Mapping the distribution of packing topologies within protein interiors shows predominant preference for specific packing motifs

Background

Mapping protein primary sequences to their three dimensional folds referred to as the 'second genetic code' remains an unsolved scientific problem. A crucial part of the problem concerns the geometrical specificity in side chain association leading to densely packed protein cores, a hallmark of correctly folded native structures. Thus, any model of packing within proteins should constitute an indispensable component of protein folding and design.

Results

In this study an attempt has been made to find, characterize and classify recurring patterns in the packing of side chain atoms within a protein which sustains its native fold. The interaction of side chain atoms within the protein core has been represented as a contact network based on the surface complementarity and overlap between associating side chain surfaces. Some network topologies definitely appear to be preferred and they have been termed 'packing motifs', analogous to super secondary structures in proteins. Study of the distribution of these motifs reveals the ubiquitous presence of typical smaller graphs, which appear to get linked or coalesce to give larger graphs, reminiscent of the nucleation-condensation model in protein folding. One such frequently occurring motif, also envisaged as the unit of clustering, the three residue clique was invariably found in regions of dense packing. Finally, topological measures based on surface contact networks appeared to be effective in discriminating sequences native to a specific fold amongst a set of decoys.

Conclusions

Out of innumerable topological possibilities, only a finite number of specific packing motifs are actually realized in proteins. This small number of motifs could serve as a basis set in the construction of larger networks. Of these, the triplet clique exhibits distinct preference both in terms of composition and geometry.

A gradient-directed Monte Carlo method for global optimization in a discrete space: application to protein sequence design and folding

We apply the gradient-directed Monte Carlo (GDMC) method to select optimal members of a discrete space, the space of chemically viable proteins described by a model Hamiltonian. In contrast to conventional Monte Carlo approaches, our GDMC method uses local property gradients with respect to chemical variables that have discrete values in the actual systems, e.g., residue types in a protein sequence. The local property gradients are obtained from the interpolation of discrete property values, following the linear combination of atomic potentials scheme developed recently [M. Wang et al., J. Am. Chem. Soc. 128, 3228 (2006)]. The local property derivative information directs the search toward the global minima while the Metropolis criterion incorporated in the method overcomes barriers between local minima. Using the simple HP lattice model, we apply the GDMC method to protein sequence design and folding. The GDMC algorithm proves to be particularly efficient, suggesting that this strategy can be extended to other discrete optimization problems in addition to inverse molecular design.

A search for energy minimized sequences of proteins

In this paper, we present numerical evidence that supports the notion of minimization in the sequence space of proteins for a target conformation. We use the conformations of the real proteins in the Protein Data Bank (PDB) and present computationally efficient methods to identify the sequences with minimum energy. We use edge-weighted connectivity graph for ranking the residue sites with reduced amino acid alphabet and then use continuous optimization to obtain the energy-minimizing sequences. Our methods enable the computation of a lower bound as well as a tight upper bound for the energy of a given conformation. We validate our results by using three different inter-residue energy matrices for five proteins from protein data bank (PDB), and by comparing our energy-minimizing sequences with 80 million diverse sequences that are generated based on different considerations in each case. When we submitted some of our chosen energy-minimizing sequences to Basic Local Alignment Search Tool (BLAST), we obtained some sequences from non-redundant protein sequence database that are similar to ours with an E-value of the order of 10^-7. In summary, we conclude that proteins show a trend towards minimizing energy in the sequence space but do not seem to adopt the global energy-minimizing sequence. The reason for this could be either that the existing energy matrices are not able to accurately represent the inter-residue interactions in the context of the protein environment or that Nature does not push the optimization in the sequence space, once it is able to perform the function.

Computational design, synthesis and biological evaluation of para-quinone-based inhibitors for redox regulation of the dual-specificity phosphatase Cdc25B

Quinoid inhibitors of Cdc25B were designed based on the Linear Combination of Atomic Potentials (LCAP) methodology. In contrast to a published hypothesis, the biological activities and hydrogen peroxide generation in reducing media of three synthetic models did not correlate with the quinone half-wave potential, E(1/2).

Protein sequence design based on the topology of the native state structure

Computational design of sequences for a given structure is generally studied by exhaustively enumerating the sequence space or by searching in such a large space, which is prohibitively expensive. However, we point out that the protein topology has a wealth of information, which can be exploited to design sequences for a chosen structure. In this paper, we present a computationally efficient method for ranking the residue sites in a given native-state structure, which enables us to design sequences for a chosen structure. The premise for the method is that the topology of the graph representing the energetically interacting neighbours in a protein plays an important role in the inverse-folding problem. While our previous work (which was also based on topology) used eigenspectral analysis of the adjacency matrix of interactions for ranking the residue sites in a given chain, here we use a simple but effective way of assigning weights to the nodes on the basis of secondary connections, along with primary connections. This indirectly accounts for the edge weight in the graph and removes degeneracy in the degree. The new scheme needs only a few multiplications and additions to compute the preferred ranking of the residue sites even for structures of real proteins of sizes of a few hundred amino acid residues. We use HP lattice model examples (for which exhaustive enumeration of sequences is practical) to validate our ranking approach in obtaining sequences of lowest energy for any H-P residue composition for a given native-state structure. Some examples of native structures of real proteins are also included. Quantitative comparison of the efficacy of the new scheme with the earlier schemes is made. The new scheme consistently performs better and with much lower computational cost. An optimization procedure is added to work with the new scheme in a few rare cases wherein the new scheme fails to provide the best sequence, an optimization procedure is added to work with the new scheme.

Designing Molecules with Optimal Properties Using the Linear Combination of Atomic Potentials Approach in an AM1 Semiempirical Framework

The linear combination of atomic potentials (LCAP) approach is implemented in the AM1 semiempirical framework and is used to design molecular structures with optimized properties. The optimization procedure uses property derivative information to search molecular space and thus avoid direct enumeration and evaluation of each molecule in a library. Two tests are described: the optimization of first hyperpolarizabilities of substituted aromatics and the optimization of a figure of merit for n-type organic semiconductors.