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.     

水分胁迫对沙棘(Hippophae rhamnoides)和中间锦鸡儿(Caragana intermedia)蒸腾作用影响的比较

多年生灌木沙棘和中间锦鸡儿是黄土高原生态重建的重要物种,设计人工模拟水分胁迫实验,测量沙棘和中间锦鸡儿蒸腾作用的各种指标,研究其蒸腾特性对水分胁迫的适应方式。结果表明,同等水分处理条件下,中间锦鸡儿单叶水平上的蒸腾速率高于沙棘。沙棘和中间锦鸡儿的蒸腾速率日进程在晴天、阴雨天和生长发育的不同阶段明显不同。夜间蒸腾占全天蒸腾的比例相当大,夜间蒸腾在不同物种之间、不同供水量之间存在明显差异,而且越干旱的环境比例越大。两种植物气孔阻力的季节变化格局在不同水分处理间大体相似。沙棘的昼夜蒸腾节律在各种水分处理条件下都表现出明显的气孔振荡现象,而中间锦鸡儿没有。叶片温度、光合有效辐射和气孔阻力是各种水分条件下沙棘和中间锦鸡儿蒸腾作用的共同的限制因子,相对于沙棘,中间锦鸡儿还更多地受到空气相对湿度的影响。     

Synchronous plasma membrane electrochemical potential oscillations during yeast colony development and aging

Microorganisms that survive in natural environments form organized multicellular communities, biofilms and colonies with specific properties. During stress and nutrient limitation, slow growing and senescent cells in such communities retain vital processes by maintaining plasma membrane integrity and retaining the ability to generate transmembrane electrochemical gradients. We report the use of a Saccharomyces cerevisiae colonial model to show that population growth in a multicellular community depends on nutrient diffusion and that resting cells start to accumulate from the beginning of the second acidic phase of colony development. Despite differentiation of colony members, synchronous transmembrane potential oscillation was detected in the organized colony. The electrochemical membrane potential periodically oscillated at frequencies between those for circadian to infradian rhythms during colony aging and transiently decreased at time points previously linked with rebuilding of yeast metabolism. Despite extensive decreases in the intracellular ATP concentration and in the amount and activity of the plasma membrane proton pump during nutrient limited growth and colony aging, the transmembrane electrochemical potential appeared to be maintained above a level critical for population survival.     

Caffeine-induced Ca2+ oscillations in type I horizontal cell of carp retina: A mathematical model

Oscillations in intracellular free Ca²⁺ concentration ([Ca²⁺]_i) have been observed in a variety of cell types. In the present study, we constructed a mathematical model to simulate the caffeine-induced [Ca²⁺]_i oscillations based on experimental data obtained from isolated type I horizontal cell of carp retina. The results of model analysis confirm the notion that the caffeine-induced [Ca²⁺]_i oscillations involve a number of cytoplasmic and endoplasmic Ca²⁺ processes that interact with each other. Using this model, we evaluated the importance of store-operated channel (SOC) in caffeine-induced [Ca²⁺]_i oscillations. The model suggests that store-operated Ca²⁺ entry (SOCE) is elicited upon depletion of the endoplasmic reticulum (ER). When the SOC conductance is set to 0, caffeine-induced [Ca²⁺]_i oscillations are abolished, which agrees with the experimental observation that [Ca²⁺]_i oscillations were abolished when SOC was blocked pharmacologically, verifying that SOC is necessary for sustained [Ca²⁺]_i oscillations.     

Deconvolution as a novel approach to analyze moment-to-moment free fatty acid release

Objective: Recent studies have shown that free fatty acid (FFA) release is pulsatile and that this pattern is controlled by the sympathetic nervous system. It is, then, necessary to understand and characterize adipose tissue lipolysis to elucidate its effect on metabolism. In this study, we introduce deconvolution as a method to detect and quantify pulsatile FFA release. Research Methods and Procedures: Octanoate, a medium‐chain fatty acid, was infused in male mongrel dogs (n = 7) to mimic the pulsatile appearance of plasma FFAs. Deconvolution analysis was used to reconstruct the number and timing of infused octanoate pulses from plasma FFA concentrations. Results: Deconvolution analysis was able to reconstruct the exogenously infused pulses of octanoate used to mimic pulsatile appearance of FFAs (pulse frequency, 8 per hour; interpulse interval, 7 minutes). However, determination of pulse mass was less accurate (1.0 ± 0.0 vs. 0.54 ± 0.1 mM). The addition of varying levels of Gaussian noise to non‐oscillatory FFA time series did not lead to detection of extraneous FFA pulses. However, goodness of fit declined with increasing variability. Discussion: These results support the use of deconvolution as an accurate approach to determine the temporal sequence of endogenous FFA release.     

A periodicity result for a nonlinear functional integral equation

In this paper, we study the effect of introducing a delay in a model of cell proliferation considered originally by O. Arino and M. Kimmel (J. Math. Biol. 27, 341–354 (1989)). We prove that slow oscillations take place and periodic oscillations appear for appropriate values of a parameter.     

