Computational neurogenetic modelling: a pathway to new discoveries in genetic neuroscience

The paper presents a methodology for using computational neurogenetic modelling (CNGM) to bring new original insights into how genes influence the dynamics of brain neural networks. CNGM is a novel computational approach to brain neural network modelling that integrates dynamic gene networks with artificial neural network model (ANN). Interaction of genes in neurons affects the dynamics of the whole ANN model through neuronal parameters, which are no longer constant but change as a function of gene expression. Through optimization of interactions within the internal gene regulatory network (GRN), initial gene/protein expression values and ANN parameters, particular target states of the neural network behaviour can be achieved, and statistics about gene interactions can be extracted. In such a way, we have obtained an abstract GRN that contains predictions about particular gene interactions in neurons for subunit genes of AMPA, GABAA and NMDA neuro-receptors. The extent of sequence conservation for 20 subunit proteins of all these receptors was analysed using standard bioinformatics multiple alignment procedures. We have observed abundance of conserved residues but the most interesting observation has been the consistent conservation of phenylalanine (F at position 269) and leucine (L at position 353) in all 20 proteins with no mutations. We hypothesise that these regions can be the basis for mutual interactions. Existing knowledge on evolutionary linkage of their protein families and analysis at molecular level indicate that the expression of these individual subunits should be coordinated, which provides the biological justification for our optimized GRN.     

Gene co-expression network topology provides a framework for molecular characterization of cellular state

MOTIVATION: Gene expression data have become an instrumental resource in describing the molecular state associated with various cellular phenotypes and responses to environmental perturbations. The utility of expression profiling has been demonstrated in partitioning clinical states, predicting the class of unknown samples and in assigning putative functional roles to previously uncharacterized genes based on profile similarity. However, gene expression profiling has had only limited success in identifying therapeutic targets. This is partly due to the fact that current methods based on fold-change focus only on single genes in isolation, and thus cannot convey causal information. In this paper, we present a technique for analysis of expression data in a graph-theoretic framework that relies on associations between genes. We describe the global organization of these networks and biological correlates of their structure. We go on to present a novel technique for the molecular characterization of disparate cellular states that adds a new dimension to the fold-based methods and conclude with an example application to a human medulloblastoma dataset. RESULTS: We have shown that expression networks generated from large model-organism expression datasets are scale-free and that the average clustering coefficient of these networks is several orders of magnitude higher than would be expected for similarly sized scale-free networks, suggesting an inherent hierarchical modularity similar to that previously identified in other biological networks. Furthermore, we have shown that these properties are robust with respect to the parameters of network construction. We have demonstrated an enrichment of genes having lethal knockout phenotypes in the high-degree (i.e. hub) nodes in networks generated from aggregate condition datasets; using process-focused Saccharomyces cerivisiae datasets we have demonstrated additional high-degree enrichments of condition-specific genes encoding proteins known to be involved in or important for the processes interrogated by the microarrays. These results demonstrate the utility of network analysis applied to expression data in identifying genes that are regulated in a state-specific manner. We concluded by showing that a sample application to a human clinical dataset prominently identified a known therapeutic target. AVAILABILITY: Software implementing the methods for network generation presented in this paper is available for academic use by request from the authors in the form of compiled linux binary executables.     

Dynamical properties of model gene networks and implications for the inverse problem

We study the inverse problem, or the "reverse-engineering" problem, for two abstract models of gene expression dynamics, discrete-time Boolean networks and continuous-time switching networks. Formally, the inverse problem is similar for both types of networks. For each gene, its regulators and its Boolean dynamics function must be identified. However, differences in the dynamical properties of these two types of networks affect the amount of data that is necessary for solving the inverse problem. We derive estimates for the average amounts of time series data required to solve the inverse problem for randomly generated Boolean and continuous-time switching networks. We also derive a lower bound on the amount of data needed that holds for both types of networks. We find that the amount of data required is logarithmic in the number of genes for Boolean networks, matching the general lower bound and previous theory, but are superlinear in the number of genes for continuous-time switching networks. We also find that the amount of data needed scales as 2(K), where K is the number of regulators per gene, rather than 2(2K), as previous theory suggests.     

