propagation of electrical current due to the plasma membrane itself (i.e., the intracellular–extracellular electrical resistance). Membrane resistance can generally be considered as an inverse function of the number of open ion channels, whereas axial resistance can generally be considered as a function of axonal diameter. Axial resistance (푟푖 (Ω)) quantifies the hindrance due to the axoplasm, which is parallel to the membrane. Extracellular resistance (푟표 (Ω)) (negligible and typically omitted) quantifies the hindrance due to the extracellular space.

Meanwhile, Alan Lloyd Hodgkin (1914–1998) and Andrew Huxley (1917–2012) were developing their conductance-based mathematical model of action potential propagation (Hodgkin

& Huxley, 1945; Hodgkin & Rushton, 1946; Hodgkin & Huxley, 1952). However, these early experiments, although revolutionary in principle, were unable to account for exact (or even well- approximated) cable dimensions, and estimated rather erroneously that 휏푚 ≈ 2 msec. Several years later, Wilfrid Rall (1922–2018) further elucidated the integrative functions of finer processes, namely dendrites. He proposed a technique for extracting time constants by summing, or “peeling,” low-order exponents from a semilogarithmic plot of voltage decay (ref. Equation 3). 3

∞ −푡 ( ) 휏 푉푚(푥, 푡) = 푉∞(푥) − ∑ 퐶푛(푥)푒 푛 푛 = 푚

Equation 3. The passive decay transients in a multipolar neuron can be expressed as a sum of exponential decays with multiple, “equalizing” 휏푛 constants—each less than the passive membrane time constant (휏푚)—with 퐶푛 values serving as capacitance constants that depend upon nonuniform initial conditions, the effective electronic length (L, dimensionless), and upon the cable-to-soma conductance ratio (휌) (Rall, 1962).

These “equalizing” time constants (휏푛), which were independent of neuron geometry, were then used to estimate the dimensionless electronic length (L) of the cable (in this case, a dendrite) from which intracellular recordings were being made (ref. Equations 4–5) (Rall, 1969).

휏 푙 휋 휏 = 푚 ∴ 퐿 = = 푛 푛휋 2 λ 휏 1 + ( ) √ 푚 − 1 퐿 휏푛

Equations 4–5. The values of the equalizing time constants (휏푛) depend upon the dimensionless electrotonic lengths (L) of the respective cables. Rall reasoned that a cable sealed at both ends with an electrotonic length equal to the quotient of its physical length (l) divided by its space constant (λ) would possess equalizing time constants equal to the passive time constant (휏푚) scaled by its local dimensions (Rall, 1969).

He then incorporated neuron geometric parameters—namely average dendrite diameter

̅ ̅ (푑푗) and length (푙푗) as well as soma surface area (S)—into the calculations of membrane resistance for a unit area (푅푚) and the cable-to-soma conductance ratio (휌) (ref. Equations 6–7) (Rall, 1959;

Karczmar et al., 1986). Pilot studies were conducted shortly thereafter to apply Rall’s mathematical models to actual biological systems. Intracellular recordings and averaged total dendritic lengths sourced from sixteen cat spinal motoneurons revealed that the total length of dendrites was approximately 1.5 times that of the dendrites’ electrotonic length constant (L), while

휌 ratios ranged from approximately 5–10 (Nelson & Lux, 1970). However, dendritic profiles were obtained from averaging just 10–20 dendrites per cell, while the subsequent two decades revealed that cat spinal motoneurons are far more morphologically complex than originally thought (Rose,

1982). Furthermore, estimations of somatic surface area (S) were likewise technically limited,

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6 4푆 푅2 3 푁 ̅ 푅푚 ≈ 1 + 1 + 6 (∑ 퐵푗 (√푑푗) ) √ 3 4휋푅푖 푅N ̅ 푗 (∑푗 퐵푗 (√푑푗) ) 휋푅푖 ( )

Equation 6. Rall estimated the membrane resistance for a unit area (푅푚) by incorporating branch ̅ constants (퐵푗, ref. Equation 7) and average dendritic diameter (푑푗) of the jth dendrite in a ganglionic neuron, in addition to soma surface area (S), total neuron resistance (푅N), and the specific resistivity of internal media (푅푖) (Rall, 1959; Karczmar et al., 1986).

3 푅 3 √ 푚 ̅ 휌 = (∑ 퐵푗 (√푑푗) ) 휋푅푖푆 푗

Equation 7. Rall estimated the cable-to-soma conductance ratio (휌)—which, in early experiments, were dendritic-to-soma conductance ratios—by scaling the membrane resistance for a unit area with somatic surface area (S). especially considering the amorphous nature of many neuronal somata. Therefore, although Rall’s models were mathematically clever, they were not yet exact, nor were they yet able to be accurately applied to true neurons. Ultimately, the mathematical models developed around this time sought to avoid geometric parameters altogether, due to the difficulty of obtaining reliable and inclusive datasets (ref. Equations 3, 8).

−1 푅 ̅ ̅̅̅ −1 ̅ 푚 퐵 = tanh (푙푛 × (λ푛) ) = tanh (푙푛 × (√ ) ) 푅푖

Equation 8. The branching constant (B), as defined by Rall in 1959, is thus dependent upon the ̅̅̅ average length of all dendrites (푙푛) and the average dendritic space constant (λ푛). Transitively, B is thus dependent upon 푅푚, making a direct calculation of 푅푚 from Equation 6 impossible. This necessitated the method of successive iteration, or “peeling,” described in Equation 3.

As morphometric data become increasingly attainable, revisiting the geometry-based models of Rall and others may be worthwhile—and indeed are discussed further in the Results section.

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Since these laws of optimization were semi-formalized, investigators have continued attempts to experimentally validate them with quantified data from actual neurons. Many computational models have been proposed to reconcile the logic of optimization with the reality of neural geometry; and those models will be discussed more in depth later (Cuntz et al., 2010;

Cuntz et al., 2012). In the meantime, it is important to note that these early neuroanatomical experiments paved the way for some of the most groundbreaking discoveries to date in cellular neuroscience. For example, in the 1960s—about four decades after Ramón y Cajal—microscopy visualization of intercellular junctions led to the differentiation of chemical and electrical synapses.

Using horseradish peroxidase (HRP) staining, Revel and Karnovsky described in 1967 two different kinds of intercellular appositions within mouse heart and liver tissue: those that either could or could not be infiltrated by the HRP (Revel & Karnovsky, 1967). Later, Brightman and

Reese examined the intercellular histology of mouse and chick brains and noted that tight junctions

(i.e., appositions impenetrable to HRP) were primarily characteristic of parenchymal capillaries conjoined to epithelium (constituting the blood–brain barrier), whereas “gap junctions,” or labile, pentalaminar (i.e., composed of five layers) appositions, were typically interposed between electrically-coupled neurons (Brightman & Reese, 1969). In addition to discriminating between these two major classes of synapses, these were some of the earliest strides in the classification of neuronal subtypes according to morphological differences.

Neuronal subtyping expanded considerably in the following years, and researchers began scrutinizing all facets of a cell—morphology, electrophysiological character, location, etc.—in a collective effort to illuminate neuronal phylogeny. By 1977, however, the classification system for neurons was becoming increasingly precarious. Rowe and Stone emphasized that the naming of neuron subtypes—whether by electrophysiological, morphological, or functional character—was

6 rooted on the Aristotelian concept of essences; in other words, subjectivity was threatening the credibility of this practice altogether (Rowe & Stone, 1977). Neuron nomenclature therefore grew evermore hierarchical and standardized. For example, the term ‘neuronal species’ came to define anatomically localized cellular subtypes of the same species; ‘neuronal genus’ was used to describe morphologically indistinguishable cells from the same anatomical loci within two or more different species; and ‘neuronal families’ was reserved for broader categories of morphologically similar cells. Moreover, as the diversity of morphologically-characterized neurons grew (i.e., in terms of sheer number of cells, cell types, and species), it become readily apparent that morphology alone could not distinguish all cell types.

For instance, in 1984, Abdel-Maguid and Bowsher imaged thirteen electrophysiologically distinct cell types from the human dorsal horn and medulla. Although they were able to demonstrate the uniform directionality of signal pathways, they were only able to confidently categorize three cell types based on their structural properties (Abdel-Maguid & Bowsher, 1984).

Similarly, in 1986, Renehan et al. surveyed the structural stereotypy of thirty-one cellular subtypes within the rat medullary dorsal horn which had previously been identified by electrophysiological signature. This group of cells was experimentally convenient to study because their sensory sensitivities were mapped to vibrissae (whiskers), affording a modicum of control in the selective stimulation of each vibrissa. It was observed that a subset of neurons that could be activated by multiple vibrissae sent unique projections to the medial lemniscus of the medulla, whereas neurons with single-vibrissa specificity lacked these projections (Renehan et al., 1986). Additionally, they noted that low-threshold neurons tended to have neurites of wider diameter, more densely-arranged dendritic arbors, and fewer dendritic spines; in contrast, high-threshold neurons tended to have thinner dendrites and more dendritic spines (Renehan et al., 1986). Like Abdel-Maguid and

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Bowsher, Renehan et al. could not identify all known cell types by their appearance alone; and the same constraints that prevented them from doing so remains one of the most vexing problems in neuromorphology. The complexity of neurite architecture, coupled with tremendous animal-to- animal or even cell-to-cell variability, are thought to be the greatest impediments to precise neuron classification.

Section II: Putative morphological bases of disease

Perhaps the most motivating incentive to improve understanding of neuromorphology is its potential applications in human disease. To date, morphological changes to neurons and glia have been documented in numerous disorders. For example, human motor neuron disease has been linked with an overexpression of neurofilament subunit NF-L, which has been shown to cause enlargement of the soma, axonal swelling, and decreased axonal length (Xu et al., 1993). In contrast, increases in neurite length and branching frequencies is an observed feature of LRRK2- mutation-conferred familial parkinsonism (MacLeod et al., 2006). In Alzheimer’s disease, soluble oligomers of amyloid-β (peptides of 36–43 amino acids characterized by a preponderance of β- sheet secondary structure) have been shown to reduce dendritic spine density (Shankar et al.,

2008). In addition, a wide array of aberrant morphological features has been documented in both neurons and glia following various neurotraumas, including traumatic brain and spinal cord injury as well as ischemic and hemorrhagic strokes (Martone et al., 1999; Arvidsson et al., 2002). Finally, morphology even has suspected roles in various psychiatric and neurodevelopmental disorders, including major depressive disorder and autism spectrum disorders (Rajkowska et al., 1999). It is plausible that future interventions for these disorders could arise from an improved understanding of their neuromorphological etiologies. However, to accurately define morphopathology, it will be necessary to accomplish a more comprehensive grasp of normal neuromorphology first.

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Section III: Three-dimensional reconstruction and quantitation

The qualitative analysis of neuronal images in two dimensions was a sufficiently powerful tool in the early expositions of cellular neuroscience, but many questions remained impenetrable without quantified and complete accounts of neurons in three dimensions. After all, cell types could only be morphologically sorted insofar as their subjective differences were unanimously acknowledged. Even those subjective differences depended upon the microscopic perspective; neurite architecture within one plane could (and often did) appear drastically different from the same neuron in another plane. Furthermore, the paucity of quantitative data resulted in obvious limitations to what could be extracted from these images. The quantification of neuron morphology was thus the next frontier.

It should be stressed that even Ramón y Cajal was able to make some numeric measurements of his microscopy experiments, but it was several decades before some of the more salient quantitative patterns could be appreciated. In the early 1970s, Kemp and Powell—still using Golgi’s silver staining method—studied the morphologies of neurons from the feline caudate nucleus. They demonstrated a pattern in the density of dendritic spines as a function of distance from the soma. More specifically, they observed that few or no dendritic spines existed within a

20 μm radius of the soma, but that spine density gradually increased—and then decreased—as the radius expanded, with a peak density, on average, within the range of 60–80 μm (Kemp & Powell,

1971). These were some of the first numeric conjugates to Ramón y Cajal’s theories of optimization, as well as some of the earliest evidence of a topographical specificity among synaptic loci.

Two of the most important strides made by the quantitation of neuron morphology were the ability to rigorously compare neuron geometries against each other and the ability to monitor

9 individual neuron structure over time (e.g., in the presence of an experimental perturbation). Case in point, in 1982, Friedlander et al. explored the morphological consequences of monocular deprivation on the neurons within the feline lateral geniculate nucleus (LGN). Using iontophoretic application of HRP, they demonstrated that monocular deprivation resulted in significant reductions to soma area among one electrophysiologically-distinguished cell type (Friedlander et al., 1982). However, these reductions in soma size were unaccompanied by physiological changes, while another subset of cells exhibited physiological deficits in the absence of morphological change. These findings suggested that various neuronal cell types can respond to the same stimulus in morphologically distinctive ways, but that the physiological integrity of these cell types cannot necessarily be predicted in conformity to their morphological stereotype. In other words, neurite architecture is, without question, dynamically maintained and amenable to environmental influences; but structure–function correlates are far from black-and-white.

One of the most captivating features of neurons is their longevity. Whereas the lifespan of most other animal cells is just a fraction of that of the animal itself, neurons an endure entire lifetime. With very few exceptions, the neurons that compose the brain of a 100-year-old human are the same neurons present at birth. This incredible continuity has been one of the most perplexing marvels of modern science and philosophy. How does a neuron undergo decades of protein turnover, tolerate years of repeated perturbation, and continuously modulate its own network dynamics, all while preserving the ‘essence’ of its biological duty? The ability to quantitatively compare neuron morphologies across different animals has enormous implications for studying this mystery and related topics in developmental neurobiology. Questions of how and why a neuron assumes its shape—as well as how and why it modifies that shape over time— became approachable.

