Quantitative phylogenetic constancy of cerebellar Purkinje cell morphological complexity

Hormones and the neuromuscular control of courtship in the golden-collared manakin (Manacus vitellinus)

Many animals engage in spectacular courtship displays, likely recruiting specialized neural, hormonal and muscular systems to facilitate these performances. Male golden-collared manakins (Manacus vitellinus) of Panamanian rainforests perform physically elaborate courtship displays that include novel forms of visual and acoustic signaling. We study the behavioral neuroendocrinology of this male's courtship, combining field behavioral observations with anatomical, biochemical and molecular laboratory-based studies. Seasonally, male courtship is activated by testosterone with little correspondence between testosterone levels and display intensity. Females prefer males whose displays are exceptionally frequent, fast and accurate. The activation of androgen receptors (AR) is crucial for optimal display performance, with AR expressed at elevated levels in several neuromuscular tissues. Apparently, courtship enlists an elaborate androgen-dependent network that includes spinal motoneurons, skeletal muscles and somatosensory systems. This work highlights the value of studying non-traditional species to illuminate physiological adaptations and, hopefully, stimulates future research on other species with complex behaviors.

Altered branching patterns of Purkinje cells in mouse model for cortical development disorder

Disrupted cortical cytoarchitecture in cerebellum is a typical pathology in reeler. Particularly interesting are structural problems at the cellular level: dendritic morphology has important functional implication in signal processing. Here we describe a combinatorial imaging method of synchrotron X-ray microtomography with Golgi staining, which can deliver 3-dimensional(3-D) micro-architectures of Purkinje cell(PC) dendrites, and give access to quantitative information in 3-D geometry. In reeler, we visualized in 3-D geometry the shape alterations of planar PC dendrites (i.e., abnormal 3-D arborization). Despite these alterations, the 3-D quantitative analysis of the branching patterns showed no significant changes of the 77 ± 8° branch angle, whereas the branch segment length strongly increased with large fluctuations, comparing to control. The 3-D fractal dimension of the PCs decreased from 1.723 to 1.254, indicating a significant reduction of dendritic complexity. This study provides insights into etiologies and further potential treatment options for lissencephaly and various neurodevelopmental disorders.

Recovery of motor and cognitive function after cerebellar lesions in a songbird: role of estrogens

In addition to its key role in complex motor function, the cerebellum is increasingly recognized to have a role in cognition. Songbirds are particularly good models for the investigation of motor and cognitive processes but little is known about the role of the songbird cerebellum in these processes. To explore cerebellar function in a songbird, we lesioned the cerebellum of adult female zebra finches and examined the effects on a spatial working memory task and on motor function during this task. There is evidence for steroid synthesis in the songbird brain and neurosteroids may have an impact on some forms of neural plasticity in adult songbirds. We therefore hypothesized that neurosteroids would affect motor and cognitive function after a cerebellar injury. We found that cerebellar lesions produced deficits in motor and cognitive aspects of a spatial task. In line with our prediction, birds in which estrogen synthesis was blocked had impaired performance in our spatial task compared with those that had estrogen synthesis blocked but estrogen replaced. There was no clear effect of estrogen replacement on motor function. We also found that lesions induced expression of the estrogen synthetic enzyme aromatase in reactive astrocytes and Bergmann glia around a cerebellar lesion. These data suggest that the cerebellum of songbirds mediates both motor and cognitive function and that estrogens may improve the recovery of cognitive aspects of cerebellar function after injury.

Development of gerbil medial superior olive: integration of temporally delayed excitation and inhibition at physiological temperature

The sensitivity of medial superior olive (MSO) neurons to tens of microsecond differences in interaural temporal delay (ITD) derives in part from their membrane electrical characteristics, kinetics and timing of excitatory and inhibitory inputs, and dendrite structure. However, maturation of these physiological and structural characteristics are little studied, especially in relationship to the onset of auditory experience. We showed, using brain slices at physiological temperature, that MSO neurons exhibited sensitivity to simulated temporally delayed (TD) EPSCs (simEPSC), injected through the recording electrode, by the initial phase of hearing onset at P10, and TD sensitivity was reduced by block of low threshold potassium channels. The spike generation mechanism matured between P10 and P16 to support TD sensitivity to adult-like excitatory stimuli (1-4 ms duration) by P14. IPSP duration was shorter at physiological temperature than reported for lower temperatures, was longer than EPSP duration at young ages, but approached the duration of EPSPs by P16, when hearing thresholds neared maturity. Dendrite branching became less complex over a more restricted time frame between P10 and P12. Because many physiological and structural properties approximated mature values between P14 and P16, we studied temporal integration of simEPSCs and IPSPs at P15. Only a narrow range of relative onset times (< 1 ms) yielded responses showing sensitivity to TD. We propose that shaping of excitatory circuitry to mediate TD sensitivity can begin before airborne sound is detectable, and that inhibitory inputs having suboptimal neural delays may then be pruned by cellular mechanisms activated by sensitivity to ITD.

