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Dynamical characterization of residual and non-native structures in a partially folded protein by (15)N NMR relaxation using a model based on a distribution of correlation times.

A spectral density model based on a truncated lorentzian distribution of correlation times is used to analyze the nanosecond time-scale dynamics of the partially unfolded domain 2 of annexin I from its (15)N NMR relaxation parameters measured at three magnetic field strengths. The use of a distribution of correlation times enables the characterization of the dynamical features of the NH bonds of the protein in terms of heterogeneity of dynamical states in the nanosecond range. The variation along the sequence of the two dynamical parameters introduced, namely the center and the width of the distribution, points out the different types of residual secondary structures present in the D2 domain. Moreover, it allows a physically sensible interpretation of the dynamical behavior of the different residual helices and of the non-native structures. Also, a striking correspondence is found between the parameters obtained using an extended Lipari and Szabo model and the parameters obtained using the distribution of correlation times. This result led us to propose a specific interpretation of the model-free order parameter for internal motions in the nanosecond range in the case of unfolded states.

Annexin A1↗

Dynamics of mutualist populations that are demographically open.

1. Few theoretical studies have examined the impact of immigration and emigration on mutualist population dynamics, but a recent empirical study (A.R. Thompson Oecologia, 143, 61-69) on mutualistic fish and shrimp showed that immigration can prevent population collapse, and that intraspecific competition for a mutualistic partner can curb population expansion. To understand in a theoretical context the implications of these results, and to assess their generality, we present a two-species model that accounts explicitly for immigration and emigration, as well as distinguishing the impacts of mutualism on birth rates, death rates and habitat acquisition. 2. The model confirms that immigration can stabilize mutualistic populations, and predicts that high immigration, along with enhanced reproduction and/or reduced mortality through mutualism, can cause population sizes to increase until habitat availability curbs further expansion. 3. We explore in detail the effects of different forms of habitat limitation on mutualistic populations. Habitat availability commonly limits the density of both populations if mutualists acquire shelter independently. If a mutualist depends on a partner for habitat, densities of that mutualist are capped by the amount of space provided by that partner. The density of the shelter-provider is limited by the environment. 4. If a mutualism solely augments reproduction, and most locally produced individuals leave the focal patch, then the mutualism will have a minimal effect on local dynamics. If the mutualism operates by reducing rates of death or enhancing habitat availability, and there is at least some immigration, then mutualism will affect local dynamics. This finding may be particularly relevant in marine systems, where there is high variability (among species and locations) in the extent to which progeny disperse from natal locations. 5. Overall, our results demonstrate that the consequences of immigration and emigration for the dynamics of mutualists depend strongly on which demographic rate is influenced by mutualism. 6. By relating our model to a variety of terrestrial and aquatic systems, we provide a general framework to guide future empirical studies of the dynamics of mutualistic populations.

Animal Migration↗

Automated ventricular tachyarrhythmia recognition: a combination of cycle length and nonlinear dynamics measurements.

INTRODUCTION: Cardiac monitoring devices such as external cardioverter defibrillators and ICU computerized ECG monitoring systems sense individual QRS complexes to detect and subclassify ventricular tachyarrhythmias. Many algorithms that evaluate ECG morphology mark individual QRS complexes so that specific waveform characteristics can be measured. QRS sensors miss a percentage of electrogram events, especially during fibrillatory rhythms; thus, a morphology algorithm that helps subclassify arrhythmias without marking individual electrogram events may be more robust and improve arrhythmia detection accuracy. METHODS AND RESULTS: Four nonlinear dynamics calculations were evaluated for detecting ventricular tachyarrhythmias and for subclassifying monomorphic ventricular tachycardia (MVT) and polymorphic ventricular tachycardia (PVT). Five-second epochs of normal (NML, n = 48), MVT (n = 58), and PVT (n = 75) rhythms were presented to a statistical discriminant function based on cycle length (CL), and its performance was compared to two other discriminant functions, one consisting of the nonlinear dynamics calculations and one consisting of a combination of all variables. The discriminant function based on nonlinear dynamics calculations and CL detected 100% of the ventricular tachyarrhythmias, and subclassified more (P < 0.001) MVT and PVT arrhythmias (90%) than that based on CL alone (71%). CONCLUSIONS: The nonlinear dynamics measurements used in this study significantly increased the subclassification accuracy of the CL-based discriminant function, and they were calculated from ECG signals without marking individual QRS complexes. Therefore, arrhythmia detectors that use nonlinear dynamics measurements may commit fewer classification errors due to QRS undersensing and aid therapy decisions when circumstances suggest that QRS sensing is inaccurate.

