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Concept: Normal mode


Integrin clustering plays a pivotal role in a host of cell functions. Hetero-dimeric integrin adhesion receptors regulate cell migration, survival, and differentiation by communicating signals bidirectionally across the plasma membrane. Thus far, crystallographic structures of integrin components are solved only separately, and for some integrin types. Also, the sequence of interactions that leads to signal transduction remains ambiguous. Particularly, it remains controversial whether the homo-dimerization of integrin transmembrane domains occurs following the integrin activation (i.e. when integrin ectodomain is stretched out) or if it regulates integrin clustering. This study employs molecular dynamics modeling approaches to address these questions in molecular details and sheds light on the crucial effect of the plasma membrane. Conducting a normal mode analysis of the intact αllbβ3 integrin, it is demonstrated that the ectodomain and transmembrane-cytoplasmic domains are connected via a membrane-proximal hinge region, thus merely transmembrane-cytoplasmic domains are modeled. By measuring the free energy change and force required to form integrin homo-oligomers, this study suggests that the β-subunit homo-oligomerization potentially regulates integrin clustering, as opposed to α-subunit, which appears to be a poor regulator for the clustering process. If α-subunits are to regulate the clustering they should overcome a high-energy barrier formed by a stable lipid pack around them. Finally, an outside-in activation-clustering scenario is speculated, explaining how further loading the already-active integrin affects its homo-oligomerization so that focal adhesions grow in size.

Concepts: Protein, Signal transduction, Cell membrane, Cell biology, Cell signaling, G protein-coupled receptor, Gibbs free energy, Normal mode


The coupling of distinct systems underlies nearly all physical phenomena. A basic instance is that of interacting harmonic oscillators, giving rise to, for example, the phonon eigenmodes in a lattice. Of particular importance are the interactions in hybrid quantum systems, which can combine the benefits of each part in quantum technologies. Here we investigate a hybrid optomechanical system having three degrees of freedom, consisting of a microwave cavity and two micromechanical beams with closely spaced frequencies around 32 MHz and no direct interaction. We record the first evidence of tripartite optomechanical mixing, implying that the eigenmodes are combinations of one photonic and two phononic modes. We identify an asymmetric dark mode having a long lifetime. Simultaneously, we operate the nearly macroscopic mechanical modes close to the motional quantum ground state, down to 1.8 thermal quanta, achieved by back-action cooling. These results constitute an important advance towards engineering of entangled motional states.

Concepts: Quantum mechanics, Physics, Laser, Interaction, Oscillation, Wave, Normal mode, Harmonic oscillator


Time-resolved Fourier transform infrared (FTIR) spectroscopy is a powerful tool to elucidate label-free the reaction mechanisms of proteins. After assignment of the absorption bands to individual groups of the protein, the order of events during the reaction mechanism can be monitored and rate constants can be obtained. Additionally, structural information is encoded into infrared spectra and can be decoded by combining the experimental data with biomolecular simulations. We have determined recently the infrared vibrations of GTP and guanosine diphosphate (GDP) bound to Gαi1, a ubiquitous GTPase. These vibrations are highly sensitive for the environment of the phosphate groups and thereby for the binding mode the GTPase adopts to enable fast hydrolysis of GTP. In this study we calculated these infrared vibrations from biomolecular simulations to transfer the spectral information into a computational model that provides structural information far beyond crystal structure resolution. Conformational ensembles were generated using 15 snapshots of several 100 ns molecular-mechanics/molecular-dynamics (MM-MD) simulations, followed by quantum-mechanics/molecular-mechanics (QM/MM) minimization and normal mode analysis. In comparison with other approaches, no time-consuming QM/MM-MD simulation was necessary. We carefully benchmarked the simulation systems by deletion of single hydrogen bonds between the GTPase and GTP through several Gαi1 point mutants. The missing hydrogen bonds lead to blue-shifts of the corresponding absorption bands. These band shifts for α-GTP (Gαi1-T48A), γ-GTP (Gαi1-R178S), and for both β-GTP/γ-GTP (Gαi1-K46A, Gαi1-D200E) were found in agreement in the experimental and the theoretical spectra. We applied our approach to open questions regarding Gαi1: we show that the GDP state of Gαi1 carries a Mg(2+), which is not found in x-ray structures. Further, the catalytic role of K46, a central residue of the P-loop, and the protonation state of the GTP are elucidated.

