Calcium and Magnesium: Low Passive Permeability and Tubular Secretion in the Mouse Medullary Thick Ascending Limb of Henle's Loop (MTAL)

Recent studies from our laboratory have shown that in the mouse and rat nephron Ca²⁺ and Mg²⁺ are not reabsorbed in the medullary part of the thick ascending limb (mTAL) of Henle's loop. The aim of the present study was to investigate whether the absence of transepithelial Ca²⁺ and Mg²⁺ transport in the mouse mTAL is due to its relative low permeability to divalent cations. For this purpose, transepithelial ion net fluxes were measured by electron probe analysis in isolated perfused mouse mTAL segments, when the transepithelial potential difference (PD_te.) was varied by chemical voltage clamp, during active NaCl transport inhibition by luminal furosemide. The results show that transepithelial Ca²⁺ and Mg²⁺ net fluxes in the mTAL are not driven by the transepithelial PD_te. At zero voltage, a small but significant net secretion of Ca²⁺ into the tubular lumen was observed. With a high lumen-positive PD_te generated by creating a transepithelial bath-to-lumen NaCl concentration gradient, no Ca²⁺ and Mg²⁺ reabsorption was noted; instead significant and sustained Ca²⁺ and Mg²⁺ net secretion occurred. When a lumen-positive PD_te was generated in the absence of apical furosemide, but in the presence of a transepithelial bath-to-lumen NaCl concentration gradient, a huge Ca²⁺ net secretion and a lesser Mg²⁺ net secretion, not modified by ADH, were observed. Replacement of Na⁺ by K⁺ in the lumen perfusate induced, in the absence of PD_te changes, important but reversible net secretions of Ca²⁺ and Mg²⁺. In conclusion, our results indicate that the passive permeability of the mouse mTAL to divalent cations is very low and not influenced by ADH. This nephron segment can secrete Ca²⁺ and Mg²⁺ into the luminal fluid under conditions which elicit large lumen-positive transepithelial potential differences. Given the impermeability of this epithelium to Ca²⁺ and Mg²⁺, the secretory processes would appear to be of cellular origin. Received: 30 January 1996/Revised: 24 April 1996     

一个人体运动的数学模型

本文采用L-E法和铰分解法研究了人体运动的数学模型问题,给出了一种人体运动的规范建模方法。该方法适用于多种拓扑结构形式的人体运动（如空翻、步行、滑行等）,所得方程具有适合于计算机程式求解的特点。     

A Mathematical Model for Leaf Photosynthesis of Mulberry

A mathematical model of leaf photosynthesis has been established. In this model, the processes of photosynthesis are divided into two parts, ie., the carboxylation process driven by light which is dependent on temperature and CO2 concentration, and the diffusion of CO2 from atmosphere to the carboxylation site. Finatly, CO2 uptake by the leaf is understood as dependent on 1), the CO2 response curve of the leaf mesophyll and 2). the CO2 partial pressure in the intercellular space in leaf. The COs response curve of the leaf photosynthesis is described mathematically in terms of carboxylation efficiency (Ca) or its initial slope and the photosynthetic capacity (Pm) or the CO2-saturated uptake rate of CO2 uptake, and dark respiration (Rd). The dependency of photosynthesis on leaf temperature and incident light intensity is incorporated into variations of those parameters which establish an appropriate response to internal CO2 pressure for particular light and temperature conditions prevailing at any time. Secondly the interactiion of stomata with photosynthesis is represented as an empirical relation between stomatal conductance and a combined environmental physiological index, APn·Hx/CaThe parameters used in the modelwere estimated with Marquardt-Newton method for non-linear function. Field measurements of mulberry leaf photosynthesis provided a data set for model testing. The resuks show that the simulated values of the model agree well with observed data. The model was used to analyse the response surface of leaf conductance and photosynthesis to environmental factors—Applications and limitations of the model are discussed     

