The connectivity of the brain: multi-level quantitative analysis

 We develop a mathematical formalism or calculating connectivity volumes generated by specific topologies with various physical packing strategies. We consider four topologies (full, random, nearest-neighbor, and modular connectivity) and three physical models: (i) interior packing, where neurons and connection fibers are intermixed, (ii) sheeted packing where neurons are located on a sheet with fibers running underneath, and (iii) exterior packing where the neurons are located at the surfaces of a cube or sphere with fibers taking up the internal volume. By extensive cross-referencing of available human neuroanatomical data we produce a consistent set of parameters for the whole brain, the cerebral cortex, and the cerebellar cortex. By comparing these inferred values with those predicted by the expressions, we draw the following general conclusions for the human brain, cortex, and cerebellum: (i) Interior packing is less efficient than exterior packing (in a sphere). (ii) Fully and randomly connected topologies are extremely inefficient. More specifically we find evidence that different topologies and physical packing strategies might be used at different scales. (iii) For the human brain at a macrostructural level, modular topologies on an exterior sphere approach the data most closely. (iv) On a mesostructural level, laminarization and columnarization are evidence of the superior efficiency of organizing the wiring as sheets. (v) Within sheets, microstructures emerge in which interior models are shown to be the most efficient. With regard to interspecies similarities and differences we conjecture (vi) that the remarkable constancy of number of neurons per underlying square millimeter of cortex may be the result of evolution minimizing interneuron distance in grey matter, and (vii) that the topologies that best fit the human brain data should not be assumed to apply to other mammals, such as the mouse for which we show that a random topology may be feasible for the cortex. Received: 14 December 1994/Accepted in revised form: 23 May 1995     

Automatic karyotyping of plant chromosomes by imaging techniques

Chromosomes of Crepis capillaris (L.) Wallr. were analyzed using a newly developed chromosome image analyzing system, CHIAS-mini. The CHIAS-mini is a desktop system which consists of an ordinary 16-bit personal computer and an image processor as the main frames. Data acquisition, karyotyping and idiogramming of the plant chromosomes were automatically carried out with some manual interaction. The data obtained were comparable to those obtained manually and by a standard image analyzer already developed.     

Identifying core habitats and corridors for giant pandas by combining multiscale random forest and connectivity analysis

Habitat loss and fragmentation are widely acknowledged as the main driver of the decline of giant panda populations. The Chinese government has made great efforts to protect this charming species and has made remarkable achievements, such as population growth and habitat expansion. However, habitat fragmentation has not been reversed. Protecting giant pandas in a large spatial extent needs to identify core habitat patches and corridors connecting them. This study used an equal‐sampling multiscale random forest habitat model to predict a habitat suitability map for the giant panda. Then, we applied the resistant kernel method and factorial least‐cost path analysis to identify core habitats connected by panda dispersal and corridors among panda occurrences, respectively. Finally, we evaluated the effectiveness of current protected areas in representing core habitats and corridors. Our results showed high scale dependence of giant panda habitat selection. Giant pandas strongly respond to bamboo percentage and elevation at a relatively fine scale (1 km), whereas they respond to anthropogenic factors at a coarse scale (≥2 km). Dispersal ability has significant effects on core habitats extent and population fragmentation evaluation. Under medium and high dispersal ability scenarios (12,000 and 20,000 cost units), most giant panda habitats in the Qionglai mountain are predicted to be well connected by dispersal. The proportion of core habitats covered by protected areas varied between 38% and 43% under different dispersal ability scenarios, highlighting significant gaps in the protected area network. Similarly, only 43% of corridors that connect giant panda occurrences were protected. Our results can provide crucial information for conservation managers to develop wise strategies to safeguard the long‐term viability of the giant panda population.     

Coherency and connectivity in oscillating neural networks: linear partialization analysis

 This paper studies the relation between the functional synaptic connections between two artificial neural networks and the correlation of their spiking activities. The model neurons had realistic non-oscillatory dynamic properties and the networks showed oscillatory behavior as a result of their internal synaptic connectivity. We found that both excitation and inhibition cause phase locking of the oscillating activities. When the two networks excite each other the oscillations synchronize with zero phase lag, whereas mutual inhibition between the networks resulted in an anti-phase (half period phase difference) synchronization. Correlations between the activities of the two networks can also be caused by correlated external inputs driving the systems (common input). Our analysis shows that when the networks exhibit oscillatory behavior and the rate of the common input is smaller than a characteristic network oscillator frequency, the cross-correlation functions between the activities of two systems still carry information about the mutual synaptic connectivity. This information can be retrieved with linear partialization, removing the influence of the common input. We further explored the network responses to periodic external input. We found that when the input is of a frequency smaller than a certain threshold, the network responds with bursts at the same frequency as the input. Above the threshold, the network responds with a fraction of the input frequency. This frequency threshold, characterizing the oscillatory properties of the network, is also found to determine the limit to which linear partialization works. Received: 20 October 1995 / Accepted in revised form: 20 May 1996     

