All-Optical Switching and Routing with a Nonlinear Metamaterial

We report the dynamic control characteristics of electromagnetic wave propagation in a nonlinear metamaterial by an applied electric field, which is constructed by an array of metallic nanowires embedded into a nonlinear dielectric. Numerical results show that the composite structure can appear three kinds of interesting interconversion characteristics among positive refraction, negative refraction, and cut-off states by adjusting the intensity of the applied electric field. Consequently, we can switch all-optically light states between the total reflection state (OFF state) and the total transmission state (ON state), as well as control light propagation route dynamically. Moreover, we also elaborate on the dependency of the refraction angles of energy flow and wave vector, and Brewster angle on the applied electric field and the orientation angle φ. These properties open up an avenue for potential applications of nonlinear metamaterials in nanophotonic devices such as all-optical switches, routers, and wave cut-off devices.     

Femtosecond IR Pump-Probe Spectroscopy of Nonlinear Energy Localization in Protein Models and Model Proteins

This paper reviews our experimental and theoretical efforts toward understanding vibrational self-trapping of the amide I and N–H mode of crystalline acetanilide (ACN), other similar hydrogen-bonded crystals, as well as of model peptides. In contrast to previous works, we used nonlinear IR spectroscopy as the experimental tool, which is specifically sensitive to the anharmonic contributions of the intramolecular interactions (as the nonlinear IR response of set of harmonic oscillators vanishes exactly). Our work reconfirms the previous assignment of the two bands of the amide I mode of ACN as being a self-trapped and a free exciton state, but in addition also establishes the lifetimes of these states and identifies the relevant phonons. Furthermore, we provide evidence for vibrationally self-trapped states also in model α-helices. However, given the short lifetime, any biological relevance in the sense of Davydov’s initial proposal can probably be ruled out.     

Competition between supercoils and toroids in single molecule DNA condensation

The condensation of free DNA into toroidal structures in the presence of multivalent ions and polypeptides is well known. Recent single molecule experiments have shown that condensation into toroids occurs even when the DNA molecule is subjected to tensile forces. Here we show that the combined tension and torsion of DNA in the presence of condensing agents dramatically modifies this picture by introducing supercoiled DNA as a competing structure in addition to toroids. We combine a fluctuating elastic rod model of DNA with phenomenological models for DNA interaction in the presence of condensing agents to compute the minimum energy configuration for given tension and end-rotations. We show that for each tension there is a critical number of end-rotations above which the supercoiled solution is preferred and below which toroids are the preferred state. Our results closely match recent extension rotation experiments on DNA in the presence of spermine and other condensing agents. Motivated by this, we construct a phase diagram for the preferred DNA states as a function of tension and applied end-rotations and identify a region where new experiments or simulations are needed to determine the preferred state.     

A Mathematical Model of the Human Metabolic System and Metabolic Flexibility

In healthy subjects some tissues in the human body display metabolic flexibility, by this we mean the ability for the tissue to switch its fuel source between predominantly carbohydrates in the postprandial state and predominantly fats in the fasted state. Many of the pathways involved with human metabolism are controlled by insulin and insulin-resistant states such as obesity and type-2 diabetes are characterised by a loss or impairment of metabolic flexibility. In this paper we derive a system of 12 first-order coupled differential equations that describe the transport between and storage in different tissues of the human body. We find steady state solutions to these equations and use these results to nondimensionalise the model. We then solve the model numerically to simulate a healthy balanced meal and a high fat meal and we discuss and compare these results. Our numerical results show good agreement with experimental data where we have data available to us and the results show behaviour that agrees with intuition where we currently have no data with which to compare.     

Energy transport mechanism in the form of proton soliton in a one-dimensional hydrogen-bonded polypeptide chain

The dynamics of protons in a one-dimensional hydrogen-bonded (HB) polypeptide chain (PC) is investigated theoretically. A new Hamiltonian is formulated with the inclusion of higher-order molecular interactions between peptide groups (PGs). The wave function of the excitation state of a single particle is replaced by a new wave function of a two-quanta quasi-coherent state. The dynamics is governed by a higher-order nonlinear Schrödinger equation and the energy transport is performed by the proton soliton. A nonlinear multiple-scale perturbation analysis has been performed and the evolution of soliton parameters such as velocity and amplitude is explored numerically. The proton soliton is thermally stable and very robust against these perturbations. The energy transport by the proton soliton is more appropriate to understand the mechanism of energy transfer in biological processes such as muscle contraction, DNA replication, and neuro-electric pulse transfer on biomembranes.     

Variational Bayes Analysis of a Photon-Based Hidden Markov Model for Single-Molecule FRET Trajectories

Single-molecule fluorescence resonance energy transfer (smFRET) measurement is a powerful technique for investigating dynamics of biomolecules, for which various efforts have been made to overcome significant stochastic noise. Time stamp (TS) measurement has been employed experimentally to enrich information within the signals, while data analyses such as the hidden Markov model (HMM) have been successfully applied to recover the trajectories of molecular state transitions from time-binned photon counting signals or images. In this article, we introduce the HMM for TS-FRET signals, employing the variational Bayes (VB) inference to solve the model, and demonstrate the application of VB-HMM-TS-FRET to simulated TS-FRET data. The same analysis using VB-HMM is conducted for other models and the previously reported change point detection scheme. The performance is compared to other analysis methods or data types and we show that our VB-HMM-TS-FRET analysis can achieve the best performance and results in the highest time resolution. Finally, an smFRET experiment was conducted to observe spontaneous branch migration of Holliday-junction DNA. VB-HMM-TS-FRET was successfully applied to reconstruct the state transition trajectory with the number of states consistent with the nucleotide sequence. The results suggest that a single migration process frequently involves rearrangement of multiple basepairs.     

