Tests and model selection for the general growth curve model

The model considered here is a generalized multivariate analysis of variance model useful especially for many types of growth curve problems including biological growth and technology substitution. It is defined as Yp x N = Xp x m tau m x r Ar x N + epsilon p x N, where tau is unknown, and X and A are known design matrices of ranks m less than p and r less than N, respectively. Furthermore, the columns of epsilon are independent p-variate normal with mean vector 0 and common covariance matrix sigma. In general, p is the number of time (or spatial) points observed on each of the N cases, (m - 1) is the degree of polynomial in time, and r is the number of groups. The main focus of this paper is the selection of models for the general growth curve model with regard to the covariance matrix sigma. Likelihood ratio tests and selection procedures based on sample reuse and predictions are proposed. Special emphasis is on the serial covariance structure for sigma, which has been shown to be quite important in the prediction of biological data and technology substitution data. One-population and K-population problems are considered. Some of the results are illustrated with two sets of biological data.     

A dynamic model for functional mapping of biological rhythms

Functional mapping is a statistical method for mapping quantitative trait loci (QTLs) that regulate the dynamic pattern of a biological trait. This method integrates mathematical aspects of biological complexity into a mixture model for genetic mapping and tests the genetic effects of QTLs by comparing genotype-specific curve parameters. As a way of quantitatively specifying the dynamic behaviour of a system, differential equations have proved to be powerful for modelling and unravelling the biochemical, molecular, and cellular mechanisms of a biological process, such as biological rhythms. The equipment of functional mapping with biologically meaningful differential equations provides new insights into the genetic control of any dynamic processes. We formulate a new functional mapping framework for a dynamic biological rhythm by incorporating a group of ordinary differential equations (ODE). The Runge–Kutta fourth-order algorithm was implemented to estimate the parameters that define the system of ODE. The new model will find its implications for understanding the interplay between gene interactions and developmental pathways in complex biological rhythms.     

A dynamic model for functional mapping of biological rhythms

Functional mapping is a statistical method for mapping quantitative trait loci (QTLs) that regulate the dynamic pattern of a biological trait. This method integrates mathematical aspects of biological complexity into a mixture model for genetic mapping and tests the genetic effects of QTLs by comparing genotype-specific curve parameters. As a way of quantitatively specifying the dynamic behavior of a system, differential equations have proven to be powerful for modeling and unraveling the biochemical, molecular, and cellular mechanisms of a biological process, such as biological rhythms. The equipment of functional mapping with biologically meaningful differential equations provides new insights into the genetic control of any dynamic processes. We formulate a new functional mapping framework for a dynamic biological rhythm by incorporating a group of ordinary differential equations (ODE). The Runge-Kutta fourth order algorithm was implemented to estimate the parameters that define the system of ODE. The new model will find its implications for understanding the interplay between gene interactions and developmental pathways in complex biological rhythms.     

Functional model of biological neural networks

A functional model of biological neural networks, called temporal hierarchical probabilistic associative memory (THPAM), is proposed in this paper. THPAM comprises functional models of dendritic trees for encoding inputs to neurons, a first type of neuron for generating spike trains, a second type of neuron for generating graded signals to modulate neurons of the first type, supervised and unsupervised Hebbian learning mechanisms for easy learning and retrieving, an arrangement of dendritic trees for maximizing generalization, hardwiring for rotation-translation-scaling invariance, and feedback connections with different delay durations for neurons to make full use of present and past informations generated by neurons in the same and higher layers. These functional models and their processing operations have many functions of biological neural networks that have not been achieved by other models in the open literature and provide logically coherent answers to many long-standing neuroscientific questions. However, biological justifications of these functional models and their processing operations are required for THPAM to qualify as a macroscopic model (or low-order approximate) of biological neural networks.     

A model of the predator-prey relationship

A general nonlinear model of the predator-prey relationship is proposed. The model is justified on biological grounds and its parameters are constrained to reasonable biological values. Analytical and graphical methods are used to classify and to analyze the equilibrium points of the model. Finally, numerical integration on a digital computer illustrates the nature of the model solutions.     

A new model for biological pattern formation

Various non-equilibrium growth models have been used to explore the development of morphology in biological systems. Here we review a class of biological growth models which exhibit fractal structures and discuss the relationship of these models to a variety of other phenomena.     

