Life support with a mechanical ventilator is used to manage patients with a variety of lung diseases including acute respiratory distress syndrome (ARDS). Recently, management of ARDS has concentrated on ventilating at lower airway pressure using lower tidal volume. A large international study demonstrated a 22% reduction in mortality with the low tidal volume approach. The potential advantages of adding physiologic noise with fractal characteristics to the respiratory rate and tidal volume as delivered by a mechanical ventilator are discussed. A so-called biologically variable ventilator (BVV), incorporating such noise, has been developed. Here we show that the benefits of noisy ventilation - at lower tidal volumes - can be deduced from a simple probabilistic result known as Jensen’s Inequality. Using the local convexity of the pressure-volume relationship in the lung we demonstrate that the addition of noise results in higher mean tidal volume or lower mean airway pressure. The consequence is enhanced gas exchange or less stress on the lungs, both clinically desirable. Jensen’s Inequality has important considerations in engineering, information theory and thermodynamics. Here is an example of the concept applied to medicine that may have important considerations for the clinical management of critically ill patients. Life support devices, such as mechanical ventilators, are of vital use in critical care units and operating rooms. These devices usually have monotonous output. Improving mechanical ventilators and other life support devices may be as simple as adding noise to their output signals.

Heart rate (HR) fluctuations provide a well-known example of fractal stochastic dynamics of physiological functions with a 1/f power spectrum. So far, this type of HR behavior has been documented for the frequency range 0.1-10 mHz. In this paper, we report the results of a case study based on a long-term HR monitoring performed during a period of 38 months. The analyzed database consisted of over 1200 samples of R-R interval fluctuations of single person with the average sample duration of 10 minutes and average inter-sample time interval 1 day. For each of the 10-minute samples, a set of statistical and nonlinear parameters has been evaluated based on the FFT spectral analysis and the detrended fluctuation analysis technique. It has been found that time series of many of the studied parameters (mean value and standard deviation of R-R interval, spectral power of R-R fluctuations in standard frequency bands of clinical HR variability analysis, etc.) demonstrate extra-low frequency organization involving frequency range 0.00005-0.005 mHz (time scales 20 to 200 days) . The revealed correlations manifest themselves in a 1/f-like spectral behavior similar to the behavior detected earlier at considerably shorter time scales of HR fluctuations. Participation of the central nervous system in the extra slow HR variations has been confirmed experimentally and shown to reflect long-term adaptation dynamics of human homeostasis in a complex fluctuating environment.

The ear relies on nonlinear amplification to enhance its sensitivity and frequency selectivity. It has been suggested that this active process results from dynamical systems which oscillate spontaneously. In the bullfrog sacculus, hair bundles, which are the mechanosensitive elements of sensory hair cells display noisy oscillations. These oscillations can be described in a simple model which takes into account the properties of mechanosensitive ion channels coupled to motor proteins which are regulated by inflowing Ca²⁺ ions. The role of fluctuations can be studied by adding random forcing terms with characteristic amplitudes that result from the number and properties of ion channels and motor molecules. This description can account quantitatively for the experimentally measured linear and nonlinear response functions and reveals the relevance of fluctuations for signal detection.

We have previously advocated the deliberate addition of noise to cochlear implant signals to enhance the speech comprehension of cochlear implant users. The function of the additive noise is to mimic noise sources that are present in a healthy ear (originating, for example, from Brownian motion of the hair cells and the fluctuations induced by the opening and closing of ion channels) but are largely absent in a deafened ear where the hair cells have been damaged or destroyed. The normal ear, however, also contains multiplicative noise sources that result from the quantal nature of synaptic transmission between the inner hair-cells and the cochlear nerve. These noise synaptic noise sources are also largely absent in the deafened ear. Given that previous studies suggest that additive noise can enhance information coding by sensory systems, we have investigated whether multiplicative noise also enhances coding in a model of electrical stimulation of the cochlear nerve by a cochlear implant. The model was based on leaky integrate-and-fire dynamics and modelled refractory and accommodation effects by a threshold dependency derived from the sodium-inactivation dynamics of the Frankenhauser-Huxley equations for myelinated nerves. We show that multiplicative noise leads to a fundamental change in the coding mechanism and can lead to a marked increase in the transmitted information compared with additive noise or a control condition with no noise. These results suggest that multiplicative noise in the normal auditory system might have a functional role.

We have investigated information transmission in an array of threshold units with multiplicative noise that have a common input signal. We demonstrate a phenomenon similar to stochastic resonance with additive noise, and show that information transmission can be enhanced by a non-zero multiplicative noise level. Given that sensory neurons in the nervous system have multiplicative as well as additive noise sources, and they act approximately like threshold units, our results suggest that multiplicative noise might be an essential part of neural coding.

