Sturdy cycles in the chaotic Tribolium castaneum data series

Because of the inherent discreteness of individuals, population dynamical models must be discrete variable systems. In case of strong nonlinearity, such systems interacting with noise can generate a great variety of patterns from nearly periodic behavior through complex combination of nearly periodic and chaotic patterns to noisy chaotic time series. The interaction of a population consisting of discrete individuals and demographic noise has been analyzed in laboratory population data Henson et al. (Science 294 (2001) 602; Proc. Roy. Soc. Ser. B 270 (2003) 1549). In this paper we point out that some of the cycles are fragile, i.e. they are sensitive to the discretization algorithm and to small variation of the model parameters, while others remain "sturdy" against the perturbations. We introduce a statistical algorithm to detect disjoint, nearly-periodic patterns in data series. We show that only the sturdy cycles of the discrete variable models appear in the data series significantly. Our analysis identified the quasiperiodic 11-cycle (emerging in the continuous model) to be present significantly only in one of the three experimental data series. Numerical simulations confirm that cycles can be detected only if noise is smaller than a certain critical level and population dynamics display the largest variety of nearly-periodic patterns if they are on the border of "grey" and "noisy" regions, defined in Domokos and Scheuring (J. Theor. Biol. 227 (2004) 535).     

Only noise can induce chaos in discrete populations

Motivated by the papers from Ellner and Turchin 2005 and Dennis et al. 2003 we investigate the possibility to detect chaos in noisy ecological systems. One message of our paper is that if a dynamic model is available and if this model predicts chaotic behaviour, one should consider its discrete-state, noisy version when fitting numerical predictions to observations. We emphasize that deterministic discrete-state models behave periodically, thus only the interaction of these deterministic skeletons with random noise can produce non-regular dynamics. We detect and describe a relatively sharply defined range of the noise (the grey zone) where the gradual transition from periodic to chaotic behaviour happens. This zone, the upper border of which can be predicted analytically, is identified in experimental data as well as in numerical simulations. In the grey zone the global, statistical behaviour will approach the statistics produced by the chaotic, continuous model, and in this sense we claim that noise can produce chaos.     

Analysis of kinetics using a hybrid maximum-entropy/nonlinear-least-squares method: application to protein folding

A hybrid analysis that combines the maximum entropy method (MEM) with nonlinear least squares (NLS) fitting has been developed to interpret a general time-dependent signal. Data that include processes of opposite sign and a slow baseline drift can be inverted to obtain both a continuous distribution of lifetimes and a sum of discrete exponentials. Fits by discrete exponentials are performed with initial parameters determined from the distribution of lifetimes obtained with the MEM. The regularization of the parameter space achieved by the MEM stabilizes the introduction of each successive exponential in the NLS fits. This hybrid approach is particularly useful when fitting by a large number of exponentials. Revision of the MEM "prior" based on features in the data can improve the lifetime distribution obtained. Standard errors in the mean are estimated automatically for raw data. The results presented for simulated data and for fluorescence measurements of protein folding illustrate the utility and accuracy of the hybrid algorithm. Analysis of the folding of dihydrofolate reductase reveals six kinetic processes, one more than previously reported.     

High-order behaviour in learning gate networks with lateral inhibition

In this work we present a neural network model incorporating activity-dependent presynaptic facilitation with multidimensional inputs. The processing unit used is based on a slightly simplified version of the Learning Gate Model proposed by Ciaccia et al. (1992). The network topology integrates a well-known biological neural circuit with a lateral inhibition connection subnet. By means of simulation experiments, we show that the proposed networks exhibit basic and high-order features of associative learning. In particular, overshadowing and blocking are reproduced in the presence of both noise-free and noisy inputs. The role of noise in the development of high-order learning capabilities is also discussed.This article was processed by the author using the LAT_EX style file pljour2 from Springer-Verlag.     

