Effect of periodic stimulus on a neuronal diffusion model with signal-dependent noise

To relate the noise intensity with a periodically modulated input signal in a single neuron stochastic model we introduce a diffusion model with both time modulated drift and diffusion coefficient. Such a model is the continuous version of a Stein model with time oscillating frequencies for the Poisson processes describing the inputs impinging on the neuron. We focus here on some aspects of the resonance phenomenon for such a model. We compare the corresponding interspike interval distribution with the analogous distribution for a model sharing the same parameter values, but with constant noise intensity. Examples with two different levels for this noise intensity are discussed. The enhancement of the height of the peaks in the interspike interval distribution appearing at the modulation period, the improvement of the phase locking behavior and an enlargement of the noise ranges where a resonance like behavior arises are the main features observed in the considered cases.     

Development of an Exactly Solvable Model of Resonance Tunneling of Electromagnetic Waves through Gradient Barriers in a Nonuniform Magnetoactive Plasma

An exactly solvable one-dimensional model describing resonance tunneling (reflectionless transmission) of a transverse electromagnetic wave through wide layers of magnetoactive plasma is developed on the basis of the Helmholtz equation. The plasma layers include a set of spatially localized density structures the amplitudes and thicknesses of which are such that approximate methods are inapplicable for their analysis. The profiles of the plasma density structures strongly depend on the choice of the free parameters of the problem that determine the amplitudes of plasma density modulation, characteristic scale lengths of the density structures, their number, and the total thickness of the nonuniform plasma layer. The plasma layers can also include a set of random inhomogeneities. The propagation of electromagnetic waves through such complicated plasma inhomogeneities is analyzed numerically within the proposed exactly solvable model. According to calculations, there are a wide set of inhomogeneous structures for which an electromagnetic wave incident from vacuum can propagate through the plasma layer without reflection, i.e., the complete tunneling of thick plasma barriers takes place. The model also allows one to exactly solve a one-dimensional problem on the nonlinear transillumination of a nonuniform plasma layer in the presence of cubic nonlinearity. It is important that, due to nonlinearity, the thicknesses of the evanescent plasma regions can decrease substantially and, at a sufficiently strong nonlinearity, such regions will disappear completely. The problem of resonance tunneling of electromagnetic radiation through gradient wave barriers is of interest for various applications, such as efficient heating of dense plasma by electromagnetic radiation and transmission of electromagnetic signals from a source located in the near-Earth plasma or deep in the plasma of an astrophysical object through the surrounding evanescent regions.     

Parametric resonance and amplification in excitable membranes. The Hodgkin-Huxley model

It has previously been shown by different investigators that the excitable membrane shows a resonant sensitivity to periodic external perturbations, but its Q-factor is, as a rule, low. The present paper analyses the possible ways of increasing the membrane Q, using a model of the Hodgkin-Huxley type. It is found, in particular, that it can be increased considerably by modulating periodically the membrane capacitance or the activation and inactivation rate constants of ionic channels, with a frequency of about 2 fo (fo being the fundamental frequency of damped oscillations in the membrane), the extent of modulation not exceeding the critical value 2/Q. In this case, a significant parametric amplification of the membrane current takes place. If the modulation coefficient is above 2/Q, the membrane can display a parametric resonance that causes stable self-oscillations in the potential with a frequency approximately fo. The conditions for the realization of parametric amplification and resonance in biological membranes are discussed.     

Investigation of the interaction of the water oxidising manganese complex of photosystem II with the aqueous solvent environment

Interaction of the water oxidising manganese complex of photosystem II with the aqueous environment has been investigated using electron paramagnetic resonance spectroscopy and electron spin echo envelope modulation spectroscopy to detect interaction of [2H]methanol with the complex in the S2 state. The experiments show that the classical S2 multiline signal is associated with a manganese environment which is not exposed to the aqueous medium. An electron paramagnetic resonance spectroscopy signal, also induced by 200 K illumination, showing 2H modulation by methanol in the medium and a modified multiline electron paramagnetic resonance spectroscopy signal formed in parallel to it, are suggested to be associated with a second manganese environment exposed to the medium.     