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The 1990s was a burgeoning decade for the field of developmental neuromorphology. In

1992, Tang et al. studied the impact of polysialic acid (PSA) on neuromorphogenesis. Polysialic acid is a strongly anionic posttranslational modifier of neural cell adhesion molecules (NCAMs), which are glycoproteins that have long been implicated in cell–cell adhesion and synaptic plasticity, among other biological processes (Cunningham et al., 1987). In the chicken, PSA is first expressed by motoneurons when their growth cones (budding neurites first described by Ramón y

Cajal) segregate into subtype-specific groups within the plexus region (Tang et al., 1992). The degree of PSA expression was also noted to vary by the cell’s projection targets, suggesting that

PSA may have relevance to the determination of a neuron’s identity. By injecting endoneuraminidase in ovo, Tang et al. demonstrated that PSA could be removed at various gestational stages. They observed that, when PSA was eliminated during the stage of growth cone segregation, errors in axon directionality were common (i.e., the cell developed projections to loci not normally seen). When PSA was removed at later stages (e.g., during the formation of muscle nerves), no changes in axon directionality were observed. In this case, precise tracking of neuronal projections facilitated the identification of a salient biochemical mechanism—just another example of how morphological analysis can be a useful diagnostic tool even when the morphology itself is not the focus of the investigation.

Another major 1990s advancement in neuromorphogenesis was a better understanding of the role of chemotropic gradients in neurite pathfinding and whole-cell migration. Cerebral neuronal migration is the process by which newborn neurons travel through the ganglionic eminence and into their predisposed cortical layer. The reliable transport of developing neurons through cortical tissue has long been known to be assisted by radial glial cells—progenitors whose radial fibers make up a scaffold through which newborn neurons climb (Sidman & Rakic, 1973).

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Glial scaffolding has been modeled by micropatterned laminin surfaces. For instance, in 1993,

Clark et al. composed micropatterned laminin tracks of various widths onto which embryonic cerebral chick neurons were cultured (Clark et al., 1993). They observed that increasing the spacing between the adhesive tracks (on a scale from 4 μm to 50 μm) resulted in greater alignment of neurite outgrowth, whereas short spacing (4 μm) or no spacing (planar control) resulted in neurite alignment that was statistically comparable to chance. Furthermore, it was noted that cultured neonatal murine neurons from the dorsal root ganglion exhibited differences in local neuritic architecture depending on its growth substrate. When cultured on planar (control) substrata, these cells were multipolar and highly branched; but when cultured on 25 μm laminin tracks, they were usually bipolar with reduced or absent neurite branching. These trials helped the field appreciate just how fragile single-neuron development is, and how their complex morphogeneses depend heavily on their microenvironment.

Strangely, just as a neuron’s development is shaped by its microenvironment, so too is it shaped by forces in its “macro-environment”—even gravity. Indeed, the interest in this topic has been popular for many years, and academic publications on the so-called topic of “gravitational neuromorphology” have existed as early as 1994 (Krasnov, 1994). More recent research has even indicated that gravitational perturbations can drastically alter neuron morphology by disorganizing motifs of microfilaments (F-actin) and intermediate filaments and disrupting the radial orientation of microtubules (α-tubulin) (Uva et al., 2002). Whole-cell three-dimensional reconstructions have even been performed on gravitationally-perturbed murine neurons and have revealed that growth under increased gravity results in an enlargement of gross morphometrics (e.g., area of soma, area of dendritic arbor, length of neurites) but a decrease in cellular density per square centimeter (Pani et al., 2013). These experiments may be bizarre or of little practical significance for now (at least

12 for Earth dwellers), but they exemplify the fact that a neuron’s morphology can be influenced by many environmental factors, none of which should be underestimated before being studied.

The quantitative appreciation of neuron geometry in three-dimensional space also advanced the study of how neuromorphology is shaped by processes of aging. Conventional wisdom has long held that gradual cognitive decline in the late stages of life is normal; and this belief has been largely reinforced by modern techniques of morphometry, which have repeatedly demonstrated significant linear reductions in global grey matter volume as a function of age (Good et al., 2001). Some, however, have argued that reductions in global grey matter volume are not indicative of changes to underlying circuit function. For example, a study in 1997 showed that, among a group of twenty-six neurologically healthy people aged 14–106, measurements of dendritic spine density stabilized around the age of 40 years (Jacobs et al., 1997). These results did show a reduction in dendritic spine density of nearly 50% between those aged < 50 years and those aged > 50 years; but because this ostensibly linear trend was not continued through all ages, the paper challenged the notion that micromorphological degeneration after age 40 is ‘normal’ or healthy. On an optimistic note, this suggests that the neuropsychiatric decline that is simply accepted as ‘normal aging’ may in fact be a preventable aberration.

In short, the last third of the Twentieth Century saw many groundbreaking advances in neuroscience, and some of this progress is owed to the development of digital cellular reconstruction and numeric analysis. Throughout history, multiple different imaging techniques

(e.g., electron microscopy [EM], confocal laser scanning microscopy [CLSM], or even nuclear magnetic resonance [NMR]) and multiple different tracers (e.g., HRP, lectins, neurotrophins, neurotoxins, and—more recently—carbocyanine dyes, latex microspheres, and viruses) have been applied to the high-resolution visualization of neurons (Dauguet et al., 2007). Each of these

13 methods has identifiable strengths and weaknesses in terms of the facility with which they can deliver the contradictory combination of high magnification with high resolution (Halavi et al.,

2012). For example, diffusion tensor imaging (DTI) is a powerful tool in the field of tractography, or the tracing of neural pathways at the level of cellular populations; however, it is not helpful in the reconstruction of single neurons (Ropireddy & Ascoli, 2011). Similarly, electron microscopy

(EM) is so powerful that it can easily resolve all individual synapses but is constrained by a smaller field-of-view and longer processing times. Of the imaging techniques available, confocal laser scanning microscopy (CLSM) is arguably the easiest method for manual digital reconstruction in three dimensions (Schmitt et al., 2004). Though complete 3D reconstructions of neurons have been achieved using other techniques, CLSM is the most commonly-used method because of the ease with which it can filter background signal and serially scan through many (e.g., >100) “z-slices,” or thin (i.e., < 1 μm) cross-sections that are later digitally stitched and cubed into a cohesive three- dimensional interface.

Though CLSM and other imaging techniques have made it easy to visualize entire neurons as three-dimensional units, the process of manual reconstruction that follows is much more tedious.

Once confocal image stacks have been stitched and cubed, users can rapidly scroll through the z- axis, adjust magnification, and faithfully track the serpentine trajectories of individual neurites.

This ability to seamlessly move around the neuropil in three dimensions also presents the opportunity to manually trace cellular structures. When preparing whole-cell reconstructions, tracing is generally initiated at the soma and continued, point by point, down its projection(s).

These points, or ‘nodes,’ are marked along the cable, such that the chosen distance between any two contiguous nodes is sufficiently small to convey the winding directionality, or tortuosity, of

14 the process. Completely tracing each and every observable neuronal process renders a digital

‘skeleton’ of the neuron from which a wealth of quantitative data may be gleaned (Fig. 2).

Figure 2. This complete skeletonization of a gastric mill (GM) neuron from a C. borealis STG was obtained using KNOSSOS, an open-source, three-dimensional tracing program developed at the Max Planck Institute for Medical Research (Kornfeld et al., 2016). The soma is indicated by the large blue sphere in the upper-right, while each of the smaller blue nodes indicate branch points. (Stenerson et al., 2016)

Basic geometrics such as individual length, area, or even volume are not the only measurements which can be taken from skeletons; the availability of the entire neuron for statistical analysis allows for the measure of tortuosity (degree of indirectness), total cable length or volume, cable taper, branching patterns (e.g., total number of branches, distance between branches, branch angles, branch densities, etc.), space-filling patterns, etc. For an entire neuron to be prepared for these analyses, as many as 100,000 or more ‘nodes’ must be marked for every neuron (Stenerson

& Marder, 2017). Thus, the process is highly time-consuming and is not conducive to high- throughput analysis. This significant time commitment severely restricts any individual laboratory’s ability to produce reconstructive morphological data. As a result, a global online

15 repository, known as NeuroMorpho.Org, was established in 2006 for the centralization of neuronal reconstructions from all studied species in labs all over the world. In its twelve years of existence, this project has collected over 100,000 digital reconstructions from nearly 500 laboratories (Ascoli et al., 2007; George Mason University, 2018). Like the Human Genome Project, this organization addresses neuromorphological questions that perhaps only worldwide data integration can answer.

Section IV: Computational modeling

Computational modeling has greatly propelled the field of neuroscience by relating theoretical formalism to real biological systems. The complete digital reconstructions of individual neurons have powerfully informed the development of realistic neuron models. For example, the simulation framework known as NETMORPH was introduced in 2009 for the generation of biologically representative three-dimensional neurons and neural networks (Koene et al., 2009). Models such as these uniquely allow one to test the theoretical consequences of a morphological perturbation on the activity of a cell or network. These highly efficient and relatively inexpensive computational assays are invaluable, because they have the potential of greatly expediting otherwise time-consuming projects and can serve as a guide to identifying the morphological parameters required of neuronal or network function. They are also useful complements to connectomics, or the discipline concerned with elucidating the full connectivity diagram of neural networks (Schneider-Mizell et al., 2016).

Another computational application of reconstructive neuromorphology is the study of wiring optimization—that is, the dynamics that influence how a neuron develops its projections.

The topic of wiring optimization is at least as old as Ramón y Cajal, who famously hypothesized that a neuron’s structure is constrained by three basic factors: space, material, and time. The extent to which each of these three factors shapes neuron morphology remains incompletely understood;

16 but computational models have simplified the process of studying them. As an example, in 2006,

Chen et al. used optimization models to predict the layout of 279 nonpharyngeal neurons within

C. elegans. Their model, which was based on the simple premise that neurons arrange themselves to minimize wiring cost (i.e., the total investment of material resources required for optimal functioning), was shown to predict in vivo neuron placement with high accuracy (i.e., within a deviation rate of approximately 10%) (Chen et al., 2006). This report was an indication that wiring cost may have higher priority in the determination of neuron morphology than the cost of space- filling or conduction time.

As the geometric models of computational neuroscientists became more successful, the claims regarding their implications became more audacious. In 2010, Cuntz et al. published a paper entitled ‘One Rule to Grow Them All’—a reflection of their own confidence. In their paper, Cuntz et al. set out to build upon Ramón y Cajal’s laws of optimization by mathematically describing the relative importance of the ‘material’ law (i.e., axoplasmic investment) and the ‘time’ law (i.e. rate of neurotransmission). They proposed a so-called ‘balancing factor’ (variable, ranging from 0 to

1) that they believed integrated and weighed these variables as they are typically weighed in nature

(ref. Equation 9). The fruit of their labor was a mathematical framework that was ostensibly applicable to any kind of neuron. This framework was also used to artificially generate neurons whose branching properties reflected those of real neurons.

(Total cost) = (wiring cost) + (푏푓 × (path length cost))

Equation 9. Cuntz et al. (2010) proposed a balancing factor (bf), ranging from 0–1, which can variably minimize the impact of the path length cost relative to the wiring cost. The wiring cost is proportional to Ramón y Cajal’s law of optimization concerned with resources, or axoplasmic investment. The path length cost is proportional to Ramón y Cajal’s law of optimization concerned with conduction time, or the rate of neurotransmission.

17

In the summer of 2016, we applied the framework devised by Cuntz et al. to two neuronal subtypes (gastric mill [GM] and lateral gastric [LG]) of the stomatogastric ganglion of the crab, C. borealis. Confocal microscopy was used to manually reconstruct one of each cell types in their entireties, and their skeletons were used to generate distributions of branch order (i.e., the nth furcation from the soma) and path length. Then, the optimization strategy of Cuntz et al. was adopted and used for the generation of artificial GM and LG cells with various balancing factors

(0.1, 0.3, 0.5, 0.7, and 0.9). Distributions of branch order and path length were also performed for these artificially-generated neurons. Comparisons between the artificial and real neurons failed to demonstrate a reliable relationship (Stenerson et al., 2016). Branch order was grossly misrepresented for LG cells—and path length was grossly misrepresented for GM cells— regardless of which balancing factor was used. The comparison of this computational model with neurons from a real biological system was an intended litmus test for the model’s generality, and the results challenged the authors’ claims of truly finding one rule to grow them all.

Similar computational models have been devised that prioritize various morphological facets. Kim et al. in 2014 proposed a model for optimization according to the neurite terminals’ distance-from-soma; and similarly, Anton-Sanchez et al. in 2016 proposed another model based on terminals’ Euclidian distance-from-soma, but one that preserved the branching patterns observed in vivo (Cuntz et al., 2012; Kim et al., 2014; Anton-Sanchez et al., 2016). Each of these models, although useful, has been imperfect. Collectively, their reliability suggests that neuron morphology is indeed influenced by space, resources, and temporal efficiency, but that any weighted combination of these three features is insufficient at capturing the totality of a neuron’s development. Of course, in reality, the structural fate of a developing neuron is determined by

18 innumerable environmental variables. It is also intuitive to assume that at least some portion of a neuron’s morphology is stochastic, although the extent to which this is true remains unclear.

