Theoretical and Computational Molecular Biophysics

C.L. Brooks III, S.R. Brozell, J. Chen, Y. Cong, M.F. Crowley, M. Feig, P. Ferrara, J. Karanicolas, J.A. Kovacs, M.S. Lee, A.D. MacKerell, Jr.,* E. Metwally, P.C. Montes, R.T. Morton, Y.Z. Ohkubo, S. Patel, D.J. Price, T.H. Rod, F.S. Salsbury, Jr., F.M. Tama, M. Taufer, K.A. Taylor,** I.F. Thorpe, W.R. Wriggers***

* University of Maryland, Baltimore, Maryland
** Florida State University, Tallahassee, Florida
*** University of Texas Health Center, Houston, Texas

Understanding the forces that determine the structure of proteins, peptides, nucleic acids, and complexes containing these molecules and the processes by which the structures are adopted is essential to complete our knowledge of the molecular nature of structure and function. To address such questions, we use statistical mechanics, molecular simulation, statistical modeling, and quantum chemistry.

Creating atomic-level models to simulate biophysical processes (e.g., folding of a protein or binding of a ligand to a biological receptor) requires (1) the development of potential energy functions that accurately represent the atomic interactions and (2) the use of quantum chemistry to aid in parameterizing these models. Calculation of thermodynamic properties requires the development and implementation of new theoretical and computational approaches that connect averages over atomistic descriptions to experimentally measurable thermodynamic and kinetic properties.

Interpreting experimental results at more microscopic levels is fueled by the development and investigation of theoretical models for the processes of interest. Massive computational resources are needed to realize these objectives, and this need motivates our efforts aimed at the efficient use of new computer architectures, including large supercomputers, Linux Beowulf clusters, and computational grids. Each of the objectives and techniques mentioned represents an ongoing area of development within our research program. The following are highlights of a few specific projects.

MECHANISM OF PROTEIN FOLDING

The means by which a linear amino acid sequence adopts its functional 3-dimensional structure is a key challenge to scientists in many disciplines, from biology to physics. This problem is also critical to developing strategies, at the molecular level, to counter "folding diseases" such as Alzheimer's disease and mad cow disease. We use statistical mechanics and computer simulation to elucidate the principles that govern protein folding. Our explorations link protein topology and the overall mechanism of protein folding, providing new insights that promote the development of theoretical models and new experiments.

For example, recently, we collaborated with J.W. Kelly and his colleagues, Department of Chemistry, in studies to understand the folding mechanisms in a family of small proteins called WW domains. Using simplified representations of protein structure and interactions, we examined both the folding free energy landscape and the folding kinetics of 2 members of this family: WW domains from a peptidyl-prolyl cis-trans isomerase (PIN) and formin-binding protein. With our complementary theoretical and experimental studies, we elucidated the origin of the biphasic folding kinetics in the WW domain of formin-binding protein that occur as a single kinetic step for the analogous protein fold of the WW domain in PIN. In particular, we identified a small set of specific interactions that appear to be responsible for the slow phase of folding that occurs in formin-binding protein and suggested mutants that would alter this slow phase.

These studies exemplify the interactive nature of our research program in protein folding and also its primary focus on the development of principles that will assist in protein design. In addition to the recent collaboration with Dr. Kelly, our efforts in protein folding and design are closely coupled to the ongoing theoretical and experimental developments in other laboratories at TSRI and in the La Jolla area through the La Jolla Interfaces in Sciences Interdisciplinary Training Program and the Center for Theoretical Biological Physics.

LARGE-SCALE FUNCTIONAL DYNAMICS IN MOLECULAR ASSEMBLIES

Many naturally occurring "machines," such as the ribosome, which processes mRNA for protein synthesis, or myosin, which produces the force needed for the normal contraction of muscle, require large-scale dynamical motions as a component of their normal functioning. These motions often involve the "mechanical" reorganization of major parts of the structure of the machine in response to binding of effectors or to the addition of energy in the form of thermal fluctuations or provided by chemical catalysis. Exploring and understanding the character and nature of such large-scale reorganization of biological machines are ongoing in our laboratory. Using theoretical approaches derived from the treatment of elastomechanical materials, we are constructing theoretical models for the motions of large molecular assemblies, including viral capsids, ribosomes, and myosin.

Ribosomes undergo a range of structural changes during protein synthesis. Using the lower-resolution structural methods of electron cryomicroscopy, our collaborator J. Frank, Wadsworth Center, Albany, New York, characterized 2 key motions: the ratchetlike displacement of the major ribosomal domains (30S and 50S subunits) with respect to each other and large-scale displacement of the protein L1. The ratchetlike displacement occurs during the translocation of tRNA from the A and P binding sites to the P and E sites (Fig. 1); the large-scale displacement of the protein L1 may facilitate amino acid-exhausted tRNA from the E site.

