Topological analysis of binary tree structures when occasional multifurcations occur

The occurrence of multifurcations in essentially binary trees is investigated with respect to two methods for testing growth models,viz. subtree partition analysis and vertex analysis. It is shown that under certain conditions multifurcations may be incorporated in the analysis. Although the conditions are more restrictive for subtree partition analysis only minor loss of information occurs if forbidden multifurcations are simply ignored.     

Neurons of the central nervous system innervating the lips and oral area of the pond snail

By means of retrograde transport methods, CoCl2 and horseradish peroxidase, localization and morphological peculiarities of the CNS neurons, that innervate lips and oral area, have been studied in the pond snail (Gastropoda). The neurons, sending their processes into the anterior and middle labial nerves, are found nearly in all ganglia of the parapharyngeal nervous ring on the distal and ventral surface. In the cerebral ganglia they situate as several symmetrical groups. Among the neurons revealed, there are cells with rather local distribution of the terminal branches of the processes in the CNS neuropil and neurons with vast branching areas in the neuropil not only of its own ganglion, but also of the neighbouring ones. The problem concerning the zones of possible intersensory interaction in the cerebral ganglia is discussed and presence in them, together with complex reflectory arches, of bisegmental reflectory arches is considered.     

A two-phase growth strategy in cultured neuronal networks as reflected by the distribution of neurite branching angles

Neurite outgrowth and branching patterns are instrumental in dictating the wiring diagram of developing neuronal networks. We study the self-organization of single cultured neurons into complex networks focusing on factors governing the branching of a neurite into its daughter branches. Neurite branching angles of insect ganglion neurons in vitro were comparatively measured in two neuronal categories: neurons in dense cultures that bifurcated under the presence of extrinsic (cellular environment) cues versus neurons in practical isolation that developed their neurites following predominantly intrinsic cues. Our experimental results were complemented by theoretical modeling and computer simulations. A preferred regime of branching angles was found in isolated neurons. A model based on biophysical constraints predicted a preferred bifurcation angle that was consistent with this range shown by our real neurons. In order to examine the origin of the preferred regime of angles we constructed simulations of neurite outgrowth in a developing network and compared the simulated developing neurons with our experimental results. We tested cost functions for neuronal growth that would be optimized at a specific regime of angles. Our results suggest two phases in the process of neuronal development. In the first, reflected by our isolated neurons, neurons are tuned to make first contact with a target cell as soon as possible, to minimize the time of growth. After contact is made, that is, after neuronal interconnections are formed, a second branching strategy is adopted, favoring higher efficiency in neurite length and volume. The two-phase development theory is discussed in relation to previous results.     

Dendritic projections of different types of octopaminergic unpaired median neurons in the locust metathoracic ganglion

Octopaminergic dorsal unpaired median (DUM) neurons of locust thoracic ganglia are important components of motor networks and are divided into various sub-populations. We have examined individually stained metathoracic DUM neurons, their dendritic projection patterns, and their relationship to specific architectural features of the metathoracic ganglion, such as longitudinal tracts, transverse commissures, and well-defined sensory neuropils. The detailed branching patterns of individually characterized DUM neurons of various types were analyzed in vibratome sections in which architectural features were revealed by using antibodies against tubulin and synapsin. Whereas DUM3,4,5 and DUM5 neurons (the group innervating leg and "non-wing-power" muscles) had many ventral and dorsal branches, DUM1 and DUM3,4 neurons (innervating "wing-power" muscles) branched extensively only in dorsal areas. The structure of DUM3 neurons differed markedly from that of the other DUM neurons examined in that they sent branches into dorsal areas and had differently structured side branches that mostly extended laterally. The differences between the branching patterns of these neurons were quantified by using currently available new reconstruction algorithms. These structural differences between the various classes of DUM neurons corresponded to differences in their function and biophysical properties.     

