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.     

Compartment volume influences microtubule dynamic instability: a model study

Microtubules (MTs) are cytoskeletal polymers that exhibit dynamic instability, the random alternation between growth and shrinkage. MT dynamic instability plays an essential role in cell development, division, and motility. To investigate dynamic instability, simulation models have been widely used. However, conditions under which the concentration of free tubulin fluctuates as a result of growing or shrinking MTs have not been studied before. Such conditions can arise, for example, in small compartments, such as neuronal growth cones. Here we investigate by means of computational modeling how concentration fluctuations caused by growing and shrinking MTs affect dynamic instability. We show that these fluctuations shorten MT growth and shrinkage times and change their distributions from exponential to non-exponential, gamma-like. Gamma-like distributions of MT growth and shrinkage times, which allow optimal stochastic searching by MTs, have been observed in various cell types and are believed to require structural changes in the MT during growth or shrinkage. Our results, however, show that these distributions can already arise as a result of fluctuations in the concentration of free tubulin due to growing and shrinking MTs. Such fluctuations are possible not only in small compartments but also when tubulin diffusion is slow or when many MTs (de)polymerize synchronously. Volume and all other factors that influence these fluctuations can affect MT dynamic instability and, consequently, the processes that depend on it, such as neuronal growth cone behavior and cell motility in general.     

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.     

Physiological mechanisms of thermoregulation in reptiles: a review

The thermal dependence of biochemical reaction rates means that many animals regulate their body temperature so that fluctuations in body temperature are small compared to environmental temperature fluctuations. Thermoregulation is a complex process that involves sensing of the environment, and subsequent processing of the environmental information. We suggest that the physiological mechanisms that facilitate thermoregulation transcend phylogenetic boundaries. Reptiles are primarily used as model organisms for ecological and evolutionary research and, unlike in mammals, the physiological basis of many aspects in thermoregulation remains obscure. Here, we review recent research on regulation of body temperature, thermoreception, body temperature set-points, and cardiovascular control of heating and cooling in reptiles. The aim of this review is to place physiological thermoregulation of reptiles in a wider phylogenetic context. Future research on reptilian thermoregulation should focus on the pathways that connect peripheral sensing to central processing which will ultimately lead to the thermoregulatory response.     

Patterns of ongoing activity and the functional architecture of the primary visual cortex

Ongoing spontaneous activity in the cerebral cortex exhibits complex spatiotemporal patterns in the absence of sensory stimuli. To elucidate the nature of this ongoing activity, we present a theoretical treatment of two contrasting scenarios of cortical dynamics: (1) fluctuations about a single background state and (2) wandering among multiple "attractor" states, which encode a single or several stimulus features. Studying simplified network rate models of the primary visual cortex (V1), we show that the single state scenario is characterized by fast and high-dimensional Gaussian-like fluctuations, whereas in the multiple state scenario the fluctuations are slow, low dimensional, and highly non-Gaussian. Studying a more realistic model that incorporates correlations in the feed-forward input, spatially restricted cortical interactions, and an experimentally derived layout of pinwheels, we show that recent optical-imaging data of ongoing activity in V1 are consistent with the presence of either a single background state or multiple attractor states encoding many features.     

Colored extrinsic fluctuations and stochastic gene expression

Stochasticity is both exploited and controlled by cells. Although the intrinsic stochasticity inherent in biochemistry is relatively well understood, cellular variation, or ‘noise’, is predominantly generated by interactions of the system of interest with other stochastic systems in the cell or its environment. Such extrinsic fluctuations are nonspecific, affecting many system components, and have a substantial lifetime, comparable to the cell cycle (they are ‘colored’). Here, we extend the standard stochastic simulation algorithm to include extrinsic fluctuations. We show that these fluctuations affect mean protein numbers and intrinsic noise, can speed up typical network response times, and can explain trends in high‐throughput measurements of variation. If extrinsic fluctuations in two components of the network are correlated, they may combine constructively (amplifying each other) or destructively (attenuating each other). Consequently, we predict that incoherent feedforward loops attenuate stochasticity, while coherent feedforwards amplify it. Our results demonstrate that both the timescales of extrinsic fluctuations and their nonspecificity substantially affect the function and performance of biochemical networks.     

Shared kinase fluctuations between two enzymatic reactions

Kinases serve crucial roles in many cellular signaling pathways that process and transfer information. When signaling kinases phosphorylate two targets, these can serve as branch points that distribute information among two pathways. Responses to stimuli transmitted by activated kinases show high levels of cell-to-cell variation that influence cellular function. We ask how fluctuations around a steady state, due to kinase fluctuations and intrinsic noise, are distributed between two reactions with substrates phosphorylated by a shared kinase. We develop the formalism to answer this question and, for a realistic set of biological constants, we illustrate various features of fluctuations and relaxation times to a steady state. We find that the steady-state response determines the size and range in enzyme concentration of phosphorylated substrate fluctuations, and that the choice of an operating point can have a large impact on how shared kinase noise is distributed among two available pathways.     

