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Previous studies have inferred robust stability of reaction networks by utilizing linear programs or iterative algorithms. Such algorithms become tedious or computationally infeasible for large networks. In addition, they operate like…
Modeling gene regulatory networks (GRNs) is an important topic in systems biology. Although there has been much work focusing on various specific systems, the generic behavior of GRNs with continuous variables is still elusive. In…
The functioning of a living cell is largely determined by the structure of its regulatory network, comprising non-linear interactions between regulatory genes. An important factor for the stability and evolvability of such regulatory…
A single gene, regulating its own expression via a positive feedback loop, constitutes a common motif in gene regulatory networks and signalling cascades. Recent experiments on the development of competence in the bacterial population…
Timely up- or down-regulation of gene expression is crucial for cellular differentiation and function. While gene upregulation via transcriptional activators has been extensively investigated, gene silencing remains understudied, especially…
We disclose the generality of the intrinsic mechanisms underlying multistability in reciprocally inhibitory 3-cell circuits composed of simplified, low-dimensional models of oscillatory neurons, as opposed to those of a detailed Hodgkin-…
Recent research shows that supervised learning can be an effective tool for designing near-optimal feedback controllers for high-dimensional nonlinear dynamic systems. But the behavior of neural network controllers is still not well…
Neural networks have become increasingly popular in controller design due to their versatility and efficiency. However, their integration into feedback systems can pose stability challenges, particularly in the presence of uncertainties.…
The formation of DNA loops by proteins and protein complexes that bind at distal DNA sites plays a central role in many cellular processes, such as transcription, recombination, and replication. Here we review the basic thermodynamic…
We consider the problem of optimizing the steady state of a dynamical system in closed loop. Conventionally, the design of feedback optimization control laws assumes that the system is stationary. However, in reality, the dynamics of the…
Dynamic stability is imperative for the operation of the electric power system. This article provides analytical results and effective stability criteria focusing on the interplay of network structures and the local dynamics of synchronous…
This paper considers the optimization landscape of linear dynamic output feedback control with $\mathcal{H}_\infty$ robustness constraints. We consider the feasible set of all the stabilizing full-order dynamical controllers that satisfy an…
A method is presented to analyze the stability of feedback systems with neural network controllers. Two stability theorems are given to prove asymptotic stability and to compute an ellipsoidal inner-approximation to the region of attraction…
Dynamical properties of the transcriptional regulatory network of {\it Escherichia coli} and {\it Saccharomyces cerevisiae} are studied within the framework of random Boolean functions. The dynamical response of these networks to a single…
This paper proposes a feedback linearizing law for single-track dynamic models, allowing the design of a trajectory tracking controller exploiting linear control theory. The main characteristics of this algorithm are its simplicity, its…
A simple model of a circularly closed dsDNA in a poor solvent is considered as an example of a semi-flexible polymer with self-attraction. To find the ground states, the conformational energy is computed as a sum of the bending and…
The expression of one gene might be regulated by its corresponding protein, which is called autoregulation. Although gene regulation is a central topic in biology, autoregulation is much less studied. In general, it is extremely difficult…
In 2000, Elowitz and Leibler introduced the repressilator--a synthetic gene circuit with three genes that cyclically repress transcription of the next gene--as well as a corresponding mathematical model. Experimental data and model…
Biological structure and function depend on complex regulatory interactions between many genes. A wealth of gene expression data is available from high-throughput genome-wide measurement technologies, but effective gene regulatory network…
This paper introduces a novel method for the stability analysis of positive feedback systems with a class of fully connected feedforward neural networks (FFNN) controllers. By establishing sector bounds for fully connected FFNNs without…