Biologically meaningful regulatory logic enhances the convergence rate in Boolean networks and bushiness of their state transition graph.

Boolean models of gene regulatory networks (GRNs) have gained widespread traction as they can easily recapitulate cellular phenotypes via their attractor states. Their overall dynamics are embodied in a state transition graph (STG). Indeed, two Boolean networks (BNs) with the same network structure and attractors can have drastically different STGs depending on the type of Boolean functions (BFs) employed. Our objective here is to systematically delineate the effects of different classes of BFs on the structural features of the STG of reconstructed Boolean GRNs while keeping network structure and biological attractors fixed, and explore the characteristics of BFs that drive those features. Using $10$ reconstructed Boolean GRNs, we generate ensembles that differ in BFs and compute from their STGs the dynamics' rate of contraction or 'bushiness' and rate of 'convergence', quantified with measures inspired from cellular automata (CA) that are based on the garden-of-Eden (GoE) states. We find that biologically meaningful BFs lead to higher STG 'bushiness' and 'convergence' than random ones. Obtaining such 'global' measures gets computationally expensive with larger network sizes, stressing the need for feasible proxies. So we adapt Wuensche's $Z$-parameter in CA to BFs in BNs and provide four natural variants, which, along with the average sensitivity of BFs computed at the network level, comprise our descriptors of local dynamics and we find some of them to be good proxies for bushiness. Finally, we provide an excellent proxy for the 'convergence' based on computing transient lengths originating at random states rather than GoE states.

Preponderance of generalized chain functions in reconstructed Boolean models of biological networks.

Boolean networks (BNs) have been extensively used to model gene regulatory networks (GRNs). The dynamics of BNs depend on the network architecture and regulatory logic rules (Boolean functions (BFs)) associated with nodes. Nested canalyzing functions (NCFs) have been shown to be enriched among the BFs in the large-scale studies of reconstructed Boolean models. The central question we address here is whether that enrichment is due to certain sub-types of NCFs. We build on one sub-type of NCFs, the chain functions (or chain-0 functions) proposed by Gat-Viks and Shamir. First, we propose two other sub-types of NCFs, namely, the class of chain-1 functions and generalized chain functions, the union of the chain-0 and chain-1 types. Next, we find that the fraction of NCFs that are chain-0 (also holds for chain-1) functions decreases exponentially with the number of inputs. We provide analytical treatment for this and other observations on BFs. Then, by analyzing three different datasets of reconstructed Boolean models we find that generalized chain functions are significantly enriched within the NCFs. Lastly we illustrate that upon imposing the constraints of generalized chain functions on three different GRNs we are able to obtain biologically viable Boolean models.

ViCEKb: Vitiligo-linked Chemical Exposome Knowledgebase.

Vitiligo is a complex disease wherein the environmental factors, in conjunction with the underlying genetic predispositions, trigger the autoimmune destruction of melanocytes, ultimately leading to depigmented patches on the skin. While genetic factors have been extensively studied, the knowledge on environmental triggers remains sparse and less understood. To address this knowledge gap, we present the first comprehensive knowledgebase of vitiligo-triggering chemicals namely, Vitiligo-linked Chemical Exposome Knowledgebase (ViCEKb). ViCEKb involves an extensive and systematic manual effort in curation of published literature and subsequent compilation of 113 unique chemical triggers of vitiligo. ViCEKb standardizes various chemical information, and categorizes the chemicals based on their evidences and sources of exposure. Importantly, ViCEKb contains a wide range of metrics necessary for different toxicological evaluations. Notably, we observed that ViCEKb chemicals are present in a variety of consumer products. For instance, Propyl gallate is present as a fragrance substance in various household products, and Flutamide is used in medication to treat prostate cancer. These two chemicals have the highest level of evidence in ViCEKb, but are not regulated for their skin sensitizing effects. Furthermore, an extensive cheminformatics-based investigation revealed that ViCEKb chemical space is structurally diverse and comprises unique chemical scaffolds in comparison with skin specific regulatory lists. For example, Neomycin and 2,3,5-Triglycidyl-4-aminophenol have unique chemical scaffolds and the highest level of evidence in ViCEKb, but are not regulated for their skin sensitizing effects. Finally, a transcriptomics-based analysis of ViCEKb chemical perturbations in skin cell samples highlighted the commonality in their linked biological processes. Overall, we present the first comprehensive effort in compilation and exploration of various chemical triggers of vitiligo. We believe such a resource will enable in deciphering the complex etiology of vitiligo and aid in the characterization of human chemical exposome. ViCEKb is freely available for academic research at: https://cb.imsc.res.in/vicekb.