External drive to inhibitory cells induces alternating episodes of high- and low-amplitude oscillations

Electrical oscillations in neuronal network activity are ubiquitous in the brain and have been associated with cognition and behavior. Intriguingly, the amplitude of ongoing oscillations, such as measured in EEG recordings, fluctuates irregularly, with episodes of high amplitude alternating with episodes of low amplitude. Despite the widespread occurrence of amplitude fluctuations in many frequency bands and brain regions, the mechanisms by which they are generated are poorly understood. Here, we show that irregular transitions between sub-second episodes of high- and low-amplitude oscillations in the alpha/beta frequency band occur in a generic neuronal network model consisting of interconnected inhibitory and excitatory cells that are externally driven by sustained cholinergic input and trains of action potentials that activate excitatory synapses. In the model, we identify the action potential drive onto inhibitory cells, which represents input from other brain areas and is shown to desynchronize network activity, to be crucial for the emergence of amplitude fluctuations. We show that the duration distributions of high-amplitude episodes in the model match those observed in rat prefrontal cortex for oscillations induced by the cholinergic agonist carbachol. Furthermore, the mean duration of high-amplitude episodes varies in a bell-shaped manner with carbachol concentration, just as in mouse hippocampus. Our results suggest that amplitude fluctuations are a general property of oscillatory neuronal networks that can arise through background input from areas external to the network.     

Environmental fluctuations can stabilize food web dynamics by increasing synchrony

Natural food webs are species-rich, but classical theory suggests that they should be unstable and extinction-prone. Asynchronous fluctuations in the densities of competing consumers can stabilize food web dynamics in constant environments. However, environmental fluctuations often synchronize dynamics in nature. Using the same 'diamond-shape' food web model first used to demonstrate the stabilizing effects of asynchrony in constant environments, we show that weak-to-moderate environmentally induced fluctuations in consumer mortality rates stabilize food webs while disrupting asynchrony. Synchrony actually promotes stability because: (i) synchronous declines in consumer density reduce the maximum abundance of top predators and (ii) resource competition quickly converts synchronous increases in consumer density into synchronous declines. These results are robust to details of food web topology and the implementation of environmental fluctuations. The fluctuation strengths that enhance stability are within the range experienced naturally by many species, suggesting that stabilization via environmental fluctuations is a realistic possibility.     

Fluctuations in continuous mammalian cell bioreactors with retention.

Continuous flow bioreactors with cell retention have been increasingly used for the cultivation of mammalian cells. The potential advantages of such bioreactors are high cell concentrations and volumetric productivities. In many reported cases, these systems have shown fluctuations in cell concentrations of various frequency and magnitude. To analyze the dynamics of the fluctuations, a model-based approach is followed. Simulations showed that large fluctuations in biomass resulted in response to fluctuations in the retention ratio when the system is operated at high dilution rate and high cell retention. The dependence of cell concentration fluctuations on variations in dilution rate and retention ratio was established by a cross-correlation statistical analysis on available experimental data. The slower dynamics and the fluctuation propensity of retention systems suggest that continuous culture without retention is more convenient for kinetic studies. In all likelihood, continuous culture with retention can be stabilized by controlling both the retention ratio and the dilution rate.     

Resonance effects and outbreaks in ecological time series

Organismal response to environmental variability is an important aspect of ecological processes. We propose new mechanisms whereby environmental variability can cause cyclic population outbreaks due to the nonlinearity of the organismal response. We consider stage-structured populations that respond to variable environments with variable diapause or dormancy, and in which cyclic changes of the environment induce a resonance-like boost in the population size. If there is also a stochastic component of variation in the environment, the population outbreaks are magnified by the phenomenon of "stochastic resonance". The results show that large population fluctuations may not be due to extrinsic or intrinsic factors alone, but to a nonlinear interaction between the external environment and internal population processes. Indeed, in the presence of such nonlinearities even very small environmental fluctuations can cause massive fluctuations in population size. Our theoretical results may help to explain periodic population cycles and outbreak dynamics found in many infectious diseases and pest species. We also discuss the evolution of the response parameters that regulate diapause or dormancy and promote the outbreak dynamics in variable environments.     

Rodent dynamics as community processes

Small rodent fluctuations are mentioned in many textbooks as examples of regular population cycles with constant interval and amplitude. However, recent evidence and analyses have indicated much more complex patterns, with geographic trends in frequency and amplitude of fluctuations and covariation with many interacting community components. These new findings indicate that extrinsic factors are much more important for the generation of regular rodent cycles than was earlier believed, and that regular cycles represent only a minority of the dynamic patterns found in rodents.     

The More the Tubular: Dynamic Bundling of Actin Filaments for Membrane Tube Formation

Tubular protrusions are a common feature of living cells, arising from polymerization of stiff protein filaments against a comparably soft membrane. Although this process involves many accessory proteins in cells, in vitro experiments indicate that similar tube-like structures can emerge without them, through spontaneous bundling of filaments mediated by the membrane. Using theory and simulation of physical models, we have elaborated how nonequilibrium fluctuations in growth kinetics and membrane shape can yield such protrusions. Enabled by a new grand canonical Monte Carlo method for membrane simulation, our work reveals a cascade of dynamical transitions from individually polymerizing filaments to highly cooperatively growing bundles as a dynamical bottleneck to tube formation. Filament network organization as well as adhesion points to the membrane, which bias filament bending and constrain membrane height fluctuations, screen the effective attractive interactions between filaments, significantly delaying bundling and tube formation.     

