心肌细胞团搏动整数倍节律的非线性动力学机制

利用心肌细胞耦合模型研究心肌整数倍节律的动力学机理。确定性模型仿真揭示了心肌细胞团同步搏动加周期分岔的节律变化规律;随机模型仿真发现在加周期分岔序列中分岔点附近会出现整数倍节律,其中,0-1整数倍节律产生于从静息到周期1的Hopf分岔点附近,1-2整数倍节律产生于周期1和周期2极限环间的加周期分岔点附近;对系统相空间轨道的分析进一步揭示出整数倍节律是由系统运动在相邻的两个轨道之间随机跃迁形成的。上述分析结果不仅阐明了心肌整数倍节律的机理,并且揭示了各种整数倍节律与加周期分岔序列中相邻节律的内在联系,为重新认识心律变化的规律开辟了新的途径。     

Contribution to the study of periodic chronic myelogenous leukemia

The period (in the order of 40 to 80 days) in periodic chronic myelogenous leukemia (PCML) oscillations is quite long compared with the duration of the cell cycle of the hematopoietic stem cells from which the oscillations are presumed to originate (in the order of one or two days). Our objective is to understand the origin of these long-period oscillations using a G0 model for stem cell dynamics. We determine the local stability conditions and show under what conditions the Hopf bifurcation may occur. We interpret the role of each parameter in the loss of stability, and then examine a simpler model to try to deduce possible changes at the stem-cell level that might be responsible for the characteristics PCML.     

Oscillatory coexistence in a food chain model with competing predators

A food chain model with two predators feeding on a single prey in a chemostat is studied. Using a multiparameter bifurcation analysis, we find parameters values for which there is stable oscillatory coexistence of the predators. It is also shown how these coexistent states provide a transition between two possible states of competitive exclusion. It is shown that the competitive exclusion principle need not hold if one or more of the predators has oscillatory behavior in the absence of other predators.This work was partially supported by National Science Foundation Grant MCS 83-01881     

A comparative study of integrated pest management strategies based on impulsive control

The paper presents a comprehensive numerical study of mathematical models used to describe complex biological systems in the framework of integrated pest management. Our study considers two specific ecosystems that describe the application of control mechanisms based on pesticides and natural enemies, implemented in an impulsive and periodic manner, due to which the considered models belong to the class of impulsive differential equations. The present work proposes a numerical approach to study such type of models in detail, via the application of path-following (continuation) techniques for nonsmooth dynamical systems, via the novel continuation platform COCO (Dankowicz and Schilder). In this way, a detailed study focusing on the influence of selected system parameters on the effectiveness of the pest control scheme is carried out for both ecological scenarios. Furthermore, a comparative study is presented, with special emphasis on the mechanisms upon which a pest outbreak can occur in the considered ecosystems. Our study reveals that such outbreaks are determined by the presence of a branching point found during the continuation analysis. The numerical investigation concludes with an in-depth study of the state-dependent pesticide mortality considered in one of the ecological scenarios.     

Transient oscillations induced by delayed growth response in the chemostat

In this paper, in order to try to account for the transient oscillations observed in chemostat experiments, we consider a model of single species growth in a chemostat that involves delayed growth response. The time delay models the lag involved in the nutrient conversion process. Both monotone response functions and nonmonotone response functions are considered. The nonmonotone response function models the inhibitory effects of growth response of certain nutrients when concentrations are too high. By applying local and global Hopf bifurcation theorems, we prove that the model has unstable periodic solutions that bifurcate from unstable nonnegative equilibria as the parameter measuring the delay passes through certain critical values and that these local periodic solutions can persist, even if the delay parameter moves far from the critical (local) bifurcation values.When there are two positive equilibria, then positive periodic solutions can exist. When there is a unique positive equilibrium, the model does not have positive periodic oscillations and the unique positive equilibrium is globally asymptotically stable. However, the model can have periodic solutions that change sign. Although these solutions are not biologically meaningful, provided the initial data starts close enough to the unstable manifold of one of these periodic solutions they may still help to account for the transient oscillations that have been frequently observed in chemostat experiments. Numerical simulations are provided to illustrate that the model has varying degrees of transient oscillatory behaviour that can be controlled by the choice of the initial data.Mathematics Subject Classification: 34D20, 34K20, 92D25Research was partially supported by NSERC of Canada.This work was partly done while this author was a postdoc at McMaster.     

