Scientific Report 2005

Molecular Biology

Theoretical and Computational Molecular Biophysics

C.L. Brooks III, C. An, R. Armen, I. Borelli, D. Bostick, S.R. Brozell, D. Braun, L. Bu, J. Chen, M.F. Crowley, O. Guvench, R. Hills, W. Im, J. Khandogin, I. Khavrutskii, J. Lee, R. Mannige, M. Michino, H.D. Nguyen, Y.Z. Ohkubo, M. Olson,* S. Patel, D.J. Price, V. Reddy, H.A. Scheraga,** C. Shepard, A. Stoycheva, F.M. Tama, M. Taufer,*** K.A. Taylor,**** I.F. Thorpe, C. Wildman

* U.S. Army Medical Research Institute of Infectious Diseases, Fort Detrick, Maryland
** Cornell University, Ithaca, New York
*** University of Texas, El Paso, Texas
**** Florida State University, Tallahassee, Florida

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 determining the parameters for the 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 of 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 in computational biophysics. The following are highlights of a few specific projects.

Folding, Structure, and Function of Membrane-Bound Proteins

Folding, insertion, and stability of membrane proteins are directly governed by the unique hydrophilic and hydrophobic environment provided by biological membranes. Modeling this heterogeneous environment is both an obstacle and an essential requisite to experimental and computational studies of the structure and function of membrane proteins. Because of the biological importance and marked presence of membrane proteins in known genomes (i.e., they account for about 30% of all proteins), one aim of modern molecular biophysics should be the development of methods that can be used in experimental studies to understand the structure and function of these systems. We recently developed theoretical methods that enable the exploration of protein insertion and folding in membranes. These methods combine the sampling methods of replica-exchange molecular dynamics with novel generalized Born implicit solvent/implicit membrane continuum electrostatic theories.

We recently used de novo folding–membrane association–insertion simulations of a series of peptides (tryptophan-flanked α-helical peptides) designed to explore the concept of hydrophobic mismatch in modulating folding and membrane insertion. Using the simulations, we examined the detailed molecular mechanism of peptide insertion into biological membranes. Our results indicated a common mechanism for the insertion of transmembrane helices of relatively hydrophobic sequences. As illustrated in Figure 1, a peptide becomes associated with the membrane interface, transferring from the aqueous phase, and then helical structure begins to form.

Fig. 1. Mechanism of membrane association, folding, and insertion of a designed membrane peptide. The headgroup regions of the membrane are schematically represented by the parallel plates; the lipid tail–group regions, by the intervening space. Peptides first move from an aqueous environment above the membrane to the interfacial region, where they begin to form helical structure. When the fluctuating helical structure reaches a critical value near 70%–80% helix, the peptide spontaneously inserts from its N-terminal end.

The fluctuating helical structure in the interfacial peptide grows until a critical helical length is achieved, and the peptide then inserts via its N-terminal end to form a transmembrane helix. These findings suggest an emerging potential for the de novo investigation of integral membrane peptides and proteins and a mechanism to assist in experimental approaches to characterizing and determining the structure of these important systems.

Large-Scale Functional Dynamics in Molecular Assemblies

Many naturally occurring “machines,” such as ribosomes, myosin, and viruses, require large-scale dynamical motions as a component of their normal functioning. These motions 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 goals in our laboratory. Using theoretical approaches derived from the treatment of mechanoelastic materials, we are constructing theoretical models for the motions of large molecular assemblies, including viral capsids, ribosomes, and myosin.

In the life cycle of viruses, large-scale reorganization of the protein-protein interfaces of the viral capsid coat is necessary for the functioning of the virus. These motions involve the overall swelling (or shrinking) of the capsid as it reveals (or sequesters) its genome. How such large conformational changes occur is key to understanding and potentially controlling aspects of viral infectivity. Using theoretical methods called elastic network normal mode analysis, we explored putative swelling and shrinking transitions for a number of icosahedral viral capsids of various complexity, from
T-numbers of 1 to 13. We discovered a surprisingly similar mechanism for particle expansion and shrinking, despite the significant variation of individual capsid architectures. We examined the collective modes of motion that were energetically easiest to excite, while also directing the conformational change between a swollen (or contracted) icosahedrally symmetric conformation, as observed experimentally.

Our calculations (Fig. 2) show that the lowest energy modes that lead to swollen (compressed) states, despite the complexity of the underlying capsid architecture as indicated by the T-number, involves one key mode that produces a uniform deformation of the entire capsid and another that predominately distorts the structures around the 5-fold symmetry axes.

Fig. 2. Displacement directions for the swelling of the capsid of the bacteriophage HK97 during maturation from the prohead II state to the head II state as calculated by using elastic network normal mode analysis. The amplitude and direction of motion are indicated by the arrows. The first mode (A) accounts for nearly uniform displacement of all protein units in the capsid, whereas the next lowest energy mode (B) promotes “bulging” around the 5-fold axes of the capsid.

Because the mechanical properties, and the global level of deformations necessary for viral functioning, appear to depend solely on the shape of the viral particle, we can hypothesize general mechanisms for a number of viral functions, from the transfer of genetic material to a host system to the encapsulation of this genetic material in the assembly and maturation of viruses.

Publications

Chen, J., Brooks, C.L. III, Wright, P.E. Model-free analysis of protein dynamics: assessment of accuracy and model selection protocols based on molecular dynamics simulation. J. Biomol. NMR 29:243, 2004.

