Proceedings Volume 5467

Fluctuations and Noise in Biological, Biophysical, and Biomedical Systems II

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Proceedings Volume 5467

Fluctuations and Noise in Biological, Biophysical, and Biomedical Systems II

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Volume Details

Date Published: 25 May 2004
Contents: 11 Sessions, 41 Papers, 0 Presentations
Conference: Second International Symposium on Fluctuations and Noise 2004
Volume Number: 5467

Table of Contents

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Table of Contents

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  • Biomolecular Processes and Fluctuations
  • Physiological Signals
  • Population Dynamics and Diffusions
  • Stochastic Resonance
  • Noise and Neural Phenomena
  • Fluctuational Phenomena and DNA
  • Biosensing
  • Physiological Signals
  • Nonlinear Dynamics in Biology
  • Gene Expression and Regulation
  • Ion Channels
  • Posters-Wednesday
Biomolecular Processes and Fluctuations
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Non-Gaussian statistics of the vibrational fluctuations of myoglobin and the thermal fluctuations of myoglobin hydration
Jack A. Tuszynski, Tyler Luchko, Eric J. Carpenter, et al.
Experiments on the dynamics of vibrational fluctuations in myoglobin revealed an interesting behavioral cross-over occurring in the range of 180-200 K. In this temperature range the mean square displacement of atomic positions versus temperature sharply increases its slope indicating the dissociation of CO from the haeme group. In this paper we develop a theoretical framework for the description of this phenomenon assuming the existence of an effective quartic potential. We then use non-Gaussian statistics to obtain a relationship between the mean square displacement and model parameters. We compare our model to published experimental data using a physically meaningful parameter fit. While the Gaussian approximation's applicability is verified by the low-temperature régime, in the high-temperature limit deviations from the Gaussian approximation are due to the double-well nature of our effective potential. In the second part of the paper we summarize our molecular dynamics simulations of the myoglobin's hydration in the low-temperature régime and at room temperature.
Proposition of autonomous energy transducer and its working mechanism
Naoko Nakagawa, Kunihiko Kaneko, Teruhisa S. Komatsu
We propose a concept of autonomous energy transducer at a molecular scale, where output is produced by an energy input, without imposing any restriction on the magnitude or timing of input, and without any control after the input. As an example, a dynamical systems model with several degrees of freedom is proposed, which transduces input energy to output motion on the average. It is shown that this transduction is robust and the coupling between the input and output is generally loose. How this transducer works is analyzed in terms of dynamical systems theory, where chaotic dynamics of the internal degrees of freedom, as well as duration of excited conformation of an active part which is self-organized with the energy flow, is essential.
Quantum states in proteins and protein assemblies: The essence of life?
Activities in living cells are performed by protein conformational dynamics which in turn are governed by quantum mechanical van der Waals London forces in intra-protein “hydrophobic” pockets. In assemblies of proteins with periodic lattice geometry such as cytoskeletal actin and microtubules (as well as ordered water on their surfaces), Bose-Einstein condensation, quantum coherent superposition and quantum computation with entanglement may occur as a collective effect of these forces due to metabolic coherent phonon pumping. Decoherence can be avoided through isolation/shielding by actin gelation, Debye layer screening and water/ion ordering and topological quantum error correction. As an example, quantum spin transfer through organic molecules is more efficient at higher temperatures than at absolute zero. The unitary oneness and ineffability of living systems may depend on mesoscopic/macroscopic quantum states in protoplasm.
Voltage-induced "gating" of bacterial porin as reversible protein denaturation
General porin OmpF forms water-filled channels in the outer membrane of E. coli bacteria. When reconstituted into planar bilayer lipid membranes, these channels can be closed (or “gated”) by high electric fields. We discover that: (i) channel gating is sensitive to the type of cations in the membrane-bathing solution according to their position in the Hofmeister series; (ii) channel gates to a “closed” state that is represented by a set of multiple sub-conformations with at least three distinctly different conformations contributing to the closed-state conductance histogram. Taken together with the nearly symmetric response to the applied voltage of changing polarity and the hysteresis phenomena reported previously by others and reproduced here, these findings suggest that the voltage-induced closure of the OmpF channel is a consequence of reversible denaturation of the protein by the high electric field. If so, the voltage-induced gating of bacterial porins can serve as an instructive model to study the physics of protein folding at the single-molecule level.