A stimulus-dependent connectivity analysis of neuronal networks

We present an analysis of interactions among neurons in stimulus-driven networks that is designed to control for effects from unmeasured neurons. This work builds on previous connectivity analyses that assumed connectivity strength to be constant with respect to the stimulus. Since unmeasured neuron activity can modulate with the stimulus, the effective strength of common input connections from such hidden neurons can also modulate with the stimulus. By explicitly accounting for the resulting stimulus-dependence of effective interactions among measured neurons, we are able to remove ambiguity in the classification of causal interactions that resulted from classification errors in the previous analyses. In this way, we can more reliably distinguish causal connections among measured neurons from common input connections that arise from hidden network nodes. The approach is derived in a general mathematical framework that can be applied to other types of networks. We illustrate the effects of stimulus-dependent connectivity estimates with simulations of neurons responding to a visual stimulus. This research was supported by the National Science Foundation grants DMS-0415409 and DMS-0748417.     

Seeing is believing: imaging techniques to monitor plant health.

Historically, early stress-induced changes in plants have been mainly detected after destructive sampling followed by biochemical and molecular determinations. Imaging techniques that allow immediate detection of stress-situations, before visual symptoms appear and adverse effects become established, are emerging as promising tools for crop yield management. Such monitoring approaches can also be applied to screen plant populations for mutants with increased stress tolerance. At the laboratory scale, different imaging methods can be tested and one or a combination best suited for crop surveillance chosen. The system of choice can be applied under controlled laboratory conditions to guide selective sampling for the molecular characterisation of rapid stress-induced changes. Such an approach permits to isolate presymptomatically induced genes, or to obtain a panoramic view of early gene expression using gene-arrays when plants undergo physiological changes undetected by the human eye. Using this knowledge, plants can be engineered to be more stress resistant, and tested for field performance by the same methodologies. In ongoing efforts of genome characterisation, genes of unknown function are revealed at an ever-accelerating pace. By monitoring changes in phenotypic characteristics of transgenic plants expressing those genes, imaging techniques could help to identify their function.     

Flux analysis in plant metabolic networks: increasing throughput and coverage

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Proteomics, networks and connectivity indices

Describing the connectivity of chemical and/or biological systems using networks is a straight gate for the introduction of mathematical tools in proteomics. Networks, in some cases even very large ones, are simple objects that are composed at least by nodes and edges. The nodes represent the parts of the system and the edges geometric and/or functional relationships between parts. In proteomics, amino acids, proteins, electrophoresis spots, polypeptidic fragments, or more complex objects can play the role of nodes. All of these networks can be numerically described using the so-called Connectivity Indices (CIs). The transformation of graphs (a picture) into CIs (numbers) facilitates the manipulation of information and the search for structure-function relationships in Proteomics. In this work, we review and comment on the challenges and new trends in the definition and applications of CIs in Proteomics. Emphasis is placed on 1-D-CIs for DNA and protein sequences, 2-D-CIs for RNA secondary structures, 3-D-topographic indices (TPGIs) for protein function annotation without alignment, 2-D-CIs and 3-D-TPGIs for the study of drug-protein or drug-RNA quantitative structure-binding relationships, and pseudo 3-D-CIs for protein surface molecular recognition. We also focus on CIs to describe Protein Interaction Networks or RNA co-expression networks. 2-D-CIs for patient blood proteome 2-DE maps or mass spectra are also covered.     

