Characterization of melanophore morphology by fractal dimension analysis

Fractal or focal dimension (FD) analysis is a valuable tool to identify physiologic stimuli at the cellular and tissue levels that allows for quantification of cell perimeter complexity. The FD analysis was determined on fluorescence images of caffeine- or epinephrine-treated (or untreated control) killifish Fundulus heteroclitus (Linneaus) melanophores in culture. Cell perimeters were indicated by rhodamine-phalloidin labeling of cortical microfilaments using box-counting FD analysis. Caffeine-treated melanophores displayed dispersed melanosomes in cells with less serrated edges and reduced FD and complexity. Complexity in epinephrine-treated cells was significantly higher than the caffeine-treated cells or in the control. Cytoarchitectural variability of the cell perimeter is expected because cells change shape when cued with agents. Epinephrine-treated melanophores demonstrated aggregated melanosomes in cells with more serrated edges, significantly higher FD and thus complexity. Melanophores not treated with caffeine or epinephrine produced variable distributions of melanosomes and resulted in cells with variably serrated edges and intermediate FD with a larger SE of the regression and greater range of complexity. Dispersion of melanosomes occurs with rearrangements of the cytoskeleton to accommodate centrifugal distribution of melanosomes throughout the cell and to the periphery. The loading of melanosomes onto cortical microfilaments may provide a less complex cell contour, with the even distribution of the cytoskeleton and melanosomes. Aggregation of melanosomes occurs with rearrangements of the cytoskeleton to accommodate centripetal distribution of melanosomes. The aggregation of melanosomes may contribute to centripetal retraction of the cytoskeleton and plasma membrane. The FD analysis is, therefore, a convenient method to measure contrasting morphologic changes within stimulated cells.     

The effect of type 1 astrocytes on neuronal complexity: a fractal analysis

Embryonic, ventral spinal cord neurons were grown on poly(d-lysine) (PDL) or on a monolayer of type 1 astrocytes. At various times from 6 h to 2 weeks postplating, cells were fluorescently labeled and fixed with 4% paraformaldehyde. The cell surface immunoreaction allowed visualization of neurons in their entirety, namely, cell bodies and various membranous extensions that included lamellipodia, growth cones, axons, and dendrites. Outlines were drawn for individual neurons and their fractal dimension (D) was calculated. Neurons on poly(d-lysine) reached a peak D at 3 days in vitro, 1 day later than neurons on astrocytes (2 days in vitro). The maximum D was greater for cells on poly(d-lysine) when compared with neurons on astrocytes. In a second experiment the maximum D was similar for neurons on both surfaces but neurons on PDL maintained a higher D for a much longer period than neurons on astrocytes. An examination of fluorescent images revealed that neurons on poly(d-lysine) exhibited lamellipodia and large growth cones for several days and these structures were likely responsible for the high D seen in these cells. These structures were rarely observed in neurons plated on astrocytes. Interestingly, D on both surfaces decreased to a similar value at between 1 and 2 weeks in vitro. The trend for D in these cultures, an initial increase to a peak value followed by a decrease to a stable value, is discussed in light of the chemical nature of the two surfaces and synapse formation and stabilization.     

Fungal fractal morphology of pellet formation in Aspergillus niger

Mycelial fractal values were compared to the conventional fungal morphological parameters: average total mycelial length, average number of tips and average growth unit. The fractal values were between 1.47 to 1.3 for the various submerged culture conditions of Aspergillus niger. The average pellet diameter was 1.4 mm at the fractal value of 1.47. The mycelia with fractal values close to 1 were less branched and slim.     

A fractal model for the characterization of mycelial morphology

A new technique based on a fractal model has been developed for the quantification of the macroscopic morophology of mycelia. The morphological structuring is treated as a fractal object, and the fractal dimension, determined by an ultrasonic scattering procedure developed for the purpose, serves as a quantitative morphological index. Experimental observations reported earlier and simulations of mycelial growth, carried out using a probabilistic-geometric growth model developed for the purpose, both validate the applicability of the fractal model. In experiments with three different species, the fractal dimensions of pelletous structures were found to be in the range 1.45-2.0 and those of filamentous structures were in the range 1.9-2.7, with values around 2.0 representing mixed morphologies. Fractal dimensions calculated from simulated mycelia are in rough agreement with these ranges. The fractal dimension is also found to be relatively insensitive to the biomass concentration, as seen by dilution of the original broths. The relation between morphology and filtration properties of the broths has also been studied. The fractal dimension shows a strong correlation with the index of cake compressibility and with the Kozeny constant, two filtration parameters that are known to be morphology dependent. This technique could thus be used to develop correlations between the morphology, represented by the fractal dimension, and important morphology-dependent process variables. (c) 1993 John Wiley & Sons, Inc.     

