Detecting determinism in short time series, with an application to the analysis of a stationary EEG recording

We have developed a new method for detecting determinism in a short time series and used this method to examine whether a stationary EEG is deterministic or stochastic. The method is based on the observation that the trajectory of a time series generated from a differentiable dynamical system behaves smoothly in an embedded phase space. The angles between two successive directional vectors in the trajectory reconstructed from a time series at a minimum embedding dimension were calculated as a function of time. We measured the irregularity of the angle variations obtained from the time series using second-order difference plots and central tendency measures, and compared these values with those from surrogate data. The ability of the proposed method to distinguish between chaotic and stochastic dynamics is demonstrated through a number of simulated time series, including data from Lorenz, R?ssler, and Van der Pol attractors, high-dimensional equations, and 1/f noise. We then applied this method to the analysis of stationary segments of EEG recordings consisting of 750 data points (6-s segments) from five normal subjects. The stationary EEG segments were not found to exhibit deterministic components. This method can be used to analyze determinism in short time series, such as those from physiological recordings, that can be modeled using differentiable dynamical processes.     

Transient pulse formation in jasmonate signaling pathway

The jasmonate (JA) signaling pathway in plants is activated as defense response to a number of stresses like attacks by pests or pathogens and wounding by animals. Some recent experiments provide significant new knowledge on the molecular detail and connectivity of the pathway. The pathway has two major components in the form of feedback loops, one negative and the other positive. We construct a minimal mathematical model, incorporating the feedback loops, to study the dynamics of the JA signaling pathway. The model exhibits transient gene expression activity in the form of JA pulses in agreement with experimental observations. The dependence of the pulse amplitude, duration and peak time on the key parameters of the model is determined computationally. The deterministic and stochastic aspects of the pathway dynamics are investigated using both the full mathematical model and a reduced version of it. We also compare the mechanism of pulse formation with the known mechanisms of pulse generation in some bacterial and viral systems.     

Systems‐wide analysis of BCR signalosomes and downstream phosphorylation and ubiquitylation

B‐cell receptor (BCR) signaling is essential for the development and function of B cells; however, the spectrum of proteins involved in BCR signaling is not fully known. Here we used quantitative mass spectrometry‐based proteomics to monitor the dynamics of BCR signaling complexes (signalosomes) and to investigate the dynamics of downstream phosphorylation and ubiquitylation signaling. We identify most of the previously known components of BCR signaling, as well as many proteins that have not yet been implicated in this system. BCR activation leads to rapid tyrosine phosphorylation and ubiquitylation of the receptor‐proximal signaling components, many of which are co‐regulated by both the modifications. We illustrate the power of multilayered proteomic analyses for discovering novel BCR signaling components by demonstrating that BCR‐induced phosphorylation of RAB7A at S72 prevents its association with effector proteins and with endo‐lysosomal compartments. In addition, we show that BCL10 is modified by LUBAC‐mediated linear ubiquitylation, and demonstrate an important function of LUBAC in BCR‐induced NF‐κB signaling. Our results offer a global and integrated view of BCR signaling, and the provided datasets can serve as a valuable resource for further understanding BCR signaling networks.     

Temporal Beta Diversity of Bird Assemblages in Agricultural Landscapes: Land Cover Change vs. Stochastic Processes

Temporal variation in the composition of species assemblages could be the result of deterministic processes driven by environmental change and/or stochastic processes of colonization and local extinction. Here, we analyzed the relative roles of deterministic and stochastic processes on bird assemblages in an agricultural landscape of southwestern France. We first assessed the impact of land cover change that occurred between 1982 and 2007 on (i) the species composition (presence/absence) of bird assemblages and (ii) the spatial pattern of taxonomic beta diversity. We also compared the observed temporal change of bird assemblages with a null model accounting for the effect of stochastic dynamics on temporal beta diversity. Temporal assemblage dissimilarity was partitioned into two separate components, accounting for the replacement of species (i.e. turnover) and for the nested species losses (or gains) from one time to the other (i.e. nestedness-resultant dissimilarity), respectively. Neither the turnover nor the nestedness-resultant components of temporal variation were accurately explained by any of the measured variables accounting for land cover change (r²<0.06 in all cases). Additionally, the amount of spatial assemblage heterogeneity in the region did not significantly change between 1982 and 2007, and site-specific observed temporal dissimilarities were larger than null expectations in only 1% of sites for temporal turnover and 13% of sites for nestedness-resultant dissimilarity. Taken together, our results suggest that land cover change in this agricultural landscape had little impact on temporal beta diversity of bird assemblages. Although other unmeasured deterministic process could be driving the observed patterns, it is also possible that the observed changes in presence/absence species composition of local bird assemblages might be the consequence of stochastic processes in which species populations appeared and disappeared from specific localities in a random-like way. Our results might be case-specific, but if stochastic dynamics are generally dominant, the ability of correlative and mechanistic models to predict land cover change effects on species composition would be compromised.     