Eye movements of the murine P/Q calcium channel mutant tottering, and the impact of aging

Mice carrying mutations of the gene encoding the ion pore of the P/Q calcium channel (Cacna1a) are an instance in which cerebellar dysfunction may be attributable to altered electrophysiology and thus provide an opportunity to study how neuronal intrinsic properties dictate signal processing in the ocular motor system. P/Q channel mutations can engender multiple effects at the single neuron, circuit, and behavioral levels; correlating physiological and behavioral abnormalities in multiple allelic strains will ultimately facilitate determining which alterations of physiology are responsible for specific behavioral aberrations. We used videooculography to quantify ocular motor behavior in tottering mutants aged 3 mo to 2 yr and compared their performance to data previously obtained in the allelic mutant rocker and C57BL/6 controls. Tottering mutants shared numerous abnormalities with rocker, including upward deviation of the eyes at rest, increased vestibuloocular reflex (VOR) phase lead at low stimulus frequencies, reduced VOR gain at high stimulus frequencies, reduced gain of the horizontal and vertical optokinetic reflex, reduced time constants of the neural integrator, and reduced plasticity of the VOR as assessed in a cross-axis training paradigm. Unlike rocker, young tottering mutants exhibited normal peak velocities of nystagmus fast phases, arguing against a role for neuromuscular transmission defects in the attenuation of compensatory eye movements. Tottering also differed by exhibiting directional asymmetries of the gains of optokinetic reflexes. The data suggest at least four pathophysiological mechanisms (two congenital and two acquired) are required to explain the ocular motor deficits in the two Cacna1a mutant strains.

Fractal dimension in human cerebellum measured by magnetic resonance imaging

Fractal dimension has been used to quantify the structures of a wide range of objects in biology and medicine. We measured fractal dimension of human cerebellum (CB) in magnetic resonance images of 24 healthy young subjects (12 men and 12 women). CB images were resampled to a series of image sets with different 3D resolutions. At each resolution, the skeleton of the CB white matter was obtained and the number of pixels belonging to the skeleton was determined. Fractal dimension of the CB skeleton was calculated using the box-counting method. The results indicated that the CB skeleton is a highly fractal structure, with a fractal dimension of 2.57 +/- 0.01. No significant difference in the CB fractal dimension was observed between men and women.

Morphological classification of the rat lateral cerebellar nuclear neurons by principal component analysis

The deep cerebellar nuclei (DCN) constitute the major structures by which the cerebellum forwards its output to the rest of the brain. Although the connectivity of the DCN has been well studied, little is known about the interface-the neurons' soma and dendrites-between the DCN's inputs and outputs. We therefore decided to analyze the neurons' somatic and dendritic morphology by applying a multivariate approach (principal component analysis; PCA), in order to define morphological groups possibly related to distinct positions in the nuclear microcircuitry. The PCA was based on intracellularly stained neurons from the rat's lateral DCN and on 19 parameters that described the neurons' morphology. The PCA yielded two principal components that accounted for 46% of the variance. The first component, correlated with soma size, separated the majority of neurons (type I) from a population of small neurons (type II). The second component showed negative correlation with larger cells with more numerous primary dendrites and a more multipolar appearance (type Ia) and positive correlation with smaller neurons with asymmetric dendritic fields and tufted dendrites (type Ib). The preponderance of small somata in our type Ib neurons suggests that these neurons probably correspond to the inferior olive projection neurons. In summary, our results are in agreement with previous classifications, which distinguished projection neurons (type I) from local neurons (type II); furthermore, our results point to a hitherto undescribed dendritic morphological difference in the projection neurons. The latter may be important for understanding the phylogenetic changes seen in the mammalian lateral cerebellar nucleus.

