Parameter estimation for the distribution of single cell lag times

In Quantitative Microbial Risk Assessment, it is vital to understand how lag times of individual cells are distributed over a bacterial population. Such identified distributions can be used to predict the time by which, in a growth-supporting environment, a few pathogenic cells can multiply to a poisoning concentration level.We model the lag time of a single cell, inoculated into a new environment, by the delay of the growth function characterizing the generated subpopulation. We introduce an easy-to-implement procedure, based on the method of moments, to estimate the parameters of the distribution of single cell lag times. The advantage of the method is especially apparent for cases where the initial number of cells is small and random, and the culture is detectable only in the exponential growth phase.     

Parameter estimation techniques for interaction and redistribution models: a predator-prey example

Summary The use of parameter estimation techniques for partial differential equations is illustrated using a predatorprey model. Whereas ecologists have often estimated parameters in models, they have not previously been able to do so for models that describe interactions in heterogeneous environments. The techniques we describe for partial differential equations will be generally useful for models of interacting species in spatially complex environments and for models that include the movement of organisms. We demonstrate our methods using field data from a ladybird beetle (Coccinella septempunctata) and aphid (Uroleucon nigrotuberculatum) interaction. Our parameter estimation algorithms can be employed to identify models that explain better than 80% of the observed variance in aphid and ladybird densities. Such parameter estimation techniques can bridge the gap between detail-rich experimental studies and abstract mathematical models. By relating the particular bestfit models identified from our experimental data to other information on Coccinella behavior, we conclude that a term describing local taxis of ladybirds towards prey (aphids in this case) is needed in the model.     

Statistical methods for model comparison in parameter estimation problems for distributed systems

In this note we outline some recent results on the development of a statistical testing methodology for inverse problems involving partial differential equation models. Applications to several problems from biology are presented. The statistical tests, which are in the spirit of analysis of variance (ANOVA), are based on asymptotic distributional results for estimators and residuals in a least squares approach.Research supported in part under grants NSF MCS 8504316, NASA NAG-1-517, and AFOSRF-49620-86-C-0111. Part of this research was carried out while the first author was a visiting scientist at the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA, which is operated under NASA contracts NASI-18107 and NASI-18605     

Aspects of the mineral nutrition of some native British plants — inter-site variation

Fifteen common native British plants were each sampled at a range of sites in Great Britain and green tissues analysed for several inorganic nutrients. Sampling criteria are discussed. The inter-site variation of each element within a species is assessed as a frequency distribution of raw data. Sample values of parameters including arithmetic mean, variance (coefficient of variation), skewness and kurtosis are presented. Their stability is assessed from nitrogen in sub-samples of Pteridium. This suggested sample sizes were adequate but some distributions had sufficient kurtosis to affect the variance. These parameters showed distinctions between macro- and micro-elements and between species. Some mean values sharply distinguished between species and may help to assess current theories of strategy and adaptation but a wider range of species is needed to clarify trends. Coefficients of variation are discussed and were relatively low for a nation-wide survey after allowing for sampling constraints. Coefficients of skewness and kurtosis showed two-thirds of the sample distributions were non-normal. Ecological aspects of the distributions are discussed and are relevant to studies along environmental gradients. Published hypotheses linking positive skewness to stress in the field are considered and two other postulates discussed. Distribution bounds such as those confining 95% of the values are discussed in relation to possible critical levels of nutrients.Nomenclature follows Clapham et al. (1981), Excursion flora of the British Isles. 3rd ed. University Press, Cambridge, except Chamaenerion.     

Thermodynamical model for insertion and aggregate binding of caffeine to the homopolymer poly(riboadenylate) and model choice by data analysis

This paper describes the model used to estimate the parameters of caffeine-poly(riboadenylate) (poly(A)) interactions from corresponding 1H-NMR measurements. The model of insertion and aggregate binding describes the non-cooperative insertion of a molecule C into an interspace between two monomers of a homopolymer in competition with aggregate binding. It contains two binding constants, K1 for insertion and K2 for the interaction of monomeric A units of the polymer with C molecules in bound aggregates, and two cooperativity parameters, Kcc for stacking of C molecules within aggregates and tau which is thought to be due to conformational adaptation of the polymer to those bound aggregates which cover more than one A unit. In contrast to other models, the size of a binding site (within the aggregates) is less than one monomeric unit, with n denoting the maximum number of C molecules per A unit in bound aggregates. The model is developed for general n by means of the method of sequence-generating functions. For n = 2 and n = 3, the correctness of the model treatment was checked by the matrix method. The model is applicable to the binding of aggregates to homopolymers, which are flexible enough to fit their structure to the aggregates.     

Parameter identification of the calvin photosynthesis cycle

Summary This article is concerned with the determination of kinetic parameters of the Calvin photosynthesis cycle which is described by seventeen nonlinear ordinary differential equations. It is shown that the task requires dynamic data for several sets of initial conditions. The numerical technique is based upon an algorithm for non-linear optimization and Gear's numerical integration scheme for stiff systems of differential equations. The sensitivity of the parameters to noise in the data is tested with a method adapted from Rosenbrook and Storey. A preliminary set of parameters has been obtained from a preliminary set of experimental data. The numerical methods are then tested with synthetic data derived from these parameters. The mathematical model and the results obtained in the simulation are used as an aid in designing new experiments.     

利用各世代的小区平均数估计遗传参数的加权最小二乘法

本文提出了在随机区组设计下利用六个世代的小区平均数估计加性-显性-二基因互作模型的各参数、检验该模型的加权最小二乘法的基本步骤。     

用人工神经网络方法估计Ligistic方程参数

本文提出Logistic方程参数优化估计的人工神经网络方法,并选取一组标样进行具体尝试。结果表明,用这种方法估计Logistic方程参数效果极好。     

激光扫描共聚焦显微镜活细胞成像方法优化

激光扫描共聚焦显微镜可用于固定样品和活细胞样品的成像,近年来得到了广泛的应用。本文介绍了激光扫描共聚焦显微镜的基本原理及其在活细胞成像中的应用,并以FV10-ASW Viewer4.2软件为例,从扫描速度、分辨率、降噪、光电倍增调节、多参数协同优化、成像质量评估、图像后期处理等多个角度总结了激光扫描共聚焦活细胞成像系统的方法优化和推荐参数设置。本文的工作可以为活细胞实验提供一定参考。     

A combined steepest descent and genetic algorithm (SD/GA) approach for the optimization of solvation parameters

An accurate solvation model is essential for computer modeling of protein folding and other biomolecular self-assembly processes. Compared to explicit solvent models, implicit solvent models, such as the Poisson-Boltzmann (PB) with solvent accessible surface area model (PB/SA), offer a much faster speed—the most compelling reason for the popularity of these implicit solvent models. Since these implicit solvent models typically use empirical parameters, such as atomic radii and the surface tensions, an optimal fit of these parameters is crucial for the final accuracy of properties such as solvation free energy and folding free energy. In this paper, we proposed a combined approach, namely SD/GA, which takes the advantage of both local optimization with the steepest descent (SD), and global optimization with the genetic algorithm (GA), for parameters optimization in multi-dimensional space. The SD/GA method is then applied to the optimization of solvation parameters in the non-polar cavity term of the PB/SA model. The results show that the newly optimized parameters from SD/GA not only increase the accuracy in the solvation free energies for ～200 organic molecules, but also significantly improve the free energy landscape of a β-hairpin folding. The current SD/GA method can be readily applied to other multi-dimensional parameter space optimization as well.