We demonstrate experimentally that the human brain can make use of externally added noise to modulate attention switching between spatial locations. To do this we implemented a psychophysical task. Subjects were asked to respond to a weak gray-level target presented inside a marker box either in the left or right visual field while they fixated a central cross. Signal detection performance was improved by presenting a low level of randomly flickering gray-level noise between and outside the two possible target locations, and worsened by higher levels of noise. Our results suggest that noise can optimize switching behavior between multistable attentional states of the human brain via the mechanism of stochastic resonance.

We have studied the memory effect on typical complex measures such as fractal dimension and entropy based on the sample entropy algorithm. First, it is shown how is the stochastic process of complex measures (a local fractal dimension and a local sample entropy) for real EEG data from healthy people and demented ones. The features of multi-scale entropy for EEGs are also shown. Then, the natures of complex measures for theoretical models such as Brownian oscillators and stochastic complex Ginzburg-Landau equation are exhibited. The memory effects on the complex measures for real EEG data are discussed by comparing theoretical models.

Genomics represents a challenging research field for many quantitative scientists, and recently a vast variety of statistical techniques and machine learning algorithms have been proposed and inspired by cross-disciplinary work with computational and systems biologists. In genomic applications, the researcher deals with noisy and complex high-dimensional feature spaces; a wealth of genes whose expression levels are experimentally measured, can often be observed for just a few time points, thus limiting the available samples. This unbalanced combination suggests that it might be hard for standard statistical inference techniques to come up with good general solutions, likewise for machine learning algorithms to avoid heavy computational work. Thus, one naturally turns to two major aspects of the problem: sparsity and intrinsic dimensionality. These two aspects are studied in this paper, where for both denoising and dimensionality reduction, a very efficient technique, i.e., Independent Component Analysis, is used. The numerical results are very promising, and lead to a very good quality of gene feature selection, due to the signal separation power enabled by the decomposition technique. We investigate how the use of replicates can improve these results, and deal with noise through a stabilization strategy which combines the estimated components and extracts the most informative biological information from them. Exploiting the inherent level of sparsity is a key issue in genetic regulatory networks, where the connectivity matrix needs to account for the real links among genes and discard many redundancies. Most experimental evidence suggests that real gene-gene connections represent indeed a subset of what is usually mapped onto either a huge gene vector or a typically dense and highly structured network. Inferring gene network connectivity from the expression levels represents a challenging inverse problem that is at present stimulating key research in biomedical engineering and system biology. Several attempts have been made to describe gene networks with only limited interactions, thus exploiting the inherent sparsity of these systems. This in turn suggests that a certain redundancy of links in gene networks, or equivalently the inherent sparsity structure of these systems, might let the essential connections be identified and the inverse problem be given both satisfactory definition and computationally efficient tractability.

In this paper we address the fundamental issue of temperature fluctuation during the thermal denaturation (or the unzipping of the two strands on heating) of double stranded (ds) DNA. From our experiments we observe the presence of extremely high thermal fluctuations during DNA denaturation. This thermal fluctuation is several orders higher than the thermal fluctuation at temperatures away from the denaturation temperature range. This fluctuation is absent in single stranded (ss) DNA. The magnitude of fluctuation is much higher in heteropolymeric DNA and is almost absent in short homopolymeric DNA fragments. The temperature range over which the denaturation occurs (i.e., over which the thermal fluctuation is large) depends on the length of the DNA and is largest for the longest DNA.

Protein-mediated DNA looping, which occurs when a linker protein binds to two operator sites on the same DNA molecule, is an important regulatory element of many biological processes such as transcription and DNA replication. In physiologic conditions, the conformation of DNA undergoes thermal fluctuations which enable the operators to align for looping. The likelihood for the operator sites to align can be significantly altered by mechanically constraining the substrate DNA. For instance, tension extends DNA and increases the free energy of operator alignment. By modeling DNA as a wormlike chain, we use statistical mechanics to show that when the loop size is greater than 100bp a tension of 500 femtonewtons can increase the time required for loop closure by two orders of magnitude. This force is small compared to the piconewton forces that are associated with RNA polymerases and other molecular motors, indicating that intracellular mechanical forces might affect transcriptional regulation. We propose that supercoiling of DNA may help to stabilize the looping process against the disruptive effective of tension. Since DNA looping is important in gene regulation and genetic transformation, our theory suggests that thermal fluctuations and response to mechanical constraints play an important role in a living cell. Indeed, recent micromechanical measurements on DNA looping have verified the importance of mechanical constraints. Besides providing perspective on these experiments we offer suggestions for future micromechanical studies.

