Analysis of Drosophila motor neuron activity patterns with neural analogs

A network of reciprocally inhibitory motorneurons has been previously postulated to account for the firing patterns of motor units during dipteran flight. Possible activity patterns of such a network were analyzed by means of appropriately interconnected neuromimes. This theoretical analysis showed that the proposed network can account for many aspects of dipteran motor unit activity patterns including firing in specific sequences, stability, and resetting of the firing pattern by antidromic spikes. In addition, the analysis showed that one aspect of physiological activity, motor unit phase locking, can not be explained simply on the basis of network properties alone; evidently specific membrane properties of the dipteran motor units also play an essential role in establishing the activity pattern.     

Computer simulation of rhythmic oscillations in neuron pools

This paper describes computer simulation of 100 artificial neurons interconnected in mutually exciting random pools. The individual neuromimes include accommodation according to an extended version of Hill's model and adaptation according to an extended version of Kernell's model. The main finding is that the constituent cells of the pools tend to fire in coordinated bursts and that these bursts recur rhythmically. The rate of burst recurrence depends primarily on the time constant of recovery of the after-hyperpolarization conductance change although it may be slightly altered by the average level of random background activity. It does not seem possible to attribute the salient slow rhythm observed in the rat mesencephalic reticular formation to this mechanism, as matching the data requires absurdly large values of the conductance change recovery time constant.     

Environmental fluctuations,productivity, and species diversity: An experimental study

Seemingly opposing hypotheses concerning the effects of environmental fluctuations on species diversity were shown to complement one another. Studies were made on naturally occurring microbial communities growing in continuous cultures, under both low and high productivity levels. The communities consisted of species of bacteria, protozoan flagellates, and protozoan predators (sarcodinians and ciliates). Fluctuations were imposed by periodically removing a portion of the culture and refilling with sterilized medium. They were designed to mimic the effect of fluctuations periodically decreasing the demand/supply ratio of the community for the available resources. It was found that when growth rates were low (either because of low productivity levels or because of low intrinsic growth rates of the organisms concerned), fluctuations decreased species diversity, whereas when growth rates were high, fluctuations increased species diversity. It is suggested that fluctuations decrease diversity when growth rates are low because they prevent slower growing species from surviving, and increase diversity when growth rates are high because they decrease the extent of competitive domination and exclusion.     

Fractal fluctuations in human respiration.

The present study was designed to characterize respiratory fluctuations in awake, healthy adult humans under resting conditions. For this purpose, we recorded respiratory movements with a strain-gauge pneumograph in 20 subjects. We then used Allan factor, Fano factor, and dispersional analysis to test whether the fluctuations in the number of breaths, respiratory period, and breath amplitude were fractal (i.e., time-scale-invariant) or random in occurrence. Specifically, we measured the slopes of the power laws in the Allan factor, Fano factor, and dispersional analysis curves for original time series and compared these with the slopes of the curves for surrogates (randomized data sets). In addition, the Hurst exponent was calculated from the slope of the power law in the Allan factor curve to determine whether the long-range correlations among the fluctuations in breath number were positively or negatively correlated. The results can be summarized as follows. Fluctuations in all three parameters were fractal in nine subjects. There were four subjects in whom only the fluctuations in number of breaths and breath amplitude were fractal, three subjects in whom only the fluctuations in number of breaths were fractal, and two subjects in whom only fluctuations in breath number and respiratory period were fractal. Time-scale-invariant behavior was absent in the two remaining subjects. The results indicate that, in most cases, apparently random fluctuations in respiratory pattern are, in fact, correlated over more than one time scale. Moreover, the data suggest that fractal fluctuations in breath number, respiratory period, and breath amplitude are controlled by separate processes.     

The ability of non-classical meteorological parameters to penetrate into buildings

The penetration ability of four physical variables whose value in the undisturbed atmosphere is influenced by meteorological processes and which have repeatedly been mentioned in biometeorological studies has been investigated. Ion concentration, sferics, pressure fluctuations, and temperature fluctuations were simultaneously recorded outside and inside buildings. Measurements were made in a classical wood/brick house as well as in a fully airconditioned reinforced concrete/glass construction. It was found that pressure fluctuations with periods longer than one minute penetrate the buildings practically unchanged while sferics (measured at a frequency of 10 kHz) are attenuated. The attenuation depends strongly on the construction type. The concentration of ions and the temperature fluctuations inside buildings are independant of their respective values in the atmosphere. Their value is determined only by local activity such as smoking, open windows, heaters, or the presence of persons.     