Deriving physical connectivity from neuronal morphology

 A model is presented that allows prediction of the probability for the formation of appositions between the axons and dendrites of any two neurons based only on their morphological statistics and relative separation. Statistics of axonal and dendritic morphologies of single neurons are obtained from 3D reconstructions of biocytin-filled cells, and a statistical representation of the same cell type is obtained by averaging across neurons according to the model. A simple mathematical formulation is applied to the axonal and dendritic statistical representations to yield the probability for close appositions. The model is validated by a mathematical proof and by comparison of predicted appositions made by layer 5 pyramidal neurons in the rat somatosensory cortex with real anatomical data. The model could be useful for studying microcircuit connectivity and for designing artificial neural networks. Received: 11 February 2002 / Accepted: 5 November 2002 / Published online: 20 February 2003 Correspondence to: H. Markram (e-mail: Henry.Markram@epfl.ch Tel.: +41-21-6939537, Fax: +41-21-6935350) Acknowledgements. This study was supported by the National Alliance for Autism Research, the Minerva Foundation, the US Navy, the Ebner Center for Biomedical Research, and the Edith Blum Foundation.     

The development of neuronal morphology in insects

Neurons are highly polarized cells with some regions specified for information input--typically the dendrites--and others specialized for information output--the axons. By extending to a specific location and branching in a specific manner, the processes of neurons determine at a fundamental level how the nervous system is wired to produce behavior. Recent studies suggest that relatively small changes in neuronal morphology could conceivably contribute to striking behavioral distinctions between invertebrate species. We review recent data that begin to shed light on how neurons extend dendrites to their targets and acquire their particular branching morphologies, drawing primarily on data from genetic model organisms. We speculate about how and why the actions of these genes might facilitate the diversification of dendritic morphology.     

High-resolution analysis of neuronal growth cone morphology by comparative atomic force and optical microscopy

Neuronal growth cones are motile sensory structures at the tip of axons, transducing guidance information into directional movements towards target cells. The morphology and dynamics of neuronal growth cones have been well characterized with optical techniques; however, very little quantitative information is available on the three-dimensional structure and mechanical properties of distinct subregions. In the present study, we imaged the large Aplysia growth cones after chemical fixation with the atomic force microscope (AFM) and directly compared our data with images acquired by light microscopy methods. Constant force imaging in contact mode in combination with force-distant measurements revealed an average height of 200 nm for the peripheral (P) domain, 800 nm for the transition (T) zone, and 1200 nm for the central (C) domain, respectively. The AFM images show that the filopodial F-actin bundles are stiffer than surrounding F-actin networks. Enlarged filopodia tips are 60 nm higher than the corresponding shafts. Measurements of the mechanical properties of the specific growth cone regions with the AFM revealed that the T zone is stiffer than the P and the C domain. Direct comparison of AFM and optical data acquired by differential interference contrast and fluorescence microscopy revealed a good correlation between these imaging methods. However, the AFM provides height and volume information at higher resolution than fluorescence methods frequently used to estimate the volume of cellular compartments. These findings suggest that AFM measurements on live growth cones will provide a quantitative understanding of how proteins can move between different growth cone regions.     

A single-cell model to study changes in neuronal fractal dimension

Many methods have been developed to quantify neuronal morphology: measurement of neurite length, neurite number, etc. However, none of these approaches provides a comprehensive view of the complexity of neuronal morphology. In this work we have analyzed the evaluation of fractal dimension (D) as a tool to represent and quantify changes in complexity of the dendritic arbor, in in vitro cultures grown under low-density conditions. Neurons grown in isolation developed a bipolar morphology corresponding to a fractal dimension close to the unit. The analysis showed that neuronal complexity increased when cells were incubated with a depolarizing potassium concentration and there was a correlation with an increase in fractal dimension (D5 mM KCl = 1.08 +/- 0.01, D25 mM KCl =1.25 +/- 0.01). We conclude that fractal dimension is a suitable parameter to quantify changes in neuronal morphological complexity.     

