Biological diversity has evolved despite the essentially infinite complexity of protein sequence space. We present a hierarchical approach to the efficient searching of this space and quantify the evolutionary potential of our approach with Monte Carlo simulations. These simulations demonstrate that nonhomologous juxtaposition of encoded structure is the rate-limiting step in the production of new tertiary protein folds. Nonhomologous ''swapping'' of lowenergy secondary structures increased the binding constant of a simulated protein by Ϸ10 7 relative to base substitution alone. Applications of our approach include the generation of new protein folds and modeling the molecular evolution of disease.The exponential complexity of protein space limits evolution by means of DNA base substitution alone and remains a major challenge to many quantitative treatments of evolution. Random assembly and base substitution are ideally suited for searching local regions of polypeptide space, as demonstrated experimentally by the isolation of large numbers of stable structures from random encoded peptide libraries (1-3) and the rapid improvement of function seen in molecular evolutions of synthetic antibodies (4-6). However, in vitro homologous recombination experiments, termed DNA shuffling, have already demonstrated the limitations of protein evolution by means of base substitution alone (7-11). Indeed, a complete hierarchy of natural mutational events composed of rearrangements, deletions, horizontal transfers (12), transpositions (13), and other nonhomologous juxtapositions, in addition to base substitution and homologous recombination, is required for the rapid generation of protein diversity.Modern neo-Darwinism and neutral evolutionary treatments, therefore, fail to explain satisfactorily the generation of the diversity of life found on our planet. Yet most theoretical treatments of evolution consider only the limited pointmutation events that form the basis of these theories. Similarly, methods of experimental protein evolution are generally limited to point mutation and DNA shuffling. Genetic studies, on the other hand, have indicated the importance of dramatic DNA swapping events in natural evolution (12,(14)(15)(16)(17)(18).We address here, from a theoretical point of view, the question of how protein space can be searched efficiently and thoroughly, either in the laboratory or in Nature. We demonstrate that point mutation alone is incapable of evolving systems with substantially new protein folds. We demonstrate further that even the DNA shuffling approach is incapable of evolving substantially new protein folds. Our Monte Carlo simulations demonstrate that nonhomologous DNA ''swapping'' of low-energy structures is a key step in searching protein space.More generally, our simulations demonstrate that the efficient search of large regions of protein space requires a hierarchy of genetic events, each encoding higher-order structural substitutions. We show how the complex protein function landscape can be naviga...

Homeobox genes specify regional identity during development. A homeobox sequence that we have named Dbx was isolated from 13.5-day embryonic mouse telencephalon cDNA. En-i (3) and Evx-1 (4), the murine homologs ofthe Drosophila engrailed and evenskipped genes respectively, show a much greater localization oftranscripts along the dorsoventral axis.

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Nuclear protein extracts from day 12.5 mouse embryos were used to study protein binding to DNA sequences 5' of the Hox 1.5 homeo box. Embryos of this developmental stage are known to express this gene. DNA binding protein blotting and retardation gel techniques show that murine embryonic nuclear proteins specifically bind a 753-base pair (bp) DNA fragment from the region upstream of the Hox 1.5 homeo box. A fusion protein containing the Hox 1.5 homeo domain constructed in Xgtll also binds the same 753-bp DNA fragment. Specific binding of the fusion protein to the upstream DNA fragment shows that the homeo box contains the sequences required for specific protein-DNA interactions, and the 753-bp fragment contains a homeo domain binding site. These results support the hypothesis that murine homeo boxes are DNA binding domains of proteins involved in the regulation of embryonic development.Several Drosophila homeotic and segmentation genes involved in embryonic development contain an 180-bp (basepair) conserved sequence known as the homeo box (1-4). These homeo box sequences exist in about 20 loci in the Drosophila genome. Xenopus, chicken, mouse, and man were also found to contain approximately 20 homeo box sequences (5). The homeo box portion of the coded protein, termed the homeo domain (3), possesses regions ofhomology with well characterized prokaryotic DNA binding proteins, such as the X repressor, the lac repressor, cro, and eukaryotic DNA binding proteins, such as the yeast mating type proteins (6-9). It is believed that these proteins all share a common helix-turn-helix DNA binding motif. One helix (helix 2) interacts electrostatically with the phosphate backbone of DNA, while the other (helix 3) makes specific hydrogen bonds with the bases ofthe major groove of B-DNA (10). This helix-turn-helix region of the homeo domains shows the highest degree of conservation of the homeo box sequence. It has been predicted that the homeo domain of the protein specifically binds DNA on the basis of its sequence conservation, structural properties, and similarities to known DNA binding proteins (2).The protein products of several Drosophila homeo box genes have been localized in the nucleus (11)(12)(13)(14) Breeding of Mice and Dissection of Embryos. CD1 outbred mice (Charles River Laboratories) were used in this study. A successful mating was determined the next morning by the presence of a vaginal plug. This was considered day 0.5 of gestation. Dissection of embryos was done as described (17).Preparation of Nuclear Extracts. Mouse embryos (10-13) were homogenized in 5 ml ofbuffer 1 (0.25 M sucrose/50 mM Tris Cl, pH 7.5/25 mM KCl/5 mM MgCl2), and the cells were collected at 500 x g -in a refrigerated centrifuge. The cells were resuspended and lysed in 5 ml ofbuffer 2 (10 mM Hepes, pH 8.0/50 mM NaCl/0.5 M sucrose/O.1 mM EDTA/O.5% Triton X-100/1 mM dithiothreitol/5 mM MgCl2). The nuclei were pelleted at 500 x g as above. The pellet was resuspended in buffer 2 at 7 x 107 nuclei per ml. Spermidine was added to a con...