Use of fractal theory in neuroscience: methods, advantages, and potential problems

Fractal analysis has already found widespread application in the field of neuroscience and is being used in many other areas. Applications are many and include ion channel kinetics of biological membranes and classification of neurons according to their branching characteristics. In this article we review some practical methods that are now available to allow the determination of the complexity and scaling relationships of anatomical and physiological patterns. The problems of describing fractal dimensions are discussed and the concept of fractal dimensionality is introduced. Several related methodological considerations, such as preparation of the image and estimation of the fractal dimensions from the data points, as well as the advantages and problems of fractal geometric analysis, are discussed.

Fractal dimension analysis of static stabilometry in Parkinson's disease and spinocerebellar ataxia

The static stabilometry patterns associated with Parkinson's disease (PD, n = 15) and spinocerebellar ataxia (SCA, n = 15) were compared with those of normal control (n = 15) by measuring the fractal dimensions. Fractal dimensions were estimated using the modified pixel dilation (mPD) method. The fractal dimensions with closed eyes showed a significant correlation with Environmental area for SCA group (p < 0.05). The fractal dimension for SCA group was significantly higher with closed eyes than that with open eyes (p < 0.05). The fractal dimension with closed eyes was significantly higher in PD and SCA groups than that in normal group (p < 0.05). The fractal dimension with closed eyes was higher when the clinical stage was more severe with PD and SCA group while Environmental and Longitude/Environmental areas were not. These findings suggest that the fractal dimension is more sensitive than traditional stabilometric analysis in an evaluation of postural instability in PD and SCA.

Morphology of reactive microglia in the injured cerebral cortex. Fractal analysis and complementary quantitative methods

The present study focuses on application of quantitative methods measuring differences between particular morphological types of microglial cells as well as between their proliferating and non-proliferating examples. On the basis of subjective classification, microglial cells of three morphological types (ramified, hypertrophied and bushy) were selected from the neocortex of injured rat brain. Thereafter, the morphological complexity of each cell was assessed by calculation its fractal dimension as well as its form factor, convexity, ramification factor and solidity. The fractal dimension seemed a good parameter for detecting small changes in the space-filing capacity of cells, for example, it shows differences between ramified cells from control and injured brains. This measure seemed insensitive to some aspects of cell morphology. To obtain precise quantification of observed changes other morphological parameters had to be applied. Proliferating and non-proliferating microglial cells displayed significant differences in their solidity and ramification factors, but not in fractal dimension and convexity. The results indicated that proliferating microglia were more massive and less-ramified but they did not reduce their spatial complexity.

Neurons and fractals: how reliable and useful are calculations of fractal dimensions?

In the past 15 years it has become possible to determine the fractal dimension (Df) of complex objects, including neurons, by automated image analysis methods. However, there are many unresolved issues that need to be addressed. In this paper we discuss how the Df calculated by different methods may vary and how fractal analysis may be of use for retinal ganglion cell characterization. The goal of this work was to acknowledge inherent sources of variation during measurement and evaluate current fractal analysis methods for describing structure. Our results show that different algorithms and even the same algorithm performed by different computer programs and/or experimenters may give different but consistent numerical values. All described methods demonstrated their suitability for classifying cat retinal ganglion cells into distinct groups. Our results reinforce the idea that comparison of measurements of different profiles using the same measurement method may be useful and valid even if an exact numeric value of the dimension is not realised in practice.

Chick cerebellar Purkinje cells express omega-conotoxin GVIA-sensitive rather than funnel-web spider toxin-sensitive calcium channels

Voltage-gated calcium channels form a complex family of distinct molecular entities which participate in multiple neuronal functions. In cerebellar Purkinje cells these channels contribute to the characteristic electrophysiological pattern of complex spikes, first described in birds and later in mammals. A specific calcium channel, the P-type channel, has been shown to mediate the majority of the voltage-gated calcium flux in mammalian Purkinje cells. P-type channels play an essential role in synaptic transmission of mammalian cerebellum. It is unclear whether the P-type calcium channel is present in birds. Studies in chick synaptosomal preparations show that the pharmacological profile of calcium channels is complex and suggest a minimal expression of the P-type channel in avian central nervous system. In the present work, we studied voltage-gated calcium channels in dissociated chick cerebellar Purkinje cells to examine the presence of different calcium channel types. Purkinje cells were used because, in mammals, they express predominantly P-type channels and because the morphology of these cells is thought to be phylogenetically conserved. We found that omega-conotoxin GVIA (omega-CgTx GVIA), a specific antagonist of N-type calcium channel, rather than the synthetic funnel-web spider toxin (sFTX), a P-type channel antagonist, blocks the majority of the barium current flowing through calcium channels in chick Purkinje neurons.