On parameter synthesis by parallel model checking

An important problem in current computational systems biology is to analyze models of biological systems dynamics under parameter uncertainty. This paper presents a novel algorithm for parameter synthesis based on parallel model checking. The algorithm is conceptually universal with respect to the modeling approach employed. We introduce the algorithm, show its scalability, and examine its applicability on several biological models.     

Growing biological networks: beyond the gene-duplication model

In this paper we propose a generalized growth model for biological interaction networks, including a set of biological features which have been inspired by a long tradition of simulations of immune system and chemical reaction networks. In our models we include characteristics such as the heterogeneity of biological nodes, the existence of natural hubs, the nodes binding by mutual affinity and the significance of type-based networks as compared with instance-based networks. Under these assumptions, we analyse the importance of the nodes concentration with respect to the selection of incoming nodes. We show that networks with fat-tailed degree distribution and highly clustered structure naturally emerge in systems possessing certain properties: new instances need to be produced through an endogenous source and this source needs to provide a positive feedback favouring nodes with high concentration to receive new connections. Furthermore, we show that understanding the concentration dynamics of each node and the consequent correlation between connectivity and concentration is a more adequate way to capture the global properties of type-based biological networks.     

蜜蜂——新兴的模式生物

蜜蜂作为具有重要经济价值和生态价值的社会性昆虫, 在诸如神经生物学和社会生物学等研究领域也具有很高的模型价值。蜜蜂基因组工程为深入认识蜜蜂的生物学特点,进一步发挥其在多个研究领域的模型价值奠定了分子基础。本文基于蜜蜂的生物学特点,介绍了蜜蜂作为模式生物所具备的优势,及其在学习和记忆、劳动分工、级型分化、免疫等热点领域的研究价值。通过总结和展望国内外蜜蜂生物学研究形势,呼吁国内相关各学科开展合作研究。     

Refinement of the fluid-mosaic model of membrane structure

Certain molecular packing criteria previously employed in a quantitative analysis of lipid micelles and bilayers are here extended to biological membranes. The inclusion of both thermodynamic and packing considerations point to a highly complex self-assembly mechanism in which the organization of lipids and proteins is highly coupled, with far reaching consequences as regards the structure and function of biological membranes.     

Continuous hidden process model for time series expression experiments

MOTIVATION: When analyzing expression experiments, researchers are often interested in identifying the set of biological processes that are up- or down-regulated under the experimental condition studied. Current approaches, including clustering expression profiles and averaging the expression profiles of genes known to participate in specific processes, fail to provide an accurate estimate of the activity levels of many biological processes. RESULTS: We introduce a probabilistic continuous hidden process Model (CHPM) for time series expression data. CHPM can simultaneously determine the most probable assignment of genes to processes and the level of activation of these processes over time. To estimate model parameters, CHPM uses multiple time series datasets and incorporates prior biological knowledge. Applying CHPM to yeast expression data, we show that our algorithm produces more accurate functional assignments for genes compared to other expression analysis methods. The inferred process activity levels can be used to study the relationships between biological processes. We also report new biological experiments confirming some of the process activity levels predicted by CHPM. AVAILABILITY: A Java implementation is available at http:\\www.cs.cmu.edu\~yanxins\chpm. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.     

Experiments with an ecosystem adaptation model of biological treatment

In the wake of an earlier advanced multicomponent-multispecies biological treatment model, the authors suggest algorithms to substantially decrease the number of free coefficients. Operation of a number of experiments with the multicomponent-multispecies model has helped to further our understanding of the mechanism of biological treatment.     

A kinetic model for anaerobic digestion of biological sludge

The principal objective of this study was the development and evaluation of a comprehensive kinetic model capable of predicting digester performance when fed biological sludge, preliminary conversion mechanisms such as cell death, lysis, and hydrolysis responsible for rendering viable biological sludge organisms to available substrate were studied in depth. The results of this study indicate that hydrolysis of the dead, particulate biomass-primarily consisting of protein-is the slowest step, and therefore kinetically controls the overall process of anaerobic digestion of biological sludge. A kinetic model was developed which could accurately describe digester performance and predict effluent quality.     

