The interleukin-1 cytokines belong to the beta-trefoil fold family and play a key role in immune responses to infections and injury. We simulate the structure-based models of two interleukin-1 cytokines, IL-33 and IL-1 beta, and find that IL-33 has a lower barrier to folding than IL-1 beta We then design the folding motif (FM) of the IL-1 beta-trefoil fold and identify structural deviations of IL-33 and IL-1 beta from this FM. In previous work, we found that structural deviations from the FM that are large enough to lower folding free energy barriers were part of ligand binding sites. In contrast, we find that structural perturbations in IL-33 and IL-1 beta which reduce the folding free energy barrier are located in the folding core and do not bind ligands. In both proteins, such core residues are interleaved with surface residues which are proximal to receptor binding sites. However, IL-33 has a lower folding barrier because its core perturbations are larger than those in IL-1 beta. In order to understand the role of these core perturbations, we perform atomistic simulations of both proteins and find that the larger core perturbations may allow IL-33 to communicate signals differently across the protein. Integrating previous data, we also hypothesize that the larger IL-33 core perturbations may help accommodate its more charged binding site and may also aid in its inactivation by caspase-mediated cleavage. Together, our results suggest that protein folding landscapes are modulated not only by larger functional features such as binding sites but also by the details of protein function and fate. Furthermore, a comparative study of such landscapes may be a facile way to identify subtle differences in allosteric connectivity between two similar proteins.