Electrocardiography↗

Principal dynamic mode analysis of nonlinear transduction in a spider mechanoreceptor.

The nonlinear dynamics of the mechanoelectrical transduction in an arthropod mechanoreceptor (cuticular slit sense organ of the spider Cupiennius salei) were studied using Volterra kernel measurements and the recently proposed method of principal dynamic modes. Since mechanoreceptors must operate with sufficient gain sensitivity to rapidly varying displacement stimuli over a broad bandwidth and for a wide range of amplitudes, the experimental data were generated by applying pseudorandom broadband mechanical displacements of various mean levels to the cuticular slits. The recorded response data were intracellular current and potential. The purpose of this paper is to demonstrate the use of the principal dynamic mode (PDM) methodology in elucidating the nonlinear dynamics of a spider mechanoreceptor. The results obtained demonstrate that two PDMs suffice to provide a complete nonlinear dynamic model of this insect mechanoreceptor. The first PDM resembles the first-order kernel and has a low pass characteristic (position dependent), while the second PDM has a high-pass characteristic (velocity-dependent) and resides entirely in the second-order kernel (nonlinear adaptation). This study may serve as an example of the proper use of this new methodology for the analysis of nonlinear physiological systems.

Animals↗

Locally activated neural networks and stable neural controller design for nonlinear dynamic systems.

A stable neural control scheme using a locally activated neural network has been proposed for a class of nonlinear dynamic systems. The locally activated neural network, for a given input, essentially selects a small subset of the network hidden nodes for output computation using the CMAC-like content addressing mechanism. This network aims to maintain local representations of the system dynamics. Thus, the global control performance in the concerned state space is achieved by the cooperation of many local control efforts and furthermore, real-time control can be facilitated because only a small sized network is involved to control and learn at any given time. The proposed control scheme is composed of two stages: (1) prediction error based learning in which the network attempts to learn the nonlinear basis functions of the plant inverse dynamics by a modified backpropagation learning rule; and (2) tracking error based learning in which the network weights are further fine-tuned using the basis set obtained in (1). This basis set spans the locally partitioned vector space of the system inverse dynamics when the prediction error based learning is achieved within a prescribed error tolerance. For uniform stability, the sliding mode control is introduced as a safety mechanism when the network has not sufficiently learned the plant dynamics yet. With suitable assumptions on the controlled plant, global stability and tracking error convergence proof has been given. Finally, the proposed control scheme is verified with computer simulation.

Adaptation, Physiological↗

Quantifying cardiac sympathetic and parasympathetic nervous activities using principal dynamic modes analysis of heart rate variability.

