Boolean networks have been widely used in systems biology to study the dynamical characteristics of biological networks such as steady-states or cycles, yet there has been little attention to the dynamic properties of network structures. Here, we systematically reveal the core network structures using a recursive self-composite of the logic update rules. We find that all Boolean update rules exhibit repeated cyclic logic structures, where each converged logic leads to the same states, defined as kernel states. Consequently, the period of state cycles is upper bounded by the number of logics in the converged logic cycle. In order to uncover the underlying dynamical characteristics by exploiting the repeating structures, we propose leaping and filling algorithms. The algorithms provide a way to avoid large string explosions during the self-composition procedures. Finally, we present three examples-a simple network with a long feedback structure, a T-cell receptor network and a cancer network-to demonstrate the usefulness of the proposed algorithm.

This paper presents the development of a tendon-driven continuum robot segment with a modular design, simple construction and significant lifting capabilities. The segment features a continuous flexible core combined with rigid interlocking vertebrae evenly distributed along its length. This design allows bending in two degrees of freedom while minimising torsional movement. The segment is actuated by two antagonistic tendon pairs, each of which is driven by a single geared DC motor. Modularity is achieved by embedding these motors in one end of the segment, avoiding the need for a bulky actuation unit and allowing variable numbers of segments to be connected. The design features a large hollow central bore which could be used as a vacuum channel for suction-assisted gripping or to allow ingress and egress of fluids. The design process goes through four iterations, the final two of which are subjected to quantitative experiments to evaluate workspace, lifting capabilities and torsional rigidity. All iterations are fabricated using multi-material 3D printing, which allows the entire structure to be printed as a pre-assembled unit with the rigid vertebrae fused to the flexible core. Assembly is then a simple case of inserting the motors and connecting the tendons. This unconventional manufacturing approach is found to be efficient, effective and relatively cheap.

Synthetic Biologists are increasingly interested in the idea of using synthetic feedback control circuits for the mitigation of perturbations to gene regulatory networks that may arise due to disease and/or environmental disturbances. Models employing Michaelis-Menten kinetics with Hill-type nonlinearities are typically used to represent the dynamics of gene regulatory networks. Here, we identify some fundamental problems with such models from the point of view of control system design, and argue that an alternative formalism, based on so-called S-System models, is more suitable. Using tools from system identification, we show how to build S-System models that capture the key dynamics of an example gene regulatory network, and design a genetic feedback controller with the objective of rejecting an external perturbation. Using a sine sweeping method, we show how the S-System model can be approximated by a linear transfer function and, based on this transfer function, we design our controller. Simulation results using the full nonlinear S-System model of the network show that the synthetic control circuit is able to mitigate the effect of external perturbations. Our study is the first to highlight the usefulness of the S-System modelling formalism for the design of synthetic control circuits for gene regulatory networks.

This paper proposes a novel way of constructing strut-type modular robotic structures to avoid some difficulties of designing and implementing ideal compliant nodes. Rigid nodes are employed to replace the ideal compliant nodes and to reduce the structural complexity while the feasibility of hardware implementation is dramatically improved. To release some kinematic constraints caused by the rigid nodes, we introduce robotic struts that consist of two prismatic actuators linked by a passive revolute joint. Physics-based robot models are constructed using a robot simulator. A scalable distributed control method is implemented using coupled central pattern generators. And, for comparison, the same control method is applied to conventional and the proposed strut-type modular robotic structures. Simulation results show that the proposed strut-type structures have several advantages over the conventional ones including less number of passive joints and shape-maintenance property.