Release of the Ca(2+) oscillation-inducing sperm factor during mouse fertilization

A cytosolic sperm protein(s), referred to as the sperm factor (SF), is thought to induce intracellular calcium ([Ca(2+)](i)) oscillations during fertilization in mammalian eggs. These oscillations, which are responsible for inducing complete egg activation, persist for several hours. Nevertheless, whether a protracted release of SF is responsible for the duration of the oscillations is unknown. Using a combination of intracytoplasmic sperm injection (ICSI), in vitro fertilization (IVF), sperm removal, reinjection of the withdrawn sperm, and [Ca(2+)](i) monitoring, we determined that 30 min was necessary for establishing oscillations. Importantly, a significant portion of the Ca(2+) activity became dissociated from the sperm within 15-60 min after entry, and by 120 min post-ICSI or IVF, sperm were unable to induce oscillations. The initiation of oscillations coincided with exposure and solubilization of the perinuclear theca (PT), as evidenced by transmission electron microscopy, although disassembly of the PT was not required for commencement of the [Ca(2+)](i) responses. Remarkably, despite its complete release into the ooplasm, SF associated with nuclear structures at the time of pronuclear formation. Lastly, release of SF was not affected by the cell cycle. We conclude that mouse sperm serves as a carrier for SF, which is rapidly and completely solubilized to establish [Ca(2+)](i) oscillations.     

Molecular phylogeography of four endemic Sagittaria species (Alismataceae) in the Sino‐Japanese Floristic Region of East Asia

To reveal the role of climate oscillations of the Quaternary in forming the contemporary plant diversity in the temperate Sino‐Japanese Floristic Region of mainland China, we assess the phylogeographical patterns of four Sagittaria species in the region using sequence data from plastid DNA non‐coding regions (psbA‐trnH, the rpl16 intron and trnC‐ycf6) and the internal transcribed spacers of nuclear ribosomal DNA (nrITS). Based on both datasets, the divergence time among the four studied species was estimated to fall in the Late Tertiary (plastid DNA: 7.1–13.7 Mya; ITS: 11.1–16.1 Mya). The ancestral distribution analyses revealed that regions with a great diversity in topography, climate and ecological conditions, e.g. the Hengduan Mountains, Central China and East China, were the areas where the endemics originated. Mismatch distribution analyses revealed that each species had experienced a range expansion in response to Quaternary climatic oscillations. Our findings contradict the hypothesis of Quaternary origins of the endemic Sagittaria spp.; we support the view that modern species in the Northern Hemisphere originated mostly during the Tertiary. Range expansion may have profoundly modified the current distribution ranges of Sagittaria species in the Sino‐Japanese Floristic Region. © 2015 The Linnean Society of London, Botanical Journal of the Linnean Society, 2016, 180 , 6–20.     

The use of voltage-sensitive dyes to monitor signal-induced changes in membrane potential-ABA triggered membrane depolarization in guard cells

The plant membrane potential reports on the activity of electrogenic plasma membrane transport processes. The membrane potential is widely used to report for early events associated with changes in light regime, hormone action or pathogen attacks. The membrane potentials of guard cells can be precisely measured with microelectrodes, but this technique is not well suited for rapid screens with large sample numbers. To provide the basis for large-scale membrane potential recordings, we took advantage of voltage-sensitive dyes. Using the fluorescent dyes bis-(1,3-dibutylbarbituric acid)-trimethine oxonol (DiBAC(4)(3)) and the FLIPR Membrane Potential Assay Kit (FMP) dye we followed changes in the membrane potential in guard cells and vacuoles. Based on the fluorescence of DiBAC(4)(3) a method was established for quantification of the membrane potential in guard cell protoplasts which should be considered as an excellent system for high-throughput screening of plant cells. In the absence of abscisic acid (ABA), one-third of the guard cell protoplast population spontaneously oscillated for periods of 5-6 min. Upon application of ABA the hyperpolarized fraction ( approximately 50%) of the guard cell protoplast population depolarized within a few minutes. Membrane potential oscillations were terminated by ABA. Oscillations and ABA responses were found in cell populations with active anion channels. Thus time- and voltage-dependent anion channels likely represent the ABA-sensitive conductance and part of the membrane potential oscillator. The suitability of membrane potential dyes was tested on vacuoles, too. Dye-based vacuolar membrane polarization was monitored upon ATP exposure. We conclude that voltage-sensitive dyes provide an excellent tool for the study of changes in the membrane potential in vacuole as well as guard cell populations.     

River islands,refugia and genetic structuring in the endemic brown frog Rana kukunoris (Anura,Ranidae) of the Qinghai‐Tibetan Plateau

Frequently, Pleistocene climatic cycling has been found to be the diver of genetic structuring in populations, even in areas that did not have continental ice sheets, such as on the Qinghai‐Tibetan Plateau (QTP). Typically, species distributed on the plateau have been hypothesized to re‐treat to south‐eastern refugia, especially during the Last Glacial Maximum (LGM). We evaluated sequence variation in the mitochondrial DNA gene Cytb and the nuclear DNA gene RAG‐1 in Rana kukunoris, a species endemic to the QTP. Two major lineages, N and S, were identified, and lineage N was further subdivided into N1 and N2. The geographical distribution and genealogical divergences supported the hypothesis of multiple refugia. However, major lineages and sublineages diverged prior to the LGM. Demographical expansion was detected only in lineage S and sublineage N2. Sublineage N1 might have survived several glacial cycles in situ and did not expand after the LGM because of the absence of suitable habitat; it survived in river islands. Genetic analysis and environment modelling suggested that the north‐eastern edge of QTP contained a major refugium for R. kukunoris. From here, lineage S dispersed southwards after the LGM. Two microrefugia in northern Qilian Mountains greatly contributed to current level of intraspecific genetic diversity. These results were found to have important implications for the habitat conservation in Northwest China.