D1. Molecular Dynamics Simulations of Beta Sheet Polypeptides

This project will: determine the free energy change of unfolding of beta sheets by running simulations on beta hairpin models, and determine the effects of amino acid replacement on stability.

Primary Faculty co-Advisors

Randall Hall, Chemistry (Theoretical Physical Chemistry)

Dana Browne, Physics (Theoretical Physics)

Robert Hammer, Chemistry (Organic Synthesis)

Off-campus Participants:

John Straub (Boston University, expert in biosimulations)

Mark McLaughlin (University of Central Florida?, Organic synthesis)

Technical Proposal: Beta sheets are a common secondary structure that occur in folding proteins. Beta sheets tend to form when the protein chain is somewhat linear and has a “repeat distance” of approximately 7 Å. Hydrogen bonds are formed between peptide groups of polypeptide segments which are adjacent and parallel with one another, in our case the amide-carbonyl carbon bonds and amide nitrogen-аlpha carbon bonds. (1) The side chains lie alternatively above and below the main chain. This secondary structure is termed the beta structure. Several polypeptide chains can interact in this way to form a pleated structure known as a beta sheet. These sheets may be stacked together in large arrays due to Van der Waals forces and are often found in fibrous structures, but are also prevalent in biomolecules and many types of pharmaceutical drugs.

Figure 1. Basic Structure of a Beta Sheet

The ability of certain beta peptides to mimic biological functions makes the study of these compounds particularly important. Phosphonopeptides in which an amide bond is replaced with a phosphonate linkage can be used as protease inhibitors. Helical structures formed from beta sheet components can be seen to exist in molecules with as little as six peptide units in aqueous solvent. (2) This property makes them useful as protein scaffolds for applications. These particular oligomer helices are characterized by 12-membered ring bonding from the NH of the third peptide unit in the terminal direction and the carbonyls of the peptide backbone. (3) In contrast, the alpha helix found in naturally-occurring peptides possess a 13-member ring hydrogen bonds with similar orientations to the terminal groups. These conformations are sufficiently similar that some manufactured peptides can behave as naturally-occurring species.

Most multicellular organisms produce antimicrobial peptides as part of their normal biological defense behaviors, and while this fact is known there is still debate over the mechanisms by which their antimicrobial effects occur. Beta peptides have certain advantages over naturally-occurring peptides, namely their stability when in the presence of proteases. More generally, as beta peptides become more understood, the ability of scientists to construct molecules that mimic important biological functions becomes more of a possibility.

The major biomolecules we will be interested in modeling are beta peptides used to hinder the aggregation of the amyloid beta-protein into fibril structures. The self-assembly of these proteins into beta-sheet-containing protofibrils is theorized as a preliminary event in Alzheimer’s Disease. A brain with exhibits symptoms from this disease is characterized by having diffuse atropy, especially in the cortex and hippocampus, and by the presence of numerous plaques. These plaques are complex in nature, but are composed of a central core of these beta-amyloid protein units. Biochemical and neuropathological evidence has linked these deposits to the pathogenesis of the AD. Thus, finding an effective inhibitor for the proteolytic process which forms the beta-amyloid could be a possible way of controlling the disease. Alternatively, finding mechanisms which terminate or block the aggregation of the beta-amyloid may be a more effective method. The fact that beta-amyloid is synthesized in normal individuals for normal body functions, such as antimicrobial response, indicates that blocking the formation of plaques, instead of interfering with beta-amyloid production may be the preferred method of controlling Alzheimer’s Disease. The Hammer lab is involved with synthesis of these blocking beta sheet polypeptides. We will attempt to model these proteins to facilitate this function.

Calculation of ∆G of Unfolding. A basic beta hairpin scheme is used as the base molecule in these simulations. Beta hairpins are common supersecondary structures in beta sheets, so modeling these structures is relevant to modeling the formation of beta sheets as well. A beta hairpin motif is characterized by two antiparallel strands linked by a short loop. Generally this loop is between two and four peptide units long. Utilization of autonomously folding beta hairpin to explore beta sheet stability requires the ability to make these macromolecules in any specific shape required. This is greatly facilitated by the use of computer modeling, which does not require elaborate experimental synthetic considerations to create these molecules.