Using elastomechanical models based on the crystallographic structure of the 70S ribosome, we showed that these functionally critical motions arise as natural displacements of "elastic bodies" with the shape of the ribosome. Emerging from these calculations are atomic-level pathways for these steps in translocation. In particular, our calculations suggest that the ratchetlike rotation of the 50S subunit relative to the 30S subunit leads to initial displacement of the tRNA molecules in A and P sites toward the P and E sites. Also prevalent as a "normal mode" of displacement of the complex is the "reaching" of the L1 protein "arm" to possibly facilitate the removal of spent tRNA in the E site. We hypothesize that the robustness of simple shape-dependent dynamics of functional motions critical for particular biological processing is exploited in naturally occurring machines.

We are also exploiting shape-dependent dynamics to develop structural models consistent with experimental data from electron microscopy and tomography. In collaboration with K.A. Taylor, Florida State University, Tallahassee, we are developing models for the gross structural rearrangement associated with the transition from the activated state of smooth muscle heavy meromyosin to the inhibited state that forms upon regulatory dephosphorylation of the light chain of the protein (Fig. 2). Beginning with a homology model of heavy meromyosin, including a hypothetical S2 (dimerization) domain, we computed mechanoelastic normal modes of displacement of the molecule and explored the ability of the modes to account for the large reorganization of the structure required for consistency with low-resolution structural data from electron cryomicroscopy. Construction and exploration of the dynamical motions led to new interpretation of the microscopy data and to an interpretation of the role of flexibility of the S2/S1 junction region in facilitating the conformational change.

PUBLICATIONS

Brooks, C.L. III. Protein folding: with a little help . . . Nature 420:33, 2002.

Damodaran, K.V., Reddy, V.S., Johnson, J.E., Brooks, C.L. III. A general method to quantify quasi-equivalence in icosahedral viruses. J. Mol. Biol. 324:723, 2002.

Feig, M., Brooks, C.L. III. Evaluating CASP4 predictions with physical energy functions. Proteins 49:232, 2002.

Feig, M., MacKerell, A.D., Jr., Brooks, C.L. III. Force field influence on the observation of ¼-helical protein structures in molecular dynamics simulations. J. Phys. Chem. B 107:2831, 2003.

Karanicolas, J., Brooks, C.L. III. The importance of explicit chain representation in protein folding models: an examination of Ising-like models. Proteins, in press.

Karnicolas, J., Brooks, C.L. III. The origins of asymmetry in the folding transition states of protein L and protein G. Protein Sci. 11:2351, 2002.

Karanicolas, J., Brooks, C.L. III. The structural basis for biphasic kinetics in the folding of the WW domain from a formin-binding protein: lessons for protein design? Proc. Natl. Acad. Sci. U. S. A. 100:3954, 2003.

Lee, M.S., Feig, M., Salsbury, F.R., Jr., Brooks, C.L. III. New analytic approximation to the standard molecular volume definition and its application to generalized Born calculations. J. Comput. Chem. 24:1348, 2003.

Rod, T.H., Radkiewicz, J.L., Brooks, C.L. III. Correlated motion and the effect of distal mutations in dihydrofolate reductase. Proc. Natl. Acad. Sci. U. S. A. 100:6980, 2003.

Salsbury, F.R., Jr., Han, W.-G., Noodleman, L., Brooks, C.L. III. Temperature-dependent behavior of protein-chromophore interactions: a theoretical study of a blue fluorescent antibody. Chemphyschem 4:848, 2003.

Shea, J.-E., Onuchic, J.N., Brooks, C.L. III. Probing the folding free energy landscape of the Src-SH3 protein domain. Proc. Natl. Acad. Sci. U. S. A. 99:16064, 2002.

Tama, F., Valle, M., Frank, J., Brooks, C.L. III. Dynamic reorganization of the functionally active ribosome explored by normal mode analysis and cryo-electron microscopy. Proc. Natl. Acad. Sci. U. S. A. 100:9319, 2003.

Tama, F., Wriggers, W., Brooks, C.L. III. Exploring global distortions of biological macromolecules and assemblies from low-resolution structural information and continuum elastic network theory. J. Mol. Biol. 321:297, 2002.

Wu, G., Robertson, D.H., Brooks, C.L. III, Vieth, M. Detailed analysis of grid-based molecular docking: a case study of CDOCKER, a CHARMm-based MD docking algorithm. J. Comput. Chem. 24:1549, 2003.

Research Overview from 2001-2002