Mutual information between the time series of two dynamical elements measures how well their activities are coordinated. In a network of interacting elements, the average mutual information over all pairs of elements I is a global measure of the correlation between the elements' dynamics. Local topological features in the network have been shown to affect I . Here we define a generalized clustering coefficient C_{p} and show that this quantity captures the effects of local structures on the global dynamics of networks. Using random Boolean networks (RBNs) as models of networks of interacting elements, we show that the variation of I ( I averaged over an ensemble of RBNs with the number of nodes N and average connectivity k ) with N and k is caused by the variation of C_{p} . Also, the variability of I between RBNs with equal N and k is due to their distinct values of C_{p} . Consequently, we propose a rewiring method to generate ensembles of BNs, from ordinary RBNs, with fixed values of C_{p} up to order 5, while maintaining in- and out-degree distributions. Using this methodology, the dependency of C_{p} on N and k and the variability of I for RBNs with equal N and k are shown to disappear in RBNs with C_{p} set to zero. The I of ensembles of RBNs with fixed, nonzero C_{p} values, also becomes almost independent of N and k . In addition, it is shown that C_{p} exhibits a power-law dependence on N in ordinary RBNs, suggesting that the C_{p} affects even relatively large networks. The method of generating networks with fixed C_{p} values is useful to generate networks with small N whose dynamics have the same properties as those of large scale networks, or to generate ensembles of networks with the same C_{p} as some specific network, and thus comparable dynamics. These results show how a system's dynamics is constrained by its local structure, suggesting that the local topology of biological networks might be shaped by selection, for example, towards optimizing the coordination between its components.

The immunosuppressive microenvironment in glioblastoma (GBM) prevents an efficient antitumoral immune response and enables tumor formation and growth. Although an understanding of the nature of immunosuppression is still largely lacking, it is important for successful cancer treatment through immune system modulation. To gain insight into immunosuppression in GBM, we performed a computational analysis to model relative immune cell content and type of immune response in each GBM tumor sample from The Cancer Genome Atlas RNA-seq data set. We uncovered high variability in immune system-related responses and in the composition of the microenvironment across the cohort, suggesting immunologic diversity. Immune cell compositions were associated with typical alterations such as IDH mutation or inactivating NF1 mutation/deletion. Furthermore, our analysis identified three GBM subgroups presenting different adaptive immune responses: negative, humoral, and cellular-like. These subgroups were linked to transcriptional GBM subtypes and typical genetic alterations. All G-CIMP and IDH-mutated samples were in the negative group, which was also enriched by cases with focal amplification of CDK4 and MARCH9. IDH1-mutated samples showed lower expression and higher DNA methylation of MHC-I-type HLA genes. Overall, our analysis reveals heterogeneity in the immune microenvironment of GBM and identifies new markers for immunosuppression. Characterization of diverse immune responses will facilitate patient stratification and improve personalized immunotherapy in the future. This study utilizes a computational approach to characterize the immune environments in glioblastoma and shows that glioblastoma immune microenvironments can be classified into three major subgroups, which are linked to typical glioblastoma alterations such as IDH mutation, NF1 inactivation, and CDK4-MARCH9 locus amplification. http://cancerres.aacrjournals.org/content/canres/78/19/5574/F1.large.jpg .

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Boolean networks are used to study the large-scale properties of nonlinear systems and are mainly applied to model genetic regulatory networks. A statistical method called the annealed approximation is commonly used to examine the dynamical properties of randomly generated Boolean networks that are created with selected statistical features. However, in the literature there are several variations of the annealed approximation. These approximations cannot be interchangeably used in all cases due to different background assumptions. In this paper, we present the so-called four-state model, derive the different approximations from this model, and make the differences and connections between these approximations explicit. As an application of the presented results, we study the properties of the Boolean networks that are constructed with random functions, canalizing functions, and regulatory functions found in the biological literature.