Plankton-toxin interaction with a variable input nutrient

A simple model of phytoplankton–zooplankton interaction with a periodic input nutrient is presented. The model is then used to study a nutrient–plankton interaction with a toxic substance that inhibits the growth rate of plankton populations. The effects of the toxin upon the existence, magnitude, and stability of the periodic solutions are discussed. Numerical simulations are also provided to illustrate analytical results and to compare more complicated dynamical behaviour.     

Chaotic behavior in the locomotion ofamoeba proteus

Summary The locomotion ofAmoeba proteus has been investigated by algorithms evaluating correlation dimension and Lyapunov spectrum developed in the field of nonlinear science. It is presumed by these parameters whether the random behavior of the system is stochastic or deterministic. For the analysis of the nonlinear parameters, n-dimensional time-delayed vectors have been reconstructed from a time series of periphery and area ofA. proteus images captured with a charge-coupled-device camera, which characterize its random motion. The correlation dimension analyzed has shown the random motion ofA. proteus is subjected only to 3–4 macrovariables, though the system is a complex system composed of many degrees of freedom. Furthermore, the analysis of the Lyapunov spectrum has shown its largest exponent takes positive values. These results indicate the random behavior ofA. proteus is chaotic and deterministic motion on an attractor with low dimension. It may be important for the elucidation of the cell locomotion to take account of nonlinear interactions among a small number of dynamics such as the sol-gel transformation, the cytoplasmic streaming, and the relating chemical reaction occurring in the cell.     

Chaotic dynamics of the surface potential of human skeletal muscles determined in electromyography

A new method for differential evaluation of electromyographic data on straited muscles of human lower extremities was developed. This method is based on nonlinear dynamics and thermodynamics and can be used for identification of pathologies. The distance between two trajectories of the potential of two symmetric muscles was the main measured characteristic of coordinated muscle work. These data were used to determine the Lyapunov exponent and the time of forgetting initial conditions, which reflect the generally chaotic dynamics of muscle activity. Application of the theory of deterministic chaos to analysis of electromyographic patterns can improve the diagnosis of peripheral nervous system diseases and the efficacy of treatment control. Quantitation of nonlinear dynamic parameters of muscle activity, clear data representation, high prognostic information content of the Lyapunov exponent and Kolmogorov entropy are among the advantages of the new method.     

具有共生作用两种群离散耦合Logistic模型混沌控制

针对具有共生作用的离散耦合Logistic模型,首先采用Lyapunov指数方法验证了混沌现象的存在.然后详细地分析了系统随参数变化的分岔图,发现了系统中存在更复杂的现象.最后应用混沌跟踪控制方法控制系统的混沌现象,使得种群稳定到正不动点轨道上,消除了种群中存在的混沌现象.仿真结果验证了控制方法的有效性.     

Capturing the bursting dynamics of a two-cell inhibitory network using a one-dimensional map

Out-of-phase bursting is a functionally important behavior displayed by central pattern generators and other neural circuits. Understanding this complex activity requires the knowledge of the interplay between the intrinsic cell properties and the properties of synaptic coupling between the cells. Here we describe a simple method that allows us to investigate the existence and stability of anti-phase bursting solutions in a network of two spiking neurons, each possessing a T-type calcium current and coupled by reciprocal inhibition. We derive a one-dimensional map which fully characterizes the genesis and regulation of anti-phase bursting arising from the interaction of the T-current properties with the properties of synaptic inhibition. This map is the burst length return map formed as the composition of two distinct one-dimensional maps that are each regulated by a different set of model parameters. Although each map is constructed using the properties of a single isolated model neuron, the composition of the two maps accurately captures the behavior of the full network. We analyze the parameter sensitivity of these maps to determine the influence of both the intrinsic cell properties and the synaptic properties on the burst length, and to find the conditions under which multistability of several bursting solutions is achieved. Although the derivation of the map relies on a number of simplifying assumptions, we discuss how the principle features of this dimensional reduction method could be extended to more realistic model networks. Action Editor: John Rinzel     

A hexapedal jointed-leg model for insect locomotion in the horizontal plane

We develop a simple model for insect locomotion in the horizontal (ground) plane. As in earlier work by Seipel et al. (Biol Cybern 91(0):76–90, 2004) we employ six actuated legs that also contain passive springs, but the legs, with “hip” and ‘knee’ joints, better represent insect morphology. Actuation is provided via preferred angle inputs at each joint, corresponding to zero torques in the hip and knee springs. The inputs are determined from estimates of foot forces in the cockroach Blaberus discoidalis via an inverse problem. The head–thorax–body is modeled as a single rigid body, and leg masses, inertia and joint dissipation are ignored. The resulting three degree-of-freedom dynamical system, subject to feedforward joint inputs, exhibits stable periodic gaits that compare well with observations over the insect’s typical speed range. The model’s response to impulsive perturbations also matches that of freely-running cockroaches (Jindrich and Full, J Exp Biol 205:2803–2823, 2002), and stability is maintained in the face of random foot touchdowns representative of real insects. We believe that this model will allow incorporation of realistic muscle models driven by a central pattern generator in place of the joint actuators, and that it will ultimately permit the study of proprioceptive feedback pathways involving leg force and joint angle sensing.     