Cycle distributions in random nets

Characteristics of random nets are derived from assumptions concerning the distribution of connections. The single aggregate of neurons with random connections without branching and two parallel chains with normal distribution of connections are considered. The cycle saturation is derived for each type of net, that is, the fraction of neurons which are members of cycles. It is shown that in the single aggregate with random connections, the cycle saturation varies inversely as the square root of the number of neurons; in the dense two-chain net it varies inversely as the square root of the neuron density and inversely on the square root of the standard deviation of the normal distribution.     

The relationship of intramuscular nerve branching and synaptogenesis to motoneuron survival.

The target has been considered for some time to play a major role in allowing neurons to survive the period of naturally occurring cell death. For the motoneurons that innervate the chick limb, evidence is presented that suggests access to target-derived trophic factor via intramuscular nerve branches and synapses may be important in regulating neuronal survival. Alterations in branching and synapse formation produced by activity blockade as well as by alteration of adhesion molecule function are shown to result in changes in motoneuron survival consistent with the proposed hypothesis. The relevance of these observations to the numerical-matching hypothesis of vertebrate neuronal cell death is also considered.     

A two‐phase growth strategy in cultured neuronal networks as reflected by the distribution of neurite branching angles

Neurite outgrowth and branching patterns are instrumental in dictating the wiring diagram of developing neuronal networks. We study the self‐organization of single cultured neurons into complex networks focusing on factors governing the branching of a neurite into its daughter branches. Neurite branching angles of insect ganglion neurons in vitro were comparatively measured in two neuronal categories: neurons in dense cultures that bifurcated under the presence of extrinsic (cellular environment) cues versus neurons in practical isolation that developed their neurites following predominantly intrinsic cues. Our experimental results were complemented by theoretical modeling and computer simulations. A preferred regime of branching angles was found in isolated neurons. A model based on biophysical constraints predicted a preferred bifurcation angle that was consistent with this range shown by our real neurons. In order to examine the origin of the preferred regime of angles we constructed simulations of neurite outgrowth in a developing network and compared the simulated developing neurons with our experimental results. We tested cost functions for neuronal growth that would be optimized at a specific regime of angles. Our results suggest two phases in the process of neuronal development. In the first, reflected by our isolated neurons, neurons are tuned to make first contact with a target cell as soon as possible, to minimize the time of growth. After contact is made, that is, after neuronal interconnections are formed, a second branching strategy is adopted, favoring higher efficiency in neurite length and volume. The two‐phase development theory is discussed in relation to previous results. © 2004 Wiley Periodicals, Inc. J Neurobiol, 2005     

Neuronal organization of the periamygdaloid cortex in the cat brain

Neuronal organization of the fields Pmm, Pml2, Pe and epm of the periamygdaloid cortex of the cat brain has been studied by means of Golgi and Nissl methods. The field Pmm essentially differs from other fields of this cortex by primitiveness of its cytoarchitectonic an neuronal organization (two layers uniform by the composition of their neurons are distinguished, the structure of the latter is relatively primitive). In the medial part of this field long axonal rarely branching short dendritic, and in the lateral part--poorly differentiating pyramidal and spindle-like cells predominate. The field Pmm can be considered as a transitional formation between the subcortex (the medial nucleus of the amygdaloid body) and other fields of the periamygdaloid cortex. The fields Pml2, Pe and epm are built more complexly: the cells are organized in 4 layers, more complexly differentiated by their form and size than in the field Pmm and correspondingly more various (long axonal densely branching cells are observed: pyramidal and spindle-like--of the cortical type and bushy--of the subcortical type, as well as long axonal rarely branching reticular cells). The short axonal cells in the fields Pml2, Pe and epm are rather variable in their form, size and direction of axons; in the field Pmm they are less numerous. The field Pmm and the complex of the fields Pml2, Pe and epm are perhaps different in their function, this is evident from different projection of their neurons. Axons of the cells in the field Pmm get into less differentiated and the most ancient medial nucleus of the amygdaloid body and into the ancient system of connections of the latter--terminal strip, and neurons of the fields Pml2, Pe and epm are projected into the basolateral part of the amygdaloid body and into the external capsule--phylogenetically younger structures. Besides, poverty of the axonal collateralies in the long axonal neurons and a small amount and uniformity of the forms of the short axonal cells in the field Pmm and contrary, rich collateralies and variety of short axonal cells in the composition of other fields demonstrate more complex internal integrative function, performing in that composition.     