Failure of Arm Movement Control in Stroke Patients,Characterized by Loss of Complexity

We study the mechanism of human arm-posture control by means of nonlinear dynamics and quantitative time series analysis methods. Utilizing linear and nonlinear measures in combination, we find that pathological tremors emerge in patient dynamics and serve as a main feature discriminating between normal and patient groups. The deterministic structure accompanied with loss of complexity inherent in the tremor dynamics is also revealed. To probe the underlying mechanism of the arm-posture dynamics, we further analyze the coupling patterns between joints and components, and discuss their roles in breaking of the organization structure. As a result, we elucidate the mechanisms in the arm-posture dynamics of normal subjects responding to the gravitational force and for the reduction of the dynamic degrees of freedom in the patient dynamics. This study provides an integrated framework for the origin of the loss of complexity in the dynamics of patients as well as the coupling structure in the arm-posture dynamics.     

Continuum model of cell adhesion and migration

The motility of cells crawling on a substratum has its origin in a thin cell organ called lamella. We present a 2-dimensional continuum model for the lamella dynamics of a slowly migrating cell, such as a human keratinocyte. The central components of the model are the dynamics of a viscous cytoskeleton capable to produce contractile and swelling stresses, and the formation of adhesive bonds in the plasma cell membrane between the lamella cytoskeleton and adhesion sites at the substratum. We will demonstrate that a simple mechanistic model, neglecting the complicated signaling pathways and regulation processes of a living cell, is able to capture the most prominent aspects of the lamella dynamics, such as quasi-periodic protrusions and retractions of the moving tip, retrograde flow of the cytoskeleton and the related accumulation of focal adhesion complexes in the leading edge of a migrating cell. The developed modeling framework consists of a nonlinearly coupled system of hyperbolic, parabolic and ordinary differential equations for the various molecular concentrations, two elliptic equations for cytoskeleton velocity and hydrodynamic pressure in a highly viscous two-phase flow, with appropriate boundary conditions including equalities and inequalities at the moving boundary. In order to analyse this hybrid continuum model by numerical simulations for different biophysical scenarios, we use suitable finite element and finite volume schemes on a fixed triangulation in combination with an adaptive level set method describing the free boundary dynamics.     

多巴胺信号系统在衰老引起的行为和认知能力退化中的作用

衰老是生物体随时间推移各项生理功能逐渐发生改变的自然现象。动物的衰老伴随着行为和认知能力的降低,因此研究动物行为和认知功能退化的分子神经机制对于提高老年群体的生活质量具有重要意义。近年来,随着正电子发射断层扫描技术和功能性核磁共振脑成像技术在神经生物学上的广泛运用,越来越多证据表明多巴胺系统功能在衰老过程中显著降低,并且这是人类和动物行为和认知功能退化的重要原因。本文将概述自然衰老过程中多巴胺信号系统功能变化及机制和其在动物行为和认知退化中的作用等方面研究进展。     

Deterministic and stochastic features of rhythmic human movement

The dynamics of rhythmic movement has both deterministic and stochastic features. We advocate a recently established analysis method that allows for an unbiased identification of both types of system components. The deterministic components are revealed in terms of drift coefficients and vector fields, while the stochastic components are assessed in terms of diffusion coefficients and ellipse fields. The general principles of the procedure and its application are explained and illustrated using simulated data from known dynamical systems. Subsequently, we exemplify the method’s merits in extracting deterministic and stochastic aspects of various instances of rhythmic movement, including tapping, wrist cycling and forearm oscillations. In particular, it is shown how the extracted numerical forms can be analysed to gain insight into the dependence of dynamical properties on experimental conditions.     

