Quantitation of mitochondrial dynamics by photolabeling of individual organelles shows that mitochondrial fusion is blocked during the Bax activation phase of apoptosis

A dynamic balance of organelle fusion and fission regulates mitochondrial morphology. During apoptosis this balance is altered, leading to an extensive fragmentation of the mitochondria. Here, we describe a novel assay of mitochondrial dynamics based on confocal imaging of cells expressing a mitochondrial matrix–targeted photoactivable green fluorescent protein that enables detection and quantification of organelle fusion in living cells. Using this assay, we visualize and quantitate mitochondrial fusion rates in healthy and apoptotic cells. During apoptosis, mitochondrial fusion is blocked independently of caspase activation. The block in mitochondrial fusion occurs within the same time range as Bax coalescence on the mitochondria and outer mitochondrial membrane permeabilization, and it may be a consequence of Bax/Bak activation during apoptosis

An Analytical Approach to Neuronal Connectivity

This paper describes how realistic neuromorphic networks can have their connectivity properties fully characterized in analytical fashion. By assuming that all neurons have the same shape and are regularly distributed along the two-dimensional orthogonal lattice with parameter $\Delta$, it is possible to obtain the accurate number of connections and cycles of any length from the autoconvolution function as well as from the respective spectral density derived from the adjacency matrix. It is shown that neuronal shape plays an important role in defining the spatial spread of network connections. In addition, most such networks are characterized by the interesting phenomenon where the connections are progressively shifted along the spatial domain where the network is embedded. It is also shown that the number of cycles follows a power law with their respective length. Morphological measurements for characterization of the spatial distribution of connections, including the adjacency matrix spectral density and the lacunarity of the connections, are suggested. The potential of the proposed approach is illustrated with respect to digital images of real neuronal cells.Comment: 4 pages, 6 figure

Growth-Driven Percolations: The Dynamics of Community Formation in Neuronal Systems

The quintessential property of neuronal systems is their intensive patterns of selective synaptic connections. The current work describes a physics-based approach to neuronal shape modeling and synthesis and its consideration for the simulation of neuronal development and the formation of neuronal communities. Starting from images of real neurons, geometrical measurements are obtained and used to construct probabilistic models which can be subsequently sampled in order to produce morphologically realistic neuronal cells. Such cells are progressively grown while monitoring their connections along time, which are analysed in terms of percolation concepts. However, unlike traditional percolation, the critical point is verified along the growth stages, not the density of cells, which remains constant throughout the neuronal growth dynamics. It is shown, through simulations, that growing beta cells tend to reach percolation sooner than the alpha counterparts with the same diameter. Also, the percolation becomes more abrupt for higher densities of cells, being markedly sharper for the beta cells.Comment: 8 pages, 10 figure

Performance of networks of artificial neurons: The role of clustering

The performance of the Hopfield neural network model is numerically studied on various complex networks, such as the Watts-Strogatz network, the Barab{\'a}si-Albert network, and the neuronal network of the C. elegans. Through the use of a systematic way of controlling the clustering coefficient, with the degree of each neuron kept unchanged, we find that the networks with the lower clustering exhibit much better performance. The results are discussed in the practical viewpoint of application, and the biological implications are also suggested.Comment: 4 pages, to appear in PRE as Rapid Com

Global and regional brain metabolic scaling and its functional consequences

Background: Information processing in the brain requires large amounts of metabolic energy, the spatial distribution of which is highly heterogeneous reflecting complex activity patterns in the mammalian brain. Results: Here, it is found based on empirical data that, despite this heterogeneity, the volume-specific cerebral glucose metabolic rate of many different brain structures scales with brain volume with almost the same exponent around -0.15. The exception is white matter, the metabolism of which seems to scale with a standard specific exponent -1/4. The scaling exponents for the total oxygen and glucose consumptions in the brain in relation to its volume are identical and equal to $0.86\pm 0.03$, which is significantly larger than the exponents 3/4 and 2/3 suggested for whole body basal metabolism on body mass. Conclusions: These findings show explicitly that in mammals (i) volume-specific scaling exponents of the cerebral energy expenditure in different brain parts are approximately constant (except brain stem structures), and (ii) the total cerebral metabolic exponent against brain volume is greater than the much-cited Kleiber's 3/4 exponent. The neurophysiological factors that might account for the regional uniformity of the exponents and for the excessive scaling of the total brain metabolism are discussed, along with the relationship between brain metabolic scaling and computation.Comment: Brain metabolism scales with its mass well above 3/4 exponen