在环境制约情况下的人口数学模型

在文［１］Ｙｕｌｅ模型的基础上加上环境允许的极限人口数Ｎ_ｍ，用偏微分方程的特征理论进行数学研究．     

Mathematical analysis of multisolute renal flow in a single nephron model of the kidney

A single nephron model, which includes the Bowman's space, Cortical interstitium, and Pelvis as well-stirred baths, is investigated. A boundary value problem, which allows for pelvic reflux, is established for the fluid-multisolute flow in the nephron. The implicit function theorem is used to establish the existence and uniqueness of a solution of the boundary value problem for the case of small permeability coefficients and transport rates.Dedicated to Professor Emertius L. P. Burton, Auburn University, for the research guidance he gave this author thirty years agoSupported in part by NIH Grant 7-ROl-DK 38817     

The Most Recently Discovered Carbonic Anhydrase,CA XV,Is Expressed in the Thick Ascending Limb of Henle and in the Collecting Ducts of Mouse Kidney

Background

Carbonic anhydrases (CAs) are key enzymes for physiological pH regulation, including the process of urine acidification. Previous studies have identified seven cytosolic or membrane-bound CA isozymes in the kidney. Recently, we showed by in situ hybridization that the mRNA for the most novel CA isozyme, CA XV, is present in the renal cortex. CA XV is a unique isozyme among mammalian CAs, because it has become a pseudogene in primates even though expressed in several other species.

Methodology/Principal Findings

In the present study, we raised a polyclonal antibody against recombinant mouse CA XV that was produced in a baculovirus/insect cell expression system, and the antibody was used for immunohistochemical analysis in different mouse tissues. Positive immunoreactions were found only in the kidney, where the enzyme showed a very limited distribution pattern. Parallel immunostaining experiments with several other anti-CA sera indicated that CA XV is mainly expressed in the thick ascending limb of Henle and collecting ducts, and the reactions were most prominent in the cortex and outer medulla.

Conclusion/Significance

Although other studies have proposed a role for CA XV in cell proliferation, its tightly limited distribution may point to a specialized function in the regulation of acid-base homeostasis.     

苹果园光能截获率的数学模型

应用气象学原理推导了不同纬度、不同栽植行向、不同树形的苹果园光能截获率的数学模型,给出在保证树冠基部外围日照时间大于25％总日照时间的条件下,生长季中充分截获光能的最佳树形、行距、冠高、冠径的优化组合方案。实例分析表明,计算结果与专家经验基本一致。本研究为果园合理栽植,充分利用光能,合理整形修剪提供理论依据与参考方案。     

医用数学模型的格式化与显示

本文介绍医用数学模型格式化的方法,为了显示模型连续解的图象和计算机处理过程,文中提供了一些典型的格式化模型.采用数学推理手段将数学模型变换为可被模拟电路及数字电路所接受的模式,就成了格式化模型．实验结果表明,该方法是行之有效的．     

特定雌性动物群周期性地获得稳定收获量的数学模型

利用Ｌｅｓｌｉｅ矩阵,给出了特定雌性动物群周期性地获得稳定收获量的数学模型,并对模型适用于集约化饲养家畜的特殊情况进行了讨论。     

A Mathematical Model of the Human Circadian System and Its Application to Jet Lag

A mathematical model of the circadian system is described that is appropriate for application to jet lag. The core of the model is a van der Pol equation with an external force. Approximate solutions of this equation in which the external force is composed of a constant and an oscillating term are investigated. They lead to analytical expressions for the amplitude and period of free-running rhythms and for the frequency limits of the entrainment region. The free-running period increases quadratically with stiffness. Both period and amplitude depend on the value of the constant external force. The width of the range of entrainment is mostly determined by the external force, whereas the relative position of this range follows the intrinsic period of the oscillator. Experiments with forced and spontaneous internal desynchronization were evaluated using these analytical expressions, and estimates were obtained for the intrinsic period of the oscillator, its stiffness, and the external force. A knowledge of these model parameters is essential for predictions about circadian dynamics, and there are practical implications for the assessment of the adaptation after rapid transmeridian travel.     

