Recent crystallographic studies have shown that both backbone and side-chain adjustments occur when different core-packing arrangements are accommodated in proteins. Thus, modeling methods, which have typically considered only side-chain adjustments, must now also account for backbone movements to accurately predict the energies and structures of mutated or designed proteins. The 'plasticity' of protein cores demonstrated by random mutagenesis simplifies protein design by increasing the likelihood of identifying alternative core sequences.

To further examine the structural and thermodynamic basis of hydrophobic stabilization in proteins, all of the bulky non-polar residues that are buried or largely buried within the core of T4 lysozyme were substituted with alanine. In 25 cases, including eight reported previously, it was possible to determine the crystal structures of the variants. The structures of four variants with double substitutions were also determined. In the majority of cases the "large-to-small" substitutions lead to internal cavities. In other cases declivities or channels open to the surface were formed. In some cases the structural changes were minimal (mainchain shifts < or = 0.3 A); in other cases mainchain atoms moved up to 2 A. In the case of Ile 29 --> Ala the structure collapsed to such a degree that the volume of the putative cavity was zero. Crystallographic analysis suggests that the occupancy of the engineered cavities by solvent is usually low. The mutants Val 149 --> Ala (V149A) and Met 6 --> Ala (M6A), however, are exceptions and have, respectively, one and two well-ordered water molecules within the cavity. The Val 149 --> Ala substitution allows the solvent molecule to hydrogen bond to polar atoms that are occluded in the wild-type molecule. Similarly, the replacement of Met 6 with alanine allows the two solvent molecules to hydrogen bond to each other and to polar atoms on the protein. Except for Val 149 --> Ala the loss of stability of all the cavity mutants can be rationalized as a combination of two terms. The first is a constant for a given class of substitution (e.g., -2.1 kcal/mol for all Leu --> Ala substitutions) and can be considered as the difference between the free energy of transfer of leucine and alanine from solvent to the core of the protein. The second term can be considered as the energy cost of forming the cavity and is consistent with a numerical value of 22 cal mol(-1) A(-3). Physically, this term is due to the loss of van der Waal's interactions between the bulky sidechain that is removed and the atoms that form the wall of the cavity. The overall results are consistent with the prior rationalization of Leu --> Ala mutants in T4 lysozyme by Eriksson et al. (Eriksson et al., 1992, Science 255:178-183).

Several variants of T4 lysozyme have been identified that sequester small organic ligands in cavities or clefts. To evaluate potential binding sites for non-polar molecules, we screened a number of hydrophobic large-to-small mutants for stabilization in the presence of benzene. In addition to Leu99-->Ala, binding was indicated for at least five other mutants. Variants Met102-->Ala and Leu133-->Gly, and a crevice mutant, Phe104-->Ala, were further characterized using X-ray crystallography and thermal denaturation. As predicted from the shape of the cavity in the benzene complex, mutant Leu133-->Gly also bound p-xylene. We attempted to enlarge the cavity of the Met102-->Ala mutant into a deep crevice through an additional substitution, but the double mutant failed to bind ligands because an adjacent helix rearranged into a non-helical structure, apparently due to the loss of packing interactions. In general, the protein structure contracted slightly to reduce the volume of the void created by truncating substitutions and expanded upon binding the non-polar ligand, with shifts similar to those resulting from the mutations.A polar molecule binding site was also created by truncating Arg95 to alanine. This creates a highly complementary buried polar environment that can be utilized as a specific "receptor" for a guanidinium ion. Our results suggest that creating a deficiency through truncating mutations of buried residues generates "binding potential" for ligands with characteristics similar to the deleted side-chain. Analysis of complex and apo crystal structures of binding and non-binding mutants suggests that ligand size and shape as well as protein flexibility and complementarity are all determinants of binding. Binding at non-polar sites is governed by hydrophobicity and steric interactions and is relatively permissive. Binding at a polar site is more restrictive and requires extensive complementarity between the ligand and the site.

