Analysis of light scattering off photonic crystal slabs in terms of Feshbach resonances

Techniques to deal with Feshbach resonances are applied to describe resonant light scattering off one dimensional photonic crystal slabs. Accurate expressions for scattering amplitudes, free of any fitting parameter, are obtained for isolated as well as overlapping resonances. They relate the resonance properties to the properties of the optical structure and of the incident light. For the most common case of a piecewise constant dielectric function, the calculations can be carried out essentially analytically. After establishing the accuracy of this approach we demonstrate its potential in the analysis of the reflection coefficients for the diverse shapes of overlapping, interacting resonances.Comment: 12 pages, 5 figure

Understanding visual map formation through vortex dynamics of spin Hamiltonian models

The pattern formation in orientation and ocular dominance columns is one of the most investigated problems in the brain. From a known cortical structure, we build spin-like Hamiltonian models with long-range interactions of the Mexican hat type. These Hamiltonian models allow a coherent interpretation of the diverse phenomena in the visual map formation with the help of relaxation dynamics of spin systems. In particular, we explain various phenomena of self-organization in orientation and ocular dominance map formation including the pinwheel annihilation and its dependency on the columnar wave vector and boundary conditions.Comment: 4 pages, 15 figure

ANNINE-6plus, a voltage-sensitive dye with good solubility, strong membrane binding and high sensitivity

We present a novel voltage-sensitive hemicyanine dye ANNINE-6plus and describe its synthesis, its properties and its voltage-sensitivity in neurons. The dye ANNINE-6plus is a salt with a double positively charged chromophore and two bromide counterions. It is derived from the zwitterionic dye ANNINE-6. While ANNINE-6 is insoluble in water, ANNINE-6plus exhibits a high solubility of around 1 mM. Nonetheless, it displays a strong binding to lipid membranes. In contrast to ANNINE-6, the novel dye can be used to stain cells from aqueous solution without surfactants or organic solvents. In neuronal membranes, ANNINE-6plus exhibits the same molecular Stark effect as ANNINE-6. As a consequence, a high voltage-sensitivity is achieved with illumination and detection in the red end of the excitation and emission spectra, respectively. ANNINE-6plus will be particularly useful for sensitive optical recording of neuronal excitation when organic solvents and surfactants must be avoided as with intracellular or extracellular staining of brain tissue

Normalization of Voltage-Sensitive Dye Signal with Functional Activity Measures

In general, signal amplitude in optical imaging is normalized using the well-established ΔF/F method, where functional activity is divided by the total fluorescent light flux. This measure is used both directly, as a measure of population activity, and indirectly, to quantify spatial and spatiotemporal activity patterns. Despite its ubiquitous use, the stability and accuracy of this measure has not been validated for voltage-sensitive dye imaging of mammalian neocortex in vivo. In this report, we find that this normalization can introduce dynamic biases. In particular, the ΔF/F is influenced by dye staining quality, and the ratio is also unstable over the course of experiments. As methods to record and analyze optical imaging signals become more precise, such biases can have an increasingly pernicious impact on the accuracy of findings, especially in the comparison of cytoarchitechtonic areas, in area-of-activation measurements, and in plasticity or developmental experiments. These dynamic biases of the ΔF/F method may, to an extent, be mitigated by a novel method of normalization, ΔF/ΔFepileptiform. This normalization uses as a reference the measured activity of epileptiform spikes elicited by global disinhibition with bicuculline methiodide. Since this normalization is based on a functional measure, i.e. the signal amplitude of “hypersynchronized” bursts of activity in the cortical network, it is less influenced by staining of non-functional elements. We demonstrate that such a functional measure can better represent the amplitude of population mass action, and discuss alternative functional normalizations based on the amplitude of synchronized spontaneous sleep-like activity. These findings demonstrate that the traditional ΔF/F normalization of voltage-sensitive dye signals can introduce pernicious inaccuracies in the quantification of neural population activity. They further suggest that normalization-independent metrics such as waveform propagation patterns, oscillations in single detectors, and phase relationships between detector pairs may better capture the biological information which is obtained by high-sensitivity imaging