Dimensionality and dynamics in the behavior of C. elegans

A major challenge in analyzing animal behavior is to discover some underlying simplicity in complex motor actions. Here we show that the space of shapes adopted by the nematode C. elegans is surprisingly low dimensional, with just four dimensions accounting for 95% of the shape variance, and we partially reconstruct "equations of motion" for the dynamics in this space. These dynamics have multiple attractors, and we find that the worm visits these in a rapid and almost completely deterministic response to weak thermal stimuli. Stimulus-dependent correlations among the different modes suggest that one can generate more reliable behaviors by synchronizing stimuli to the state of the worm in shape space. We confirm this prediction, effectively "steering" the worm in real time.Comment: 9 pages, 6 figures, minor correction

Mitochondrial Morphogenesis, Dendrite Development, and Synapse Formation in Cerebellum Require both Bcl-w and the Glutamate Receptor δ2

Bcl-w belongs to the prosurvival group of the Bcl-2 family, while the glutamate receptor δ2 (Grid2) is an excitatory receptor that is specifically expressed in Purkinje cells, and required for Purkinje cell synapse formation. A recently published result as well as our own findings have shown that Bcl-w can physically interact with an autophagy protein, Beclin1, which in turn has been shown previously to form a protein complex with the intracellular domain of Grid2 and an adaptor protein, nPIST. This suggests that Bcl-w and Grid2 might interact genetically to regulate mitochondria, autophagy, and neuronal function. In this study, we investigated this genetic interaction of Bcl-w and Grid2 through analysis of single and double mutant mice of these two proteins using a combination of histological and behavior tests. It was found that Bcl-w does not control the cell number in mouse brain, but promotes what is likely to be the mitochondrial fission in Purkinje cell dendrites, and is required for synapse formation and motor learning in cerebellum, and that Grid2 has similar phenotypes. Mice carrying the double mutations of these two genes had synergistic effects including extremely long mitochondria in Purkinje cell dendrites, and strongly aberrant Purkinje cell dendrites, spines, and synapses, and severely ataxic behavior. Bcl-w and Grid2 mutations were not found to influence the basal autophagy that is required for Purkinje cell survival, thus resulting in these phenotypes. Our results demonstrate that Bcl-w and Grid2 are two critical proteins acting in distinct pathways to regulate mitochondrial morphogenesis and control Purkinje cell dendrite development and synapse formation. We propose that the mitochondrial fission occurring during neuronal growth might be critically important for dendrite development and synapse formation, and that it can be regulated coordinately by multiple pathways including Bcl-2 and glutamate receptor family members

Multi-Parametric Analysis and Modeling of Relationships between Mitochondrial Morphology and Apoptosis

Mitochondria exist as a network of interconnected organelles undergoing constant fission and fusion. Current approaches to study mitochondrial morphology are limited by low data sampling coupled with manual identification and classification of complex morphological phenotypes. Here we propose an integrated mechanistic and data-driven modeling approach to analyze heterogeneous, quantified datasets and infer relations between mitochondrial morphology and apoptotic events. We initially performed high-content, multi-parametric measurements of mitochondrial morphological, apoptotic, and energetic states by high-resolution imaging of human breast carcinoma MCF-7 cells. Subsequently, decision tree-based analysis was used to automatically classify networked, fragmented, and swollen mitochondrial subpopulations, at the single-cell level and within cell populations. Our results revealed subtle but significant differences in morphology class distributions in response to various apoptotic stimuli. Furthermore, key mitochondrial functional parameters including mitochondrial membrane potential and Bax activation, were measured under matched conditions. Data-driven fuzzy logic modeling was used to explore the non-linear relationships between mitochondrial morphology and apoptotic signaling, combining morphological and functional data as a single model. Modeling results are in accordance with previous studies, where Bax regulates mitochondrial fragmentation, and mitochondrial morphology influences mitochondrial membrane potential. In summary, we established and validated a platform for mitochondrial morphological and functional analysis that can be readily extended with additional datasets. We further discuss the benefits of a flexible systematic approach for elucidating specific and general relationships between mitochondrial morphology and apoptosis