Topology, vorticity, and limit cycle in a stabilized Kuramoto-Sivashinsky equation.

A noisy stabilized Kuramoto-Sivashinsky equation is analyzed by stochastic decomposition. For values of the control parameter for which periodic stationary patterns exist, the dynamics can be decomposed into diffusive and transverse parts which act on a stochastic potential. The relative positions of stationary states in the stochastic global potential landscape can be obtained from the topology spanned by the low-lying eigenmodes which interconnect them. Numerical simulations confirm the predicted landscape. The transverse component also predicts a universal class of vortex-like circulations around fixed points. These drive nonlinear drifting and limit cycle motion of the underlying periodic structure in certain regions of parameter space. Our findings might be relevant in studies of other nonlinear systems such as deep learning neural networks.

Global potential, topology, and pattern selection in a noisy stabilized Kuramoto-Sivashinsky equation.

We formulate a general method to extend the decomposition of stochastic dynamics developed by Ao et al. [J. Phys. Math. Gen. 37, L25-L30 (2004)] to nonlinear partial differential equations which are nonvariational in nature and construct the global potential or Lyapunov functional for a noisy stabilized Kuramoto-Sivashinsky equation. For values of the control parameter where singly periodic stationary solutions exist, we find a topological network of a web of saddle points of stationary states interconnected by unstable eigenmodes flowing between them. With this topology, a global landscape of the steady states is found. We show how to predict the noise-selected pattern which agrees with those from stochastic simulations. Our formalism and the topology might offer an approach to explore similar systems, such as the Navier Stokes equation.

Resonant Confinement of an Excitonic Polariton and Ultraefficient Light Harvest in Artificial Photosynthesis.

We uncover a novel phenomenon from a recent artificial light-harvesting experiment [P.-Z. Chen et al., Angew. Chem., Int. Ed. Engl. 55, 2759 (2016)ACIEAY0570-083310.1002/anie.201510503] on organic nanocrystals of self-assembled difluoroboron chromophores. A resonant confinement of a polariton under strong photon-exciton coupling is predicted to exist within the microcavity of the crystal's own natural boundaries. Moreover, the radiative energy of a localized exciton falls into the spectrum of confinement. Hence, in the experiment, the spontaneous emission of an excited pigment would undergo a two-step process. It should first decay to an excitonic polariton trapped by the cavity resonance. The intermediate polariton could then funnel the energy directly to a doped acceptor, leading to the over 90% transfer efficiency observed at less than 1/1000 acceptor/donor ratio. The proposed mechanism is supported by parameter-free analyses entirely based on experiment data. Our finding may imply possible polariton-mediated pathways for energy transfers in biological photosynthesis.

Potential therapeutic targets of gastric cancer explored under endogenous network modeling of clinical data.

Improvement in the survival rate of gastric cancer, a prevalent global malignancy and the leading cause of cancer-related mortality calls for more avenues in molecular therapy. This work aims to comprehend drug resistance and explore multiple-drug combinations for enhanced therapeutic treatment. An endogenous network modeling clinic data with core gastric cancer molecules, functional modules, and pathways is constructed, which is then transformed into dynamics equations for in-silicon studies. Principal component analysis, hierarchical clustering, and K-means clustering are utilized to map the attractor domains of the stochastic model to the normal and pathological phenotypes identified from the clinical data. The analyses demonstrate gastric cancer as a cluster of stable states emerging within the stochastic dynamics and elucidate the cause of resistance to anti-VEGF monotherapy in cancer treatment as the limitation of the single pathway in preventing cancer progression. The feasibility of multiple objectives of therapy targeting specified molecules and/or pathways is explored. This study verifies the rationality of the platform of endogenous network modeling, which contributes to the development of cross-functional multi-target combinations in clinical trials.

Dynamical modelling of secondary metabolism and metabolic switches in Streptomyces xiamenensis 318.

The production of secondary metabolites, while important for bioengineering purposes, presents a paradox in itself. Though widely existing in plants and bacteria, they have no definite physiological roles. Yet in both native habitats and laboratories, their production appears robust and follows apparent metabolic switches. We show in this work that the enzyme-catalysed process may improve the metabolic stability of the cells. The latter can be responsible for the overall metabolic behaviours such as dynamic metabolic landscape, metabolic switches and robustness, which can in turn affect the genetic formation of the organism in question. Mangrove-derived Streptomyces xiamenensis 318, with a relatively compact genome for secondary metabolism, is used as a model organism in our investigation. Integrated studies via kinetic metabolic modelling, transcriptase measurements and metabolic profiling were performed on this strain. Our results demonstrate that the secondary metabolites increase the metabolic fitness of the organism via stabilizing the underlying metabolic network. And the fluxes directing to NADH, NADPH, acetyl-CoA and glutamate provide the key switches for the overall and secondary metabolism. The information may be helpful for improving the xiamenmycin production on the strain.

Kinetic model of metabolic network for xiamenmycin biosynthetic optimisation.

Xiamenmycins, a series of prenylated benzopyran compounds with anti-fibrotic bioactivities, were isolated from a mangrove-derived Streptomyces xiamenensis. To fulfil the requirements of pharmaceutical investigations, a high production of xiamenmycin is needed. In this study, the authors present a kinetic metabolic model to evaluate fluxes in an engineered Streptomyces lividans with xiamenmycin-oriented genetic modification based on generic enzymatic rate equations and stability constraints. Lyapunov function was used for a viability optimisation. From their kinetic model, the flux distributions for the engineered S. lividans fed on glucose and glycerol as carbon sources were calculated. They found that if the bacterium can utilise glucose simultaneously with glycerol, xiamenmycin production can be enhanced by 40% theoretically, while maintaining the same growth rate. Glycerol may increase the flux for phosphoenolpyruvate synthesis without interfering citric acid cycle. They therefore believe this study demonstrates a possible new direction for bioengineering of S. lividans.

Towards stable kinetics of large metabolic networks: Nonequilibrium potential function approach.

While the biochemistry of metabolism in many organisms is well studied, details of the metabolic dynamics are not fully explored yet. Acquiring adequate in vivo kinetic parameters experimentally has always been an obstacle. Unless the parameters of a vast number of enzyme-catalyzed reactions happened to fall into very special ranges, a kinetic model for a large metabolic network would fail to reach a steady state. In this work we show that a stable metabolic network can be systematically established via a biologically motivated regulatory process. The regulation is constructed in terms of a potential landscape description of stochastic and nongradient systems. The constructed process draws enzymatic parameters towards stable metabolism by reducing the change in the Lyapunov function tied to the stochastic fluctuations. Biologically it can be viewed as interplay between the flux balance and the spread of workloads on the network. Our approach allows further constraints such as thermodynamics and optimal efficiency. We choose the central metabolism of Methylobacterium extorquens AM1 as a case study to demonstrate the effectiveness of the approach. Growth efficiency on carbon conversion rate versus cell viability and futile cycles is investigated in depth.