Plant transformation by microinjection techniques

Several techniques have been developed for introducing cloned genes into plant cells. Vectorless delivery systems such as PEG-mediated direct DNA uptake (e.g. Pasz-kowski et al. 1984), electroporation (e.g. Shillito et al. 1985), and fusion of protoplasts with liposomes (Deshayes et al. 1985) are routinely used in many experiments (see several chapters of this issue). A wide range of plant species, dicotyledonous as well as monocotyledonous, has been transformed by these vectorless DNA transfer systems. However, the availability of an efficient protoplast regeneration system is a prerequisite for the application of these techniques. For cells with intact cell walls and tissue explants the biological delivery system of virulent Agrobacterium species has been routinely used (for review see Fraley et al. 1986). However, the host range of Agrobacterium restricts the plant species, which can be transformed using this vector system. In addition, all these methods depend on selection systems for recovery of transformants. Therefore a selection system has to be established first for plant species to be transformed. The microinjection technique is a direct physical approach, and therefore host-range independent, for introducing substances under microscopical control into defined cells without damaging them. These two facts differentiate this technique from other physical approaches, such as biolistic transformation and macroinjection (see chapters in this issue). In these other techniques, damaging of cells and random manipulation of cells without optical control cannot be avoided so far. In recent years microinjection technology found its application in plant sciences, whereas this technique has earlier been well established for transformation of animal tissue culture cells (Capecchi 1980) and the production of transgenic animals (Brin-ster et al. 1981, Rusconi and Schaffner 1981). Furthermore, different parameters affecting the DNA transfer via microinjection, such as the nature of microinjected DNA, and cell cycle stage, etc, have been investigated extensively in animal cells (Folger et al. 1982, Wong and Capecchi 1985), while analogous experiments on plant cells are still lacking.     

Building the cellular puzzle: control in multi-level reaction networks

Quantitative conceptual tools dealing with control and regulation of cellular processes have been mostly developed for and applied to the pathways of intermediary metabolism. Yet, cellular processes are organized in different levels, metabolism forming the lowest level in a cascade of processes. Well-known examples are the DNA-mRNA-enzyme-metabolism cascade and the signal transduction cascades consisting of covalent modification cycles. The reaction network that constitutes each level can be viewed as a "module" in which reactions are linked by mass transfer. Although in principle all of these cellular modules are ultimately linked by mass transfer, in practice they can often be regarded as "isolated" from each other in terms of mass transfer. Here modules can interact with each other only by means of regulatory or catalytic effects-a chemical species in one module may affect the rate of a reaction in another module by binding to an enzyme or transport system or by acting as a catalyst. This paper seeks to answer two questions about the control and regulation of such multi-level reaction networks: (i) How can the control properties of the system as a whole be expressed in terms of the control properties of individual modules and the effects between modules? (ii) How do the control properties of a module in its isolated state change when it is embedded in the whole system through its connections with the other modules? In order to answer these questions a quantitative theoretical framework is developed and applied to systems containing two, three or four fully interacting modules; it is shown how it can be extended in principle to n modules. This newly developed theory therefore makes it possible to quantitatively dissect intermodular, internal and external regulation in multi-level systems.     

X-ray microscopy enables multiscale high-resolution 3D imaging of plant cells,tissues, and organs

Capturing complete internal anatomies of plant organs and tissues within their relevant morphological context remains a key challenge in plant science. While plant growth and development are inherently multiscale, conventional light, fluorescence, and electron microscopy platforms are typically limited to imaging of plant microstructure from small flat samples that lack a direct spatial context to, and represent only a small portion of, the relevant plant macrostructures. We demonstrate technical advances with a lab-based X-ray microscope (XRM) that bridge the imaging gap by providing multiscale high-resolution three-dimensional (3D) volumes of intact plant samples from the cell to the whole plant level. Serial imaging of a single sample is shown to provide sub-micron 3D volumes co-registered with lower magnification scans for explicit contextual reference. High-quality 3D volume data from our enhanced methods facilitate sophisticated and effective computational segmentation. Advances in sample preparation make multimodal correlative imaging workflows possible, where a single resin-embedded plant sample is scanned via XRM to generate a 3D cell-level map, and then used to identify and zoom in on sub-cellular regions of interest for high-resolution scanning electron microscopy. In total, we present the methodologies for use of XRM in the multiscale and multimodal analysis of 3D plant features using numerous economically and scientifically important plant systems.

Lab-based X-ray microscopy allows high-resolution 3D imaging of intact plant samples over a wide range of sample types and sizes, filling the imaging gap between light and electron microscopy.     