Mitochondrial trafficking and morphology in neuronal injury

Alterations in mitochondrial function may have a central role in the pathogenesis of many neurodegenerative diseases. The study of mitochondrial dysfunction has typically focused on ATP generation, calcium homeostasis and the production of reactive oxygen species. However, there is a growing appreciation of the dynamic nature of mitochondria within cells. Mitochondria are highly motile organelles, and also constantly undergo fission and fusion. This raises the possibility that impairment of mitochondrial dynamics could contribute to the pathogenesis of neuronal injury. In this review we describe the mechanisms that govern mitochondrial movement, fission and fusion. The key proteins that are involved in mitochondrial fission and fusion have also been linked to some inherited neurological diseases, including autosomal dominant optic atrophy and Charcot–Marie–Tooth disease 2A. We will discuss the evidence that altered movement, fission and fusion are associated with impaired neuronal viability. There is a growing collection of literature that links impaired mitochondrial dynamics to a number of disease models. Additionally, the concept that the failure to deliver a functional mitochondrion to the appropriate site within a neuron could contribute to neuronal dysfunction provides an attractive framework for understanding the mechanisms underlying neurologic disease. However, it remains difficult to clearly establish that altered mitochondrial dynamics clearly represent a cause of neuronal dysfunction.     

Small-world connectivity, motif composition, and complexity of fractal neuronal connections

Connection patterns of the cerebral cortex consist of pathways linking neuronal populations across multiple levels of scale, from whole brain regions to local minicolumns. This nested interconnectivity suggests the hypothesis that cortical connections are arranged in fractal or self-similar patterns. We describe a simple procedure to generate fractal connection patterns that aim at capturing the potential self-similarity and hierarchical ordering of neuronal connections. We examine these connection patterns by calculating a broad range of structural measures, including small-world attributes and motif composition, as well as some global measures of functional connectivity, including complexity. As we vary fractal patterns by changing a critical control parameter, we find strongly correlated changes in several structural and functional measures, suggesting that they emerge together and are mutually linked. Measures obtained from some modeled fractal patterns closely resemble those of real neuroanatomical data sets, supporting the original hypothesis.     

Slow axonal transport and the genesis of neuronal morphology

The classic view of slow axonal transport maintains that microtubules, neurofilaments, and actin filaments move down the axon relatively coherently at rates significantly slower than those characteristic of known motor proteins. Recent studies indicate that the movement of these cytoskeletal polymers is actually rapid, asynchronous, intermittent, and most probably fueled by familiar motors such as kinesins, myosins, and cytoplasmic dynein. This new view, which is supported by both live-cell imaging and mechanistic analyses, suggests that slow axonal transport is both rapid and plastic, and hence could underlie transformations in neuronal morphology.     

Cdc42: an important regulator of neuronal morphology

Regulation of neuronal morphology and activity-dependent synaptic modifications involves reorganization of the actin cytoskeleton. Dynamic changes of the actin cytoskeleton in many cell types are controlled by small GTPases of the Rho family, such as RhoA, Rac1 and Cdc42. As key regulators of both actin and microtubule cytoskeleton, Rho GTPases have also emerged as important regulators of dendrite and spine structural plasticity. Multiple studies suggest that Rac1 and Cdc42 are positive regulators promoting neurite outgrowth and growth cone protrusion, while the activation of RhoA induces stress fiber formation, leading to growth cone collapse and neurite retraction. This review focuses on recent advances in our understanding of the molecular mechanisms underlying physiological and pathological functions of Cdc42 in the nervous system. We also discuss application of different FRET-based biosensors as a powerful approach to examine the dynamics of Cdc42 activity in living cells.     

Applications of fractal analysis to physiology

This review describes approaches to the analysis of fractal properties of physiological observations. Fractals are useful to describe the natural irregularity of physiological systems because their irregularity is not truly random and can be demonstrated to have spatial or temporal correlation. The concepts of fractal analysis are introduced from intuitive, visual, and mathematical perspectives. The regional heterogeneities of pulmonary and myocardial flows are discussed as applications of spatial fractal analysis, and methods for estimating a fractal dimension from physiological data are presented. Although the methods used for fractal analyses of physiological data are still under development and will require additional validation, they appear to have great potential for the study of physiology at scales of resolution ranging from the microcirculation to the intact organism.     