The contribution of transient counterion imbalances to DNA bending fluctuations

A two-sided model for DNA is employed to analyze fluctuations of the spatial distribution of condensed counterions and the effect of these fluctuations on transient bending. We analyze two classes of fluctuations. In the first, the number of condensed counterions on one side of the DNA remains at its average value, while on the other side, counterions are lost to bulk solution or gained from it. The second class of fluctuations is characterized by movement of some counterions from one side of the DNA to the other. The root-mean-square fluctuation for each class is calculated from counterion condensation theory. The amplitude of the root-mean-square fluctuation depends on the ionic strength as well as the length of the segment considered and is of the order 5-10%. Both classes of fluctuation result in transient bends toward the side of greater counterion density. The bending amplitudes are approximately 15% of the total root-mean-square bends associated with the persistence length of DNA. We are thus led to suggest that asymmetric fluctuations of counterion density contribute modestly but significantly toward the aggregate of thermalized solvent fluctuations that cause bending deformations of DNA free in solution. The calculations support the idea that counterions may exert some modulating influence on the fine structure of DNA.     

Absolute measurement of enhanced fluctuations in assemblies of biomolecules by ultrasonic techniques.

By expressing the fluctuation-dissipation theorem explicitly, equations are obtained for the ultrasonic relaxation amplitudes that contain one single molecular parameter, i.e., the fluctuation, or the sum of fluctuations. The absolute measurement of this parameter is therefore possible. The equations apply to a two-state system, to a multistate system and to a linear Ising chain as well. In an aqueous medium, where molar volume changes are important, the ultrasonic relaxation amplitudes are proportional to the volume fluctuations. For assemblies of biomolecules that exhibit enhanced ultrasonic absorption on assembly it is possible to measure the increase on assembly of the sum of fluctuations. In view of application to tobacco mosaic virus protein aggregates, examples are given in which the fluctuations associated with two normal modes of relaxation are equally enhanced when the difference of conformational stability of the states is reduced. The corresponding observable changes of the ultrasonic spectra are described.     

Molecular crowding inhibits intramolecular breathing motions in proteins

In aqueous solution some proteins undergo large-scale movements of secondary structures, subunits or domains, referred to as protein “breathing”, that define a native-state ensemble of structures. These fluctuations are sensitive to the nature and concentration of solutes and other proteins and are thereby expected to be different in the crowded interior of a cell than in dilute solution. Here we use a combination of wide angle X-ray scattering (WAXS) and computational modeling to derive a quantitative measure of the spatial scale of conformational fluctuations in a protein solution. Concentration-dependent changes in the observed scattering intensities are consistent with a model of structural fluctuations in which secondary structures undergo rigid-body motions relative to one another. This motion increases with decreasing protein concentration or increasing temperature. Analysis of a set of five structurally and functionally diverse proteins reveals a diversity of kinetic behaviors. Proteins with multiple disulfide bonds exhibit little or no increase in breathing in dilute solutions. The spatial extent of structural fluctuations appears highly dependent on both protein structure and concentration and is universally suppressed at very high protein concentrations.     

Modelling of the active reaction of stick insects by a network of neuromimes

Depending on the activity status of the animal, the control system of the femur-tibia joint in stick insects exhibits either a resistance reflex, or the active reaction, a totally different action pattern (Bässler 1988a). Using analog electronic neuron models, several different neuronal circuits are explored that model the active reaction with all its features. The models differ in complexity, redundance and the robustness against small variations of network parameters (e.g. coupling strengths). The circuit with the highest robustness and redundancy requires interneurons with special features, such as found in real animals. When inserted into a closed loop modeling movement and sensory feedback from the periphery, this circuit produces oscillations similar to searching movements found in the real animal. In addition to intracellular recording methods, the authors propose modeling with realistic neuromimes as a complementary method in the investigation of neuronal networks which have well documented input-output relationships.     

