Structure-function correlation in transient amacrine cells of goldfish retina: basic and multifractal analyses of dendritic trees in distinct synaptic layers

Morphology and Fractal-Based Classifications of Neurons and Microglia in Two and Three Dimensions

Microglia and neurons live physically intertwined, intimately related structurally and functionally in a dynamic relationship in which microglia change continuously over a much shorter timescale than do neurons. Although microglia may unwind and depart from the neurons they attend under certain circumstances, in general, together both contribute to the fractal topology of the brain that defines its computational capabilities. Both neuronal and microglial morphologies are well-described using fractal analysis complementary to more traditional measures. For neurons, the fractal dimension has proved valuable for classifying dendritic branching and other neuronal features relevant to pathology and development. For microglia, fractal geometry has substantially contributed to classifying functional categories, where, in general, the more pathological the biological status, the lower the fractal dimension for individual cells, with some exceptions, including hyper-ramification. This chapter provides a review of the intimate relationships between neurons and microglia, by introducing 2D and 3D fractal analysis methodology and its applications in neuron-microglia function in health and disease.

Calbindin-D28k and calretinin in chicken inner retina during postnatal development and neuroplasticity by dim red light

Members of the family of calcium binding proteins (CBPs) are involved in the buffering of calcium (Ca2+) by regulating how Ca2+ can operate within synapses or more globally in the entire cytoplasm and they are present in a particular arrangement in all types of retinal neurons. Calbindin D28k and calretinin belong to the family of CBPs and they are mainly co-expressed with other CBPs. Calbindin D28k is expressed in doubles cones, bipolar cells and in a subpopulation of amacrine and ganglion neurons. Calretinin is present in horizontal cells as well as in a subpopulation of amacrine and ganglion neurons. Both proteins fill the soma at the inner nuclear layer and the neuronal projections at the inner plexiform layer. Moreover, calbindin D28k and calretinin have been associated with neuronal plasticity in the central nervous system. During pre and early postnatal visual development, the visual system shows high responsiveness to environmental influences. In this work we observed modifications in the pattern of stratification of calbindin immunoreactive neurons, as well as in the total amount of calbindin through the early postnatal development. In order to test whether or not calbindin is involved in retinal plasticity we analyzed phosphorylated p38 MAPK expression, which showed a decrease in p-p38 MAPK, concomitant to the observed decrease of calbindin D28k. Results showed in this study suggest that calbindin is a molecule related with neuroplasticity, and we suggest that calbindin D28k has significant roles in neuroplastic changes in the retina, when retinas are stimulated with different light conditions.

Fractal analysis and ionic dependence of endocytotic membrane activity of human breast cancer cells

The endocytic membrane activities of two human breast cancer cell lines (MDA-MB-231 and MCF-7) of strong and weak metastatic potential, respectively, were studied in a comparative approach. Uptake of horseradish peroxidase was used to follow endocytosis. Dependence on ionic conditions and voltage-gated sodium channel (VGSC) activity were characterized. Fractal methods were used to analyze quantitative differences in vesicular patterning. Digital quantification showed that MDA-MB-231 cells took up more tracer (i.e., were more endocytic) than MCF-7 cells. For the former, uptake was totally dependent on extracellular Na(+) and partially dependent on extracellular and intracellular Ca(2+) and protein kinase activity. Analyzing the generalized fractal dimension (D(q )) and its Legendre transform f(alpha) revealed that under control conditions, all multifractal parameters determined had values greater for MDA-MB-231 compared with MCF-7 cells, consistent with endocytic/vesicular activity being more developed in the strongly metastatic cells. All fractal parameters studied were sensitive to the VGSC blocker tetrodotoxin (TTX). Some of the parameters had a "simple" dependence on VGSC activity, if present, whereby pretreatment with TTX reduced the values for the MDA-MB-231 cells and eliminated the differences between the two cell lines. For other parameters, however, there was a "complex" dependence on VGSC activity. The possible physical/physiological meaning of the mathematical parameters studied and the nature of involvement of VGSC activity in control of endocytosis/secretion are discussed.

Patterning of endocytic vesicles and its control by voltage-gated Na+ channel activity in rat prostate cancer cells: fractal analyses

Fractal methods were used to analyze quantitative differences in secretory membrane activities of two rat prostate cancer cell lines (Mat-LyLu and AT-2) of strong and weak metastatic potential, respectively. Each cell's endocytic activity was determined by horseradish peroxidase uptake. Digital images of the patterns of vesicular staining were evaluated by multifractal analyses: generalized fractal dimension (Dq) and its Legendre transform f(alpha), as well as partitioned iterated function system -- semifractal (PIFS-SF) analysis. These approaches revealed consistently that, under control conditions, all multifractal parameters and PIFS-SF codes determined had values greater for Mat-LyLu compared with AT-2 cells. This would agree generally with the endocytic/vesicular activity of the strongly metastatic Mat-LyLu cells being more developed than the corresponding weakly metastatic AT-2 cells. All the parameters studied were sensitive to tetrodotoxin (TTX) pre-treatment of the cells, which blocked voltage-gated Na+ channels (VGSCs). Some of the parameters had a "simple" dependence on VGSC activity, whereby pre-treatment with TTX reduced the values for the MAT-LyLu cells and eliminated the differences between the two cell lines. For other parameters, however, there was a "complex" dependence on VGSC activity. The possible physical/physiological meaning of the mathematical parameters studied and the nature of involvement of VGSC activity in control of endocytosis/secretion are discussed.