Neuronal types in the lateral geniculate nucleus of man

Summary Nerve cell types of the lateral geniculate body of man were investigated with the use of a transparent Golgi technique that allows study of not only the cell processes but also the pigment deposits. Three types of neurons have been distinguished:Type-I neurons are medium-to large-sized multipolar nerve cells with radiating dendrites. Dendritic excrescences can often be encountered close to the main branching points. Type-I neurons comprise a variety of forms and have a wide range of dendritic features. Since all intermediate forms can be encountered as well, it appears inadequate to subdivide this neuronal type. One pole of the cell body contains numerous large vacuolated lipofuscin granules, which stain weakly with aldehyde fuchsin.Type-II and type-III neurons are small cells with few, sparsely branching and extended dendrites devoid of spines. In Golgi preparations they cannot be distinguished from each other. Pigment preparations reveal that the majority of these cells contains small and intensely stained lipofuscin granules within their cell bodies (type II), whereas a small number of them remains devoid of any pigment (type III). Intermediate forms do not occur.     

The relationship of intramuscular nerve branching and synaptogenesis to motoneuron survival

The target has been considered for some time to play a major role in allowing neurons to survive the period of naturally occurring cell death. For the motoneurons that innervate the chick limb, evidence is presented that suggests access to target-derived trophic factor via intramuscular nerve branches and synapses may be important in regulating neuronal survival. Alterations in branching and synapse formation produced by activity blockade as well as by alteration of adhesion molecule function are shown to result in changes in motoneuron survival consistent with the proposed hypothesis. The relevance of these observations to the numerical-matching hypothesis of vertebrate neuronal cell death is also considered. © 1992 John Wiley & Sons, Inc.     

Difference of pericentral NADPH-d positive neurons in the rabbit spinal cord segments

The purpose of the present investigation was to characterize and determine the number of NADPH-diaphorase positive neurons around the central canal in the rabbit spinal cord. These neurons are known to function as interneurons and are present in all spinal cord segments. They differ in shape of their bodies and in length and branching of their processes. The main differentiation was observed in their number, depending on the place of their localization. The highest number of these NADPH-diaphorase positive neurons was in sacral part (6 in average), the lowest one was noticeable in thoracic spinal cord (1-2 in average). It can be concluded that pericentral neurons of the rabbit spinal cord are capable of synthesizing nitric oxide and that they differ in number, depending on the place of their localization in each spinal cord segment.     

DiI-Labeling of DRG Neurons to Study Axonal Branching in a Whole Mount Preparation of Mouse Embryonic Spinal Cord

Here we present a technique to label the trajectories of small groups of DRG neurons into the embryonic spinal cord by diffusive staining using the lipophilic tracer 1,1''-dioctadecyl-3,3,3'',3''-tetramethylindocarbocyanine perchlorate (DiI)¹. The comparison of axonal pathways of wild-type with those of mouse lines in which genes are mutated allows testing for a functional role of candidate proteins in the control of axonal branching which is an essential mechanism in the wiring of the nervous system. Axonal branching enables an individual neuron to connect with multiple targets, thereby providing the physical basis for the parallel processing of information. Ramifications at intermediate target regions of axonal growth may be distinguished from terminal arborization. Furthermore, different modes of axonal branch formation may be classified depending on whether branching results from the activities of the growth cone (splitting or delayed branching) or from the budding of collaterals from the axon shaft in a process called interstitial branching² (Fig. 1).The central projections of neurons from the DRG offer a useful experimental system to study both types of axonal branching: when their afferent axons reach the dorsal root entry zone (DREZ) of the spinal cord between embryonic days 10 to 13 (E10 - E13) they display a stereotyped pattern of T- or Y-shaped bifurcation. The two resulting daughter axons then proceed in rostral or caudal directions, respectively, at the dorsolateral margin of the cord and only after a waiting period collaterals sprout from these stem axons to penetrate the gray matter (interstitial branching) and project to relay neurons in specific laminae of the spinal cord where they further arborize (terminal branching)³. DiI tracings have revealed growth cones at the dorsal root entry zone of the spinal cord that appeared to be in the process of splitting suggesting that bifurcation is caused by splitting of the growth cone itself⁴ (Fig. 2), however, other options have been discussed as well⁵.This video demonstrates first how to dissect the spinal cord of E12.5 mice leaving the DRG attached. Following fixation of the specimen tiny amounts of DiI are applied to DRG using glass needles pulled from capillary tubes. After an incubation step, the labeled spinal cord is mounted as an inverted open-book preparation to analyze individual axons using fluorescence microscopy.     