Physiological Signals
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Statistical analysis of heartbeat data with wavelet techniques
The purpose of this paper is to demonstrate the use of some methods of signal analysis, performed on ECG and in some cases blood pressure signals, for the classification of the health status of the heart of mice and rats. Spectral and wavelet analysis were performed on the raw signals. FFT-based coherence and phase was also calculated between blood pressure and raw ECG signals. Finally, RR-intervals were deduced from the ECG signals and an analysis of the fractal dimensions was performed. The analysis was made on data from mice and rats. A correlation was found between the health status of the mice and the rats and some of the statistical descriptors, most notably the phase of the cross-spectra between ECG and blood pressure, and the fractal properties and dimensions of the interbeat series (RR-interval fluctuations).
A comparison of nonlinear noise reduction and independent component analysis using a realistic dynamical model of the electrocardiogram
Accurate performance metrics for removing noise from the electrocardiogram (ECG) are difficult to define due to the inherently complicated nature of the noise and the absence of knowledge about the underlying dynamical processes. By using a previously published model for generating realistic artificial ECG signals and adding both stochastic and deterministic noise, a method for assessing the performance of noise reduction techniques is presented. Independent component analysis (ICA) and nonlinear noise reduction (NNR) are employed to remove noise from an ECG with known characteristics. Performance as a function of the signal to noise ratio is measured by both a noise reduction factor and the correlation between the cleaned signal and the original noise-free signal.
Techniques for noise removal from EEG, EOG, and airflow signals in sleep patients
Matthew J. Berryman, Sheila Messer, Andrew Allison, et al.
Noise is present in the wide variety of signals obtained from sleep patients. This noise comes from a number of sources, from presence of extraneous signals to adjustments in signal amplification and shot noise in the circuits used for data collection. The noise needs to be removed in order to maximize the information gained about the patient using both manual and automatic analysis of the signals. Here we evaluate a number of new techniques for removal of that noise, and the associated problem of separating the original signal sources.
Population Dynamics and Diffusions
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Effects of seasonality and of internal fluctuations on the spreading of Hantavirus
We present an analysis of two features that generalize the original model for the spread of the Hantavirus introduced by Abramson and Kenkre [Phys. Rev. E Vol. 66, 011912 (2002)]. One, the effect of seasonal alternations, may cause the virus to spread under conditions that do not lead to an epidemic under the action of either season alone. The other, the effect of internal fluctuations, modifies the distribution of infected mice and may lead to extinction of the infected population even when the mean population is above epidemic conditions.
Habitat size and extinction in population dynamics
Carlos Escudero, Javier Buceta, Francisco Javier de la Rubia, et al.
We review the critical patch size problem, already classic in the mathematical biology literature. We consider a logistic population living in a finite patch of length L and undergoing random dispersal. The patch presents good conditions for life, while the conditions are so harsh outside that they lead to certain extinction. The usual mean field approach leads to a critical patch size Lc, such that if the actual length of the patch is smaller than Lc the population becomes extinct with certainty, whereas a longer patch leads to certain survival. We study the fluctuations in the population due to its low density near extinction and analyze their effects on the probability of extinction. We find that there is no patch size that can be considered absolutely safe for the population and that, under certain circumstances, the population is under risk of extinction for any patch size.
Repulsive delayed random walk
Tadaaki Hosaka, Toru Ohira
We study here a random walk with delayed feedback around an unstable fixed point. It is found that the random walker can be kept longer around the fixed point with larer delay. This is in contrast to the normal role of delay, which is generally thought to be a source of instability. We discuss a possibility of our model to stick balancing experiments.
Stochastic Resonance
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Super-sensitive stochastic resonance in a small-dimensional excitable network
We study a system of globally coupled FitzHugh-Nagumo equations as a stochastic resonator. Each unit is either excitatory or inhibitory. If the numbers of units of both types are nearly equal (balanced coupling), we observe the presence of multistable oscillatory states with different excitation or firing rates. In the presence of noise, random transitions between high- and low-frequency oscillatory states are observed and the resultant firing pattern is long-range correlated. Compared to other coupling types, the system demonstrates considerably improved rate-coding ability for both subthreshold and suprathreshold signals, even with a tiny level of noise.
