Emergence of Modular Structure in a Large-Scale Brain Network with Interactions between Dynamics and Connectivity

A network of 32 or 64 connected neural masses, each representing a large population of interacting excitatory and inhibitory neurons and generating an electroencephalography/magnetoencephalography like output signal, was used to demonstrate how an interaction between dynamics and connectivity might explain the emergence of complex network features, in particular modularity. Network evolution was modeled by two processes: (i) synchronization dependent plasticity (SDP) and (ii) growth dependent plasticity (GDP). In the case of SDP, connections between neural masses were strengthened when they were strongly synchronized, and were weakened when they were not. GDP was modeled as a homeostatic process with random, distance dependent outgrowth of new connections between neural masses. GDP alone resulted in stable networks with distance dependent connection strengths, typical small-world features, but no degree correlations and only weak modularity. SDP applied to random networks induced clustering, but no clear modules. Stronger modularity evolved only through an interaction of SDP and GDP, with the number and size of the modules depending on the relative strength of both processes, as well as on the size of the network. Lesioning part of the network, after a stable state was achieved, resulted in a temporary disruption of the network structure. The model gives a possible scenario to explain how modularity can arise in developing brain networks, and makes predictions about the time course of network changes during development and following acute lesions.

Leaders of neuronal cultures in a quorum percolation model

We present a theoretical framework using quorum percolation for describing the initiation of activity in a neural culture. The cultures are modeled as random graphs, whose nodes are excitatory neurons with k_in inputs and k_out outputs, and whose input degrees k_in = k obey given distribution functions p_k. We examine the firing activity of the population of neurons according to their input degree (k) classes and calculate for each class its firing probability Φ_k(t) as a function of t. The probability of a node to fire is found to be determined by its in-degree k, and the first-to-fire neurons are those that have a high k. A small minority of high-k-classes may be called “Leaders,” as they form an interconnected sub-network that consistently fires much before the rest of the culture. Once initiated, the activity spreads from the Leaders to the less connected majority of the culture. We then use the distribution of in-degree of the Leaders to study the growth rate of the number of neurons active in a burst, which was experimentally measured to be initially exponential. We find that this kind of growth rate is best described by a population that has an in-degree distribution that is a Gaussian centered around k = 75 with width σ = 31 for the majority of the neurons, but also has a power law tail with exponent −2 for 10% of the population. Neurons in the tail may have as many as k = 4,700 inputs. We explore and discuss the correspondence between the degree distribution and a dynamic neuronal threshold, showing that from the functional point of view, structure and elementary dynamics are interchangeable. We discuss possible geometric origins of this distribution, and comment on the importance of size, or of having a large number of neurons, in the culture.

Identifying Basal Ganglia divisions in individuals using resting-state functional connectivity MRI

Studies in non-human primates and humans reveal that discrete regions (henceforth, "divisions") in the basal ganglia are intricately interconnected with regions in the cerebral cortex. However, divisions within basal ganglia nuclei (e.g., within the caudate) are difficult to identify using structural MRI. Resting-state functional connectivity MRI (rs-fcMRI) can be used to identify putative cerebral cortical functional areas in humans (Cohen et al., 2008). Here, we determine whether rs-fcMRI can be used to identify divisions in individual human adult basal ganglia. Putative basal ganglia divisions were generated by assigning basal ganglia voxels to groups based on the similarity of whole-brain functional connectivity correlation maps using modularity optimization, a network analysis tool. We assessed the validity of this approach by examining the spatial contiguity and location of putative divisions and whether divisions' correlation maps were consistent with previously reported patterns of anatomical and functional connectivity. Spatially constrained divisions consistent with the dorsal caudate, ventral striatum, and dorsal caudal putamen could be identified in each subject. Further, correlation maps associated with putative divisions were consistent with their presumed connectivity. These findings suggest that, as in the cerebral cortex, subcortical divisions can be identified in individuals using rs-fcMRI. Developing and validating these methods should improve the study of brain structure and function, both typical and atypical, by allowing for more precise comparison across individuals.

