Search for: All records

Abstract Over the last twenty years, dynamic modeling of biomolecular networks has exploded in popularity. Many of the classical tools for understanding dynamical systems are unwieldy in the highly nonlinear, poorly constrained, high-dimensional systems that often arise from these modeling efforts. Understanding complex biological systems is greatly facilitated by purpose-built methods that leverage common features of such models, such as local monotonicity, interaction graph sparsity, and sigmoidal kinetics. Here, we review methods for controlling the systems of ordinary differential equations used to model biomolecular networks. We focus on methods that make use of the structure of the network of interactions to help inform, which variables to target for control, and highlight the computational and experimental advantages of such approaches. We also discuss the importance of nonperturbative methods in biomedical and experimental molecular biology applications, where finely tuned interventions can be difficult to implement. It is well known that feedback loops, and positive feedback loops in particular, play a major determining role in the dynamics of biomolecular networks. In many of the methods we cover here, control over system trajectories is realized by overriding the behavior of key feedback loops. 

In network control theory, driving all the nodes in the Feedback Vertex Set (FVS) by node-state override forces the network into one of its attractors (long-term dynamic behaviors). The FVS is often composed of more nodes than can be realistically manipulated in a system; for example, only up to three nodes can be controlled in intracellular networks, while their FVS may contain more than 10 nodes. Thus, we developed an approach to rank subsets of the FVS on Boolean models of intracellular networks using topological, dynamics-independent measures. We investigated the use of seven topological prediction measures sorted into three categories—centrality measures, propagation measures, and cycle-based measures. Using each measure, every subset was ranked and then evaluated against two dynamics-based metrics that measure the ability of interventions to drive the system toward or away from its attractors: To Control and Away Control. After examining an array of biological networks, we found that the FVS subsets that ranked in the top according to the propagation metrics can most effectively control the network. This result was independently corroborated on a second array of different Boolean models of biological networks. Consequently, overriding the entire FVS is not required to drive a biological network to one of its attractors, and this method provides a way to reliably identify effective FVS subsets without the knowledge of the network dynamics. 

Abstract Summarypystablemotifs is a Python 3 library for analyzing Boolean networks. Its non-heuristic and exhaustive attractor identification algorithm was previously presented in Rozum et al. (2021). Here, we illustrate its performance improvements over similar methods and discuss how it uses outputs of the attractor identification process to drive a system to one of its attractors from any initial state. We implement six attractor control algorithms, five of which are new in this work. By design, these algorithms can return different control strategies, allowing for synergistic use. We also give a brief overview of the other tools implemented in pystablemotifs. Availability and implementationThe source code is on GitHub at https://github.com/jcrozum/pystablemotifs/. Supplementary informationSupplementary data are available at Bioinformatics online. 

We present new applications of parity inversion and time reversal to the emergence of complex behavior from simple dynamical rules in stochastic discrete models. Our parity-based encoding of causal relationships and time-reversal construction efficiently reveal discrete analogs of stable and unstable manifolds. We demonstrate their predictive power by studying decision-making in systems biology and statistical physics models. These applications underpin a novel attractor identification algorithm implemented for Boolean networks under stochastic dynamics. Its speed enables resolving a long-standing open question of how attractor count in critical random Boolean networks scales with network size and whether the scaling matches biological observations. Via 80-fold improvement in probed network size ( N = 16,384), we find the unexpectedly low scaling exponent of 0.12 ± 0.05, approximately one-tenth the analytical upper bound. We demonstrate a general principle: A system’s relationship to its time reversal and state-space inversion constrains its repertoire of emergent behaviors. 