The ratio between low-frequency (LF) and high-frequency (HF) spectral power of heart rate has been used as an approximate index for determining the autonomic nervous system (ANS) balance. An accurate assessment of the ANS balance can only be achieved if clear separation of the dynamics of the sympathetic and parasympathetic nervous activities can be obtained, which is a daunting task because they are nonlinear and have overlapping dynamics. In this study, a promising nonlinear method, termed the principal dynamic mode (PDM) method, is used to separate dynamic components of the sympathetic and parasympathetic nervous activities on the basis of ECG signal, and the results are compared with the power spectral approach to assessing the ANS balance. The PDM analysis based on the 28 subjects consistently resulted in a clear separation of the two nervous systems, which have similar frequency characteristics for parasympathetic and sympathetic activities as those reported in the literature. With the application of atropine, in 13 of 15 supine subjects there was an increase in the sympathetic-to-parasympathetic ratio (SPR) due to a greater decrease of parasympathetic than sympathetic activity (P=0.003), and all 13 subjects in the upright position had a decrease in SPR due to a greater decrease of sympathetic than parasympathetic activity (P<0.001) with the application of propranolol. The LF-to-HF ratio calculated by the power spectral density is less accurate than the PDM because it is not able to separate the dynamics of the parasympathetic and sympathetic nervous systems. The culprit is equivalent decreases in both the sympathetic and parasympathetic activities irrespective of the pharmacological blockades. These findings suggest that the PDM shows promise as a noninvasive and quantitative marker of ANS imbalance, which has been shown to be a factor in many cardiac and stress-related diseases.

Adult↗

Gaze orienting in dynamic visual double steps.

Visual stimuli are initially represented in a retinotopic reference frame. To maintain spatial accuracy of gaze (i.e., eye in space) despite intervening eye and head movements, the visual input could be combined with dynamic feedback about ongoing gaze shifts. Alternatively, target coordinates could be updated in advance by using the preprogrammed gaze-motor command ("predictive remapping"). So far, previous experiments have not dissociated these possibilities. Here we study whether the visuomotor system accounts for saccadic eye-head movements that occur during target presentation. In this case, the system has to deal with fast dynamic changes of the retinal input and with highly variable changes in relative eye and head movements that cannot be preprogrammed by the gaze control system. We performed visual-visual double-step experiments in which a brief (50-ms) stimulus was presented during a saccadic eye-head gaze shift toward a previously flashed visual target. Our results show that gaze shifts remain accurate under these dynamic conditions, even for stimuli presented near saccade onset, and that eyes and head are driven in oculocentric and craniocentric coordinates, respectively. These results cannot be explained by a predictive remapping scheme. We propose that the visuomotor system adequately processes dynamic changes in visual input that result from self-initiated gaze shifts, to construct a stable representation of visual targets in an absolute, supraretinal (e.g., world) reference frame. Predictive remapping may subserve transsaccadic integration, thus enabling perception of a stable visual scene despite eye movements, whereas dynamic feedback ensures accurate actions (e.g., eye-head orienting) to a selected goal.

Adult↗

Kinematic and dynamic synergies of human precision-grip movements.

We analyzed the adaptability of human thumb and index finger movement kinematics and dynamics to variations of precision grip aperture and movement velocity. Six subjects performed precision grip opening and closing movements under different conditions of movement velocity and movement aperture (thumb and index finger tip-to-tip distance). Angular motion of the thumb and index finger joints was recorded with a CyberGlove and a three-dimensional biomechanical model was used for solving the inverse dynamics problem during precision grip movements, i.e., for calculating joint torques from experimentally obtained angular variations. The time-varying joint angles and joint torques were analyzed by principal-component analysis to quantify the contributions of individual joints in kinematic and dynamic synergies. At the level of movement kinematics, we found subject-specific angular contributions. However, the adaptation to large aperture, achieved by an increase of the relative contribution of the proximal joints, was subject-invariant. At the level of movement dynamics, the adaptation of thumb-index finger movements to task constraints was similar among all subjects and required the linear scaling of joint torques, the synchronization of joint torques under high velocity conditions, and a flexible redistribution of joint torques between the proximal joint of the thumb and that of the index finger. This work represents one of the first attempts at calculating the joint torques during human precision-grip movements and indicates that the dynamic synergies seem to be remarkably simple compared with the synergies found for movement kinematics.

Adult↗

Hierarchical organization in smooth dynamical systems.

