Leveraging network structure in nonlinear control

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.

Modularity of biological systems: a link between structure and function

“…Therefore, the decomposition theorems can reduce the time needed to perform various computations by orders of magnitude for networks with several larger modules. Besides an efficient strategy to compute all attractors of a Boolean network, the structural decomposition theorem can also be applied to efficiently identify controls of Boolean networks, a topic that has received recent attention [27][28][29]. Drug developers wonder, for example, which nodes in a gene regulatory network need to be controlled by an external drug to ensure the network transitions to a desired phenotype, typically corresponding to a specific network attractor.…”

Modularity of biological systems: a link between structure and function

“…Therefore, the decomposition theorems can reduce the time needed to perform various computations by orders of magnitude for networks with several larger modules. Besides an efficient strategy to compute all attractors of a Boolean network, the structural decomposition theorem can also be applied to efficiently identify controls of Boolean networks, a topic that has received recent attention (23)(24)(25). Drug developers wonder, for example, which nodes in a gene regulatory network need to be controlled by an external drug to ensure the network transitions to a desired phenotype, typically corresponding to a specific network attractor.…”

Phenotype control techniques for Boolean gene regulatory networks

“…One way mathematicians are able to assist biological researchers is through modeling cell signal transduction pathways. However, these pathways can be highly complex due to signaling motifs like feedback loops, crosstalk, and high-dimensional nonlinearity [3]. To address these complexities, mathematical modelers have developed many strategies for creating and analyzing networks, traditionally classified based on the time and population of gene products.…”

“…To address these complexities, mathematical modelers have developed many strategies for creating and analyzing networks, traditionally classified based on the time and population of gene products. For instance, there are techniques for continuous population with continuous time such as ordinary differential equations [3,4], discrete population with continuous time such as the Gillespie formulation [5,6], and discrete population with discrete time such as BNs, logical models, and also their related stochastic counterparts [7][8][9][10][11]. There are also numerous well developed statistical, agent based, and PDE models which are outside the scope of this review [2].…”