Cellular diversity promotes intercellular Ca2+ wave propagation

Calcium ions are an important second messenger in living cells. Calcium signals in form of waves serve as a means of intercellular communication and thus represent a vibrant subject for experimental and theoretical investigations. Here we study the role of cellular variability on the occurrence of Ca2+ wave propagation in a net of diffusively coupled cells. Dynamics of individual cells is simulated by a mathematical model for Ca2+ oscillations. Structural diversity of cells is introduced via variations of the bifurcation parameters, which signify cell sensitivity for external stimulation. Remarkably, for sufficient values of variability Ca2+ waves emerge, which are mostly ordered for intermediate variability strength. We analyze the spatial profile via the autocorrelation function, which confirms a resonance-like response due to the cellular variability. Thus, the reported phenomenon is a novel observation of diversity-induced spatial coherence resonance in a tissue-like media.     

Stochastic resonance in a single neuron model: theory and analog simulation.

Here, we consider a noisy, bistable, single neuron model in the presence of periodic external modulation. The modulation induces a correlated switching between states driven by the noise. The information flow through the system, from the modulation, or signal, to the output switching events, leads to a succession of strong peaks in the power spectrum. The signal-to-noise ratio (SNR) obtained from this power spectrum is a measure of the information content in the neuron response. With increasing noise intensity, the SNR passes through a maximum: an effect which has been called stochastic resonance, and which was first advanced as a possible explanation of the observed periodicity in the recurrences of the Earth's ice ages. We treat the problem within the framework of a recently developed approximate theory, valid in the limits of weak noise intensity, weak periodic forcing and low forcing frequency, for both additive and multiplicative noise. Moreover, we have constructed an analog simulator of the neuron which demonstrates the stochastic resonance effect, and with which we have measured the SNRs for comparison with the theoretical results. Our model should be of interest in situations where a single inherently noisy neuron is the receptor of a periodic signal, which is itself noisy, either from the network or from an external source.     

Spatiotemporal BOLD dynamics from a poroelastic hemodynamic model

A quantitative theory is developed for the relationship between stimulus and the resulting blood oxygen level dependent (BOLD) functional magnetic resonance imaging (fMRI) signal, including both spatial and temporal dynamics for the first time. The brain tissue is modeled as a porous elastic medium, whose interconnected pores represent the vasculature. The model explicitly incorporates conservation of blood mass, interconversion of oxygenated and deoxygenated hemoglobin, force balance within the blood and of blood pressure with vessel walls, and blood flow modulation due to neuronal activity. In appropriate limits it is shown to reproduce prior Balloon models of hemodynamic response, which do not include spatial variations. The regime of validity of such models is thereby clarified by elucidating their assumptions, and when these break down, for example when voxel sizes become small.     

Oscillations in stomatal conductance and plant functioning associated with stomatal conductance: Observations and a model

Summary Measurements of transpiration, leaf water content, and flux of water in a cotton plant exhibiting sustained oscillations, in stomatal conductance are presented, and a model of the mechanism causing this behaviour is developed. The dynamic elements, of the model are capacitors—representing the change of water content with water potential in mesophyll, subsidiary and guard cells—interconnected by resistances representing flow paths in the plant. Increase of water potential in guard cells causes an increase in stomatal conductance. Increase of water potential in the subsidiary cells has the opposite effect and provides the positive feed-back which can cause stomatal conductance to oscillate. The oscillations are shown to have many of the characteristics of free-running oscillations in real plants. The behaviour of the model has been examined, using an analogue computer, with constraints and perturbations representing some of those which could be applied to real plants in physiological experiments. Aspects of behaviour which have been simulated are (a) opening and closing of stomata under the influence of changes in illumination, (b) transient responses due to step changes in potential transpiration, root permeability and potential of water surrounding the roots, (c) the influence of these factors on the occurrence and shape of spontaneous oscillations, and (d) modulation of sustained oscillations due to a circadian rhythm in the permeability of roots.     

