Partial phase synchronization of neural populations due to random Poisson inputs

We show that populations of identical uncoupled neurons exhibit partial phase synchronization when stimulated with independent, random unidirectional current spikes with interspike time intervals drawn from a Poisson distribution. We characterize this partial synchronization using the phase distribution of the population, and consider analytical approximations and numerical simulations of phase-reduced models and the corresponding conductance-based models of typical Type I (Hindmarsh-Rose) and Type II (Hodgkin-Huxley) neurons, showing quantitatively how the extent of the partial phase synchronization depends on the magnitude and mean interspike frequency of the stimulus. Furthermore, we present several simple examples that disprove the notion that phase synchrony must be strongly related to spike synchrony. Instead, the importance of partial phase synchrony is shown to lie in its influence on the response of the population to stimulation, which we illustrate using first spike time histograms.     

The frustrated brain: from dynamics on motifs to communities and networks

Cognitive function depends on an adaptive balance between flexible dynamics and integrative processes in distributed cortical networks. Patterns of zero-lag synchrony likely underpin numerous perceptual and cognitive functions. Synchronization fulfils integration by reducing entropy, while adaptive function mandates that a broad variety of stable states be readily accessible. Here, we elucidate two complementary influences on patterns of zero-lag synchrony that derive from basic properties of brain networks. First, mutually coupled pairs of neuronal subsystems—resonance pairs—promote stable zero-lag synchrony among the small motifs in which they are embedded, and whose effects can propagate along connected chains. Second, frustrated closed-loop motifs disrupt synchronous dynamics, enabling metastable configurations of zero-lag synchrony to coexist. We document these two complementary influences in small motifs and illustrate how these effects underpin stable versus metastable phase-synchronization patterns in prototypical modular networks and in large-scale cortical networks of the macaque (CoCoMac). We find that the variability of synchronization patterns depends on the inter-node time delay, increases with the network size and is maximized for intermediate coupling strengths. We hypothesize that the dialectic influences of resonance versus frustration may form a dynamic substrate for flexible neuronal integration, an essential platform across diverse cognitive processes.     

Probing the interaction between cHAVc3 peptide and the EC1 domain of E-cadherin using NMR and molecular dynamics simulations

The goal of this work is to probe the interaction between cyclic cHAVc3 peptide and the EC1 domain of human E-cadherin protein. Cyclic cHAVc3 peptide (cyclo(1,6)Ac-CSHAVC-NH₂) binds to the EC1 domain as shown by chemical shift perturbations in the 2D ¹H,-¹⁵N-HSQC NMR spectrum. The molecular dynamics (MD) simulations of the EC1 domain showed folding of the C-terminal tail region into the main head region of the EC1 domain. For cHAVc3 peptide, replica exchange molecular dynamics (REMD) simulations generated five structural clusters of cHAVc3 peptide. Representative structures of cHAVc3 and the EC1 structure from MD simulations were used in molecular docking experiments with NMR constraints to determine the binding site of the peptide on EC1. The results suggest that cHAVc3 binds to EC1 around residues Y36, S37, I38, I53, F77, S78, H79, and I94. The dissociation constants (K_d values) of cHAVc3 peptide to EC1 were estimated using the NMR chemical shifts data and the estimated K_ds are in the range of .5 × 10^?5–7.0 × 10^?5 M.     

On synchronization in semelparous populations

Synchronization, i.e., convergence towards a dynamical state where the whole population is in one age class, is a characteristic feature of some population models with semelparity. We prove some rigorous results on this, for a simple class of nonlinear one- population models with age structure and semelparity: (i) the survival probabilities are assumed constant, and (ii) only the last age class is reproducing (semelparity), with fecundity decreasing with total population. For this model we prove: (a) The synchronized, or Single Year Class (SYC), dynamical state is always attracting. (b) The coexistence equilibrium is often unstable; we state and prove simple results on this. (c) We describe dynamical states with some, but not all, age classes populated, which we call Multiple Year Class (MYC) patterns, and we prove results extending (a) and (b) into these patterns.Acknowledgement Boris Kruglikov contributed the nonlinear part of the formulation as well as the proof of Theorem 1. The authors are grateful for critical and constructive comments by N. Davydova and O. Diekmann. E.M. is also grateful for discussions with Marius Overholt concerning problems of proving Theorem 2.     