Characterization of the distribution of internal motions in the basic pancreatic trypsin inhibitor using a large number of internal NMR probes

The experimental observations described in this article indicated that a distribution of many different fluctuations is present in a globular protein. These fluctuations were characterized by observation of many natural internal probes such as the labile peptide protons and the aromatic side chains. The conditions which are necessary to get reactions of the internal probes have been discussed in detail. The structural interpretation of the data was facilitated by the development and the use of new NMR techniques which provided the identification of the resonances of all the labile peptide protons. With NOE measurements a distinction between correlated and uncorrelated exchange events was obtained. This enabled us to elucidate the exchange mechanism over a wide range of p2H and temperature and to classify different subsets of fluctuations with respect to their lifetimes. It was further demonstrated that a change of external conditions such as temperature, p2H or pressure can change the distribution of fluctuations in the protein. The mechanisms responsible for rotation of internal aromatic side chains were also found to change with temperature, and mechanistic aspects of these fluctuations were discussed. This demonstration of a manifold of spatial fluctuations in a small protein provides an impression on the kind of fluctuations which have to be expected for larger proteins. When studying protein reactions one should therefore consider the presence of a large number of different, transiently formed, spatial structures available for the partner in the reaction, which may pick out only that structure which will optimally perform a particular reaction with the highest efficiency.     

Respiratory effect on the blood volume of pulmonary capillaries

We measured the density variations of aortic blood from rabbits ventilated by a positive end inspiratory pressure of 6 mmHg or a negative box pressure of the same magnitude. When calculated from the density variations, the fluctuations in blood volume of the pulmonary capillaries within one cycle as induced by an intermittent positive pressure ventilation were found to be similar to the ones induced by an intermittent negative pressure ventilation. Using these volumetric fluctuations as a means to assess the transpulmonary pressure and the transmural pressure across the pulmonary capillaries, we conclude that the switching of the ventilation method did not alter the cyclic fluctuations of these pressures.     

Modification of sodium inactivation in myelinated nerve by Anemonia toxin II and iodate. Analysis of current fluctuations and current relaxations

(1) Na+ currents and Na+ current fluctuations were measured in single myelinated nerve fibres of Rana esculenta under voltage-clamp conditions. The process of Na+ inactivation was modified by external treatment with 7 microM Anemonia Toxin II or by internal application of 20 or 40 mM IO3(-). (2) At depolarization of 24 and 32 mV the spectral density of Na+ current fluctuations could be described as the sum of two contributions, Sh(f) and Sm(f), representing the spectrum from fluctuations of the inactivation (h) and activation (m) gates, respectively. At higher depolarizations of 40 and 48 mV the low frequency (h) fluctuations could be better fitted by the sum, Sh1(f)+Sh2(f), of two separate Lorentzian functions. (3) The Na+ current and the variance of Na+ current fluctuations between 150 and 450 ms after depolarization are increased by one order of magnitude after application of Anemonia Toxin II or IO3(-). (4) The kinetics of Na+ current inactivation were described as A1 x exp(-t/tau h1) + A2 x exp(-t/tau h2) + B. The constant, tau h1, of fast Na+ inactivation was the same in normal and modified nerve fibres. The slow inactivation time constant, tau h2, increased with increasing depolarizations in modified fibres but decreased under control conditions. In all cases tau h2 showed a similar voltage dependence as the time constant found by fitting the low frequency fluctuations of Na+ current with one Lorentzian function, Sh(f). (5) It is concluded that Anemonia Toxin II and IO3(-) modify a fraction of Na+ channels in an all-or-none manner. A lower limit of the number of modified Na+ channels is estimated from the Na+ current and the variance Na+ current fluctuations. 7 microM external Anemonia Toxin II modifies more than 17% and 20 or 40 mM internal IO3(-) more than 8% of all Na+ channels. The inactivation gates in modified channels experience an electric field different from that in normal fibres.     

Adrenergic origin of very low-frequency blood pressure oscillations in the unanesthetized rat