Section V: Multi-cell reconstruction and synaptic mapping

The next obvious stepping stone along the path of reconstructive neuromorphology is the three-dimensional analysis of multiple neurons in relation to one another. The identification of a synapse has long been possible, and even basic light microscopy has the power to resolve single synapses or multiple neighboring synapses. However, the complete indexing of all synaptic loci in a given neuron remains an experimental challenge. Though immunohistochemical methods can readily stain for synapses, the quantification or precise spatial pinpointing of those synapses is obfuscated by the sheer concentration of synapses per unit of membrane area—a property that often results in high-intensity fluorescence that is chiefly useful for relative comparisons.

The practice of performing double-dye-fills of two or more neurons with known synaptic coupling was attempted as early as the 1960s. A double-dye-fill experiment involving an inhibitory motor interneuron and an excitatory motor neuron in the leech, H. medicinalis, was reported in 1985 (Granzow et al., 1985). Their results showed that varicosities along the inhibitory interneuron appeared to be intentionally concentrated around processes of the excitatory motor neuron. They were able to identify close appositions between the two cells but were not able to quantify them. Fifteen years later, in 2000, Cabirol-Pol et al. attempted a similar double-dye-fill involving two neurons (lateral pyloric [LP] and pyloric dilator [PD]) from the stomatogastric ganglion of the lobster, H. gammarus. They first performed confocal laser scanning microscopy in order to identify candidate synaptic regions within the neuropil, followed by electron microscopy of those regions to identify close appositions. This technique, although inventive, only revealed 3 candidate synapse sites between the two cells—obviously much fewer than what

19 is expected between the two. Cabirol-Pol et al. suggested that electron microscopy may not be ideal for this kind of analysis because spatially small appositions between the two cells does not necessarily indicate synapse sites. While this is true, another more technical issue is the inability to standardize what is defined as ‘close.’ Reconstructive quantitative neuromorphology of two synaptically-connected neurons in tandem creates the opportunity to set and modify such definitions. More importantly, they once again have the potential of characterizing entire cells or groups of cells, without which any representation of a neuron’s synaptic web would be incomplete.

Section VI: The stomatogastric nervous system

The stomatogastric nervous system (STNS) of the decapod crustacean has long been a fruitful experimental model for small rhythmic motor circuits. This nervous system is responsible for two electrophysiologically distinguishable rhythms: the pyloric rhythm, which innervates muscles involved in filtering, and the gastric mill rhythm, which innervates muscles involved in intragastric mastication (Marder et al., 2015). In crabs, the stomatogastric ganglion (STG) is the most well-studied component of the STNS and is typically composed of around twenty-six neurons in the Jonah crab, Cancer borealis, or around thirty neurons in the American lobster, Homarus americanus, which have been subtyped by their electrophysiological signatures (Kilman &

Marder, 1996; Otopalik et al., 2019) (ref. Figs. 3, 7). Elucidation of the number of neurons composing the STG, as well as their gross ultrastructural arrangement within the ganglion, was aided by immunoreactivity studies focusing on a variety of biomolecules, including peptide modulators, octopamine, serotonin, and gamma-aminobutyric acid (GABA) (Christie, 1995;

Kilman & Marder, 1996; Christie et al., 1997; Fénelon et al., 1999; Heinrich et al., 2000). Once cell body counts were obtained, the determination of a putative connectome was gradually made

20 possible by a long series of electrophysiological experiments (Marder, 2012; Bargmann & Marder,

2013; Goeritz et al., 2013; Swallie et al., 2015).

Figure 3. The neuronal subtypes that compose the stomatogastric ganglion of the Jonah crab, Cancer borealis, have been putatively arranged in a connectivity diagram. The region highlighted in the upper-left comprises the pacemaker kernel, which consists of one anterior burster (AB) neuron and two pyloric dilator (PD) neurons. The other subtypes include: lateral posterior gastric (LPG, quantity ≈ 2), lateral pyloric (LP, quantity ≈ 1), inferior cardiac (IC, quantity ≈ 1), lateral gastric (LG, quantity ≈ 1), medial gastric (MG, quantity ≈ 1), gastric mill (GM, quantity ≈ 4), pyloric (PY, quantity ≈ 5), ventricular dilator (VD, quantity ≈ 1), interneuron 1 (Int1, quantity ≈ 1), anterior median (AM, quantity ≈ 1), and dorsal gastric (DG, quantity ≈ 1). (Gray circles: inhibitory chemical synapses; black resistors: electrical synapses). (Otopalik et al., 2019)

The identification of electrophysiologically distinctive STG cell types set the foundations for more accurate morphological comparisons. For example, in 2005, Bucher et al. compared the gross morphological features of PD neurons from ninety-nine adult and twelve juvenile American lobsters (H. americanus), which had been prepared using confocal microscopy of dye-fills.

Qualitative differences in size were noted, which were approximately proportional to the age- related changes in the size of the entire animal (Bucher et al., 2005). Discriminating age-related nuances within global morphological features was not possible because three-dimensional reconstructions were not prepared; however, the general appearance of the dendritic arbor and neuritic varicosities were similar between the two age groups. A more complete morphological report was made available by Bucher et al. in 2007, once high-resolution confocal images were

21 attained for each of the thirteen STG subtypes (Figs. 4A,B). At the same time, quantitative analysis revealed that branching patterns were largely nondichotomous across all cell types, with up to a twentyfold change in axonal diameter at branch points (Bucher et al., 2007). More descriptive accounts of STG neuronal branching strategies were published by Goeritz et al. in 2013, whose data exposed tremendous variability within branch order and length across subtypes (Goeritz et al., 2013).

Later, full three-dimensional reconstructions were manually obtained from confocal image stacks of STG dye-fills. Comparisons between two genera (The Jonah crab, Cancer borealis, and the American lobster, Homarus americanus), two age groups (juvenile and adult), and four cellular subtypes (LG, LP, PD, PY) were made, and each skeleton was used to quantify the total number of branches, distributions of branch order, volume of the neuropil, whole-cell tortuosity, and other morphometrics (ref. Equation 10). Results showed that total branching, branch order, and tortuosity did not differ significantly between the two age groups; however, neuropilar volume did differ significantly, with adult PD neuropils occupying about three times the volume of juveniles

(p < 0.01) (Stenerson & Marder, 2017). Comparisons between the two genera failed to reveal any significant differences within the same parameters; however, all STG neuronal subtypes from

Homarus americanus have been repeatedly observed to have a qualitatively outstretched appearance in comparison to Cancer borealis, whose neuropils tend to be more circular in comparison.

path length 휏 = (∑ ) ∙ 푛−1 Euclidean distance Equation 10. Tortuosity (휏) is a global measure of wiring ‘indirectness.’ It is calculated by summing the ratio of path length to the Euclidean distance for each branch in the entire neuron, and then dividing by the total number of branches (n).

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(A)

Figure 4A. Confocal laser scanning microscopy was used to develop these maximum z-projections from dye-fills of stomatogastric ganglionic neurons (anterior burster [AB], pyloric dilator [PD], lateral pyloric [LP], pyloric [PY], ventricular dilator [VD], and gastric mill [GM]) in the adult American lobster, Homarus americanus. Scale bar = 100 μm. (Bucher et al., 2007)

23

(B)

Figure 4B. Confocal laser scanning microscopy-rendered maximum z-projections of various STG neuron dye-fills (lateral gastric [LG], medial gastric [MG], gastric mill [GM], interneuron-1 [Int1], dorsal gastric [DG], and lateral posterior gastric [LPG]) in the adult American lobster, Homarus americanus. Scale bar = 100 μm. (Bucher et al., 2007)

24

Among Cancer borealis STG neurons, total branching and tortuosity did not significantly differ between cell types. In general, quantitative analysis from these manual reconstructions has emphasized an overwhelming degree of variability in morphology—between animals as well as between neurons from the same animal (Bucher et al., 2005; Otopalik, 2017; Otopalik et al., 2017a;

Otopalik et al., 2017b; Otopalik & Marder, 2019). Nevertheless, it is possible that salient differences will become clearer as more reconstructions become available.

Ongoing studies of STG neuronal morphology have now begun focusing on the task of mapping candidate synapse sites from double-dye-fills. Couplets of PD and LP neurons, which participate in the same rhythmic circuit, have been prepared and await quantitative analysis.

Among the most pressing questions pertaining to these ongoing experiments is how well two- neuron digital reconstructions can identify candidate synapses simply by calculating the distance between nodes on each skeleton and setting a space threshold (e.g., < 5 μm). Earlier work, which combined confocal and electron microscopy to assess appositions between LP–PD double-dye- fills, was unable to generate a considerable list of candidate synapses sites; however, full manual reconstructions were not completed (Cabirol-Pol et al., 2000). The presumed benefits of the ongoing efforts to produce dual-cell skeletonizations include greater control in selecting for apposition space and the simple totality of quantitative analysis. Assuming dual reconstructions can produce a list of close intercellular appositions, these data may be useful in assessing the commonality of close intercellular appositions, the proportion of close appositions which are truly synaptic (a question that may be answered in part by immunohistochemical staining of synaptic markers), and spatiotemporal trends in synaptic density.

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METHODS

Section I: Dissection of the stomatogastric nervous system

Cancer borealis (35 adults) and Homarus americanus (5 adults and 5 juveniles) specimens were sourced from Commercial Lobster (Boston, MA) at various times of the year. The animals, which were all male, were kept in recirculating artificial seawater tanks, which were maintained at approximately 10–13 ˚C, pH 7.4–8.3, dissolved oxygen (DO) ≈ 6–7 mg/L and run on a 12-hr. light–12-hr. dark cycle. The animals were not fed. Prior to dissection of the stomatogastric nervous system (STNS), the crustaceans were anesthetized in ice for > 30 minutes. Removal of the intact nervous system and de-sheathing of the membrane surrounding the stomatogastric ganglion (STG) was performed as previously described (Gutierrez & Grashow, 2009). Dissections were performed at room temperature, but the tissues were submersed in physiological saline

+ − + − 2+ − 2+ − ([Na Cl ] ≈ 440 mM; [K Cl ] ≈ 11 mM; [Mg Cl2 ] ≈ 13 mM; [Ca Cl2 ] ≈ 11 mM;

[tris(hydroxymethyl) aminomethane] ≈ 5 mM; [maleic acid] ≈ 5 mM, pH 7.4–7.5), which was chilled to approximately 1.5 ˚C and replenished approximately every 30 minutes. Each of the dissections necessarily contained the following intact anatomical features: two bilateral commissural ganglia (CoG), each projecting medially via right and left superior oesophageal nerves (son) into one oesophageal ganglion (OG); a stomatogastric nerve (stn) ramifying inferiorly into a stomatogastric ganglion (STG); and at least one of each of the following nerves respectively downstream of the STG: a medial ventricular nerve (mvn), a dorsal gastric nerve (dgn), a dorsal ventricular nerve (dvn), and a lateral ventricular nerve (lvn) (ref. Figs. 5–6).

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(A) (B)

Figure 5. Schematics of the stomatogastric nervous system (STNS). (A) Detailed diagram of the STNS in Cancer borealis. Ganglia are illustrated with yellow spots and denoted by uppercase letters; nerves are denoted by lowercase letters; encircled are the neuronal subtypes with projections found in the designated nerve. (Brandeis University, 2019) (B) A simplified diagram of the STNS in Homarus americanus demonstrates highly-conserved anatomy between the two species. Ganglia are once again denoted by uppercase letters, while nerves are denoted by lowercase letters. (Dickinson et al., 2015)

Figure 6. Procedural schematic before morphology analysis. (Adapted from Otopalik et al., 2017a) 27

Upon completion of the STNS dissection, the preparations were pinned into custom-made,

SYLGARD™-coated (approximately 10 mL) petri dishes, which were continuously superfused with physiological saline. Electrophysiological identification of STG subtypes and intracellular dye injections were completed no longer than 24 hours after the start of the experiment.

Section II: Electrophysiological subtyping of STG neurons

+ − De-sheathed STG somata were impaled with glass microelectrodes (12–40 MΩ; [K SO4 ]

≈ 600 mM; [K+Cl−] ≈ 20 mM) which were amplified by 1 × HS headstages and Axoclamp™

2A/2B amplifiers (Molecular Devices™, San Jose, CA; Axon Instruments, Foster City, CA), as described (Otopalik et al., 2017a). Wells composed of petroleum jelly were created around the major inferior nerves (mvn, dgn, dvn, and lvn), and stainless-steel electrodes were used to monitor extracellular activity at each of these wells. STG cellular subtypes were unambiguously identified by relating intracellular activity at somata with extracellular activity at axons—e.g., GM with dgn,

LG with lgn, and LP/PD with lvn (Fig. 7). Once subtyped, the locations and identities of the somata were carefully recorded for future reference during intracellular dye-fills.

Section III: Neuron dye-fills, amplification, and immunohistochemistry

Electrophysiologically-identified somata were impaled with low-resistance glass electrodes (3–16 MΩ) which were backfilled with various intracellular dyes13—e.g., Alexa

Fluor™ 568 in 200 mM K+Cl− (Thermo Fisher Scientific™, Waltham, MA), 2% Lucifer Yellow

CH dipotassium salt (Sigma-Aldrich®, St. Louis, MO), calcium green™-1 AM (Thermo Fisher

Scientific™, Waltham, MA), neurobiotin tracer (Vector Laboratories, Inc., Burlingame, CA), etc.14 Somata were injected over the course of approximately 20–50 min. along with negative

13 For emissions spectra of the most commonly-used dyes in these experiments, ref. Appendix A. 14 For a complete catalog of all reconstructed cells’ identities, dye types, and microscope objectives, ref. Appendix B. 28

Figure 7. Intracellular and extracellular signatures of STG neurons. (A) An intracellular recording from a pyloric dilator (PD) neuron in frame with extracellular recordings from inferior motor nerves (pyn, pdn, and lvn) illustrates the triphasic nature of the pyloric rhythm. Synchronous intracellular and extracellular activities enable the unequivocal identification of PD, pyloric (PY), and lateral pyloric (LP) neuronal subtypes. (B) Similarly, intracellular recordings from lateral gastric (LG) and dorsal gastric (DG) neurons mirror extracellular recordings from the lgn and dgn, respectively. (Stein, 2017) pulses of between −3 and −7 nA over 0.5 sec. at 0.1 – 1 Hz, as described (Otopalik et al., 2017a).