Graph-based network analysis of resting-state functional MRI

In the past decade, resting-state functional MRI (R-fMRI) measures of brain activity have attracted considerable attention. Based on changes in the blood oxygen level-dependent signal, R-fMRI offers a novel way to assess the brain's spontaneous or intrinsic (i.e., task-free) activity with both high spatial and temporal resolutions. The properties of both the intra- and inter-regional connectivity of resting-state brain activity have been well documented, promoting our understanding of the brain as a complex network. Specifically, the topological organization of brain networks has been recently studied with graph theory. In this review, we will summarize the recent advances in graph-based brain network analyses of R-fMRI signals, both in typical and atypical populations. Application of these approaches to R-fMRI data has demonstrated non-trivial topological properties of functional networks in the human brain. Among these is the knowledge that the brain's intrinsic activity is organized as a small-world, highly efficient network, with significant modularity and highly connected hub regions. These network properties have also been found to change throughout normal development, aging, and in various pathological conditions. The literature reviewed here suggests that graph-based network analyses are capable of uncovering system-level changes associated with different processes in the resting brain, which could provide novel insights into the understanding of the underlying physiological mechanisms of brain function. We also highlight several potential research topics in the future.

Integration of Diverse Research Methods to Analyze and Engineer Ca-Binding Proteins: From Prediction to Production

In recent years, increasingly sophisticated computational and bioinformatics tools have evolved for the analyses of protein structure, function, ligand interactions, modeling and energetics. This includes the development of algorithms to recursively evaluate side-chain rotamer permutations, identify regions in a 3D structure that meet some set of search parameters, calculate and minimize energy values, and provide high-resolution visual tools for theoretical modeling. Here we discuss the interdependency between different areas of bioinformatics, the evolution of different algorithm design approaches, and finally the transition from theoretical models to real-world design and application as they relate to Ca(2+)-binding proteins. Within this context, it has become evident that significant pre-experimental design and calculations can be modeled through computational methods, thus eliminating potentially unproductive research and increasing our confidence in the correlation between real and theoretical models. Moving from prediction to production, it is anticipated that bioinformatics tools will play an increasingly significant role in research and development, improving our ability to both understand the physiological roles of Ca(2+) and other metals and to extend that knowledge to the design of function-specific synthetic proteins capable of fulfilling different roles in medical diagnostics and therapeutics.

Synergistic Coding by Cortical Neural Ensembles

An essential step towards understanding how the brain orchestrates information processing at the cellular and population levels is to simultaneously observe the spiking activity of cortical neurons that mediate perception, learning, and motor processing. In this paper, we formulate an information theoretic approach to determine whether cooperation among neurons may constitute a governing mechanism of information processing when encoding external covariates. Specifically, we show that conditional independence between neuronal outputs may not provide an optimal encoding strategy when the firing probability of a neuron depends on the history of firing of other neurons connected to it. Rather, cooperation among neurons can provide a "message-passing" mechanism that preserves most of the information in the covariates under specific constraints governing their connectivity structure. Using a biologically plausible statistical learning model, we demonstrate the performance of the proposed approach in synergistically encoding a motor task using a subset of neurons drawn randomly from a large population. We demonstrate its superiority in approximating the joint density of the population from limited data compared to a statistically independent model and a maximum entropy (MaxEnt) model.