Using effective subnetworks to predict selected properties of gene networks

Background

Difficulties associated with implementing gene therapy are caused by the complexity of the underlying regulatory networks. The forms of interactions between the hundreds of genes, proteins, and metabolites in these networks are not known very accurately. An alternative approach is to limit consideration to genes on the network. Steady state measurements of these influence networks can be obtained from DNA microarray experiments. However, since they contain a large number of nodes, the computation of influence networks requires a prohibitively large set of microarray experiments. Furthermore, error estimates of the network make verifiable predictions impossible.

Methodology/Principal Findings

Here, we propose an alternative approach. Rather than attempting to derive an accurate model of the network, we ask what questions can be addressed using lower dimensional, highly simplified models. More importantly, is it possible to use such robust features in applications? We first identify a small group of genes that can be used to affect changes in other nodes of the network. The reduced effective empirical subnetwork (EES) can be computed using steady state measurements on a small number of genetically perturbed systems. We show that the EES can be used to make predictions on expression profiles of other mutants, and to compute how to implement pre-specified changes in the steady state of the underlying biological process. These assertions are verified in a synthetic influence network. We also use previously published experimental data to compute the EES associated with an oxygen deprivation network of E.coli, and use it to predict gene expression levels on a double mutant. The predictions are significantly different from the experimental results for less than of genes.

Conclusions/Significance

The constraints imposed by gene expression levels of mutants can be used to address a selected set of questions about a gene network.     

Network Class Superposition Analyses

Networks are often used to understand a whole system by modeling the interactions among its pieces. Examples include biomolecules in a cell interacting to provide some primary function, or species in an environment forming a stable community. However, these interactions are often unknown; instead, the pieces'' dynamic states are known, and network structure must be inferred. Because observed function may be explained by many different networks (e.g., for the yeast cell cycle process [1]), considering dynamics beyond this primary function means picking a single network or suitable sample: measuring over all networks exhibiting the primary function is computationally infeasible. We circumvent that obstacle by calculating the network class ensemble. We represent the ensemble by a stochastic matrix , which is a transition-by-transition superposition of the system dynamics for each member of the class. We present concrete results for derived from Boolean time series dynamics on networks obeying the Strong Inhibition rule, by applying to several traditional questions about network dynamics. We show that the distribution of the number of point attractors can be accurately estimated with . We show how to generate Derrida plots based on . We show that -based Shannon entropy outperforms other methods at selecting experiments to further narrow the network structure. We also outline an experimental test of predictions based on . We motivate all of these results in terms of a popular molecular biology Boolean network model for the yeast cell cycle, but the methods and analyses we introduce are general. We conclude with open questions for , for example, application to other models, computational considerations when scaling up to larger systems, and other potential analyses.     

Construction and analysis of gene-gene dynamics influence networks based on a Boolean model

Background

Identification of novel gene-gene relations is a crucial issue to understand system-level biological phenomena. To this end, many methods based on a correlation analysis of gene expressions or structural analysis of molecular interaction networks have been proposed. They have a limitation in identifying more complicated gene-gene dynamical relations, though.

Results

To overcome this limitation, we proposed a measure to quantify a gene-gene dynamical influence (GDI) using a Boolean network model and constructed a GDI network to indicate existence of a dynamical influence for every ordered pair of genes. It represents how much a state trajectory of a target gene is changed by a knockout mutation subject to a source gene in a gene-gene molecular interaction (GMI) network. Through a topological comparison between GDI and GMI networks, we observed that the former network is denser than the latter network, which implies that there exist many gene pairs of dynamically influencing but molecularly non-interacting relations. In addition, a larger number of hub genes were generated in the GDI network. On the other hand, there was a correlation between these networks such that the degree value of a node was positively correlated to each other. We further investigated the relationships of the GDI value with structural properties and found that there are negative and positive correlations with the length of a shortest path and the number of paths, respectively. In addition, a GDI network could predict a set of genes whose steady-state expression is affected in E. coli gene-knockout experiments. More interestingly, we found that the drug-targets with side-effects have a larger number of outgoing links than the other genes in the GDI network, which implies that they are more likely to influence the dynamics of other genes. Finally, we found biological evidences showing that the gene pairs which are not molecularly interacting but dynamically influential can be considered for novel gene-gene relationships.