On the dynamics of electrically-coupled neurons with inhibitory synapses

We study the dynamics and bifurcations of noise-free neurons coupled by gap junctions and inhibitory synapses, using both delayed delta functions and alpha functions to model the latter. We focus on the case of two cells, as in the studies of Chow and Kopell (2000) and Lewis and Rinzel (2003), but also show that stable asynchronous splay states exist for globally coupled networks of N cells dominated by subthreshold electrical coupling. Our results agree with those of Lewis and Rinzel (2003) in the weak coupling range, but our Poincaré map analysis yields more information about global behavior and domains of attraction, and we show that the explicit discontinuous maps derived using delayed delta functions compare well with the continuous history-dependent, implicitly-defined maps derived from alpha functions. We find that increased bias currents, super-threshold electrical coupling and synaptic delays promote synchrony, while sub-threshold electrical coupling and fast synapses promote asynchrony. We compare our analytical results with simulations of an ionic current model of spiking cells, and briefly discuss implications for stimulus response modes of locus coeruleus and for central pattern generators. Action Editor: F. Skinner     

An analysis of the reliability phenomenon in the FitzHugh-Nagumo model

The reliability of single neurons on realistic stimuli has been experimentally confirmed in a wide variety of animal preparations. We present a theoretical study of the reliability phenomenon in the FitzHugh-Nagumo model on white Gaussian stimulation. The analysis of the model's dynamics is performed in three regimes—the excitable, bistable, and oscillatory ones. We use tools from the random dynamical systems theory, such as the pullbacks and the estimation of the Lyapunov exponents and rotation number. The results show that for most stimulus intensities, trajectories converge to a single stochastic equilibrium point, and the leading Lyapunov exponent is negative. Consequently, in these regimes the discharge times are reliable in the sense that repeated presentation of the same aperiodic input segment evokes similar firing times after some transient time. Surprisingly, for a certain range of stimulus intensities, unreliable firing is observed due to the onset of stochastic chaos, as indicated by the estimated positive leading Lyapunov exponents. For this range of stimulus intensities, stochastic chaos occurs in the bistable regime and also expands in adjacent parts of the excitable and oscillating regimes. The obtained results are valuable in the explanation of experimental observations concerning the reliability of neurons stimulated with broad-band Gaussian inputs. They reveal two distinct neuronal response types. In the regime where the first Lyapunov has negative values, such inputs eventually lead neurons to reliable firing, and this suggests that any observed variance of firing times in reliability experiments is mainly due to internal noise. In the regime with positive Lyapunov exponents, the source of unreliable firing is stochastic chaos, a novel phenomenon in the reliability literature, whose origin and function need further investigation.     

Circadian rhythm of atrioventricular conduction predicts long-term survival in patients with chronic atrial fibrillation

The R–R interval of the electrocardiogram during atrial fibrillation (AF) appears absolutely irregular. However, the Poincaré plot of the R–R interval reveals a sector shape of distribution that is unique to AF. Furthermore, the height of lower envelope (LE_1.0) of the distribution and the degree of scatter above the envelope (scattering index) may reflect the refractoriness and concealment of atrioventricular (AV) conduction, respectively. We previously observed that both the LE_1.0 and scattering index show clear circadian rhythms in patients with chronic AF and that the rhythms are blunted in those with congestive heart failure and chronic AF. In the present study, we examined if the blunted circadian rhythm of the AV conduction has prognostic value in patients with chronic AF. We studied a retrospective cohort of 120 patients who underwent 24h Holter monitoring at baseline. During an observation period of 33±16 mon, there were 25 deaths (21%) including 13 cardiac and 8 stroke deaths. All patients showed significant circadian rhythms in both LE_1.0 and scattering index with acrophases occurring at night; however, patients dying subsequently from cardiac causes, but not those from fatal stroke were blunted in the circadian rhythms (the amplitudes were <55% of those in surviving patients). Furthermore, the reduced circadian amplitude of scattering index was an increased risk for cardiac death even after adjustment of coexisting cardiovascular risks [adjusted relative risk (95% confidence interval) per 1-SD decrement, 4.24 (1.54–11.6)]. When patients were divided by the circadian amplitude of the scattering index of 36.5 msec (mean minus 1-SD), the 5yr cardiac mortality below and above the cutoff was 57 and 6%, respectively (log-rank test, p<0.001). We conclude that the blunted circadian rhythm of AV conduction is an independent risk for cardiac death in patients with chronic AF.     