Chen, J., Im, W., Brooks, C.L. III. Refinement of NMR structures using implicit solvent and advanced sampling techniques. J. Am. Chem. Soc. 126:16038, 2004.

Chen, J., Won, H.S., Im, W., Dyson, H.J., Brooks, C.L. III. Generation of native-like protein structures from limited NMR data, modern force fields and advanced conformational sampling. J. Biomol. NMR 31:59, 2005.

Dominy, B.N., Minoux, H., Brooks, C.L. III. An electrostatic basis for the stability of thermophilic proteins. Proteins 57:128, 2004.

Falke, S., Tama, F., Brooks, C.L. III, Gogol, E.P., Fisher, M.T. The 13 Å structure of a chaperonin GroEL-protein substrate complex by cryo-electron microscopy. J. Mol. Biol. 348:219, 2005.

Feig, M., Brooks, C.L. III. Recent advances in the development and application of implicit solvent models in biomolecule simulations. Curr. Opin. Struct. Biol. 14:217, 2004.

Feig, M., Im, W., Brooks, C.L. III. Implicit solvation based on generalized Born theory in different dielectric environments. J. Chem. Phys. 120:903, 2004.

Feig, M., Onufriev, A., Lee, M.S., Im, W., Case, D.A., Brooks, C.L. III. Performance comparison of generalized Born and Poisson methods in the calculation of electrostatic solvation energies for protein structures. J. Comput. Chem. 25:265, 2004.

Ferrara, P., Gohlke, H., Price, D.J., Klebe, G., Brooks, C.L. III. Assessing scoring functions for protein-ligand interactions. J. Med. Chem. 47:3032, 2004.

Guvench, O., Brooks, C.L. III. Efficient approximate all-atom solvent accessible surface area method parameterized for folded and denatured protein conformations. J. Comput. Chem. 25:1005, 2004.

Guvench, O., Brooks, C.L. III. Tryptophan side chain electrostatic interactions determine edge-to-face vs parallel-displaced tryptophan side chain geometries in the designed β-hairpin ”trpzip2.” J. Am. Chem. Soc. 127:4668, 2005.

Guvench, O., Price, D.J., Brooks, C.L. III. Receptor rigidity and ligand mobility in trypsin-ligand complexes. Proteins 58:407, 2005.

Im, W., Brooks, C.L. III. Interfacial folding and membrane insertion of designed peptides studied by molecular dynamics simulations. Proc. Natl. Acad. Sci. U. S. A. 102:6771, 2005.

Karanicolas, J., Brooks, C.L. III. An evolution of minimalist models for protein folding: from the behavior of protein-like polymers to protein function. Biosilico 2:127, 2004.

Mackerell, A.D., Jr., Feig, M., Brooks, C.L. III. Extending the treatment of backbone energetics in protein force fields: limitations of gas-phase quantum mechanics in reproducing protein conformational distributions in molecular dynamics simulations. J. Comput. Chem. 25:1400, 2004.

Natrajan, A., Crowley, M., Wilkins-Diehr, N., Humphrey, M.A., Fox, A.D., Grimshaw, A.S., Brooks, C.L. III. Studying protein folding on the Grid: experiences using CHARMM on NPACI resources under Legion. Concurr. Comput. Pract. Exp. 16:385-397, 2004.

Patel, S., Brooks, C.L., III. A nonadditive methanol force field: bulk liquid and liquid-vapor interfacial properties via molecular dynamics simulations using a fluctuating charge model. J. Chem. Phys. 122:24508, 2005.

Patel, S., Mackerell, A.D., Jr., Brooks, C.L. III. CHARMM fluctuating charge force field for proteins, 2: protein/solvent properties from molecular dynamics simulations using a nonadditive electrostatic model. J. Comput. Chem. 25:1504, 2004.

Price, D.J., Brooks, C.L. III. A modified TIP3P water potential for simulation with Ewald summation. J. Chem. Phys. 121:10096, 2004.

Stoycheva, A.D., Brooks, C.L. III, Onuchic, J.N. Gatekeepers in the ribosomal protein S6: thermodynamics, kinetics, and folding pathways revealed by a minimalist protein model. J. Mol. Biol. 340:571, 2004.

Tama, F., Brooks, C.L. III. Diversity and identity of mechanical properties of icosahedral viral capsids studied with elastic network normal mode analysis. J. Mol. Biol. 345:299, 2005.

Tama, F., Feig, M., Liu, J., Brooks, C.L. III, Taylor, K.A. The requirement for mechanical coupling between head and S2 domains in smooth muscle myosin ATPase regulation and its implications for dimeric motor function. J. Mol. Biol. 345:837, 2005.

Tama, F., Miyashita, O., Brooks, C.L. III. Normal mode based flexible fitting of high-resolution structure into low-resolution experimental data from cryo-EM. J. Struct. Biol. 147:315, 2004.

Taufer, M., Crowley, M., Price, D.J., Chien, A.A., Brooks, C.L. III. Study of a highly accurate and fast protein-ligand docking method based on molecular dynamics. Concurr. Comput. Pract. Exp., in press.

Thorpe, I.F., Brooks, C.L. III. The coupling of structural fluctuations to hydride transfer in dihydrofolate reductase. Proteins 57:444, 2004.