Noise-enhanced information transmission in a model of multichannel cochlear implantation
Cochlear implants are used to restore functional hearing to people with profound deafness. Success, as measured by speech intelligibility scores, varies greatly amongst patients; a few receive almost no benefit while some are able to use a telephone under favourable listening conditions. Using a novel nerve model and the principles of suprathreshold stochastic resonance, we demonstrate that the rate of information transfer through a cochlear implant system can be globally maximized by the addition of noise. If this additional information could be used by the brain then it would lead to greater speech intelligibility, which is important given that the intelligibility of all cochlear implant recipients is poorer than that of people with normal hearing, particularly in adverse listening conditions.
Integro-differential stochastic resonance
A new class of stochastic resonator (SRT) and Stochastic Resonance (SR) phenomena are described. The new SRT consist of a classical SRT, one or more time derivative circuits and the same number of time integrators. The incoming signal with additive noise is first time derivated, then passes through the classical SRT and finally it is time integrated. The resulting SR phenomena show a well defined SR. Moreover the signal transfer and SNR are the best at the high frequency end. A particular property of the new system is the much smoother output signal due to the time integration.
Generalized noise resonance: using noise for signal enhancement
Noise is a key factor in information processing systems. This fact will be even more critical in new technologies, as dimensions continue to scale down. New design methodologies tolerant to or even taking advantage of noise need to be considered. In this work the possibility of using stochastic resonance (SR) in electronic circuits is studied. We demonstrate the validity of nearly any kind of perturbing signal in producing a noise resonance, thus extending the stochastic resonance concept. In this paper we have explored stochastic, chaotic, deterministic and coupled noise perturbations. The relationship between input signal and input noise amplitude on the noise resonance regime is analyzed, providing a rule for operation under this situation. Finally, we present a simulation study demonstrating that noise resonance is robust to non-ideal behaviors of non-linear devices. All three facts allow direct use of generalized noise resonance (GNR) in electronic circuits.
Noise and Neural Phenomena
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Consciousness from neurons and waves
This paper presents a theory of consciousness based on the following evidence: [1] Complex stimuli are decomposed by the exogenous system into attributes transmitted to synapses of pyramidal neurons in lower cortical layers, encoding fragments of sensations as nonrandom synchronization that increases local voltages; [2] Endogenous readouts from representational systems encoding memories in a mesolimbic system are transmitted to synapses of the pyramidal neurons in upper layers; [3] Excitability of pyramidal neurons receiving convergent exogenous and endogenous inputs is enhanced, converting fragments of sensations to fragments of perception and creating high voltage islands of non-random synchrony; [4] Local Field Potential (LFP) oscillations are homeostatically regulated, imposing dynamically maintained local voltage thresholds that define a “Ground State”; [5] Deviations from these most probable levels constitute local perturbations of entropy; [6] Modulation of cortex by LFPs, facilitating coherent cortico-thalamic (C-T) volleys of cells with suprathreshold excitability, binds dispersed fragments of local perturbations of entropy; [7] The thalamic cells from which convergence arose respond to these volleys by coherent T-C-T-C reverberations; [8] Sustained reverberation establishes a resonating electromagnetic field of information, the vehicle sustaining unified perception; [9] The resonating field of information constitutes Global Negative and generates the content of consciousness; [10] Invariant reversible LFP changes occur upon loss of consciousness and persistent shifts accompany many clinical disorders.
Resonant activation in single and coupled stochastic FitzHugh-Nagumo elements
The response of a noisy FitzHugh-Nagumo (FHN) neuron-like model to weak periodic forcing is analyzed. The mean activation time is investigated as a function of noise intensity and of the parameters of the external signal. It is shown by numerical simulation that there exists a frequency range within which the phenomenon of resonant activation occurs; resonant activation is also observed in coupled FHN elements. The mean activation time with small noise intensity is compared with the theoretical results.
The application of Gaussian channel theory to the estimation of information transmission rates in neural systems
We consider the application of Gaussian channel theory (GCT) to the problem of estimating the rate of information transmission through a nonlinear channel such as a neural element. We suggest that, contrary to popular belief, GCT can be applied to neural systems even when the dynamics are highly nonlinear. We show that, under suitable conditions, the Gaussianity of the response is not compromised and hence GCT can be usefully applied. Using the GCT approach we develop a new method for estimating information rates in the time domain. Finally, using this new method, we show that a recently introduced form of stochastic resonance, termed suprathreshold stochastic resonance, is also displayed by the information rate.
Probing feature selectivity of neurons in primary visual cortex with natural stimuli
Tatyana Sharpee, Hiroki Sugihara, A. V. Kurgansky, et al.
