End-to-end time-course analysis from expression matrix to temporal patterns and enrichment. Covers temporal DE, Mfuzz soft clustering, optional rhythm detection, GAM trajectory fitting, and per-cluster pathway enrichment. Use when analyzing bulk time-series expression experiments from any omics platform.
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End-to-end time-course analysis from expression matrix to temporal patterns and enrichment. Covers temporal DE, Mfuzz soft clustering, optional rhythm detection, GAM trajectory fitting, and per-cluster pathway enrichment. Use when analyzing bulk time-series expression experiments from any omics platform.
[{"after_de":"Significant temporal genes >100 at FDR <0.05; model fit residuals reasonable"},{"after_clustering":"Membership >0.5 for soft clustering; no empty clusters; validated by gap statistic or silhouette (typical range 4-20 clusters depending on complexity)"},{"after_enrichment":"At least 3 clusters with significant GO terms at FDR <0.05"}]
Time-Course Analysis Pipeline
Complete workflow from expression matrix through temporal differential expression, soft clustering,
optional rhythm detection, trajectory fitting, and per-cluster pathway enrichment.
Pipeline Overview
Expression matrix + time metadata
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[1. Temporal DE] ---------> limma splines / DESeq2 LRT
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[2. Filter] --------------> Significant temporal genes (FDR <0.05)
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[3. Mfuzz Clustering] ----> Soft clustering of expression profiles
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| +---> QC: membership >0.5, no empty clusters
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+--- Circadian design? ---> [4a. Rhythm Detection] (MetaCycle / CosinorPy)
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| Rhythmic genes + period/phase estimates
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[4b. GAM Trajectory] -----> mgcv GAM fitting for top clusters
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[5. Pathway Enrichment] --> clusterProfiler per-cluster GO/KEGG
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Temporal gene modules + enriched pathways + trajectory plots
Step 1: Temporal Differential Expression
R (limma splines)
library(limma)
library(splines)
expr <- as.matrix(read.csv('counts_normalized.csv', row.names =1))
meta <- read.csv('metadata.csv')
time_points <- meta$time
design <- model.matrix(~ ns(time_points, df =3))
fit <- lmFit(expr, design)
fit <- eBayesfit
temporal_results topTablefit coef ncoldesign number sort.by
(
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# Test all spline coefficients jointly for temporal significance
<-
(
,
=
2
:
(
)
,
=
Inf
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=
'F'
)
# topTable already returns adj.P.Val (BH-corrected); use it directly
# Gate 1: Sufficient temporal genes detected
sig_genes <- temporal_results[temporal_results$adj.P.Val <0.05,]
n_sig <- nrow(sig_genes)
message(sprintf('Significant temporal genes: %d', n_sig))if(n_sig <100) message('WARNING: Few temporal genes. Check time point spacing or consider relaxing FDR.')if(n_sig >10000) message('WARNING: Many temporal genes. Consider stricter FDR or inspect batch effects.')# Gate 2: Residual distribution check
residuals <- residuals(fit, expr)
message(sprintf('Residual mean: %.4f, SD: %.4f', mean(residuals), sd(residuals)))
Step 2: Filter Significant Genes
# FDR <0.05: Standard threshold for temporal DE# More permissive (0.1) acceptable for exploratory clustering
sig_genes <- rownames(temporal_results[temporal_results$adj.P.Val <0.05,])
expr_sig <- expr[sig_genes,]
message(sprintf('Genes passing FDR <0.05: %d',length(sig_genes)))
Step 3: Mfuzz Soft Clustering
library(Mfuzz)
eset <- ExpressionSet(assayData = as.matrix(expr_sig))# Standardize expression profiles (mean=0, sd=1 per gene)
eset <- standardise(eset)# Estimate fuzzifier m# mestimate() calculates optimal m from data geometry; typical range 1.5-2.5
m <- mestimate(eset)
message(sprintf('Estimated fuzzifier m = %.2f', m))# Cluster count: start with sqrt(n_genes/2), refine with gap statistic# Typical range 4-20 depending on temporal complexity
n_clusters <- 8
cl <- mfuzz(eset,c= n_clusters, m = m)# Filter low-membership genes# Membership >0.5: gene clearly belongs to one cluster# Lower to 0.3 for exploratory analysis with more overlap
core_genes <- acore(eset, cl, min.acore =0.5)
Python Alternative (tslearn)
from tslearn.clustering import TimeSeriesKMeans
# Row-wise z-scoring: normalize each gene across its timepoints (not per-timepoint)
expr_scaled = (expr_sig.values - expr_sig.values.mean(axis=1, keepdims=True)) / expr_sig.values.std(axis=1, keepdims=True)
# n_clusters: 4-20 depending on complexity; evaluate with silhouette score
model = TimeSeriesKMeans(n_clusters=8, metric='softdtw', metric_params={'gamma': 0.01},
max_iter=50, random_state=42)
labels = model.fit_predict(expr_scaled.reshape(expr_scaled.shape[0], expr_scaled.shape[1], 1))
Only applicable when sampling covers 24h+ cycles with sufficient resolution (every 2-4h).