Selective stabilization of neuronal representations by resonance between spontaneous prerepresentations of the cerebral network and percepts evoked by interaction with the outside world

Changeux et al. (Changeux, Heidmann and Patte, in "The Biology of Learning" Dahlem Conference, 1984, pp. 115-133, Springer Verlag) have recently discussed a model of "learning by selection" in which the storage of patterns of activity--or prerepresentations--within a network of neurons, results from the coincidence or "resonance" between a spontaneous activity of the neurons and external signals applied to the network--for instance sensory stimuli. In this Note, a mathematical formulation of the model is presented, based on that proposed by Little and Shaw (Little, Math. Biosci., 19, 1974, pp. 101-120; Little and Shaw, Math. Biosci., 39, 1978, pp. 281-290) for the statistical analysis of neuronal activity within a network, and on a rule for modulation of synaptic efficacies derived from that proposed by Hebb (Hebb, The Organisation of Behaviour, 1949, Wiley). The effect of an external signal sigma on the probability P(beta) of occurrence of a given prerepresentation beta under stationary conditions has been analytically derived [cf. equation (16) in text]. Taking into account that the system spontaneously fluctuates between various prerepresentations, it is shown that P(beta) is increased by the external signal sigma when (1) beta is close to sigma--namely the external signal significantly modifies the probabilities of those prerepresentations that resemble sigma--, and (2) when the external signal sigma sets the neurons precisely in the state that they would have more probably reached at the moment when the external signal was applied. Namely there should exist a "resonance" between sigma and the prerepresentation of the network when sigma is applied.     

Model analysis of nonlinear modification of neutrophil calcium homeostasis under the influence of modulated electromagnetic radiation of extremely high frequencies

The problem of resonance effects of electromagnetic radiation (EMR) on biological objects remained unsolved till now. Previously we demonstrated that low-intensity amplitude-modulated EMR of extremely high frequencies (EHF) modified the activity of mouse neutrophils in the synergistic reaction of calcium ionophore A23187 and phorbol ester PMA. The EHF EMR influence on the neutrophils was significant at the carrier frequencies of radiation within a narrow range of 41.8–42.05 GHz and at the modulation frequency of 1 Hz. The purpose of the work was the analysis of frequency-dependent modification of intracellular free calcium concentration ([Ca²⁺]_i) by modulated EHF EMR on the basis of a special model for [Ca²⁺]_i oscillations in the neutrophils. The calcium channels of plasma membrane were chosen as the action target of external modulation in the model. The computer simulation demonstrated the rise in [Ca²⁺]_i at the influence of the external field with a threshold dependence on the modulation amplitude. The effect depended heavily on a sequence of delivery of the chemical and electromagnetic stimuli. The narrow-band rise in [Ca²⁺]_i had a phase-frequency dependence. With the modulation amplitudes exceeding the threshold value, the rise in [Ca²⁺]_i of more than 50% of the initial level was observed at the frequency of about 1 Hz and in the phase range of 0.3–2.5 radians. The results of the model analysis are in good correspondence with the experimental data obtained before, namely, with the resonance modification of the neutrophil activity at the modulation frequency of 1 Hz and with the presence of the effect only at high concentrations of calcium ionophore.     

Numerical simulations of ECE spectra under the L-2M experimental conditions

Results are presented from numerical simulations of electron-cyclotron emission spectra from the plasma of the L-2M stellarator under the conditions corresponding to experiments on electron-cyclotron resonance heating. The spectra are calculated in the model of a two-component electron plasma, each component (thermal and suprathermal) having a Maxwellian distribution. It is shown that, even when suprathermal electrons contribute insignificantly to the total plasma energy, they may considerably affect both the shape and intensity of the electron-cyclotron emission spectrum. The occurrence of a high spectral peak at the frequency corresponding to the resonance ω = 2ω_ce on the low-field side of the plasma column in regimes with a high specific heating power is explained.     

Stochastic resonance in a sinusoidally forced LIF model with noisy threshold

In this report, the LIF neural model driven by underthreshold sinusoidal signals but with a gaussian-distributed noise on the threshold, is approximated by suitably defining an instantaneous firing (or escape) rate, which depends only on the momentary value of the voltage variable. This allows us to obtain, by analytically solving the relevant equations, the main statistical functions describing the "firing activity"; namely, the probability density function of firing phases and that of interspike intervals. From these functions two quantities can be derived, whose dependence on the noise intensity allows the Stochastic Resonance (SR) to be demonstrated. Besides the "regular" SR, the analysed system was found to produce, either for low frequencies and large amplitudes of modulation or for high modulation frequencies, resonance curves displaying two peaks. This bimodal feature of the resonance curves is accounted for on the basis of phase locked firing patterns.     

