Multi-funnel Landscapes Research Articles

Analysis and interpretation of first passage time distributions featuring rare events.

In this contribution we consider theory and associated computational tools to treat the kinetics associated with competing pathways on multifunnel energy landscapes. Multifunnel landscapes are associated with molecular switches and multifunctional materials, and are expected to exhibit multiple relaxation time scales and associated thermodynamic signatures in the heat capacity. Our focus here is on the first passage time distribution, which is encoded in a kinetic transition network containing all the locally stable states and the pathways between them. This network can be renormalised to reduce the dimensionality, while exactly conserving the mean first passage time and approximately conserving the full distribution. The structure of the reduced network can be visualised using disconnectivity graphs. We show how features in the first passage time distribution can be associated with specific kinetic traps, and how the appearance of competing relaxation time scales depends on the starting conditions. The theory is tested for two model landscapes and applied to an atomic cluster and a disordered peptide. Our most important contribution is probably the reconstruction of the full distribution for long time scales, where numerical problems prevent direct calculations. Here we combine accurate treatment of the mean first passage time with the reliable part of the distribution corresponding to faster time scales. Hence we now have a fundamental understanding of both thermodynamic and kinetic signatures of multifunnel landscapes.

Dynamical Signatures of Multifunnel Energy Landscapes

Multifunctional systems, such as molecular switches, exhibit multifunnel energy landscapes associated with the alternative functional states. In this contribution the multifunnel organization is decoded from dynamical signatures in the first passage time distribution between reactants and products. Characteristic relaxation rates are revealed by analyzing the kinetics as a function of the observation time scale, which scans the underlying distribution. Extracting the corresponding dynamical signatures provides direct insight into the organization of the molecular energy landscape, which will facilitate a rational design of target functionality. Examples are illustrated for multifunnel landscapes in biomolecular systems and an atomic cluster.

Energy Landscapes for Proteins: From Single Funnels to Multifunctional Systems

AbstractThis report advances the hypothesis that multifunctional systems may be associated with multifunnel potential and free energy landscapes, with particular focus on biomolecules. It compares systems that exhibit single, double, and multiple competing structures, and contrasts multifunnel landscapes associated with misfolded amyloidogenic oligomers, which presumably do not arise as an evolutionary target. In this context, intrinsically disordered proteins could be considered intrinsically multifunctional molecules, associated with multifunnel landscapes. Potential energy landscape theory enables biomolecules to be treated in a common framework together with self‐organizing and multifunctional systems based on inorganic materials, atomic and molecular clusters, crystal polymorphs, and soft matter.

Evolved Minimal Frustration in Multifunctional Biomolecules.

Protein folding is often viewed in terms of a funneled potential or free energy landscape. A variety of experiments now indicate the existence of multifunnel landscapes, associated with multifunctional biomolecules. Here, we present evidence that these systems have evolved to exhibit the minimal number of funnels required to fulfill their cellular functions, suggesting an extension to the principle of minimum frustration. We find that minimal disruptive mutations result in additional funnels, and the associated structural ensembles become more diverse. The same trends are observed in an atomic cluster. These observations suggest guidelines for rational design of engineered multifunctional biomolecules.

Multifunnel Landscape of the Fold-Switching Protein RfaH-CTD.

Proteins such as the transcription factor RfaH can change biological function by switching between distinct three-dimensional folds. RfaH regulates transcription if the C-terminal domain folds into a double helix bundle and promotes translation when this domain assumes a β-barrel form. This fold-switch has been also observed for the isolated C-terminal domain, dubbed by us as RfaH-C-terminal domain (RfaH-CTD), and is studied here with a variant of the replica-exchange-with-tunneling approach recently introduced by us. We use the enhanced sampling properties of this technique to map the free-energy landscape of RfaH-CTD and to propose a mechanism for the conversion process.

Computational investigation of simple memetic approaches for continuous global optimization

In Locatelli et al. (2014) [20] a memetic approach, called MDE (Memetic Differential Evolution), for the solution of continuous global optimization problems, has been introduced and proved to be quite efficient in spite of its simplicity. In this paper we computationally investigate some variants of MDE. The investigation reveals that the best tested variant of MDE outperforms the original MDE itself, but also that the best variant depends on some properties of the function to be optimized. In particular, a greedy variant of MDE turns out to perform very well over functions with a single-funnel landscape, while another variant, based on a diversity measure applied to the members of the population, works better over functions with a multi-funnel landscape. A hybrid approach is also proposed which combines both the previous variants in order to obtain an overall performance which is good over all functions.