Funneled Landscape Research Articles

Structural relaxation in atomic clusters: master equation dynamics.

The role of the potential energy landscape in determining the relaxation dynamics of model clusters is studied using a master equation. Two types of energy landscape are examined: a single funnel, as exemplified by 13-atom Morse clusters, and the double funnel landscape of the 38-atom Lennard-Jones cluster. Interwell rate constants are calculated using Rice-Ramsperger-Kassel-Marcus theory within the harmonic approximation, but anharmonic model partition functions are also considered. Decreasing the range of the potential in the Morse clusters is shown to hinder relaxation toward the global minimum, and this effect is related to the concomitant changes in the energy landscape. The relaxation modes that emerge from the master equation are interpreted and analyzed to extract interfunnel rate constants for the Lennard-Jones cluster. Since this system is too large for a complete characterization of the energy landscape, the conditions under which the master equation can be applied to a limited database are explored. Connections are made to relaxation processes in proteins and structural glasses.

Multiple pathways on a protein-folding energy landscape: kinetic evidence.

The funnel landscape model predicts that protein folding proceeds through multiple kinetic pathways. Experimental evidence is presented for more than one such pathway in the folding dynamics of a globular protein, cytochrome c. After photodissociation of CO from the partially denatured ferrous protein, fast time-resolved CD spectroscopy shows a submillisecond folding process that is complete in approximately 10(-6) s, concomitant with heme binding of a methionine residue. Kinetic modeling of time-resolved magnetic circular dichroism data further provides strong evidence that a 50-microseconds heme-histidine binding process proceeds in parallel with the faster pathway, implying that Met and His binding occur in different conformational ensembles of the protein, i.e., along respective ultrafast (microseconds) and fast (milliseconds) folding pathways. This kinetic heterogeneity appears to be intrinsic to the diffusional nature of early folding dynamics on the energy landscape, as opposed to the late-time heterogeneity associated with nonnative heme ligation and proline isomers in cytochrome c.

The folding funnel landscape for the peptide Met-enkephalin.

We study the free energy landscape of the small peptide Met-enkephalin. Our data were obtained from a generalized-ensemble Monte Carlo simulation taking the interactions among all atoms into account. We show that the free energy landscape resembles that of a funnel, indicating that this peptide is a good folder. Our work demonstrates that the energy landscape picture and folding concept, developed in the context of simplified protein models, can also be used to describe the folding in more realistic models.

Scaling behavior of stochastic minimization algorithms in a perfect funnel landscape

We determined scaling laws for the numerical effort to find the optimal configurations of a simple model potential energy surface (PES) with a perfect funnel structure that reflects key characteristics of the protein interactions. Generalized Monte-Carlo methods(MCM, STUN) avoid an enumerative search of the PES and thus provide a natural resolution of the Levinthal paradox. We find that the computational effort grows with approximately the eighth power of the system size for MCM and STUN, while a genetic algorithm was found to scale exponentially. The scaling behaviour of a derived lattice model is also rationalized.

Exploring the protein folding funnel landscape

Energy landscape ideas have proved extremely useful in the understanding of the protein folding process. The central idea is that folding can be described as the movement of an ensemble of conformations on a funnel-like energy landscape, and that one can study folding by analyzing (or measuring) key statistical parameters that characterize this energy landscape. In this work simple lattice models of protein-like heteropolymers are used to identify important statistical parameters and demonstrate their effect on folding behavior. In these models, thermodynamic sampling can accurately characterize the kinetic behavior of the system and can be used with a simple diffusive theory to understand macroscopic folding behavior.

Statistical mechanics of a correlated energy landscape model for protein folding funnels

In heteropolymers, energetic correlations exist due to polymeric constraints and the locality of interactions. Pair correlations in conjunction with the a priori specification of the existence of a particularly low energy state provide a method of introducing the aspect of minimal frustration to the energy landscapes of random heteropolymers. The resulting funneled landscape exhibits both a phase transition from a molten globule to a folded state, and the heteropolymeric glass transition in the globular state. We model the folding transition in the self-averaging regime, which together with a simple theory of collapse allows us to depict folding as a double-well free energy surface in terms of suitable reaction coordinates. Observed trends in barrier positions and heights with protein sequence length and thermodynamic conditions are discussed within the context of the model. We also discuss the new physics which arises from the introduction of explicitly cooperative many-body interactions, as might arise from sidechain packing and nonadditive hydrophobic forces.