Leveraging developmental landscapes for model selection in Boolean gene regulatory networks.

Boolean models are a well-established framework to model developmental gene regulatory networks (DGRNs) for acquisition of cellular identities. During the reconstruction of Boolean DGRNs, even if the network structure is given, there is generally a large number of combinations of Boolean functions that will reproduce the different cell fates (biological attractors). Here we leverage the developmental landscape to enable model selection on such ensembles using the relative stability of the attractors. First we show that previously proposed measures of relative stability are strongly correlated and we stress the usefulness of the one that captures best the cell state transitions via the mean first passage time (MFPT) as it also allows the construction of a cellular lineage tree. A property of great computational importance is the insensitivity of the different stability measures to changes in noise intensities. That allows us to use stochastic approaches to estimate the MFPT and thereby scale up the computations to large networks. Given this methodology, we revisit different Boolean models of Arabidopsis thaliana root development, showing that a most recent one does not respect the biologically expected hierarchy of cell states based on relative stabilities. We therefore developed an iterative greedy algorithm that searches for models which satisfy the expected hierarchy of cell states and found that its application to the root development model yields many models that meet this expectation. Our methodology thus provides new tools that can enable reconstruction of more realistic and accurate Boolean models of DGRNs.

Relative importance of composition structures and biologically meaningful logics in bipartite Boolean models of gene regulation.

Boolean networks have been widely used to model gene networks. However, such models are coarse-grained to an extent that they abstract away molecular specificities of gene regulation. Alternatively, bipartite Boolean network models of gene regulation explicitly distinguish genes from transcription factors (TFs). In such bipartite models, multiple TFs may simultaneously contribute to gene regulation by forming heteromeric complexes, thus giving rise to composition structures. Since bipartite Boolean models are relatively recent, an empirical investigation of their biological plausibility is lacking. Here, we estimate the prevalence of composition structures arising through heteromeric complexes. Moreover, we present an additional mechanism where composition structures may arise as a result of multiple TFs binding to cis-regulatory regions and provide empirical support for this mechanism. Next, we compare the restriction in BFs imposed by composition structures and by biologically meaningful properties. We find that though composition structures can severely restrict the number of Boolean functions (BFs) driving a gene, the two types of minimally complex BFs, namely nested canalyzing functions (NCFs) and read-once functions (RoFs), are comparatively more restrictive. Finally, we find that composition structures are highly enriched in real networks, but this enrichment most likely comes from NCFs and RoFs.

A preference for link operator functions can drive Boolean biological networks towards critical dynamics.

Boolean modelling is a powerful framework to understand the operating principles of biological networks. The regulatory logic between biological entities in these networks is expressed as Boolean functions (BFs). There exist various types of BFs (and thus regulatory logic rules) which are meaningful in the biological context. In this contribution, we explore one such type, known as link operator functions (LOFs). We theoretically enumerate these functions and show that, among all BFs and even within the biologically consistent effective and unate functions (EUFs), the LOFs form a tiny subset. We then find that the AND-NOT LOFs are particularly abundant in reconstructed biological Boolean networks. By leveraging these facts, namely, the tiny representation of LOFs in the space of EUFs and their presence in the biological dataset, we show that the space of acceptable models can be shrunk by applying steady-state constraints to BFs, followed by the choice of LOFs which satisfy those constraints. Finally, we demonstrate that among a wide range of BFs, the LOFs drive biological network dynamics towards criticality.

Minimum complexity drives regulatory logic in Boolean models of living systems.

The properties of random Boolean networks have been investigated extensively as models of regulation in biological systems. However, the Boolean functions (BFs) specifying the associated logical update rules should not be expected to be random. In this contribution, we focus on biologically meaningful types of BFs, and perform a systematic study of their preponderance in a compilation of 2,687 functions extracted from published models. A surprising feature is that most of these BFs have odd "bias", that is they produce "on" outputs for a total number of input combinations that is odd. Upon further analysis, we are able to explain this observation, along with the enrichment of read-once functions (RoFs) and its nested canalyzing functions (NCFs) subset, in terms of 2 complexity measures: Boolean complexity based on string lengths in formal logic, which is yet unexplored in biological contexts, and the so-called average sensitivity. RoFs minimize Boolean complexity and all such functions have odd bias. Furthermore, NCFs minimize not only the Boolean complexity but also the average sensitivity. These results reveal the importance of minimum complexity in the regulatory logic of biological networks.