Intrinsic coherence resonance in excitable membrane patches

The influence of intrinsic channel noise on the spiking activity of excitable membrane patches is studied by use of a stochastic generalization of the Hodgkin-Huxley model. Internal noise stemming from the stochastic dynamics of individual ion channels does affect the electric properties of the cell-membrane patches. There exists an optimal size of the membrane patch for which the internal noise alone can cause a nearly regular spontaneous generation of action potentials. We consider the influence of intrinsic channel noise in presence of a constant and an oscillatory current driving for both, the mean interspike interval and the phenomenon of coherence resonance for neuronal spiking. Given small membrane patches, implying that channel noise dominates the excitable dynamics, we find the phenomenon of intrinsic coherence resonance. In this case, the relatively regular spiking behavior becomes essentially independent of an applied stimulus. We observed, however, the occurrence of a skipping of supra-threshold input events due to channel noise for intermediate patch sizes. This effect consequently reduces the overall coherence of the spiking.     

Elucidation of direct competition and allosteric modulation of small‐molecular‐weight protein ligands using surface plasmon resonance methods

The present work introduces a surface plasmon resonance‐based method for the discrimination of direct competition and allosteric effects that occur in ternary systems comprising a receptor protein and two small‐molecular‐weight ligands that bind to it. Fatty acid binding protein 4, fructose‐1,6‐bisphosphatase and human serum albumin were used as model receptor molecules to demonstrate the performance of the method. For each of the receptor molecules, pairs of ligand molecules were selected for which either direct competition or an allosteric effect had already been determined by other methods. The method of discrimination introduced here is based on the surface plasmon resonance responses observed at equilibrium when an immobilized receptor protein is brought into contact with binary mixtures of interacting ligands. These experimentally determined responses are compared with the responses calculated using a theoretical model that considers both direct competition and allosteric ligand interaction modes. This study demonstrates that the allosteric ternary complex model, which enables calculation of the fractional occupancy of the protein by each ligand in such ternary systems, is well suited for the theoretical calculation of these types of responses. For all of the ternary systems considered in this work, the experimental and calculated responses in the chosen concentration ratio range were identical within a five‐σ confidence interval when the calculations considered the correct interaction mode of the ligands (direct competition or different types of allosteric regulation), and in case of allosteric modulation, also the correct strength of this effect. This study also demonstrates that the allosteric ternary complex model‐based calculations are well suited to predict the ideal concentration ratio range or even single concentration ratios that can serve as hot spots for discrimination, and such hot spots can drastically reduce the numbers of measurements needed for discrimination between direct competition and distinct modulation modes (neutral, positive or negative allostery). Copyright © 2015 John Wiley & Sons, Ltd.     

An explanation of contextual modulation by short-range isotropic connections and orientation map geometry in the primary visual cortex

Recent experimental studies on the primary visual cortex have revealed complicated nonclassical neuronal activities. Contextual modulation on orientation-contrast is one typical example of nonclassical neuronal behavior. This modulation by surrounding stimuli in a nonclassical receptive field is mainly thought to be mediated by short- and long-range horizontal connections within the primary visual cortex. Short-range connections are circularly symmetrical and relatively independent of orientation preferences, while long-range connections are patchy, asymmetrical, and orientation specific. Although this modulation can be explained by long-range specific connections qualitatively, recent studies suggest that long-range connections alone may be insufficient with respect to the balance between two types of connections. Here, in order to clarify the role of short-range connections in the process of contextual modulation, we propose a model of the primary visual cortex with isotropic short-range connections and a geometric orientation map. Computational simulations using the model have demonstrated that contextual modulation can be explained by short-range connections alone. This is due to the interaction between the spatial periodicity of orientation domains and the excitatory-inhibitory regions arising from the propagation of activities.Acknowledgement We gratefully acknowledge useful conversations with Hiromichi, Sato. The present work was partly supported by Grant-in-Aid for Scientific Research on Priority Areas (C) Advanced Brain Science Project from the Japanese Ministry of Education, Science, Sports, and Culture.     