Fractals in pathology

Many natural objects, including most objects studied in pathology, have complex structural characteristics and the complexity of their structures, for example the degree of branching of vessels or the irregularity of a tumour boundary, remains at a constant level over a wide range of magnifications. These structures also have patterns that repeat themselves at different magnifications, a property known as scaling self-similarity. This has important implications for measurement of parameters such as length and area, since Euclidean measurements of these may be invalid. The fractal system of geometry overcomes the limitations of the Euclidean geometry for such objects and measurement of the fractal dimension gives an index of their space-filling properties. The fractal dimension may be measured using image analysis systems and the box-counting, divider (perimeter-stepping) and pixel dilation methods have all been described in the published literature. Fractal analysis has found applications in the detection of coding of coding regions in DNA and measurement of the space-filling properties of tumours, blood vessels and neurones. Fractal concepts have also been usefully incorporated into models of biological processes, including epithelial cell growth, blood vessel growth, periodontal disease and viral infections.

Complexity analysis of oligodendroglial processes expressing myelin-associated glycoprotein

Oligodendroglia synthesize myelin in the mammalian central nervous system. Mature oligodendroglia have been identified in culture by two criteria; the expression of molecules characteristic of myelin, such as galactocerebroside (galC) and myelin-associated glycoprotein (MAG), and the elaboration of complex processes. Myelin gene expression can be documented by the binding of specific antibodies and antisera to the myelin-specific molecules; process complexity can be described by the fractal dimension, D. In this study, anti-MAG antisera was used to document MAG expression in the processes of oligodendroglia. Eighty percent of the galC+ oligodendroglia bound anti-MAG antiserum. With time in culture, MAG immunoreactivity seemed to extend from the cell soma into the oligodendroglial processes. To quantify this observation, fractal dimensions were calculated using either galC or MAG immunoreactivity to visualize oligodendroglial processes. A fractal dimension of 1.5 was calculated for O1+ processes by day 4 of culture; this value for D remained constant over the course of 1 month in culture. The fractal dimension calculated for MAG+ processes increased from 1.2 to 1.5 over the course of 28 days in culture. This change in fractal dimension confirms our visual impression that galC-containing processes acquire MAG slowly over the course of several weeks in culture.

Retinal neurons and vessels are not fractal but space-filling

Many branched patterns in nature are hypothesized to be fractal, i.e., statistically self-similar across a range of scales. We tested this hypothesis on the two-dimensional arbors of retinal neurons and blood vessels. First, we measured fractalness on synthetic fractal and nonfractal patterns. The synthetic fractal patterns exhibited self-similarity over a decade of scale, but the nonfractal "controls" showed hardly any self-similarity. Neuronal and vascular patterns showed no greater self-similarity than the controls. Second, we manipulated a synthetic fractal pattern to remove its self-similarity and found this to be reflected in a loss of measured fractalness. The same manipulation of the nonfractal control and also of the neural and vascular patterns did not alter their measured fractalness. Third, we "grew" patterns of branched line segments according to a variety of nonfractal algorithms. These patterns were, if anything slightly more fractal than the neural and vascular patterns. We conclude that the biological patterns studied here are not fractal. Finally, we measured extended versions of these patterns: a contiguous array of homotypic neuron arbors and a vascular pattern with a high degree of total detail. These patterns showed a "fractal dimension" of 2, which implies that down to some cut-off scale they fill space completely. Thus, neural and vascular patterns might best be described as quasi-regular lattices.

Quantification of tight junction complexity by means of fractal analysis

The concept of fractal geometry provides an elegant tool for the quantitative and objective structural description of various objects, the fractal analysis. Fractal analysis quantifies the structural complexity of objects by a characteristic singular value, the fractal dimension (FD). It can be estimated, e.g. by the box-counting method and provides a highly integrated measure in the range 1 < FD < 2 for curves extending within a plane. In this study, fractal analysis is used for the first time to evaluate the complexity of the tight junction network between adjoining cells. Bovine brain endothelial cells were cultured under various experimental conditions and the tight junctions were drawn to scale as visualized by the freeze fracture technique. These drawings were analyzed by fractal analysis, and by two other methods commonly used in this field, viz. the strand counting (SC) and complexity index (CI) methods. In contrast to the latter methods, the FD shows no directional preference and therefore no assumptions on the dynamic properties of the network's complexity are required. Thus, FD is demonstrated to provide the most sensitive, reliable and complete measure of tight junction complexity. In combination with SC and CI, additional information can be achieved concerning the directionality of the altered arrangement of tight junctional strands. Our analysis allows for the following conclusions. (1) Defined experimental influences can modify the complexity of tight junctions that are formed between endothelial cells in vitro, and (2) these structural modifications of the tight junctions are mainly due to an altered strand branching pattern.