Kinematic Analysis of the Neck and Upper Extremities During Walking in Healthy Young Adults

The objective of this paper is to quantify the local stabilities of the neck and upper extremities (right/left shoulders and right/left elbows), and investigate differences between linear and nonlinear measurements of the associated joint motions and differences in the local stability between the upper and lower extremities. This attempt involves the calculation of a nonlinear parameter, Lyapunov Exponent (LE), and a linear parameter, Range of Motion (ROM), during treadmill walking in conjunction with a large population of healthy subjects. Joint motions of subjects were captured using a three-dimensional motion-capture system. Then mathematical chaos theory and the Rosenstein algorithm were employed to calculate LE of joints as the extent of logarithmic divergence between the neighboring state-space trajectories of flexion-extension angles. LEs computed over twenty males and twenty females were 0.037±0.023 for the neck, 0.043±0.021 for the right shoulder, 0.045±0.030 for the left shoulder, 0.032±0.021 for the right elbow, and 0.034±0.026 for the left elbow. Although statistically significant difference in the ROM was observed between all pairs of the neck and upper extremity joints, differences in the LE between all pairs of the joints as well as between males and females were not statistically significant. Between the upper and lower extremities, LEs of the neck, shoulder, and elbow were significantly smaller than those of the hip (∼0.064) and the knee (∼0.062). These results indicate that a statistical difference in the local stability between the upper extremity joints is not significant. However, the different result between the ROM and LE gives a strong rationale for applying both linear and nonlinear tools together to the evaluation of joint movement. The LEs of the joints calculated from a large population of healthy subjects could provide normative values for the associated joints and can be used to evaluate the recovery progress of patients with joint related diseases.     

Comparison of reaction-diffusion simulations with experiment in self-organised microtubule solutions

This article deals with the physical chemical processes underlying biological self-organization by which an initially homogenous solution of reacting chemicals spontaneously self-organizes so as to give rise to a preparation of macroscopic order and form. Theoreticians have predicted that self-organization can arise from a coupling of reactive processes with molecular diffusion. In addition, the presence or absence of an external field, such as gravity, at a critical moment early in the self-organizing process may determine the morphology that subsequently develops. We have found that the formation in vitro of microtubules, a major element of the cellular skeleton, show this type of behaviour. The microtubule preparations spontaneously self-organise by way of reaction and diffusion, and the morphology of the state that forms depends on the presence of gravity at a critical moment early in the process. We have developed a numerical reaction-diffusion scheme, based on the chemical dynamics of a population of microtubules, which simulates the experimental self-organisation. In this article we outline the main features of these simulations and discuss the manner by which a permanent dialogue with experiment has helped develop a microscopic understanding of the collective behaviour.     

Approximate expressions of the bifurcating periodic solutions in a neuron model with delay-dependent parameters by perturbation approach

This paper is interested in gaining insights of approximate expressions of the bifurcating periodic solutions in a neuron model. This model shares the property of involving delay-dependent parameters. The presence of such dependence requires the use of suitable criteria which usually makes the analytical work so harder. Most existing methods for studying the nonlinear dynamics fail when applied to such a class of delay models. Although Xu et al. (Phys Lett A 354:126–136, 2006) studied stability switches, Hopf bifurcation and chaos of the neuron model with delay-dependent parameters, the dynamics of this model are still largely undetermined. In this paper, a detailed analysis on approximation to the bifurcating periodic solutions is given by means of the perturbation approach. Moreover, some examples are provided for comparing approximations with numerical solutions of the bifurcating periodic solutions. It shows that the dynamics of the neuron model with delay-dependent parameters is quite different from that of systems with delay-independent parameters only.     

Research strategies in the pharmaceutical industry to cope with the problems of ageing

The present research strategies for ageing are focussed around three areas. The first area is the demographic study of the present-day populations and those in the future. The analysis of the evolution of the metropolitan French population from 1950 to 2050 indicates that the proportion of subjects aged greater than 60 years will pass from 16% to 35%. In addition, the level of dependence of these subjects will vary considerably from one to another. The second area is the integration of epidemiological data of the pathologies related to the aged subject. Numerous epidemiological studies of the aged show that the elderly population is in better health, better informed about the diseases that affect them and also financially more secure, which allows them to take better care of themselves. The epidemiological studies of certain dementias show, for example, that if we reduce the delay to when the disease appears by five years, then we reduce the prevalence by a factor of 2. The third area relates to the important new progress in the understanding of the biological mechanisms involved in cellular ageing. The recent progress in the area of cellular biology has started to decode the complex mechanisms underlying cellular ageing. The important understanding of the phenomena of apoptose with the development of relevant biological models of the natural ageing process have anticipated future treatments and, eventually, the prophylactic treatment of specific pathologies of the elderly patient.     