Crosstalk between endogenous and synthetic components--synthetic signaling meets endogenous components

Synthetic biology uses biological components to engineer new functionality in living organisms. We have used the tools of synthetic biology to engineer detector plants that can sense man-made chemicals, such as the explosive trinitrotoluene, and induce a response detectable by eye or instrumentation. A goal of this type of work is to make the designed system orthogonal, that is, able to function independently of systems in the host. In this review, the design and function of two partially synthetic signaling pathways for use in plants is discussed. We describe observed interactions (crosstalk) with endogenous signaling components. This crosstalk can be beneficial, allowing the creation of hybrid synthetic/endogenous signaling pathways, or detrimental, resulting in system noise and/or false positives. Current approaches in the field of synthetic biology applicable to the design of orthogonal signaling systems, including the design of synthetic components, partially synthetic systems that utilize crosstalk to signal through endogenous components, computational redesign of proteins, and the use of heterologous components, are discussed.     

健康人心率变异性中的不稳定周期轨道

为刻划心脏节律存在的确定性动力学特征,运用不稳定周期轨道分析方法对健康青年人的RR间期时间序列数据进行分析。研究结果揭示健康人心脏节律中存在显著的不稳定周期轨道及不稳定周期轨道分级（周期1、周期2,周期3,周期4）现象,表明健康青年人心脏节律的动力学特性中包含着显著的确定性行为。通过跟踪不周期轨道随时间的演变,迹表明心脏节律的变化中存在着因有的非平稳性。     

Dynamic control of TGF-beta signaling and its links to the cytoskeleton

Transforming growth factor beta (TGF-beta) regulates cellular behavior in embryonic and adult tissues. TGF-beta binding to serine/threonine kinase receptors on the plasma membrane activates Smad molecules and additional signaling proteins that coordinately regulate gene expression or cytoplasmic processes such as cytoskeletal dynamics. In turn, the activity and duration of the Smad pathway seems to be regulated by cytoskeletal components, which facilitate the shuttling process that segregates Smad proteins in the cytoplasm and nucleus. We discuss mechanisms and models that aim at explaining the coordination between several components of the signaling network downstream of the TGF-beta signal.     

Geographical gradients in the population dynamics of North American prairie ducks

1. Geographic gradients in population dynamics may occur because of spatial variation in resources that affect the deterministic components of the dynamics (i.e. carrying capacity, the specific growth rate at small densities or the strength of density regulation) or because of spatial variation in the effects of environmental stochasticity. To evaluate these, we used a hierarchical Bayesian approach to estimate parameters characterizing deterministic components and stochastic influences on population dynamics of eight species of ducks (mallard, northern pintail, blue-winged teal, gadwall, northern shoveler, American wigeon, canvasback and redhead (Anas platyrhynchos, A. acuta, A. discors, A. strepera, A. clypeata, A. americana, Aythya valisineria and Ay. americana, respectively) breeding in the North American prairies, and then tested whether these parameters varied latitudinally. 2. We also examined the influence of temporal variation in the availability of wetlands, spring temperature and winter precipitation on population dynamics to determine whether geographical gradients in population dynamics were related to large-scale variation in environmental effects. Population variability, as measured by the variance of the population fluctuations around the carrying capacity K, decreased with latitude for all species except canvasback. This decrease in population variability was caused by a combination of latitudinal gradients in the strength of density dependence, carrying capacity and process variance, for which details varied by species. 3. The effects of environmental covariates on population dynamics also varied latitudinally, particularly for mallard, northern pintail and northern shoveler. However, the proportion of the process variance explained by environmental covariates, with the exception of mallard, tended to be small. 4. Thus, geographical gradients in population dynamics of prairie ducks resulted from latitudinal gradients in both deterministic and stochastic components, and were likely influenced by spatial differences in the distribution of wetland types and shapes, agricultural practices and dispersal processes. 5. These results suggest that future management of these species could be improved by implementing harvest models that account explicitly for spatial variation in density effects and environmental stochasticity on population abundance.     

Hybrid stochastic and deterministic simulations of calcium blips

Intracellular calcium release is a prime example for the role of stochastic effects in cellular systems. Recent models consist of deterministic reaction-diffusion equations coupled to stochastic transitions of calcium channels. The resulting dynamics is of multiple time and spatial scales, which complicates far-reaching computer simulations. In this article, we introduce a novel hybrid scheme that is especially tailored to accurately trace events with essential stochastic variations, while deterministic concentration variables are efficiently and accurately traced at the same time. We use finite elements to efficiently resolve the extreme spatial gradients of concentration variables close to a channel. We describe the algorithmic approach and we demonstrate its efficiency compared to conventional methods. Our single-channel model matches experimental data and results in intriguing dynamics if calcium is used as charge carrier. Random openings of the channel accumulate in bursts of calcium blips that may be central for the understanding of cellular calcium dynamics.     