One way to characterize neural feature selectivity is to model the response probability as a nonlinear function of the output of a set of linear filters applied to incoming signals. Traditionally these linear filters are measured by probing neurons with correlated Gaussian noise ensembles and calculating correlation functions between incoming signals and neural responses. It is also important to derive these filters in response to natural stimuli, which have been shown to have strongly non-Gaussian spatiotemporal correlations. An information-theoretic method has been proposed recently for reconstructing neural filters using natural stimuli in which one looks for filters whose convolution with the stimulus ensemble accounts for the maximal possible part of the overall information carried the sequence of neural responses. Here we give a first-time demonstration of this method on real neural data, and compare responses of neurons in cat primary visual cortex driven with natural stimuli, noise ensembles, and moving gratings. We show that the information-theoretic method achieves the same quality of filter reconstruction for natural stimuli as that of well-established white-noise methods. Major parameters of neural filters derived from noise ensembles and natural stimuli, as well as from moving gratings are consistent with one another. We find that application of the reverse correlation method to natural stimuli ensembles leads to significant distortions in filters for a majority of studied cells with non-zero reverse-correlation filter.
Resonant effects in a voltage-activated channel gating
The non-selective voltage activated cation channel from the human red cells, which is activated at depolarizing potentials, has been shown to exhibit counter-clockwise gating hysteresis. We have analyzed the phenomenon with the simplest possible phenomenological models by assuming 2×2 discrete states, i.e. two normal open/closed states with two different states of "gate tension." Rates of transitions between the two branches of the hysteresis curve have been modeled with single-barrier kinetics by introducing a real-valued "reaction coordinate" parameterizing the protein's conformational change. When described in terms of the effective potential with cyclic variations of the control parameter (an activating voltage), this model exhibits typical "resonant effects": synchronization, resonant activation and stochastic resonance. Occurrence of the phenomena is investigated by running the stochastic dynamics of the model and analyzing statistical properties of gating trajectories.
Fluctuational Phenomena and DNA
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Thermally induced coherent vibrations in DNA
Kim O Rasmussen, George Kalosakas, N. K. Voulgarakis, et al.
We compare numerical calculations and experimental data showing that large, slow thermally-induced openings of double stranded DNA coincide with the location of functionally relevant sites for transcription. Investigating a bacteriophage DNA gene promoter segment, we find that the large opening tends to occur at the transcription start site. Other probable large openings appear to be related to other regulatory sites. Sequence specificity, nonlinearity and entropy, are the basic elements for controlling coherent dynamics. To further characterize the dynamics related to the bubble formation we investigate the temperature dependence on the dynamic structure factor. A distinct feature in the dynamics structure factor is identified and attributed to the denaturation bubbles.
Disorder and fluctuations in nonlinear excitations in DNA
Sara Cuenda, Angel Sanchez
We study the effects of the sequence on the propagation of nonlinear excitations in simple models of DNA, and how those effects are modified by noise. Starting from previous results on soliton dynamics on lattices defined by aperiodic potentials, [F. Dominquez-Adame et al., Phys. Rev. E 52, 2183 (1995)], we analyze the behavior of lattices built from real DNA sequences obtained from human genome data. We confirm the existence of threshold forces, already found in Fibonacci sequences, and of stop positions highly dependent on the specific sequence. Another relevant conclusion is that the effective potential, a collective coordinate formalism introduced by Salerno and Kivshar [Phys. Lett. A 193, 263 (1994)] is a useful tool to identify key regions that control the behaviour of a larger sequence. We then study how the fluctuations can assist the propagation process by helping the excitations to escape the stop positions. Our conclusions point out to improvements of the model which look promising to describe mechanical denaturation of DNA. Finally, we also consider how randomly distributed energy focus on the chain as a function of the sequence.