Concepts: DNA, Protein, Spectroscopy, Infrared spectroscopy, Fourier transform spectroscopy, Mode shape, Normal mode, Guanosine triphosphate


Tapping or clapping to an auditory beat, an easy task for most individuals, reveals precise temporal synchronization with auditory patterns such as music, even in the presence of temporal fluctuations. Most models of beat-tracking rely on the theoretical concept of pulse: a perceived regular beat generated by an internal oscillation that forms the foundation of entrainment abilities. Although tapping to the beat is a natural sensorimotor activity for most individuals, not everyone can track an auditory beat. Recently, the case of Mathieu was documented (Phillips-Silver et al. 2011 Neuropsychologia 49, 961-969. (doi:10.1016/j.neuropsychologia.2011.02.002)). Mathieu presented himself as having difficulty following a beat and exhibited synchronization failures. We examined beat-tracking in normal control participants, Mathieu, and a second beat-deaf individual, who tapped with an auditory metronome in which unpredictable perturbations were introduced to disrupt entrainment. Both beat-deaf cases exhibited failures in error correction in response to the perturbation task while exhibiting normal spontaneous motor tempi (in the absence of an auditory stimulus), supporting a deficit specific to perception-action coupling. A damped harmonic oscillator model was applied to the temporal adaptation responses; the model’s parameters of relaxation time and endogenous frequency accounted for differences between the beat-deaf cases as well as the control group individuals.

Concepts: Quantum mechanics, Oscillation, Resonance, Normal mode, Harmonic oscillator, Simple harmonic motion, Pendulum, Ordinary differential equations


Neuroprosthetic devices, such as cochlear and retinal implants, work by directly stimulating neurons with extracellular electrodes. This is commonly modeled using the cable equation with an applied extracellular voltage. In this paper a framework for modeling extracellular electrical stimulation is presented. To this end, a cylindrical neurite with confined extracellular space in the subthreshold regime is modeled in three-dimensional space. Through cylindrical harmonic expansion of Laplace’s equation, we derive the spatio-temporal equations governing different modes of stimulation, referred to as longitudinal and transverse modes, under types of boundary conditions. The longitudinal mode is described by the well-known cable equation, however, the transverse modes are described by a novel ordinary differential equation. For the longitudinal mode, we find that different electrotonic length constants apply under the two different boundary conditions. Equations connecting current density to voltage boundary conditions are derived that are used to calculate the trans-impedance of the neurite-plus-thin-extracellular-sheath. A detailed explanation on depolarization mechanisms and the dominant current pathway under different modes of stimulation is provided. The analytic results derived here enable the estimation of a neurite’s membrane potential under extracellular stimulation, hence bypassing the heavy computational cost of using numerical methods.

Concepts: Mathematics, Cell membrane, Maxwell's equations, Action potential, Differential equation, Partial differential equation, Normal mode, Ordinary differential equation


The electronic excitations of three noble-metall chains-copper, silver, and gold-have been investigated at the time-dependent density functional theory level. The reduced single-electron density matrix is propagated according to the Liouville-von Neumann equation in the real-time domain after an impulse excitation. The propagation in the real-time domain enables us to investigate the formation and size evolution of electronic excitations in these metallic chains with different number of atoms, up to a total of 26 atoms. The longitudinal oscillations at lower excitation energies are dominated by s → p transitions in these chains and have collective or central resonances, while the first peak involving d → p transitions in the longitudinal mode appears at a higher excitation energy and shows collective resonances. In the transverse oscillations, there are in most cases d → p transitions in each resonance, which can be attributed to either central or end resonances. Convergence of the oscillations, in particular those involving the collective and central resonances in the three noble-metal chains can only be observed for chains with 18 atoms or more. Different spectroscopic characteristics among these three metallic chains can be attributed to their different electronic structures, in particular the relativistic effects in the gold chains have a dramatic effect on their electronic structures and excitations.

Concepts: Quantum mechanics, Resonator, Kinetic energy, Uranium, Density functional theory, Normal mode, Standing wave, Optical cavity


A high-slope-efficiency single-frequency (SF) ytterbium-doped fiber laser, based on a Sagnac loop mirror filter (LMF), was demonstrated. It combined a simple linear cavity with a Sagnac LMF that acted as a narrow-bandwidth filter to select the longitudinal modes. And we introduced a polarization controller to restrain the spatial hole burning effect in the linear cavity. The system could operate at a stable SF oscillating at 1064 nm with the obtained maximum output power of 32 mW. The slope efficiency was found to be primarily dependent on the reflectivity of the fiber Bragg grating. The slope efficiency of multi-longitudinal modes was higher than 45%, and the highest slope efficiency of the single longitudinal mode we achieved was 33.8%. The power stability and spectrum stability were <2% and <0.1%, respectively, and the signal-to-noise ratio measured was around 60 dB.