A Mathematical Model of the Human Circadian System and Its Application to Jet Lag

A mathematical model of the circadian system is described that is appropriate for application to jet lag. The core of the model is a van der Pol equation with an external force. Approximate solutions of this equation in which the external force is composed of a constant and an oscillating term are investigated. They lead to analytical expressions for the amplitude and period of free-running rhythms and for the frequency limits of the entrainment region. The free-running period increases quadratically with stiffness. Both period and amplitude depend on the value of the constant external force. The width of the range of entrainment is mostly determined by the external force, whereas the relative position of this range follows the intrinsic period of the oscillator. Experiments with forced and spontaneous internal desynchronization were evaluated using these analytical expressions, and estimates were obtained for the intrinsic period of the oscillator, its stiffness, and the external force. A knowledge of these model parameters is essential for predictions about circadian dynamics, and there are practical implications for the assessment of the adaptation after rapid transmeridian travel.     

A General Model for the Dynamics of the Cell Volume

The conservation of the cell volume within values compatible with the overall cell functions represents an ubiquitous property, shared by cells comprising the whole biological world. Water transport across membranes constitutes the main process associated to the dynamics of the cell volume, its chronic and acute regulations therefore represent crucial aspects of cell homeostasis. In spite of the biological diversity, the dynamics of the cell volume exhibits common basic features in the diverse types of cells. The purpose of this study is to show that there is a general model capable to describe the basic aspects of the dynamics of the cell volume. It is demonstrated here that the steady states of this model represent asymptotically stable configurations. As illustrations, several cases of non-polarized (i.e., symmetrical) and polarized (e.g., epithelial) cells performing water transport are shown here to represent particular cases of the general model. From a biological perspective, the existence of a general model for the dynamics of the cell volume reveals that, in spite of physiological and morphological peculiarities, there is a basic common design of the membrane transport processes. In view of its stability properties, this basic design may represent an ancestral property that has proven to be successful regarding the overall homeostatic properties of cells.     

A Mathematical Model for the Actions of Activin,Inhibin, and Follistatin on Pituitary Gonadotrophs

The timed secretion of the luteinizing hormone (LH) and follicle stimulating hormone (FSH) from pituitary gonadotrophs during the estrous cycle is crucial for normal reproductive functioning. The release of LH and FSH is stimulated by gonadotropin releasing hormone (GnRH) secreted by hypothalamic GnRH neurons. It is controlled by the frequency of the GnRH signal that varies during the estrous cycle. Curiously, the secretion of LH and FSH is differentially regulated by the frequency of GnRH pulses. LH secretion increases as the frequency increases within a physiological range, and FSH secretion shows a biphasic response, with a peak at a lower frequency. There is considerable experimental evidence that one key factor in these differential responses is the autocrine/paracrine actions of the pituitary polypeptides activin and follistatin. Based on these data, we develop a mathematical model that incorporates the dynamics of these polypeptides. We show that a model that incorporates the actions of activin and follistatin is sufficient to generate the differential responses of LH and FSH secretion to changes in the frequency of GnRH pulses. In addition, it shows that the actions of these polypeptides, along with the ovarian polypeptide inhibin and the estrogen-mediated variations in the frequency of GnRH pulses, are sufficient to account for the time courses of LH and FSH plasma levels during the rat estrous cycle. That is, a single peak of LH on the afternoon of proestrus and a double peak of FSH on proestrus and early estrus. We also use the model to identify which regulation pathways are indispensable for the differential regulation of LH and FSH and their time courses during the estrous cycle. We conclude that the actions of activin, inhibin, and follistatin are consistent with LH/FSH secretion patterns, and likely complement other factors in the production of the characteristic secretion patterns in female rats.     

