The study of protein dynamics using Elastic Network Models (See Figs. 1-5 and Table I). We will develop a mixed coarse-grained method where the ‘interesting’ or functional parts of proteins are modeled at a higher resolution than the remainder of the structure. By using this approach, normal mode analysis can be performed to discern the important functional motions with high computational efficiency for large biologically important molecules. This model will allow project investigators to focus on the details of the functionally most important parts of these molecules, and study the stability and dynamics associated with their function. This approach has potential significant and practical applications to drug design and to cell simulations. Application of this method furthers the study of large-scale motions in biological molecules, specifically to study domain swapping. We will study diphtheria toxin (DT) – a protein that is subject to dimerization and examine motions involved in such domain swapping in DT and several other systems.

We developed a mixed coarse-grained method where the ‘interesting’ or functional parts of proteins are modeled at a higher resolution than the remainder of the structure and applied this to triose phosphate isomerase (Fig. 1). Normal mode analysis was performed to discern the important functional motions. Among a number of new applications of the elastic network approach being developed is its use for the study of proteins having multiple binding sites (Fig. 2). This method was also applied to the study of large-scale motions in biological molecules, including domain swapping. We studied domain swapping in a number of proteins and developed new ways to identify domain swapping hinge sites (Fig. 3, Fig. 4 and Table I). Other applications included a general treatment of conformational transitions where parts of the structure are taken to be rigid (Fig. 5). Three papers were published (1-3) and two others are in draft manuscript form.

The elastic network models for describing the motions of proteins are finding broad application now by us and many others, from use in structure refinement to predicting protein conformational transitions. These studies will aid in developing methods for predicting conformational changes from a single structure.

Related Papers

1. Kloczkowski, A., Sen, T.Z and Jernigan, R.L., Promiscuous vs. native protein function. Insights from studying collective motions in proteins by elastic network models, J. Biomol. Struct. Dyn., 22, 621-624, 2005.
2. Kim, M.K., Jernigan, R.L. and Chirikjian, G.S. Rigid-cluster models of conformational transitions in macromolecular machines and assemblies, Biophys. J., 2005, in press.
3. Kundu, S. and Jernigan, R.L., Molecular mechanism of domain swapping in proteins: an analysis of slower motions, Biophys. J., 86, 3846-3854, 2004.

Develop an extremely efficient transfer matrix method for attrition-free generation of lattice proteins on the square lattice in 2-dimensions and for the cubic lattice in 3-dimensions (See Fig. 6 and Table II). The proposed method is an extension of the transfer matrix method for generating and enumerating compact self-avoiding walks on lattices previously developed by the project’s investigators. In the original method, only the number of chain conformations was calculated. We will extend this method by incorporating the potentials of interactions between the nearest-neighbor contacts on the lattice. We will use the hydrophobic-polar (HP) model for the detailed calculations. In the future this approach will be extended to encompass the full twenty letters amino acid alphabet by using the Miyazawa-Jernigan-types of contact potentials. We will reformulate the transfer matrix method by applying the technique of direct products of matrices developed by Jernigan and Flory for the statistical mechanics of polymer chains. We will also develop coarse-graining for these protein lattice models.

In the original method, only the number of chain conformations was calculated. We have now extended this method by incorporating the potentials for interactions between the nearest-neighbor contacts on the lattice, to investigate the variation of simple potentials used for the Elastic Network Models (Fig. 6). This establishes an important new connection between the two which had not been previously planned. This was viewed as more important than the original planned applications. In addition we have developed the facility to factor such pairwise potentials into functional dependences on the hydrophobicities and charges of the individual residues (Table II), which is important for the planned applications of this lattice generation approach to realistic proteins. This will allow us to extend the transfer matrix approach in more general ways than had originally been anticipated. Two related papers are given below.

The lattice transfer matrix method for efficiently generating large numbers of coarse-grained protein structures will lead to a way to make initial predictions of the protein structure family for new sequences.

Related Papers

1. Kloczkowski, A., Sen, T.Z. and Jernigan, R.L.: The transfer matrix method for lattice proteins - an application with cooperative interactions, Polymer, 45, 707-716, 2004.
2. Pokarowski, P., Kloczkowski, A., Jernigan, R.L., Kothari, N.S., Pokarowska, M. and Kolinski, A., Inferring ideal amino acid interaction forms from statistical protein contact potentials, Proteins: Struct. Funct. Bioinf., 59, 49-57, 2005.