Comparison of characteristics between region-and voxel-based network analyses in resting-state fMRI data

Small-world networks are a class of networks that exhibit efficient long-distance communication and tightly interconnected local neighborhoods. In recent years, functional and structural brain networks have been examined using network theory-based methods, and consistently shown to have small-world properties. Moreover, some voxel-based brain networks exhibited properties of scale-free networks, a class of networks with mega-hubs. However, there are considerable inconsistencies across studies in the methods used and the results observed, particularly between region-based and voxel-based brain networks. We constructed functional brain networks at multiple resolutions using the same resting-state fMRI data, and compared various network metrics, degree distribution, and localization of nodes of interest. It was found that the networks with higher resolutions exhibited the properties of small-world networks more prominently. It was also found that voxel-based networks were more robust against network fragmentation compared to region-based networks. Although the degree distributions of all networks followed an exponentially truncated power law rather than true power law, the higher the resolution, the closer the distribution was to a power law. The voxel-based analyses also enhanced visualization of the results in the 3D brain space. It was found that nodes with high connectivity tended have high efficiency, a co-localization of properties that was not as consistently observed in the region-based networks. Our results demonstrate benefits of constructing the brain network at the finest scale the experiment will permit.

Scoring function for DNA-drug docking of anticancer and antiparasitic compounds based on spectral moments of 2D lattice graphs for molecular dynamics trajectories

We introduce here a new class of invariants for MD trajectories based on the spectral moments pi(k)(L) of the Markov matrix associated to lattice network-like (LN) graph representations of Molecular Dynamics (MD) trajectories. The procedure embeds the MD energy profiles on a 2D Cartesian coordinates system using simple heuristic rules. At the same time, we associate the LN with a Markov matrix that describes the probabilities of passing from one state to other in the new 2D space. We construct this type of LNs for 422 MD trajectories obtained in DNA-drug docking experiments of 57 furocoumarins. The combined use of psoralens+ultraviolet light (UVA) radiation is known as PUVA therapy. PUVA is effective in the treatment of skin diseases such as psoriasis and mycosis fungoides. PUVA is also useful to treat human platelet (PTL) concentrates in order to eliminate Leishmania spp. and Trypanosoma cruzi. Both are parasites that cause Leishmaniosis (a dangerous skin and visceral disease) and Chagas disease, respectively; and may circulate in blood products collected from infected donors. We included in this study both lineal (psoralens) and angular (angelicins) furocoumarins. In the study, we grouped the LNs on two sets; set1: DNA-drug complex MD trajectories for active compounds and set2: MD trajectories of non-active compounds or no-optimal MD trajectories of active compounds. We calculated the respective pi(k)(L) values for all these LNs and used them as inputs to train a new classifier that discriminate set1 from set2 cases. In training series the model correctly classifies 79 out of 80 (specificity=98.75%) set1 and 226 out of 238 (Sensitivity=94.96%) set2 trajectories. In independent validation series the model correctly classifies 26 out of 26 (specificity=100%) set1 and 75 out of 78 (sensitivity=96.15%) set2 trajectories. We propose this new model as a scoring function to guide DNA-docking studies in the drug design of new coumarins for anticancer or antiparasitic PUVA therapy.

Hierarchical modularity in human brain functional networks

The idea that complex systems have a hierarchical modular organization originated in the early 1960s and has recently attracted fresh support from quantitative studies of large scale, real-life networks. Here we investigate the hierarchical modular (or "modules-within-modules") decomposition of human brain functional networks, measured using functional magnetic resonance imaging in 18 healthy volunteers under no-task or resting conditions. We used a customized template to extract networks with more than 1800 regional nodes, and we applied a fast algorithm to identify nested modular structure at several hierarchical levels. We used mutual information, 0 < I < 1, to estimate the similarity of community structure of networks in different subjects, and to identify the individual network that is most representative of the group. Results show that human brain functional networks have a hierarchical modular organization with a fair degree of similarity between subjects, I = 0.63. The largest five modules at the highest level of the hierarchy were medial occipital, lateral occipital, central, parieto-frontal and fronto-temporal systems; occipital modules demonstrated less sub-modular organization than modules comprising regions of multimodal association cortex. Connector nodes and hubs, with a key role in inter-modular connectivity, were also concentrated in association cortical areas. We conclude that methods are available for hierarchical modular decomposition of large numbers of high resolution brain functional networks using computationally expedient algorithms. This could enable future investigations of Simon's original hypothesis that hierarchy or near-decomposability of physical symbol systems is a critical design feature for their fast adaptivity to changing environmental conditions.

