Fragment-free approach to protein folding using conditional neural fields

Abstract

Motivation: One of the major bottlenecks with ab initio protein folding is an effective conformation sampling algorithm that can generate native-like conformations quickly. The popular fragment assembly method generates conformations by restricting the local conformations of a protein to short structural fragments in the PDB. This method may limit conformations to a subspace to which the native fold does not belong because (i) a protein with really new fold may contain some structural fragments not in the PDB and (ii) the discrete nature of fragments may prevent them from building a native-like fold. Previously we have developed a conditional random fields (CRF) method for fragment-free protein folding that can sample conformations in a continuous space and demonstrated that this CRF method compares favorably to the popular fragment assembly method. However, the CRF method is still limited by its capability of generating conformations compatible with a sequence.

Results: We present a new fragment-free approach to protein folding using a recently invented probabilistic graphical model conditional neural fields (CNF). This new CNF method is much more powerful than CRF in modeling the sophisticated protein sequence-structure relationship and thus, enables us to generate native-like conformations more easily. We show that when coupled with a simple energy function and replica exchange Monte Carlo simulation, our CNF method can generate decoys much better than CRF on a variety of test proteins including the CASP8 free-modeling targets. In particular, our CNF method can predict a correct fold for T0496_D1, one of the two CASP8 targets with truly new fold. Our predicted model for T0496 is significantly better than all the CASP8 models.

Fig. 1.

A first-order CNF model consists of three layers: input, output and hidden layer. A second-order model is similar but not shown for the purpose of simplicity. In contrast, a CRF model consists of only input and output.

Fig. 2.

The relationship between RMSD (y-axis) and energy (x-axis) for (a) T0397_D1, (b) T0416_D2, (c) T0476, (d) T0482, (e) T0496_D1 and (f) T0510_D3. The red and blue colors represent the CRF and CNF methods, respectively. See text for the energy normalization methods.

Fig. 3.

Two typical mirror images generated by the CRF method for T0416_D2. The decoys in blue and gold represent the lower and upper regions in Figure 2b, respectively.

Fig. 4.

Ranking of our CNF predictions for (a) T0416_D2, (b) T0476, (c) T0496_D1 and (d) T0510_D3 (x-axis is percentile ranking and y-axis GDT-TS). Our first and best cluster centroids are plotted in black and magenta lines, respectively. The #1 models submitted by the CASP8 server are ordered by their GDT-TS and their percentile ranking is displayed as a cyan curve, so are the best models from each server but as a green curve.