Enthalpic and Entropic Controls on 2D Self-Assembly of Proteins on Substrates

Enthalpic and entropic forces are two knobs that can be used to control the assembly of colloidal particles. On the one hand, driving assembly through the enthalpy of binding can be achieved by functionalizing the particles with ligands, such as DNA strands, to enable fine control. On the other hand, particle assembly can also be driven by entropy maximization; particles can spontaneously align and assemble into structures to increase the configurational space available to the system. This phenomenon typically drives the particles into a close-packed geometry to maximize the free volume of free solvent and release the waters of hydration that are otherwise bound to free particles, which results in an effective directional entropic force. Although colloidal particle assembly has been extensively investigated from the perspective of understanding and controlling these entropic and enthalpic drivers, the assembly of biomacromolecules, like proteins, is a rapidly growing field in which such efforts have been limited.<br/>Herein, we create patchy proteins, L-rhamnulose-1-phosphate aldolase (RhuA), with tunable bonding interactions by varying the chemistry of appended functional groups to manipulate the enthalpic driver of assembly. In addition, because the proteins have a well-defined 3D shape and the length and size of the functional groups can be varied, the entropic driver of assembly — shape complementarity — provides a knob with which to tune the resulting structure. In this project, we used <i>in-situ </i>atomic force microscopy (AFM) to observe 2D assembly of distinct assembled phases of specially designed β-cyclodextrin and azobenzene modified RhuA (^CDRhuA and ^AzoRhuA) at mica-water interfaces, as well as the transition between them. In the case of ^AzoRhuA, the presence of suitable long functional groups and weak inter-protein interactions leads to the formation of various polymorphs and between which phase transitions occur via two distinct pathways. However, when functional groups become excessively long or large, as with ^CDRhuA, densely packed configurations are obtained. We hypothesize these configurations arise because the entropic interaction, driven by shape complementarity, becomes the dominant factor in determining the outcome of assembly. We also find that ^CDRhuA follows an unusual multistep assembly and disassembly pathway on substrates due to crowding near the crystal edge in a substrate-controlled unfavorable configuration prior to forming the densely packed crystal. To test our proposed picture of competing enthalpic and entropic interactions, we applied coarse grain simulations in which we varied the relative contributions of protein-substrate interaction and protein-protein interactions, which include both enthalpic attractive interactions and entropic forces due to the shape of the protein. Our findings indicate that, indeed, adjusting the strength and flexibility of the inter-molecular bonds can modulate the entropic forces associated with shape complementarity and the enthalpic forces that facilitate polymorph formation and phase transitions. This insight suggests fundamental design principles for the synthesis of novel 2D macromolecular materials.