A weighted pair graph representation for reconstructibility of Boolean control networks

A new concept of weighted pair graphs (WPGs) is proposed to represent a new reconstructibility definition for Boolean control networks (BCNs), which is a generalization of the reconstructibility definition given in [Fornasini & Valcher, TAC2013, Def. 4]. Based on the WPG representation, an effective algorithm for determining the new reconstructibility notion for BCNs is designed with the help of the theories of finite automata and formal languages. We prove that a BCN is not reconstructible iff its WPG has a complete subgraph. Besides, we prove that a BCN is reconstructible in the sense of [Fornasini & Valcher, TAC2013, Def. 4] iff its WPG has no cycles, which is simpler to be checked than the condition in [Fornasini & Valcher, TAC2013, Thm. 4].Comment: 20 pages, 10 figures, accepted by SIAM Journal on Control and Optimizatio

Structural Properties of Invariant Dual Subspaces of Boolean Networks

In this paper, we obtain the following results on dual subspaces of Boolean networks (BNs). For a BN, there is a one-to-one correspondence between partitions of its state-transition graph (STG) and its dual subspaces (i.e., the subspaces generated by a number of Boolean functions of the BN's variables). Moreover, a dual subspace is invariant if and only if the corresponding partition is equitable, i.e., for every two (not necessarily different) cells of the partition, every two states in the former have equally many out-neighbors in the latter. With the help of equitable partitions of an STG, we study the structural properties of the smallest invariant dual subspaces containing a number of Boolean functions. And then, we give algorithms for computing the equitable partition corresponding to the smallest invariant dual subspace containing a given dual subspace. Moreover, we reveal that the unobservable subspace of a BN is the smallest invariant dual subspace containing the output function. We analyze properties of the unobservable subspace by using the obtained structural properties. The graphical representation provides an easier and more intuitive way to characterizing the (smallest) invariant dual subspaces of a BN

Model Evaluation of the Stochastic Boolean Control Networks

National Key Research and Development Program of China under Grant 2018AAA0100202; National Natural Science Foundation of China under Grants 62003083, 61873059, 61873148, 61922024 and 61933007; Shanghai Science and Technology Program of China under Grant 20JC1414500; Shanghai Sailing Program of China under Grant 19YF1402400; Program of Shanghai Academic/Technology Research Leader of China under Grant 20XD1420100; Royal Society of the UK; Alexander von Humboldt Foundation of Germany

Towards the control of cell states in gene regulatory networks by evolving Boolean networks

Biological cell behaviours emerge from complex patterns of interactions between genes and their products, known as gene regulatory networks (GRNs). More specifically, GRNs are complex dynamical structures that orchestrate the activities of biological cells by governing the expression of mRNA and proteins. Many computational models of these networks have been shown to be able to carry out complex computation in an efficient and robust manner, particularly in the domains of control and signal processing. GRNs play a central role within living organisms and efficient strategies for controlling their dynamics need to be developed. For instance, the ability to push a cell towards or away from certain behaviours, is an important aim in fields such as medicine and synthetic biology. This could, for example, help to find novel approaches in the design of therapeutic drugs. However, current approaches to controlling these networks exhibit poor scalability and limited generality. This thesis proposes a new approach and an alternative method for performing state space targeting in GRNs, by coupling an artificial GRN to an existing GRN. This idea is tested in simulation by coupling together Boolean networks that represent controlled and controller systems. Evolutionary algorithms are used to evolve the controller Boolean networks. Controller Boolean networks are applied to a range of controlled Boolean networks including Boolean models of actual biological circuits, each with different dynamics. The results show that controller Boolean networks can be optimised to control trajectories in the target networks. Also, the approach scales well as the target network size increases. The use of Boolean modelling is potentially advantageous from an implementation perspective, since synthetic biology techniques can be used to refine an optimised controller Boolean network into an in vivo form, which could then control a genetic network directly from within a cell