A Stochastic Model for Coupled Enzyme System

The molecular biology of transformed cancer cells singles out key enzymes as sensitive targets of anti-cancer drugs. Here we use one substrate–one intermediate–one final product model for a coupled enzyme system. The transfer rates for the mechanism are taken as continuous but subject to random fluctuations. Explicit formulae for the first moments of the distribution of the process are obtained. These formulae allow us to take into account not only the variability between the subjects, but also the variability of the process for a single subject. The present results allow us also to build the prediction interval for a particular time period given the observations for some preceding moments.     

A Derivative Matching Approach to Moment Closure for the Stochastic Logistic Model

Continuous-time birth-death Markov processes serve as useful models in population biology. When the birth-death rates are nonlinear, the time evolution of the first n order moments of the population is not closed, in the sense that it depends on moments of order higher than n. For analysis purposes, the time evolution of the first n order moments is often made to be closed by approximating these higher order moments as a nonlinear function of moments up to order n, which we refer to as the moment closure function. In this paper, a systematic procedure for constructing moment closure functions of arbitrary order is presented for the stochastic logistic model. We obtain the moment closure function by first assuming a certain separable form for it, and then matching time derivatives of the exact (not closed) moment equations with that of the approximate (closed) equations for some initial time and set of initial conditions. The separable structure ensures that the steady-state solutions for the approximate equations are unique, real and positive, while the derivative matching guarantees a good approximation, at least locally in time. Explicit formulas to construct these moment closure functions for arbitrary order of truncation n are provided with higher values of n leading to better approximations of the actual moment dynamics. A host of other moment closure functions previously proposed in the literature are also investigated. Among these we show that only the ones that achieve derivative matching provide a close approximation to the exact solution. Moreover, we improve the accuracy of several previously proposed moment closure functions by forcing derivative matching.     

A Stochastic Model for Estimating Adolescent Sterility Among Married Women

In this paper a stochastic model is presented for the time to the first conception of a cohort of married women. By identifying three states “adolescent sterility”, “ovulation” and “conceived”, into which the women can be placed, the model incorporates individual differences for the women in the “adolescent sterility” state which allow for the individual characteristics to affect the conversion of these women into the “ovulation” state. Using straightforward probabilistic arguments it is shown that the model provides a close fit to recently published data, compares favorably with previously published models on the same subject and it is useful for planning purposes in predicting future developments.     

A Stochastic Model for Oviposition Tactics in the Bean Weevil

In a recent paper, MITCHELL (1975) experimentally investigated the oviposition behavior of weevils on mung beans. In this paper, we develop a stochastic model to study the oviposition tactics of the female weevils on beans.     

A Stochastic Compartmental Model with Long Lasting Infusion

Most of the compartmental models in current use to model pharmacokinetic systems are deterministic. Stochastic formulations of pharmacokinetic compartmental models introduce stochasticity through either a probabilistic transfer mechanism or the randomization of the transfer rate constants. In this paper we consider a linear stochastic differential equation (LSDE) which represents a stochastic version of a one‐compartment linear model when input function undergoes random fluctuations. The solution of the LSDE, its mean value and covariance structure are derived. An explicit likelihood function is obtained either when the process is observed continuously over a period of time or when sampled data are available, as it is generally feasible. We discuss some asymptotic properties of the maximum likelihood estimators for the model parameters. Furthermore we develop expressions for two random variables of interest in pharmacokinetics: the area under the time‐concentration curve, M₀(T), and the plateau concentration, x_ss. Finally the estimation procedure is illustrated by an application to real data.     

A Stochastic Epidemic Model with Seasonal Variations in Infection Rate

In this paper we consider a modification of Bailey's stochastic model for the spread of an epidemic when there are seasonal variations in infection rate. The resulting nonlinear model is analyzed by employing the diffusion approximation technique. We have shown that for a large population the process, on suitable scaling and normalization, converges to a non-stationary Ornstein-Uhlenbeck process. Consequently the number of infectives has in the steady state a gaussian distribution.     