MOTIVATION: Inherent non-linearities in biomolecular interactions make the identification of network interactions difficult. One of the principal problems is that all methods based on the use of linear time-invariant models will have fundamental limitations in their capability to infer certain non-linear network interactions. Another difficulty is the multiplicity of possible solutions, since, for a given dataset, there may be many different possible networks which generate the same time-series expression profiles. RESULTS: A novel algorithm for the inference of biomolecular interaction networks from temporal expression data is presented. Linear time-varying models, which can represent a much wider class of time-series data than linear time-invariant models, are employed in the algorithm. From time-series expression profiles, the model parameters are identified by solving a non-linear optimization problem. In order to systematically reduce the set of possible solutions for the optimization problem, a filtering process is performed using a phase-portrait analysis with random numerical perturbations. The proposed approach has the advantages of not requiring the system to be in a stable steady state, of using time-series profiles which have been generated by a single experiment, and of allowing non-linear network interactions to be identified. The ability of the proposed algorithm to correctly infer network interactions is illustrated by its application to three examples: a non-linear model for cAMP oscillations in Dictyostelium discoideum, the cell-cycle data for Saccharomyces cerevisiae and a large-scale non-linear model of a group of synchronized Dictyostelium cells. AVAILABILITY: The software used in this article is available from http://sbie.kaist.ac.kr/software

BACKGROUND: We consider the problem of identifying the dynamic interactions in biochemical networks from noisy experimental data. Typically, approaches for solving this problem make use of an estimation algorithm such as the well-known linear Least-Squares (LS) estimation technique. We demonstrate that when time-series measurements are corrupted by white noise and/or drift noise, more accurate and reliable identification of network interactions can be achieved by employing an estimation algorithm known as Constrained Total Least Squares (CTLS). The Total Least Squares (TLS) technique is a generalised least squares method to solve an overdetermined set of equations whose coefficients are noisy. The CTLS is a natural extension of TLS to the case where the noise components of the coefficients are correlated, as is usually the case with time-series measurements of concentrations and expression profiles in gene networks. RESULTS: The superior performance of the CTLS method in identifying network interactions is demonstrated on three examples: a genetic network containing four genes, a network describing p53 activity and mdm2 messenger RNA interactions, and a recently proposed kinetic model for interleukin (IL)-6 and (IL)-12b messenger RNA expression as a function of ATF3 and NF-kappaB promoter binding. For the first example, the CTLS significantly reduces the errors in the estimation of the Jacobian for the gene network. For the second, the CTLS reduces the errors from the measurements that are corrupted by white noise and the effect of neglected kinetics. For the third, it allows the correct identification, from noisy data, of the negative regulation of (IL)-6 and (IL)-12b by ATF3. CONCLUSION: The significant improvements in performance demonstrated by the CTLS method under the wide range of conditions tested here, including different levels and types of measurement noise and different numbers of data points, suggests that its application will enable more accurate and reliable identification and modelling of biochemical networks.

Stable and robust oscillations in the concentration of adenosine 3', 5'-cyclic monophosphate (cAMP) are observed during the aggregation phase of starvation-induced development in Dictyostelium discoideum. In this paper we use mathematical modelling together with ideas from robust control theory to identify two factors which appear to make crucial contributions to ensuring the robustness of these oscillations. Firstly, we show that stochastic fluctuations in the molecular interactions play an important role in preserving stable oscillations in the face of variations in the kinetics of the intracellular network. Secondly, we show that synchronisation of the aggregating cells through the diffusion of extracellular cAMP is a key factor in ensuring robustness of the oscillatory waves of cAMP observed in Dictyostelium cell cultures to cell-to-cell variations. A striking and quite general implication of the results is that the robustness analysis of models of oscillating biomolecular networks (circadian clocks, Ca(2+) oscillations, etc.) can only be done reliably by using stochastic simulations, even in the case where molecular concentrations are very high.

The application of two evolutionary optimization methods, namely, differential evolution and genetic algorithms, to the clearance of nonlinear flight control laws for highly augmented aircraft is described. The algorithms are applied to the problem of evaluating a nonlinear handling quality clearance criterion for a simulation model of a high-performance aircraft with a delta canard configuration and a full-authority flight control law. Hybrid versions of both algorithms, incorporating local gradient-based optimization, are also developed and evaluated. Statistical comparisons of computational cost and global convergence properties reveal the benefits of hybridization for both algorithms. The differential evolution approach in particular, when appropriately augmented with local optimization methods, is shown to have significant potential for improving both the reliability and efficiency of the current industrial flight clearance process