Circadian rhythm and cell population growth

Molecular circadian clocks, that are found in all nucleated cells of mammals, are known to dictate rhythms of approximately 24 h (circa diem) to many physiological processes. This includes metabolism (e.g., temperature, hormonal blood levels) and cell proliferation. It has been observed in tumor-bearing laboratory rodents that a severe disruption of these physiological rhythms results in accelerated tumor growth.The question of accurately representing the control exerted by circadian clocks on healthy and tumor tissue proliferation to explain this phenomenon has given rise to mathematical developments, which we review. The main goal of these previous works was to examine the influence of a periodic control on the cell division cycle in physiologically structured cell populations, comparing the effects of periodic control with no control, and of different periodic controls between them. We state here a general convexity result that may give a theoretical justification to the concept of cancer chronotherapeutics. Our result also leads us to hypothesize that the above mentioned effect of disruption of circadian rhythms on tumor growth enhancement is indirect, that is, this enhancement is likely to result from the weakening of healthy tissue that is at work fighting tumor growth.     

Simulated test of electric activity of neurons by using Josephson junction based on synchronization scheme

The chaotic circuit of resistive–capacitive–inductive-shunted Josephson junction is used to simulate behavior of Hindmarsh–Rose neuronal discharges. Based on tracking control theory, the controller contains two gain coefficients was constructed to control the chaotic system of Josephson junction to synchronize the chaotic Hindmarsh–Rose system, and the single controller was approached analytically. The results confirmed that the controller with appropriate gain coefficients was effective to reach complete synchronization (the amplitudes and rhythms of two systems are identical), phase synchronization (rhythms of two systems are identical) of Josephson junction and Hindmarsh–Rose neurons, respectively. The power consumption is estimated in a feasible way. As a result, the electric activities of Hindmarsh–Rose neurons could be simulated by using Josephson junction model completely.     

Mutual synchronization behavior for chaotic systems via limited capacity communication channels

Several important properties of chaos synchronization of bidirectional coupled systems remain still unexplored. This article investigates synchronization behavior for chaotic systems subject to states quantization. Based on the invariance principle of differential equations, an adaptive feedback scheme is proposed to strictly synchronize chaotic systems via limited capacity communication channels. Furthermore, it is important to point out that the mutual synchronization behavior for bidirectional coupled systems is determined by the amount of transmitting information and the initial states of coupled systems. © 2015 Wiley Periodicals, Inc. Complexity 21: 335–342, 2016     

An evolutionary fitness enhancement conferred by the circadian system in cyanobacteria

Circadian clocks are found in a wide variety of organisms from cyanobacteria to mammals. Many believe that the circadian clock system evolved as an adaption to the daily cycles in light and temperature driven by the rotation of the earth. Studies on the cyanobacterium, Synechococcus elongatus PCC 7942, have confirmed that the circadian clock in resonance with environmental cycles confers an adaptive advantage to cyanobacterial strains with different clock properties when grown in competition under light–dark cycles. The results thus far suggest that in a cyclic environment, the cyanobacterial strains whose free running periods are closest to the environmental period are the most fit and the strains lacking a functional circadian clock are at a competitive disadvantage relative to strains with a functional clock. In contrast, the circadian system provides little or no advantage to cyanobacteria grown in competition in constant light.To explain the potential mechanism of this clock-mediated enhancement in fitness in cyanobacteria, several models have been proposed; these include the limiting resource model, the diffusible inhibitor model and the cell-to-cell communication model. None of these models have been excluded by the currently available experimental data and the mechanistic basis of clock-mediated fitness enhancement remains elusive.     

基于弹性壳的三维群体细胞动力学模型

群体细胞迁移常见于胚胎发育、伤口愈合和肿瘤侵袭等各种生理和病理过程中,关于其动力学的研究对于揭示群体细胞迁移机理、深刻理解有关生物过程十分重要.该文构建了群体细胞的三维可变形壳状模型,提出了一种考虑细胞弹性形变和细胞间接触与黏附相互作用的群体细胞动力学理论,并发展了相应的数值算法.基于所发展的动力学模型与算法,对多细胞在嚢腔里的受限旋转运动进行了模拟,复现了相关实验现象,分析了细胞极性、细胞形变、胞间相互作用等因素对多细胞三维动力学的影响规律.     

Synchronization of discrete-time spatiotemporal chaos via adaptive fuzzy control

A discrete-time adaptive fuzzy control scheme is presented to synchronize model-unknown coupled Henon-map lattices (CHMLs). The proposed method is robust to approximate errors, parameter mismatches and disturbances, because it integrates the merits of the adaptive fuzzy systems and the variable structure control with a sector. The simulation results of synchronization of CHMLs show that it not only can synchronize model-unknown CHMLs but also is robust against parameter mismatches and noise of the systems. These merits are advantageous for engineering realization.     