A Stochastic Model for Estimating Adolescent Sterility

In this article, a simple stochastic model for the time to first conception of a cohort of married women is developed, by identifying three states, ‘adolescent sterile’, ‘ovulating’ and ‘conceived‘, into which they can be placed. It is demonstrated that the model provides a close fit to observed data. The estimates of the parameters in the model, can be used to calculate the number of women in each state at different points of time and also to obtain estimates of the probabilities of conception for the two categories of women, adolescent sterile and biologically mature.     

随机时滞Lotka-Volterra模型数值解的收敛性

通常情况下,随机时滞Lotka-Volterra模型没有解析解,因而数值逼近方法是研究其性质的有效工具.本文根据Euler数值方法,利用鞅不等式和Ito公式讨论了一类随机时滞Lotka-Volterra模型数值解的收敛性,给出了数值解收敛于解析解的条件.最后通过数值算例对数值计算方法进行了验证.     

A Simple Unforced Oscillatory Growth Model in the Chemostat

In a chemostat, transient oscillations in cell number density are often experimentally observed during cell growth. The aim of this paper is to propose a simple autonomous model which is able to generate these oscillations, and to investigate it analytically. Our point of view is based on a simplification of the cell cycle in which there are two states (mature and immature) with the transfer between the two dependent on the available resources. We use the mathematical global properties of competitive differential systems to prove the existence of a limit cycle. A comparison between our model and a more complex model consisting of partial differential equations is made with the help of numerical simulations, giving qualitatively similar results.     

随机Lotka-Volterra系统的稳定性

利用Lyapunov方法与K．lto公式及鞅的理论,研究了随机Lotka-Volterra系统正平衡点的全局渐近稳定性．得到了随机全局渐近稳定的主要定理,并以确定性系统的全局稳定性作为定理的推论．     

On the stability of a model of testosterone dynamics

We prove the global asymptotic stability of a well-known delayed negative-feedback model of testosterone dynamics, which has been proposed as a model of oscillatory behavior. We establish stability (and hence the impossibility of oscillations) even in the presence of delays of arbitrary length.Supported in part by AFOSR Grant F49620-01-1-0063, NIH Grant P20 GM64375, and Dimacs.E.D. Sontag: Supported in part by AFOSR Grant F49620-01-1-0063 and NIH Grant R01 GM46383.Acknowledgement We would like to thank Augusto Ponce for useful suggestions.     

A Stochastic Spatial Dynamical Model for Aedes Aegypti

We develop a stochastic spatial model for Aedes aegypti populations based on the life cycle of the mosquito and its dispersal. Our validation corresponds to a monitoring study performed in Buenos Aires. Lacking information with regard to the number of breeding sites per block, the corresponding parameter (BS) was adjusted to the data. The model is able to produce numerical data in very good agreement with field results during most of the year, the exception being the fall season. Possible causes of the disagreement are discussed. We analyzed the mosquito dispersal as an advantageous strategy of persistence in the city and simulated the dispersal of females from a source to the surroundings along a 3-year period observing that several processes occur simultaneously: local extinctions, recolonization processes (resulting from flight and the oviposition performed by flyers), and colonization processes resulting from the persistence of eggs during the winter season. In view of this process, we suggest that eradication campaigns in temperate climates should be performed during the winter time for higher efficiency.     

