Gene expression of Caenorhabditis elegans neurons carries information on their synaptic connectivity

The claim that genetic properties of neurons significantly influence their synaptic network structure is a common notion in neuroscience. The nematode Caenorhabditis elegans provides an exciting opportunity to approach this question in a large-scale quantitative manner. Its synaptic connectivity network has been identified, and, combined with cellular studies, we currently have characteristic connectivity and gene expression signatures for most of its neurons. By using two complementary analysis assays we show that the expression signature of a neuron carries significant information about its synaptic connectivity signature, and identify a list of putative genes predicting neural connectivity. The current study rigorously quantifies the relation between gene expression and synaptic connectivity signatures in the C. elegans nervous system and identifies subsets of neurons where this relation is highly marked. The results presented and the genes identified provide a promising starting point for further, more detailed computational and experimental investigations.     

A Morpho-Density Approach to Estimating Neural Connectivity

Neuronal signal integration and information processing in cortical neuronal networks critically depend on the organization of synaptic connectivity. Because of the challenges involved in measuring a large number of neurons, synaptic connectivity is difficult to determine experimentally. Current computational methods for estimating connectivity typically rely on the juxtaposition of experimentally available neurons and applying mathematical techniques to compute estimates of neural connectivity. However, since the number of available neurons is very limited, these connectivity estimates may be subject to large uncertainties. We use a morpho-density field approach applied to a vast ensemble of model-generated neurons. A morpho-density field (MDF) describes the distribution of neural mass in the space around the neural soma. The estimated axonal and dendritic MDFs are derived from 100,000 model neurons that are generated by a stochastic phenomenological model of neurite outgrowth. These MDFs are then used to estimate the connectivity between pairs of neurons as a function of their inter-soma displacement. Compared with other density-field methods, our approach to estimating synaptic connectivity uses fewer restricting assumptions and produces connectivity estimates with a lower standard deviation. An important requirement is that the model-generated neurons reflect accurately the morphology and variation in morphology of the experimental neurons used for optimizing the model parameters. As such, the method remains subject to the uncertainties caused by the limited number of neurons in the experimental data set and by the quality of the model and the assumptions used in creating the MDFs and in calculating estimating connectivity. In summary, MDFs are a powerful tool for visualizing the spatial distribution of axonal and dendritic densities, for estimating the number of potential synapses between neurons with low standard deviation, and for obtaining a greater understanding of the relationship between neural morphology and network connectivity.     

Asymmetry in neural fields: a spatiotemporal encoding mechanism

Neural field models have been successfully applied to model diverse brain mechanisms like visual attention, motor control, and memory. Most theoretical and modeling works have focused on the study of the dynamics of such systems under variations in neural connectivity, mainly symmetric connectivity among neurons. However, less attention has been given to the emerging properties of neuron populations when neural connectivity is asymmetric, although asymmetric activity propagation has been observed in cortical tissue. Here we explore the dynamics of neural fields with asymmetric connectivity and show, in the case of front propagation, that it can bias the population to follow a certain trajectory with higher activation. We find that asymmetry relates linearly to the input speed when the input is spatially localized, and this relation holds for different kernels and input shapes. To illustrate the behavior of asymmetric connectivity, we present an application: standard video sequences of human motion were encoded using the asymmetric neural field and compared to computer vision techniques. Overall, our results indicate that asymmetric neural fields are a competitive approach for spatiotemporal encoding with two main advantages: online classification and distributed operation.     

Discovering tightly regulated and differentially expressed gene sets in whole genome expression data

MOTIVATION: Recently, a new type of expression data is being collected which aims to measure the effect of genetic variation on gene expression in pathways. In these datasets, expression profiles are constructed for multiple strains of the same model organism under the same condition. The goal of analyses of these data is to find differences in regulatory patterns due to genetic variation between strains, often without a phenotype of interest in mind. We present a new method based on notions of tight regulation and differential expression to look for sets of genes which appear to be significantly affected by genetic variation. RESULTS: When we use categorical phenotype information, as in the Alzheimer's and diabetes datasets, our method finds many of the same gene sets as gene set enrichment analysis. In addition, our notion of correlated gene sets allows us to focus our efforts on biological processes subjected to tight regulation. In murine hematopoietic stem cells, we are able to discover significant gene sets independent of a phenotype of interest. Some of these gene sets are associated with several blood-related phenotypes. AVAILABILITY: The programs are available by request from the authors.     