Once a high standard of resolution was achieved within the fine neuronal processes, the dye-filled samples were promptly fixed with 3.5% paraformaldehyde in phosphate-buffered saline (PBS, pH

+ − + − + 2− + − 7.4) ([Na Cl ] ≈ 440 mM; [K Cl ] ≈ 11 mM; [Na2 HPO4 ] ≈ 10 mM; [K H2PO4 ] ≈ 10 mM) for 40–90 min. at room temperature. The samples were then washed multiple times (typically

29

thrice) with 0.01 M PBS-T (0.1–0.3% Triton™ X-100, Sigma-Aldrich®, St. Louis, MO, dissolved in PBS) and stored at 4 ˚C prior to amplification and immunohistochemistry.

The emission signals from the various dyes were then often amplified by the addition of antibodies—e.g., a polyclonal rabbit anti-Lucifer Yellow antibody (Molecular Probes™, Eugene,

OR) (1:500, 16 hr.). Secondary detection was carried out most commonly using Alexa Fluor™

488-conjugated goat anti-rabbit antibody (IgG H+L chains, highly cross-absorbed) (Molecular

Probes™, Eugene, OR) (1:500, 2 hr.). The samples were then washed three or four times with filtered PBS for 15 min. and mounted using pre-cleaned slides (25 × 75 × 1 mm, Superfrost™

Plus, VWR International, Radnor, PA) in VECTASHIELD® antifade mounting medium (Vector

Laboratories, Inc., Burlingame, CA) with 9 mm diameter, 0.12 mm depth silicone seal spacers

(Electron Microscopy Sciences, Hatfield, PA) under #1.5 (170 μm) coverslips (Thermo Fisher

Scientific™, Waltham, MA), as described (Otopalik et al., 2017a).

Various confocal laser scanning microscopes (CLSMs) were used by numerous individuals in the rendering of these 48 neurons, including: (1) an SP5 correlative light and electron microscope (CLEM) equipped with Leica™ Application Suite Advanced Fluorescence (LAS AF) software; (2) a Leica™ TCS SP5 confocal microscope; (3) a Leica SP2MP confocal microscope equipped with an infrared pulsed laser (Chameleon Ti:Sapphire, Coherent®, Santa Clara, CA); and

(4) a ZEISS LSM880 equipped with ZEISS ZEN acquisition software.15 Confocal images were acquired as multiple tiles (ranging in number from as few as four to as many as thirty), or “z- stacks,” in the x–y plane with various objective magnifications: 16 (33% of all reconstructions) using 20×, 2 (4%) using 40×, 7 (15%) using 50×, 20 (42%) using 63×, and 3 (6%) using 100× (ref.

Appendix B). Resolution was typically set at either 2048 × 2048 or 1024 × 1024. The width of the

15 Ref. Appendix B, which lists the microscope used (when known) for each of the 48 neurons. 30

z-steps varied from 0.083–1.091 μm. The complete voxel configurations for each of the reconstructed cells can be found in Appendix C. Overlap between z-stacks was typically equal to

10% (i.e., there was a 5% redundancy around contiguous z-stack margins) (Fig. 8A).

Section IV: Confocal microscopy and image processing The variable number of z-stacks were then stitched using the pairwise stitching plugin of

ImageJ, which was developed in 2009 by biologists at the Max Planck Institute of Molecular Cell

Biology and Genetics in Dresden, Germany (Preibisch et al., 2009). This proved an onerous computing task that necessitated powerful operating systems. The z-stacks were typically generated in a “snaking” fashion, as illustrated in Fig. 8. Although successive pairwise stitching beginning and ending with the first and last z-stack was sometimes successful, the compounding size of the stitched image files often exceeded the computing capacity. Furthermore, the computational processing within the pairwise stitching module appeared to be prone to errors caused from large proportions of empty space within the field of vision (such as tile #12 in Fig. 8).

This meant that distal z-stacks

containing little of the resolved

neuropil often failed to sequentially

stitch. The simplest solution to the

constraint of computing capacity was to

stitch z-stacks into individual rows or

columns, save those rows as separate z-

stacks, and then stitch the rows

Figure 8. Schematic of a hypothetical 4 × 3 tile vertically (or the columns horizontally) configuration with snaking progression and standard 10% overlap. Red numbers and arrows (Fig. 9). indicate order of tile generation and successive pairwise stitching. Dye-fill credit: Adam Taylor

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Figure 9. For data sets that exceed available computing capacity, a “stitch-by-rows” or “stitch-by-columns” method may be used. In this hypothetical example, z-stacks 1–4, 5–8, and 9–12 were individually stitched into rows and then saved as new image sequences.

Vertical pairwise stitching of the rows (as shown), or horizontal pairwise stitching of the columns, then completes the process.

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Figure 10. When computational errors arise due to a preponderance of negative space within any z-stack (such as the two above denoted by the ☆ symbols), a more meticulous approach can be taken. This involves manually cropping each contiguous z-stack by one–half of its overlap (in this example, 5%), and then using a “stack combination” feature in ImageJ.

However, the only solution to the computational errors caused by empty space was to manually crop each of the contiguous z-stacks by one–half its overlap, and then use the “combine stacks” tool in ImageJ, which is analogous to copying and pasting tiles onto one another as opposed to stitching, which computationally resolves the overlap and would correct for any frameshift incontinuities (Fig. 10). Despite the variation in stitching requirements from one reconstruction to another, all three of these stitching methods led to the same product: a new image sequence containing all tiles (in other words, an inclusive z-stack). Completely-stitched file sets were then visually sharpened using ImageJ’s image adjustment plugins. The color balancing feature was consistently the most helpful in resolving fine processes in both channels. Once adjusted, maximum-intensity z-projections were produced for illustrative purposes. Finally, once stitching was complete, a “cubing” step was necessary before the image stacks could be interpreted by

KNOSSOS.

Section V: Manual reconstruction

Once the data set was stitched, optimized, and cubed, it could be imported into KNOSSOS, an open-source, three-dimensional visualization and annotation program developed at the Max

Planck Institute for Medical Research in Heidelberg, Germany. Annotations were started, with the first point (node) traced being that of the soma. Subsequent nodes were placed in the centermost positions of the cable and were spaced semi-uniformly (Fig. 11). Every branch point—i.e., node attached to more than two other nodes—was marked accordingly and illustrated by blue nodes.

The 48 reconstructions were performed over several months by a team of tracers. Some degree of stylistic variation was observed between tracers and was a recognized challenge throughout the tracing process. Consistency in training and meticulous records of tracing progress helped to limit and monitor this variability. Of the 48 reconstructions, 31 (65%) were completed entirely by me,

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Figure 11. Manual tracing process in KNOSSOS (same cell in each of the three images). Left: the large blue sphere represents the soma and node #1. Middle: a high-density skeletonization (containing > 70,000 nodes) illustrating the shortness of segments within a given z-slice. Right: a two-dimensional collapsed rendering of the completed skeletonization showing the vast density of the neuropil. A 100× microscope objective was used. Dye-fill credit: Marie Goeritz while the remaining 17 (35%) were completed by a cohort of seven (ref. Appendix D). In 2018, it was discovered that several of the reconstructions contained breaks in their skeletons, which were distorting the data extracted from it. All these breaks were anastomosed, and data analyses were redone on all affected data sets. It is important to note that the data presented here differ— albeit not meaningfully—from the data published in Otopalik et al., 2017a,b.

Section VI: Post-reconstruction analysis

Once the tracing process was complete, the annotation was exported as an .xml file of edges and nodes and were then adapted into .hoc (extendable high-order calculator) files using a customized Python conversion program available at: https://github.com/marderlab/

Quantifying_Morphology. Many of the quantitative analysis programs—such as the generation of radial dendrograms, Sholl analysis, spatial heatmaps of neurite density, and distributions of branch

34

order—were developed by Dr. Alex Sutton (currently employed at UTC Aerospace Systems) and

Dr. Ted Brookings (currently employed at the Broad Institute), which are also available for download via the Marder Lab GitHub. Branch angle and Rall power were computed using

Equations 11 and 12, respectively.

2 2 2 −1 푃mid − 푃1 − 푃2 휃mid = cos ( ) 2 × 푃1 × 푃2

Equation 11. The endpoints of each segment contributing to a furcation (branch) were collected into groups containing a midpoint (푃mid, which is the proximal endpoint of the parent and daughter) and the distal endpoints of the parent (푃1) and daughter (푃2). In the event of a multi- furcation (i.e., one branch point directly connected to > 4 other nodes), the procedure was repeated for all possible combinations of contributing segments. Triangulation then allowed for the computation of 휃mid as defined above. Angles were reported in degrees and expressed as 180 ˚ − 휃mid, as described (Otopalik et al., 2017a).

푋 푋 푋 parent = daughter1 + daughter2

Equation 12. Rall power was calculated using the originally-devised 1959 formula, wherein parent푋 refers to the radius of the parent branch and daughter푋 refers to the radius of the daughter neurites. Rall power values in neurons have been previously reported in the range of approximately 1.5 to 3 (Rall, 1959; Chklovskii & Stepanyants, 2003).

Sholl analysis is a spatial density metric that superimposes concentric spheres originating from the soma and then quantifies the number of intersections made between neurites at each sphere. Standard Sholl analysis assumes a centric origin; but in the crustacean STG, the soma is not always oriented near the center, nor do ramifications always occur radially. This metric was therefore of limited value to these reconstructions. As such, equivalent somatofugal Sholl distances were calculated by establishing linearly-spaced distances ranging from zero to the maximal path length. Each pair of nodes was then assessed for whether the traversing line crossed said distance, as described (Otopalik et al., 2017a).

Some morphometrics were obtained by manual measurement. For example, neurite diameter was evaluated as a function of branch order (i.e., the nth number of branches a given

35

node is from the soma) by randomly sampling 25 nodes of each branch order ranging from 2–5.

These randomly-selected nodes were then identified in KNOSSOS and their respective cable diameters were manually assessed in six neurons (three adult C. borealis PDs and three adult C. borealis LPs).

To better gauge taxonomic differences in neuropilar space occupation—i.e., the volume of space occupied by a preponderance of neurites—a custom volume analysis program was developed in MATLAB (MathWorks®, Natick, MA). This program algorithmically identifies a group of distal nodes (variable in number) which encapsulates, with maximum precision, 95% of all nodes. It effectively outlines the bulk three-dimensional space of its neuropil while eliminating distal axons and diffuse arborizations (Fig. 12). These boundaries are then used to calculate the volume occupied by 95% of the neuropil.

Figure 12. A custom analysis of the volume occupied by 95% of the neuropil generates these unique polyhedra with a variable number of faces. Volume was estimated using Equation 13. Axes (x, y, z) represent distance in μm.

푛 1 1 푛−1 1 푛 1 푉푛(푃) = (−1) ∑ ( ∑ 푣푖 ) × det ( ⋯ ) 푛 (푛 − 1)! 푛 푛 휎 ∈ 푇 푖=1 푣̂푖 푣̂푛

Equation 13. Triangulation-based estimation of the volume (푉푛) of a polyhedron (푃) wherein 푣푖s are the ordered vertices of the (푛 − 1)-simple (휎), ordered according to the orientation of 휎; thus 푛 푛 푛−1 푣푖 is the nth coordinate of 푣푖 and 푣̂푖 is the projection of 푣푖 into the convex polyhedral (푹 ), obtained by deleting the nth coordinate from 푣푖, as described (Allgower & Schmidt, 1986).

36

RESULTS

Section I: Macroscopic features

Forty-eight neurons in total were completely reconstructed and quantitatively assayed. This cohort consisted of two genera, two developmental stages, and five STG cell types (ref. Table 1).