Conduct an off-lattice study of the dependencies between protein shapes and their conformations (See Figs. 7-11). The goal is to generate libraries of possible three-dimensional protein structures using a minimal set of assumptions. We constrict the shape of the protein within a three-dimensional ellipsoid of revolution and generate all possible compact protein conformations within the shape. The generation of structures will not be fully random; rather we will use a bias towards secondary structures of a-helices and b-sheets. Biased generation of conformations is quite realistic, since proteins (due to their evolutionary origin) contain larger amounts of secondary structures than would result from the random packing. We will study the dependence between the shape of the ellipsoid and the compact structures generated inside this shape. We will extend the transfer matrix method developed for lattice proteins to these off-lattice models of proteins contained within the ellipsoids. We will also study in a systematic way the interdependence between the structures and the shapes of the proteins, as well as their dynamics with Elastic Network Models.

The original goal was to generate libraries of possible three-dimensional protein structures using a minimal set of assumptions. Prior to this, we decided that two other aspects of protein structure were important to investigate. Packing density is a critical parameter for these chain generations in compact spaces, so we investigated the relationship between amino acid packing density and sequence conservation (Fig. 7). In addition, we viewed the prior generation of a range of shapes important as a step preceding embarking upon the generation of the chain conformations, and thus we began an investigation of the shapes of a set of protein structures, in ellipsoid, convex hull, and Delaunay tesselated representations (Fig. 8). This has been an extensive investigation of protein shapes that also included computations of surface areas and volumes (Fig. 9). In addition we have exhaustively generated conformations within one size of ellipsoid (Fig. 10) as originally planned. The generation of structures was not fully random but relied on specific biases towards overall fractions of a-helices and b-sheets. Biased generations of conformations are realistic, since proteins (due to their evolutionary origin) contain larger amounts of secondary structures than would result from the packing of all possible random conformations. Our promising results are beginning to show how these sets of conformations can be used for predictions of structure (Fig. 11). One paper related to this is in Ref. (6).

The strong relationship between packing density and sequence conservation that we uncovered (Fig. 7) provides an important new way to consider sequence conservation in structures, not for separate residues but for clusters of residues, and points toward better approaches for combining sequence conservation information with a broad range of protein structural computations and predictions. The conformation generation within compact shapes can aid in structure prediction. We have already seen cases where the generation within an ellipsoid suggests native-like structures (Fig. 11). Because of the loose fit to the native structure within the ellipsoid it would appear that these results do not depend strongly upon the details of the confining shape.

During the next period, we will study the interdependence between the shape of the ellipsoid and the compact structures generated inside a shape. We will extend the transfer matrix method developed for lattice proteins to these off-lattice models of proteins contained within the ellipsoids and extend the off-lattice conformation generation within an ellipsoid for a set of 25 larger proteins and investigate better ways to select native-like conformations. We will also study in a systematic way the interdependence between the structures and the shapes of the proteins, as well as their dynamics with the Elastic Network Models. Also we will begin investigating how significantly the detailed roughness of the surface as given by the convex hull representation (see Fig. 8) may affect the conformations generated, in comparison with their generation within smooth ellipsoids. We will continue developing ways to select conformations from this set with various coarse-grained potentials (see Fig. 11), with the eventual aim of making structure predictions.

Related Paper

1. Liao, H., Yeh, W., Chiang, D., Jernigan, R.L. and Lustig, B. Protein sequence entropy is closely related to packing density and hydrophobicity. Prot. Eng. Des. Select, 18, 59-64, 2005.

Twelve other recent papers all relating to coarse-grained molecular models.

(For summaries see Figs. 12-15 and Tables III-V)

1. Sen, T.Z., Kloczkowski, A., Jernigan, R.L., Yan, C., Honavar, V., Ho, K.M., Wang, C.Z., Ihm, Y., Cao, H., Gu, X. and Dobbs, D., Predicting binding sites of hydrolase-inhibitor complexes by combining several methods, BMC Bioinformatics, 5, 205, 2004.