Concepts: Diffraction, Optical fiber, Laser, Normal mode, Bragg's law, Optical cavity, Analog-to-digital converter, Longitudinal mode


Internal waves and bathymetric variation create time- and space-dependent alterations in the ocean acoustic waveguide, and cause subsequent coupling of acoustic energy between propagating normal modes. In this paper, the criterion for adiabatic invariance is extended to the case of an internal solitary wave (ISW) encountering a sloping bathymetry (i.e., continental shelfbreak). Predictions based on the extended criterion for adiabatic invariance are compared to experimental observations from the Asian Seas International Acoustics Experiment. Using a mode 1 starter field, results demonstrate time-dependent coupling of mode 1 energy to higher adjacent modes, followed by abrupt coupling of mode 5-7 energy to nonadjacent modes 8-20, produces enhanced mode coupling and higher received levels downrange of the oceanographic and bathymetric features. Numerical simulations demonstrate that increasing ISW amplitude and seafloor slope enhance the coupling of energy to adjacent and nonadjacent modes. This enhanced coupling is the direct result of the simultaneous influence of the ISW and its proximity to the shelfbreak, and, compared to the individual effect of the ISW or shelfbreak, has the capacity to scatter 2-4 times the amount of acoustic energy from below the thermocline into the upper water column beyond the shelfbreak in realistic environments.

Concepts: Quantum mechanics, Oceanography, Wave, Acoustics, Sound, South China Sea, Normal mode, Waves


The vibration spectrum of single-walled zigzag boron nitride (BN) nanotubes is simulated with an ab initio periodic quantum chemical method. The trend towards the hexagonal monolayer (h-BN) in the limit of large tube radius R is explored for a variety of properties related to the vibrational spectrum: vibration frequencies, infrared intensities, oscillator strengths, and vibration contributions to the polarizability tensor. The (n,0) family is investigated in the range from n = 6 (24 atoms in the unit cell and tube radius R = 2.5 Å) to n = 60 (240 atoms in the cell and R = 24.0 Å). Simulations are performed using the CRYSTAL program which fully exploits the rich symmetry of this class of one-dimensional periodic systems: 4n symmetry operators for the general (n,0) tube. Three sets of infrared active phonon bands are found in the spectrum. The first one lies in the 0-600 cm(-1) range and goes regularly to zero when R increases; the connection between these normal modes and the elastic and piezoelectric constants of h-BN is discussed. The second (600-800 cm(-1)) and third (1300-1600 cm(-1)) sets tend regularly, but with quite different speed, to the optical modes of the h-BN layer. The vibrational contribution of these modes to the two components (parallel and perpendicular) of the polarizability tensor is also discussed.

Concepts: Spectroscopy, Crystal, Quantum mechanics, Chemistry, Frequency, Molecular vibration, Normal mode, Boron nitride


When patient anatomy is positioned away from a CT scanner’s isocenter, scans of limited diagnostic value may result. Yet in some cases, positioning of patient anatomy far from isocenter is unavoidable. This study examines the effect of posi-tion and reconstruction algorithm on image resolution achieved by a CT scanner operating in a high resolution (HR) scan mode which incorporates focal spot deflection and acquires an increased number of projections per rotation. Images of a metal bead contained in a phantom were acquired on a GE CT750 HD scanner with multiple reconstruction algorithms, in the normal and HR scan mode, and at two positions, scanner isocenter and 15 cm directly above isocenter. The images of the metal bead yielded two-dimensional point spread functions which were averaged along two perpendicular directions to yield line spread functions. Fourier transforms of the line spread functions yielded radial and azimuthal modulation transfer functions (MTFs). At isocenter, the radial and azimuthal MTFs were aver-aged. MTF improvement depended on image position and modulation direction. The results from a single algorithm, Edge, can be generalized to other algorithms. At isocenter, the 10% MTF cutoff was 14.4 cycles/cm in normal and HR mode. At 15 cm above isocenter, the 10% cutoff was 6.0 and 8.5 cycles/cm for the azimuthal and radial MTFs in normal mode. In HR mode, the azimuthal and radial MTF 10% cutoff was 8.3 and 10.3 cycles/cm. Our results indicate that the best image resolu-tion is achieved at scanner isocenter and that the azimuthal resolution degrades more significantly than the radial resolution. For the GE CT750 HD CT scanner, the resolution is significantly enhanced by the HR scan mode away from scanner isocenter, and the use of the HR scan mode has much more of an impact on image resolution away from isocenter than the choice of algorithm.

Concepts: Medical imaging, Computer graphics, Normal distribution, Display resolution, Mode shape, Normal mode, Reconstruction algorithm, Digital image