Noise

The proliferation of DNA sequence data has generated a concern about the effects of "noise" on phylogeny reconstruction. This concern has led to various recommendations for weighting schemes and for separating data types prior to analysis. A new technique is explored to examine directly how noise influences the stability of parsimony reconstruction. By appending purely random characters onto a matrix of pure signal, or by replacing characters in a matrix of signal by random states, one can measure the degree to which a matrix is robust against noise. Reconstructions were sensitive to tree topology and clade size when noise was added, but were less so when character states were replaced with noise. When a signal matrix is complemented with a noise matrix of equal size, parsimony will trace the original signal about half the time when there is only one synapomorphy per node, and about 90% of the time when there are three synapomorphies per node. Similar results obtain when 20% of a matrix is replaced by noise. Successive weighting does not improve performance. Adding noise to only some taxa is more damaging, but replacing characters in only some taxa is less so. The bootstrap and g1 (tree skewness) statistics are shown to be uninterpretable measures of noise or departures from randomness. Empirical data sets illustrate that commonly recommended schemes of differential weighting (e.g. downweighting third positions) are not well supported from the point of view of reducing the influence of noise nor are more noisy data sets likely to degrade signal found in less noisy data sets.     

On the Origins of Suboptimality in Human Probabilistic Inference

Humans have been shown to combine noisy sensory information with previous experience (priors), in qualitative and sometimes quantitative agreement with the statistically-optimal predictions of Bayesian integration. However, when the prior distribution becomes more complex than a simple Gaussian, such as skewed or bimodal, training takes much longer and performance appears suboptimal. It is unclear whether such suboptimality arises from an imprecise internal representation of the complex prior, or from additional constraints in performing probabilistic computations on complex distributions, even when accurately represented. Here we probe the sources of suboptimality in probabilistic inference using a novel estimation task in which subjects are exposed to an explicitly provided distribution, thereby removing the need to remember the prior. Subjects had to estimate the location of a target given a noisy cue and a visual representation of the prior probability density over locations, which changed on each trial. Different classes of priors were examined (Gaussian, unimodal, bimodal). Subjects'' performance was in qualitative agreement with the predictions of Bayesian Decision Theory although generally suboptimal. The degree of suboptimality was modulated by statistical features of the priors but was largely independent of the class of the prior and level of noise in the cue, suggesting that suboptimality in dealing with complex statistical features, such as bimodality, may be due to a problem of acquiring the priors rather than computing with them. We performed a factorial model comparison across a large set of Bayesian observer models to identify additional sources of noise and suboptimality. Our analysis rejects several models of stochastic behavior, including probability matching and sample-averaging strategies. Instead we show that subjects'' response variability was mainly driven by a combination of a noisy estimation of the parameters of the priors, and by variability in the decision process, which we represent as a noisy or stochastic posterior.     

Model of the pathway of –1 frameshifting: Kinetics

Programmed –1 translational frameshifting is a process where the translating ribosome shifts the reading frame, which is directed by at least two stimulatory elements in the mRNA—a slippery sequence and a downstream secondary structure. Despite a lot of theoretical and experimental studies, the detailed pathway and mechanism of the –1 frameshifting remain unclear. Here, in order to understand the pathway and mechanism we consider two models to study the kinetics of the –1 frameshifting, providing quantitative explanations of the recent biochemical data of Caliskan et al. (Cell 2014, 157, 1619–1631). One model is modified from that proposed by Caliskan et al. and the other is modified from that proposed in the previous work to explain the single-molecule experimental data. It is shown that by adjusting values of some fundamental parameters both models can give quantitative explanations of the biochemical data of Caliskan et al. on the kinetics of EF-G binding and dissociation and on the kinetics of movement of tRNAs inside the ribosome. However, for the former model some adjusted parameter values deviate significantly from those determined from the available single-molecule experiments, while for the latter model all parameter values are consistent with the available biochemical and single-molecule experimental data. Thus, the latter model most likely reflects the pathway and mechanism of the –1 frameshifting.     