Control of dendritic field formation in Drosophila: the roles of flamingo and competition between homologous neurons

Neurons elaborate dendrites with stereotypic branching patterns, thereby defining their receptive fields. These branching patterns may arise from properties intrinsic to the neurons or competition between neighboring neurons. Genetic and laser ablation studies reported here reveal that different multiple dendritic neurons in the same dorsal cluster in the Drosophila embryonic PNS do not compete with one another for dendritic fields. In contrast, when dendrites from homologous neurons in the two hemisegments meet at the dorsal midline in larval stages, they appear to repel each other. The formation of normal dendritic fields and the competition between dendrites of homologous neurons require the proper expression level of Flamingo, a G protein-coupled receptor-like protein, in embryonic neurons. Whereas Flamingo functions downstream of Frizzled in specifying planar polarity, Flamingo-dependent dendritic outgrowth is independent of Frizzled.     

Neuronal organization of field 4 of the motor cortex of the cat brain

By means of the silver nitrate impregnation method after Golgi-Kopsch in kittens and young cats the field 4 in the cerebral motor cortex has been studied. The motor cortex of the field 4 possesses certain heteromorphism. Besides usual stellate and pyramidal neurons, that differ from real ones by some morphological signs: their body is often round, the apical dendrite is much thinner than the corresponding dendrite of a pyramidal neuron, it does not produce oblique branches along the course, never gets into the I layer, the spines arrange less densely. According to the mode of dendrites setting off, the atypical pyramidal neurons can be divided into multipolar and spindle-like with horizontal or vertical branching of the dendrites. According to the spines distribution, the multipolar atypical neurons can be divided into spinous, rare-spinous and aspinous. With respect to various cellular forms and distribution of various types of neurons in layers, every of the areas (gamma, alpha, sfu, fu) possesses specific peculiarities. The greatest variability of the neurons have the field 4 gamma and 4 alpha, where, besides stellate and pyramidal, atypical neurons can be found. The stellate neurons of the field 4 gamma are characterized with a deep arrangement, their number is essentially less, than in other areas of the field 4. In the field 4 alpha they are situated in the layers II-III. Suprafundal and fundal parts of the field do not possess pyramidal atypical neurons and are characterized with presence of large amount of the stellate neurons. In respect to the axonal branching in the suprafundal part of the field 4, 2 types of the stellate cells are distinguished.     

Synaptoarchitectonics of the ganglia of the celiac plexus in white rats

In 50 intact white rats at the age of 6, 15, 23 and 30 months synapsoarchitectonics of the celiac plexus nodes was studied by an electron microscopy method. Peculiarities in synapsoarchitectonics are stipulated by pericaryon processes in neurons, some of them have no contacts with the axonal terminals, while others have contacts with the axonal terminals. The former include small (about 0.5 mkm) drop-like and large (up to 1.5 mkm) polymorphous processes within the limits of perisomatic membrane, as well as processes penetrating the neuronal capsule. All of them contain, in different combinations, vesicles, ribosomas, fibrillae, and the largest processes--small cisterns of granular cytoplasmatic network and single mitochondria. The processes of the first group are considered as original stages for the development of the second group processes. The latter are represented by different in size (about 1.0--2.0 mkm) in form (digital, cone-, pin-, goblet-shaped, cylindrical, branching) and in content formations. There is, as a rule, one contact on the processes of an uncomplicated form, while on the branching processes there can be up to three and more contacting axonal terminals. Peculiar features in the composition of the processes taken as a whole (specific forms, absence of dendritic tubes, sometimes numerous contacts with axonal terminals in spite of small size) distinguish them from newly forming dendritic processes and these formations are considered as independent specialized receptor apparatus in the pericaryon of neurons of the celiac plexus.     