High‐resolution analysis of neuronal growth cone morphology by comparative atomic force and optical microscopy

Neuronal growth cones are motile sensory structures at the tip of axons, transducing guidance information into directional movements towards target cells. The morphology and dynamics of neuronal growth cones have been well characterized with optical techniques; however, very little quantitative information is available on the three‐dimensional structure and mechanical properties of distinct subregions. In the present study, we imaged the large Aplysia growth cones after chemical fixation with the atomic force microscope (AFM) and directly compared our data with images acquired by light microscopy methods. Constant force imaging in contact mode in combination with force‐distant measurements revealed an average height of 200 nm for the peripheral (P) domain, 800 nm for the transition (T) zone, and 1200 nm for the central (C) domain, respectively. The AFM images show that the filopodial F‐actin bundles are stiffer than surrounding F‐actin networks. Enlarged filopodia tips are 60 nm higher than the corresponding shafts. Measurements of the mechanical properties of the specific growth cone regions with the AFM revealed that the T zone is stiffer than the P and the C domain. Direct comparison of AFM and optical data acquired by differential interference contrast and fluorescence microscopy revealed a good correlation between these imaging methods. However, the AFM provides height and volume information at higher resolution than fluorescence methods frequently used to estimate the volume of cellular compartments. These findings suggest that AFM measurements on live growth cones will provide a quantitative understanding of how proteins can move between different growth cone regions. © 2006 Wiley Periodicals, Inc. J Neurobiol, 2006     

Flexible search for single-axon morphology during neuronal spontaneous polarization

Polarization, a disruption of symmetry in cellular morphology, occurs spontaneously, even in symmetrical extracellular conditions. This process is regulated by intracellular chemical reactions and the active transport of proteins and it is accompanied by cellular morphological changes. To elucidate the general principles underlying polarization, we focused on developing neurons. Neuronal polarity is stably established; a neuron initially has several neurites of similar length, but only one elongates and is selected to develop into an axon. Polarization is flexibly controlled; when multiple neurites are selected, the selection is eventually reduced to yield a single axon. What is the system by which morphological information is decoded differently based on the presence of a single or multiple axons? How are stability and flexibility achieved? To answer these questions, we constructed a biophysical model with the active transport of proteins that regulate neurite growth. Our mathematical analysis and computer simulation revealed that, as neurites elongate, transported factors accumulate in the growth cone but are degraded during retrograde diffusion to the soma. Such a system effectively works as local activation-global inhibition mechanism, resulting in both stability and flexibility. Our model shows good accordance with a number of experimental observations.     

Role of mechanical cues in shaping neuronal morphology and connectivity

Neuronal circuits, the functional building blocks of the nervous system, assemble during development through a series of dynamic processes including the migration of neurons to their final position, the growth and navigation of axons and their synaptic connection with target cells. While the role of chemical cues in guiding neuronal migration and axonal development has been extensively analysed, the contribution of mechanical inputs, such as forces and stiffness, has received far less attention. In this article, we review the in vitro and more recent in vivo studies supporting the notion that mechanical signals are critical for multiple aspects of neuronal circuit assembly, from the emergence of axons to the formation of functional synapses. By combining live imaging approaches with tools designed to measure and manipulate the mechanical environment of neurons, the emerging field of neuromechanics will add a new paradigm in our understanding of neuronal development and potentially inspire novel regenerative therapies.     

Growth and morphology of neuronal cell lines cultured in perfusion

Summary To optimize culture conditions and gain a more reliable culturing system for studies of metabolic properties of neuronal cells, a simplified perfusion chamber was developed. It consists of two parts: a perfusion block and a standard plastic culture dish. To confirm the suitability of this chamber for continuous culturing of anchorage-dependent cells, the growth and morphology of the four neuronal cell lines glioma C6 and glioma 138MG, neuroblastoma C1300, clones N1E115 and N18 were followed for 4 d using both traditional and perfusion techniques. A marked increase in growth and a decrease in the degree of morphological differentiation were obtained with the latter technique compared to the former. This work was supported by grants from the National Swedish Board for Technical Development (Grant 81-5009), the Swedish Work Environmental Foundation (Grant 76-53), and Ollie and Elof Ericssons Foundation for Scientific Research.     

Control of neuronal morphology by the atypical cadherin Fat3

Neurons receive signals through dendrites that vary widely in number and organization, ranging from one primary dendrite to multiple complex dendritic trees. For example, retinal amacrine cells (ACs) project primary dendrites into a discrete synaptic layer called the inner plexiform layer (IPL) and only rarely extend processes into other retinal layers. Here, we show that the atypical cadherin Fat3 ensures that ACs develop this unipolar morphology. AC precursors are initially multipolar but lose neurites as they migrate through the neuroblastic layer. In fat3 mutants, pruning is unreliable and ACs elaborate two dendritic trees: one in the IPL and a second projecting away from the IPL that stratifies to form an additional synaptic layer. Since complex nervous systems are characterized by the addition of layers, these results demonstrate that mutations in a single gene can cause fundamental changes in circuit organization that may drive nervous system evolution.