This article is concerned with defining and characterizing hierarchical structures in smooth dynamical systems. We define transitions between levels in a dynamical hierarchy by smooth projective maps from a phase space on a lower level, with high dimensionality, to a phase space on a higher level, with lower dimensionality. It is required that each level describe a self-contained deterministic dynamical system. We show that a necessary and sufficient condition for a projective map to be a transition between levels in the hierarchy is that the kernel of the differential of the map is tangent to an invariant manifold with respect to the flow. The implications of this condition are discussed in detail. We demonstrate two different causal dependences between degrees of freedom, and how these relations are revealed when the dynamical system is transformed into global Jordan form. Finally these results are used to define functional components on different levels, interaction networks, and dynamical hierarchies.

Linear Models↗

A neuro-mimetic dynamic scheduling algorithm for control: analysis and applications.

A simple neuronal network model of the baroreceptor reflex is analyzed. From a control perspective, the analysis suggests a dynamic scheduled control mechanisms by which the baroreflex may perform regulation of the blood pressure. The main objectives of this work are to investigate the static and dynamic response characteristics of the single neurons and the network, to analyze the neuromimetic dynamic scheduled control function of the model, and to apply the algorithm to nonlinear process control problems. The dynamic scheduling activity of the network is exploited in two control architectures. Control structure I is drawn directly from the present model of the baroreceptor reflex. An application of this structure for level control in a conical tank is described. Control structure II employs an explicit set point to determine the feedback error. The performance of this control structure is illustrated on a nonlinear continuous stirred tank reactor with van de Vusse kinetics. The two case studies validate the dynamic scheduled control approach for nonlinear process control applications.

Algorithms↗

Dynamic spatial processing originates in early visual pathways.

A variety of studies in the visual system demonstrate that coarse spatial features are processed before those of fine detail. This aspect of visual processing is assumed to originate in striate cortex, where single cells exhibit a refinement of spatial frequency tuning over the duration of their response. However, in early visual pathways, well known temporal differences are present between center and surround components of receptive fields. Specifically, response latency of the receptive field center is relatively shorter than that of the surround. This spatiotemporal inseparability could provide the basis of coarse-to-fine dynamics in early and subsequent visual areas. We have investigated this possibility with three separate approaches. First, we predict spatial-frequency tuning dynamics from the spatiotemporal receptive fields of 118 cells in the lateral geniculate nucleus (LGN). Second, we compare these linear predictions to measurements of tuning dynamics obtained with a subspace reverse correlation technique. We find that tuning evolves dramatically in thalamic cells, and that tuning changes are generally consistent with the temporal differences between spatiotemporal receptive field components. Third, we use a model to examine how different sources of dynamic input from early visual pathways can affect tuning in cortical cells. We identify two mechanisms capable of producing substantial dynamics at the cortical level: (1) the center-surround delay in individual LGN neurons, and (2) convergent input from multiple cells with different receptive field sizes and response latencies. Overall, our simulations suggest that coarse-to-fine tuning in the visual cortex can be generated completely by a feedforward process.

Action Potentials↗

[Continuous-discrete models of the dynamics of an isolated population and of 2 competing species].

The paper presents the analysis of various mathematical models for dynamics of isolated population and for competition between two species. It is assumed that mortality is continuous and birth of individuals of new generations takes place in certain fixed moments. Influence of winter upon the population dynamics and conditions of classic discrete model "deduction" of population dynamics (in particular, Moran-Ricker and Hassel's models) are investigated. Dynamic regimes of models under various assumptions about the birth and death rates upon the population states are also examined. Analysis of models of isolated population dynamics with nonoverlapping generations showed the density changes regularly if the birth rate is constant. Moreover, there exists a unique global stable level and population size stabilizes asymptotically at this equilibrium, i.e. cycle and chaotic regimes in various discrete models depend on correlation between individual productivity and population state in previous time. When the correlation is exponential upon mean population size the discrete Hassel model is realized. Modification of basis model, based on the assumption that during winter survival/death changes are constant, showed that population size at global level is stable. Generally, the dependence of population rate upon "winter parameters" has nonlinear character. Nonparametric models of competition between two species does not vary if the individual productivity is constant. In a phase space there are several stable stationary states and population stabilizes at one or other level asymptotically. So, in discrete models of competition between two species oscillation can be explained by dependence of population growth rate on the population size at previous times.