Heavy-Tailed Fluctuations in the Spiking Output Intensity of Semiconductor Lasers with Optical Feedback

Although heavy-tailed fluctuations are ubiquitous in complex systems, a good understanding of the mechanisms that generate them is still lacking. Optical complex systems are ideal candidates for investigating heavy-tailed fluctuations, as they allow recording large datasets under controllable experimental conditions. A dynamical regime that has attracted a lot of attention over the years is the so-called low-frequency fluctuations (LFFs) of semiconductor lasers with optical feedback. In this regime, the laser output intensity is characterized by abrupt and apparently random dropouts. The statistical analysis of the inter-dropout-intervals (IDIs) has provided many useful insights into the underlying dynamics. However, the presence of large temporal fluctuations in the IDI sequence has not yet been investigated. Here, by applying fluctuation analysis we show that the experimental distribution of IDI fluctuations is heavy-tailed, and specifically, is well-modeled by a non-Gaussian stable distribution. We find a good qualitative agreement with simulations of the Lang-Kobayashi model. Moreover, we uncover a transition from a less-heavy-tailed state at low pump current to a more-heavy-tailed state at higher pump current. Our results indicate that fluctuation analysis can be a useful tool for investigating the output signals of complex optical systems; it can be used for detecting underlying regime shifts, for model validation and parameter estimation.     

Fluctuations in repressor control: thermodynamic constraints on stochastic focusing

The influence of fluctuations in molecule numbers on genetic control circuits has received considerable attention. The consensus has been that such fluctuations will make regulation less precise. In contrast, it has more recently been shown that signal fluctuations can sharpen the response in a regulated process by the principle of stochastic focusing (SF) (, Proc. Natl. Acad. Sci. USA. 97:7148-7153). In many cases, the larger the fluctuations are, the sharper is the response. Here we investigate how fluctuations in repressor or corepressor numbers can improve the control of gene expression. Because SF is found to be constrained by detailed balance, this requires that the control loops contain driven processes out of equilibrium. Some simple and realistic out-of-equilibrium steps that will break detailed balance and make room for SF in such systems are discussed. We conclude that when the active repressors are controlled by corepressor molecules that display large ("coherent") number fluctuations or when corepressors can be irreversibly removed directly from promoter-bound repressors, the response in gene activity can become significantly sharper than without intrinsic noise. A simple experimental design to establish the possibility of SF for repressor control is suggested.     

Effect of various physical factors on oscillations of light-dispersion in water and aqueous biopolymer solutions

Study of the dependence of light scattering fluctuation on temperature, mechanic perturbation and magnetic field in water and water hemoglobin and DNA solution has shown that an increase in temperature results in the decline of long-term fluctuation amplitude and in the increase of short-term fluctuation amplitude. Mechanical mixing removes long-term fluctuations and over 10 hours are spent for their recovery. Regular fluctuations appear when the constant magnetic field above 240 A/m is applied; the fluctuations are retained for many hours after the removal of the field (when the field is off). It was supposed that maintenance of long-range correlation of molecular rotation-translation fluctuation by the effect of long-range forces and external fields underlies the mechanism of long-term light scattering fluctuations.     

Enhanced internal dynamics of a membrane transport protein during substrate translocation

Conformational changes are essential for the activity of many proteins. If, or how fast, internal fluctuations are related to slow conformational changes that mediate protein function is not understood. In this study, we measure internal fluctuations of the transport protein lactose permease in the presence and absence of substrate by tryptophan fluorescence spectroscopy. We demonstrate that nanosecond fluctuations of alpha-helices are enhanced when the enzyme transports substrate. This correlates with previously published kinetic data from transport measurements showing that millisecond conformational transitions of the substrate-loaded carrier are faster than those in the absence of substrate. These findings corroborate the hypothesis of the hierarchical model of protein dynamics that predicts that slow conformational transitions are based on fast, thermally activated internal motions.     

On the origin and characteristics of noise-induced Lévy walks of E. coli

Lévy walks as a random search strategy have recently attracted a lot of attention, and have been described in many animal species. However, very little is known about one of the most important issues, namely how Lévy walks are generated by biological organisms. We study a model of the chemotaxis signaling pathway of E. coli, and demonstrate that stochastic fluctuations and the specific design of the signaling pathway in concert enable the generation of Lévy walks. We show that Lévy walks result from the superposition of an ensemble of exponential distributions, which occurs due to the shifts in the internal enzyme concentrations following the stochastic fluctuations. With our approach we derive the power-law analytically from a model of the chemotaxis signaling pathway, and obtain a power-law exponent μ ≈ 2.2, which coincides with experimental results. This work provides a means to confirm Lévy walks as natural phenomenon by providing understanding on the process through which they emerge. Furthermore, our results give novel insights into the design aspects of biological systems that are capable of translating additive noise on the microscopic scale into beneficial macroscopic behavior.