Metalloproteins, supramolecular composites of polymeric peptides and metal species, are essential organic transformation systems for maintaining vital activity to promote highly efficient enzymatic reactions.[1] For example, the metalloprotein catalase provides extremely high turnover efficiencies of 40 000 000 sec À1 . However, metalloproteins are easily disassimilated and exhibit substrate specificity. Therefore, the development of a metalloprotein-inspired polymeric metal catalyst is an important objective for organic, organometallic, and supramolecular chemistry, as well as sustainable and industrial process chemistry.[2] These catalysts are expected to provide highly active and selective organic transformation systems with high reusability, safety, cleanness, ease of use, and substrate tolerance. In metalloproteins, the basic imidazole unit within histidine plays an important role for binding with metal species, thus forming catalytic sites within a supramolecular structure; therefore imidazole ligands are widely utilized as the building blocks of artificial metalorganic self-assembled supramolecules for functional materials including catalysts.[3] We believe that some insoluble selfassembled complexes of amphiphilic polymeric imidazoles and metal species could offer catalytic activities as high as that of metalloproteins, but with much greater reusability.We recently reported the preparation of highly active, reusable, heterogeneous polymeric metal catalysts for organic transformations, also known as molecular convolution, where a soluble linear polymer having multiple ligand groups is convoluted (noncovalently cross-linked) with transition metals through coordinative or ionic complexation.[4] We envisioned applying this concept to the preparation of metalloprotein-inspired polymeric imidazole metal catalysts to produce highly active, reusable, heterogeneous, selfassembled catalysts. Herein we report the development of a novel polymeric imidazole/acrylamide palladium catalyst that was utilized for the allylic arylation/alkenylation of allylic esters with aryl/alkenylboronic acids and tetraaryl borates. Even 0.8-40 ppm of the catalyst efficiently promoted the allylic arylation/alkenylation in alcohol or water with a catalytic turnover number (TON) of 20 000-1 250 000, and the catalyst was reusable without loss of catalytic activity. We found that our molecular convolution methodology provided the globular-aggregated, self-assembled structure of the catalyst.The metalloprotein-inspired polymeric imidazole/palladium catalyst 3 (MPPI-Pd) was readily prepared as follows. When the coordinative convolution of [(NH 4 ) 2 PdCl 4 ] (2; 1 mol equiv Pd) and poly[(N-vinylimidazole)-co-(N-isopropylacrylamide) 5 ][5] (1; 2 mol equiv imidazole) was carried out in a methanol/water (1:1) solution at 80 8C for 30 minutes, the resulting compound 3 (brown powder) was precipitated out (Scheme 1). The precipitates were hardly soluble in water, methanol, DMF, EtOAc, CH 2 Cl 2 , or n-hexane. As shown in the top left panel of Figure...