Timeline: Neurospora: a model of model microbes

In the 1940s, studies with Neurospora pioneered the use of microorganisms in genetic analysis and provided the foundations for biochemical genetics and molecular biology. What has happened since this orange mould was used to show that genes control metabolic reactions? How did it come to be the fungal counterpart of Drosophila? We describe its continued use during the heyday of research with Escherichia coli and yeast, and its emergence as a biological model for higher fungi.     

Bayesian hierarchical error model for analysis of gene expression data

MOTIVATION: Analysis of genome-wide microarray data requires the estimation of a large number of genetic parameters for individual genes and their interaction expression patterns under multiple biological conditions. The sources of microarray error variability comprises various biological and experimental factors, such as biological and individual replication, sample preparation, hybridization and image processing. Moreover, the same gene often shows quite heterogeneous error variability under different biological and experimental conditions, which must be estimated separately for evaluating the statistical significance of differential expression patterns. Widely used linear modeling approaches are limited because they do not allow simultaneous modeling and inference on the large number of these genetic parameters and heterogeneous error components on different genes, different biological and experimental conditions, and varying intensity ranges in microarray data. RESULTS: We propose a Bayesian hierarchical error model (HEM) to overcome the above restrictions. HEM accounts for heterogeneous error variability in an oligonucleotide microarray experiment. The error variability is decomposed into two components (experimental and biological errors) when both biological and experimental replicates are available. Our HEM inference is based on Markov chain Monte Carlo to estimate a large number of parameters from a single-likelihood function for all genes. An F-like summary statistic is proposed to identify differentially expressed genes under multiple conditions based on the HEM estimation. The performance of HEM and its F-like statistic was examined with simulated data and two published microarray datasets-primate brain data and mouse B-cell development data. HEM was also compared with ANOVA using simulated data. AVAILABILITY: The software for the HEM is available from the authors upon request.     

Bilayer structure in phospholipid-cytochromec model membranes

The Journal of Membrane Biology - Lipid protein interactions in biological membranes differ markedly depending on whether the protein is intrinsic or extrinsic. These interactions are studied using...     

A mathematical model for radiation-induced myelopoiesis

A model for damage, repair, killing, and repopulation of myelopoietic marrow is presented. Evaluation produces time and dose-rate profiles during and following any complex irradiation. Equations model variable dose rates, multiple exposures, different sources, and arbitrary intervals between treatments. If factors which dominate the control of biological processes can be demonstrated, an option is to set biological rate constants to experimentally determined values. Previously, knowledge did not permit identification of dominating biological processes and their temporal rates. But a unique feature of this study is that unspecified lesions for killing and injury of cells are evaluated from mortality data on the animal species of choice. "Unspecified" is used to indicate a condition of assumption-free modeling of molecular processes, whereby rate constants for cellular effects are simply computed directly from animal mortality data. Coefficients (estimated by maximum-likelihood methods for nonspecific processes) are compared with experimental values for specific processes. The model has many uses, including modeling of the myelopoietic potential as a function of time. Another option is to calculate the whole-body survival curve for cells that control myelopoiesis as a result of the treatment schedule. Also through simple extensions of the model, an extremely complex protocol can be identified with an equivalent prompt dose value--even for partial-body, fractionated exposures.     

The myosin swinging cross-bridge model

No biological system has been studied by more diverse approaches than the actin-based molecular motor myosin. Biophysics, biochemistry, physiology, classical genetics and molecular genetics have all made their contributions, and myosin is now becoming one of the best-understood enzymes in biology.     

Membrane fusion in model systems

The mechanism of biological membrane fusion was studied with the use of a fluorescent dye, R18. It was shown that ATP-induced membrane fusion is supporessed by calcium/calmodulin-dependent protein kinase inhibitors. L protein changed the character of fusion of different types of membranes.     

修正非齐次马尔可夫模型应用的研究

修正非齐次模型是在齐次模型和非齐次模型基础上提出的适用于蛋白质编码区的马尔可夫模型。此模型可以用来分析生物物种进化和基因突变,模型中的马尔可夫度与序列进化水平相关联,转移矩阵与基因突变相关联。本文通过比较7类不同物种-1度马尔可夫链的含量,验证了生物物种进化反映在密码子使用上的特征;通过密码子位点间转移矩阵的计算,分析了基因突变在密码子不同位点上发生的可能性。