Scale-invariant transition probabilities in free word association trajectories

Free-word association has been used as a vehicle to understand the organization of human thoughts. The original studies relied mainly on qualitative assertions, yielding the widely intuitive notion that trajectories of word associations are structured, yet considerably more random than organized linguistic text. Here we set to determine a precise characterization of this space, generating a large number of word association trajectories in a web implemented game. We embedded the trajectories in the graph of word co-occurrences from a linguistic corpus. To constrain possible transport models we measured the memory loss and the cycling probability. These two measures could not be reconciled by a bounded diffusive model since the cycling probability was very high (16% of order-2 cycles) implying a majority of short-range associations whereas the memory loss was very rapid (converging to the asymptotic value in ∼7 steps) which, in turn, forced a high fraction of long-range associations. We show that memory loss and cycling probabilities of free word association trajectories can be simultaneously accounted by a model in which transitions are determined by a scale invariant probability distribution.

The lexical restructuring hypothesis and graph theoretic analyses of networks based on random lexicons

PURPOSE

The mental lexicon of words used for spoken word recognition has been modeled as a complex network or graph. Do the characteristics of that graph reflect processes involved in its growth (M. S. Vitevitch, 2008) or simply the phonetic overlap between similar-sounding words?

METHOD

Three pseudolexicons were generated by randomly selecting phonological segments from a fixed set. Each lexicon was then modeled as a graph, linking words differing by one segment. The properties of those graphs were compared with those of a graph based on real English words.

RESULTS

The properties of the graphs built from the pseudolexicons matched the properties of the graph based on English words. Each graph consisted of a single large island and a number of smaller islands and hermits. The degree distribution of each graph was better fit by an exponential than by a power function. Each graph showed short path lengths, large clustering coefficients, and positive assortative mixing.

CONCLUSION

The results suggest that there is no need to appeal to processes of growth or language acquisition to explain the formal properties of the network structure of the mental lexicon. These properties emerged because the network was built based on the phonetic overlap of words.

[Not Available]

The scale-free and small-world network models reflect the functional units of networks. However, when we investigated the network properties of a signaling pathway using these models, no significant differences were found between the original undirected graphs and the graphs in which inactive proteins were eliminated from the gene expression data. We analyzed signaling networks by focusing on those pathways that best reflected cellular function. Therefore, our analysis of pathways started from the ligands and progressed to transcription factors and cytoskeletal proteins. We employed the Python module to assess the target network. This involved comparing the original and restricted signaling cascades as a directed graph using microarray gene expression profiles of late onset Alzheimer's disease. The most commonly used method of shortest-path analysis neglects to consider the influences of alternative pathways that can affect the activation of transcription factors or cytoskeletal proteins. We therefore introduced included k-shortest paths and k-cycles in our network analysis using the Python modules, which allowed us to attain a reasonable computational time and identify k-shortest paths. This technique reflected results found in vivo and identified pathways not found when shortest path or degree analysis was applied. Our module enabled us to comprehensively analyse the characteristics of biomolecular networks and also enabled analysis of the effects of diseases considering the feedback loop and feedforward loop control structures as an alternative path.

The influence of ageing on complex brain networks: a graph theoretical analysis

OBJECTIVE

To determine the functional connectivity of different EEG bands at the "baseline" situation (rest) and during mathematical thinking in children and young adults to study the maturation effect on brain networks at rest and during a cognitive task.

METHODS

Twenty children (8-12 years) and twenty students (21-26 years) were studied. The synchronization likelihood was used to evaluate the interregional synchronization of different EEG frequency bands in children and adults, at rest and during math. Then, graphs were constructed and characterized in terms of local structure (clustering coefficient) and overall integration (path length) and the "optimal" organization of the connectivity i.e., the small world network (SWN).

RESULTS

The main findings were: (i) Enhanced synchronization for theta band during math more prominent in adults. (ii) Decrease of the optimal SWN organization of the alpha2 band during math. (iii) The beta and especially gamma bands showed lower synchronization and signs of lower SWN organization in both situations in adults.

