The SMM model as a boundary value problem using the discrete diffusion equation

A generalized single-step stepwise mutation model (SMM) is developed that takes into account an arbitrary initial state to a certain partial difference equation. This is solved in both the approximate continuum limit and the more exact discrete form. A time evolution model is developed for Y DNA or mtDNA that takes into account the reflective boundary modeling minimum microsatellite length and the original difference equation. A comparison is made between the more widely known continuum Gaussian model and a discrete model, which is based on modified Bessel functions of the first kind. A correction is made to the SMM model for the probability that two individuals are related that takes into account a reflecting boundary modeling minimum microsatellite length. This method is generalized to take into account the general n-step model and exact solutions are found. A new model is proposed for the step distribution.     

田间作物蒸腾量测算方法研究

本文依据Penman-Monteith方法对田间蒸腾量的测算进行了探讨,从理论上分析并导出蒸腾量的估算模式,对参数的估算也做了详细分析和讨论。最后用大屯农业生态系统试验站的观测资料对模式进行验证,结果表明,采用本模式计算田间蒸腾量效果很好。     

Model fitting and model testing in the method of joint mapping of quantitative trait loci

A previous paper proposed a new method of QTL mapping called joint mapping (JM). Some problems have been found in model fitting and model testing due to the neglect of the correlations among different observations of the dependent variable in this model. The present paper reports a method of solving the problems. The coefficient of correlation between two observations of the dependent variable is derived. A generalized least square (GLS) approach is developed for model fitting and a strategy and procedure of model testing based on a chi-square test is suggested. A simulated example is given. The example shows that the JM method is quite efficient in mapping multiple linked QTLs.     

The side-by-side model of two tRNA molecules allowing the alpha-helical conformation of the nascent polypeptide during the ribosomal transpeptidation.

Lim and Spirin [25] proposed a preferable conformation of the nascent peptide during the ribosomal transpeptidation. Spirin and Lim [26] excluded the possibilities of the side-by-side model proposed by Johnson et al [13] and the three-tRNA binding model (A, P and E sites) of Rheinberger and Nierhaus [3]. However, a slight conformational change at the 3' end regions of both A and P site tRNA molecules can enable the three different tRNA binding models to converge. With a modification of the angles of the ribose rings of both anticodon and mRNA this model can also be related to the model of Sundaralingam et al [19]. In this model of E coli rRNA the 3' end sequence ACCA76 or GCCA76 of P site tRNA is base-paired to UGGU810 of 23S rRNA, while the ACC75 or GCC75 of A site tRNA are base-paired to GGU1621 23S rRNA. The conformation of the A76 of A site tRNA is necessarily different from that of P site tRNA, at least during the course of the transpeptidation. The A76 of A site tRNA overlaps the binding region of puromycin. The C1400 of 16S rRNA in this model is located at a distance of 4 A from the 5' end of the anticodon of P site tRNA [14] and 17 A from the 5' end of the anticodon of A site tRNA [15]. It is also shown that a considerable but reasonable modification in the conformation of the anticodon loops could lead to accommodation of three deacylated tRNA(Phe) molecules at a time on 70S ribosome in the presence of poly(U) as observed experimentally [6]. A sterochemical explanation for the negatively-linked allosteric interactions between the A and E sites is also shown in the present model.     

The theory of sliding filament models for muscle contraction. II. Biochemically-based models of the contraction cycle

A seven-state sliding filament model is proposed which differs from the model of Eisenberg & Greene. It is based on a simplified version of the in-vitro contraction cycle of Stein et al., and also has some desirable dynamical features of the empirical three-state model of Nishiyama & Murase. Appropriate x-dependences for all reaction rates are derived from the transition-state theory. The seventh-state is assumed to be a high-tension intermediate of A.M.ATP, from which direct but x-dependent dissociation can occur. If the final A.M.ATP state has a sufficiently lower tension than that of A.M.ADP.Pi, then the dominant escape path from the intermediate state is shown to be direct dissociation of the actin-myosin bond. This leads to an approximate five-state model for active and relaxed muscle in which A.M and the final A.M.ATP state are omitted.     

Quantitative description of the adaptation of vagal effects by means of an electromechanical coupling model]

A four compartments model describes the electrotropic and the inotropic vagal effect time courses during long time stimulation. The model realises electro-mechanical coupling. A differential equation for the coupling model is developed, solutions are given and a numerical treatment is described. The model shows the essential properties of effect adaptation: time delay and smaller extent of electrotropic effect adaptation.     