The Gellman YKL model (4) will be the first beta hairpin model will be the first macromolecule we study. Further molecules will be studied by modification of the side chains to determine their effects on free energy stability. The force field functions of the molecular dynamics simulation program CHARMm will be used to determine the energies associated with different conformations, at least in the early stages of simulation. These current generation force fields (potential energy functions) are a decent compromise between accuracy and computational efficiency for use in our simulations. Computerized molecular simulation and graphics are an enormous improvement over the earlier more traditional methods because the computer models can be generated in real time and the modeling parameters can be varied interactively with minimal effort from the programmer.

Figure 2. Gellman YKL beta hairpin

The change in free energy (∆G = ∆H – T∆S or ∆A = ∆E - T∆S) of folding of most proteins is negative, but runs only on the order of a few Kcals/mol for most of these proteins. A major cause of the marginal stability of the protein is that in most cases, both the unfolded and folded states may create a large number of hydrogen bonds. An unfolded beta sheet contains many hydrogen bonds between the side chains and the solvent, which would be lost as the protein folds. However, the folded protein may hydrogen bond with itself, which may offset some or all of the bonds lost from the side chain-solvent interactions. The nature of these interactions is a characteristic of the particular polypeptide being studied along with the solvent being used, and cause variations in the enthalpy between the folded and unfolded states of the sheet.

The entropic term of the free energy equation is a major factor in the stability of the beta sheet and is also considered by the simulations. As the beta sheet unfolds, more of the solvent molecules will be hydrogen-bonded to the side chains which are now freed from hydrogen bonding with the adjacent chains, thus lowering the entropy of the solvent sphere. The conformations (unfolded and folded) offer two competing entropies, that of the solvent and that of the beta sheet itself. This competition may also affect the liklihood of a beta sheet to unfold in solution.

The free energy of folding is difficult to calculate, but methods are available (Ref. C. Brooks Acc. Chem. Res. Article). These methods focus on calculating the free energy change for the folding of a specific protein or polypeptide. Our task may be simplified since we are more interested in ∆∆A (or G), the difference in free energies of folding 2 different molecules (see below). This is because

Each of these ratios can be in principle calculated using thermodynamic perturbation theory or by using a “basin hopping” scheme recently used in our simulations of cationic Xe clusters (ref is . Jose A. Gascon, Randall W. Hall, Christoph Ludewigt, and Hellmut Haberland, "Structure of Xen+ clusters (N=3-30): simulation and experiment ", J. Chem. Phys., 117, 8391-8403, 2002.). We will investigate each of these methods in order to determine which is most efficient computationally.

All calculations will use the CHARMm force field and the NAMD molecular dynamics package (available free from the University of Illinois). One of us (Hall) will be attending a workshop at the University of Illinois in the Summer of 2003 to learn how to run the NAMD package and to use it for the calculations described above. Calculations will also use the SuperMike supercomputer at LSU or possibly the BCVC 128-node cluster also located at LSU.

Effects on R-group Alteration on Beta Sheet Stability. Later work in the project involves modification of the R-group side chains of the basic hairpin structure. Experimentally, the substitution of the terminal peptides with a series of different dipeptide units has been shown to significantly stabilize the beta sheet conformation. Further, it is indicated that side chain-side chain interactions between the neighboring stands can help to stablize the beta hairpin as well. Our goal is to determine computationally what factor these side chains have on the stability of the hairpin structure. Modification of the side groups are relatively easy within the CHARMm programming system, allowing easy ability to determine substituent effects. Primary work will involve the CHARMm force fields. However, later work will require potential energy functions which are not present in CHARMm and thus must be derived quantum mechanically for insertion into the force field package. Dr. Straub of Boston University will be of great help in this effort.

Number of IGERT apprentices to be recruited and probable home departments:

Two – one from Chemistry and one from Chemistry or Physics

Consistency with the Macromolecular Education, Research & Training theme:

Several macromolecular small beta hairpin comformations produced will be analyzed by CHARMm programs created to determine their stability in aqueous solvent. An understanding of interactions of large peptide structures is necessary.

