Design of Toy Proteins Capable to Rearrange Conformations in a Mechanical Fashion

We design toy protein mimicking a machine-like function of an enzyme. Using an insight gained by the study of conformation space of compact lattice polymers, we demonstrate the possibility of a large scale conformational rearrangement which occurs (i) without opening a compact state, and (ii) along a linear (one-dimensional) path. We also demonstrate the possibility to extend sequence design method such that it yields a ”collective funnel” landscape in which the toy protein (computationally) folds into the valley with rearrangement path at its bottom. Energies of the states along the path can be designed to be about equal, allowing for diffusion along the path. They can also be designed to provide for a significant bias in one certain direction. Together with a toy ligand molecule, our ”enzimatic” machine can perform the entire cycle, including conformational relaxation in one direction upon ligand binding and conformational relaxation in the opposite direction upon ligand release. This model, however schematic, should be useful as a test ground for phenomenological theories of machine-like properties of enzymes.