Revisited measles and chickenpox dynamics through orthogonal transformation

The question addressed is whether or not childhood epidemics such as measles and chickenpox are characterized by low-dimensional chaos. We propose a new method for the detection and extraction of hidden periodic components embedded in an irregular cyclical series, and study the characterization of the epidemiological series in terms of the characteristic features or periodicity attributes of the extracted components. It is shown that the measles series possesses two periodic components each having a period of one year. Both the periodic components have time-varying pattern, and the process is nonlinear and deterministic; there is no evidence of strong chaoticity in the measles dynamics. The chickenpox series has one seasonal component with stable pattern, and the process is deterministic but linear, and hence non-chaotic. We also propose surrogate generators based on null hypotheses relating to the variability of the periodicity attributes to analyse the dynamics in the epidemic series. The process dynamics is also studied using seasonally forced SEIR epidemic model, and the characterization performance of the proposed schemes is assessed.     

Nonlinear Time Series Analysis of Nodulation Factor Induced Calcium Oscillations: Evidence for Deterministic Chaos?

Legume plants form beneficial symbiotic interactions with nitrogen fixing bacteria (called rhizobia), with the rhizobia being accommodated in unique structures on the roots of the host plant. The legume/rhizobial symbiosis is responsible for a significant proportion of the global biologically available nitrogen. The initiation of this symbiosis is governed by a characteristic calcium oscillation within the plant root hair cells and this signal is activated by the rhizobia. Recent analyses on calcium time series data have suggested that stochastic effects have a large role to play in defining the nature of the oscillations. The use of multiple nonlinear time series techniques, however, suggests an alternative interpretation, namely deterministic chaos. We provide an extensive, nonlinear time series analysis on the nature of this calcium oscillation response. We build up evidence through a series of techniques that test for determinism, quantify linear and nonlinear components, and measure the local divergence of the system. Chaos is common in nature and it seems plausible that properties of chaotic dynamics might be exploited by biological systems to control processes within the cell. Systems possessing chaotic control mechanisms are more robust in the sense that the enhanced flexibility allows more rapid response to environmental changes with less energetic costs. The desired behaviour could be most efficiently targeted in this manner, supporting some intriguing speculations about nonlinear mechanisms in biological signaling.     

Evolution of BMP signaling in Drosophila oogenesis: a receptor-based mechanism

The bone morphogenetic protein (BMP) signaling pathway is a conserved regulator of cellular and developmental processes in animals. The mechanisms underlying BMP signaling activation differ among tissues and mostly reflect changes in the expression of pathway components. BMP signaling is one of the major pathways responsible for the patterning of the Drosophila eggshell, a complex structure derived from a layer of follicle cells (FCs) surrounding the developing oocyte. Activation of BMP signaling in the FCs is dynamic. Initially, signaling is along the anterior-posterior (A/P) axis; later, signaling acquires dorsal-ventral (D/V) polarity. These dynamics are regulated by changes in the expression pattern of the type I BMP receptor thickveins (tkv). We recently found that signaling dynamics and TKV patterning are highly correlated in the FCs of multiple Drosophila species. In addition, we showed that signaling patterns are spatially different among species. Here, we use a mathematical model to simulate the dynamics and differences of BMP signaling in numerous species. This model predicts that qualitative and quantitative changes in receptor expression can lead to differences in the spatial pattern of BMP signaling. We tested these predications experimentally in three different Drosophila species and through genetic perturbations of BMP signaling in D. melanogaster. On the basis of our results, we concluded that changes in tkv patterning can account for the experimentally observed differences in the patterns of BMP signaling in multiple Drosophila species.     

MAPK signaling in equations and embryos

The Extracellularly Regulated Kinase/Mitogen Activated Protein Kinase (ERK/MAPK) signaling pathway is a critical regulator of cellular processes in adult and developing tissues. Depending on the cellular context, MAPK cascade can act as a rheostat, a switch, or an oscillator. The highly conserved structure of the cascade does not imply a rigid function, as was suggested by the early mathematical models of MAPK signaling, and can instead produce a wide range of input-output maps. Given a large number of pathway components and modes of regulation, it is essential to establish experimental systems that will allow both manipulating the MAPK cascade and monitoring its dynamics. The terminal patterning system in the Drosophila embryo appears to be ideally suited for this purpose. Our recent experiments characterized dynamics of the MAPK phosphorylation gradient in the terminal system and proposed that it is regulated by a cascade of diffusion-trapping modules. Here we discuss a biophysical model that can describe the observed dynamics and guide future experiments for exploring the relative importance of multiple layers of MAPK cascade regulation.