Orientation variance as a quantifier of structure in texture

I consider how structure is derived from texture containing changes in orientation over space, and propose that multi-local orientation variance (the average orientation variance across a series of discrete images locales) is an estimate of the degree of organization that is useful both for spatial scale selection and for discriminating structure from noise. The oriented textures used in this paper are Glass patterns, which contain structure at a narrow range of scales. The effect of adding noise to Glass patterns, on a structure versus noise task (Maloney et al., 1987), is compared to discrimination based on orientation variance and template matching (i.e. having prior knowledge of the target's orientation structure). At all but very low densities, the variance model accounts well for human data. Next, both models' estimates of tolerable orientation variance are shown to be broadly consistent with human discrimination of texture from noise. However, neither model can account for subjects' lower tolerance to noise for translational patterns than other (e.g. rotational) patterns. Finally, to investigate how well these structural measures preserve local orientation discontinuities, I show that the presence of a patch of unstructured dots embedded in a Glass pattern produces a change in multi-local orientation variance that is sufficient to account for human detection (Hel Or and Zucker, 1989). Together, these data suggest that simple orientation statistics could drive a range of 'texture tasks', although the dependency of noise resistance on the pattern type (rotation, translation, etc.) remains to be accounted for.     

When can noise induce chaos and why does it matter: a critique

Noise‐induced chaos illustrates how small amounts of exogenous noise can have disproportionate qualitative impacts on the long term dynamics of a nonlinear system. This property is particularly clear in chaotic systems but is also important for the majority of ecological systems which are nonchaotic, and has direct implications for analyzing ecological time series and testing models against field data. Dennis et al. point out that a definition of chaos which we advocated allows a noise‐dominated system to be classified as chaotic when its Lyapunov exponent λ is positive, which misses what is really going on. As a solution, they propose to eliminate the concept of noise‐induced chaos: chaos “should retain its strictly deterministic definition”, hence “ecological populations cannot be strictly chaotic”. Instead, they suggest that ecologists ask whether ecological systems are strongly influenced by “underlying skeletons with chaotic dynamics or whatever other dynamics”– the skeleton being the hypothetical system that would result if all external and internal noise sources were eliminated. We agree with Dennis et al. about the problem – noise‐dominated systems should not be called chaotic – but not the solution. Even when an estimated skeleton predicts a system's short term dynamics with extremely high accuracy, the skeleton's long term dynamics and attractor may be very different from those of the actual noisy system. Using theoretical models and empirical data on microtine rodent cycles and laboratory populations of Tribolium, we illustrate how data analyses focusing on attributes of the skeleton and its attractor – such as the “deterministic Lyapunov exponent”λ₀ that Dennis et al. have used as their primary indicator of chaos – will frequently give misleading results. In contrast, quantitative measures of the actual noisy system, such as λ, provide useful information for characterizing observed dynamics and for testing proposed mechanistic explanations.     

Time-resolved room temperature protein phosphorescence: nonexponential decay from single emitting tryptophans.

The single room temperature phosphorescent (RTP) residue of horse liver alcohol dehydrogenase (LADH). Trp-314, and of alkaline phosphatase (AP), Trp-109, show nonexponential phosphorescence decays when the data are collected to a high degree of precision. Using the maximum entropy method (MEM) for the analysis of these decays, it is shown that AP phosphorescence decay is dominated by a single Gaussian distribution, whereas for LADH the data reveal two amplitude packets. The lifetime-normalized width of the MEM distribution for both proteins is larger than that obtained for model monoexponential chromophores (e.g., terbium in water and pyrene in cyclohexane). Experiments show that the nonexponential decay is fundamental; i.e., an intrinsic property of the pure protein. Because phosphorescence reports on the state of the emitting chromophore, such nonexponential behavior could be caused by the presence of excited state reactions. However, it is also well known that the phosphorescence lifetime of a tryptophan residue is strongly dependent on the local flexibility around the indole moiety. Hence, the nonexponential phosphorescence decay may also be caused by the presence of at least two states of different local rigidity (in the vicinity of the phosphorescing tryptophan) corresponding to different ground state conformers. The observation that in the chemically homogeneous LADH sample the phosphorescence decay kinetics depends on the excitation wavelength further supports this latter interpretation. This dependence is caused by the wavelength-selective excitation of Trp-314 in a subensemble of LADH molecules with differing hydrophobic and rigid environments. With this interpretation, the data show that interconversion of these states occurs on a time scale long compared with the phosphorescence decay (0.1-1.0 s). Further experiments reveal that with increasing temperature the distributed phosphorescence decay rates for both AP and LADH broaden, thus indicating that either 1) the number of conformational states populated at higher temperature increases or 2) the temperature differentially affects individual conformer states. The nature of the observed heterogeneous triplet state kinetics and their relationship to aspects of protein dynamics are discussed.     