A model of the breakdown and removal of the chromatin components during Feulgen acid hydrolysis

Synopsis A stochastic model of Feulgen hydrolysis is proposed. The model, constructed so as to embody the main features of chromatin structure, is simple enough to allow the calculation of extraction rates. Extraction rate curves generated by the model are compared with experimental curves obtained under various conditions (different fixatives and hydrolysis solutions). A good correspondence is found between the experiments and the predictions of the model.     

Stochastic dynamic population model for northern corn rootworm (Coleoptera: Chrysomelidae).

A stochastic dynamic population model for the complete life cycle of northern corn rootworm, Diabrotica barberi Smith & Lawrence, is described. Adult population dynamics from emergence to oviposition are based on a published single-season model for which temperature-dependent development and age-dependent advancement determine adult population dynamics and oviposition. Randomly generated daily temperatures make this model component stochastic. Stochastic hatch is 50+/-8%. A stochastic nonlinear density-dependent larval survival model is estimated using field data from artificial infestation experiments. A regional model of corn phenology is estimated to incorporate the effect of dispersal on adult mortality. Random daily weather is generated using parameters for Brookings, SD. Model performance is evaluated with deterministic simulations, which show that the population converges to zero unless adult mortality is reduced by the availability of corn pollen from the regional model of corn phenology. Stochastic model performance is evaluated with stochastic daily weather, egg hatch, and larval survival in various combinations. Sensitivity analysis is conducted to evaluate model responsiveness to each parameter. Model results are generally consistent with published data.     

Peptide models of four possible insulin folding intermediates with two disulfides

The single-chain insulin (PIP) can spontaneously fold into native structure through preferred kinetic intermediates. During refolding, pairing of the first disulfide A20-B19 is highly specific, whereas pairing of the second disulfide is likely random because two two-disulfide intermediates have been trapped. To get more details of pairing property of the second disulfide, four model peptides of possible folding intermediates with two disulfides were prepared by protein engineering, and their properties were analyzed. The four model peptides were named [A20-B19, A7-B7]PIP, [A20-B19, A6-B7]PIP, [A20-B19, A6-A11]PIP, and [A20-B19, A7-A11]PIP according to their remaining disulfides. The four model peptides all adopt partially folded structure with moderate conformational differences. In redox buffer, the disulfides of the model peptides are more easily reduced than those of the wild-type PIP. During in vitro refolding, the reduced model peptides share similar relative folding rates but different folding yields: The refolding efficiency of the reduced [A20-B19, A7-A11]PIP is about threefold lower than that of the other three peptides. The present results indicate that the folding intermediates corresponding to the present model peptides all adopt partially folded conformation, and can be formed during PIP refolding, but the chance of forming the intermediate with disulfide [A20-B19, A7-A11] is much lower than that of forming the other three intermediates.     

Experimental evaluation of a model for cometabolism: Prediction of simultaneous degradation of trichloroethylene and methane by a methanotrophic mixed culture

A model for cometabolism is verified experimentally for a defined methanotrophic mixed culture. The model includes the effects of cell growth, endogenous cell decay, product toxicity, and competitive inhibition with the assumption that cometabolic transformation rates are enhanced by reducing power obtained from oxidation of growth substrates. A theoretical transformation yield is used to quantify the enhancement resulting from growth substrate oxidation. A systematic method for evaluating model parameters independently is described. The applicability of the model is evaluated by comparing experimental data for methanotrophic cometabolism of TCE with model predictions from independently measured model parameters. Propagation of errors is used to quantify errors in parameter estimates and in the final prediction. The model successfully predicts TCE transformation and methane utilization for a wide range of concentrations of TCE (0.5 to 9 mg/L) and methane (0.05 to 6 mg/L). (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 56: 492-501, 1997.     