Spectral analysis of cardiovascular signals has been extensively used to investigate circulatory homeostatic mechanisms. However, the nature of very low-frequency (VLF) fluctuations remains unclear. Because we previously observed enhanced VLF fluctuations in blood pressure (BP) in the sympathectomized rat (a model characterized by markedly increased plasma epinephrine levels), the aims of our study were to assess whether the genesis of VLF fluctuations in BP depends on circulating catecholamines and to determine which adrenergic receptor(s) and which membrane ion channel(s) are involved. We used continuous intra-arterial BP recordings from unanesthetized unrestrained rats to compute the power of VLF fluctuations in BP in the intact condition, during acute ganglionic blockade with hexamethonium, and after restoration of BP levels by infusion (in addition to hexamethonium) of adrenergic agonists (epinephrine, norepinephrine, and clonidine) or nonadrenergic vasoconstrictors (vasopressin). Effects of infusion of specific adrenergic receptor blockers (propranolol, prazosin, and yohimbine) with hexamethonium and catecholamines and infusion of various membrane ion channel blockers on VLF fluctuations in BP were also evaluated. Our results are as follows. 1) Ganglionic blockade drastically reduced BP levels and VLF fluctuations. 2) All vasoconstrictors restored BP levels, but only adrenergic vasoconstrictors generated striking VLF fluctuations in BP. 3) Catecholamine-induced fluctuations were abolished by alpha2-, but not alpha1- or beta-, adrenergic receptor blockade and by Ba2+-sensitive K+ channel or L-type Ca2+ channel, but not by other ion channel, blockers. We conclude that, in the conscious, unrestrained ganglion-blocked rat, catecholamine infusion generates VLF fluctuations in BP through stimulation of alpha2-receptors and activation of Ba2+-sensitive K+ channels. These fluctuations may have (patho)physiological relevance under conditions of disrupted circulatory homeostasis.     

Nonlinear time-series modeling of vole population fluctuations

A central goal of population ecology is to understand and predict fluctuations in population numbers. Until recently, much of the debate focused on the issue of population regulation by density-dependent factors. In this paper, I describe an approach to nonlinear modeling of time-series data that is designed to go beyond this question by investigating the possibility of complex population dynamics, characterized by lags in regulation and periodic or chaotic oscillations. The questions motivating this approach are: what are relative contributions of endogenous vs. exogenous components of dynamics? Is the irregular component in fluctuations entirely due to exogenous noise, or do nonlinearities contribute to it, too? I describe the philosophy and the technical details of the nonlinear modeling approach, and then apply it to a collection of time-series data on vole population fluctuations in northern Europe. The results suggest that population dynamics of European voles undergo a latitudinal shift from stability to chaos. Dynamics in northern Fennoscandia are characterized by positive Lyapunov exponent estimates, and a high degree of short-term (one year ahead) predictability, suggesting a strong endogenous component. In more southerly populations estimated Lyapunov exponents are negative, and there is no one-step ahead predictability, suggesting that fluctuations are driven by exogenous factors.     

pH dependence of conformational fluctuations of the protein backbone

Proton binding equilibria (pK_a values) of ionizable groups in proteins are exquisitely sensitive to their microenvironments. Apparent pK_a values measured for individual ionizable residues with NMR spectroscopy are actually population‐weighted averages of the pK_a in different conformational microstates. NMR spectroscopy experiments with staphylococcal nuclease were used to test the hypothesis that pK_a values of surface Glu and Asp residues are affected by pH‐sensitive fluctuations of the backbone between folded and locally unfolded conformations. ¹⁵N spin relaxation studies showed that as the pH decreases from the neutral into the acidic range the amplitudes of backbone fluctuations in the ps‐ns timescale increase near carboxylic residues. Hydrogen exchange experiments suggested that backbone conformational fluctuations promoted by decreasing pH also reflect slower local or sub‐global unfolding near carboxylic groups. This study has implications for structure‐based pK_a calculations: (1) The timescale of the backbone's response to ionization events in proteins can range from ps to ms, and even longer; (2) pH‐sensitive fluctuations of the backbone can be localized to both the segment the ionizable residue is attached to or the one that occludes the ionizable group; (3) Structural perturbations are not necessarily propagated through Coulomb interactions; instead, local fluctuations appear to be coupled through the co‐operativity inherent to elements of secondary structure and to networks of hydrogen bonds. These results are consistent with the idea that local conformational fluctuations and stabilities are important determinants of apparent pK_a values of ionizable residues in proteins. Proteins 2014; 82:3132–3143. © 2014 Wiley Periodicals, Inc.     

Fluctuations in tension during contraction of single muscle fibers.