Application of the maximum entropy method to absorption kinetic rate processes

The maximum entropy method, originally developed for astronomical image restoration, has already been successfully applied to a variety of biophysical problems. Through numerical inverse Laplace transformation, the method determines the lifetime distribution function with the largest informational entropy. Starting from a flat distribution, it results in the consistent selection of a single distribution from the numerous possible ones that correctly fit the data. In this paper, we discuss the application of the method to kinetic processes that have both rise and decay components, and test the algorithm with different signal to noise ratio generated data. It is proved that the mass conservation constraint can be taken into account by reducing the search to a lower dimensional subspace. The effect of noise on the width of lifetime distribution is studied and it is shown that an inherent entropy connected to the underlying kinetics can be separated from the noise generated entropy. The possibility of the application of the method to the photocycle kinetics of bacteriorhodopsin is also shown.     

Heterogeneity of human adipose blood flow

Background

The long time pharmacokinetics of highly lipid soluble compounds is dominated by blood-adipose tissue exchange and depends on the magnitude and heterogeneity of adipose blood flow. Because the adipose tissue is an infinite sink at short times (hours), the kinetics must be followed for days in order to determine if the adipose perfusion is heterogeneous. The purpose of this paper is to quantitate human adipose blood flow heterogeneity and determine its importance for human pharmacokinetics.

Methods

The heterogeneity was determined using a physiologically based pharmacokinetic model (PBPK) to describe the 6 day volatile anesthetic data previously published by Yasuda et. al. The analysis uses the freely available software PKQuest and incorporates perfusion-ventilation mismatch and time dependent parameters that varied from the anesthetized to the ambulatory period. This heterogeneous adipose perfusion PBPK model was then tested by applying it to the previously published cannabidiol data of Ohlsson et. al. and the cannabinol data of Johansson et. al.

Results

The volatile anesthetic kinetics at early times have only a weak dependence on adipose blood flow while at long times the pharmacokinetics are dominated by the adipose flow and are independent of muscle blood flow. At least 2 adipose compartments with different perfusion rates (0.074 and 0.014 l/kg/min) were needed to describe the anesthetic data. This heterogeneous adipose PBPK model also provided a good fit to the cannabinol data.

Conclusion

Human adipose blood flow is markedly heterogeneous, varying by at least 5 fold. This heterogeneity significantly influences the long time pharmacokinetics of the volatile anesthetics and tetrahydrocannabinol. In contrast, using this same PBPK model it can be shown that the long time pharmacokinetics of the persistent lipophilic compounds (dioxins, PCBs) do not depend on adipose blood flow. The ability of the same PBPK model to describe both the anesthetic and cannabinol kinetics provides direct qualitative evidence that their kinetics are flow limited and that there is no significant adipose tissue diffusion limitation.     

Monensin inhibits ligand dissociation only transiently and partially and distinguishes two galactosyl receptor pathways in isolated rat hepatocytes