Studying the thermal fluctuations of DNA molecules reveals not only a wealth of interesting equilibrium and non-equilibrium statistical mechanics, but is also of importance for understanding the dynamics of DNA in vivo. An instance of the latter is in the context of regulatory functions that require collaborative interactions of distant operator sites on the DNA molecule. These thermal fluctuations are extremely sensitive to mechanical constraints, such as supercoiling or mechanical tension in the DNA. The natural force scale f_c on which these fluctuations are sensitive to tension is related to the persistence length l_p by f_c = k_BT/l_p = 80 fN, which is generally considered small for a crowded cellular environment. We are studying the dynamics of single DNA molecules under tension under equilibrium conditions using a modified scanning-line laser trap. This technique allows us to apply a constant force between 20 fN and 3 pN to a λ-DNA molecule while we measure fluctuations of its extension with sub-millisecond time resolution. We compute the time-correlation functions of these fluctuations to determine their time constants, and model them with a simple bead-and-spring model. We observe a decrease of the fundamental time constant with increasing extension of the molecule. This suggests that the change in spring constant dominates changes in the intra-chain hydrodynamic coupling between segments as the Gaussian coil unravels into an extended conformation.

Ionizing radiation is responsible for production of double strand breaks (DSB) in a DNA structure. In contrast to sparsely ionizing radiation, densely ionizing radiation produces DSBs that are randomly distributed along the DNA molecule and can form clusters of various size. The paper discusses minimalistic models that describe observable pattern of distribution of fragment lengths in DNA segments irradiated with heavy ions and applies the formalism to interpret the recent experimental data collected by use of the atomic force microscope (AFM).

The breakdown of biogeographic barriers allows some invasive species to reshape ecological communities and threaten local biodiversity. Most introductions of exotic species fail to generate an invasion. However, once introduction succeeds, invader density increases rapidly. We apply nucleation theory to describe spatio-temporal patterns of the invasion process under preemptive competition. The predictions of the theory are confirmed by Monte Carlo simulations of the underlying discrete spatial stochastic dynamics. In particular, for large enough spatial regions, invasion occurs through the nucleation and subsequent growth of many clusters of the invasive species, and the global densities are well approximated by Avrami's law for homogeneous nucleation. For smaller systems or very small introduction rates, invasion typically occurs through a single cluster, whose appearance is inherently stochastic.

A method for increasing the specificity of an MR image using noise correlation measurements is presented. From an MR image different regions within the body are identified based on contrast. Noise signals measured at the ports of the experimental setup are functions of the conductivity at each region and the sensitivity map of the field probes. For a simulated sensitivity map, the ratio of conductivities of two regions of a phantom containing saline and distilled water was determined from the measured noise correlation at the ports.

Preliminary results are reported from a research project analysing congestive heart failure in terms a stochastic coupled-oscillator model of the cardiovascular system. Measurements of blood flow by laser Doppler flowmetry (LDF) have been processed by use of the wavelet transform to separate its oscillatory components, which number at least five. Particular attention was concentrated on the frequency content near 0.01 Hz, which is known to be associated with endothelial function. The LDF was carried out in conjunction with iontophoretically administered acetylcholine (ACh) and sodium nitroprusside (SNP) in order to evaluate endothelial reactivity. Measurements were made on 17 congestive heart failure (CHF) patients (a) on first diagnosis, and (b) again several weeks later after their treatment with a β-blocker had been stabilised. The results of these two sets of measurements are being compared with each other, and with data from an age and sex-matched group of healthy controls. It is confirmed that endothelial reactivity is reduced in CHF patients, as compared to healthy controls, and it is found that one effect of the Beta-blocker is to ameliorate the loss of endothelial function in CHF. The implications of these results are discussed.

The electrical activity of the heart (ECG), respiratory function and electric activity of the brain (EEG) were simultaneously recorded in conscious, healthy humans. Instantaneous frequencies of the heart beat, respiration and α-waves were then determined from 30-minutes recordings. The instantaneous cardiac frequency was defined as the inverse value of the time interval between two consecutive R-peaks. The instantaneous respiratory frequency was obtained from recordings of the excursions of thorax by application of the Hilbert transform. To obtain the instantaneous frequency of α-waves, the EEG signal recorded from the forehead was first analysed using the wavelet transform. Then the frequency band corresponding to α-waves was extracted and the Hilbert transform applied. Synchronization analysis was performed and the direction of coupling was ascertained, using pairs of instantaneous frequencies in each case. It is shown that the systems are weakly bidirectionally coupled. It was confirmed that, in conscious healthy humans, respiration drives cardiac activity. We also demonstrate from these analyses that α-activity drives both respiration and cardiac activity.

Neurons often display complex patterns of action potential firing in response to a wide variety of inputs. Correlations amongst the interspike interval sequence are often seen in experimental data from sensory neurons including electroreceptor afferents from weakly electric fish. Here we review some of our recent computational, theoretical, and experimental results on the mechanism by which negative interspike interval correlations increase information transfer: noise shaping. This mechanism might explain the behavioral hypersensitivity displayed by weakly electric fish when detecting prey.