A multi-body dynamics study on a weight-drop test of rat brain injury

Traumatic brain injury (TBI), induced by impact of an object with the head, is a major health problem worldwide. Rats are a well-established animal analogue for study of TBI and the weight-drop impact-acceleration (WDIA) method is a well-established model in rats for creating diffuse TBI, the most common form of TBI seen in humans. However, little is known of the biomechanics of the WDIA method and, to address this, we have developed a four-degrees-of-freedom multi-body mass-spring-damper model for the WDIA test in rats. An analytical expression of the maximum skull acceleration, one of the important head injury predictor, was derived and it shows that the maximum skull acceleration is proportional to the impact velocity but independent of the impactor mass. Furthermore, a dimensional analysis disclosed that the maximum force on the brain and maximum relative displacement between brain and skull are also linearly proportional to impact velocity. Additionally, the effects of the impactor mass were examined through a parametric study from the developed multi-body dynamics model. It was found that increasing impactor mass increased these two brain injury predictors.     

Probing the effects of the well-mixed assumption on viral infection dynamics

Viral kinetics have been extensively studied in the past through the use of spatially well-mixed ordinary differential equations describing the time evolution of the diseased state. However, emerging spatial structures such as localized populations of dead cells might adversely affect the spread of infection, similar to the manner in which a counter-fire can stop a forest fire from spreading. In a previous publication [Beauchemin, C., Samuel, J., Tuszynski, J., 2005. A simple cellular automaton model for influenza A viral infections. J. Theor. Biol. 232(2), 223-234], a simple two-dimensional cellular automaton model was introduced and shown to be accurate enough to model an uncomplicated infection with influenza A. Here, this model is used to investigate the effects of relaxing the well-mixed assumption. Particularly, the effects of the initial distribution of infected cells, the regeneration rule for dead epithelial cells, and the proliferation rule for immune cells are explored and shown to have an important impact on the development and outcome of the viral infection in our model.     

Maintaining robust size across environmental conditions through plastic brain growth dynamics

Organ growth is tightly regulated across environmental conditions to generate an appropriate final size. While the size of some organs is free to vary, others need to maintain constant size to function properly. This poses a unique problem: how is robust final size achieved when environmental conditions alter key processes that regulate organ size throughout the body, such as growth rate and growth duration? While we know that brain growth is ‘spared’ from the effects of the environment from humans to fruit flies, we do not understand how this process alters growth dynamics across brain compartments. Here, we explore how this robustness in brain size is achieved by examining differences in growth patterns between the larval body, the brain and a brain compartment—the mushroom bodies—in Drosophila melanogaster across both thermal and nutritional conditions. We identify key differences in patterns of growth between the whole brain and mushroom bodies that are likely to underlie robustness of final organ shape. Further, we show that these differences produce distinct brain shapes across environments.     

昆虫种群动态模拟模型

昆虫是动物界中最大的类群,与人类有着密切的利害关系。对昆虫的数量预测与符合经济和生态规律的管理,一直都被国内外列入重点研究课题。种群动态模拟是害虫管理中重要的基础工作。近十年来,关于昆虫种群动态模型的理论和实验研究进展迅速。现分别从单种种群和多种种群两个方面对国内外近些年来昆虫种群动态模拟模型的研究进展进行了概括和总结。单种种群从两个方面阐述:一是最基本的种群动态模拟模型Log istic方程的研究成果,包括方程的修正、参数的拟合与最优捕获策略等;另一个方面是对种群动态模拟常用的矩阵模型的概述,主要介绍不等期年龄组、矩阵维数的变化、矩阵维数与历期的关系、个体之间的发育差异以及发育速率差异等等对昆虫种群动态模型的影响。多种群主要从建模和模型应用两个部分对国内外研究成果进行综述。最后,对种群动态模拟模型研究的发展方向做了深入地讨论,即在原有的数据采集工作的基础上,使用面向对象程序设计语言,把各种要素包括各种物种及各种环境条件抽象成类,用消息传递来表示昆虫种群内个体与个体、昆虫种群与环境之间的相互作用,再结合先进的数学算法,建立一个直观的、操作简单的昆虫种群动态模型库,使模型结构与现实世界有最大的相似性。这样就可以实现昆虫种群动态的可视化、立体化、实时化和精确化的监测及预测。     