Biosensing
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Nanopore detection using channel current cheminformatics
A novel detector is used for analysis of single DNA molecules. The detector is based on current blockade measurements through a single, nanometer-scale, α-hemolysin ion channel. The biologically based alpha-hemolysin channel self-assembles in lipid bilayers, permitting highly reproducible experiments with Angstrom resolution. In previous work the spectrum of dsDNA blockade states could be explained in terms of the dsDNA-protein binding kinetics, and dsDNA terminus fraying (bond dissociation) kinetics. Results presented here strengthen the hypothesis that conformational dynamics can be observed as well, when the channel-captured dsDNA end is in an unbound state. Feature discovery methods: include a time-domain finite state automaton (FSA), a wavelet domain FSA, and a Hidden Markov Model (HMM). Classifier feature extraction methods: includes a time-domain FSA for signal acquisition and a generalized HMM with EM for features extraction. Classification method: Support Vector Machines (SVMs) are used with novel kernel designs. Kinetic feature extraction tool: a time-domain FSA projects current observations to a (small) set of blockade states. Those states are provided by the generalized HMM analysis. Noise sources limit the resolution of the nanopore device, and its multiclass scaling capabilities, and this is discussed in the context of ongoing refinements to the device.
Characterization of photoelectric polymeric material by using capacitive transducers
Alessandro Auditore, Salvatore Baglio, Paola Barrera, et al.
Electrical properties of polymeric materials, in which a transition metal complex [tris(2,2'-bipyridyl)Ru(II)]Cl2 is dispersed, are investigated, under light irradiation conditions, as a function of the complex concentration and of the light intensity and pulse duration. This idea is based on the fact that light absorption produces, as result of the electronic excitation, a temporary change in the electrical dipole moment of the metal complex and this in turn results in changes induced, under light stimulus, in capacitances, whose dielectric is mainly made by the polymeric compound. The material characterization system is therefore based on interdigitated planar capacitors over which the polymeric compound is deposited. The light action induces changes in the dielectric properties of the polymer and these changes reflect into the capacitance value and are in turn converted into an output voltage by suitable capacitance-to-voltage signal conditioning circuits. A differential configuration is adopted in these circuits, based on a dummy interdigitated transducers coated with the same polymer but shielded from the light stimulus, in order to filter out unwanted spurious signals.
Physiological Signals
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Stochastic dynamics of the cardiovascular system
The human cardiovascular system (CVS), responsible for the delivery of nutrients and removal of waste products to/from the entire body, is a highly complex system involving many control mechanisms. Signals derived from the CVS are inherently difficult to analyse because they are noisy, time-varying, and of necessarily limited duration. The application of techniques drawn from nonlinear science has, however, yielded many insights into the nature of the CVS, and has provided strong evidence for a large degree of determinism in the way it functions. Yet there is compelling evidence that random fluctuations (noise) also play an essential role. There are at least five oscillatory processes of widely differing frequency involved in the blood distribution. The evidence for them, and their probable physiological origins, are discussed. Interactions between some of the processes can give rise to modulation and synchronization phenomena, very similar to those observed in classical oscillators in many areas of physics. The extent to which the CVS can be modelled as a stochastic nonlinear dynamical system is reviewed, and future research directions and possible applications based on this perception are considered.
Nonlinear Dynamics in Biology
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Noise and synchronization on micro and macroscopic scales
The complexities exhibited by biological systems are highly intriguing. Their activity can span both micro and macroscopic scales simultaneously. Often noise plays an important role. So, the analysis of the dynamical properties of such systems poses a major challenge. In this paper we introduce an approach that is applicable within both the micro and macroscopic worlds, where a large number of oscillators acting on a similar time scale can be represented as an ensemble that, on the macroscopic scale, may be taken as a single oscillator. On the macroscopic scale they interact with other similar type of oscillators, but usually on widely different time scales. We use recently introduced nonlinear dynamics methods and methods derived from information theory, and extend their application to oscillations acting on micro and macroscopic scales at the same time. We demonstrate such interactions using numerical examples and real physiological data related to cardiac, respiratory and brain activities.
Evidence for the origins and breakdown of 1/f noise in heart rate
Zbigniew R. Struzik, Junichiro Hayano, Seiichiro Sakata, et al.
We present the first systematic evidence for the origins and breakdown of 1/f scaling in human heart rate. We confirm a previously posed conjecture that 1/f scaling in heart rate is caused by the intricate balance between antagonistic activity of sympathetic (SNS) and parasympathetic (PNS) nervous systems. We demonstrate that modifying the relative importance of either of the two branches leads to a substantial decrease of 1/f scaling. In particular, the relative PNS suppression both by congestive heart failure (CHF) and by the parasympathetic blocker atropine results in a substantial increase in the Hurst exponent H and a shift of the multifractal spectrum f(α) from 1/f towards random walk scaling 1/f2. Surprisingly, we observe a similar breakdown in the case of relative and neurogenic SNS suppression by primary autonomic failure (PAF). Further, we observe an intriguing interaction between multifractality of heart rate and absolute variability. While it is generally believed that lower absolute variability results in monofractal behaviour, as has been demonstrated both for CHF and the parasympathetic blockade, in PAF patients we observe conservation of multifractal properties at substantially reduced absolute variability to levels closer to CHF. This novel and intriguing result leads us to the conjecture that the multifractality of the heart rate can be traced back to the intrinsic dynamics of the parasympathetic nervous system.