Evidence for a 2-oxoglutarate dehydrogenase complex activity in mitochondria of Neurospora crassa and compared localization with the pyruvate dehydrogenase complex

A 2-oxoglutarate dehydrogenase complex activity is demonstrated in Neurospora crassa mitochondria. A submitochondrial fractionation by digitonin treatment followed by freeze-thawing enables measurement of a well preserved activity in the mitochondrial matrix. In contrast to other reports, the pyruvate dehydrogenase activity is also found to be localized in the matrix.     

Morphological correlates of the first metacarpal proximal articular surface with manipulative capabilities in apes,humans and South African early hominins

This study quantifies the metacarpal 1 (MC 1) proximal articular surface using three-dimensional morphometrics in extant hominids and fossil hominins (SK 84, cf. Paranthropus robustus/Homo erectus and StW 418, Australopithecus africanus) to understand which characteristics of the proximal metacarpal 1 are potentially correlated with human manipulative abilities and if they can be used in a paleoanthropological setting. A principal components (PC) analysis was used to compare MC 1 proximal articular surface shape and ANOVA and Tukey's HSD post-hoc tests were conducted to determine differences among groups. Homo is significantly different from nonhuman hominids having a less radioulnarly and dorsovolarly curved articular surface. All nonhuman hominids have more curved articular surface with Gorilla showing the most curved joint. Moreover, this study highlights the presence of a radially extended surface in Homo that may be related to the greater thumb abduction in human manipulation activities. Both fossils analyzed show a great ape-like MC 1 proximal articular surface which, associated with recent trabecular and archaeological evidence, may indicate that the ability to make/use stone tools preceded the morphological adaptations associated today with such behavior.     

Predicting the activity phase of a follower neuron with A-current in an inhibitory network

The transient potassium A-current is present in most neurons and plays an important role in determining the timing of action potentials. We examine the role of the A-current in the activity phase of a follower neuron in a rhythmic feed-forward inhibitory network with a reduced three-variable model and conduct experiments to verify the usefulness of our model. Using geometric analysis of dynamical systems, we explore the factors that determine the onset of activity in a follower neuron following release from inhibition. We first analyze the behavior of the follower neuron in a single cycle and find that the phase plane structure of the model can be used to predict the potential behaviors of the follower neuron following release from inhibition. We show that, depending on the relative scales of the inactivation time constant of the A-current and the time constant of the recovery variable, the follower neuron may or may not reach its active state following inhibition. Our simple model is used to derive a recursive set of equations to predict the contribution of the A-current parameters in determining the activity phase of a follower neuron as a function of the duration and frequency of the inhibitory input it receives. These equations can be used to demonstrate the dependence of activity phase on the period and duty cycle of the periodic inhibition, as seen by comparing the predictions of the model with the activity of the pyloric constrictor (PY) neurons in the crustacean pyloric network.     

中国对虾抗WSSV及其它经济性状的QTL定位初步研究

以中国对虾抗WSSV选育群体第四代雌虾和野生中国对虾雄虾为亲本,采用人工精荚移植方式产生F1代家系,家系内个体姊妹交获得R家系材料,42尾R家系个体采用口饲法进行WSSV（White Spot Syndrome Virus）攻毒实验,获得个体抗WSSV及其它相关数据。构建了中国对虾的AFLP（Amphfied Fragment Length Polymorphism）分子标记遗传连锁图谱。利用MAPMAKER／QTL1．1软件进行了中国对虾体长、全长、体重及抗WSSV性状的QTL（Quantitative TraitsLoci）定位分析,首次实现了中国对虾重要经济性状的QTL定位。在LOD值大于2．0的条件下,共检测到和体长相关的QTL位点1个,与全长相关的QTL位点2个,与体重相关的QTL位点2个,与抗WSSV性状相关的位点2个,分别位于3个连锁群上,位点变异解释率从26．6％-66．9％不等。在其中的1个连锁群上检测到了体重、全长和抗WSSV性状相关的三个QTL位点,1个连锁群上检测到了体重和抗WSSV性状相关的两个QTL位点,1个连锁群上检测到了全长和体长相关的两个QTL位点。表明在中国对虾在此生长阶段,抗WSSV性状和个体大小存在一定程度的正相关关系[动物学报54（6）：1075-1081,2008]。