Peak-to-peak dynamics in food chain models

We show in this paper that the chaotic regimes of many food chain models often enjoy a very peculiar property, known as peak-to-peak dynamics. This means that the maximum (peak) density of the populations of any trophic level can be easily forecasted provided the last two peaks of the same population are known. Moreover, extensive simulation shows that only the last peak is needed if the forecast concerns the population at the top of the food chain and that peaks variability often increases from bottom to top. All these findings bring naturally to the conclusion that top populations should be sampled in order to have higher chances to detect peak-to-peak dynamics. The analysis is carried out by studying ditrophic food chain models with seasonally varying parameters, tritrophic food chain models with constant parameters, and more complex food chain and food web models.     

Ovarian follicular wave synchronization and pregnancy rate after fixed-time natural mating in llamas

The study was designed to compare the efficacy of treatments intended to induce follicular wave synchronization among llamas (Experiment 1), and to determine the effect of these treatments on pregnancy rates after fixed-time natural mating (Experiment 2). In Experiment 1, llamas were treated with: (1) saline (control, n=20); (2) estradiol and progesterone (E/P, n=20); (3) LH (LH, n=20); or (4) transvaginal ultrasound-guided follicle ablation (FA, n=20). The ovarian response was monitored daily by transrectal ultrasonography. The intervals from treatment to follicular wave emergence and to the day on which the new dominant follicle reached ≥7 mm, respectively, did not differ between the LH (2.1±0.3 days and 5.2±0.5 days, respectively) and FA groups (2.3±0.3 days and 5.0±0.5 days), but both were shorter (P<0.05) and less variable (P<0.01) than in the control group (5.5±1.0 days and 8.4±2.0 days), while the E/P group (4.5±0.8 days and 7.7±0.5 days) was intermediate. In Experiment 2, llamas at unknown stages of follicular development were assigned randomly to control, E/P, and LH groups (n=30 per group). A single, fixed-time natural mating was permitted 10–12 days after treatment. Ovulation rates did not differ among groups (control, 93%; E/P, 90%; LH, 90%; P=0.99), but the pregnancy rate was higher (P<0.05) for synchronized llamas (LH and E/P groups combined, 41/54) than for non-synchronized llamas (control group, 15/28). In conclusion, LH and FA treatments were most effective for inducing follicular wave synchronization, while E/P treatment was intermediate. Synchronization treatments did not influence ovulation rate subsequent to fixed-time natural mating, but a higher pregnancy rate in synchronized than non-synchronized llamas warrants critical evaluation of the effects of follicular status on the developmental competence of the contained oocyte.     

Evolutionary game dynamics with non-uniform interaction rates

The classical setting of evolutionary game theory, the replicator equation, assumes uniform interaction rates. The rate at which individuals meet and interact is independent of their strategies. Here we extend this framework by allowing the interaction rates to depend on the strategies. This extension leads to non-linear fitness functions. We show that a strict Nash equilibrium remains uninvadable for non-uniform interaction rates, but the conditions for evolutionary stability need to be modified. We analyze all games between two strategies. If the two strategies coexist or exclude each other, then the evolutionary dynamics do not change qualitatively, only the location of the equilibrium point changes. If, however, one strategy dominates the other in the classical setting, then the introduction of non-uniform interaction rates can lead to a pair of interior equilibria. For the Prisoner's Dilemma, non-uniform interaction rates allow the coexistence between cooperators and defectors. For the snowdrift game, non-uniform interaction rates change the equilibrium frequency of cooperators.     

The influence of the astrocyte field on neuronal dynamics and synchronization

Astrocytes can sense local synaptic release of glutamate by metabotropic glutamate receptors. Receptor activation in turn can mediate transient increases of astrocytic intracellular calcium concentration through inositol 1,4,5-trisphosphate production. Notably, the perturbation of calcium concentration can propagate to other adjacent astrocytes. Astrocytic calcium signaling can therefore be linked to synaptic information transfer between neurons. On the other hand, astrocytes can also modulate neuronal activity by feeding back onto synaptic terminals in a fashion that depends on their intracellular calcium concentration. Thus, astrocytes can also be active partners in neuronal network activity. The aim of our study is to provide a computationally simple network model of mutual neuron–astrocyte interactions, in order to investigate the possible roles of astrocytes in neuronal network dynamics. In particular, we focus on the information entropy of neuronal firing of the whole network, considering how it could be affected by neuron–glial interactions.     