Complexity and scaling properties of amacrine, ganglion, horizontal, and bipolar cells in the turtle retina

In the present study we have evaluated the complexity and scaling properties of the morphology of retinal neurons using fractal dimension as a quantitative parameter. We examined a large number of cells from Pseudemys scripta and Mauremys caspica turtles that had been labeled using Golgi-impregnation techniques, intracellular injection of Lucifer Yellow followed by photooxidation, intracellular injection of rhodamine conjugated horseradish peroxidase, or intracellular injection of Lucifer Yellow or horseradish peroxidase alone. The fractal dimensions of two-dimensional projections of the cells were calculated using a box counting method. Discriminant analysis revealed fractal dimension to be a significant classification parameter among several other parameters typically used for placing turtle retinal neurons in different cell classes. The fractal dimension of amacrine cells was significantly correlated with dendritic field diameters, while the fractal dimensions of ganglion cells did not vary with dendritic field span. There were no significant differences between the same cell types in two different turtle species, or between the same types of neurons in the same species after labeling with different techniques. The application of fractal dimension, as a quantitative measure of complexity and scaling properties and as a classification criterion of neuronal types, appears to be useful and may have wide applicability to other parts of the central nervous system.

Preserved features of thalamocortical projection neuron dendritic architecture in the somatosensory thalamus of the rat, cat and macaque

A number of studies have shown that the organization of the mammalian somatosensory thalamus varies between species. As differences in cellular and synaptic thalamic organization would be expected to influence neuronal dendritic architecture, we compared somatosensory thalamocortical projection (TCP) neurons from the rat, cat and macaque. The results show that key features of the dendritic branching pattern remain unchanged despite large differences in the size of TCP neurons between the species. The features examined were: (i) ratio of the length of terminal branches to the length of the entire dendritic tree; (ii) the percentage of branch points that gave rise to two daughter branches as opposed to those that gave rise to three or more daughter branches; (iii) the proportional sum of absolute deviations (a measure of branching symmetry), and (iv) the mean branch order of the terminal segments. The present study provides evidence that somatosensory TCP neurons in these species comprise a homogeneous class and share a common dendritic architecture that is conserved across species despite changes in other aspects of thalamic circuitry. This suggests that TCP neuronal form is based on relatively stable genetic blueprint and that epigenetic factors (e.g. synaptic input) resulting from evolutionary changes in thalamic organization have had less influence on dendritic architecture.

Comparative fractal analysis of cultured glia derived from optic nerve and brain demonstrate different rates of morphological differentiation

O-2A progenitor cells derived from neonatal rat cerebral hemispheres or optic nerves, were induced to differentiate in culture into either oligodendrocytes or type 2 astrocytes. The fractal dimensions, a measure of morphological complexity, of the differentiating glial cells were measured over time. Analysis of the changes in fractal dimension (D) with respect to time revealed specific rates of growth for each glial phenotype and a specific final D. The time course of these changes is well fit by a simple mathematical model. While brain-derived oligodendrocytes matured faster than the astrocytes, they ultimately attained comparable levels of complexity, with similar maximum fractal dimensions. Oligodendrocytes from nerve also matured faster than nerve derived astrocytes, in contrast, however, they attained a greater morphological complexity than nerve astrocytes. While the brain-derived oligodendrocytes showed a faster rate of maturation than their optic nerve counterparts, astrocytes from both regions had similar rates of morphological differentiation. Self-similarity, a defining property of fractal objects was investigated, by determining the fractal dimension of cells over a range of magnifications. The calculated fractal dimension remained constant over a 10-fold range in optical magnification, illustrating that cultured glial cells exhibit this important characteristic of fractal objects. In addition, we analyzed the branching patterns of glial processes by the Sholl method and found that the results were not as interpretable or meaningful as those of fractal analysis.