A realistic coupled nonlinear artificial ECG, BP, and respiratory signal generator for assessing noise performance of biomedical signal processing algorithms
Extensions to a previously published nonlinear model for generating realistic artificial electrocardiograms to include blood pressure and respiratory signals are presented. The model accurately reproduces many of the important clinical qualities of these signals such as QT dispersion, realistic beat to beat variability in timing and morphology and pulse transit time. The advantage of this artificial model is that the signal is completely known (and therefore its clinical descriptors can be specified exactly) and contains no noise. Artifact and noise can therefore be added in a quantifiable and controlled manner in order to test relevant biomedical signal processing algorithms. Application examples using Independent Component Analysis to remove artifacts are presented.
Memory in diffusive systems
Steffen Trimper, Knud Zabrocki
The classical rate equations for the concentration p(x,t) or the probability density in the diffusion-limited regime are extended by including non-Markovian terms. We present analytical and numerical results for a whole class of evolution models with conserved p, where the underlying equations are of convolution type with temporally and spatially varying memory kernels. Based on our recent studies in the reaction-limited case with memory, we study now the influence of time and spatial couplings. Due to the balance between the conventional diffusive current and the additional force, originated by the feedback, the system exhibits a non-trivial stationary solution which depends on both the initial distribution and the memory strength. For a non-linear memory kernel of KPZ-type we get an asymptotic exact solution. Although the mean square displacement offers ultimately diffusion, the distribution function is determined by the memory strength, too. Differences to diffusion are observed in higher order cumulants. For an arbitrary memory kernel we find a criteria which enables us to get a non-trivial stationary solution.
Gene Expression and Regulation
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Effective simulation techniques for biological systems
Kevin Burrage, Tianhai Tian
In this paper we give an overview of some very recent work on the stochastic simulation of systems involving chemical reactions. In many biological systems (such as genetic regulation and cellular dynamics) there is a mix between small numbers of key regulatory proteins, and medium and large numbers of molecules. In addition, it is important to be able to follow the trajectories of individual molecules by taking proper account of the randomness inherent in such a system. We describe different types of simulation techniques (including the stochastic simulation algorithm, Poisson Runge-Kutta methods and the Balanced Euler method) for treating simulations in the three different reaction regimes: slow, medium and fast. We then review some recent techniques on the treatment of coupled slow and fast reactions for stochastic chemical kinetics and discuss how novel computing implementations can enhance the performance of these simulations.
Ion Channels
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Near-membrane protein dynamics revealed by evanescent field microscopy
Evanescent Field (EF) microscopy is used to investigate the spatial and temporal dynamics of proteins in living cells. A genetically engineered ion channel fused to a fluorescent tag is expressed in cells and imaged with an objective-based EF microscope. Images are obtained from a CCD and analyzed to determine fluorescence and velocity of individual protein containing vesicles. An inverse correlation between fluorescent intensity and average motility provides a method for determination of membrane localization. Stimulation and subsequent decrease in ion channel activity is correlated with loss of protein from membrane as shown by EF microscopy and patch-clamp electrophysiology.
Ionic current through an open channel: a low-dimensional model of coupling with vibrations of the wall
Rodrigue Tindjong, Alan Applegate, Robert S. Eisenberg, et al.
Ionic motion through an open ion channel is analyzed within the framework of self-consistent Brownian dynamics formalism. A novel conceptual model of coupling of the ion's motion to the vibrations of the pore walls is introduced. The model allows one to include into simulations an important additional mechanism of energy dissipation and the effects of self-induced strong modulation of the channel conductivity.
Models of boundary behavior of particles diffusing between two concentrations
Amit Singer, Zeev Schuss, Boaz Nadler, et al.