CONCLUSION

There are interesting findings related to the two age groups and the two situations. The theta band showed higher synchronization during math in adults as a result of higher capacity of the working memory in this age group. The alpha2 band showed some SWN disorganization during math, a process analog to the known desynchronization. In adults, a dramatic reduction of the connections in gray matter occurs. Although this maturation process is probably related to higher efficiency, reduced connectivity is expressed by lower synchronization and lower mean values of the graph parameters in adults.

GT-Miner: a graph-theoretic data miner, viewer, and model processor

Inexpensive computational power combined with high-throughput experimental platforms has created a wealth of biological information requiring analytical tools and techniques for interpretation. Graph-theoretic concepts and tools have provided an important foundation for information visualization, integration, and analysis of datasets, but they have often been relegated to background analysis tasks. GT-Miner is designed for visual data analysis and mining operations, interacts with other software, including databases, and works with diverse data types. It facilitates a discovery-oriented approach to data mining wherein exploration of alterations of the data and variations of the visualization is encouraged. The user is presented with a basic iterative process, consisting of loading, visualizing, transforming, and then storing the resultant information. Complex analyses are built-up through repeated iterations and user interactions. The iterative process is optimized by automatic layout following transformations and by maintaining a current selection set of interest for elements modified by the transformations. Multiple visualizations are supported including hierarchical, spring, and force-directed self-organizing layouts. Graphs can be transformed with an extensible set of algorithms or manually with an integral visual editor. GT-Miner is intended to allow easier access to visual data mining for the non-expert.

AVAILABILITY

The GT-Miner program and supplemental materials, including example uses and a user guide, are freely available from http://www.cifr.ncsu.edu/bioinformatics/downloads/

Applications of graph theory to landscape genetics

We investigated the relationships among landscape quality, gene flow, and population genetic structure of fishers (Martes pennanti) in ON, Canada. We used graph theory as an analytical framework considering each landscape as a network node. The 34 nodes were connected by 93 edges. Network structure was characterized by a higher level of clustering than expected by chance, a short mean path length connecting all pairs of nodes, and a resiliency to the loss of highly connected nodes. This suggests that alleles can be efficiently spread through the system and that extirpations and conservative harvest are not likely to affect their spread. Two measures of node centrality were negatively related to both the proportion of immigrants in a node and node snow depth. This suggests that central nodes are producers of emigrants, contain high-quality habitat (i.e., deep snow can make locomotion energetically costly) and that fishers were migrating from high to low quality habitat. A method of community detection on networks delineated five genetic clusters of nodes suggesting cryptic population structure. Our analyses showed that network models can provide system-level insight into the process of gene flow with implications for understanding how landscape alterations might affect population fitness and evolutionary potential.

What can graph theory tell us about word learning and lexical retrieval?

PURPOSE

Graph theory and the new science of networks provide a mathematically rigorous approach to examine the development and organization of complex systems. These tools were applied to the mental lexicon to examine the organization of words in the lexicon and to explore how that structure might influence the acquisition and retrieval of phonological word-forms.

METHOD

Pajek, a program for large network analysis and visualization (V. Batagelj & A. Mvrar, 1998), was used to examine several characteristics of a network derived from a computerized database of the adult lexicon. Nodes in the network represented words, and a link connected two nodes if the words were phonological neighbors.

RESULTS

The average path length and clustering coefficient suggest that the phonological network exhibits small-world characteristics. The degree distribution was fit better by an exponential rather than a power-law function. Finally, the network exhibited assortative mixing by degree. Some of these structural characteristics were also found in graphs that were formed by 2 simple stochastic processes suggesting that similar processes might influence the development of the lexicon.

CONCLUSIONS

The graph theoretic perspective may provide novel insights about the mental lexicon and lead to future studies that help us better understand language development and processing.