R (MetaCycle)
library(MetaCycle)# Expects genes as rows, time points as columns# Column names must be numeric time values (hours)
expr_for_meta <- expr_sig
colnames(expr_for_meta)<- meta$time_hours
write.csv(expr_for_meta,'expr_for_metacycle.csv')# Period range 20-28h: standard circadian search window# Adjust for ultradian (4-12h) or infradian (>28h) rhythms
meta2d('expr_for_metacycle.csv', filestyle ='csv',
minper =20, maxper =28,
timepoints = sort(unique(meta$time_hours)),
outdir ='metacycle_results')
Python (CosinorPy)
from cosinorpy import file_parser, cosinor
# fit_group expects long-format DataFrame with columns 'x' (time), 'y' (expression), 'test' (gene name)# Reshape expression matrix to long format before passing# period=24: standard circadian; adjust for other periodicities
results = cosinor.fit_group(expr_long, period=24, n_components=1)
rhythmic = results[results['p'] < 0.05]
Step 4b: GAM Trajectory Fitting
R (mgcv)
library(mgcv)
cluster_trajectories <-list()for(cl_id in1:n_clusters){
cl_genes <-names(cl$cluster[cl$cluster == cl_id])
mean_profile <- colMeans(expr_sig[cl_genes,])
df_gam <- data.frame(time = meta$time, expr = mean_profile)# k: basis dimension; k=5 sufficient for most time courses# Increase to k=10 for >20 time points; decrease to k=3 for <6 time points
gam_fit <- gam(expr ~ s(time, k =5), data = df_gam)
cluster_trajectories[[cl_id]]<-list(
fit = gam_fit,
r_squared = summary(gam_fit)$r.sq,
edf = summary(gam_fit)$edf
)
message(sprintf('Cluster %d: R^2 = %.3f, EDF = %.2f', cl_id,
summary(gam_fit)$r.sq, summary(gam_fit)$edf))}
Python (pygam)
from pygam import LinearGAM, s
import numpy as np
for cl_id inrange(n_clusters):
cl_mask = labels == cl_id
mean_profile = expr_scaled[cl_mask].mean(axis=0)
# n_splines=5: sufficient for most time courses
gam = LinearGAM(s(0, n_splines=5)).fit(meta['time'].values.reshape(-1, 1), mean_profile)
print(f'Cluster {cl_id}: GCV = {gam.statistics_["GCV"]:.4f}')
Step 5: Per-Cluster Pathway Enrichment
R (clusterProfiler)
library(clusterProfiler)
library(org.Hs.eg.db)
enrichment_results <-list()for(i inseq_along(core_genes)){
genes <- core_genes[[i]]$NAME
# Convert symbols to Entrez IDs
entrez <- bitr(genes, fromType ='SYMBOL', toType ='ENTREZID', OrgDb = org.Hs.eg.db)# GO Biological Process enrichment# pvalueCutoff 0.05: standard; qvalueCutoff 0.05 for FDR control
ego <- enrichGO(gene = entrez$ENTREZID, OrgDb = org.Hs.eg.db,
ont ='BP', pAdjustMethod ='BH',
pvalueCutoff =0.05, qvalueCutoff =0.05,
readable =TRUE)
enrichment_results[[i]]<- ego
message(sprintf('Cluster %d: %d significant GO terms', i, nrow(as.data.frame(ego))))}
Python (gseapy)
import gseapy as gp
for cl_id inrange(n_clusters):
cl_genes = [g for g, l inzip(expr_sig.index, labels) if l == cl_id]
enr = gp.enrichr(gene_list=cl_genes, gene_sets='GO_Biological_Process_2023',
organism='human', outdir=f'enrichr_cluster_{cl_id}')
sig_terms = enr.results[enr.results['Adjusted P-value'] < 0.05]
print(f'Cluster {cl_id}: {len(sig_terms)} significant GO terms')
QC Checkpoint: Enrichment
# Gate: At least 3 clusters should have significant GO terms
clusters_with_terms <-sum(sapply(enrichment_results,function(x) nrow(as.data.frame(x))>0))
message(sprintf('Clusters with significant GO terms: %d / %d', clusters_with_terms,length(enrichment_results)))if(clusters_with_terms <3){
message('WARNING: Few clusters enriched. Check gene ID conversion or relax thresholds.')}
Parameter Recommendations
Step
Parameter
Recommendation
Temporal DE
Spline df
3 (default); increase to 4-5 for >10 time points
Temporal DE
FDR
0.05 (standard); 0.1 for exploratory clustering
Mfuzz
fuzzifier m
Use mestimate(); typical range 1.5-2.5
Mfuzz
n_clusters
4-20; start with sqrt(n_genes/2), refine with gap statistic
Mfuzz
min membership
0.5 (core genes); 0.3 (exploratory)
MetaCycle
period range
20-28h (circadian); adjust for other periodicities
GAM
k (basis dim)
5 (default); 3 for <6 time points; 10 for >20
clusterProfiler
pvalueCutoff
0.05 (standard); 0.1 (permissive)
Troubleshooting
Issue
Likely Cause
Solution
< 100 temporal genes
Insufficient replicates or noisy data
Add replicates; use DESeq2 LRT instead of limma
Empty Mfuzz clusters
Too many clusters
Reduce n_clusters; check gap statistic
All genes in one cluster
Fuzzifier too low or too few clusters
Increase m or n_clusters
No rhythmic genes
Non-circadian design or low power
Verify 24h+ sampling; increase resolution
GAM overfitting
k too high for time points
Set k = min(n_timepoints - 1, 5)
Few enriched clusters
Gene ID conversion failure
Check species; verify Entrez ID mapping
Low membership scores
High expression noise
Increase fuzzifier m; apply stricter gene filtering
Related Skills
differential-expression/timeseries-de - Temporal DE methods