Primer to Voltage Imaging With ANNINE Dyes and Two-Photon Microscopy

ANNINE-6 and ANNINE-6plus are voltage-sensitive dyes that when combined with two-photon microscopy are ideal for recording of neuronal voltages in vivo, in both bulk loaded tissue and the dendrites of single neurons. Here, we describe in detail but for a broad audience the voltage sensing mechanism of fast voltage-sensitive dyes, with a focus on ANNINE dyes, and how voltage imaging can be optimized with one-photon and two-photon excitation. Under optimized imaging conditions the key strengths of ANNINE dyes are their high sensitivity (0.5%/mV), neglectable bleaching and phototoxicity, a linear response to membrane potential, and a temporal resolution which is faster than the optical imaging devices currently used in neurobiology (order of nanoseconds). ANNINE dyes in combination with two-photon microscopy allow depth-resolved voltage imaging in bulk loaded tissue to study average membrane voltage oscillations and sensory responses. Alternatively, if ANNINE-6plus is applied internally, supra and sub threshold voltage changes can be recorded from dendrites of single neurons in awake animals. Interestingly, in our experience ANNINE-6plus labeling is impressively stable in vivo, such that voltage imaging from single Purkinje neuron dendrites can be performed for 2 weeks after a single electroporation of the neuron. Finally, to maximize their potential for neuroscience studies, voltage imaging with ANNINE dyes and two-photon microscopy can be combined with electrophysiological recording, calcium imaging, and/or pharmacology, even in awake animals

Hyperbolic planforms in relation to visual edges and textures perception

We propose to use bifurcation theory and pattern formation as theoretical probes for various hypotheses about the neural organization of the brain. This allows us to make predictions about the kinds of patterns that should be observed in the activity of real brains through, e.g. optical imaging, and opens the door to the design of experiments to test these hypotheses. We study the specific problem of visual edges and textures perception and suggest that these features may be represented at the population level in the visual cortex as a specific second-order tensor, the structure tensor, perhaps within a hypercolumn. We then extend the classical ring model to this case and show that its natural framework is the non-Euclidean hyperbolic geometry. This brings in the beautiful structure of its group of isometries and certain of its subgroups which have a direct interpretation in terms of the organization of the neural populations that are assumed to encode the structure tensor. By studying the bifurcations of the solutions of the structure tensor equations, the analog of the classical Wilson and Cowan equations, under the assumption of invariance with respect to the action of these subgroups, we predict the appearance of characteristic patterns. These patterns can be described by what we call hyperbolic or H-planforms that are reminiscent of Euclidean planar waves and of the planforms that were used in [1, 2] to account for some visual hallucinations. If these patterns could be observed through brain imaging techniques they would reveal the built-in or acquired invariance of the neural organization to the action of the corresponding subgroups.Comment: 34 pages, 11 figures, 2 table

Cortical Dynamics Subserving Visual Apparent Motion

Motion can be perceived when static images are successively presented with a spatial shift. This type of motion is an illusion and is termed apparent motion (AM). Here we show, with a voltage sensitive dye applied to the visual cortex of the ferret, that presentation of a sequence of stationary, short duration, stimuli which are perceived to produce AM are, initially, mapped in areas 17 and 18 as separate stationary representations. But time locked to the offset of the 1st stimulus, a sequence of signals are elicited. First, an activation traverses cortical areas 19 and 21 in the direction of AM. Simultaneously, a motion dependent feedback signal from these areas activates neurons between areas 19/21 and areas 17/18. Finally, an activation is recorded, traveling always from the representation of the 1st to the representation of the next or succeeding stimuli. This activation elicits spikes from neurons situated between these stimulus representations in areas 17/18. This sequence forms a physiological mechanism of motion computation which could bind populations of neurons in the visual areas to interpret motion out of stationary stimuli