We have searched for fluctuations in the steady-state tension developed by stimulated single muscle fibers. Such tension "noise" is expected to be present as a result of the statistical fluctuations in the number and/or state of myosin cross-bridges interacting with thin filament sites at any time. A sensitive electro-optical tension transducer capable of resolving the expected fluctuations in magnitude and frequency was constructed to search for the fluctuations. The noise was analyzed by computing the power spectra and amplitude of stochastic fluctuations in the photomultiplier counting rate, which was made proportional to muscle force. The optical system and electronic instrumentation together with the minicomputer software are described. Tensions were measured in single skinned glycerinated rabbit psoas muscle fibers in rigor and during contraction and relaxation. The results indicate the presence of fluctuations in contracting muscles and a complete absence of tension noise in eith rigor or relaxation. Also, a numerical method was developed to simulate the power spectra and amplitude of fluctuations, given the rate constants for association and dissociation of the cross-bridges and actin. The simulated power spectra and the frequency distributions observed experimentally are similar.     

Population Fluctuations and Synchrony of Grassland Butterflies in Relation to Species Traits

Population fluctuations and synchrony influence population persistence; species with larger fluctuations and more synchronised population fluctuations face higher extinction risks. Here, we analyse the effect of diet specialisation, mobility, length of the flight period, and distance to the northern edge of the species’ distribution in relation to between-year population fluctuations and synchrony of butterfly species. All butterfly species associated with grasslands were surveyed over five successive years at 19 grassland sites in a forest-dominated landscape (50 km²) in southern Sweden. At both the local and regional level, we found larger population fluctuations in species with longer flight periods. Population fluctuations were more synchronous among localities in diet specialists. Species with a long flight period might move more to track nectar resources compared to species with shorter flight period, and if nectar sources vary widely between years and localities it may explain that population fluctuations increase with increasing flight length. Diet generalists can use different resources (in this case host plants) at different localities and this can explain the lower synchrony in population fluctuations among generalist species. Higher degree of synchrony is one possible explanation for the higher extinction risks that have been observed for more specialised species. Therefore, diet specialists are more often threatened and require more conservation efforts than generalists.     

The nature and perception of fluctuations in human musical rhythms

Although human musical performances represent one of the most valuable achievements of mankind, the best musicians perform imperfectly. Musical rhythms are not entirely accurate and thus inevitably deviate from the ideal beat pattern. Nevertheless, computer generated perfect beat patterns are frequently devalued by listeners due to a perceived lack of human touch. Professional audio editing software therefore offers a humanizing feature which artificially generates rhythmic fluctuations. However, the built-in humanizing units are essentially random number generators producing only simple uncorrelated fluctuations. Here, for the first time, we establish long-range fluctuations as an inevitable natural companion of both simple and complex human rhythmic performances. Moreover, we demonstrate that listeners strongly prefer long-range correlated fluctuations in musical rhythms. Thus, the favorable fluctuation type for humanizing interbeat intervals coincides with the one generically inherent in human musical performances.     

Does red noise increase or decrease extinction risk? Single extreme events versus series of unfavorable conditions

Recent theoretical studies have shown contrasting effects of temporal correlation of environmental fluctuations (red noise) on the risk of population extinction. It is still debated whether and under which conditions red noise increases or decreases extinction risk compared with uncorrelated (white) noise. Here, we explain the opposing effects by introducing two features of red noise time series. On the one hand, positive autocorrelation increases the probability of series of poor environmental conditions, implying increasing extinction risk. On the other hand, for a given time period, the probability of at least one extremely bad year ("catastrophe") is reduced compared with white noise, implying decreasing extinction risk. Which of these two features determines extinction risk depends on the strength of environmental fluctuations and the sensitivity of population dynamics to these fluctuations. If extreme (catastrophic) events can occur (strong noise) or sensitivity is high (overcompensatory density dependence), then temporal correlation decreases extinction risk; otherwise, it increases it. Thus, our results provide a simple explanation for the contrasting previous findings and are a crucial step toward a general understanding of the effect of noise color on extinction risk.     

Analysis of three amphibian populations with quarter-century long time-series.

Amphibians are in decline in many parts of the world. Long tme-series of amphibian populations are necessary to distinguish declines from the often strong fluctuations observed in natural populations. Time-series may also help to understand the causes of these declines. We analysed 23-28-year long time-series of the frog Rana temporaria. Only one of the three studied populations showed a negative trend which was probably caused by the introduction of fish. Two populations appeared to be density regulated. Rainfall had no obvious effect on the population fluctuations. Whereas long-term studies of amphibian populations are valuable to document population declines, most are too short to reveal those factors that govern population dynamics or cause amphibian populations to decline.