Each of the 26–27 neurons of the stomatogastric ganglion in both Cancer borealis and Homarus americanus were invariably characterized by a N Values of Reconstruction Identities Genus Age Cell Type singular primary projection from its soma, which Adult AB (1) Homarus (5) PD (4) americanus can exceed 25 μm in diameter along the initial Juvenile LP (1) (10) (5) PD (4) 200+ μm of cable and ultimately innervates GM (19) Cancer Adult LG (4) specific stomach muscles or anterior ganglia. borealis (38) LP (7) (38) Additionally, this primary projection often, but not PD (8) always, ramified into one or multiple distinctive Table 1. N values among all reconstructed neurons are given in parentheses for each “distal projections.” These “distal projections” of the possible identities. were easily distinguished, since they exceeded the field-of-view of the microscope and had no branches in their outermost 300 µm of cable. These projections have previously been referred to as axons; however, this terminology has contradicted the expectation of just one axon existing in each neuron (Otopalik et al., 2017a). Since it was not possible to confirm these features as axons, they were defined more ambiguously as “distal projections.” Across all 48 reconstructions, the number of “distal projections” per neuron ranged from 1 to 20, with a mean ± SD of 6.5 ± 4.3 and a median of 6. Distributions of projection number did not significantly differ between genera,

37

t(46) = 0.5161, p = 0.6083, or developmental stage, t(8) = 0.2969, p = 0.7741 and t(6) = 0.5333, p

= 0.6130 when adjusted for PD cells only (Fig. 13). However, a one-way analysis of variance

(ANOVA) found very significant (**) differences in mean number of distal projections across four

Cancer borealis neuronal subtypes, F(37) = 11.3995, p = 0.0001, with LG neurons having significantly more than PD and LP (Fig. 14).

per Neuron per

Number of Distal Projections Distal of Number

Figure 13. The variable number of distal projections per neuron did not significantly differ when compared across (A) genera or (B,C) developmental stage. (A) All ten reconstructions from Homarus americanus and all thirty-eight reconstructions from Cancer borealis were sampled. (B) N = 5 adults and 5 juveniles. (C) N = 4 adult PD and 4 juvenile PD. (Error bars = ± standard deviation)

38

(A) (B)

per Neuron per per Neuron per

Number of Distal Projections Distal of Number Number of Distal Projections Distal of Number

Figure 14. (A) Lateral gastric (LG) neurons had significantly more distal projections on average than pyloric dilator (PD) or lateral pyloric (LP) neurons. NPD = 8, NLG = 4, NGM = 19, NLP =7. (B) Juvenile lateral pyloric (LP, N = 1) and adult anterior burster (AB, N = 1) are compared with other STG subtypes from H. americanus. (Error bars = ± standard deviation

Measurements of the carapace were made in eight of the ten H. americanus specimens used for reconstructions (N = 4 juvenile PDs and 4 adult PDs). Juvenile cephalothoraxes were, on average, 10.2 ± 1.8 μm × 16.8 ± 3.0 μm, while juvenile abdomens were, on average, 9.4 ± 1.7 μm × 22.8 ± 5.5 μm (width × length, mean ± standard deviation). In comparison, adult cephalothoraxes were, on average, 44.9 ± 7.7 μm × 83.8 ± 14.6

μm, while adult abdomens were, on average, 39.6 ± 7.5 μm × Figure 15. Schematic of 111.7 ± 17.0 μm (width × length, mean ± standard deviation). Not carapace dimensions in H. americanus juveniles and surprisingly, these dimensions differ significantly (p < 0.05 for adults, scaled to measure- both cephalothorax-based and abdomen-based independent ments taken across eight samples t-tests) (Fig. 15). animals (4 of each develop- mental stage).

39

In all 48 reconstructions combined, there were over one million nodes identified. The number of nodes per neuron ranged from 845 to 120,256. The mean number and standard deviation of nodes per neuron across all reconstructions were 22,673 ± 28,915, with a median of 12,225. Objective magnification did not appear to have a significant impact on skeleton complexity, with a linear R2 < 0.25 (Fig. 16). However, using a 63× objective did tend to result in reconstructions with significantly more nodes per neuron on average. While magnification would indeed be expected to influence the resolution of fine processes to some extent, in practice, the quality of the neuron dye-fill appeared to be the best determinant of high-quality reconstructions. In addition, as objective magnification increased, so too did the number of necessary tiles, or z-stacks. Therefore, preparations that used higher- magnification objectives tended to

Figure 16. Skeleton complexity—defined by mean be more computationally number of nodes per neuron—as a function of cumbersome, which likely negated objective power. N = 16; N = 2; 20× 40× any practical benefit gained from N50× = 7; N63× = 20; N100× = 3. (Error bars = ± standard deviation) the objective power. Distributions of total nodes did not significantly differ between genera, t(46) = 1.1738, p = 0.2465, or developmental stage, t(8) = 0.4484, p = 0.6658 and t(6) = 0.7582, p = 0.4770 when adjusted for PD cells only (Fig. 17). A one-way analysis of variance (ANOVA) failed to find any significant differences in across four the four Cancer borealis neuronal subtypes , F(37) = 0.1615, p = 0.9215 (Fig. 18).

40

Neuron per

Nodes of

Number

Figure 17. The mean number of nodes per neuron (skeleton) do not significantly differ when compared across (A) genera or (B,C) developmental stage. (A) All ten reconstructions from Homarus americanus and all thirty-eight reconstructions from Cancer borealis were sampled. (B) N = 5 adults and 5 juveniles. (C) N = 4 adult PD and 4 juvenile PD. (Error bars = ± standard deviation)

per Neuron per per Neuron per

of Nodes Nodes of Nodes of

Number Number Number

Figure 18. Mean number of nodes per neuron (skeleton) do not significantly differ among cell types in either genera. (A) NPD = 8, NLG = 4, NGM = 19, NLP =7. (B) NLP, juv. = 1, NAB, adu. = 1. (Error bars = ± standard deviation)

41

Section II: Qualitative features

Although H. americanus and C. borealis share a high degree of

conservation in STNS anatomy and electrophysiology, the general forms of

their neurons exhibited dramatic differences. As illustrated in these

maximum-intensity z-projections (Fig. 19), the STG neurons of H.

americanus tended to be much more oblong than those of C. borealis, which

were more compact and radially symmetric. This was not entirely

surprising, considering the sizes of the animals themselves. However, these

comparisons made for an interesting opportunity to evaluate how

macromorphological features such as these influence global morphometrics

(e.g., tortuosity, total cable length, distributions of branch orders, etc.).

Consistent with current opinion in the neuroscientific community, it was

speculated that these differences may reflect yet another example of how

similar or even identical physiological mechanisms, such as neural

circuitry, can arise from dramatically different sets of physical properties.

100 μm

Figure 19. Left: maximum-intensity z-projection of an adult H. americanus

PD neuron. Dye-fill credit: Dirk Bucher

Center (above): maximum-intensity z-projection of an adult C. borealis PD neuron. The scale bar (100 μm) applies to both. Dye-fill credit: Adam Taylor

42

Another noteworthy qualitative feature of STG morphology was the almost ubiquitous

“hand-like” region, which occurred approximately within the initial 100–500 μm of cable projecting from the soma. This “hand-like” structure was characterized by large cable diameter and multifurcations and/or closely spaced bifurcations which thereafter ramified and gave rise to most of the neuropil (Fig. 20).

Figure 20. Maximum-intensity z-projections of (left to right): H. americanus juvenile PD neuron; H. americanus adult PD neuron; and H. americanus adult AB neuron. All are examples of neurons containing “hand-like” ramification patterns within the first 500 μm from the soma. Dye-fill credit: Dirk Bucher (all)

Interestingly, it was previously observed that LP neurons were the only cell type that appeared devoid of this “hand-like” structure (Bucher et al., 2007; Otopalik et al., 2017a). From a physiological standpoint, LP neurons do not have any patent differences in their functionality that could explain this rather dramatic exception in morphology. This observation therefore inspired several interesting questions. First, can any examples of LP neurons containing this feature be found? Do neurons with this “hand-like” feature differ from those without in terms of

43

their space-filling patterns or conduction properties? What, if any, evolutionary pressures caused this cell-type-specific deviation in morphology? Could these features—however pronounced— simply have arisen by chance?

When comparing the qualitative, macromorphological profiles of H. americanus pyloric dilator (PD) neurons across two developmental stages—juvenile and adult—it was rather difficult to pinpoint obvious differences (Figs. 21–22). Adult neuropils tended to be more extended longitudinally; however, the two groups appeared to be very similar in terms of their mediolateral widths. Juvenile neuropils had a higher degree of radial symmetry, which was reminiscent of C. borealis STG neurons. When compared qualitatively, the shapes and sizes of the somata did not differ in any obvious ways. There was a considerable degree of variability in size between the cells, such that it would have been difficult to confidently make analytical judgements by simple inspection alone.

44

Figure 21. Maximum-intensity z-projections of the four adult H. americanus PD neurons. Scale bars for each image = 100 µm. All four were rendered using a 50× microscope objective. Dye-fill credit: Dirk Bucher

45

100× 50×

46 100×

50×

Figure 22. Maximum-intensity z-projections of the four juvenile H. americanus PD neurons. Scale bars for each image = 100 µm. The objective powers for each of the cells are reported in the bottom right corners. Dye-fill credit: Dirk Bucher 46

Section III: Geometry of somata

Although scaled visualization of juvenile and adult neurons (Figs. 21–22) alone does not suggest any clear relationship between developmental stage and size, estimations of soma dimensions reveal extremely significant (***) differences between juveniles and adults (Fig. 23).

This finding suggests that somata and distal neurites may arise from differential growth patterns in which the maximum expanse of the neuropil is realized earlier in development, while the soma progressively enlarges up to, and perhaps past, adulthood. One plausible speculation for this is that newborn neurons first prioritize the establishment of synaptic connections—and then, as they mature, invest resources into amplifying, strengthening, and optimizing those connections.

(A) (B)

Figure 23. (A) The PD neurons originating from adult specimens exhibited an extremely significant lead in (maximal) soma area over juvenile PD specimens, t(6) = 6.1085, p < 0.0001, (B) as well as an extremely significant lead in ellipsoid- approximated soma volumes, t(6) = 8.0567, p < 0.0001. Nadu. = 4, Njuv. = 4.

47

This optimization period would likely be energetically expensive, and augmentation of the soma may be precipitated in part by this demand. If so, this could explain why, in Fig. 21, the

mediolateral limits of the neuropil do not appear to differ

be-tween developmental stages. Nevertheless, it is also

possible that the growth patterns of STG somata depend

more heavily on forces that have either not yet been

considered or ones unrelated to cellular geometry.

Between genera, average soma area did not differ

significantly (Fig. 24). Somata from C. borealis STG

neurons exhibited more variability in area; however, the

sample size was nearly fourfold that of H. americanus. It

Figure 24. Average area of the would be interesting if the areas of somata between these somata between H. americanus (N = 10) and C. borealis two genera were truly comparable, given their other (N = 38) did not significantly differ. (Error bars = ± standard notable differences. deviation).

Section IV: Neurite diameter

The six neuronal reconstructions that were completed as three sets of double-neuron dye- fills (each containing one PD and one LP neuron) were used in an assay of neurite taper. Up to twenty-five nodes of each branch order between 2 and 5 were randomly selected for each of the six cells. These nodes were then identified within the skeleton, and manual measurements of neurite diameter were taken at each of those points. LP and PD neurons exhibited similar reductions in mean neurite diameter as a function of branch order (Fig. 25). Furthermore, these reductions were well-modeled by linear regressions, with all R2 values > 0.95.

48

49

Figure 25. Plots of mean neurite diameter, in μm, as a function of branch order for three adult C. borealis PD neurons and three adult C. borealis LP neurons. Outlined in red is the plot of the same relationship averaged across the three neurons. (Error bars = ± standard deviation)

49

In addition to this neurite taper assay, the diameters of each of these six neurons’ Axon

Hillocks were estimated by measuring the maximal diameter of the approximate threshold between the soma and the primary neurite, as shown in Fig. 26A. The LP neurons had Axon Hillocks with a mean (± standard deviation) diameter of 30.8 ± 11.3 μm, while PD neurons had Axon Hillocks with a mean (± standard deviation) diameter of 45.0 ± 2.9 μm (Fig. 26B). An independent-samples t-test failed to find a significant difference between these two distributions, t(4) = 2.1082, p = 0.1027.

(A) (B)

Figure 26. (A) Example of an Axon Hillock diameter approximation. (B) PD neurons (N = 3), on average, had wider Axon Hillock diameters than LP (N = 3) neurons, but this difference was not statistically significant. (Error bars = ± standard deviation)

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Section V: Neuropil space-filling

Polyhedra encompassing 95% of the neuropil were generated as previously described for all four juvenile and all four adult H. americanus PD neurons, as well as several other STG neuronal subtypes from C. borealis (Fig. 27). The mean (± standard deviation) estimated volume occupied by the neuropils of H. americanus juvenile PD neurons (N = 4) was 448,885 ± 307,829

µm3—significantly smaller than those of H. americanus adult PD neurons (N = 4), which had a mean (± standard deviation) of 1,799,525 ± 625,662 µm3, t(6) = 3.8740, p = 0.0082 (Fig. 28).

Figure 27. Polyhedra generated from the skeletonizations of various STG neurons encapsulating the space occupied by 95% of all nodes. (Top, “878o57”): the polyhedron generated from an adult 3 C. borealis GM neuron with an estimated volume of 3,320,300 µm . (Bottom Left, “659106”): the polyhedron generated from an adult H. americanus PD neuron with an estimated volume of 3 1,181,300 μm . (Bottom Right, “696027”): the polyhedron generated from a juvenile H. americanus PD neuron with an estimated volume of 805,800 µm3. Volume was estimated using Equation 13. Axes (x, y, z) represent distance (μm).

51

This very significant (**) statistical finding

contradicted the initial impression gleaned from

Figs. 21–22, which was that the dimensions of the

neuropil did not obviously differ between the two

developmental stages. This demonstrates one of

the greatest benefits of manual neuronal

skeletonization: the ability to quantitatively

compare abstract morphometrics, such as neuropil

Figure 28. Mean estimated neuropil space occupation, which could otherwise not be spaces of juvenile and adult H. americanus PD neurons. (Error bars = ± standard accurately measured. deviation)

Next, the pattern of neurite outgrowth occurring between the juvenile and adult developmental stages was assessed by pooling all path (or cable) lengths in each of the eight neurons and comparing the distributions of path lengths for juvenile versus adult specimens.

This revealed that adult H. americanus PD neurons possess individual paths that span much wider ranges in length than those observed in juvenile H. americanus PD neurons (Fig. 29). The distribution of path lengths for the juvenile neurons resembled statistical normality; however, the same was not true of the adults, whose distribution contained a large, positively skewed tail.

