Scientific Report 2005

Molecular Biology

Computer Modeling of Proteins and Nucleic Acids

D.A. Case, M. Crowley, Q. Cui, P. Dasgupta, F. Dupradeau,* N. Grivel,* R. Lelong,* S. Moon, D. Nguyen, D. Shivakumar, R. Torres, R.C. Walker, L., Yan,* J. Ziegler**

* Université Jules Verne, Amiens, France
** Universität Bayreuth, Bayreuth, Germany

Computer simulations offer an exciting approach to the study of many aspects of biochemical interactions. We focus primarily on molecular dynamics simulations (in which Newton’s equations of motions are solved numerically) to model the solution behavior of biomacromolecules. Recent applications include detailed analyses of electrostatic interactions in short peptides (folded and unfolded), proteins, and oligonucleotides in solution.

In addition, molecular dynamics methods are useful in refining solution structures of proteins by using constraints derived from nuclear magnetic resonance (NMR) spectroscopy, and we continue to explore new methods in this area. Our developments are incorporated into the Amber molecular modeling package, designed for large-scale biomolecular simulations, and into other software, including Nucleic Acid Builder, for developing 3-dimensional models of unusual nucleic acid structures; SHIFTS, for analyzing chemical shifts in proteins and nucleic acids; and RNAmotif, for finding structural motifs in genomic sequence databases.

Additional studies on active sites of nitrogenase and other metalloenzymes are described in the report of L. Noodleman, Department of Molecular Biology.

NMR And The Structure And Dynamics Of Proteins And Nucleic Acids

Our overall goal is to extract the maximum amount of information on biomolecular structure and dynamics from NMR experiments. To this end, we are studying the use of direct refinement methods for determining biomolecular structures in solution, going beyond distance constraints to generate closer connections between calculated and observed spectra. We are also using quantum chemistry to study chemical shifts and spin-spin coupling constants. Other types of data, such as chemical shift anisotropies, direct dipolar couplings in partially oriented samples, and analysis of cross-correlated relaxation, are also being used to guide structure refinement. In recent structural studies, we focused on minor groove–binding drugs in complex with DNA and on complexes of zinc finger proteins with RNA.

Nucleic Acid Modeling

Another project centers on the development of novel computer methods to construct models of “unusual” nucleic acids that go beyond traditional helical motifs. We are using these methods to study circular DNA, small RNA fragments, and 3- and 4-stranded DNA complexes, including models for recombination sites. We continue to develop efficient computer implementations of continuum solvent methods to allow simplified simulations that do not require a detailed description of the solvent (water) molecules; this approach also provides a useful way to study salt effects.

This research is part of a larger effort to develop low-resolution models for nucleic acids that can be extended to much larger structures such as circular DNA, viruses, or models of ribosomal particles. A computer language, NAB, was developed to make it easier to construct and simulate molecular models for complex and often low-resolution problems. The language is being used to study compact and swollen viruses, to analyze curved and circular DNA, and to simulate assembly of ribosomes.

Dynamics And Energetics Of Native And Nonnative States Of Proteins

Analysis methods similar to those described for nucleic acids are also being used to estimate thermodynamic properties of “molten globules” and unfolded states of proteins. These studies are an extension of our earlier work on the folding of peptide fragments of proteins. A key feature is the development of computational methods that can be used to model pH and salt dependence of complex conformational transitions, such as unfolding events.

A second aspect of this research is a detailed interpretation of NMR results for protein nonnative states through molecular dynamics simulations and the construction of models for molecular motion and disorder. In a parallel effort, we are studying correlated fluctuations about native conformations in a variety of proteins, including dihydrofolate reductase, metallo-β-lactamase, binase, and cyclic-dependent kinase, in an effort to make more secure connections between the motions of proteins and the activities of enzymes.

All of these modeling activities are based on molecular mechanics force fields, which provide estimates of energies as a function of conformation. We continue to work on improvements in force fields; recently, we focused on adding aspects of electronic polarizability, going beyond the usual fixed-charge models, and on methods for handling arbitrary organic molecules that might be considered potential inhibitors in drug discovery efforts. Overall, the new models should provide a better picture of the noncovalent interactions between peptide groups and the groups’ surroundings, leading ultimately to more faithful simulations.

Biochemical Simulations at Constant pH

Like temperature and pressure, the solution pH is an important intensive thermodynamic variable that is commonly varied in experiments and that is used by cells to influence biochemical function. It is now becoming feasible to carry out practical molecular dynamics simulations that mimic the thermodynamics of such experiments, by allowing proton transfer between the system of interest and a hypothetical bath of protons at a given pH. These calculations are demanding, both because the changes in the energetics of charge that occur upon protonation or deprotonation must be accurately modeled and because such simulations must sample both molecular configurations and the large number of protonation states that are possible in a molecule with many acidic or basic sites.

This problem is difficult, because almost all biomolecules have multiple sites that can bind or release protons, and these sites are coupled to one another in complex ways. In recent years, however, increases in computational power and new models for estimating the energetics of protonation and deprotonation events have led to serious attempts at simulations that allow the solution pH to be specified as an external variable in a manner that parallels the ways in which temperature or pressure are specified.

We recently developed practical methods for estimating ionization probabilities and for allowing the solution pH to be entered as an input variable. Figure 1 shows the results for an acidic group in the protein thioredoxin.

Fig. 1. Probability profile for the energy gap (the energy difference between the protonated and deprotonated forms, in kcal/mol) for the side chain of aspartic acid at position 26 in thioredoxin. Values of λ (shown beside the curves) interpolate between the neutral form at λ = 0 and the ionized form at λ = 1. Simple behavior would appear as an inverted parabola; multiple conformations lead to the more complex behavior seen at λ = 0.11.

The curves show the distribution of energy differences between the protonated and deprotonated forms of the acid or base residue. We can examine the behavior of this variable near the ionized form, corresponding to ordinary pH, or near the neutral, protonated form, at low pH. The results show complex behavior at low pH, which can be analyzed and related to the nature of the acid-base transition under those conditions. These ideas can form the foundation of powerful methods to explore the response of proteins to changes in solvent pH.

Publications

Baker, N.A., Bashford, D., Case, D.A. Implicit solvent electrostatics in biomolecular simulation. Adv. Macromol. Simul., in press.

Beveridge, D.L., Barreiro, G., Byun, K.S., Case, D.A., Cheatham, T.E. III, Dixit, S.B., Giudice, E., Lankas, F., Lavery, R., Maddocks, J.H., Osman, R., Siebert, E., Sklenar, H., Stoll, G., Thayer, K.M., Varnai, P., Young, M.A. Molecular dynamics simulations of the 136 unique tetranucleotide sequences of DNA oligonucleotides, 1: research design, informatics, and results on d(CpG) steps. Biophys. J. 87:3799, 2004.

Case, D.A., Cheatham, T.E., Darden, T., Gohlke, H., Luo, R., Merz, K.M., Onufriev, A., Simmerling, C., Wang, B., Woods, R. The Amber biomolecular simulation programs. J. Comput. Chem., in press.

Mongan, J., Case, D.A. Biomolecular simulations at constant pH. Curr. Opin. Struct. Biol. 15:157, 2005.

Mongan, J., Case, D.A., McCammon, J.A. Constant pH molecular dynamics in generalized Born implicit solvent. J. Comput. Chem. 25:2038, 2004.

Zhang., Q., Dwyer, T., Tsui, V., Case, D.A., Cho, J., Dervan, P.B., Wemmer, D.E. NMR structure of a cyclic polyamide-DNA complex. J. Am. Chem. Soc. 126:7958, 2004.