Conclusion

Taken together, construction and analysis of the GDI network can be a useful approach to identify novel gene-gene relationships in terms of the dynamical influence.

     

The spectrum of covariance matrices of randomly connected recurrent neuronal networks with linear dynamics

A key question in theoretical neuroscience is the relation between the connectivity structure and the collective dynamics of a network of neurons. Here we study the connectivity-dynamics relation as reflected in the distribution of eigenvalues of the covariance matrix of the dynamic fluctuations of the neuronal activities, which is closely related to the network dynamics’ Principal Component Analysis (PCA) and the associated effective dimensionality. We consider the spontaneous fluctuations around a steady state in a randomly connected recurrent network of stochastic neurons. An exact analytical expression for the covariance eigenvalue distribution in the large-network limit can be obtained using results from random matrices. The distribution has a finitely supported smooth bulk spectrum and exhibits an approximate power-law tail for coupling matrices near the critical edge. We generalize the results to include second-order connectivity motifs and discuss extensions to excitatory-inhibitory networks. The theoretical results are compared with those from finite-size networks and the effects of temporal and spatial sampling are studied. Preliminary application to whole-brain imaging data is presented. Using simple connectivity models, our work provides theoretical predictions for the covariance spectrum, a fundamental property of recurrent neuronal dynamics, that can be compared with experimental data.     

A Boolean Model of the Gene Regulatory Network Underlying Mammalian Cortical Area Development

The cerebral cortex is divided into many functionally distinct areas. The emergence of these areas during neural development is dependent on the expression patterns of several genes. Along the anterior-posterior axis, gradients of Fgf8, Emx2, Pax6, Coup-tfi, and Sp8 play a particularly strong role in specifying areal identity. However, our understanding of the regulatory interactions between these genes that lead to their confinement to particular spatial patterns is currently qualitative and incomplete. We therefore used a computational model of the interactions between these five genes to determine which interactions, and combinations of interactions, occur in networks that reproduce the anterior-posterior expression patterns observed experimentally. The model treats expression levels as Boolean, reflecting the qualitative nature of the expression data currently available. We simulated gene expression patterns created by all possible networks containing the five genes of interest. We found that only of these networks were able to reproduce the experimentally observed expression patterns. These networks all lacked certain interactions and combinations of interactions including auto-regulation and inductive loops. Many higher order combinations of interactions also never appeared in networks that satisfied our criteria for good performance. While there was remarkable diversity in the structure of the networks that perform well, an analysis of the probability of each interaction gave an indication of which interactions are most likely to be present in the gene network regulating cortical area development. We found that in general, repressive interactions are much more likely than inductive ones, but that mutually repressive loops are not critical for correct network functioning. Overall, our model illuminates the design principles of the gene network regulating cortical area development, and makes novel predictions that can be tested experimentally.     

Large-scale properties of clustered networks: implications for disease dynamics

We consider previously proposed procedures for generating clustered networks and investigate how these procedures lead to differences in network properties other than clustering. We interpret our findings in terms of the effect of the network structure on the disease outbreak threshold and disease dynamics. To generate null-model networks for comparison, we implement an assortativity-conserving rewiring algorithm that alters the level of clustering while causing minimal impact on other properties. We show that many theoretical network models used to generate networks with a particular property often lead to significant changes in network properties other than that of interest. For high levels of clustering, different procedures lead to networks that differ in degree heterogeneity and assortativity, and in broader scale measures such as ?(0) and the distribution of shortest path lengths. Hence, care must be taken when investigating the implications of network properties for disease transmission or other dynamic process that the network supports.     

