Shinji Hara

Yongqiang Wang, Yutaka Hori, Shinji Hara et al. · meta-ai

Many biological oscillators are arranged in networks composed of many inter-coupled cellular oscillators. However, results are still lacking on the collective oscillation period of inter-coupled gene regulatory oscillators, which, as has been reported, may be different from the oscillation period of an autonomous cellular oscillator. Based on the Goodwin oscillator, we analyze the collective oscillation pattern of coupled cellular oscillator networks. First we give a condition under which the oscillator network exhibits oscillatory and synchronized behavior, then we estimate the collective oscillation period based on a multivariable harmonic balance technique. Analytical results are derived in terms of biochemical parameters, thus giving insight into the basic mechanism of biological oscillation and providing guidance in synthetic biology design. Simulation results are given to confirm the theoretical predictions.

Yutaka Hori, Hiroki Miyazako, Soichiro Kumagai et al.

This paper proposes a control theoretic framework to model and analyze the self-organized pattern formation of molecular concentrations in biomolecular communication networks, emerging applications in synthetic biology. In biomolecular communication networks, bionanomachines, or biological cells, communicate with each other using a cell-to-cell communication mechanism mediated by a diffusible signaling molecule, thereby the dynamics of molecular concentrations are approximately modeled as a reaction-diffusion system with a single diffuser. We first introduce a feedback model representation of the reaction-diffusion system and provide a systematic local stability/instability analysis tool using the root locus of the feedback system. The instability analysis then allows us to analytically derive the conditions for the self-organized spatial pattern formation, or Turing pattern formation, of the bionanomachines. We propose a novel synthetic biocircuit motif called activator-repressor-diffuser system and show that it is one of the minimum biomolecular circuits that admit self-organized patterns over cell population.

Yutaka Hori, Shinji Hara

This paper is concerned with stochastic reaction-diffusion kinetics governed by the reaction-diffusion master equation. Specifically, the primary goal of this paper is to provide a mechanistic basis of Turing pattern formation that is induced by intrinsic noise. To this end, we first derive an approximate reaction-diffusion system by using linear noise approximation. We show that the approximated system has a certain structure that is associated with a coupled dynamic multi-agent system. This observation then helps us derive an efficient computation tool to examine the spatial power spectrum of the intrinsic noise. We numerically demonstrate that the result is quite effective to analyze noise-induced Turing pattern. Finally, we illustrate the theoretical mechanism behind the noise-induced pattern formation with a H2 norm interpretation of the multi-agent system.

Dinh Hoa Nguyen, Tatsuo Narikiyo, Michihiro Kawanishi et al.

This paper proposes novel approaches to design hierarchical decentralized robust controllers for homogeneous linear multi-agent systems (MASs) perturbed by disturbances/noise. Firstly, based on LQR method, we present a systematic procedure to design hierarchical decentralized optimal stabilizing controllers for MASs without disturbances/noise. Next, a method for deriving reduced-order hierarchical decentralized stabilizing controllers is presented by suitable selections of the weighting matrices in the LQR performance index. Secondly, the hierarchical decentralized robust controller designs in terms of $H_{\infty}$ and $H_{2}$ norms are introduced, which include two different scenarios namely general and LQR-based synthesis. For the general synthesis, the robust controller gains are computed as solutions of a distributed convex optimization problem with LMI constraints. On the other hand, for the LQR-based design, the robust controller gains obtained from the general synthesis are further verified as LQR stabilizing gains to be unified with the LQR-based design when there are no disturbances/noise. This results in a hierarchical decentralized inverse optimal control problem, for which we will propose a new method to resolve it. Finally, several numerical examples are presented to illustrate the effectiveness of the proposed approaches.

Yutaka Hori, Shinji Hara

Oscillatory chemical reactions often serve as a timing clock of cellular processes in living cells. The temporal dynamics of protein concentration levels is thus of great interest in biology. Here we propose a theoretical framework to analyze the frequency, phase and amplitude of oscillatory protein concentrations in gene regulatory networks with negative cyclic feedback. We first formulate the analysis framework of oscillation profiles based on multivariable harmonic balance. With this framework, the frequency, phase and amplitude are obtained analytically in terms of kinetic constants of the reactions despite the nonlinearity of the dynamics. These results are demonstrated with the Pentilator and Hes7 self-repression network, and it is shown that the developed analysis method indeed predicts the profiles of the oscillations. A distinctive feature of the presented result is that the waveform of oscillations is analytically obtained for a broad class of biochemical systems. Thus, it is easy to see how the waveform is determined from the system's parameters and structures. We present general biological insights that are applicable for any gene regulatory networks with negative cyclic feedback.

Masaaki Takada, Yutaka Hori, Shinji Hara

This paper is concerned with conditions for the existence of oscillations in gene regulatory networks with negative cyclic feedback, where time delays in transcription, translation and translocation process are explicitly considered. The primary goal of this paper is to propose systematic analysis tools that are useful for a broad class of cyclic gene regulatory networks, and to provide novel biological insights. To this end, we adopt a simplified model that is suitable for capturing the essence of a large class of gene regulatory networks. It is first shown that local instability of the unique equilibrium state results in oscillations based on a Poincare-Bendixson type theorem. Then, a graphical existence condition, which is equivalent to the local instability of a unique equilibrium, is derived. Based on the graphical condition, the existence condition is analytically presented in terms of biochemical parameters. This allows us to find the dimensionless parameters that primarily affect the existence of oscillations, and to provide biological insights. The analytic conditions and biological insights are illustrated with two existing biochemical networks, Repressilator and the Hes7 gene regulatory networks.

G. Q. Bao Tran, Yutaka Hori, Shinji Hara

We address the conditions and design of controllers and observers for homogeneous networks of linear MIMO agents. We develop networked controllers and observers that ensure the stability of both the system state and the estimation error, leveraging the concept of generalized frequency variables. A separation principle for networks is then established, showing that the observer and controller can be designed independently and combined to achieve a stable output feedback. Our results are illustrated via a highly unstable, oscillatory network of locally actuated pendulums on carts. Finally, necessary conditions for controllability and observability -- derived from agent properties and network structure -- are established and discussed.