Flux between regions of different concentration occurs in nearly every device involving diffusion, whether an electrochemical cell, a bipolar transistor, or a protein channel in a biological membrane. Diffusion theory has calculated that flux since the time of Fick (1855), and the flux has been known to arise from the stochastic behavior of Brownian trajectories since the time of Einstein (1905), yet the mathematical description of the behavior of trajectories corresponding to different types of boundaries is not complete. We consider the trajectories of non-interacting particles diffusing in a finite region connecting two baths of fixed concentrations. Inside the region, the trajectories of diffusing particles are governed by the Langevin equation. At the interface between the region and the baths, trajectories are set by a control mechanism that modifies dynamics so the concentration of particles remains (nearly) constant. We analyze different models of controllers and derive equations for the time evolution and spatial distribution of particles inside the domain. Our analysis shows a distinct difference between the time evolution and the steady state concentrations. While the time evolution of the density is governed by an integral operator, the spatial distribution is governed by the familiar Fokker-Planck operator. The boundary conditions for the time dependent density depend on the model of the controller; however, this dependence disappears in the steady state, if the controller is of a renewal type. Renewal-type controllers, however, produce spurious boundary layers that can be catastrophic in simulations of charged particles, because even a tiny net charge can have global effects. The design of a non-renewal controller that maintains concentrations of non-interacting particles without creating spurious boundary layers at the interface requires the solution of the time-dependent Fokker-Planck equation with absorption of outgoing trajectories and a source of ingoing trajectories on the boundary (the so called albedo problem).
Posters-Wednesday
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Behavioral stochastic resonance associated with large-scale synchronization of human brain activity
Keiichi Kitajo, Kentaro Yamanaka, Daichi Nozaki, et al.
We demonstrate experimentally that enhanced detection of weak visual signals by addition of visual noise is accompanied by an increase in phase synchronization of EEG signals across widely-separated areas of the human brain. In our sensorimotor integration task, observers responded to a weak rectangular gray-level signal presented to their right eyes by pressing and releasing a button whenever they detected an increment followed by a decrement in brightness. Signal detection performance was optimized by presenting randomly-changing-gray-level noise separately to observers' left eyes using a mirror stereoscope. We measured brain electrical activity at the scalp by electroencephalograph (EEG), calculated the instantaneous phase for each EEG signal, and evaluated the degree of large-scale phase synchronization between pairs of EEG signals. Dynamic synchronization-desynchronization patterns were observed and we found evidence of noise-enhanced large-scale synchronization associated with detection of the brightness changes under conditions of noise-enhanced performance. Our results suggest that behavioral stochastic resonance might arise from noise-enhanced synchronization of neural activities across widespread brain regions.
Exchange of information in the brain: from biological neural networks to electrical neural networks
Luigi Fortuna, Maide Bucolo, Manuela La Rosa, et al.
In this work neuron information exchanges have been investigated by modeling nonlinear lattices by connecting Hindmarsh-Rose neurons. In the first phase, regular network models have been characterized by varying the coupling strength in bidimensional arrays of neurons. In the second one, dynamical behavior of 2-D small world configurations, with long term connections, has been considered. Several experiments have been characterized by quantifying a synchronization index. A trade off between network architecture complexity and information exchange performances has been discussed.
Stochastic resonance in arrays of neurons
Luigi Fortuna, Mattia Frasca, Manuela La Rosa, et al.
The concept of stochastic resonance introduced the idea that the presence of noise in nonlinear systems may have benefic effects. In this paper different regular topologies of populations of FitzHugh-Nagumo neurons have been investigated with respect to the presence of noise in the network. Each neuron is subjected to an independent source of noise. In these conditions the behavior of the population depend on the connection among the elements. In population of uncoupled neurons the so-called stochastic resonance without tuning was observed. Moreover, we show that globally coupled neurons have increasing response-to-stimulus coherence for increasing values of the coupling strength. In locally coupled neurons the performance depend on the neighborhood radius and in general are higher than in the case of uncoupled neurons.