Nonlinear Right-Hand Polarized Wave in Plasma in the Electron Cyclotron Resonance Region

The propagation of a nonlinear right-hand polarized wave along an external magnetic field in subcritical plasma in the electron cyclotron resonance region is studied using numerical simulations. It is shown that a small-amplitude plasma wave excited in low-density plasma is unstable against modulation instability with a modulation period equal to the wavelength of the excited wave. The modulation amplitude in this case increases with decreasing detuning from the resonance frequency. The simulations have shown that, for large-amplitude waves of the laser frequency range propagating in plasma in a superstrong magnetic field, the maximum amplitude of the excited longitudinal electric field increases with the increasing external magnetic field and can reach 30% of the initial amplitude of the electric field in the laser wave. In this case, the energy of plasma electrons begins to substantially increase already at magnetic fields significantly lower than the resonance value. The laser energy transferred to plasma electrons in a strong external magnetic field is found to increase severalfold compared to that in isotropic plasma. It is shown that this mechanism of laser radiation absorption depends only slightly on the electron temperature.     

Single effective neuron: dendritic coupling effects and stochastic resonance

We consider a model of a neuron coupled with a surrounding dendritic network subject to Langevin noise and a weak periodic modulation. Through an adiabatic elimination procedure, the single-neuron dynamics are extracted from the coupled stochastic differential equations describing the network of dendrodendritic interactions.Our approach yields areduced neuron model whose dynamics may correspond to neurophysiologically realistic behavior for certain ranges of soma and bath parameters. Cooperative effects (e.g., stochastic resonance) arising from the interplay between the noise and modulation are discussed in detail.     

Comprehensive Surface-Wave Description for the Nano-scale Energy Concentration with Resonant Dipole Antennas

Resonant optical dipole nano-antennas allow giant field enhancement within nano-gaps. To show how the energy of external illumination waves is delivered and concentrated in nano-gaps, we build up a model by considering the dynamical launching and multiple scattering processes of surface plasmon polaritions (SPPs) on both antenna arms. The model captures the main feature of the antenna resonance as evidenced by comparison of the model prediction with fully vectorial numerical results and provides an intuitive picture that the energy of external wave is initially transferred into SPP and is then coupled into the nano-gap. The enhanced field in the nano-gap oscillates quasi-periodically with the increase of the antenna-arm length, and the resonance peaks can be predicted with a phase-matching condition derived from the model, showing that antenna resonance is due to a constructive interference of the multiple-scattered SPPs. Analytical equation for determining the complex resonance wavelength and the quality factor of the resonant modes is obtained. The model however exhibits observable deviation from fully vectorial numerical results for the lowest resonance order (for antenna with the shortest arms), evidencing that, for this case, surface waves other than SPPs contribute to the antenna resonance. The present results are helpful for clarifying the underlying physics for the energy concentration with resonant dipole antennas and may provide recipes for intuitive design of antenna devices, such as those used for optical nonlinearity enhancement and biochemical sensing.     

Conformational epitope of the type III group B Streptococcus capsular polysaccharide.

The protective epitope of the type III group B streptococcal polysaccharide (GBSPIII) is length dependent and conformational. To obtain a more accurate characterization of the conformational epitope, ELISA inhibition and surface plasmon resonance studies were conducted on two GBSPIII-specific mAbs using a large panel of oligosaccharide probes. The results of the studies confirmed that 2 repeating units (RU) is the minimum binding unit and that, while increases in chain length from 2 RU to 7 RU caused further optimization of the epitope, it remained monovalent. A 3-fold increase in affinity was observed between 7 RU and 20 RU, which, by surface plasmon resonance studies on a Fab, was shown to be due to both further optimization of the individual epitope and the occurrence of multivalency of epitope. The data support our hypothesis that the conformational epitope is an extended helical segment of the GBSPIII. GBSPIII exists mainly in the random coil form, which structurally mimics short oligosaccharide self Ags, but it can infrequently and spontaneously form extended helices. Although not prevalent in GBSPIII, the immune system preferentially selects these helical epitopes because they are unique to the polysaccharide. Contrary to a previously proposed model of GBSPIII binding in which the binding of the first Ab propagates a continuum of helical epitopes, our binding kinetics are consistent only with the helical epitope's being discontinuous and infrequent.