矮嵩草草甸生长季节生产者亚系统分室模型

本文报道了高寒矮嵩草草甸生产者亚系统六分室模型(GCS 01模型)。六分室包括地上部分的禾草类(V1)、莎草类(V2)、杂类草(V3)、枯枝落叶(V4)四个分室以及地下部分的活根(V5)、死根(V6)两个分室。并建造了相应的微分方程组数学模型,用含有龙格库塔法的BASIC程序可求其数值解。本模型可供高寒草甸生态系统研究人员研究系统行为、探索系统内部规律使用。     

A peptide model of insulin folding intermediate with one disulfide

Insulin folds into a unique three-dimensional structure stabilized by three disulfide bonds. Our previous work suggested that during in vitro refolding of a recombinant single-chain insulin (PIP) there exists a critical folding intermediate containing the single disulfide A20-B19. However, the intermediate cannot be trapped during refolding because once this disulfide is formed, the remaining folding process is very quick. To circumvent this difficulty, a model peptide ([A20-B19]PIP) containing the single disulfide A20-B19 was prepared by protein engineering. The model peptide can be secreted from transformed yeast cells, but its secretion yield decreases 2-3 magnitudes compared with that of the wild-type PIP. The physicochemical property analysis suggested that the model peptide adopts a partially folded conformation. In vitro, the fully reduced model peptide can quickly and efficiently form the disulfide A20-B19, which suggested that formation of the disulfide A20-B19 is kinetically preferred. In redox buffer, the model peptide is reduced gradually as the reduction potential is increased, while the disulfides of the wild-type PIP are reduced in a cooperative manner. By analysis of the model peptide, it is possible to deduce the properties of the critical folding intermediate with the single disulfide A20-B19.     

Microdomain dynamics in folding proteins

The basic formulas for the incorporation into the diffusion–collision model of the stabilities of intermediate states on the folding pathway are derived and discussed. A hypothetical two-step folding pathway is calculated in detail. A model for the production of incorrectly folded intermediates is suggested and some numerical estimates made. Implications and future directions in the evolution of the model are discussed. Three appendices deal with some mathematical aspects of the model.     

Estimating the size of closed populations using inverse multiple-recapture sampling

A log-linear model for estimating the size of a closed population is defined for inverse multiple-recapture sampling with dependent samples. Efficient estimators of the log-linear model parameters and the population size are obtained by the method of minimum chi-square. A chi-square test of the general linear hypothesis regarding the log-linear model parameters is defined.     

Mixture Markov regression model with application to mosquito surveillance data analysis

A mixture Markov regression model is proposed to analyze heterogeneous time series data. Mixture quasi‐likelihood is formulated to model time series with mixture components and exogenous variables. The parameters are estimated by quasi‐likelihood estimating equations. A modified EM algorithm is developed for the mixture time series model. The model and proposed algorithm are tested on simulated data and applied to mosquito surveillance data in Peel Region, Canada.     

A model for the competitive growth of two diatoms

A parallel between an experimental situation in marine microecology and its analytical model is presented. Two diatoms are cultured in a continuous flow apparatus and are studied for their competitive performance. A differential equations model is proposed to represent their growth behavior. The parameters of the model are evaluated from the experimental data and it is then identified from additional data.     

Closed loop identification of transfer function model for unstable bioreactors for tuning PID controllers

Closed loop identification of transfer function model for an unstable bioreactor is proposed based on an optimization method using either a step or a pulse response of PI/PID controlled bioreactor. A simple method is proposed for the initial guesses of the parameters of the first order plus time delay (FOPTD) transfer function model. A PID controller is designed for the identified model. Simulation study on the nonlinear model equations of an unstable bioreactor exhibiting multiple steady-states shows that the PID controller designed on the identified FOPTD model gives a good closed loop response similar to the one designed based on the linearized model from the nonlinear model equations.     

A Mixture‐of‐Genotypes Model for the Distribution of Thermostable Phenol Sulfotransferase Activity

A statistical method for parametric density estimation based upon a mixture‐of‐genotypes model is developed for the thermostable phenol sulfotransferase (SULT1A1) activity which has a putative role in modifying risk for colon and prostate cancer/polyps. The EM algorithm for the general mixture model is modified to accommodate the genetic constraints and is used to estimate genotype frequencies from the distribution of the SULT1A1 phenotype. A parametric bootstrap likelihood ratio test is considered as a testing method for the number of mixing components. The size and power of the test is then investigated and compared with the conventional chi‐squared test. The relative risk associated with genotypes defined by this model is also investigated through the generalized linear model. This analysis revealed that a genotype with the highest mean value of SULT1A1 activity has greater impact on cancer risk than others. This result suggests that the phenotype with a higher SULT1A1 activity might be important in studying the association between the cancer risk and SULT1A1 activity. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)