Monensin has been shown to inhibit the dissociation of internalized asialoorosomucoid (ASOR) from galactosyl (Gal) receptors in hepatocytes (Harford et al., J. Cell. Biol., 96:1824, 1983). Examination of the long-term kinetics of dissociation of a single round of surface-bound 125I-ASOR in the presence of monensin revealed, however, that dissociation resumed after a lag of 30-40 min. Dissociation proceeded slowly with apparent first order kinetics (k = 0.006-0.022 min-1) and reached a plateau after 4 h, both in freshly isolated cells in suspension and in cells cultured for 24 h. Only a portion of the ligand bound to surface Gal receptors was capable of dissociating. The degree of dissociation was correlated with the expression of a subpopulation of receptors we have recently designated as state 1 Gal receptors (Weigel et al., Biochem. Biophys. Res. Commun. 140:43, 1986). The recovery and dissociation of a portion of 125I-ASOR-receptor complexes after the lag period is not due to a depletion of monensin, since a second addition of the drug has no affect once dissociation resumes. Furthermore, as assessed by the accumulation of the fluorescent dye acridine orange, cells have not recovered the ability to acidify intracellular compartments during the time that dissociation occurs. The results support a model for the hepatic Gal receptor system, in which there are two functionally different receptor populations, recycling pathways, and ligand processing pathways. Monensin blocks dissociation of 125I-ASOR from receptors in the major pathway completely. In the minor pathway dissociation proceeds to completion only after a lag. In this minor pathway monensin appears to temporarily delay a maturation or translocation process that must occur prior to dissociation. We conclude that the observed dissociation in the presence of monensin cannot be mediated by low pH, or by pH or pNa gradients.     

A new method for inferring hidden markov models from noisy time sequences

We present a new method for inferring hidden Markov models from noisy time sequences without the necessity of assuming a model architecture, thus allowing for the detection of degenerate states. This is based on the statistical prediction techniques developed by Crutchfield et al. and generates so called causal state models, equivalent in structure to hidden Markov models. The new method is applicable to any continuous data which clusters around discrete values and exhibits multiple transitions between these values such as tethered particle motion data or Fluorescence Resonance Energy Transfer (FRET) spectra. The algorithms developed have been shown to perform well on simulated data, demonstrating the ability to recover the model used to generate the data under high noise, sparse data conditions and the ability to infer the existence of degenerate states. They have also been applied to new experimental FRET data of Holliday Junction dynamics, extracting the expected two state model and providing values for the transition rates in good agreement with previous results and with results obtained using existing maximum likelihood based methods. The method differs markedly from previous Markov-model reconstructions in being able to uncover truly hidden states.     

Pure and mixed lipid black foam films as models of membrane fusion

Black foam films (BFF) from water solutions of the phospholipid dilauroyl lecithin (DLL) with admixtures of palmitoyl lysolecithin (Lyso) were formed. Microscopic BFF were studied by the method of Scheludko and Exerowa. The formation probability for BFF and the BFF lifetime in a black state before film rupture were measured as functions of the film composition. At a fixed overal lipid concentration it was shown that an increased percentage of Lyso exponentially increased the lifetime of the film up to the CMC of Lyso. This stabilizing Lyso effect nicely corresponds with its stabilizing action on the waiting time for fusion of two contacting black lipid membranes (BLM), as found by Chernomordik et al. In contrast, Lyso is known to destabilize a single BLM. In this way we have found experimental proof of our earlier prediction that Lyso should have opposite effects on the lifetimes of BLM and BFF. In addition, we have shown for the first time that foam films made of lipids are a convenient model for monlayer membrane fusion studies. This model is characterized by its simplicity and experimental reliability and provides a means for quick screening of the fusogenic capacity of various amphiphilic and hydrophilic admixtures.     

Redundancy and synergy arising from pairwise correlations in neuronal ensembles

Multielectrode arrays allow recording of the activity of many single neurons, from which correlations can be calculated. The functional roles of correlations can be revealed by measures of the information conveyed by neuronal activity; a simple formula has been shown to discriminate the information transmitted by individual spikes from the positive or negative contributions due to correlations (Panzeri et al., 1999). Here, this analysis, previously applied to recordings from small ensembles, is developed further by considering a model of a large ensemble, in which correlations among the signal and noise components of neuronal firing are small in absolute value and entirely random in origin. Even such small random correlations are shown to lead to large possible synergy or redundancy, whenever the time window for extracting information from neuronal firing extends to the order of the mean interspike interval. In addition, a sample of recordings from rat barrel cortex illustrates the mean time window at which such corrections dominate when correlations are, as often in the real brain, neither random nor small. The presence of this kind of correlations for a large ensemble of cells restricts further the time of validity of the expansion.