1. Mathematical Architecture of MACS3

Model-based Analysis of ChIP-Seq (MACS3) models read enrichment along the genome using a Poisson distribution. Because chromatin compaction and sequencing accessibility vary across chromosomes, MACS3 replaces a static global Poisson parameter ($\lambda_{\text{BG}}$) with a dynamic local background parameter ($\lambda_{\text{local}}$):

$$\lambda_{\text{local}} = \max(\lambda_{\text{BG}}, \lambda_{\text{1kb}}, \lambda_{\text{5kb}}, \lambda_{\text{10kb}})$$

This dynamic calculation from the matched input control guards against false positives in open chromatin or copy-number amplified regions.

2. Executing MACS3 Peak Calling for Narrow Histone Marks (H3K4me3)

# Call peaks for Huntington's Disease Replicate 1 against matched Input
macs3 callpeak \
    -t 03_filtered/HD_Rep1.clean.bam \
    -c 03_filtered/HD_Input.clean.bam \
    -f BAM \
    -g hs \
    -n HD_Rep1 \
    --outdir 04_peaks/ \
    -q 0.05 \
    --keep-dup all

# Repeat for all biological replicates
for rep in HD_Rep2 Control_Rep1 Control_Rep2; do
    ctrl="Control_Input"
    [[ "$rep" =~ "HD" ]] && ctrl="HD_Input"
    
    macs3 callpeak \
        -t 03_filtered/${rep}.clean.bam \
        -c 03_filtered/${ctrl}.clean.bam \
        -f BAM \
        -g hs \
        -n ${rep} \
        --outdir 04_peaks/ \
        -q 0.05 \
        --keep-dup all
done

3. Output File Formats & FRiP Score Quality Control

MACS3 generates three primary files per sample:

1. ${sample}_peaks.narrowPeak: Standard ENCODE 10-column BED format containing peak boundaries, signal value, p-value (-log10), q-value (-log10), and the exact single-base summit coordinate.
2. ${sample}_summits.bed: Single-nucleotide peak summits, ideal for transcription factor motif discovery.
3. ${sample}_peaks.xls: Tab-delimited summary containing fold-enrichment, coordinates, and statistics.

Fraction of Reads in Peaks (FRiP): Calculated as the total number of reads falling within called peaks divided by total mapped reads. For punctate marks like H3K4me3, high-quality experiments yield $\text{FRiP} \ge 1\%-5\%$.