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Extraction: Partition and Distribution Coefficients01:14

Extraction: Partition and Distribution Coefficients

The distribution law or Nernst's distribution law is the law that governs the distribution of a solute between two immiscible solvents. This law, also known as the partition law, states that if a solute is added to the mixture of two immiscible solvents at a constant temperature, the solute is distributed between the two solvents in such a way that the ratio of solute concentrations in the solvents remains constant at equilibrium.
For extracting a solute from an aqueous phase into an organic...
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Analysis Methods of Pharmacokinetic Data: Model and Model-Independent Approaches

Drug disposition in the body is a complex process and can be studied using two major approaches: the model and the model-independent approaches.
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Model Approaches for Pharmacokinetic Data: Compartment Models

Compartmental analysis is a widely adopted approach to characterizing drug pharmacokinetics. It uses compartment models that conceptualize the body as a collection of reversibly communicating compartments, each representing a group of tissues exhibiting similar drug distribution characteristics. The movement rate of the drug between these compartments is typically described by first-order kinetics.
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Mechanistic Models: Compartment Models in Individual and Population Analysis01:23

Mechanistic Models: Compartment Models in Individual and Population Analysis

Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least squares (OLS)...
Model Approaches for Pharmacokinetic Data: Distributed Parameter Models01:06

Model Approaches for Pharmacokinetic Data: Distributed Parameter Models

Pharmacokinetic models are mathematical constructs that represent and predict the time course of drug concentrations in the body, providing meaningful pharmacokinetic parameters. These models are categorized into compartment, physiological, and distributed parameter models.
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Model-Independent Approaches for Pharmacokinetic Data: Noncompartmental Analysis

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A Novel Bayesian Change-point Algorithm for Genome-wide Analysis of Diverse ChIPseq Data Types
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A Bayesian mixture model for partitioning gene expression data.

Chuan Zhou1, Jon Wakefield

  • 1Department of Biostatistics, S-2323 MCN, Vanderbilt University, Nashville, Tennessee 37232-2158, USA. chuan.zhou@vanderbilt.edu

Biometrics
|August 22, 2006
PubMed
Summary
This summary is machine-generated.

This study introduces a novel Bayesian model for analyzing time-course gene expression data. The method partitions gene expression profiles based on a random walk model, offering a flexible alternative to conventional clustering approaches.

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Area of Science:

  • Genomics
  • Computational Biology
  • Statistical Modeling

Background:

  • Time-course gene expression data analysis is crucial for understanding dynamic biological processes.
  • Conventional clustering methods may not fully capture temporal dependencies or acknowledge measurement error.
  • There is a need for advanced statistical models to infer patterns in longitudinal gene expression data.

Purpose of the Study:

  • To present a Bayesian hierarchical mixture model for partitioning gene expression data collected over time.
  • To offer a flexible and robust approach that respects the temporal order of observations and incorporates prior knowledge.
  • To enable inference on the number of partitions directly from the data.

Main Methods:

  • Development of a nonparametric, random walk model for gene expression profiles.
  • Application of Bayesian hierarchical mixture modeling.
  • Utilizing birth-death Markov chain Monte Carlo (MCMC) algorithms for inference when the number of partitions is unknown.
  • Comparison with conventional clustering approaches using simulated data.

Main Results:

  • The proposed Bayesian model effectively partitions time-course gene expression data.
  • The model demonstrates flexibility in handling measurement error and incorporating prior information.
  • Simulated data analysis shows comparable or improved performance against conventional methods.
  • Successful application to meiotic gene expression data in fission yeast.

Conclusions:

  • The Bayesian hierarchical mixture model provides a powerful tool for analyzing temporal gene expression data.
  • This approach enhances the understanding of dynamic gene regulation by accurately partitioning expression profiles.
  • The model's ability to infer the number of partitions adds significant value for exploratory data analysis.