Co-activators and co-repressors do not directly bind to DNA. Instead, they interact with transcription factors that are bound to promoter regions of target genes. Co-activators typically possess histone acetyltransferase (HAT) activity, which helps in loosening the chromatin structure, making it more accessible for transcription. On the other hand, co-repressors often have histone deacetylase (HDAC) activity, leading to chromatin condensation and transcriptional repression.