影响林火灾变生态阈值数学模拟的潜在因子的数学模型

用多元统计分析方法对大兴安岭林区的林火灾变的有关观测数据进行综合分析,提出了影响林火灾变性生态阈值数学模拟的潜在因子的数学模型,并对该模型作出了一些有益的讨论。     

干扰素基因工程菌产物表达数学模型的研究

根据阻遏蛋白,辅阻遏因子与启动基因之间的相互作用,建立了采用色氨酸启动子的基因工程重组徽生物的产物表达数学模型。提出了mRNA最大转录速率常数和产物表达速率常数与比生长速率呈线性关系的假设,用干扰素基因工程菌培养过程中的实验数据估计了mR—NA转录速率常数,干扰素表达速率常数和干扰素降解速率常数。推导出了发酵过程中干扰素表达量和细胞内干扰素比活计算公式。运用这些公式可以通过检测色氨酸浓度和细胞比生长速率来计算预测干扰紊表达量。确定最佳的终止培养时间。     

A Mathematical Model of the Pancreatic Ductal Epithelium

A mathematical model of the HCO⁻ ₃-secreting pancreatic ductal epithelium was developed using network thermodynamics. With a minimal set of assumptions, the model accurately reproduced the experimentally measured membrane potentials, voltage divider ratio, transepithelial resistance and short-circuit current of nonstimulated ducts that were microperfused and bathed with a CO₂/HCO⁻ ₃-free, HEPES-buffered solution, and also the intracellular pH of duct cells bathed in a CO₂/HCO⁻ ₃-buffered solution. The model also accurately simulated: (i) the effect of step changes in basolateral K⁺ concentration, and the effect of K⁺ channel blockers on basolateral membrane potential; (ii) the intracellular acidification caused by a Na⁺-free extracellular solution and the effect of amiloride on this acidification; and (iii) the intracellular alkalinization caused by a Cl⁻-free extracellular solution and the effect of DIDS on this alkalinization. In addition, the model predicted that the luminal Cl⁻ conductance plays a key role in controlling both the HCO⁻ ₃ secretory rate and intracellular pH during HCO⁻ ₃ secretion. We believe that the model will be helpful in the analysis of experimental data and improve our understanding of HCO⁻ ₃-transporting mechanisms in pancreatic duct cells. Received: 18 October 1995/Revised: 5 July 1996     

木材横断面六棱规则细胞数学描述理论研究

本文采用微观力学和细胞学理论,在横观各向同性的假设下,提出了一种木材规则细胞主方向截面形状描述的理论方法。应用本文提出的理论,可以根据纤维、木质素、细胞直径和排列的程度,绘出理想状态下木材的主方向规则细胞结构形状,为木材学运用数学手术深入到细胞结构研究的深度提供了一种新的数学方法,并且可以为定量解释木材规则细胞变异后材性与性能提高的原因提供定量解释的数学手段。     

A numerical study of the nonsteady transport of gases in the pulmonary capillaries

A mathematical model is formulated for simulating the unsteady transport of gases in the blood flowing through the pulmonary capillaries. The formulation takes into account the transport mechanisms of molecular diffusion, convection and facilitated diffusion of the species due to haemoglobin. A time dependent situation is created by allowing to vary suddenly the partial pressures of the gases either in the venous blood or in the alveolar air. A numerical technique is described to solve the resulting time-dependent system of nonlinear coupled partial differential equations with the physiologically relevant boundary, entrance and initial conditions. The time required by the gases to achieve equilibrium is computed. It is shown that the dissolved oxygen takes longest in reaching equilibration whereas the carbon dioxide is the fastest. The various physiologically relevant unsteady situations have been examined.     

微生物在多孔介质中渗流的数学模型

建立了一个完整的描述微生物在地层多孔介质中渗流的数学模型,模型中考虑了微生物的生长、营养物的消耗和微生物的存在对多孔介质物理性质的影响．此外,提供了该方程的求解过程和方法。实例计算结果表明,该方法能较好的描述微生物在多孔介质中的运移状况。