Such studies compare gene expression across time by measuring mRNA levels from samples collected at different timepoints 1. Such time-course studies can vary from measuring a few distinct timepoints, to sampling ten to 20 time points. These longer time series are particularly interesting for investigating development over time.
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Identifying groups of genes with similar expression time-courses is a crucial first step in the analysis. As biologically relevant groups frequently overlap, due to genes having several distinct roles in those cellular processes, this is a difficult problem for classical clustering methods. We use a mixture model to circumvent this principal problem, with hidden Markov models (HMMs) …
Time course gene expression experiments provide opportunities to explore patterns of gene expression change over a time and understand the dynamic behavior of gene expression, which is crucial for study on development and progression of biology and disease. Analysis of the gene expression time-course profiles has not been fully exploited so far.
I am doing time course study for gene expression in cell culture. I am doing 0, 1, 2, 4, 8, 16, 24 hours. ... Gene Expression Analysis. Gene Expression Profiling. …
Aug 01, 2005 · Abstract and Figures. Measuring gene expression over time can provide important insights into basic cellular processes. Identifying groups …
I think you should normalize each value first by the control gene at each given time point, calculating the SD as you would with the raw data. Then you should express it in relation to the time 0, which should not change the SD, just do the same calculation with the data. It is advisable to do three biological replicates per time point/treatment.
I would take each time point individually (1,2,4,8hrs etc) lysing the cells and freezing. The day after your experiment extract all RNA at the same time and normalise to a housekeeper gene (or two if you can - normalise to the geometric mean) such as BActin, Gapdh, Bmn etc.
where dCt are the delta-Ct values from qPCR, TIME is the variable coding the time points (if you have a good and relatively simple functional model, like for instance a linear or logistic change, then you can use TIME as a metric variable with appropriate transformations; otherwise I would suggest to code TIME as a categorical variable), and TREATMENT is the categorical variable specifying the treatmen ("control" or "treated").
While many expression studies are designed to compare the gene expression between distinct groups, there is also a long history of time-course expression studies. Such studies compare gene expression across time by measuring mRNA levels from samples collected at different timepoints 1. Such time-course studies can vary from measuring a few distinct timepoints, to sampling ten to 20 time points. These longer time series are particularly interesting for investigating development over time. More recently, a new variety of time course studies have come from single-cell sequencing experiments ( Habib et al ., 2016; Shalek et al ., 2014; Trapnell et al ., 2014) which can sequence single cells at different stages of development; in this case, the time point is the stage of the cell in the process of development -- a value that is not know but estimated from the data as its "pseudo-time."
The next step in a gene expression analysis is typically to run a differential expression analysis, generally to find genes different between different conditions. For time-course data, there are two different approaches for determining differentially expressed genes,
Before clustering the genes, we first reduce the set of genes of interest to genes that (1) are found to be significantly differentially expressed; (2) have a large-fold change between conditions. Reducing the set of genes on which to perform the clustering allows the estimation of the centroids of the clusters with more stability.
moanin and timecoursedata are available from bioconductor, and can be installed using the install function in the package BiocManager, along with the corresponding package that contains time course datasets we will use:
Typically, two quality control and exploratory analysis steps are performed before and after normalization: (1) low dimensionality embedding of the samples; (2) correlation plots between each sample. In both cases, we expect a strong biological signal, while replicate samples should be strongly clustered or correlated with one another.
Samples are colored by condition (top row) and sampling time (bottom row).
Further, a fitted spline function for each group is plotted to aid in comparing global trends across conditions.
The estimated gene expression y^ijin a particular cluster can be expressed as a linear combination of the observed gene expression, i.e. y^ij=∑l=1n∑m=1Taijlmylm. The matrix obtained by arranging aijlmin proper entries is called the smoothing matrix.
Mixed-effect model representation of gene expression over time. The deviation of gene y1's expression from the mean curve μ(t) in cluster k, is a combination of the so-called random effect band the measurement error ɛ. Ψ1represents the ‘real’ expression curve of gene 1. Note that the bis constant over all time-points and captures between time-point dependence.
Here, we introduce a data-driven clustering method, called smoothing spline clustering (SSC), that overcomes the aforementioned obstacles using a mixed-effect smoothing spline model and the rejection-controlled EM algorithm (11). The SSC method not only provides gene-to-cluster assignment but a predicted mean curve for each cluster and associated confidence bands and R2value for each cluster. A distinguishing feature of SSC is that it accurately estimates individual gene expression profiles and the mean gene expression profile within clusters simultaneously, making it extremely powerful for clustering time course data.
The maximization step of the EM algorithm involves computing and maximizing the weighted version of the penalized log-likelihood (Equation 7) for each cluster:
Finally, in order to avoid local optima , the RCEM is run with multiple chains.
To incorporate the cluster assignment proportions described in Equation 5, we combine 5 and 6 to yield the complete data penalized log-likelihood:
Since directly maximizing the penalized log-likelihood (Equation 7) is not analytically possible, we develop a variation of the EM algorithm (11) in conjunction with generalized cross-validation (GCV) (17,18) for the task. In our case, the expectation step of the EM algorithm is the computation of the probability that a particular gene belongs to each cluster given all the parameters in the model, which is simply,