Nonexponential Kinetics of Loop Formation in Proteins and Peptides: A Signature of Rugged Free Energy Landscapes?

Abstract

The kinetics of loop formation, i.e., the occurrence of contact between two atoms of a polypeptide, remains the focus of continuing interest. One of the reasons is that contact formation is the elementary event underlying processes such as folding and binding. More importantly, it is experimentally measurable and can be predicted theoretically for ideal polymers. Deviations from single exponential kinetics have sometimes been interpreted as a signature of rugged, protein-like, free energy landscapes. Here we present simulations, with different atomistic models, of short peptides with varied structural propensity, and of a structured protein. Results show exponential contact formation kinetics (or relaxation) at long times, and a power law relaxation at very short times. At intermediate times, a deviation from either power law or simple exponential kinetics is observed that appears to be characteristic of polypeptides with either specific or nonspecific attractive interactions but disappears if attractive interactions are absent. Our results agree with recent experimental measurements on peptides and proteins and offer a comprehensive interpretation for them.

Comparison of Structure and Local Dynamics of Two Peptide Dendrimers with the Same Backbone but with Different Side Groups in Their Spacers

“…The potential energy of the system includes the deformation energy of the covalent bonds, the valence and the dihedral angles (including the improper dihedrals that maintain a plane conformation of peptide groups), and the energy of the van der Waals and electrostatic interactions. We used several computer programs, which were elaborated in previous papers, on MD [ 69 , 70 , 71 ] and BD simulations of dendrimers and dendrigrafts [ 72 , 73 ], linear polymers [ 74 , 75 , 76 , 77 ], polysaccharides [ 78 ], and peptides [ 79 ], as well as linear polyelectrolytes [ 80 , 81 , 82 , 83 , 84 , 85 , 86 ], for numerical calculations the properties of peptide dendrimers.…”

Why the Orientational Mobility in Arginine and Lysine Spacers of Peptide Dendrimers Designed for Gene Delivery Is Different?

“…The Gromacs package [68] and the AMBER-99SB-ILDN force field [69] were used in all molecular dynamics simulations. We have used the computer programs to calculate the characteristics of our dendrimer as described in our previous papers on simulation of linear polymers and polyelectrolytes, polymers brushes [70], AFM of linear biopolymers [71], dendrimers and hyperbranched polymers in shear and elongational flow [72,73] and cyclization of linear peptides [74].…”

Non-Markovian barrier crossing with two-time-scale memory is dominated by the faster memory component

“…Due to the coupling to intra-and intermolecular orthogonal degrees of freedom, the dynamics of the reaction coordinate becomes non-Markovian and can be characterized by a memory function that describes for how long a system remembers its past state [6][7][8][9][10][11]. Memory effects have been studied in the context of ion-pair kinetics [12,13], conformational transitions in small molecules [14][15][16], diffusive motion of particles and molecules in liquids [17][18][19][20], cell locomotion [21], polymer looping kinetics [22][23][24][25][26] and protein folding [27,28], and have been demonstrated to substantially influence barrier-crossing times for slowly decaying memory functions [29][30][31][32][33][34].…”