Neural development features: spatio-temporal development of the Caenorhabditis elegans neuronal network

The nematode Caenorhabditis elegans, with information on neural connectivity, three-dimensional position and cell linage, provides a unique system for understanding the development of neural networks. Although C. elegans has been widely studied in the past, we present the first statistical study from a developmental perspective, with findings that raise interesting suggestions on the establishment of long-distance connections and network hubs. Here, we analyze the neuro-development for temporal and spatial features, using birth times of neurons and their three-dimensional positions. Comparisons of growth in C. elegans with random spatial network growth highlight two findings relevant to neural network development. First, most neurons which are linked by long-distance connections are born around the same time and early on, suggesting the possibility of early contact or interaction between connected neurons during development. Second, early-born neurons are more highly connected (tendency to form hubs) than later-born neurons. This indicates that the longer time frame available to them might underlie high connectivity. Both outcomes are not observed for random connection formation. The study finds that around one-third of electrically coupled long-range connections are late forming, raising the question of what mechanisms are involved in ensuring their accuracy, particularly in light of the extremely invariant connectivity observed in C. elegans. In conclusion, the sequence of neural network development highlights the possibility of early contact or interaction in securing long-distance and high-degree connectivity.     

Interlinked nonlinear subnetworks underlie the formation of robust cellular patterns in Arabidopsis epidermis: a dynamic spatial model

Background

Analysis of microarray data has been used for the inference of gene-gene interactions. If, however, the aim is the discovery of disease-related biological mechanisms, then the criterion for defining such interactions must be specifically linked to disease.

Results

Here we present a computational methodology that jointly analyzes two sets of microarray data, one in the presence and one in the absence of a disease, identifying gene pairs whose correlation with disease is due to cooperative, rather than independent, contributions of genes, using the recently developed information theoretic measure of synergy. High levels of synergy in gene pairs indicates possible membership of the two genes in a shared pathway and leads to a graphical representation of inferred gene-gene interactions associated with disease, in the form of a "synergy network." We apply this technique on a set of publicly available prostate cancer expression data and successfully validate our results, confirming that they cannot be due to pure chance and providing a biological explanation for gene pairs with exceptionally high synergy.

Conclusion

Thus, synergy networks provide a computational methodology helpful for deriving "disease interactomes" from biological data. When coupled with additional biological knowledge, they can also be helpful for deciphering biological mechanisms responsible for disease.     

Expression2Kinases: mRNA profiling linked to multiple upstream regulatory layers

MOTIVATION: Genome-wide mRNA profiling provides a snapshot of the global state of cells under different conditions. However, mRNA levels do not provide direct understanding of upstream regulatory mechanisms. Here, we present a new approach called Expression2Kinases (X2K) to identify upstream regulators likely responsible for observed patterns in genome-wide gene expression. By integrating chromatin immuno-precipitation (ChIP)-seq/chip and position weight matrices (PWMs) data, protein-protein interactions and kinase-substrate phosphorylation reactions, we can better identify regulatory mechanisms upstream of genome-wide differences in gene expression. We validated X2K by applying it to recover drug targets of food and drug administration (FDA)-approved drugs from drug perturbations followed by mRNA expression profiling; to map the regulatory landscape of 44 stem cells and their differentiating progeny; to profile upstream regulatory mechanisms of 327 breast cancer tumors; and to detect pathways from profiled hepatic stellate cells and hippocampal neurons. The X2K approach can advance our understanding of cell signaling and unravel drugs mechanisms of action. AVAILABILITY: The software and source code are freely available at: http://www.maayanlab.net/X2K. CONTACT: avi.maayan@mssm.edu SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.     

The information theory of developmental pruning: Optimizing global network architectures using local synaptic rules

During development, biological neural networks produce more synapses and neurons than needed. Many of these synapses and neurons are later removed in a process known as neural pruning. Why networks should initially be over-populated, and the processes that determine which synapses and neurons are ultimately pruned, remains unclear. We study the mechanisms and significance of neural pruning in model neural networks. In a deep Boltzmann machine model of sensory encoding, we find that (1) synaptic pruning is necessary to learn efficient network architectures that retain computationally-relevant connections, (2) pruning by synaptic weight alone does not optimize network size and (3) pruning based on a locally-available measure of importance based on Fisher information allows the network to identify structurally important vs. unimportant connections and neurons. This locally-available measure of importance has a biological interpretation in terms of the correlations between presynaptic and postsynaptic neurons, and implies an efficient activity-driven pruning rule. Overall, we show how local activity-dependent synaptic pruning can solve the global problem of optimizing a network architecture. We relate these findings to biology as follows: (I) Synaptic over-production is necessary for activity-dependent connectivity optimization. (II) In networks that have more neurons than needed, cells compete for activity, and only the most important and selective neurons are retained. (III) Cells may also be pruned due to a loss of synapses on their axons. This occurs when the information they convey is not relevant to the target population.     

