Multiresonant plasmonics with spatial mode overlap: overview and outlook

Plasmonic nanostructures can concentrate light and enhance light-matter interactions in the subwavelength domain, which is useful for photodetection, light emission, optical biosensing, and spectroscopy. However, conventional plasmonic devices and systems are typically optimized for the operation in a single wavelength band and thus are not suitable for multiband nanophotonics applications that either prefer nanoplasmonic enhancement of multiphoton processes in a quantum system at multiple resonant wavelengths or require wavelength-multiplexed operations at nanoscale. To overcome the limitations of “single-resonant plasmonics,” we need to develop the strategies to achieve “multiresonant plasmonics” for nanoplasmonic enhancement of light-matter interactions at the same locations in multiple wavelength bands. In this review, we summarize the recent advances in the study of the multiresonant plasmonic systems with spatial mode overlap. In particular, we explain and emphasize the method of “plasmonic mode hybridization” as a general strategy to design and build multiresonant plasmonic systems with spatial mode overlap. By closely assembling multiple plasmonic building blocks into a composite plasmonic system, multiple nonorthogonal elementary plasmonic modes with spectral and spatial mode overlap can strongly couple with each other to form multiple spatially overlapping new hybridized modes at different resonant energies. Multiresonant plasmonic systems can be generally categorized into three types according to the localization characteristics of elementary modes before mode hybridization, and can be based on the optical coupling between: (1) two or more localized modes, (2) localized and delocalized modes, and (3) two or more delocalized modes. Finally, this review provides a discussion about how multiresonant plasmonics with spatial mode overlap can play a unique and significant role in some current and potential applications, such as (1) multiphoton nonlinear optical and upconversion luminescence nanodevices by enabling a simultaneous enhancement of optical excitation and radiation processes at multiple different wavelengths and (2) multiband multimodal optical nanodevices by achieving wavelength multiplexed optical multimodalities at a nanoscale footprint.

Computing Signal Transduction in Signaling Networks modeled as Boolean Networks, Petri Nets, and Hypergraphs

Mathematical frameworks circumventing the need of mechanistic detail to build models of signal transduction networks include graphs, hypergraphs, Boolean Networks, and Petri Nets. Predicting how a signal transduces in a signaling network is essential to understand cellular functions and disease. Different formalisms exist to describe how a signal transduces in a given intracellular signaling network represented in the aforementioned modeling frameworks: elementary signaling modes, T-invariants, extreme pathway analysis, elementary flux modes, and simple paths. How do these formalisms compare?We present an overview of how signal transduction networks have been modelled using graphs, hypergraphs, Boolean Networks, and Petri Nets in the literature. We provide a review of the different formalisms for capturing signal transduction in a given model of an intracellular signaling network. We also discuss the existing translations between the different modeling frameworks, and the relationships between their corresponding signal transduction representations that have been described in the literature. Furthermore, as a new formalism of signal transduction, we show how minimal functional routes proposed for signaling networks modeled as Boolean Networks can be captured by computing topological factories, a methodology found in the metabolic networks literature. We further show that in the case of signaling networks represented with an acyclic B-hypergraph structure, the definitions are equivalent. In signaling networks represented as directed graphs, it has been shown that computations of elementary modes via its incidence matrix correspond to computations of simple paths and feedback loops. We show that computing elementary modes based on the incidence matrix of a B-hypergraph fails to capture minimal functional routes.

A Portable Structural Analysis Library for Reaction Networks

The topology of a reaction network can have a significant influence on the network’s dynamical properties. Such influences can include constraints on network flows and concentration changes or more insidiously result in the emergence of feedback loops. These effects are due entirely to mass constraints imposed by the network configuration and are important considerations before any dynamical analysis is made. Most established simulation software tools usually carry out some kind of structural analysis of a network before any attempt is made at dynamic simulation. In this paper we describe a portable software library, libStructural, that can carry out a variety of popular structural analyses that includes conservation analysis, flux dependency analysis and enumerating elementary modes. The library employs robust algorithms that allow it to be used on large networks with more than a two thousand nodes. The library accepts either a raw or fully labeled stoichiometry matrix or models written in SBML format. The software is written in standard C/C++ and comes with documentation and a test suite. The software is available for Windows, Mac OS X, and can be compiled easily on any Linux operating system. A language binding for Python is also available through the pip package manager making it trivial to install on any standard Python distribution. As a second example, we also create a new libStructural plugin for PathwayDesigner that allows solutions to be viewed graphically. The source code is licensed under the open source BSD license and is available on GitHub (https://github.com/sys-bio/Libstructural)

Effective Dynamic Models of Metabolic Networks

Mathematical models of biochemical networks are useful tools to understand and ultimately predict how cells utilize nutrients to produce valuable products. Hybrid cybernetic models in combination with elementary modes (HCM) is a tool to model cellular metabolism. However, HCM is limited to reduced metabolic networks because of the computational burden of calculating elementary modes. In this study, we developed the hybrid cybernetic modeling with flux balance analysis or HCM-FBA technique which uses flux balance solutions instead of elementary modes to dynamically model metabolism. We show HCM-FBA has comparable performance to HCM for a proof of concept metabolic network and for a reduced anaerobicE. colinetwork. Next, HCM-FBA was applied to a larger metabolic network of aerobicE. colimetabolism which was infeasible for HCM (29 FBA modes versus more than 153,000 elementary modes). Global sensitivity analysis further reduced the number of FBA modes required to describe the aerobicE. colidata, while maintaining model fit. Thus, HCM-FBA is a promising alternative to HCM for large networks where the generation of elementary modes is infeasible.

PT symmetry and a dynamical realization of the SU(1, 1) algebra

We show that the elementary modes of the planar harmonic oscillator can be quantized in the framework of quantum mechanics based on pseudo-hermitian Hamiltonians. These quantized modes are demonstrated to act as dynamical structures behind a new Jordan–Schwinger realization of the SU(1, 1) algebra. This analysis complements the conventional Jordan–Schwinger construction of the SU(2) algebra based on hermitian Hamiltonians of a doublet of oscillators.

Elementary modes of coupled oscillators as whispering-gallery microresonators

We obtain the elementary modes of a system of parity-time reversal (PT)-symmetric coupled oscillators with balanced loss and gain. These modes are used to give a physical picture of the phase transition recently reported [C. M. Bender, M. Gianfreda, B. Peng, S. K. Özdemir and L. Yang, Phys. Rev. A 88, 062111 (2013); L. Yang, S. K. Özdemir and B. Peng, 12th Int. Workshop and Conf. Pseudo-Hermitian Hamiltonians in Quantum Physics, Istanbul, Turkey, July 2013; B. Peng, S. K. Özdemir, F. Lei, F. Monifi, M. Gianfreda, G. L. Long, S. Fan, F. Nori, C. M. Bender and L. Yang, Nat. Phys. 10, 394 (2014)] in experiments with whispering-gallery microresonators.