Animals↗

[Non linear analysis of infection diseases dynamics in Chile].

BACKGROUND: The incidence of infectious diseases generally has large fluctuations, probably due to interactions between seasonal fluctuations and those secondary to case-susceptible host interactions. AIM: To analyze the complexity and attractant topological resemblance of seven infectious diseases in Chile. MATERIAL AND METHODS: The annual incidence of measles, whooping cough, scarlet fever, meningococcal meningitis, diphtheria, typhoid fever and poliomyelitis was obtained from the annual reports of diseases. Correlation dimensions and the largest Lyapunov series exponents were estimated. The resemblance among their attractants was assessed by Hausdorff distance. The measures were performed both before and after seasonal filtering. RESULTS: All series showed a dynamics near low dimensional chaos. The correlation dimensions ranged between 2.12 and 2.76. The correlation dimensions did not change after seasonal differentiation. Apart from one, all disease dynamics had large Lyapunov exponents, near 0.6 Bits/year. These decreased if series were differentiated. Before differentiation, the topological resemblance was mainly caused by the seasonal component of the dynamics but thereafter, the resemblance increased. In spite of different transmission mechanisms and etiologies, all analyzed infectious diseases conformed a truly single group, during cluster analyses. CONCLUSIONS: These results suggest that beneath the dynamics of infectious diseases, obscured by seasonal environmental factors, lays a very consistent nonlinear agent-susceptible host dynamics.

Chile↗

Complex dynamics and the structure of small neural networks.

The discrete-time dynamics of small neural networks is studied empirically, with emphasis laid on non-trivial bifurcation scenarios. For particular two- and three-neuron networks interesting dynamical properties like periodic, quasi-periodic and chaotic attractors are observed, many of them co-existing for one and the same set of parameters. An appropriate equivalence class of networks is defined, describing them as parametrized dynamical systems with identical dynamical capacities. Combined symmetries in phase space and parameter space are shown to generate different representatives of such a class. Moreover, conditions on the connectivity structure are suggested, which guarantee the existence of complex dynamics for a considered equivalence class of network configurations.

Algorithms↗

[Application of fuzzy cluster in analyzing population dynamics of Chorthippus fallax].

The population dynamics includes quantity dynamics, space dynamics and temporal dynamics. They are interdependent and mutually influential. Fuzzy cluster analysis was carried out with the data of mean densities, indices of patchiness and occupied plot rates of Chorthippus fallax(Zubovsky) on Ganjia High Mountain Grassland in Xia-he County, Gansu Province. The results showed that the population dynamics of this grasshopper could be divided into four distinct periods, i.e., the initial stage of hatching and the last stage of adult, the peak stage of nymph, the initial stage of adult, and the peak stage of first nymph and the adult. The peak period of nymph was in the middle ten days to the last ten days of July. In this period, the eggs were completely hatched, the population was mainly composed of nymphs of 2 and 3 instars, and the population size was related to the numbers and harmful levels of this grasshopper in the same year. Therefore, this period was the key time for population prediction and chemical control.

Animals↗

A dynamic life table model of Psorophora columbiae in the southern Louisiana rice agroecosystem with supporting hydrologic submodel. Part 1. Analysis of literature and model development.