Network structure of cerebral cortex shapes functional connectivity on multiple time scales

Neuronal dynamics unfolding within the cerebral cortex exhibit complex spatial and temporal patterns even in the absence of external input. Here we use a computational approach in an attempt to relate these features of spontaneous cortical dynamics to the underlying anatomical connectivity. Simulating nonlinear neuronal dynamics on a network that captures the large-scale interregional connections of macaque neocortex, and applying information theoretic measures to identify functional networks, we find structure-function relations at multiple temporal scales. Functional networks recovered from long windows of neural activity (minutes) largely overlap with the underlying structural network. As a result, hubs in these long-run functional networks correspond to structural hubs. In contrast, significant fluctuations in functional topology are observed across the sequence of networks recovered from consecutive shorter (seconds) time windows. The functional centrality of individual nodes varies across time as interregional couplings shift. Furthermore, the transient couplings between brain regions are coordinated in a manner that reveals the existence of two anticorrelated clusters. These clusters are linked by prefrontal and parietal regions that are hub nodes in the underlying structural network. At an even faster time scale (hundreds of milliseconds) we detect individual episodes of interregional phase-locking and find that slow variations in the statistics of these transient episodes, contingent on the underlying anatomical structure, produce the transfer entropy functional connectivity and simulated blood oxygenation level-dependent correlation patterns observed on slower time scales.

How Good Can the Characteristic Polynomial Be for Correlations?

The aim of this study was to investigate the characteristic polynomials resulting from the molecular graphs used as molecular descriptors in the characterization of the properties of chemical compounds. A formal calculus method is proposed in order to identify the value of the characteristic polynomial parameters for which the extremum values of the squared correlation coefficient are obtained in univariate regression models. The developed calculation algorithm was applied to a sample of nonane isomers. The obtained results revealed that the proposed method produced an accurate and unique solution for the best relationship between the characteristic polynomial as molecular descriptor and the property of interest.

A computational proposal for designing structured RNA pools for in vitro selection of RNAs

Although in vitro selection technology is a versatile experimental tool for discovering novel synthetic RNA molecules, finding complex RNA molecules is difficult because most RNAs identified from random sequence pools are simple motifs, consistent with recent computational analysis of such sequence pools. Thus, enriching in vitro selection pools with complex structures could increase the probability of discovering novel RNAs. Here we develop an approach for engineering sequence pools that links RNA sequence space regions with corresponding structural distributions via a "mixing matrix" approach combined with a graph theory analysis. We define five classes of mixing matrices motivated by covariance mutations in RNA; these constructs define nucleotide transition rates and are applied to chosen starting sequences to yield specific nonrandom pools. We examine the coverage of sequence space as a function of the mixing matrix and starting sequence via clustering analysis. We show that, in contrast to random sequences, which are associated only with a local region of sequence space, our designed pools, including a structured pool for GTP aptamers, can target specific motifs. It follows that experimental synthesis of designed pools can benefit from using optimized starting sequences, mixing matrices, and pool fractions associated with each of our constructed pools as a guide. Automation of our approach could provide practical tools for pool design applications for in vitro selection of RNAs and related problems.

Adaptive reconfiguration of fractal small-world human brain functional networks

Brain function depends on adaptive self-organization of large-scale neural assemblies, but little is known about quantitative network parameters governing these processes in humans. Here, we describe the topology and synchronizability of frequency-specific brain functional networks using wavelet decomposition of magnetoencephalographic time series, followed by construction and analysis of undirected graphs. Magnetoencephalographic data were acquired from 22 subjects, half of whom performed a finger-tapping task, whereas the other half were studied at rest. We found that brain functional networks were characterized by small-world properties at all six wavelet scales considered, corresponding approximately to classical delta (low and high), , alpha, beta, and gamma frequency bands. Global topological parameters (path length, clustering) were conserved across scales, most consistently in the frequency range 2-37 Hz, implying a scale-invariant or fractal small-world organization. Dynamical analysis showed that networks were located close to the threshold of order/disorder transition in all frequency bands. The highest-frequency gamma network had greater synchronizability, greater clustering of connections, and shorter path length than networks in the scaling regime of (lower) frequencies. Behavioral state did not strongly influence global topology or synchronizability; however, motor task performance was associated with emergence of long-range connections in both beta and gamma networks. Long-range connectivity, e.g., between frontal and parietal cortex, at high frequencies during a motor task may facilitate sensorimotor binding. Human brain functional networks demonstrate a fractal small-world architecture that supports critical dynamics and task-related spatial reconfiguration while preserving global topological parameters.