Condition-dependent functional connectivity: syntax networks in bilinguals

This paper introduces a method to study the variation of brain functional connectivity networks with respect to experimental conditions in fMRI data. It is related to the psychophysiological interaction technique introduced by Friston et al. and extends to networks of correlation modulation (CM networks). Extended networks containing several dozens of nodes are determined in which the links correspond to consistent correlation modulation across subjects. In addition, we assess inter-subject variability and determine networks in which the condition-dependent functional interactions can be explained by a subject-dependent variable. We applied the technique to data from a study on syntactical production in bilinguals and analysed functional interactions differentially across tasks (word reading or sentence production) and across languages. We find an extended network of consistent functional interaction modulation across tasks, whereas the network comparing languages shows fewer links. Interestingly, there is evidence for a specific network in which the differences in functional interaction across subjects can be explained by differences in the subjects' syntactical proficiency. Specifically, we find that regions, including ones that have previously been shown to be involved in syntax and in language production, such as the left inferior frontal gyrus, putamen, insula, precentral gyrus, as well as the supplementary motor area, are more functionally linked during sentence production in the second, compared with the first, language in syntactically more proficient bilinguals than in syntactically less proficient ones. Our approach extends conventional activation analyses to the notion of networks, emphasizing functional interactions between regions independently of whether or not they are activated. On the one hand, it gives rise to testable hypotheses and allows an interpretation of the results in terms of the previous literature, and on the other hand, it provides a basis for studying the structure of functional interactions as a whole, and hence represents a further step towards the notion of large-scale networks in functional imaging.     

Egg laying by a butterfly on a fragmented host plant: a multi-level approach

Egg placement by herbivorous insects is an important step in their interaction with their host plants, and is the result of processes operating at different spatial and temporal scales. Although several studies have examined egg-placement patterns at different scales, this has rarely been achieved simultaneously using a multi-scale hierarchical approach. We studied egg placement in a rare European butterfly, Iolana iolas , whose larvae specifically feed on seeds of plants of the genus Colutea, using a hierarchical approach and Generalised Linear Mixed Modelling. The study was carried out in 2002 and 2003 in a ca 60 km² area in southern Madrid province, Spain, where the host plant, Colutea hispanica , has a highly fragmented distribution. We monitored in detail 132 plants in 24 patches and estimated the abundance of butterflies over the whole reproductive period of C. hispanica . We measured phenological, morphological and landscape variables potentially affecting egg-placement at three hierarchical levels: fruit, plant and host plant patch. Using egg presence–absence on mature fruits as the response variable, we found that eggs were more likely to be laid on fruits aged 1–2 weeks at the middle of the flowering period (fruit level), on large plants with a small number of shoots at the base (plant level), and in well connected host plant patches (patch level). Our results suggest that egg-placement is a process determined by factors operating at different levels: fruit, plant and host plant patch. Because egg-placement studies are often made with spatially correlated data, neglecting their intrinsic hierarchical nature could lead to equivocal conclusions.     

Loss of 'small-world' networks in Alzheimer's disease: graph analysis of FMRI resting-state functional connectivity

Background

Local network connectivity disruptions in Alzheimer''s disease patients have been found using graph analysis in BOLD fMRI. Other studies using MEG and cortical thickness measures, however, show more global long distance connectivity changes, both in functional and structural imaging data. The form and role of functional connectivity changes thus remains ambiguous. The current study shows more conclusive data on connectivity changes in early AD using graph analysis on resting-state condition fMRI data.

Methodology/Principal Findings

18 mild AD patients and 21 healthy age-matched control subjects without memory complaints were investigated in resting-state condition with MRI at 1.5 Tesla. Functional coupling between brain regions was calculated on the basis of pair-wise synchronizations between regional time-series. Local (cluster coefficient) and global (path length) network measures were quantitatively defined. Compared to controls, the characteristic path length of AD functional networks is closer to the theoretical values of random networks, while no significant differences were found in cluster coefficient. The whole-brain average synchronization does not differ between Alzheimer and healthy control groups. Post-hoc analysis of the regional synchronization reveals increased AD synchronization involving the frontal cortices and generalized decreases located at the parietal and occipital regions. This effectively translates in a global reduction of functional long-distance links between frontal and caudal brain regions.

Conclusions/Significance

We present evidence of AD-induced changes in global brain functional connectivity specifically affecting long-distance connectivity. This finding is highly relevant for it supports the anterior-posterior disconnection theory and its role in AD. Our results can be interpreted as reflecting the randomization of the brain functional networks in AD, further suggesting a loss of global information integration in disease.     

Plant development: hidden networks

How the complex patterns of plant vascular systems are generated is largely unknown. Advances in understanding vascular pattern formation at various levels are likely to follow recent large-scale genetic screens for Arabodopsis mutants with abnormal vascular systems.