The Cytochrome c (Cytc) is a small heme protein of ~100 amino acids. It presents in the mitochondrion of eukaryotic cells and it is loosely associated with their inner membrane. Cytc is highly water-soluble and is an essential component of the electron transport chain in mitochondria where it carries one electron. It also involved in the initiation of the apoptosis of the cell (a controlled form of cell death used to kill cells in the process of development or in response to infection or DNA damage) when it binds apoptotic protease activating factor-1 in the cytoplasm. Cytc is an ancestral protein with amino acid sequence strongly conserved and for this reason, it has been used as a molecular clock in molecular genetics.

Figure 1: Crystal structure of the Cytc.

The folding/unfolding mechanism of protein has been studied in great details for 20 years using plenty of experimental methods and computer simulations.  Despite the size of the protein, only recently a more clear picture of this mechanism starts to emerge. In this direction, we have contributed to two computational studies on the stability and folding of this protein in solution.

In a first paper,  the effect of temperature on the activation of native fluctuation motions during molecular dynamics unfolding simulations of horse heart Cytochrome c [1] was investigated. The principal component analysis (essential dynamics analysis, see illustration below) of trajectories has provided the preferred directions of motion along the unfolding trajectories obtained by high-temperature simulations.

The analysis evidenced a clear correlation between the directions of the deformation motions that occur in the first stage of the unfolding process and few specific essential motions characterizing the dynamics of the protein at 300K. In particular, one of those collective motions, involved in the fluctuation of a loop region, was specifically excited during the thermal denaturation process, becoming progressively dominant within the first 500 ps of the unfolding simulations. As further evidence, the essential dynamics sampling performed along this collective motion has shown a tendency of the protein to promptly unfold. According to these results, the mechanism of thermal induced denaturation process involves the selective excitation of one or few equilibrium collective motions.

In a second study, we have also developed a novel approach for simulating the folding process of any protein [2]. The method is based on the essential dynamics sampling (EDS) technique (Amadei et al., 1996; de Groot et al., 1996). This method is based on the information on the collective motion of the protein obtained from a previous principal component analysis of a standard MD simulation. The method is used to increase (in the so-called expansion mode) or decrease (in the contraction mode) the distance from a reference conformation. In each step of the EDS, a standard MD calculation is first performed hence the distance in the subspace of the eigenvectors used for the EDS, between the current structure and the reference structure is calculated. In the expansion mode, the propagation step is accepted if the distance between the current structure and the reference does not decrease or, in the contraction mode, does not increase, otherwise the coordinates and velocities are projected radially onto the hypersphere (in the chosen subspace) centered in the reference, with radius given by the distance from the reference in the previous step. It has to be pointed out that no additional deterministic forces are added and that the eigenvectors were obtained by the diagonalization of the matrix of the positional fluctuations of the Ca or backbone carbon atoms, so that they do not contain any information on the other atoms, in particular on the side chains.

The method was applied to the folding process of horse heart cytochrome c. Only the 104 Ca carbons were used as the folding constraints for a total of Nx3=312 eigenvectors. Starting from structures, with a root-mean-square deviation of 2.0 nm from the crystal structure, the correct folding was obtained, by utilizing only 106 generalized degrees of freedom, chosen among those accounting for the backbone carbon atoms motions, hence not containing any information on the side chains. The constrained generalized degree of freedom used constituted only the 3.5% of overall ~3000 degrees of freedom of the proteins. The folding pathways found are in agreement with experimental data on the same molecule.

1. Roccatano, I. Daidone, M. A. Ceruso, C. Bossa, A. Di Nola. Selective excitation of native fluctuations during thermal unfolding simulations: the horse heart cytochrome c as a case study. Bioph. J., 84, 1876-1883 (2003).
2. Daidone, D. Roccatano, A. Amadei, A. Di Nola. Molecular dynamics simulation of protein folding by essential dynamics sampling: the folding landscape of horse heart cytochrome c. Bioph. J., 85, 2865-2871 (2003).