GnRH-A免疫去势对雄兔血清睾酮和血液细胞的作用

目的研究促性腺激素释放激素-A（GnRH-A）免疫去势时血清睾酮含量和血液细胞成分的变化特点及其相互关系,从而探讨GnRH-A免疫去势的效果和作用机理。方法将GnRH-A与BSA连接为复合物,加入弗氏不完全佐剂制成抗原乳剂;30只兔均分为实验1组（EG-1）、实验2组（EG-2）和对照组（CG）,EG-1和EG-2注射1.0mL（100μg/mL）GnRH-A抗原,EG-2组3周后再加强注射一次;用间接ELISA法测定睾酮含量,用CD-1200全自动血液分析仪测定15项参数值;统计分析血清睾酮含量和血液细胞之间的相关关系和回归方程。结果EG-2的血清睾酮含量显著低于EG-1和对照组（P〈0.05）,EG-1在前4周明显下降,低于对照组（P〈0.05）,此后持续上升并明显高于实验前值,至第16周时与对照组相近;而对照组血清睾酮含量呈不断增高,到第13周明显高于第1周（P〈0.05）。EG-2的WBC、LYM、MID和GRN在第4～7周明显高于正常值（P〈0.05）,而RBC、HGB和HCT则低于正常值（P〈0.05）;到13周后,EG-2和EG-1的15项血液细胞逐渐恢复正常水平,与对照组差异无显著性（P〉0.05）。血清睾酮含量和血液细胞的相关系数和回归方程无明显的规律性和特征性。结论GnRH-A主动免疫对家兔的血清睾酮和血液细胞WBC、LYM、MID、GRN、WBC、LYM、MID和GRN等具有明显的影响,但作用持续时间仅4～7周。     

实时剪切波弹性定量分析不同睾酮水平大鼠阴茎组织硬度

目的:利用实时剪切波弹性成像(shear wave elastography,SWE)定量分析不同睾酮水平阴茎组织硬度之间的差异。方法:睾酮水平不同SD大鼠两组,低睾酮水平组(1月龄,睾酮水平1.00~1.50 ng/m L,n=10)和高睾酮水平组(13月龄,睾酮水平2.00~2.50ng/m L,n=10)。采用放射免疫法测定各组大鼠血清睾酮水平。选用法国Super Sonic Imagine公司生产的Aixplorer超声诊断仪,启动SWE模式对阴茎进行SWE成像并测量其剪切波硬度(shear wave stiffness,SWS)。分析比较两组大鼠血清睾酮水平之间的差异及SWS之间的差异。结果:所有大鼠血清睾酮水平及阴茎组织SWS的测量均成功完成。低睾酮水平组大鼠血清睾酮水平为(1.30±0.16)ng/m L,高睾酮水平组为(2.29±0.14)ng/m L,两组大鼠血清睾酮水平存在显著差异(P0.01);低睾酮水平组大鼠阴茎组织SWS为(9.86±0.72)k Pa,高睾酮水平组为(7.80±1.43)k Pa,两组大鼠阴茎组织SWS存在显著差异(P0.01)。结论:SWE可以检测出睾酮水平不同导致的阴茎组织硬度的差异,提示SWE可作为一项评价阴茎组织硬度的无创新技术。     

A Model of Oscillatory Blood Cell Counts in Chronic Myelogenous Leukaemia

In certain blood diseases, oscillations are found in blood cell counts. Particularly, such oscillations are sometimes found in chronic myelogenous leukaemia, and then occur in all the derived blood cell types: red blood cells, white blood cells, and platelets. It has been suggested that such oscillations arise because of an instability in the pluri-potential stem cell population, associated with its regulatory control system. In this paper, we consider how such oscillations can arise in a model of competition between normal (S) and genetically altered abnormal (A) stem cells, as the latter population grows at the expense of the former. We use an analytic model of long period oscillations to describe regions of oscillatory behaviour in the S–A phase plane, and give parametric criteria to describe when such oscillations will occur. We also describe a mechanism which can explain dynamically how the transformation from chronic phase to acute phase and blast crisis can occur.     