Robust meta-analysis of gene expression using the elastic net

Meta-analysis of gene expression has enabled numerous insights into biological systems, but current methods have several limitations. We developed a method to perform a meta-analysis using the elastic net, a powerful and versatile approach for classification and regression. To demonstrate the utility of our method, we conducted a meta-analysis of lung cancer gene expression based on publicly available data. Using 629 samples from five data sets, we trained a multinomial classifier to distinguish between four lung cancer subtypes. Our meta-analysis-derived classifier included 58 genes and achieved 91% accuracy on leave-one-study-out cross-validation and on three independent data sets. Our method makes meta-analysis of gene expression more systematic and expands the range of questions that a meta-analysis can be used to address. As the amount of publicly available gene expression data continues to grow, our method will be an effective tool to help distill these data into knowledge.     

Efficient in vivo electroporation of the postnatal rodent forebrain

Functional gene analysis in vivo represents still a major challenge in biomedical research. Here we present a new method for the efficient introduction of nucleic acids into the postnatal mouse forebrain. We show that intraventricular injection of DNA followed by electroporation induces strong expression of transgenes in radial glia, neuronal precursors and neurons of the olfactory system. We present two proof-of-principle experiments to validate our approach. First, we show that expression of a human isoform of the neural cell adhesion molecule (hNCAM-140) in radial glia cells induces their differentiation into cells showing a neural precursor phenotype. Second, we demonstrate that p21 acts as a cell cycle inhibitor for postnatal neural stem cells. This approach will represent an important tool for future studies of postnatal neurogenesis and of neural development in general.     

Reconstructing the temporal ordering of biological samples using microarray data

MOTIVATION: Accurate time series for biological processes are difficult to estimate due to problems of synchronization, temporal sampling and rate heterogeneity. Methods are needed that can utilize multi-dimensional data, such as those resulting from DNA microarray experiments, in order to reconstruct time series from unordered or poorly ordered sets of observations. RESULTS: We present a set of algorithms for estimating temporal orderings from unordered sets of sample elements. The techniques we describe are based on modifications of a minimum-spanning tree calculated from a weighted, undirected graph. We demonstrate the efficacy of our approach by applying these techniques to an artificial data set as well as several gene expression data sets derived from DNA microarray experiments. In addition to estimating orderings, the techniques we describe also provide useful heuristics for assessing relevant properties of sample datasets such as noise and sampling intensity, and we show how a data structure called a PQ-tree can be used to represent uncertainty in a reconstructed ordering. AVAILABILITY: Academic implementations of the ordering algorithms are available as source code (in the programming language Python) on our web site, along with documentation on their use. The artificial 'jelly roll' data set upon which the algorithm was tested is also available from this web site. The publicly available gene expression data may be found at http://genome-www.stanford.edu/cellcycle/ and http://caulobacter.stanford.edu/CellCycle/.     

Dynamic patterns of correlated activity in the prefrontal cortex encode information about social behavior

New technologies make it possible to measure activity from many neurons simultaneously. One approach is to analyze simultaneously recorded neurons individually, then group together neurons which increase their activity during similar behaviors into an “ensemble.” However, this notion of an ensemble ignores the ability of neurons to act collectively and encode and transmit information in ways that are not reflected by their individual activity levels. We used microendoscopic GCaMP imaging to measure prefrontal activity while mice were either alone or engaged in social interaction. We developed an approach that combines a neural network classifier and surrogate (shuffled) datasets to characterize how neurons synergistically transmit information about social behavior. Notably, unlike optimal linear classifiers, a neural network classifier with a single linear hidden layer can discriminate network states which differ solely in patterns of coactivity, and not in the activity levels of individual neurons. Using this approach, we found that surrogate datasets which preserve behaviorally specific patterns of coactivity (correlations) outperform those which preserve behaviorally driven changes in activity levels but not correlated activity. Thus, social behavior elicits increases in correlated activity that are not explained simply by the activity levels of the underlying neurons, and prefrontal neurons act collectively to transmit information about socialization via these correlations. Notably, this ability of correlated activity to enhance the information transmitted by neuronal ensembles is diminished in mice lacking the autism-associated gene Shank3. These results show that synergy is an important concept for the coding of social behavior which can be disrupted in disease states, reveal a specific mechanism underlying this synergy (social behavior increases correlated activity within specific ensembles), and outline methods for studying how neurons within an ensemble can work together to encode information.

Behaviorally-specific patterns of correlated activity between prefrontal neurons normally enhance the information that neuronal ensembles transmit about social behavior. This study shows that in a mouse model of autism, individual neurons continue to encode social information, but this additional information carried by patterns of correlated activity is lost.     