Coverage, Continuity and Visual Cortical Architecture

The primary visual cortex of many mammals contains a continuous representation of visual space, with a roughly repetitive aperiodic map of orientation preferences superimposed. It was recently found that orientation preference maps (OPMs) obey statistical laws which are apparently invariant among species widely separated in eutherian evolution. Here, we examine whether one of the most prominent models for the optimization of cortical maps, the elastic net (EN) model, can reproduce this common design. The EN model generates representations which optimally trade of stimulus space coverage and map continuity. While this model has been used in numerous studies, no analytical results about the precise layout of the predicted OPMs have been obtained so far. We present a mathematical approach to analytically calculate the cortical representations predicted by the EN model for the joint mapping of stimulus position and orientation. We find that in all previously studied regimes, predicted OPM layouts are perfectly periodic. An unbiased search through the EN parameter space identifies a novel regime of aperiodic OPMs with pinwheel densities lower than found in experiments. In an extreme limit, aperiodic OPMs quantitatively resembling experimental observations emerge. Stabilization of these layouts results from strong nonlocal interactions rather than from a coverage-continuity-compromise. Our results demonstrate that optimization models for stimulus representations dominated by nonlocal suppressive interactions are in principle capable of correctly predicting the common OPM design. They question that visual cortical feature representations can be explained by a coverage-continuity-compromise.Comment: 100 pages, including an Appendix, 21 + 7 figure

Imaging Chromophores With Undetectable Fluorescence by Stimulated Emission Microscopy

Fluorescence, that is, spontaneous emission, is generally more sensitive than absorption measurement, and is widely used in optical imaging. However, many chromophores, such as haemoglobin and cytochromes, absorb but have undetectable fluorescence because the spontaneous emission is dominated by their fast non-radiative decay. Yet the detection of their absorption is difficult under a microscope. Here we use stimulated emission, which competes effectively with the nonradiative decay, to make the chromophores detectable, and report a new contrast mechanism for optical microscopy. In a pump-probe experiment, on photoexcitation by a pump pulse, the sample is stimulated down to the ground state by a time-delayed probe pulse, the intensity of which is concurrently increased. We extract the miniscule intensity increase with shot-noise-limited sensitivity by using a lock-in amplifier and intensity modulation of the pump beam at a high megahertz frequency. The signal is generated only at the laser foci owing to the nonlinear dependence on the input intensities, providing intrinsic three-dimensional optical sectioning capability. In contrast, conventional one-beam absorption measurement exhibits low sensitivity, lack of three-dimensional sectioning capability, and complication by linear scattering of heterogeneous samples. We demonstrate a variety of applications of stimulated emission microscopy, such as visualizing chromoproteins, non-fluorescent variants of the green fluorescent protein, monitoring lacZ gene expression with a chromogenic reporter, mapping transdermal drug distributions without histological sectioning, and label-free microvascular imaging based on endogenous contrast of haemoglobin. For all these applications, sensitivity is orders of magnitude higher than for spontaneous emission or absorption contrast, permitting nonfluorescent reporters for molecular imaging.Chemistry and Chemical Biolog

Hemodynamic Responses Evoked by Neuronal Stimulation via Channelrhodopsin-2 Can Be Independent of Intracortical Glutamatergic Synaptic Transmission

Maintenance of neuronal function depends on the delivery of oxygen and glucose through changes in blood flow that are linked to the level of ongoing neuronal and glial activity, yet the underlying mechanisms remain unclear. Using transgenic mice expressing the light-activated cation channel channelrhodopsin-2 in deep layer pyramidal neurons, we report that changes in intrinsic optical signals and blood flow can be evoked by activation of a subset of channelrhodopsin-2-expressing neurons in the sensorimotor cortex. We have combined imaging and pharmacology to examine the importance of glutamatergic synaptic transmission in this form of neurovascular coupling. Blockade of ionotropic glutamate receptors with the antagonists CNQX and MK801 significantly reduced forepaw-evoked hemodynamic responses, yet resulted in no significant reduction of channelrhodopsin-evoked hemodynamic responses, suggesting that stimulus-dependent coupling of neuronal activity to blood flow can be independent of local excitatory synaptic transmission. Together, these results indicate that channelrhodopsin-2 activation of sensorimotor excitatory neurons produces changes in intrinsic optical signals and blood flow that can occur under conditions where synaptic activation of neurons or other cells through ionotropic glutamate receptors would be blocked