Though mean path length did not significantly differ between the two developmental stages, it seems that paths with lengths near the mean within juvenile neurons simply disperse into longer ones by the time the neuron reaches adulthood. Note in Fig. 29 how total wiring appears very similar between the two groups: this suggests that the volume of the entire neuron does not grow dramatically between the juvenile and adult stages; rather, the neurites simply elongate recursively

52

back throughout the neuropil, forming longer, presumably narrower, paths. This observation is consistent with the hypothesis that neuropilar boundaries may become at least partially fixed early in development, constraining mean neurite path length. Were neurites to simply amplify in an outward fashion between these two developmental stages, we would expect their mean values to differ significantly.

Adult (N = 4) Juvenile (N = 4)

Figure 29. Histogram of combined individual path lengths among juvenile and adult H. americanus PD neurons.

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Section VI: Branching patterns

Three variations on the previously-discussed metric, tortuosity (휏), were considered in the quantitative analysis of branching patterns: absolute tortuosity (휏A), path tortuosity (휏p), and branch tortuosity (휏b), defined by Equations 14, 15, and 16, respectively.

1 path length푛 휏A = ∑ 푛 2 2 2 √(푥2 − 푥1)푛 + (푦2 − 푦1)푛 + (푧2 − 푧1)푛

Equation 14. Absolute tortuosity is defined simply as the average tortuosity among all possible combinations of two nonidentical nodes in a given reconstruction.

1 path length 휏 = ∑ 푡 p 푁 2 2 2 푡 √(푥2 − 푥1)푡 + (푦2 − 푦1)푡 + (푧2 − 푧1)푡

Equation 15. Path tortuosity is defined as the total tortuosity among N number of path lengths and Euclidian distances involving termianl tips (t).

1 path length(푏+1, 푏−1) 휏b = ∑ 푁 2 2 2 푏 √(푥푏+1 − 푥푏−1) + (푦푏+1 − 푦푏−1) + (푧푏+1 − 푧푏−1)

Equation 16. Branch tortuosity is defined as the total tortuosity among N number of branch points (b) wherein the path length is equal to the sum of the segments between a given branch point and each node to which that branch point connects.

Maxima and minima individual path and branch tortuosities were surveyed across four adult and four juvenile H. americanus PD neurons and were shown to be strikingly similar in their ranges (Fig. 30A,B).

54

(A)

(B)

Figure 30. Maxima and minima values for individual (A) path and (B) branch tortuosities within four adult and four juvenile H. americanus PD neurons.

55

Similarly, absoulte tortuosity values were not found to differ significantly between STG cell type among C. borealis (Fig. 31). In general, all measures of tortuosity illustrated these 48 neurons as having a moderate degree of variability that does not signifiacntly differ between cell type, genera, or developmental stage.

8

7

6

5

4

3

Absolute Tortuosity Absolute 2

1

0

LP LP LP LP

PD PD PD PD PD

LG LG LG LG

GM GM GM GM GM GM GM GM GM GM GM GM GM GM GM GM GM GM GM

Cell Type (C. borealis only)

Fig. 31. Absolute (average) tortuosities among 32 Cancer borealis STG neurons. (Error bars = + standard deviation)

56

A comparison of average branch angles

between adult and juvenile H. americanus PD neurons

failed to reveal a statistically significant difference, p =

0.1697 (Fig. 32).

Finally, radial dendrograms were generated

and qualitatively compared across the same eight H.

americanus PD neurons (Figs. 33–34). These

dendrograms depict how branching frequency changes

as a function of branch order. In these cases, branches

Figure 32. Mean branch angles among were fixed to equal lengths, such that the axes 4 adult and 4 juvenile H. americanus PD neurons. (Error bars = ± standard represent bidirectional branch order. These deviation) dendrograms illustrate a high degree of variability in branching patterns. Whereas some neurons’ branches are more evenly distributed about its soma, others exhibit discrete bundles in which branching appears densest. In the adult neurons, branching density appears to be generally more evenly disbursed.

57

58

Figure 33. Radial dendrograms of the four juvenile H. americanus PD neurons.

58

59

Figure 34. Radial dendrograms of the four adult H. americanus PD neurons.

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Section VII: Double–neuron reconstructions

Three sets of double-neuron dye-fills—each containing one adult C. borealis lateral pyloric

(LP) neuron in the red channel and one adult C. borealis pyloric dilator (PD) neuron in the green channel—were manually reconstructed (Figs. 35–36). The three LP neurons contained, on average, 4300 ± 921 (mean ± standard deviation) nodes, whereas the three PD neurons contained, on average, 7308 ± 3168 (mean ± standard deviation) nodes. An independent-samples t-test failed to find a significant difference in mean number of nodes between LPs and PDs, t(4) = 1.5790, p = 0.1895, suggesting that the two cells in each double-neuron preparation were resolved with comparable levels of complexity.

60

61

Figure 35. (Left): Maximum-intensity z-projection of the first of three PD–LP double-dye-fills. (Right): Two-dimensional rendering of the completed skeletonizations of the same two neurons.

62

Figure 36. (Left): Maximum-intensity z-projection of the second of three PD–LP double-dye-fills. (Right): Two-dimensional rendering of the completed skeletonizations of the same two neurons.

63

Figure 37. (Left): Maximum-intensity z-projection of the last of three PD–LP double-dye-fills. (Right): Two-dimensional rendering of the completed skeletonizations of the same two neurons.

A customized, .xml-compatible program was then developed to calculate—using Equation

17—the Euclidian distances (푑) between each node (푛LP) in the LP reconstruction and each node

(푛PD) in the PD reconstruction for all possible combinations of nodes.

2 2 2 푑(푛LP, 푛PD) = √(푥푛LP − 푥푛PD) + (푦푛LP − 푦푛PD) + (푧푛LP − 푧푛PD)

Equation 17. Euclidian distance between two points with coordinates (x, y, z).

Various distance thresholds were then set (ranging from 0.25 to 4.00 µm in 0.25-μm increments), and the number of distance values < threshold was plotted for each of the three double-neuron preparations as a function of threshold, wherein 0.25 µm < threshold < 4.00 µm (Fig. 38). Sets 2 and 3 had similar distributions in candidate synaptic appositions; distance minima were identified using threshold values of 0.75 µm and 0.50 µm, respectively, which captured one candidate

Figure 38. Cumulative number of candidate synaptic appositions identified as a function of distance threshold across the three double-neuron sets.

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apposition in set 2 and five candidate appositions in set 3. Set 1, however, differed in that candidate appositions were identified using much lower thresholds. As a result, an excess of 250 candidate appositions were generated for all thresholds above 1.25 μm. This noticeably lower threshold sensitivity is likely a computational artefact produced by set 1’s large deviation from the mean number of z-slices. During microscopic acquisition of set 1, a conservative number of z-slices was chosen as a sort of pilot experiment. When the workflow from this first image acquisition to reconstruction proved seamless, more ambitious z-resolutions were pursued in sets 2 and 3. Future replication attempts should prioritize avoiding this confound by keeping the number of z-slices relatively constant across samples.

Next, visual corroboration of these close appositions was sought in the data sets’ confocal z-stacks and superimposed skeletons (Fig. 39). Close appositions less than 2 μm could not be readily identified using either interface alone, which again demonstrates the advantage of working with digital skeletonizations.

Figure 39. Attempts to visually corroborate algorithmically identified close appositions within the fully stitched confocal z-stack (left) and superimposed skeletonizations (right). The proximity of these close appositions could often be visually confirmed using these methods; however, neither of these two interfaces alone are particularly useful in the identification process.

65

Another challenge encountered with this technique involved the spurious identification of multiple candidate appositions in regions containing stretches of quasi-parallel neuritic processes.

The generated list of candidate appositions plotted in Fig. 38 was effectively adjusted through a process of manually eliminating spatial redundancies. Specifically, candidate appositions between nodes 푛LP and 푛PD were omitted if another candidate apposition existed between nodes (푛 ± 2)LP and (푛 ± 2)PD. The newly adjusted plot of number of candidates as a function of distance threshold flanked a much more spatially sensitive window of thresholds (Fig. 40).

Section VIII: Generalizability of wiring optimization models

Section IX: Applying Rall’s biophysical formalism

Figure 40. The same relationship plotted in Fig. 38 following manual omission of spatial redundancies.

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CONCLUSION

These forty-eight reconstructions—totaling over 1,000,000 nodes—ultimately testify to a high and widespread degree of variability across all the many quantitative metrics that have been considered hitherto. Previous reports have argued that this variability reflects the cells’ capacity to function normally despite the apparent vastness of their wiring inefficiencies (Otopalik et al.,

2017a). Although there does not appear to be a clear relationship between microscope objective power and the level of detail ultimately achieved in the reconstructions, there is certainly a large degree of variability in both image quality and skeleton complexity (defined as number of total nodes per reconstruction). Image quality is dependent on several factors, including the dye choice

(or choices), the effectiveness of the fill, and the optimization of the microscope acquisition parameters. This report would be woefully incomplete were it not to emphasize one exemplar reconstruction which contained 120,256 nodes—over three standard deviations above the mean.

It seems very unlikely that such a neuron would be dramatically more complex than the others; rather, this outlier can probably be owed to a serendipitous combination of ideal or nearly ideal conditions, such as 100× objective power, an excess of 400 z-slices, an excellent fill, and a very high-resolution scan. The somewhat unsettling implication of this would be that most reconstructions in this sample captured but a fraction of the neuropil’s actual complexity.

Furthermore, this is an important caveat to the discussion on variability. If all these reconstructions had been completed with the level of detail as the abovementioned exemplar, it is possible that

67 patterns in variability and other morphometrics would meaningfully differ. Another important caveat is that an analysis of central tendency may not be the best way to capture all the morphological properties of interest. For example, a focus on distributions within these parameters would better capture the variability among cells.

What is clear, although unsurprising, is that the STG neurons of H. americanus grow between juvenile and adult developmental stages. The longitudinal expanses of the adult neuropils are far longer than that of juveniles; however, the mediolateral widths of the neuropils are more comparable between the two age groups. This may result from some anatomical constraint on the width of the STG itself. Alternatively, it could reflect these neurons’ tendency to reach their maximal neuropil width earlier in development, after which time the somata and neurites continue to grow markedly. Computational estimates of the space occupied by the neuropil did reveal that juvenile H. americanus PD neurons occupy significantly less space than their adult counterparts.

This change, judging by the images of the cells themselves, appears to be due primarily to the lengthening—not widening—of the neurons. Finally, the somata also grow significantly between the juvenile and adult developmental stages.

Neurite taper appears to be an example of a morphological property that is highly uniform.

The diameter of neurites with branch orders 2–5 can be predicted by branch order using linear regressions with R2s over 0.95. In the future, it would be interesting to expand this analysis to include neurites of higher branch orders, as well as increase the cell sample size. Judging by the observations during tracing, the expectation would be that very fine neurites approach a plateau, or minimal diameter. If so, the relationship between branch order and neurite diameter may be better modeled by a logarithmic, rather than linear, regression.

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The double-neuron dye-fills appear to be a useful approach in assessing intercellular relationships such as close appositions. An interesting future experiment would be to transform one cell’s coordinates in one dimension (e.g., add 0.2 μm to all x-coordinates) and then repeat the analysis of candidate synaptic appositions. By shifting one of the cells arbitrarily, one could assess how many candidate appositions were still identified, thus assessing the positional uniqueness of these candidate sites as well as the fidelity of this reconstruction-based approach.

Ultimately, reconstruction-based morphology research offers an inimitable array of analytical tools such as the ones used for these forty-eight neurons. The various parameters assessed among these STG neurons are all promising tools with diverse experimental applications.

As global repositories of manually-reconstructed neurons—such as NeuroMorpho.Org—continue to grow, high-throughput morphometric assays are very likely to improve statistical power and reveal more meaningful relationships between a neuron’s form and its underlying physiology or pathophysiology.

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APPENDICES

Excitation Emission Label Dye Maximum (nm) Maximum (nm) 1 Alexa Fluor™ 488 499 520 2 Calcium Green™-1 AM 506 531 3 Lucifer Yellow 428 544 4 Alexa Fluor™ 568 579 603 5 Alexa Fluor™ 594 590 618

Appendix A. Emission and excitation properties of the major injected dyes used in these reconstructions. (A) Major emission spectra. (Courtesy of ATT Bioquest, Inc., Sunnyvale, CA) (B) Tabulated excitation and emission maxima for each of the five dyes.