To investigate the structural and thermodynamic basis of the binding of solvent at internal sites within proteins a number of mutations were constructed in T4 lysozyme. Some of these were designed to introduce new solvent-binding sites. Others were intended to displace solvent from preexisting sites. In one case Val-149 was replaced with alanine, serine, cysteine, threonine, isoleucine, and glycine. Crystallographic analysis shows that, with the exception of isoleucine, each of these substitutions results in the binding of solvent at a polar site that is sterically blocked in the wild-type enzyme. Mutations designed to perturb or displace a solvent molecule present in the native enzyme included the replacement of Thr-152 with alanine, serine, cysteine, valine, and isoleucine. Although the solvent molecule was moved in some cases by up to 1.7 A, in no case was it completely removed from the folded protein. The results suggest that hydrogen bonds from the protein to bound solvent are energy neutral. The binding of solvent to internal sites within proteins also appears to be energy neutral except insofar as the bound solvent may prevent a loss of energy due to potential hydrogen bonding groups that would otherwise be unsatisfied. The introduction of a solvent-binding site appears to require not only a cavity to accommodate the water molecule but also the presence of polar groups to help satisfy its hydrogen-bonding potential. It may be easier to design a site to accommodate two or more water molecules rather than one as the solvent molecules can then hydrogen-bond to each other. For similar reasons it is often difficult to design a point mutation that will displace a single solvent molecule from the core of a protein.

Augmented reality (AR) devices, as smart glasses, enable users to see both the real world and virtual images simultaneously, contributing to an immersive experience in interactions and visualization. Recently, to reduce the size and weight of smart glasses, waveguides incorporating holographic optical elements in the form of advanced grating structures have been utilized to provide light-weight solutions instead of bulky helmet-type headsets. However current waveguide displays often have limited display resolution, efficiency and field-of-view, with complex multi-step fabrication processes of lower yield. In addition, current AR displays often have vergence-accommodation conflict in the augmented and virtual images, resulting in focusing-visual fatigue and eye strain. Here we report metasurface optical elements designed and experimentally implemented as a platform solution to overcome these limitations. Through careful dispersion control in the excited propagation and diffraction modes, we design and implement our high-resolution full-color prototype, via the combination of analytical-numerical simulations, nanofabrication and device measurements. With the metasurface control of the light propagation, our prototype device achieves a 1080-pixel resolution, a field-of-view more than 40°, an overall input-output efficiency more than 1%, and addresses the vergence-accommodation conflict through our focal-free implementation. Furthermore, our AR waveguide is achieved in a single metasurface-waveguide layer, aiding the scalability and process yield control.

Previous analysis of randomly generated multiple mutations within the core of bacteriophage T4 lysozyme suggested that the "large-to-small" substitution Leu121 to Ala (L121A) and the spatially adjacent "small-to-large" substitution Ala129 to Met (A129M) might be mutually compensating. To test this hypothesis, the individual variants L121A and A129M were generated, as well as the double "size-switch" mutant L121A/A129M. To make the interchange symmetrical, the combination of L121A with A129L to give L121A/A129L was also constructed. The single mutations were all destabilizing. Somewhat surprisingly, the small-to-large substitutions, which increase hydrophobic stabilization but can also introduce strain, were less deleterious than the large-to-small replacements. Both Ala129 --> Leu and Ala129 --> Met offset the destabilization of L121A by about 50%. Also, in contrast to typical Leu --> Ala core substitutions, which destabilize by 2 to 5 kcal/mol, Leu121 --> Ala slightly stabilized A129L and A129M. Crystal structure analysis showed that a combination of side-chain and backbone adjustments partially accommodated changes in side-chain volume, but only to a limited degree. For example, the cavity that was created by the Leu121 to Ala replacement actually became larger in L121A/A129L. The results demonstrate that the destabilization associated with a change in volume of one core residue can be specifically compensated by an offsetting volume change in an adjacent residue. It appears, however, that complete compensation is unlikely because it is difficult to reconstitute an equivalent set of interactions. The relatively slow evolution of core relative to surface residues appears, therefore, to be due to two factors. First, a mutation in a single core residue that results in a substantial change in size will normally lead to a significant loss in stability. Such mutations will presumably be selected against. Second, if a change in bulk does occur in a buried residue, it cannot normally be fully compensated by a mutation of an adjacent residue. Thus, the most probable response will tend to be reversion to the parent protein.