A field scale model for the spread of fungal diseases in crops: the example of a powdery mildew epidemic over a large vineyard

The aim of this article is to derive an asymptotic two‐scale model for the propagation of a fungal disease over a large vineyard. The original model is based on a singularly perturbed system of two linear reaction‐diffusion equations coupled with a set of nonlinear ordinary differential equations in a highly heterogeneous medium. We prove the well‐posedness of the asymptotic model and obtain a convergence result confirmed by numerical simulations. Copyright © 2014 John Wiley & Sons, Ltd.     

A mathematical model for solute coupled water transport in the production of aqueous humor

A simple mathematical model for the transport of solute and water in the production of aqueous humor by ciliary epithelium in the eye has been developed. The model introduces the intercellular channel, caped with a leaky (porous) tight junction between the layers of non-pigmented ciliary epithelium, as a bisectional channel which consists of two sections: one representing the tight junction which constitutes the blood-aqueous barrier and the other intercellular space with the active solute transport pumps on its lateral surfaces near the junction. The intercellular space and porous tight junction are modeled as electroneutral, uniform, semi-permeable channels of unequal cross-sectional area. Both the cylindrical pore- and rectangular-slit models for the transport through the channels are simultaneously introduced. The approximate analytical solutions to the governing non-linear coupled equations are obtained in normalized forms by employing Segal’s “Isotonic Convection Approximation”. The computational results for the scaled variables are presented through the graphs. The effects of important parameters on the flow/transport produced by (1) the hydrostatic pressure difference alone, (2) the concentration difference alone, and (3) the active transport alone, are examined and discussed. The results of the model may contribute to the present understanding of the mechanisms governing transport processes involved in the aqueous production.     

Failure risk propagation and protection schemes in coupled systems

Many modern systems have the property of coupling, which weakens the system against the outburst of failure. The risks to fail in a single layer may propagate to the entire system through inter-layer connections. In the field of propagation process, the existing literatures mainly focus on the global phenomena in coupled systems through some statistic methods, the dynamical evolution of failure risk propagation and the protection schemes for coupled systems are seldom mentioned. In this paper, we model the coupled systems using six types of coupled networks, over which the failure risk propagation occurs. Then, three cellular automata (CA) models are performed to describe the protection schemes in case of failure risk propagation. Based on a newly presented measurement, a series of experiments are conducted on the coupled networks as well as the single-layered networks, where the propagation processes with and without protection schemes are demonstrated. The results show that the failure risk propagation varies depending on the type and structure of the coupled networks. Moreover, with a small fraction of nodes protected based on some immunization strategies, the system’s robustness to the failure risk propagation is highly improved.     

Dynamics of three coupled van der Pol oscillators with application to circadian rhythms

In this work we study a system of three van der Pol oscillators. Two of the oscillators are identical, and are not directly coupled to each other, but rather are coupled via the third oscillator. We investigate the existence of the in-phase mode in which the two identical oscillators have the same behavior. To this end we use the two variable expansion perturbation method (also known as multiple scales) to obtain a slow flow, which we then analyze using the computer algebra system MACSYMA and the numerical bifurcation software AUTO.Our motivation for studying this system comes from the presence of circadian rhythms in the chemistry of the eyes. We model the circadian oscillator in each eye as a van der Pol oscillator. Although there is no direct connection between the two eyes, they are both connected to the brain, especially to the pineal gland, which is here represented by a third van der Pol oscillator.     

Tracking control and synchronization of two coupled neurons

This paper studies the problem of two coupled neurons tracking control. A controller based on the reference signal is designed. It is proved that the controller can make the error converge to zero exponentially, theoretically. Numerical results have verified the validity of the controller. The two coupled neurons can not only track any reference signal fast, but can synchronize with identical or different chaotic systems.     

Reciprocal inhibitory coupling: Measure and control of chaos on a biophysically motivated model of bursting

