All-atom generalized-ensemble simulations of small proteins
Introduction
The successful deciphering of whole genomes has aggravated an old challenge in protein science: for most of the resolved protein sequences one does not know the corresponding structures and functions. Since proteins are only functional if they fold into their specific shape, and misfolded proteins can even cause a variety of diseases, it is important to understand how the structure and function of proteins emerge from their sequence of amino acids. Computer experiments offer one way to gain such knowledge but are extremely difficult for realistic protein models. This is because all-atom models of proteins lead to a rough energy landscape with a huge number of local minima separated by high energy barriers. Consequently, sampling of low-energy conformations becomes a hard computational task, and physical quantities cannot be calculated accurately from simple low-temperature molecular dynamics or Monte Carlo simulations.
A number of novel simulation techniques have been developed that promise to alleviate the above-stated multiple-minima problem (for a review, see [1]). One successful method is the so-called genera1ized-ensemb1e approach [2] that was first applied to protein simulations in [3]. In the following we will present a short review of this approach and demonstrate its usefulness for protein simulations. We will focus in our examples on one particularly important aspect of the protein-folding problem, namely the role of secondary structure formation in the folding process.
Section snippets
Generalized-ensemble techniques
The complex form of the intramolecular forces and of the interaction with the solvent, containing both repulsive and attractive terms, leads for all-atom models of proteins to a very rough energy landscape with a huge number of local minima. Hence, a typical thermal energy of the order kBT is much less than the energy barriers that the protein has to overcome in the low-temperature region. This is because the probability to cross an energy barrier is proportional to ∝exp(−ΔE/kBT) where ΔE is
Helix formation for non-polar amino acids
In the following, we want to demonstrate that generalized-ensemble techniques are well suited for protein research. While our understanding of the folding physics has increased considerably over the last few years, many questions remain unsolved. One example is the role of secondary structure formation in the folding process, and we focus here on the formation of α-helices.
It is long known that α-helices undergo a sharp transition toward a random coil state when the temperature is increased.
Helix formation and folding
In order to understand in greater detail the relation between secondary structure formation and folding we have further studied the artificial peptide Ala10–Gly5–Ala10 in gas phase [17]. Since polyalanine has a pronounce helix–coil transition in gas phase, we expect formation of α-helices in our peptide, and we observe indeed a sharp transition between a coil phase at high temperatures and a helical phase at low temperatures in Fig. 3a, where the average number of helical residues 〈nH〉 is
Structure prediction of small proteins
The importance of secondary structure formation in the folding process can be seen again in recent simulations of the villin headpiece subdomain, a 36-residue peptide (HP-36), whose experimental structure was determined by NMR analysis [19]. We have chosen this peptide here because it has raised in the past considerable interest in both theoretical [22] and experimental studies [23]. Its structure consists of three helices between residues 4–8, 15–18, and 23–32, respectively, which are
Conclusion
We gave a brief introduction into generalized-ensemble techniques and their applications to the protein folding problem. Our examples demonstrate that these techniques are well-suited for investigations into the physics of proteins. With the advent of these and other modern sampling techniques, all-atom simulations of proteins may now be more restricted by the accuracy of the present energy functions than by the efficiency of the search algorithms.
Acknowledgements
Parts of the results presented in this article are also published in [17], [21]. Financial supports from a research grant (CHE-9981874) of the National Science Foundation (USA) is gratefully acknowledged.
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