The quantitative morphological characteristics of the neurons of the anterior horns of the spinal cord in the kitten]

Golgi preparations of cervical part of the spinal cord of 30-day kittens were used to study sparely and densely branching neurons of lamina VII, sparely and densely branching neurons of lamina VIII and big densely branching motor neurons (as classified by Leontovich) of medial and lateral regions of lamina IX. Qualitative morphological characteristics of geometry of each cell type were obtained by the method of computerized morphometry. The details of the structure of neurons belonging to different laminae of grey matter are discussed.     

Genetic manipulation of single neurons in vivo reveals specific roles of flamingo in neuronal morphogenesis

To study the roles of intracellular factors in neuronal morphogenesis, we used the mosaic analysis with a repressible cell marker (MARCM) technique to visualize identifiable single multiple dendritic (MD) neurons in living Drosophila larvae. We found that individual neurons in the peripheral nervous system (PNS) developed clear morphological polarity and diverse dendritic branching patterns in larval stages. Each MD neuron in the same dorsal cluster developed a unique dendritic field, suggesting that they have specific physiological functions. Single-neuron analysis revealed that Flamingo did not affect the general dendritic branching patterns in postmitotic neurons. Instead, Flamingo limited the extension of one or more dorsal dendrites without grossly affecting lateral branches. The dendritic overextension phenotype was partially conferred by the precocious initiation of dorsal dendrites in flamingo mutant embryos. In addition, Flamingo is required cell autonomously to promote axonal growth and to prevent premature axonal branching of PNS neurons. Our molecular analysis also indicated that the amino acid sequence near the first EGF motif is important for the proper localization and function of Flamingo. These results demonstrate that Flamingo plays a role in early neuronal differentiation and exerts specific effects on dendrites and axons.     

Differential effects of ret and TRKB on axonal branching and survival of parasympathetic neurons

Interactions between neurons and their targets of innervation influence many aspects of neural development. To examine how synaptic activity interacts with neurotrophic signaling, we determined the effects of blocking neuromuscular transmission on survival and axonal outgrowth of ciliary neurons from the embryonic chicken ciliary ganglion. Ciliary neurons undergo a period of cell loss due to programmed cell death between embryonic Days (E) 8 and 14 and they innervate the striated muscle of the iris. The nicotinic antagonist d‐tubocurarine (dTC) induces an increase in branching measured by counting neurofilament‐positive voxels (NF‐VU) in the iris between E14‐17 while reducing ciliary neuron survival. Blocking ganglionic transmission with dihyro‐β‐erythroidin and α‐methyllycacontine does not mimic dTC. At E8, many trophic factors stimulate neurite outgrowth and branching of neurons placed in cell culture; however, at E13, only GDNF stimulates branching selectively in cultured ciliary neurons. The GDNF‐induced branching at E13 could be inhibited by BDNF. Blocking ret signaling in vivo with a dominant negative (dn)ret decreases survival of ciliary and choroid neurons at E14 and prevents dTC induced increases in NF‐VU in the iris at E17. Blocking TRKB signaling with dn TRKB increases NF‐VU in the iris at E17 and decreases neuronal survival at E17, but not at E14. Thus, RET promotes survival during programmed cell death in the ciliary ganglion and contributes to promoting branching when synaptic transmission is blocked while TRKB inhibits branching and promotes maintenance of neuronal survival. These studies highlight the multifunctional nature of trophic molecule function during neuronal development. © 2012 Wiley Periodicals, Inc. Develop Neurobiol, 2013