How does the project form a vector cross-product of existing research themes by the participants?

Existing research directions. Dr. Browne’s major research area concerns the behavior of systems of many degrees of freedom whose steady state is far from equilibrium, such as fluid motion, chemical reactions, and biological systems. Drs. Hammer’s and McLaughlin’s groups are primarily focused on the design and synthesis of the structures and biological characterization. Dr. Hall’s expertise resides in quantum mechanical simulation of various systems, primarily using ab initio and modeling calculations on clusters, glasses, and the effect of mutation and crossover on evolution and protein folding.

New research direction. Dr. Hall’s work with modeling simulation programs and methodology and Dr. Browne’s knowledge of the physical aspects of interactions between atoms in a macromolecule to ultimately create simplified models that can be used to investigate long time behavior and inter-sheet interactions that occur during the aggregation phase of AD.

How do students benefit from the team-oriented research, beyond what would be available to them from either advisor separately? The primary benefit from the student’s perspective is a greater resource of various backgrounds from which to pool information. Drs. Hammer and McLaughlin bring expertise at creating molecules capable of the functions we desire will allow the student the chance to run simulation on real molecules, while Dr. Hall and Dr. Browne's expertise in molecular dynamics, computer simulations, and physical properties will allow the student to understand more fully the calculations by which we will determine energy calculations and actually run them

Briefly describe the support level available to each individual faculty or off-campus participant (i.e., without IGERT) Dr. Hall is supported by an NSF-GOALI grant. Dr. Hammer is supported by an NIH grant.

Interdisciplinary strengths of the team project: The team of Drs. Browne, Hammer, McLaughlin, and Hall combine to form a complimentary conjunction of ideas which will assist the projects of this group. Dr. Hammer is a synthetic chemist in his research, and he and Dr. McLaughlin have both contributed much in making advances in understanding molecules which may be useful in biological functions of interest to the group. Dr. Hall's main interest in research is in computer simulations involving numerous types of systems. He brings years of knowledge of computer simulation and technique to the group. Dr. Brown is a physicist specializing in the statistical mechanics of systems with multiple degrees of freedom, such as chemical reactions and fluid motions. He brings expertise of building simplified models for complicated manybody systems and will be extremely useful in developing models for the aggregation of the beta-Amyloid.

Commitment of faculty & off-campus participants to work side-by-side with apprentices: Hall, a full professor within the Department of Chemistry, actively pursues research using computer simulations and many different simulation programs. Dr. Hall will meet with the students to discuss the development of programs which will be used to run the molecular dynamics simulations on the beta hairpin model. He and off-campus Professor Straub may assist with discussions regarding the CHARMm programming as it is necessary. Much of this time commitment would be fulfilled during the summers and winter breaks.

Hammer, a full professor within the Department of Chemistry, maintains a lab which focuses on the development and synthesis of the compounds which the group intends to study in its goal. Dr. McLaughlin has recently left LSU to take up a position at The University of Central Florida. Drs. Hammer and McLaughlin will actively pursue development of new molecules of interest which may be helpful in blocking the plaque formation of the beta-amyloid molecules, which will allow us to model real potential candidates which could use used for treatment. Dr. Hammer will also assist in the determination of the structures and functions of these compounds be more easily construct them to model.

Dr. Browne is presently a full professor within the Department of Physics. His major involvement will include collaboration in the empirical energy functions which must be calculated as the base hairpin structure is modified significantly and the CHARMm force field parameters are no longer adequate for us to use in the research, as well as the development of simplified models that can be used to study aggregation

References:

(1) McLaughlin, M. L. In preparation.

(2) Wang, X., Espinosa, J. F., Gellman, S. H. J. Am. Chem. Soc. 2000, 122, 4821-4822.

(3) Porter, E. A., Weisblum, B., Gellman, S. H. J. Am. Chem. Soc. 2002, 124, 7324-7330.

(4) Syud, F., Stanger, H. E., Gellman, S. H. J. Am. Chem. Soc. 2001, 123, 8667-8677.