Bursting activity is an interesting feature of the temporal organization in many cell firing patterns. This complex behavior is characterized by clusters of spikes (action potentials) interspersed with phases of quiescence. As shown in experimental recordings, concerning the electrical activity of real neurons, the analysis of bursting models reveals not only patterned periodic activity but also irregular behavior [1], [2]. The interpretation of experimental results, particularly the study of the influence of coupling on chaotic bursting oscillations, is of great interest from physiological and physical perspectives. The inability to predict the behavior of dynamical systems in presence of chaos suggests the application of chaos control methods, when we are more interested in obtaining regular behavior. In the present article, we focus our attention on a specific class of biophysically motivated maps, proposed in the literature to describe the chaotic activity of spiking–bursting cells [Cazelles B, Courbage M, Rabinovich M. Anti-phase regularization of coupled chaotic maps modelling bursting neurons. Europhys Lett 2001;56:504–9]. More precisely, we study a map that reproduces the behavior of a single cell and a map used to examine the role of reciprocal inhibitory coupling, specially on two symmetrically coupled bursting neurons. Firstly, using results of symbolic dynamics, we characterize the topological entropy associated to the maps, which allows us to quantify and to distinguish different chaotic regimes. In particular, we exhibit numerical results about the effect of the coupling strength on the variation of the topological entropy. Finally, we show that complicated behavior arising from the chaotic coupled maps can be controlled, without changing of its original properties, and turned into a desired attracting time periodic motion (a regular cycle). The control is illustrated by an application of a feedback control technique developed by Romeiras et al. [Romeiras FJ, Grebogi C, Ott E, Dayawansa WP. Controlling chaotic dynamical systems. Physica D 1992;58:165–92]. This work provides an illustration of how our understanding of chaotic bursting models can be enhanced by the theory of dynamical systems.     

Numerical stability of chaotic synchronization using a nonlinear coupling function

Nonlinear coupling has been used to synchronize some chaotic systems. The difference evolutional equation between coupled systems, determined via the linear approximation, can be used to analyze the stability of the synchronization between drive and response systems. According to the stability criteria the coupled chaotic systems are asymptotically synchronized, if all eigenvalues of the matrix found in this linear approximation have negative real parts. There is no synchronization, if at least one of these eigenvalues has positive real part. Nevertheless, in this paper we have considered some cases on which there is at least one zero eigenvalue for the matrix in the linear approximation. Such cases demonstrate synchronization-like behavior between coupled chaotic systems if all other eigenvalues have negative real parts.     

Evolution of social networks

Modeling the evolution of networks is central to our understanding of large communication systems, and more general, modern economic and social systems. The research on social and economic networks is truly interdisciplinary and the number of proposed models is huge. In this survey we discuss a small selection of modeling approaches, covering classical random graph models, and game-theoretic models to analyze the evolution of social networks. Based on these two basic modeling paradigms, we introduce co-evolutionary models of networks and play as a potential synthesis.     

细胞骨架与细胞外基质的力学建模与分析

细胞和生物组织需要适应人体内复杂的力学生物学环境,一方面要被动地承受外部环境中的机械力,另一方面在组织生长、修复等生理过程中要积极主动地产生机械力调整自身的结构和形态.细胞和生物组织的力学性质主要由细胞骨架和细胞外基质决定,它们在微观上都是生物聚合物交联形成的复杂的、各向异性的三维网络结构.这方面早期的力学研究主要集中在通过各种网络模型,理解其普遍存在的非线性响应和硬化行为.近年来随着实验方法、理论建模和计算机模拟技术的大幅进步,这些生命介质的力学性质及其潜在的力学机理得到了更深入的理解.该文回顾了近些年细胞骨架和细胞外基质研究方面取得的部分进展,主要侧重动态交联属性、生物聚合物力学化学耦合赋予的主动材料属性、交联网络塑性和断裂,以及力学训练引发的自适应网络重构.发展细胞骨架与细胞外基质的力学模型与计算方法,分析该类生命介质的复杂力学行为,理解这些力学行为的潜在机制,可以加深我们对细胞和组织的力学生物学认识,并为人造生物材料和细胞组织工程提供基础和参考.     

The spatial behavior of a strongly coupled non-autonomous elliptic system

This article is concerned with the spatial behavior of a strongly coupled non-autonomous elliptic system modeling the steady state of populations that compete in some region. As the competition rate tends to infinity, we obtain the uniform convergence result and prove that non-negative solution of the system converges to the positive and negative parts of a solution of a scalar limit problem.     

Transition to turbulence in coupled maps on hierarchical lattices

General hierarchical lattices of coupled maps are considered as dynamical systems. These models may describe many processes occurring in heterogeneous media with tree-like structures. The transition to turbulence via spatiotemporal intermittency is investigated for these geometries. Critical exponents associated to the onset of turbulence are calculated as functions of the parameters of the systems. No evidence of non-trivial collective behavior is observed in the global quantity used to characterize the spatiotemporal dynamics.     

Uniform Hölder bounds for a strongly coupled elliptic system with strong competition

This article is concerned with a strongly coupled elliptic system modeling the steady state of populations that compete in some region. We prove that the solutions are uniformly Hölder bounded, as the competition rate tends to infinity. The proof relies on the blow-up technique and the monotonicity formula.     

Synchronization of the unified chaotic systems via active control

This paper investigates the synchronization of coupled unified chaotic systems via active control. The synchronization is given in the slave–master scheme and the controller ensures that the states of the controlled chaotic slave system exponentially synchronize with the state of the master system. Numerical simulations are provided for illustration and verification of the proposed method.