A Stochastic Model of Gene Evolution with Time Dependent Pseudochaotic Mutations

We develop here a new class of stochastic models of gene evolution in which a random subset of the 64 possible trinucleotides mutates at each evolutionary time t according to some time dependent substitution probabilities. Therefore, at each time t, the numbers and the types of mutable trinucleotides are unknown. Thus, the mutation matrix changes at each time t. This pseudochaotic model developed generalizes the standard model in which all the trinucleotides mutate at each time t. It determines the occurrence probabilities at time t of trinucleotides which pseudochaotically mutate according to 3 time dependent substitution parameters associated with the 3 trinucleotide sites. The main result proves that under suitable assumptions, this pseudochaotic model converges to a uniform probability vector identical to that of the standard model. Furthermore, an application of this pseudochaotic model allows an evolutionary study of the 3 circular codes identified in both eukaryotic and prokaryotic genes. A circular code is a particular set of trinucleotides whose main property is the retrieval of the frames in genes locally, i.e., anywhere in genes and particularly without start codons, and automatically with a window of a few nucleotides. After a certain evolutionary time and with particular time dependent functions for the 3 substitution parameters, precisely an exponential decrease in the 1st and 2nd trinucleotide sites and an exponential increase in the 3rd one, this pseudochaotic model retrieves the main statistical properties of the 3 circular codes observed in genes. Furthermore, it leads to a circular code asymmetry stronger than the standard model (nonpseudochaotic) and, therefore, to a better correlation with the genes.     

Stochastic S-system modeling of gene regulatory network

Microarray gene expression data can provide insights into biological processes at a system-wide level and is commonly used for reverse engineering gene regulatory networks (GRN). Due to the amalgamation of noise from different sources, microarray expression profiles become inherently noisy leading to significant impact on the GRN reconstruction process. Microarray replicates (both biological and technical), generated to increase the reliability of data obtained under noisy conditions, have limited influence in enhancing the accuracy of reconstruction . Therefore, instead of the conventional GRN modeling approaches which are deterministic, stochastic techniques are becoming increasingly necessary for inferring GRN from noisy microarray data. In this paper, we propose a new stochastic GRN model by investigating incorporation of various standard noise measurements in the deterministic S-system model. Experimental evaluations performed for varying sizes of synthetic network, representing different stochastic processes, demonstrate the effect of noise on the accuracy of genetic network modeling and the significance of stochastic modeling for GRN reconstruction . The proposed stochastic model is subsequently applied to infer the regulations among genes in two real life networks: (1) the well-studied IRMA network, a real-life in-vivo synthetic network constructed within the Saccharomycescerevisiae yeast, and (2) the SOS DNA repair network in Escherichiacoli.     

脑胶质瘤患者手术前后睾酮水平变化及临床意义

目的:研究脑胶质瘤患者手术前后睾酮水平变化,并分析其临床意义。方法:选取2010年2月到2015年6月我院脑胶质瘤患者80例为研究组,并选择同期颅脑良性肿瘤患者80例为对照组,两组均给予手术治疗,检测术前和术后3天、术后1周患者睾酮水平。结果:研究组术后各病理类型睾酮水平较治疗前显著降低(P0.05),但不同病理类型之间睾酮水平比较无统计学意义(P0.05);研究组术前睾酮水平显著高于对照组,比较差异具有统计学意义(P0.05);术后3天、术后一周研究组睾酮水平与术前比较显著降低,差异具有统计学意义(P0.05);术后1周研究组睾酮水平与术后3天比较无统计学意义(P0.05);对照组术前和术后各时间睾酮水平比较无统计学意义(P0.05)。结论:脑胶质瘤患者会出现睾酮水平紊乱,当睾酮水平明显增高时应警惕脑胶质瘤的可能性。     

A Stochastic Model for the Synthesis and Degradation of Natural Organic Matter. Part I. Data Structures and Reaction Kinetics

Here we present a stochastic biogeochemical model for the formation, transformation and mineralization of natural organic matter (NOM). The model is agent-based, with each software agent representing a single molecule of defined composition. Molecular properties and reactivities are estimated from composition and environmental parameters. Environmental parameters including temperature, pH, light intensity, dissolved O₂, moisture and enzyme activities are user controlled. Time is treated in discrete steps, and during each step potential reaction probabilities are evaluated for each molecule based on its structure and the environmental parameters. When reactions occur, the molecular composition is modified accordingly. The model uses small natural products and biopolymers for inputs, and the composition of the molecules produced is constrained only by the inputs and reaction stoichiometries, not by pre-defined structures. Example simulations using the program AlphaStep are presented, in which the breakdown of biopolymers and the condensation of small molecules both lead to molecular assemblages with elemental composition and average properties similar to those of aquatic NOM. This batch-reactor model can be expanded to include spatial information and environmental feedback.