Incorporating anatomically realistic cellular-level connectivity in neural network models of the rat hippocampus

The specific connectivity patterns among neuronal classes can play an important role in the regulation of firing dynamics in many brain regions. Yet most neural network models are built based on vastly simplified connectivity schemes that do not accurately reflect the biological complexity. Taking the rat hippocampus as an example, we show here that enough quantitative information is available in the neuroanatomical literature to construct neural networks derived from accurate models of cellular connectivity. Computational simulations based on this approach lend themselves to a direct investigation of the potential relationship between cellular connectivity and network activity. We define a set of fundamental parameters to characterize cellular connectivity, and are collecting the related values for the rat hippocampus from published reports. Preliminary simulations based on these data uncovered a novel putative role for feedforward inhibitory neurons. In particular, "mopp" cells in the dentate gyrus are suitable to help maintain the firing rate of granule cells within physiological levels in response to a plausibly noisy input from the entorhinal cortex. The stabilizing effect of feedforward inhibition is further shown to depend on the particular ratio between the relative threshold values of the principal cells and the interneurons. We are freely distributing the connectivity data on which this study is based through a publicly accessible web archive (http://www.krasnow.gmu.edu/L-Neuron).     

Monosynaptic restriction of transsynaptic tracing from single, genetically targeted neurons

There has never been a wholesale way of identifying neurons that are monosynaptically connected either to some other cell group or, especially, to a single cell. The best available tools, transsynaptic tracers, are unable to distinguish weak direct connections from strong indirect ones. Furthermore, no tracer has proven potent enough to label any connected neurons whatsoever when starting from a single cell. Here we present a transsynaptic tracer that crosses only one synaptic step, unambiguously identifying cells directly presynaptic to the starting population. Based on rabies virus, it is genetically targetable, allows high-level expression of any gene of interest in the synaptically coupled neurons, and robustly labels connections made to single cells. This technology should enable a far more detailed understanding of neural connectivity than has previously been possible.     

Relationships between gene expression and brain wiring in the adult rodent brain

We studied the global relationship between gene expression and neuroanatomical connectivity in the adult rodent brain. We utilized a large data set of the rat brain "connectome" from the Brain Architecture Management System (942 brain regions and over 5000 connections) and used statistical approaches to relate the data to the gene expression signatures of 17,530 genes in 142 anatomical regions from the Allen Brain Atlas. Our analysis shows that adult gene expression signatures have a statistically significant relationship to connectivity. In particular, brain regions that have similar expression profiles tend to have similar connectivity profiles, and this effect is not entirely attributable to spatial correlations. In addition, brain regions which are connected have more similar expression patterns. Using a simple optimization approach, we identified a set of genes most correlated with neuroanatomical connectivity, and find that this set is enriched for genes involved in neuronal development and axon guidance. A number of the genes have been implicated in neurodevelopmental disorders such as autistic spectrum disorder. Our results have the potential to shed light on the role of gene expression patterns in influencing neuronal activity and connectivity, with potential applications to our understanding of brain disorders. Supplementary data are available at http://www.chibi.ubc.ca/ABAMS.     

A Bayesian network classification methodology for gene expression data.

We present new techniques for the application of a Bayesian network learning framework to the problem of classifying gene expression data. The focus on classification permits us to develop techniques that address in several ways the complexities of learning Bayesian nets. Our classification model reduces the Bayesian network learning problem to the problem of learning multiple subnetworks, each consisting of a class label node and its set of parent genes. We argue that this classification model is more appropriate for the gene expression domain than are other structurally similar Bayesian network classification models, such as Naive Bayes and Tree Augmented Naive Bayes (TAN), because our model is consistent with prior domain experience suggesting that a relatively small number of genes, taken in different combinations, is required to predict most clinical classes of interest. Within this framework, we consider two different approaches to identifying parent sets which are supported by the gene expression observations and any other currently available evidence. One approach employs a simple greedy algorithm to search the universe of all genes; the second approach develops and applies a gene selection algorithm whose results are incorporated as a prior to enable an exhaustive search for parent sets over a restricted universe of genes. Two other significant contributions are the construction of classifiers from multiple, competing Bayesian network hypotheses and algorithmic methods for normalizing and binning gene expression data in the absence of prior expert knowledge. Our classifiers are developed under a cross validation regimen and then validated on corresponding out-of-sample test sets. The classifiers attain a classification rate in excess of 90% on out-of-sample test sets for two publicly available datasets. We present an extensive compilation of results reported in the literature for other classification methods run against these same two datasets. Our results are comparable to, or better than, any we have found reported for these two sets, when a train-test protocol as stringent as ours is followed.     

A simple method to improve probe set estimates from oligonucleotide arrays

A popular commercially available oligonucleotide microarray technology employs sets of 25 base pair oligonucleotide probes for measurement of gene expression levels. A mathematical algorithm is required to compute an estimate of gene expression from the multiple probes. Previously proposed methods for summarizing gene expression data have either been substantially ad hoc or have relied on model assumptions that may be easily violated. Here we present a new algorithm for calculating gene expression from probe sets. Our approach is functionally related to leave-one-out cross-validation, a non-parametric statistical technique that is often applied in limited data situations. We illustrate this approach using data from our study seeking a molecular fingerprint of STAT3 regulated genes for early detection of human cancer.