Surface comparison of active and inactive protein kinases identifies a conserved activation mechanism

The surface comparison of different serine-threonine and tyrosine kinases reveals a set of 30 residues whose spatial positions are highly conserved. The comparison between active and inactive conformations identified the residues whose positions are the most sensitive to activation. Based on these results, we propose a model of protein kinase activation. This model explains how the presence of a phosphate group in the activation loop determines the position of the catalytically important aspartate in the Asp-Phe-Gly motif. According to the model, the most important feature of the activation is a "spine" formation that is dynamically assembled in all active kinases. The spine is comprised of four hydrophobic residues that we detected in a set of 23 eukaryotic and prokaryotic kinases. It spans the molecule and plays a coordinating role in activated kinases. The spine is disordered in the inactive kinases and can explain how stabilization of the whole molecule is achieved upon phosphorylation.

The cognitive phenotype of Down syndrome: insights from intracellular network analysis

Down syndrome (DS) is caused by trisomy of chromosome 21. All individuals with DS exhibit some level of cognitive dysfunction. It is generally accepted that these abnormalities are a result of the upregulation of genes encoded by chromosome 21. Many chromosome 21 proteins are known or predicted to function in critical neurological processes, but typically they function as modulators of these processes, not as key regulators. Thus, upregulation in DS is expected to cause only modest perturbations of normal processes. Systematic approaches such as intracellular network construction and analysis have not been generally applied in DS research. Networks can be assembled from high-throughput experiments or by text-mining of experimental literature. We survey some new developments in constructing such networks, focusing on newly developed network analysis methodologies. We propose how these methods could be integrated with creation and manipulation of mouse models of DS to advance our understanding of the perturbed cell signaling pathways in DS. This understanding could lead to potential therapeutics.

In vitro RNA random pools are not structurally diverse: a computational analysis

In vitro selection of functional RNAs from large random sequence pools has led to the identification of many ligand-binding and catalytic RNAs. However, the structural diversity in random pools is not well understood. Such an understanding is a prerequisite for designing sequence pools to increase the probability of finding complex functional RNA by in vitro selection techniques. Toward this goal, we have generated by computer five random pools of RNA sequences of length up to 100 nt to mimic experiments and characterized the distribution of associated secondary structural motifs using sets of possible RNA tree structures derived from graph theory techniques. Our results show that such random pools heavily favor simple topological structures: For example, linear stem-loop and low-branching motifs are favored rather than complex structures with high-order junctions, as confirmed by known aptamers. Moreover, we quantify the rise of structural complexity with sequence length and report the dominant class of tree motifs (characterized by vertex number) for each pool. These analyses show not only that random pools do not lead to a uniform distribution of possible RNA secondary topologies; they point to avenues for designing pools with specific simple and complex structures in equal abundance in the goal of broadening the range of functional RNAs discovered by in vitro selection. Specifically, the optimal RNA sequence pool length to identify a structure with x stems is 20x.