Free Energy Calculations Reveal Rotating-Ratchet Mechanism for DNA Supercoil Relaxation by Topoisomerase IB and its Inhibition

Topoisomerases maintain the proper topological state of DNA. Human topoisomerase I removes DNA supercoils by clamping a duplex DNA segment, nicking one strand at a phosphodiester bond, covalently attaching to the 3′ end of the nick, and allowing the DNA downstream of the cut to rotate around the intact strand. Using molecular dynamics simulations and umbrella sampling free energy calculations, we show that the rotation of downstream DNA in the grip of the enzyme that brings about release of positive or negative supercoils occurs by thermally assisted diffusion on ratchet energy profiles. The ratchetlike free-energy-versus-rotation profile that we compute provides a model for the function of topoisomerase in which the periodic maxima along the profile modulate the rate of supercoil relaxation, while the minima provide metastable conformational states for DNA religation. The results confirm previous experimental and computational work, and suggest that relaxation of the two types of supercoils involves distinct protein pathways. Additionally, simulations performed with the ternary complex of topoisomerase, DNA, and the chemotherapeutic drug topotecan show important differences in the mechanisms for supercoil relaxation when the drug is present, accounting for the relative values of relaxation rates measured in single-molecule experiments. Good agreement is found between rate constants from tweezer experiments and those calculated from simulations. Evidence is presented for the existence of semiopen states of the protein, which facilitate rotations after the initial one, as a result of biasing the protein into a conformation more favorable to strand rotation than the closed state required for nicking of the DNA.     

Local denaturation in DNA molecules

A two-dimensional anharmonic model, the so-called Toda-Lennard-Jones model, is considered in order to investigate the problems related to the lifetime of the open states precursors to full denaturation, in inhomogeneous ring-shaped DNA molecules. It is found that a transition from double-stranded to single-stranded DNA occurs locally around physiological temperature. Moreover, the presence of inhomogeneities enhances the hydrogen bond breaking.     

Spatial and spatio-temporal patterns in a cell-haptotaxis model

We investigate a cell-haptotaxis model for the generation of spatial and spatio-temporal patterns in one dimension. We analyse the steady state problem for specific boundary conditions and show the existence of spatially hetero-geneous steady states. A linear analysis shows that stability is lost through a Hopf bifurcation. We carry out a nonlinear multi-time scale perturbation procedure to study the evolution of the resulting spatio-temporal patterns. We also analyse the model in a parameter domain wherein it exhibits a singular dispersion relation.     

Quantum Mechanical Model for Conformons

The purpose of this paper is the investigation of the role of entropy in the conformon, based on a model Hamiltonian approach. There are three stages of our considerations. (1) Quadratic terms are introduced into the potential energy terms of harmonic oscillators in the presence of an electron, leading to an increase in entropy and thus to an increased number of thermally activated electrons. (2) The number of activated electrons is not just increased, but they are also mobile if electronphonon bound states are formed. (3) A compensation rule cannot be obtained in this harmonic approximation, and therefore anharmonic coupling is introduced. This leads to a mobility edge and the analogy to amorphous semiconductors is pointed out.     

Light Energy Distribution in the Brown Alga Macrocystis pyrifera (Giant Kelp)

The brown alga Macrocystis pyrifera (giant kelp) was studied by a combination of fluorescence spectroscopy at 77 kelvin, room temperature modulated fluorimetry, and photoacoustic techniques to determine how light energy is partitioned between photosystems I and II in states 1 and 2. Preillumination with farred light induced the high fluorescence state (state 1) as determined by fluorescence emission spectra measured at 77K and preillumination with green light produced a low fluorescence state (state 2). Upon transition from state 1 to state 2, there was an almost parallel decrease of all of the fluorescence bands at 693, 705, and 750 nanometers and not the expected decrease of fluorescence of photosystem II and increase of fluorescence in photosystem I. The momentary level of room temperature fluorescence (fluorescence in the steady state, F_s), as well as the fluorescence levels corresponding to all closed (F_m) or all open (F_o) reaction-center states were measured following the kinetics of the transition between states 1 and 2. Calculation of the distribution of light 2 (540 nanometers) between the two photosystems was done assuming both the `separate package' and `spill-over' models. Unlike green plants, red algae, and cyanobacteria, the changes here of the light distribution were rather small in Macrocystis so that there was approximately an even distribution of the photosystem II light at 540 nanometers to photosystem I and photosystem II in both states 1 and 2. Photoacoustic measurements confirmed the conclusions reached as a result of fluorescence measurements, i.e. an almost equal distribution of light-2 quanta to both photosystems in each state. This conclusion was reached by analyzing the enhancement phenomenon by light 2 of the energy storage measured in far red light. The effect of light 1 in decreasing the energy storage measured in light 2 is also consistent with this conclusion. The photoacoustic experiments showed that there was a significant energy storage in light 1 which could be explained by cyclic electron transport around photosystem I. From a quantitative analysis of the enhancement effect of background light 2 (maximum enhancement of 1.4-1.5) it was shown that around 70% of light 1 was distributed to this cyclic photosystem I transport.