During the past decade, the rice agroecosystem and its associated mosquitoes have been the subject of an extensive research effort directed toward the development and implementation of integrated pest management (IPM) strategies. The objective of this work was to synthesize the literature and unpublished data on the rice agroecosystem into a comprehensive simulation model of the key elements of the system known to influence the population dynamics of Psorophora columbiae. Subsequent companion papers will present a validation of these models, provide an in-depth analysis of the population dynamics of Ps. columbiae, and evaluate current and proposed IPM strategies for this mosquito. This paper describes the development of 2 models: WaterMod: Because spatial and temporal distributions of surface water and soil moisture play a decisive role in the dynamics of Ps. columbiae, an essentially hydrological simulator was developed. Its purpose is to provide environmental inputs for a second model (PcSim) which simulates the population dynamics of Ps. columbiae. WaterMod utilizes data on weather, agricultural practices, and soil characteristics for a particular region to generate a data set containing daily estimates of soil moisture and depth of water table for 12 representative areas comprising the rice agroecosystem. This model could be used to provide hydrologic inputs for additional simulation models of other riceland mosquito species. PcSim: This model simulates the population dynamics of Ps. columbiae by using the computer to maintain a daily accounting of the absolute number of mosquitoes within each daily age class for each life stage. The model creates estimates of the number of eggs, larvae, pupae, and adults for a representative l-ha area of a rice agroecosystem.

Actuarial Analysis↗

Population dynamics of two species of Eimeria (Apicomplexa: Eimeriidae) in deer mice (Peromyscus maniculatus): biotic and abiotic factors.

I investigated whether biotic factors (competitive exclusion between parasites and host immunity), abiotic factors (high temperature, low temperature, and rainfall), or a combination of the 2 affected the population dynamics of Eimeria arizonensis and Eimeria delicata in naturally infected deer mice (Peromyscus maniculatus). There was no evidence of competitive exclusion between E. arizonensis and E. delicata, nor were E. arizonensis population dynamics affected by host immunity (young deer mice were not infected significantly more frequently than adults). However, high temperatures were negatively associated with the prevalence of observed infections (r = -0.725, P < 0.001), suggesting sporulation of oocysts might be affected. In contrast, juvenile deer mice were infected with E. delicata more frequently than adults (z = 2.05, P < 0.02), suggesting that host immunity plays a role in the population dynamics of E. delicata. Temperature and rainfall during oocyst sporulation were not significantly associated with the prevalence of observed E. delicata infections. Finally, there was no evidence that a combination of biotic and abiotic factors was important in the population dynamics of either eimerian. Thus, the population dynamics of E. arizonensis seem to be controlled by abiotic factors, whereas those of E. delicata seem to be affected by biotic factors.

Age Factors↗

The application of methods of non-linear dynamics for the improved and predictive recognition of patients threatened by sudden cardiac death.

OBJECTIVES: This study introduces new methods of non-linear dynamics (NLD) and compares these with traditional methods of heart rate variability (HRV) and high resolution ECG (HRECG) analysis in order to improve the reliability of high risk stratification. METHODS: Simultaneous 30 min high resolution ECG's and long-term ECG's were recorded from 26 cardiac patients after myocardial infarction (MI). They were divided into two groups depending upon the electrical risk, a low risk group (group 2, n = 10) and a high risk group (group 3, n = 16). The control group consisted of 35 healthy persons (group 1). From these electrocardiograms we extracted standard measures in time and frequency domain as well as measures from the new non-linear methods of symbolic dynamics and renormalized entropy. RESULTS: Applying discriminant function techniques on HRV analysis the parameters of non-linear dynamics led to an acceptable differentiation between healthy persons and high risk patients of 96%. The time domain and frequency domain parameters were successful in less than 90%. The combination of parameters from all domains and a stepwise discriminant function separated these groups completely (100%). Use of this discriminant function classified three patients with apparently low (no) risk into the same cluster as high risk patients. The combination of the HRECG and HRV analysis showed the same individual clustering but increased the positive value of separation. CONCLUSIONS: The methods of NLD describe complex rhythm fluctuations and separate structures of non-linear behavior in the heart rate time series more successfully than classical methods of time and frequency domains. This leads to an improved discrimination between a normal (healthy persons) and an abnormal (high risk patients) type of heart beat generation. Some patients with an unknown risk exhibit similar patterns to high risk patients and this suggests a hidden high risk. The methods of symbolic dynamics and renormalized entropy were particularly useful measures for classifying the dynamics of HRV.

Death, Sudden, Cardiac↗