Abstract: Nucleosomes cluster together when chromatin folds in the cell to form heterogeneous groups termed "clutches". These structural units add another level of chromatin regulation, for example during cell differentiation. Yet, the mechanisms that regulate their size and compaction remain obscure. Here, using our chromatin mesoscale model, we dissect clutch patterns in fibers with different combinations of nucleosome positions, linker histone density, and acetylation levels to investigate their role in clutch regulation. First, we isolate the effect of each chromatin parameter by studying systems with regular nucleosome spacing; second, we design systems with naturally-occurring linker lengths that fold onto specific clutch patterns; third, we model gene-encoding fibers to understand how these combined factors contribute to gene structure. Our results show how these chromatin parameters act together to produce different-sized nucleosome clutches. The length of nucleosome free regions (NFRs) profoundly affects clutch size, while the length of linker DNA has a moderate effect. In general, higher linker histone densities produce larger clutches by a chromatin compaction mechanism, while higher acetylation levels produce smaller clutches by a chromatin unfolding mechanism. We also show that it is possible to design fibers with naturally-occurring DNA linkers and NFRs that fold onto specific clutch patterns. Finally, in gene-encoding systems, a complex combination of variables dictates a gene-specific clutch pattern. Together, these results shed light into the mechanisms that regulate nucleosome clutches and suggest a new epigenetic mechanism by which chromatin parameters regulate transcriptional activity via the three-dimensional folded state of the genome at a nucleosome level.