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Specimen ID Cell Genus Age Dye(s) Microscope Objective (Notebook_Page) Type 659_106 Homarus PD Adult Alexa Fluor™ 568 Leica™ TCS SP5 50× 696_017 Homarus PD Adult Alexa Fluor™ 568 Leica™ TCS SP5 50× 696_019 Homarus PD Adult Alexa Fluor™ 568 Leica™ TCS SP5 50× 696_022 Homarus PD Juvenile Alexa Fluor™ 568 Leica™ TCS SP5 100× 696_025 Homarus PD Juvenile Alexa Fluor™ 568 Leica™ TCS SP5 50× 696_026 Homarus PD Juvenile Alexa Fluor™ 568 Leica™ TCS SP5 50× 696_027 Homarus PD Juvenile Alexa Fluor™ 568 Leica™ TCS SP5 100× 696_033 Homarus LP Juvenile Alexa Fluor™ 568 Leica™ TCS SP5 100× 696_047 Homarus AB Adult Alexa Fluor™ 568 Leica™ TCS SP5 50× 705_047 Homarus PD Adult Alexa Fluor™ 568 Leica™ TCS SP5 50× 709_013 Cancer PD Adult Calcium Green™-1 AM (2 mM) Leica™ SP2MP 20× 785_040 Cancer LG Adult Lucifer Yellow CH dipotassium salt (2%) Leica™ SP5 CLEM 63× 786_062 Cancer LG Adult Alexa Fluor™ 594 biocytin, sodium salt Leica™ SP5 CLEM 63× 791_076 Cancer LG Adult Lucifer Yellow CH dipotassium salt (2%) Leica™ SP5 CLEM 63× 791_088 Cancer LG Adult Lucifer Yellow CH dipotassium salt (2%) Leica™ SP5 CLEM 63× 791_127 Cancer GM Adult 2% Neurobiotin Leica™ SP5 CLEM 63× 798_002 Cancer GM Adult Lucifer Yellow CH dipotassium salt (2%) Leica™ SP5 CLEM 63× 71 798_007 Cancer GM Adult Lucifer Yellow CH dipotassium salt (2%) Leica™ SP5 CLEM 63× 798_032 Cancer PD Adult 4% Neurobiotin Leica™ SP5 CLEM 63× Lucifer Yellow CH dipotassium salt (2%); 803_133 Cancer PD Adult Leica™ SP5 CLEM 63× Red fluorescent protein eqFP611 (mRuby) Lucifer Yellow CH dipotassium salt (2%); 803_151 Cancer PD Adult Leica™ SP5 CLEM 63× Red fluorescent protein eqFP611 (mRuby) Lucifer Yellow CH dipotassium salt; 803_155 Cancer PD Adult Leica™ SP5 CLEM 63× Red fluorescent protein eqFP611 (mRuby) 815_144 Cancer GM Adult Lucifer Yellow CH dipotassium salt (2%) Leica™ SP5 CLEM 63× Appendix B. (Part 1 of 2) Complete catalog of all reconstructions herein reported.

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Specimen ID Cell Genus Age Dye(s) Microscope Objective (Notebook_Page) Type 815_144 Cancer GM Adult Lucifer Yellow CH dipotassium salt (2%) Leica™ SP5 CLEM 63× 836_047 Cancer LP Adult Lucifer Yellow CH dipotassium salt (2%) Leica™ SP5 CLEM 63× 836_095 Cancer LP Adult Lucifer Yellow CH dipotassium salt (2%) Leica™ SP5 CLEM 63× 837_103 Cancer LP Adult Lucifer Yellow CH dipotassium salt (2%) Leica™ SP5 CLEM 63× 837_123 Cancer LP Adult Lucifer Yellow CH dipotassium salt (2%) Leica™ SP5 CLEM 63× 878_041 Cancer GM Adult Lucifer Yellow CH dipotassium salt (2%) Leica™ SP5 CLEM 20× 878_043 Cancer GM Adult Lucifer Yellow CH dipotassium salt (2%) Leica™ SP5 CLEM 20× 878_045 Cancer GM Adult Lucifer Yellow CH dipotassium salt (2%) Leica™ SP5 CLEM 20× 878_049 Cancer GM Adult Lucifer Yellow CH dipotassium salt (2%) Leica™ SP5 CLEM 20× 878_053 Cancer GM Adult Lucifer Yellow CH dipotassium salt (2%) Leica™ SP5 CLEM 20× 878_056 Cancer GM Adult Lucifer Yellow CH dipotassium salt (2%) Leica™ SP5 CLEM 20× 878_057 Cancer GM Adult Lucifer Yellow CH dipotassium salt (2%) Leica™ SP5 CLEM 20× Lucifer Yellow CH dipotassium salt (2%); 878_058 Cancer GM Adult Leica™ SP5 CLEM 20× Alexa Fluor™ 488 Lucifer Yellow CH dipotassium salt (2%);

878_061 Cancer GM Adult Leica™ SP5 CLEM 20× Alexa Fluor™ 488 Lucifer Yellow CH dipotassium salt (2%); 72 878_062 Cancer GM Adult Leica™ SP5 CLEM 20× Alexa Fluor™ 488 878_063 Cancer GM Adult Lucifer Yellow CH dipotassium salt (2%) Leica™ SP5 CLEM 20× 878_064 Cancer GM Adult Lucifer Yellow CH dipotassium salt (2%) Leica™ SP5 CLEM 20× 878_065 Cancer GM Adult Lucifer Yellow CH dipotassium salt (2%) Leica™ SP5 CLEM 20× 878_066 Cancer GM Adult Lucifer Yellow CH dipotassium salt (2%) Leica™ SP5 CLEM 20× 878_067 Cancer GM Adult Lucifer Yellow CH dipotassium salt (2%) Leica™ SP5 CLEM 20× Lucifer Yellow CH dipotassium salt (2%); 896_055A Cancer PD Adult ZEISS™ LSM880 40× Alexa Fluor™ 488 896_055B Cancer LP Adult Alexa Fluor™ 594 ZEISS™ LSM880 40× Lucifer Yellow CH dipotassium salt (2%); 896_056A Cancer PD Adult ZEISS™ LSM880 63× Alexa Fluor™ 488 896_056B Cancer LP Adult Alexa Fluor™ 594 ZEISS™ LSM880 63× Lucifer Yellow CH dipotassium salt (2%); 896_057A Cancer PD Adult ZEISS™ LSM880 63× Alexa Fluor™ 488 896_057B Cancer LP Adult Alexa Fluor™ 594 ZEISS™ LSM880 63×

Appendix B. (Part 2 of 2) Complete catalog of all reconstructions herein reported.

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Specimen ID Voxel (μm) Specimen ID Voxel (μm) (Notebook_Page) Width (x ) Height (y ) Depth (z ) (Notebook_Page) Width (x ) Height (y ) Depth (z ) 659_106 0.977 0.977 0.982 836_095 0.183 0.183 0.501 696_017 0.586 0.586 0.488 837_103 0.070 0.070 0.293 696_019 0.585 0.585 0.488 837_123 0.050 0.050 0.168 696_022 0.146 0.146 0.285 878_041 0.732 0.732 0.488 696_025 0.586 0.586 0.488 878_043 0.732 0.732 0.488 696_026 0.293 0.293 0.407 878_045 0.732 0.732 0.488 696_027 0.146 0.146 0.285 878_049 0.732 0.732 0.488 696_033 0.146 0.146 0.285 878_053 0.732 0.732 0.488 696_047 0.293 0.293 0.814 878_056 0.732 0.732 0.488 705_047 0.293 0.293 0.488 878_057 0.732 0.732 0.488 709_013 0.586 0.586 0.488 878_058 0.732 0.732 0.488 785_040 0.067 0.067 0.380 878_061 0.732 0.732 0.488

786_062 0.176 0.176 0.460 878_062 0.732 0.732 0.488

791_076 0.180 0.180 0.400 878_063 0.732 0.732 0.488 73 791_088 0.353 0.353 0.353 878_064 0.732 0.732 0.488 791_127 0.353 0.353 0.353 878_065 0.732 0.732 0.488 798_002 0.184 0.184 0.713 878_066 0.732 0.732 0.488 798_007 0.181 0.181 0.588 878_067 0.732 0.732 0.488 798_032 0.093 0.093 0.504 896_055A 0.208 0.208 1.091 803_133 0.922 0.922 0.500 896_055B 0.208 0.208 1.091 803_151 0.089 0.089 0.504 896_056A 0.178 0.178 0.420 803_155 0.183 0.183 0.420 896_056B 0.178 0.178 0.420 815_144 0.047 0.047 0.126 896_057A 0.132 0.132 0.083 836_047 0.137 0.137 0.500 896_057B 0.132 0.132 0.083

Appendix C. Complete three-dimensional voxel configurations for all 48 reconstructed neurons.

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Specimen ID Number of Specimen ID Number of (Notebook_Page) Tracers (Notebook_Page) Tracers 659_106 1 836_095 7 696_017 1 837_103 7 696_019 1 837_123 7 696_022 1 878_041 1 696_025 1 878_043 1 696_026 1 878_045 1 696_027 1 878_049 1 696_033 1 878_053 1 Collaborative (7 Tracers) 696_047 1 878_056 1 35% 705_047 1 878_057 1 709_013 7 878_058 1 785_040 7 878_061 1

786_062 7 878_062 1 791_076 7 878_063 1 791_088 7 878_064 1 791_127 7 878_065 1 74 Individual (1 Tracer) 65% 798_002 7 878_066 1 798_007 7 878_067 1 798_032 7 896_055A 1 803_133 7 896_055B 1 803_151 7 896_056A 1 803_155 7 896_056B 1 815_144 7 896_057A 1 836_047 7 896_057B 1

Appendix D. Tabulated number of tracers contributing to each reconstruction, along with proportional illustration of the two formats.

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BIBLIOGRAPHY

Abdel-Maguid, T. E., & Bowsher, D. (1984). Classification of neurons by dendritic branching pattern: A categorisation based on Golgi impregnation of spinal and cranial somatic and visceral afferent and efferent cells in the adult human. Journal of Anatomy, 138(4), 689–702.

Allgower, E. L., & Schmidt, P. H. (1986). Computing volumes of polyhedral. Mathematics of Computation, 46(173), 171–174.

Anton-Sanchez, L., Bielza, C., Benavides-Piccione, R., DeFelipe, J., & Larrañaga, P. (2016). Dendritic and axonal wiring optimization of cortical GABAergic interneurons. Neuroinformatics, 14(4), 453–464.

Arvidsson, A., Collin, T., Kirik, D., Kokaia, Z., & Lindvall, O. (2002). Neuronal replacement from endogenous precursors in the adult brain after stroke. Nature Medicine, 8(9), 963–970.

Ascoli, G. A., Donohue, D. E., & Halavi, M. (2007). NeuroMorpho.Org: A central resource for neuronal morphologies. Journal of Neuroscience, 27(35), 9247–9251.

Bargmann, C. I., & Marder, E. (2013). From the connectome to brain function. Nature Methods, 10(6), 483–490.

Bock, O. (2013). Cajal, Golgi, Nansen, Schäfer, and the neuron doctrine. Endeavour, 37(4), 228–234.

Brandeis University. (2019). The Marder lab: Modulation of neural networks. Retrieved from blogs.brandeis.edu/marderlab/resources.

Brightman, M. W., & Reese, T. S. (1969). Junctions between intimately apposed cell membranes in the vertebrate brain. Journal of Cell Biology, 40(3), 648–677.

Brock, L. G., Coombs, J. S., & Eccles, J. C. (1952). The recording of potentials from motoneurons with an intracellular electrode. Journal of Physiology, 117(4), 431–460.

Bucher, D., Johnson, C. D., & Marder, E. (2007). Neuronal morphology and neuropil structure in the stomatogastric ganglion of the lobster, Homarus americanus. Journal of Comparative Neurology, 501(2), 185–205.

Bucher, D., Prinz, A. A., & Marder, E. (2005). Animal-to-animal variability in motor pattern production in adults and during growth. Journal of Neuroscience, 25(7), 1611–1619.

75

Cabirol-Pol, M.-J., Mizrahi, A., & Simmers, J. (2000). Combining laser scanning confocal microscopy and electron microscopy to determine sites of synaptic contact between two identified neurons. Journal of Neuroscience Methods, 97(2), 175–181.

Campbell, D. S., & Holt, C. E. (2001). Chemotropic responses of retinal growth cones mediated by rapid local protein synthesis and degradation. Neuron, 32(6), 1013–1026.

Chen, B. L., Hall, D. H., & Chklovskii, D. B. (2006). Wiring optimization can relate neuronal structure and function. Proceedings of the National Academy of Sciences of the United States of America, 103(12), 4723–4728.

Chklovskii, D. B., & Stepanyants, A. (2003). Power-law for axon diameters at branch point. BioMedCentral Neuroscience, 4, 18.

Christie, A. E. (1995). Chemical neuroanatomy of the crab stomatogastric ganglion: A study using immunocytochemistry and laser scanning confocal microscopy. (Unpublished doctoral dissertation). Brandeis University, Waltham, MA.

Christie, A. E., Baldwin, D. H., Marder, E., & Graubard, K. (1997). Organization of the stomatogastric neuropil of the crab, Cancer borealis, as revealed by modulator immunocytochemistry. Cell and Tissue Research, 288(1), 135–148.

Clark, P., Britland, S., & Connolly, P. (1993). Growth cone guidance and neuron morphology on micropatterned laminin surfaces. Journal of Cell Science, 105(1), 203–212.

Cunningham, B. A., Hemperly, J. J., Murray, B. A., Prediger, E. A., Brackenbury, R., & Edelman, G. M. (1987). Neural cell adhesion molecules: Structure, immunoglobulin-like domains, cell surface modulation, and alternative RNA splicing. Science, 236(4803), 799–806.

Cuntz, H., Forstner, F., Borst, A., & Häusser, M. (2010). One rule to grow them all: A general theory of neuronal branching and its practical application. PLOS Computational Biology, 6(8), e1000877.

Cuntz, H., Mathy, A., & Häusser, M. (2012). A scaling law derived from optimal dendritic wiring. Proceedings of the National Academy of Sciences of the United States of America, 109(27), 11014–11018.

Dauguet, J., Peled, S., Berezovskii, V., Delzescaux, T., Warfield, S. K., Born, R., & Westin, C.-F. (2007). Comparison of fiber tracts derived from in-vivo DTI tractography with 3D histological neural tract tracer reconstruction on a macaque brain. NeuroImage, 37(2), 530–538.

