Protein folding in high-dimensional spaces:hypergutters and the role of non-native interactions

The folding of naturally occurring, single domain proteins is usually well-described as a simple, single exponential process lacking significant trapped states. Here we further explore the hypothesis that the smooth energy landscape this implies, and the rapid kinetics it engenders, arises due to the extraordinary thermodynamic cooperativity of protein folding. Studying Miyazawa-Jernigan lattice polymers we find that, even under conditions where the folding energy landscape i...

In the framework of a lattice-model study of protein folding, we investigate the interplay between designability, thermodynamic stability, and kinetics. To be ``protein-like'', heteropolymers must be thermodynamically stable, stable against mutating the amino-acid sequence, and must be fast folders. We find two criteria which, together, guarantee that a sequence will be ``protein like'': i) the ground state is a highly designable stucture, i. e. the native structure is the gr...

Protein folding is a universal process, very fast and accurate, which works consistently (as it should be) in a wide range of physiological conditions. The present work is based on three premises, namely: ($i$) folding reaction is a process with two consecutive and independent stages, namely the search mechanism and the overall productive stabilization; ($ii$) the folding kinetics results from a mechanism as fast as can be; and ($iii$) at nanoscale dimensions, local thermal f...

A complex network approach to protein folding is proposed. The graph object is the network of shortcut edges present in a native-state protein (SCN0). Although SCN0s are found via an intuitive message passing algorithm (S. Milgram, Psychology Today, May 1967 pp. 61-67), they are meaningful enough that the logarithm form of their contact order (SCN0_lnCO) correlates significantly with protein kinetic rates, regardless of protein size. Further, the clustering coefficient of a S...

Understanding how monomeric proteins fold under in vitro conditions is crucial to describing their functions in the cellular context. Significant advances both in theory and experiments have resulted in a conceptual framework for describing the folding mechanisms of globular proteins. The experimental data and theoretical methods have revealed the multifaceted character of proteins. Proteins exhibit universal features that can be determined using only the number of amino acid...

Protein structures are a very special class among all possible structures. It was suggested that a ``designability principle'' plays a crucial role in nature's selection of protein sequences and structures. Here we provide a theoretical base for such a selection principle, using a novel formulation of the protein folding problem based on hydrophobic interactions. A structure is reduced to a string of 0's and 1's which represent the surface and core sites, respectively, as the...

Growing experimental evidence shows that proteins follow one or a few distinct paths when folding. We propose in this paper a procedure to parametrize these observed pathways, and from this parametrization construct effective Hamiltonians for the proteins. We furthermore study the denaturated-native transitions for a wide class of possible effective Hamiltonians based on this scheme, and find that the sharpness (tightness) of the transitions typically are close to their theor...

A geometric analysis of the global properties of the energy landscape of a minimalistic model of a polypeptide is presented, which is based on the relation between dynamical trajectories and geodesics of a suitable manifold, whose metric is completely determined by the potential energy. We consider different sequences, some with a definite protein-like behavior, a unique native state and a folding transition, and the others undergoing a hydrophobic collapse with no tendency t...

A kinetic model for the nucleation mechanism of protein folding is proposed. A protein is modeled as a heteropolymer consisting of hydrophobic and hydrophilic beads with equal constant bond lengths and bond angles. The total energy of the heteropolymer is determined by the repulsive/attractive interactions of non-linked beads and the contribution from the dihedral angles involved. Their parameters can be rigorously defined, unlike the ill defined surface tension of a cluster ...

A general theoretical framework is developed using free energy functional methods to understand the effects of heterogeneity in the folding of a well-designed protein. Native energetic heterogeneity arising from non-uniformity in native stability, as well as entropic heterogeneity intrinsic to the topology of the native structure are both investigated as to their impact on the folding free energy landscape and resulting folding mechanism. Given a minimally frustrated protein,...