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.     

Entrainment, Instability, Quasi-periodicity, and Chaos in a Compound Neural Oscillator

We studied the dynamical behavior of a class of compound central pattern generator (CPG) models consisting of a simple neural network oscillator driven by both constant and periodic inputs of varying amplitudes, frequencies, and phases. We focused on a specific oscillator composed of two mutually inhibiting types of neuron (inspiratory and expiratory neurons) that may be considered as a minimal model of the mammalian respiratory rhythm generator. The simulation results demonstrated how a simple CPG model— with a minimum number of neurons and mild nonlinearities— may reproduce a host of complex dynamical behaviors under various periodic inputs. In particular, the network oscillated spontaneously only when both neurons received adequate and proportionate constant excitations. In the presence of a periodic source, the spontaneous rhythm was overriden by an entrained oscillation of varying forms depending on the nature of the source. Stable entrained oscillations were inducible by two types of inputs: (1) anti-phase periodic inputs with alternating agonist-antagonist drives to both neurons and (2) a single periodic drive to only one of the neurons. In-phase inputs, which exert periodic drives of similar magnitude and phase relationships to both neurons, resulted in varying disruptions of the entrained oscillations including magnitude attenuation, harmonic and phase distortions, and quasi-periodic interference. In the absence of significant phasic feedback, chaotic motion developed only when the CPG was driven by multiple periodic inputs. Apneic episodes with repetitive alternation of active (intrinsic oscillation) and inactive (cessation of oscillation) states developed when the network was driven by a moderate periodic input of low frequency. %and amplitudes of intermediate strength, Similar results were demonstrated in other, more complex oscillator models (that is, half-center oscillator and three-phase respiratory network model). These theoretical results may have important implications in elucidating the mechanisms of rhythmogenesis in the mature and developing respiratory CPG as well as other compound CPGs in mammalian and invertebrate nervous systems.     

Blau syndrome polymorphisms in NOD2 identify nucleotide hydrolysis and helical domain 1 as signalling regulators

Understanding how single nucleotide polymorphisms (SNPs) lead to disease at a molecular level provides a starting point for improved therapeutic intervention. SNPs in the innate immune receptor nucleotide oligomerisation domain 2 (NOD2) can cause the inflammatory disorders Blau Syndrome (BS) and early onset sarcoidosis (EOS) through receptor hyperactivation. Here, we show that these polymorphisms cluster into two primary locations: the ATP/Mg²⁺-binding site and helical domain 1. Polymorphisms in these two locations may consequently dysregulate ATP hydrolysis and NOD2 autoinhibition, respectively. Complementary mutations in NOD1 did not mirror the NOD2 phenotype, which indicates that NOD1 and NOD2 are activated and regulated by distinct methods.     

A periodic analysis of longitudinal binary responses: a case study of clinical mastitis in Norwegian Red cows

A Bayesian procedure for analyzing longitudinal binary responses using a periodic cosine function was developed. It was assumed that, after adjustment for "seasonal" effects, the oscillation of the underlying latent variables for longitudinal binary responses was a stationary series. Based on this assumption, a single dimension sinusoidal analysis of longitudinal binary responses using the Gibbs sampling and Metropolis algorithms was implemented in a study of clinical mastitis records of Norwegian Red cows taken over five lactations.     