It is shown that Suprathreshold Stochastic Resonance (SSR) is effectively a way of using noise to perform quantization or lossy signal compression with a population of identical threshold-based devices. Quantization of an analog signal is a fundamental requirement for its efficient storage or compression in a digital system. This process will always result in a loss of quality, known as distortion, in a reproduction of the original signal. The distortion can be decreased by increasing the number of states available for encoding the signal (measured by the rate, or mutual information). Hence, designing a quantizer requires a tradeoff between distortion and rate. Quantization theory has recently been applied to the analysis of neural coding and here we examine the possibility that SSR is a possible mechanism used by populations of sensory neurons to quantize signals. In particular, we analyze the rate-distortion performance of SSR for a range of input SNR's and show that both the optimal distortion and optimal rate occurs for an input SNR of about 0 dB, which is a biologically plausible situation. Furthermore, we relax the constraint that all thresholds are identical, and find the optimal threshold values for a range of input SNRs. We find that for sufficiently small input SNRs, the optimal quantizer is one in which all thresholds are identical, that is, the SSR situation is optimal in this case.

We study the response time of a neuron in the transient regime of FitzHugh-Nagumo model, in the presence of a suprathreshold signal and noise sources. In the deterministic regime we find that the activation time of the neuron has a minimum as a function of the signal driving frequency. In the stochastic regime we consider two cases: (a) the fast variable of the model is noisy, and (b) the slow variable, that is the recovery variable, is subjected to fluctuations. In both cases we find two noise-induced effects, namely the resonant activation-like and the noise enhanced stability phenomena. The role of these noise-induced effects is analyzed. The first one produces suppression of noises, while the second one delays the neuron response. Finally, the role of the phase of the driving signal on the transient dynamics of the neuron is analyzed.

In an era of potential bioterrorism and pandemics of antibiotic-resistant microbes, bacterial contaminations of food and water supplies is a major concern. There is an urgent need for the rapid, inexpensive and specific identification of bacteria under field conditions. Here we describe a method that combines the specificity and avidity of bacteriophages with fluctuation analysis of electrical noise. The method is based on the massive, transitory ion leakage that occurs at the moment of phage DNA injection into the host cell. The ion fluxes require only that the cells be physiologically viable (i.e., have energized membranes) and can occur within seconds after mixing the cells with sufficient concentrations of phage particles. To detect these fluxes, we have constructed a nano-well, a lateral, micron-size capacitor of titanium electrodes with gap size of 150 nm, and used it to measure the electrical field fluctuations in microliter (mm³) samples containing phage and bacteria. In mixtures where the analyte bacteria were sensitive to the phage, large stochastic waves with various time and amplitude scales were observed, with power spectra of approximately 1/f² shape over at 1 - 10 Hz. Development of this SEPTIC (SEnsing of Phage-Triggered Ion Cascades) technology could provide rapid detection and identification of live, pathogenic bacteria on the scale of minutes, with unparalleled specificity. The method has a potential ultimate sensitivity of 1 bacterium/microliter (1 bacterium/mm³).

The fluctuation of the distance between a fluorescein-tyrosine pair within a single protein complex was directly monitored in real time by photo-induced electron transfer, and found to be a stationary, time-reversible and non-Markovian Gaussian process. Within the generalized Langevin equation (GLE) formalism, we experimentally determine the memory kernel, K(t), which is proportional to the autocorrelation function of the random fluctuating force. K(t) is a power-law decay, t^{- 0.51 ± 0.07} in a broad range of time-scales (10^-3 s -10s. Such a long time memory effect, which is associated with sub-diffusion within a harmonic bound, has implications to protein functions.

We propose a quantum information scheme that builds on the interference properties of entangled ion states that are transiently confined by local potentials within the permeation path of voltage-gated, ion-conducting membrane proteins. We show, that the sub-molecular organization of parts of the protein, as revealed by the recent progress in high-resolution atomic-level spectroscopy and accompaning molecular dynamics simulations, carries a logical coding potency that goes beyond the pure catalytic function of the channel, subserving the transmembrane crossing of an electrodiffusive barrier. As we argue that 'within channel states' can become super-correlated with the environment , this also sheds new light on the role of noise in controlling the access of ions to voltage-gated ion channels ('channel noise').

Electroencephalograph (EEG) analysis enables the dynamic behavior of the brain to be examined. If the behavior is nonlinear then nonlinear tools can be used to glean information on brain behavior, and aid in the diagnosis of sleep abnormalities such as obstructive sleep apnea syndrome (OSAS). In this paper the sleep EEGs of a set of normal children and children with mild OSAS are evaluated for nonlinear brain behaviour. We found that there were differences in the nonlinearity of the brain behaviour between different sleep stages, and between the two groups of children.