Deiters, V. S., & Guillery, R. W. (2013). Otto Friedrich Karl Deiters (1834–1863). Journal of Comparative Neurology, 521(9), 1929–1953.

76

Dickinson, P. S., Kurland, S. C., Qu, X., Parker, B. O., Sreekrishnan, A., Kwiatkowski, M. A., Williams, A. H., Ysasi, A. B., & Christie, A. E. (2015). Distinct or shared actions of peptide family isoforms: II. Multiple pyrokinins exert similar effects in the lobster stomatogastric nervous system. Journal of Experimental Biology, 218(18), 2905–2917.

Fénelon, V. S., Kilman, V., Meyrand, P., & Marder, E. (1999). Sequential developmental acquisition of neuromodulatory inputs to a central pattern-generating network. Journal of Comparative Neurology, 408(3), 335–351.

Friedlander, M. J., Stanford, L. R., & Sherman, S. M. (1982). Effects of monocular deprivation on the structure–function relationship of individual neurons in the cat’s lateral geniculate nucleus. Journal of Neuroscience, 2(3), 321–330.

George Mason University. (2018). NeuroMorpho.Org. Retrieved from www.neuromorpho.org.

Goeritz, M. L., Bowers, M. R., Slepian, B., & Marder, E. (2013). Neuropilar projections of the anterior gastric receptor neuron in the stomatogastric ganglion of the Jonah crab, Cancer borealis. PLOS ONE, 8(12), e79306.

Good, C. D., Johnsrude, I. S., Ashburner, J., Henson, R. N. A., Friston, K. J., & Frackowiak, R. S. J. (2001). A voxel-based morphometric study of ageing in 465 normal adult human brains. NeuroImage, 14(1), 21–36.

Graham, J., & Gerard, R. W. (1946). Membrane potentials and excitation of impaled single muscle fibers. Journal of Cellular and Comparative Physiology, 28(1), 99–117.

Granzow, B., Friesen, W. O., & Kristan, W. B., Jr. (1985). Physiological and morphological analysis of synaptic transmission between leech motor neurons. Journal of Neuroscience, 5(8), 2035–2050.

Gutierrez, G. J., & Grashow, R. G. (2009). Cancer borealis stomatogastric nervous system dissection. Journal of Visualized Experiments, 25, 1207.

Halavi, M., Hamilton, K. A., Parekh, R., & Ascoli, G. A. (2012). Digital reconstructions of neuronal morphology: Three decades of research trends. Frontiers in Neuroscience, 6(49).

Heinrich, R., Bräunig, P., Walter, I., Schneider, H., & Kravitz, E. A. (2000). Aminergic neuron systems of lobsters: morphology and electrophysiology of octopamine-containing neurosecretory cells. Journal of Comparative Physiology, Series A, Neuroethology, Sensory, Neural, and Behavioral Physiology, 186(7–8), 617–629.

Hodgkin, A. L., & Huxley, A. F. (1945). Resting and action potentials in single nerve fibers. Journal of Physiology, 104(2), 176–195.

Hodgkin, A. L., & Rushton, W. A. (1946). The electrical constants of a crustacean nerve fibre. Proceedings of the Royal Society of Medicine, 134(873), 444–479.

77

Hodgkin, A. L., & Huxley, A. F. (1952). The components of membrane conductance in the giant axon of Loligo. Journal of Physiology, 116(4), 473–496.

Jacobs, B., Driscoll, L., & Schall, M. (1997). Life-span dendritic and spine changes in areas 10 and 18 of human cortex: A quantitative Golgi study. Journal of Comparative Neurology, 386(4), 661–680.

Karczmar, A. G., Koketsu, K., & Nishi, S. (Eds.). (1986). Autonomic and enteric ganglia: Transmission and its pharmacology. New York, NY: Plenum.

Kemp, J. M., & Powell, T. P. S. (1971). The termination of fibers from the cerebral cortex and thalamus upon dendritic spines in the caudate nucleus: A study with the Golgi method. Philosophical Transactions of the Royal Society of London, Series B, Biological Sciences, 262(845), 429–439.

Kilman, V. L., & Marder, E. (1996). Ultrastructure of the stomatogastric ganglion neuropil of the crab, Cancer borealis. Journal of Comparative Neurology, 374(3), 362–375.

Kim, J., Greene, M. J., Zlateski, A., Lee, K., Richardson, M., Turaga, S. C., Purcaro, M., Balkam, M., Robinson, A., Behabadi, B. F., Campos, M., Denk, W., Seung, H. S., & The EyeWirers. (2014). Space–time wiring specificity supports direction selectivity in the retina. Nature, 509(7500), 331–336.

Koene, R. A., Tijms, B., Hees, P., Postma, F., Ridder, A., Ramakers, G. J. A., Pelt, J., & Ooyen, A. (2009). NETMORPH: A framework for the stochastic generation of large scale neuronal networks with realistic neuron morphologies. Neuroinformatics, 7(3), 195–210.

Kornfeld, J., Svara, F., Nguyen, M.-T., Pfeiler, N., Pronkin, M., Spaar, S., & Stepanov, A. (2016). KNOSSOS — 3D image annotation. Max Planck Institute for Medical Research, Heidelberg, Germany. Retrieved from https://knossos.app.

Krasnov, I. (1994). Gravitational neuromorphology. In S. L. Bonting & L. Sjoerd (Eds.), Advances in space biology and medicine (1st ed., Vol. 1). Greenwich: JAI Press.

Llinás, R. R. (2003). The contribution of Santiago Ramón y Cajal to functional neuroscience. Nature Reviews Neuroscience, 4(1), 77–80.

MacLeod, D., Dowman, J., Hammond, R., Leete, T., Inoue, K., & Abeliovich, A. (2006). The familial parkinsonism gene LRRK2 regulates neurite process morphology. Neuron, 52(4), 587–593.

Marder, E. (2012). Neuromodulation of neuronal circuits: Back to the future. Neuron, 76(1), 1–11.

78

Marder, E., Goeritz, M. L., & Otopalik, A. G. (2015). Robust circuit rhythms in small circuits arise from variable circuit components and mechanisms. Current Opinion in Neurobiology, 31, 156–163.

Markram, H. (2006). The blue brain project. Nature Reviews Neuroscience, 7(2), 153–160.

Martone, M. E., Jones, Y. Z., Young, S. J., Ellisman, M. H., Zivin, J. A., & Hu, B.-R. (1999). Modification of postsynaptic densities after transient cerebral ischemia: A quantitative and three-dimensional ultrastructural study. Journal of Neuroscience, 19(6), 1988–1997.

McCulloch, W. S., & Pitts, W. H. (1943). A logical calculus of the ideas immanent in nervous activity. Bulletin of Mathematical Biology, 52(1–2), 99–115.

Nelson, P. G., & Lux, H. D. (1970). Some electrical measurements of motoneuron parameters. Biophysical Journal, 10(1), 55–73.

Newman, E. A. (Ed.), Araque, A. (Ed.), Dubinsky, J. M. (Ed.), Swanson, L. W., King, L., & Himmel, E. (2017). The beautiful brain: The drawings of Santiago Ramón y Cajal. New York: Abrams.

Otopalik, A. G. (2017). Mapping neuronal morphology to physiology in a rhythmic motor circuit. (Unpublished doctoral dissertation). Brandeis University, Waltham, MA.

Otopalik, A. G., Goeritz, M. L., Sutton, A. C., Brookings, T., Guerini, C., & Marder, E. (2017a). Sloppy morphological tuning in identified neurons of the crustacean stomatogastric ganglion. eLife, 6, e22352.

Otopalik, A. G., Sutton, A. C., Banghart, M., & Marder, E. (2017b). When complex neuronal structures may not matter. eLife, 6, e23508.

Otopalik, A. G., Lane, B., Schulz, D. J., & Marder, E. (2019). Innexin expression in electrically coupled motor circuits. Neuroscience Letters.

Otopalik, A. G., & Marder, E. (2019). Neuronal morphologies built for reliable physiology in a rhythmic motor circuit. eLife, 8, e41728.

Pani, G., Samari, N., Quintens, R., Saint-Georges, L., Meloni, M., Baatout, S., Oostveldt, P. V., & Benotmane, M. A. (2013). Morphological and physiological changes in mature in vitro neuronal networks towards exposure to short-, middle- or long-term simulated microgravity. PLOS ONE, 8(9), e73857.

Preibisch, S., Saalfeld, S., & Tomancak, P. (2009). Globally optimal stitching of tiled 3D microscopic image acquisitions. Bioinformatics, 25(11), 1463–1465.

79

Rajkowska, G., Miguel-Hidalgo, J. J., Wei, J., Dilley, G., Pittman, S. D., Meltzer, H. Y., Overholser, J. C., Roth, B. L., & Stockmeier, C. A. (1999). Morphometric evidence for neuronal and glial prefrontal cell pathology in major depression. Biological Psychiatry, 45(9), 1085–1098.

Rall, W. (1959). Branching dendritic trees and motoneuron resistivity. Experimental Neurology, 1(5), 491–527.

Rall, W. (1962). Theory of physiological properties of dendrites. Annals of the New York Academy of Sciences, 96(4), 1071–1092.

Rall, W. (1969). Time constants and electrotonic length of membrane cylinders and neurons. Biophysical Journal, 9(12), 1483–1508.

Ramón y Cajal, S. (1959). Degeneration and regeneration of the nervous system (Vol. 1). R. M. May (Ed., Trans.). New York: Hafner. (Original work published 1928)

Renehan, W. E., Jacquin, M. F., Mooney, R. D., & Rhoades, R. W. (1986). Structure–function relationships in rat medullary and cervical dorsal horns. II. Medullary dorsal horn cells. Journal of Neurophysiology, 55(6), 1187–1201.

Revel, J. P., & Karnovsky, M. J. (1967). Hexagonal array of subunits in intercellular junctions of the mouse heart and liver. Journal of Cell Biology, 33(3), C7–C12.

Ropireddy, D., & Ascoli, G. A. (2011). Potential synaptic connectivity of different neurons onto pyramidal cells in a 3D reconstruction of rat hippocampus. Frontiers in Neuroinformatics, 5(5).

Rose, P. K. (1982). Branching structure of motoneuron stem dendrites: A study of neck muscle motoneurons intracellularly stained with horseradish peroxidase in the cat. Journal of Neuroscience, 2(11), 1596–1607.

Rowe, M. H., & Stone, J. (1977). Naming of neurones: Classification and naming of cat retinal ganglion cells. Brain, Behavior and Evolution, 14(3), 185–216.

Schmitt, S., Evers, J. E., Duch, C., Scholz, M., & Obermayer, K. (2004). New methods for the computer-assisted 3-D reconstruction of neurons from confocal image stacks. NeuroImage, 23(4), 1283–1298.

Schneider-Mizell, C. M., Gerhard, S., Longair, M., Kazimiers, T., Li, F., Zwart, M., Champion, A., Midgley, F. M., Fetter, F. D., Saalfeld, S., & Cardona, A. (2016). Quantitative neuroanatomy for connectomics in Drosophila. eLife, 5, e12059.

80

Shankar, G. M., Li, S., Mehta, T. H., Garcia-Munoz, A., Shepardson, N. E., Smith, I., Brett, F. M., Farrell, M. A., Rowan, M. J., Lemere, C. A., Regan, C. M., Walsh, D. M., Sabatini, B. L., & Selkoe, D. J. (2008). Amyloid-β protein dimers isolated directly from Alzheimer’s brains impair synaptic plasticity and memory. Nature Medicine, 14(8), 837–842.

Sidman, R. L., & Rakic, P. (1973). Neuronal migration, with special reference to developing human brain: A review. Brain Research, 62(1), 1–35.

Stein, W. (2017). Stomatogastric nervous system. Oxford Research Encyclopedia of Neuroscience. New York, NY: Oxford University Press.

Stenerson, M.,* Guerini, C.,* Otopalik, A., Sutton, A., & Marder, E. (2016). Predominant algorithm for computationally modeling single-neuron morphology shown insufficient in the stomatogastric ganglion. Poster session presented at SciFest VI, Brandeis University, Waltham, MA.

Stenerson, M., & Marder, E. (2017). The roles of age, cell type, and genus on crustacean neuro- morphology. Poster session presented at SciFest VII, Brandeis University, Waltham, MA.

Swallie, S. E., Monti, A. M., & Blitz, D. M. (2015). Anatomical organization of multiple modulatory inputs in a rhythmic motor system. PLOS ONE, 10(11), e0142956.

Tang, J., Landmesser, L., & Rutishauser, U. (1992). Polysialic acid influences specific pathfinding by avian motoneurons. Neuron, 8(6), 1031–1044.

Uva, B. M., Masini, M. A., Sturla, M., Prato, P., Passalacqua, M., Giuliani, M., Tagliafierro, G., & Strollo, F. (2002). Clinorotation-induced weightlessness influences the cytoskeleton of glial cells in culture. Brain Research, 934(2), 132–139.

Woodbury, J. W., & Patton, H. D. (1952). Electrical activity of single spinal cord elements. Cold Spring Harbor Symposia on Quantitative Biology, 17, 185–188.

Xu, Z., Cork, L. C., Griffin, J. W., & Cleveland, D. W. (1993). Increased expression of neurofilament subunit NF-L produces morphological alterations that resemble the pathology of human motor neuron disease. Cell, 73(1), 23–33.

Yang, Y., Coleman, M., Zhang, L., Zheng, X., & Yue, Z. (2013). Autophagy in axonal and dendritic degeneration. Cell, 36(7), 418–428.

81