A modified metabolic model for mixed culture fermentation with energy conserving electron bifurcation reaction and metabolite transport energy

A modified metabolic model for mixed culture fermentation (MCF) is proposed with the consideration of an energy conserving electron bifurcation reaction and the transport energy of metabolites. The production of H₂ related to NADH/NAD⁺ and Fdred/Fdox is proposed to be divided in three processes in view of energy conserving electron bifurcation reaction. This assumption could fine‐tune the intracellular redox balance and regulate the distribution of metabolites. With respect to metabolite transport energy, the proton motive force is considered to be constant, while the transport rate coefficient is proposed to be proportional to the octanol–water partition coefficient. The modeling results for a glucose fermentation in a continuous stirred tank reactor show that the metabolite distribution is consistent with the literature: (1) acetate, butyrate, and ethanol are main products at acidic pH, while the production shifts to acetate and propionate at neutral and alkali pH; (2) the main products acetate, ethanol, and butyrate shift to ethanol at higher glucose concentration; (3) the changes for acetate and butyrate are following an increasing hydrogen partial pressure. The findings demonstrate that our modified model is more realistic than previous proposed model concepts. It also indicates that inclusion of an energy conserving electron bifurcation reaction and metabolite transport energy for MCF is sound in the viewpoint of biochemistry and physiology. Biotechnol. Bioeng. 2013; 110: 1884–1894. © 2013 Wiley Periodicals, Inc.     

Cannibalism as a life boat mechanism

Under certain conditions a cannibalistic population can survive when food for the adults is too scarce to support a non-cannibalistic population. Cannibalism can have this lifeboat effect if (i) the juveniles feed on a resource inaccessible to the adults; and (ii) the adults are cannibalistic and thus incorporate indirectly the inaccessible resource. Using a simple model we conclude that the mechanism works when, at low population densities, the average yield, in terms of new offspring, due to the energy provided by one cannibalized juvenile is larger than one.     

Conformational analysis of endomorphin-2 by molecular dynamics methods

Endomorphin-2 (EM2, H-Tyr-Pro-Phe-Phe-NH(2)) is a highly potent and selective mu-opioid receptor agonist. A conformational analysis of EM2 was carried out by simulated annealing (SA) and molecular dynamics (MD) methods. Molecular modeling was conducted on both neutral (N-terminal NH(2)) and charged (N-terminal NH(3) (+)) molecules. Based on the results of NMR investigations showing an equilibrium mixture of cis and trans Tyr(1)-Pro(2) peptide bonds for EM2 in solution, simulations were performed with restrained cis-Pro and trans-Pro peptide bonds, too. A separate SA study with unrestrained Pro peptide bonds was also conducted. Preferred conformational states are presented in Ramachandran plots. The g(+), g(-), and trans populations of the aromatic amino acid residue side chains were determined in chi(1) space. The distances between the N-terminal N atom and the other backbone N and O atoms, and the distances between the centers of the aromatic rings and the Pro(2) ring, were determined. The energy distribution of the structures obtained by SA was calculated. The preferred secondary structural elements were different kinds of beta-turns, an inverse gamma-turn located in the N-terminal region, and regular and inverse gamma-turns located in the C-terminal region. These turns were stabilized by intramolecular H-bonds and bifurcated H-bonds.     

生态系统稳态转换检测研究进展

在气候变化、人类活动等影响下,生态系统结构和功能可能发生大规模的突变,导致生态系统从一个相对稳定的状态进入另一个稳定状态,这种现象称为稳态转换。由于生态系统的复杂性,准确刻画生态系统多稳态并界定其临界点尚存在挑战,提升对生态系统稳态转换的检测和预测能力依旧是生态学领域研究的热点和难题。基于多稳态理论和稳态转换经典概念框架,阐释了稳态转换检测的理论基础;归纳总结出四种稳态转换检测方法的原理和优劣势;鉴于稳态转换的尺度依赖性,梳理了单一生态系统、区域综合生态系统和全球生态系统不同尺度下的稳态转换检测方法、研究思路和应用案例。基于研究进展和问题现状,提出在未来研究中,亟待发展适应复杂系统的综合检测方法;创新稳态转换多尺度分析的技术方法体系;深化生态系统稳态转换驱动机制研究,构建多元耦合机理模型;进而深化稳态转换检测结果链接生态系统管理的实践研究;解析生态系统服务和可持续发展机制。     

On the choice of the optimal periodic operation for a continuous fermentation process

In this contribution we investigate the impact of the forcing waveform on the productivity of a continuous bioreactor governed by an unstructured, nonlinear kinetic model. The (periodic) forcing is applied on the substrate concentration in the feed. To this end, some alternative waveforms commonly encountered in practice are evaluated and their performance is compared. An analytical/numerical approach is used. The preliminary analytical step is based on the π‐criterion that gives useful information for small amplitudes. The extension to larger amplitudes, when significant improvements are expected, is then performed through a continuation‐optimization procedure. It is found that the choice of the specific waveform has an impact on the performance of the process and there is no unique best forcing for any process condition, but its choice depends on the operating parameters and the forcing amplitude and frequency values. Further, the influence of the waveform functions on the wash‐out conditions are extensively examined. The analysis shows that all the waveforms examined in this work may lead to significant enlargement of the nontrivial regime with respect to a steady state operation. In particular, square‐wave forcing leads in practice to the extinction of the wash‐out conditions for any feed substrate concentration and for a well defined choice of the forcing parameters. © 2010 American Institute of Chemical Engineers Biotechnol. Prog., 2010