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Team:NYMU-Taipei/modeling/m1
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<h1>Introduction: Growth Curve</h1> | <h1>Introduction: Growth Curve</h1> | ||
<p>A growth curve for a population of bacteria illustrates some of the dynamics that affect the population size over time.<br><br>Four distinct phases are recognized:<br><br> | <p>A growth curve for a population of bacteria illustrates some of the dynamics that affect the population size over time.<br><br>Four distinct phases are recognized:<br><br> | ||
| - | <b>The lag phase:</b><br> | + | <b>The lag phase:</b><br> |
The curve remains at a plateau. During this time, bacteria adapt to their new environment, store nutrients and prepare for binary fission.<br> | The curve remains at a plateau. During this time, bacteria adapt to their new environment, store nutrients and prepare for binary fission.<br> | ||
| - | <b>The logarithmic phase:</b><br> | + | <b>The logarithmic phase:</b><br> |
This phase is also called the exponential growth phase: the population of bacteria enters an active stage of growth, the mass of each cell increases rapidly, and the number of bacteria doubles.<br> | This phase is also called the exponential growth phase: the population of bacteria enters an active stage of growth, the mass of each cell increases rapidly, and the number of bacteria doubles.<br> | ||
| - | <b>The stationary phase:</b><br> | + | <b>The stationary phase:</b><br> |
At this stage reproductive and death rates equalize, the population enters another plateau.<br> | At this stage reproductive and death rates equalize, the population enters another plateau.<br> | ||
| - | <b>The decline phase:</b><br> | + | <b>The decline phase:</b><br> |
If the conditions of the stationary phase continue, the decline phase will ensue: the number of dying cells exceeds the number of new cells produced.<br></p> | If the conditions of the stationary phase continue, the decline phase will ensue: the number of dying cells exceeds the number of new cells produced.<br></p> | ||
<h1>Models and mathematic equations</h1> | <h1>Models and mathematic equations</h1> | ||
Revision as of 11:14, 14 September 2014
Purpose
Introduction: Growth Curve
A growth curve for a population of bacteria illustrates some of the dynamics that affect the population size over time.
Four distinct phases are recognized:
The lag phase:
The curve remains at a plateau. During this time, bacteria adapt to their new environment, store nutrients and prepare for binary fission.
The logarithmic phase:
This phase is also called the exponential growth phase: the population of bacteria enters an active stage of growth, the mass of each cell increases rapidly, and the number of bacteria doubles.
The stationary phase:
At this stage reproductive and death rates equalize, the population enters another plateau.
The decline phase:
If the conditions of the stationary phase continue, the decline phase will ensue: the number of dying cells exceeds the number of new cells produced.
Models and mathematic equations
Three well known growth models (Logistic, Gompertz, and Richartz)are used in this work. Characteristic model parameters (such as lag phase (λ), maximal growth rate (µ-max slope), stationary phase (A-max growth value)) are derived from our experimental data. Bootstrap and cross-validation techniques are used for estimating confidence intervals of
all derived parameters.
The aim is to integrate the experimental data into different growth models and to compare the models using statistical methods (AIC and maximum likelihood were used). We believe, and many scientists do, that model selection is the most important part in model-experiment based research-
Result and model validation
Reference
