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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. 

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.