Global network analysis of phenotypic effects: protein networks and toxicity modulation in Saccharomyces cerevisiae

Using genome-wide information to understand holistically how cells function is a major challenge of the postgenomic era. Recent efforts to understand molecular pathway operation from a global perspective have lacked experimental data on phenotypic context, so insights concerning biologically relevant network characteristics of key genes or proteins have remained largely speculative. Here, we present a global network investigation of the genotype/phenotype data set we developed for the recovery of the yeast Saccharomyces cerevisiae from exposure to DNA-damaging agents, enabling explicit study of how protein-protein interaction network characteristics may be associated with phenotypic functional effects. We show that toxicity-modulating proteins have similar topological properties as essential proteins, suggesting that cells initiate highly coordinated responses to damage similar to those needed for vital cellular functions. We also identify toxicologically important protein complexes, pathways, and modules. These results have potential implications for understanding toxicity-modulating processes relevant to a number of human diseases, including cancer and aging.

Caveats: numerical requirements in graph theory based quantitation of tissue architecture

Graph theory based methods represent one approach to an objective and reproducible structural analysis of tissue architecture. By these methods, neighborhood relations between a number of objects (e.g., cells) are explored and inherent to these methods are therefore certain requirements as to the number of objects to be included in the analysis. However, the question of how many objects are required to achieve reproducible values in repeated computations of proposed structural features, has previously not been adressed specifically. After digitising HE stained slides and storing them as grey level images, cell nuclei were segmented and their geometrical centre of gravity were computed, serving as the basis for construction of the Voronoi diagram (VD) and its subgraphs. Variations in repeated computations of structural features derived from these graphs were related to the number of cell nuclei included in the analysis. We demonstrate a large variation in the values of the structural features from one computation to another in one and the same section when only a limited number of cells (100-500) are included in the analysis. This variation decreased with increasing number of cells analyzed. The exact number of cells required to achieve reproducible values differ significantly between tissues, but not between separate cases of similar lesions. There are no significant differences between normal and malignantly changed tissues in oral mucosa with respect to how many cells must be included. For graph theory based analysis of tissue architecture, care must be taken to include an adequate number of objects; for some of the structural features we have tested, more than 3000 cells.

New algorithms based on the Voronoi Diagram applied in a pilot study on normal mucosa and carcinomas

An adequate reproducibility in the description of tissue architecture is still a challenge to diagnostic pathology, sometimes with unfortunate prognostic implications. To assess a possible diagnostic and prognostic value of quantitiative tissue architecture analysis, structural features based on the Voronoi Diagram (VD) and its subgraphs were developed and tested. A series of 27 structural features were developed and tested in a pilot study of 30 cases of prostate cancer, 10 cases of cervical carcinomas, 8 cases of tongue cancer and 8 cases of normal oral mucosa. Grey level images were acquired from hematoxyline-eosine (HE) stained sections by a charge coupled device (CCD) camera mounted on a microscope connected to a personal computer (PC) with an image array processor. From the grey level images obtained, cell nuclei were automatically segmented and the geometrical centres of cell nuclei were computed. The resulting 2-dimensional (2D) swarm of pointlike seeds distributed in a flat plane was the basis for construction of the VD and its subgraphs. From the polygons, triangulations and arborizations thus obtained, 27 structural features were computed as numerical values. Comparison of groups (normal vs. cancerous oral mucosa, cervical and prostate carcinomas with good and poor prognosis) with regard to distribution in the values of the structural features was performed with Student's t-test. We demonstrate that some of the structural features developed are able to distinguish structurally between normal and cancerous oral mucosa (P = 0.001), and between good and poor outcome groups in prostatic (P = 0.001) and cervical carcinomas (P = 0.001). We present results confirming previous findings that graph theory based algorithms are useful tools for describing tissue architecture (e.g., normal versus malignant). The present study also indicates that these methods have a potential for prognostication in malignant epithelial lesions.

A theory of the epigenesis of neuronal networks by selective stabilization of synapses

A formalism is introduced to represent the connective organization of an evolving neuronal network and the effects of environment on this organization by stabilization or degeneration of labile synapses associated with functioning. Learning, or the acquisition of an associative property, is related to a characteristic variability of the connective organization: the interaction of the environment with the genetic program is printed as a particular pattern of such organization through neuronal functioning. An application of the theory to the development of the neuromuscular junction is proposed and the basic selective aspect of learning emphasized.