Discrete Breathers in Nonlinear Network Models of Proteins

We introduce a topology-based nonlinear network model of protein dynamics with the aim of investigating the interplay of spatial disorder and nonlinearity. We show that spontaneous localization of energy occurs generically and is a site-dependent process. Localized modes of nonlinear origin form spontaneously in the stiffest parts of the structure and display site-dependent activation energies. Our results provide a straightforward way for understanding the recently discovered link between protein local stiffness and enzymatic activity. They strongly suggest that nonlinear phenomena may play an important role in enzyme function, allowing for energy storage during the catalytic process.

Figure 1

Energy as a function of time, when citrate synthase is cooled down as a consequence of surface friction. Dashed line: total energy. Solid line: energy of Threonine 208, the amino acid the most involved in the DB. Dotted line: energy of Alanine 209, also involved in the DB. $k_B{T}_{\mathrm{eq}}=20\mathrm{kcal}/\mathrm{mol}$.

Figure 2

Locality of citrate synthase harmonic modes, as a function of their frequencies, together with the locality and frequency of a DB.

Figure 3

Stiffness of dimeric citrate synthase as a function of residue number (dashed line). The number of DBs found at a given site out of 500 instances is also reported (black diamonds, right $y$ axis).

Figure 4

DB frequencies in citrate synthase as a function of their energy (pluses). The cases of Threonine 208 (closed circles) and Alanine 209 (closed squares) are highlighted. Using our protocol, no DB with an energy lower than $37.8\mathrm{kcal}/\mathrm{mole}$ was observed, out of a total of 500 cases.

Figure 5

Stiffness of the environment of amino-acid residues involved in enzymatic activity (black squares), compared to that of amino acids of the same chemical type (crosses) randomly chosen within the same set of enzyme structures. The broken line is only a guide for the eye.