Local synchronization of one-to-one coupled neural networks with discontinuous activations

In this paper, local synchronization is considered for coupled delayed neural networks with discontinuous activation functions. Under the framework of Filippov solution and in the sense of generalized derivative, a novel sufficient condition is obtained to ensure the synchronization based on the Lyapunov exponent and the detailed analysis in Danca (Int J Bifurcat Chaos 12(8):1813–1826, 2002; Chaos Solitons Fractals 22:605–612, 2004). Simulation results are given to illustrate the theoretical results.     

Flap opening dynamics in HIV-1 protease explored with a coarse-grained model

We present a one-bead coarse-grained model that enables dynamical simulations of proteins on the time scale of tens of microseconds. The parameterization of the force field includes accurate conformational terms that allow for fast and reliable exploration of the configurational space. The model is applied to the dynamics of flap opening in HIV-1 protease. The experimental structure of the recently crystallized semi-open conformation of HIV-1 protease is well reproduced in the simulation, which supports the accuracy of our model. Thanks to very long simulations and extensive sampling of opening and closing events, we also investigate the thermodynamics and kinetics of the opening process. We have shown that the effect of the solvent slows down the dynamics to the experimentally observed time scales. The model is found to be reliable for application to substrate docking simulations, which are currently in progress.     

Understanding interaction and dynamics of water molecules in the epoxy via molecular dynamics simulation

The robust structural integrity of the epoxy plays an important role in ensuring the long-term service life of its applications, which is affected by the absorbed moisture. In order to understand the mechanism of the moisture effect, the knowledge of the interaction and dynamics of the water molecules inside the epoxy is of great interest. Molecular dynamics simulation is used in this work to investigate the structure and bonding behaviour of the water molecules in the highly cross-linked epoxy network. When the moisture concentration is low, the water molecules are well dispersed in the cross-linked structure and located in the vicinity of the epoxy functional groups, which predominantly form the hydrogen bond (H-bond) with the epoxy network, resulting in the low water mobility in the epoxy. At the high concentration, the water favourably forms the large cluster due to the predominant water–water H-bond interaction, and the water molecules diffuse primarily inside the cluster, which leads to the high water mobility and the accelerated H-bond dynamics. The variation of the bonding behaviour and dynamics of the water molecules reported here could be exploited to understand the material change and predict the long-term performance of the epoxy-based products during the intended service life.     

内源性神经干细胞与脑老化的治疗

近十几年研究发现成年人脑神经元可以再生,使人们重新认识老年脑神经细胞的可塑性,它为脑损伤的修复带来新的希望。最新研究表明,神经再生可被调控,是一种新的修复机制。这使得利用内源性神经干细胞治疗老龄相关的神经退行性疾病成为可能。     

Complexity measures of brain wave dynamics

To understand the nature of brain dynamics as well as to develop novel methods for the diagnosis of brain pathologies, recently, a number of complexity measures from information theory, chaos theory, and random fractal theory have been applied to analyze the EEG data. These measures are crucial in quantifying the key notions of neurodynamics, including determinism, stochasticity, causation, and correlations. Finding and understanding the relations among these complexity measures is thus an important issue. However, this is a difficult task, since the foundations of information theory, chaos theory, and random fractal theory are very different. To gain significant insights into this issue, we carry out a comprehensive comparison study of major complexity measures for EEG signals. We find that the variations of commonly used complexity measures with time are either similar or reciprocal. While many of these relations are difficult to explain intuitively, all of them can be readily understood by relating these measures to the values of a multiscale complexity measure, the scale-dependent Lyapunov exponent, at specific scales. We further discuss how better indicators for epileptic seizures can be constructed.     

复合种群动态研究进展

复合种群动态研究是当今保护生物学和生态学中最热门的课题之一。在此较为详细地介绍了复合种群动态的有关概念和术语、经验研究和理论探索的最新进展以及相关的预测模型 ,对我国开展相关研究有参考价值。