Abstract We analyze networks of functional correlations between brain regions to identify changes in their structure caused by Attention Deficit Hyperactivity Disorder (adhd). We express the task for finding changes as a network anomaly detection problem on temporal networks. We propose the use of a curvature measure based on the Forman–Ricci curvature, which expresses higher-order correlations among two connected nodes. Our theoretical result on comparing this Forman–Ricci curvature with another well-known notion of network curvature, namely the Ollivier–Ricci curvature, lends further justification to the assertions that these two notions of network curvatures are not well correlated and therefore one of these curvature measures cannot be used as an universal substitute for the other measure. Our experimental results indicate nine critical edges whose curvature differs dramatically in brains ofadhdpatients compared to healthy brains. The importance of these edges is supported by existing neuroscience evidence. We demonstrate that comparative analysis of curvature identifies changes that more traditional approaches, for example analysis of edge weights, would not be able to identify. 

FLT3-mutant acute myeloid leukemia (AML) is an aggressive form of leukemia with poor prognosis. Treatment with FLT3 inhibitors frequently produces a clinical response, but the disease nevertheless often recurs. Recent studies have revealed system-wide gene expression changes in FLT3-mutant AML cell lines in response to drug treatment. Here we sought a systems-level understanding of how these cells mediate these drug-induced changes. Using RNAseq data from AML cells with an internal tandem duplication FLT3 mutation (FLT3-ITD) under six drug treatment conditions including quizartinib and dexamethasone, we identified seven distinct gene programs representing diverse biological processes involved in AML drug-induced changes. Based on the literature knowledge about genes from these modules, along with public gene regulatory network databases, we constructed a network of FLT3-ITD AML. Applying the BooleaBayes algorithm to this network and the RNAseq data, we created a probabilistic, data-driven dynamical model of acquired resistance to these drugs. Analysis of this model reveals several interventions that may disrupt targeted parts of the system-wide drug response. We anticipate co-targeting these points may result in synergistic treatments that can overcome resistance and prevent eventual recurrence. 

Candida albicans , an opportunistic fungal pathogen, is a significant cause of human infections, particularly in immunocompromised individuals. Phenotypic plasticity between two morphological phenotypes, yeast and hyphae, is a key mechanism by which C . albicans can thrive in many microenvironments and cause disease in the host. Understanding the decision points and key driver genes controlling this important transition and how these genes respond to different environmental signals is critical to understanding how C . albicans causes infections in the host. Here we build and analyze a Boolean dynamical model of the C . albicans yeast to hyphal transition, integrating multiple environmental factors and regulatory mechanisms. We validate the model by a systematic comparison to prior experiments, which led to agreement in 17 out of 22 cases. The discrepancies motivate alternative hypotheses that are testable by follow-up experiments. Analysis of this model revealed two time-constrained windows of opportunity that must be met for the complete transition from the yeast to hyphal phenotype, as well as control strategies that can robustly prevent this transition. We experimentally validate two of these control predictions in C . albicans strains lacking the transcription factor UME6 and the histone deacetylase HDA1 , respectively. This model will serve as a strong base from which to develop a systems biology understanding of C . albicans morphogenesis. 

The dynamics of complex biological networks may be modeled in a Boolean framework, where the state of each system component is either abundant (ON) or scarce/absent (OFF), and each component's dynamic trajectory is determined by a logical update rule involving the state(s) of its regulator(s). It is possible to encode the update rules in the topology of the so-called expanded graph, analysis of which reveals the long-term behavior, or attractors, of the network. Here, we develop an algorithm to perturb the expanded graph (or, equivalently, the logical update rules) to eliminate stable motifs: subgraphs that cause a subset of components to stabilize to one state. Depending on the topology of the expanded graph, these perturbations lead to the modification or loss of the corresponding attractor. While most perturbations of biological regulatory networks in the literature involve the knockout (fixing to OFF) or constitutive activation (fixing to ON) of one or more nodes, we here consider edgetic perturbations, where a node's update rule is modified such that one or more of its regulators is viewed as ON or OFF regardless of its actual state. We apply the methodology to two biological networks. In a network representing T-LGL leukemia, we identify edgetic perturbations that eliminate the cancerous attractor, leaving only the healthy attractor representing cell death. In a network representing drought-induced closure of plant stomata, we identify edgetic perturbations that modify the single attractor such that stomata, instead of being fixed in the closed state, oscillates between the open and closed states.