Efficient conformational space exploration in ab initio protein folding simulation

Abstract

Ab initio protein folding simulation largely depends on knowledge-based energy functions that are derived from known protein structures using statistical methods. These knowledge-based energy functions provide us with a good approximation of real protein energetics. However, these energy functions are not very informative for search algorithms and fail to distinguish the types of amino acid interactions that contribute largely to the energy function from those that do not. As a result, search algorithms frequently get trapped into the local minima. On the other hand, the hydrophobic-polar (HP) model considers hydrophobic interactions only. The simplified nature of HP energy function makes it limited only to a low-resolution model. In this paper, we present a strategy to derive a non-uniform scaled version of the real 20×20 pairwise energy function. The non-uniform scaling helps tackle the difficulty faced by a real energy function, whereas the integration of 20×20 pairwise information overcomes the limitations faced by the HP energy function. Here, we have applied a derived energy function with a genetic algorithm on discrete lattices. On a standard set of benchmark protein sequences, our approach significantly outperforms the state-of-the-art methods for similar models. Our approach has been able to explore regions of the conformational space which all the previous methods have failed to explore. Effectiveness of the derived energy function is presented by showing qualitative differences and similarities of the sampled structures to the native structures. Number of objective function evaluation in a single run of the algorithm is used as a comparison metric to demonstrate efficiency.

Keywords: discrete lattices; energy function; genetic algorithms; optimization; protein folding simulation; protein structure prediction.

Figure 1.

Comparison of partial energy distribution assigned by HP, GW and BM energy functions for protein 1CTF. Both GW and BM energy distributions are normalized.

Figure 2.

Differences of average energy obtained by using derived energy function and mixed model [12].

Figure 3.

Differences of best energy obtained by using derived energy function and mixed model [12].

Figure 4.

Differences of average energy obtained by using derived energy function (GW) and using real energy function (BM).

Figure 5.

Differences of best energy obtained by using derived energy function (GW) and using real energy function (BM).

Figure 6.

Ratio of average number of objective function evaluation by using derived energy function (GW) to the same using real energy function (BM).

Figure 7.

Differences of average energy obtained by using derived energy function exhaustively (GW) and using derived energy function non-exhaustively (GWN).

Figure 8.

Ratio of average number of iterations by using derived energy function non-exhaustively (GWN) to the same using derived energy function exhaustively (GW).