齐口裂腹鱼血细胞的发生

为了探讨齐口裂腹鱼(Schizothorax prenanti)血细胞发生发育的模式,采用Wright’s、碘酸雪夫氏(PAS)和苏丹黑B(SBB)染色方法对齐口裂腹鱼的头肾、中肾、脾和肝组织印片进行染色,了解其发生的具体组织和发育的一般过程。结果表明:齐口裂腹鱼血细胞可分为红细胞系、淋巴细胞系、单核细胞系、粒细胞系和其他细胞,且这些细胞系的发育均经过3个阶段,即原始阶段、幼稚阶段、成熟阶段。通过观察和统计不同阶段各种血细胞的形态、大小、比例及染色特征,发现原始阶段的血细胞体积较大,其中原始单核细胞最大,大小为(18.90±1.59)μm×(16.32±0.70)μm,在4种组织中原始阶段的红细胞和单核细胞在头肾中所占比例最大,分别为0.64%和0.59%,原粒细胞和原淋巴细胞分别在中肾和脾中比例最大,在肝中少量存在,此外在各组织印片中均发现血栓细胞的存在,在肝中发现巨噬细胞。因此头肾、中肾和脾是齐口裂腹鱼的主要造血组织,少量细胞在肝中产生。粒细胞发育过程中,除原始粒细胞PAS染色阴性外,其他阶段均呈阳性,且阳性随不断成熟逐渐增强;单核细胞从原单核细胞到成熟的单核细胞,PAS阳性逐渐增强;而SBB染色发现,粒细胞、淋巴细胞及单核细胞均呈阳性,未成熟的细胞染色程度不一致,成熟的细胞阳性染色最为强烈。在红细胞系发育过程中经历了细胞由大变小再变大的过程,而粒细胞和淋巴细胞发育过程仅出现由大变小的过程,在红细胞的发育过程中还出现了染色质固缩和血红蛋白增加。     

旋转向量场中的阶二周期解

建立了一类具有状态脉冲控制的害虫控制模型以及一类特殊模型,根据半连续动力系统几何理论,研究了旋转向量场中阶二周期解的存在性和稳定性及变化规律.为现实的生物资源管理提供了可靠的策略依据,也丰富了半连续动力系统理论.     

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.     

Delayed administration of pituitary adenylate cyclase-activating polypeptide 38 ameliorates renal ischemia/reperfusion injury in mice by modulating Toll-like receptors

We investigated whether pituitary adenylate cyclase-activating polypeptide 38 (PACAP38) ameliorates kidney injury after ischemia/reperfusion (IR) by modulating Toll-like receptor (TLR)-associated signaling pathways. Male C57BL/6 mice were subjected to bilateral renal ischemia for 45 min. PACAP38, 20 μg in 100 μl of saline, was administered i.p. at 24 and 48 h after IR, and mice were euthanized at 72 h. In IR mice, PACAP38 maintained serum creatinine near control levels (0.81 ± 0.08 vs. 0.69 ± 0.17 mg/dl in controls, p = NS, vs. 1.8 ± 0.03 in saline-treated IR mice, p < 0.01) and significantly reduced the expression of kidney injury biomarkers. PACAP38 significantly reduced the levels of apoptosis and neutrophil infiltration, and protected against tubular damage. With PCR arrays, 59 of 83 TLR-related genes significantly changed their expression after IR. TLR2 increased 162 fold, followed by Fas-associated death domain (37 fold) and TLR6 (24 fold), while ubiquitin-conjugating enzyme E2 variant 1 (UBE2V1) decreased 55 fold. PACAP38 given 24 and 48 h after IR injury significantly reversed these changes in 56 genes, including TLR2, TLR3, TLR4, TLR6, and genes in the NF-κB pathways. The alterations in TLR2, TLR3, TLR6, and UBE2V1 were confirmed by RT-PCR. After IR, PACAP38 also suppressed protein levels of TLR-associated cytokines. PACAP38 reversed the changes in IR-activated TLR-associated NF-κB signaling pathways even when treatment was delayed 24 h. Therefore, PACAP38 could be an effective therapeutic for unexpected IR-mediated renal injury. The prominently IR-induced TLR-related genes identified in this study could be novel drug targets.     

具有两个状态脉冲控制的害虫治理模型的阶一周期解的存在性和吸引性

在文献[10]的基础上,基于害虫治理问题,建立具有两个状态脉冲控制的HollingⅡ功能性反应的害虫治理模型,利用所定义的后继函数和分析的方法研究了系统阶一周期解的存在性和吸引性.