Pseudo-attractors in Random Boolean Network Models and Single-Cell Data

In this extended abstract two novel concepts are defined in the study of Random Boolean Networks, i.e. those of “pseudoattractors” and “common sea”, and it is shown how their analogues can be measured in experimental data on gene expression in single cells

Exploring the Dynamic Organization of Random and Evolved Boolean Networks

The properties of most systems composed of many interacting elements are neither determined by the topology of the interaction network alone, nor by the dynamical laws in isolation. Rather, they are the outcome of the interplay between topology and dynamics. In this paper, we consider four different types of systems with critical dynamic regime and with increasingly complex dynamical organization (loosely defined as the emergent property of the interactions between topology and dynamics) and analyze them from a structural and dynamic point of view. A first noteworthy result, previously hypothesized but never quantified so far, is that the topology per se induces a notable increase in dynamic organization. A second observation is that evolution does not change dramatically the size distribution of the present dynamic groups, so it seems that it keeps track of the already present organization induced by the topology. Finally, and similarly to what happens in other applications of evolutionary algorithms, the types of dynamic changes strongly depend upon the used fitness functi

A Fast and Effective Method to Identify Relevant Sets of Variables in Complex Systems

In many complex systems one observes the formation of medium-level structures, whose detection could allow a high-level description of the dynamical organization of the system itself, and thus to its better understanding. We have developed in the past a powerful method to achieve this goal, which however requires a heavy computational cost in several real-world cases. In this work we introduce a modified version of our approach, which reduces the computational burden. The design of the new algorithm allowed the realization of an original suite of methods able to work simultaneously at the micro level (that of the binary relationships of the single variables) and at meso level (the identification of dynamically relevant groups). We apply this suite to a particularly relevant case, in which we look for the dynamic organization of a gene regulatory network when it is subject to knock-outs. The approach combines information theory, graph analysis, and an iterated sieving algorithm in order to describe rather complex situations. Its application allowed to derive some general observations on the dynamical organization of gene regulatory networks, and to observe interesting characteristics in an experimental cas

On the Detection of Significant Pairwise Interactions in Complex Systems

Many systems in nature, society and technology are complex systems, i.e., they are composed of numerous parts that interact in a non-linear way giving rise to positive and negative feedback. The dynamic organization of these systems often allows the emergence of intermediate structures that once formed profoundly influence the system and therefore play a key role in understanding its behavior. In the recent past our group has devised an effective method for identifying groups of interacting variables within a system, based on their observation. The result is a set of entities, each of which connects two or more nodes of the system: this result can therefore be represented by a hypergraph, which can be of considerable use for understanding the system under consideration. In particular, we use an index that allows us to evaluate the level of integration of a group of variables. In order for a group to be identified as significant, the value of this index must exceed a threshold that corresponds (under appropriate hypotheses) to a level of statistical significance decided by the user. In this work we propose a more elaborate approach to determining the significance threshold, which is (i) in itself theoretically interesting and (ii) of considerable practical utility. We use the new approach to determine collections of pairwise relationships in meaningful cases, such as relationships in gene regulatory networks

Attractor-Specific and Common Expression Values in Random Boolean Network Models (with a Preliminary Look at Single-Cell Data)

Random Boolean Networks (RBNs for short) are strongly simplified models of gene regulatory networks (GRNs), which have also been widely studied as abstract models of complex systems and have been used to simulate different phenomena. We define the “common sea” (CS) as the set of nodes that take the same value in all the attractors of a given network realization, and the “specific part” (SP) as the set of all the other nodes, and we study their properties in different ensembles, generated with different parameter values. Both the CS and of the SP can be composed of one or more weakly connected components, which are emergent intermediate-level structures. We show that the study of these sets provides very important information about the behavior of the model. The distribution of distances between attractors is also examined. Moreover, we show how the notion of a “common sea” of genes can be used to analyze data from single-cell experiments

Two-Level Detection of Dynamic Organization in Cancer Evolution Models

Many systems in nature, society and technology are composed of numerous nonlinearly interacting parts. The dynamic organization of these systems often allows the emergence of intermediate structures that once formed deeply affect the system, and therefore play a key role in understanding its behavior. An interesting hypothesis is that the simultaneous analysis of a system at both levels of description (the microlevel of the relationships between single entities, and the mesolevel constituted by their dynamically organized groups) can allow a better understanding of the phenomenon under examination. In this work we apply this idea to a cancer evolution model, of which each individual patient represents a particular instance. Specifically, in order to validate the idea we analyze the same synthetic dataset – whose ground truth is known – with two methods of analysis, and we merge the results in an innovative way. In doing this, we also evaluate the effectiveness of a new method of reconstructing networks of relationships

Serum Mass Spectrometry Proteomics and Protein Set Identification in Response to FOLFOX-4 in Drug-Resistant Ovarian Carcinoma

Ovarian cancer is a highly lethal gynecological malignancy. Drug resistance rapidly occurs, and different therapeutic approaches are needed. So far, no biomarkers have been discovered to predict early response to therapies in the case of multi-treated ovarian cancer patients. The aim of our investigation was to identify a protein panel and the molecular pathways involved in chemotherapy response through a combination of studying proteomics and network enrichment analysis by considering a subset of samples from a clinical setting. Differential mass spectrometry studies were performed on 14 serum samples from patients with heavily pretreated platinum-resistant ovarian cancer who received the FOLFOX-4 regimen as a salvage therapy. The serum was analyzed at baseline time (T0) before FOLFOX-4 treatment, and before the second cycle of treatment (T1), with the aim of understanding if it was possible, after a first treatment cycle, to detect significant proteome changes that could be associated with patients responses to therapy. A total of 291 shared expressed proteins was identified and 12 proteins were finally selected between patients who attained partial response or no-response to chemotherapy when both response to therapy and time dependence (T0, T1) were considered in the statistical analysis. The protein panel included APOL1, GSN, GFI1, LCATL, MNA, LYVE1, ROR1, SHBG, SOD3, TEC, VPS18, and ZNF573. Using a bioinformatics network enrichment approach and metanalysis study, relationships between serum and cellular proteins were identified. An analysis of protein networks was conducted and identified at least three biological processes with functional and therapeutic significance in ovarian cancer, including lipoproteins metabolic process, structural component modulation in relation to cellular apoptosis and autophagy, and cellular oxidative stress response. Five proteins were almost independent from the network (LYVE1, ROR1, TEC, GFI1, and ZNF573). All proteins were associated with response to drug-resistant ovarian cancer resistant and were mechanistically connected to the pathways associated with cancer arrest. These results can be the basis for extending a biomarker discovery process to a clinical trial, as an early predictive tool of chemo-response to FOLFOX-4 of heavily treated ovarian cancer patients and for supporting the oncologist to continue or to interrupt the therapy