<p>R packages like <a href="https://bioconductor.org/packages/release/bioc/html/DESeq2.html" rel="nofollow noreferrer">DESeq2</a>, <a href="https://bioconductor.org/packages/release/bioc/html/edgeR.html" rel="nofollow noreferrer">edgeR</a>, and <a href="https://github.com/pachterlab/sleuth" rel="nofollow noreferrer">sleuth</a> will help you perform differential gene expression analysis.
These are typically used for control-vs-treatment experimental designs.
So you could use them like this and perform a bunch of pair-wise comparisons between the time points (i.e. what are the differentially expressed genes between timepoint <span class="math-container">$t_0$</span> and timepoint <span class="math-container">$t_1$</span>, <span class="math-container">$t_0$</span> and <span class="math-container">$t_2$</span>, etc.).</p>
<p>But all of these methods make use of <a href="https://en.wikipedia.org/wiki/Generalized_linear_model" rel="nofollow noreferrer">generalized linear models</a> to perform the statistical inference on coefficients.
For the simple control-vs-treatment design, above, this looks something like</p>
<p><span class="math-container">$$g \left(\mathbb{E} \left[Y_i | X \right] \right) = \mu_i + \beta_i X$$</span></p>
<p>where <span class="math-container">$g$</span> is the link function, <span class="math-container">$\mu_i$</span> is the mean expression of gene <span class="math-container">$i$</span>, <span class="math-container">$\beta_i$</span> is the expression fold change estimate, and <span class="math-container">$X$</span> is the indicator variable saying if the sample is a treatment or control sample.</p>
<p>You can modify this equation by adding a time component to it.</p>
<p><span class="math-container">$$g \left(\mathbb{E} \left[Y_i | X \right] \right) = \mu_i + \beta_i^{(group)} X + \beta_i^{(time)} t$$</span></p>
<p>If you specify the timepoint of the sample in the experimental design matrix for DESeq2, edgeR, or Sleuth, you can get information about the effect of the perturbation as well as the effect over time.</p>
<p>You can try more complicated designs, too, like a coefficient for the interaction between timepoint and perturbation status, but with 3 replicates in each, it's probably best to stick with simple, linear models.</p>

CC BY-SA 4.0
2021-04-01T20:17:16.877Z
2021-04-01T20:17:16.877Z
James Hawley
<p>I have a dataset that has two groups, perturbed vs control. Each group has 3 replicates. Each replicate has 8 time points. How do we do Differential gene expression analysis to find significantly expressed genes? Any packages in R or web tools etc?</p>

<rna-seq><gene><differential-expression>
Differential gene expression analysis of time series with replicates
# Differential gene expression analysis of time series with replicates

(Asked by: username_0 on 2021-03-31)

I have a dataset that has two groups, perturbed vs control. Each group has 3 replicates. Each replicate has 8 time points. How do we do Differential gene expression analysis to find significantly expressed genes? Any packages in R or web tools etc?

**Tags:** rna-seq, gene, differential-expression

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## 1 answers

### Answer by username_1 on 2021-04-01. Score: 1

R packages like [DESeq2](https://bioconductor.org/packages/release/bioc/html/DESeq2.html), [edgeR](https://bioconductor.org/packages/release/bioc/html/edgeR.html), and [sleuth](https://github.com/pachterlab/sleuth) will help you perform differential gene expression analysis.
These are typically used for control-vs-treatment experimental designs.
So you could use them like this and perform a bunch of pair-wise comparisons between the time points (i.e. what are the differentially expressed genes between timepoint $t\_0$ and timepoint $t\_1$, $t\_0$ and $t\_2$, etc.).

But all of these methods make use of [generalized linear models](https://en.wikipedia.org/wiki/Generalized_linear_model) to perform the statistical inference on coefficients.
For the simple control-vs-treatment design, above, this looks something like

$$g \left(\mathbb{E} \left[Y\_i | X \right] \right) = \mu\_i + \beta\_i X$$

where $g$ is the link function, $\mu\_i$ is the mean expression of gene $i$, $\beta\_i$ is the expression fold change estimate, and $X$ is the indicator variable saying if the sample is a treatment or control sample.

You can modify this equation by adding a time component to it.

$$g \left(\mathbb{E} \left[Y\_i | X \right] \right) = \mu\_i + \beta\_i^{(group)} X + \beta\_i^{(time)} t$$

If you specify the timepoint of the sample in the experimental design matrix for DESeq2, edgeR, or Sleuth, you can get information about the effect of the perturbation as well as the effect over time.

You can try more complicated designs, too, like a coefficient for the interaction between timepoint and perturbation status, but with 3 replicates in each, it's probably best to stick with simple, linear models.


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