Estimation of the variance of the variance: implications for multiple-probability fluctuation analysis at central synapses
Chiara Saviane, R. Angus Silver
Synapses play a crucial role in information processing in the brain. Amplitude fluctuations of synaptic responses can be used to extract information about the mechanisms underlying synaptic transmission and its modulation. In particular, multiple-probability fluctuation analysis uses the variance and mean amplitude of postsynaptic responses, recorded at different probabilities, to estimate the number of functional releasing sites, the mean probability of release and the amplitude of single quantal responses. We investigated the best estimators of the variance of the variance in order to improve the estimates of quantal parameters. We used simulations of synaptic transmission to test the accuracy and reliability of estimators under different experimental conditions. For central synapses, which generally have a low number of releasing sites, the amplitude distribution of synaptic responses is not normal, thus the use of a theoretical variance of the variance based on the normal assumption is not a good approximation. However, appropriate estimators can be derived for the population and for limited sample sizes using a more general expression that involves higher moments and introducing unbiased estimators based on the h-statistics. Our results are likely to be relevant for various applications of fluctuation analysis when few channels or releasing sites are present.
A kinetic model of NMDA ion channel under varying noise
Rubin Wang, Hao Chen, Zhikang Zhang
It is well known that when transmitters are applied to the postsynaptic membrane, the resulting depolarization is noisy that is due to the random opening and closing of the ion channels activated by the transmitters[1]. In other words, the energy of noise is associated with changes in ion channels. On the base of these ideas, we explore a model of relationship between NMDA (n-methyl-D-aspartate) ion channels and LTP (long-term synaptic potentiation). We have proved that NMDA ion channel and calcium-dependent protein kinases, which are the triggers for the inducement of LTP, could be regarded as “molecular machines”. In this system all of these molecules require energy and the energy of the system is supplied from the random motion of water molecules generated through heat energy of ATP hydrolysis[2]. So the appropriate framework to describe them comes from bioenergetics. Models of LTP previously reported are all on the macroscopic level [3-7]. Instead, we research a model at the molecular level by applying energy parameters [8].
Probing temporal correlation in ventricular interbeat intervals during atrial fibrillation with local continuous DFA
Using the method of local Continuous Detrended Fluctuation Analysis CDFA) we analyze the correlations of ventricular interbeat intervals of patients with Atrial Fibrillation (AF). CDFA yields a local Hoelder exponent h for a neighborhood around each point in the time series by determining the scaling of fluctuations with window size after detrending. We compare the histograms of Hoelder exponents for original data with those of randomly shuffled data and find some correlations not only in long-range windows but also at short time scales where interbeat intervals during AF have been believed to be random in nature. Furthermore, we find unique temporal correlation structures to occur only in the heart rate of patients who were in the survivor group when a follow up was conducted at least one year after data acquisition. We conclude that ventricular interbeat intervals during AF contain richer information than previously considered and the study of the local correlations may be useful in predicting mortality of the patients.
Activation process driven by strong non-Gaussian noises
The constructive role of non-Gaussian random fluctuations is studied in the context of the passage over the dichotomously switching potential barrier. Our attention focuses on the interplay of the effects of independent sources of fluctuations: an additive stable noise representing non-equilibrium external random force acting on the system and a fluctuating barrier. In particular, the influence of the structure of stable noises on the mean escape time and on the phenomenon of resonant activation (RA) is investigated. By use of the numerical Monte Carlo method it is documented that the suitable choice of the barrier switching rate and random external fields may produce resonant phenomenon leading to the enhancement of the kinetics and the shortest, most efficient reaction time.
Motion analysis of flagellar bacteria
Maide Bucolo, Adriano Basile, Luigi Fortuna, et al.
Nanotechnology finds in flagellar bacteria an uncomparable example of a very efficient and miniaturized motor. This and the complex behavior of the bacteria colonies growth in a self-organized way make the study of flagellar bacteria very important and appealing for possible applications. For these reasons in this work single bacterium motion and colonies growth have been studied by applying nonlinear methods. The characterization of the single bacterium motion leads to the conclusion that determinism (due to chemotaxis) is predominant with respect to random terms. This result is confirmed by the possibility of modelling the case study of colonies growth through an activation/inhibition dynamics.
Cloud denoising
Salvador Gabarda, Gabriel Cristobal, Lorenzo Galleani, et al.
We address the issue of cloud removal from images. Typically a cloud on an image is not uniform and we develop methods that do denoising on a local level. In this paper we present preliminary studies of such methods and also a method for image fusion. The procedure is based on the use of a denoising pixel-level measure. The measure is defined through a 1-D Pseudo Wigner Distribution (PWD) applied to non-overlapping N-pixel window slices of the original image. The method is illustrated with different set of artificial and natural cloudy or foggy images, which are partially occluded by clouds in different regions. Another advantage of the present approach is its reduced computational cost in comparison with other methods based on a full 2-D implementation of the PWD.