High-confidence discovery of genetic network regulators in expression quantitative trait loci data

Expression QTL (eQTL) studies involve the collection of microarray gene expression data and genetic marker data from segregating individuals in a population to search for genetic determinants of differential gene expression. Previous studies have found large numbers of trans-regulated genes (regulated by unlinked genetic loci) that link to a single locus or eQTL "hotspot," and it would be desirable to find the mechanism of coregulation for these gene groups. However, many difficulties exist with current network reconstruction algorithms such as low power and high computational cost. A common observation for biological networks is that they have a scale-free or power-law architecture. In such an architecture, highly influential nodes exist that have many connections to other nodes. If we assume that this type of architecture applies to genetic networks, then we can simplify the problem of genetic network reconstruction by focusing on discovery of the key regulatory genes at the top of the network. We introduce the concept of "shielding" in which a specific gene expression variable (the shielder) renders a set of other gene expression variables (the shielded genes) independent of the eQTL. We iteratively build networks from the eQTL to the shielder down using tests of conditional independence. We have proposed a novel test for controlling the shielder false-positive rate at a predetermined level by requiring a threshold number of shielded genes per shielder. Using simulation, we have demonstrated that we can control the shielder false-positive rate as well as obtain high shielder and edge specificity. In addition, we have shown our method to be robust to violation of the latent variable assumption, an important feature in the practical application of our method. We have applied our method to a yeast expression QTL data set in which microarray and marker data were collected from the progeny of a backcross of two species of Saccharomyces cerevisiae (Brem et al. 2002). Seven genetic networks have been discovered, and bioinformatic analysis of the discovered regulators and corresponding regulated genes has generated plausible hypotheses for mechanisms of regulation that can be tested in future experiments.     

Mutualistic networks: moving closer to a predictive theory

Plant–animal mutualistic networks sustain terrestrial biodiversity and human food security. Global environmental changes threaten these networks, underscoring the urgency for developing a predictive theory on how networks respond to perturbations. Here, I synthesise theoretical advances towards predicting network structure, dynamics, interaction strengths and responses to perturbations. I find that mathematical models incorporating biological mechanisms of mutualistic interactions provide better predictions of network dynamics. Those mechanisms include trait matching, adaptive foraging, and the dynamic consumption and production of both resources and services provided by mutualisms. Models incorporating species traits better predict the potential structure of networks (fundamental niche), while theory based on the dynamics of species abundances, rewards, foraging preferences and reproductive services can predict the extremely dynamic realised structures of networks, and may successfully predict network responses to perturbations. From a theoretician's standpoint, model development must more realistically represent empirical data on interaction strengths, population dynamics and how these vary with perturbations from global change. From an empiricist's standpoint, theory needs to make specific predictions that can be tested by observation or experiments. Developing models using short‐term empirical data allows models to make longer term predictions of community dynamics. As more longer term data become available, rigorous tests of model predictions will improve.     

Accelerated search for biomolecular network models to interpret high-throughput experimental data

Background  

The functions of human cells are carried out by biomolecular networks, which include proteins, genes, and regulatory sites within DNA that encode and control protein expression. Models of biomolecular network structure and dynamics can be inferred from high-throughput measurements of gene and protein expression. We build on our previously developed fuzzy logic method for bridging quantitative and qualitative biological data to address the challenges of noisy, low resolution high-throughput measurements, i.e., from gene expression microarrays. We employ an evolutionary search algorithm to accelerate the search for hypothetical fuzzy biomolecular network models consistent with a biological data set. We also develop a method to estimate the probability of a potential network model fitting a set of data by chance. The resulting metric provides an estimate of both model quality and dataset quality, identifying data that are too noisy to identify meaningful correlations between the measured variables.