2. Miyazawa, S. and Jernigan, R.L., How effective for fold recognition is a potential of mean force that includes relative orientations between contacting residues in proteins? J. Chem. Phys., 122, 024901, 2005.

3.Aimin, Y. and Jernigan R.L., How do sidechains orient globally in protein structures? Proteins, 2005, in press.

4. Cheng, H., Sen, T.Z., Kloczkowski, A., Margaritis, D. and Jernigan, R.L., Prediction of protein secondary structure by mining structural fragment database, Polymer, 2005, in press.

5. Kloczkowski, A., Sen, T.Z, and Sharaf, M.A., The largest eigenvalue method for stereo regular vinyl chains, Polymer, 2005, in press.

6. Sen, T.Z., Jernigan, R.L., Garnier J., and Kloczkowski, A., GOR V server for protein secondary structure prediction, Bioinformatics, 2005, in press.

7. Plewczynski, D., Jaroszewski, L., Godzik, A., Kloczkowski, A., and Rychlewski, L., Molecular modeling of phosphorylation sites in proteins using database of local structure segments., J. Mol. Model., 2005, in press.

8. Plewczynski, D., Tkacz, A., Wyrwicz, L.S., Godzik, A., Kloczkowski, A. and Rychlewski, L., The Support Vector Machine classification of linear functional motifs in proteins, J. Mol. Mod., 2005, in press.

9. Kloczkowski, A. and Kolinski, A., Theoretical models and simulations for polymer chains, In: J. E. Mark (Editor), Physical Properties of Polymers Handbook, 2nd Edition, New York, Springer Verlag, 2005, in press.

10. Kloczkowski, A. and Sen, T.Z., Magnetic, Piezoelectric, pyroelectric and ferroelectric properties of synthetic and biological polymers, In: J. E. Mark (Editor) Physical Properties of Polymers Handbook, 2nd Edition, New York, Springer Verlag, 2005, in press.

11. Sen, T.Z. and Jernigan, R.L., Optimizing cutoff distances and spring constants for the Gaussian Network Model of ATP-binding proteins, in “Normal Mode Analysis: Theory and Applications to Biological and Chemical Systems,” CRC Press, in press.

12. Sen, T.Z, Sharaf, M.A., Mark, J.E., and Kloczkowski, A., Modeling the elastomeric properties of stereo-regular polypropylenes in nanocomposites with spherical fillers, Polymer, 2005, in press.

* Liu, Y., and D. Eisenberg. 2002. 3D domain swapping: as domains continue to swap. Protein Sci. 11:1285–1299.

⁺Slowest mode of GNM

(from Kundu, S. and Jernigan, R.L. Molecular Mechanism of Domain Swapping in Proteins: An Analysis of Slower Motions Biophys. J. 2004, 3846–3854.

Related

(A)

(B)

Figure 3. Domain swapping in diphtheria toxin. (A) shows the monomeric state (closed), (B) is the corresponding cartoon; (C) shows the monomer in the dimeric state (open), (D) is the corresponding cartoon; (E) shows the dimer in the dimeric state (two open monomers intertwined), and (F) is its corresponding cartoon. For these structures there is an axis of rotation perpendicular to the linking segment (shown as the z axis) about which a rotation takes place during the transition to the dimer with a additional slight twist along the x axis. (from Kundu, S. and Jernigan, R.L., Molecular mechanism of domain swapping in proteins: an analysis of slower motions, Biophys. J., 86, 3846-3854, 2004.)

residue index

Figure 7. Relationship between sequence variability, expressed as sequence entropy (for each sequence position, the sum of p ln p for each of the 20 types of residues from a multiple sequence alignment) and inverse residue packing density. These results are shown for a set of 113 proteins. Note that there are two different regions seen in the figure on the left - a nearly linear region for high packing densities and a more constant region for lower packing densities, except that at extremely low packing densities a broad range of values are seen. In the right figure, the data for the higher packing densities have been fit with a straight line. (from Liao, H., Yeh, W., Chiang, D., Jernigan, R.L. and Lustig, B., Protein sequence entropy is closely related to packing density and hydrophobicity. Prot Eng Des Select, 18, 59-64, 2005.)