Exploring the multi-dimensional energy landscape of a large protein in detail is a computational challenge. Such investigations may include analysis of multiple folding pathways, rate constants for important conformational transitions, locating intermediate states populated during folding, estimating energetic and entropic barriers that separate populated basins, and visualising a high-dimensional surface. The complexity of the landscape can be simplified through coarse-grained structure-based models (SBMs). These widely used coarse-grained representations of proteins provide a minimalist approximation to the free energy landscape, which subsumes the folding behaviour of many single-domain proteins. Here we describe the combination of SBMs with discrete path sampling (DPS), and show how this approach can provide details of the landscape and folding pathways. Combining SBMs and DPS provides an efficient framework for sampling the protein free energy landscape and for calculating various kinetic and thermodynamic quantities.
Protein Folding , Proteins , Entropy , Kinetics , Thermodynamics
Coarse-grained GoÌ -like models, based on the principle of minimal frustration, provide valuable insight into fundamental questions in the field of protein folding and dynamics. In conjunction with commonly used molecular dynamics (MD) simulations, energy landscape exploration methods like discrete path sampling (DPS) with GoÌ -like models can provide quantitative details of the thermodynamics and kinetics of proteins. Here we present Go-kit, a software that facilitates the setup of MD and DPS simulations of several flavors of GoÌ -like models. Go-kit is designed for use with MD (GROMACS) and DPS (PATHSAMPLE) simulation engines that are open source. The Go-kit code is written in python2.7 and is also open source. A case study for the ribosomal protein S6 is discussed to illustrate the utility of the software, which is available at https://github.com/gokit1/gokit .
Molecular Dynamics Simulation , Proteins/chemistry , Software , Thermodynamics , Bacterial Proteins/chemistry , Kinetics , Protein Conformation , Protein Folding , Ribosomal Protein S6/chemistry , Thermus thermophilus/chemistry
To fold on biologically relevant time scales, proteins have evolved funnelled energy landscapes with minimal energetic trapping. However, the polymeric nature of proteins and the spatial arrangement of secondary structural elements can create topological traps and slow folding. It is challenging to identify, visualize, and quantify such topological trapping. Designed proteins have not had the benefit of evolution, and it has been hypothesized that de novo designed protein topologies may therefore feature more topological trapping. Structure-based models (SBMs) are inherently funnelled, removing most energetic trapping, and can thus be used to isolate the effect of protein topology on the landscape. Here, we compare Top7, a designed protein with a topology unknown in nature, to S6, a naturally occurring ribosomal protein of similar size and topology. Possible kinetic traps and the energetic barriers separating them from the native state are elucidated. We find that, even with an SBM, the potential energy landscape (PEL) of the designed protein is more frustrated than that of the natural protein. We then quantify the effect of adding non-native hydrophobic interactions and coarse-grained side-chains through a frustration density parameter. A clear increase in frustration is observed including side-chains, whereas adding hydrophobic interactions leads to a narrowing of the funnel and a decrease in complexity. The most likely (un)folding routes for all models are derived through the construction of probability contact maps. The ability to quantitatively understand and optimize the organization of the PEL for designed proteins may enable us to design structure-seeking landscapes, mimicking the effect of evolution.
Proteins/chemistry , Hydrophobic and Hydrophilic Interactions , Molecular Dynamics Simulation , Protein Conformation , Protein Unfolding , Ribosomal Protein S6/chemistry , Thermodynamics , Thermus thermophilus/chemistry
Understanding the dynamics of complex systems requires the investigation of their energy landscape. In particular, the flow of probability on such landscapes is a central feature in visualizing the time evolution of complex systems. To obtain such flows, and the concomitant stable states of the systems and the generalized barriers among them, the threshold algorithm has been developed. Here, we describe the methodology of this approach starting from the fundamental concepts in complex energy landscapes and present recent new developments, the threshold-minimization algorithm and the molecular dynamics threshold algorithm. For applications of these new algorithms, we draw on landscape studies of three disaccharide molecules: lactose, maltose, and sucrose.
We present a scheme, called the threshold-minimization method, for globally exploring the energy landscapes of small systems of biomolecular interest where typical exploration moves always require a certain degree of subsequent structural relaxation in order to be efficient, e.g., systems containing small or large circular carbon chains such as cyclic peptides or carbohydrates. We show that using this threshold-minimization method we can not only reproduce the global minimum and relevant local minima but also overcome energetic barriers associated with different types of isomerism for the example of a cyclic peptide, cyclo-(Gly)4. We then apply the new method to the disaccharide α-d-glucopyranose-1-2-ß-d-fructofuranose, report energetically preferred configurations and barriers to boat-chair isomerization in the glucopyranosyl ring, and discuss the energy landscape.
Disaccharides/chemistry , Monte Carlo Method , Peptides, Cyclic/chemistry , Disaccharides/metabolism , Peptides, Cyclic/metabolism , Protein Conformation
The homochirality of natural amino acids facilitates the formation of regular secondary structures such as α-helices and ß-sheets. Here, we study the relationship between chirality and backbone structure for the example of hexa-alanine. The most stable stereoisomers are identified through global optimisation. Further, the energy landscape, a database of connected low-energy local minima and transition points, is constructed for various neutral and zwitterionic stereoisomers of hexa-alanine. Three order parameters for partial helicity are applied and metric disconnectivity graphs are presented with partial helicity as a metric. We also apply the Zimm-Bragg model to derive average partial helicities for Ace-(L-Ala)6-NHMe, Ace-(D-Ala-L-Ala)3-NHMe, and Ace-(L-Ala)3-(D-Ala)3-NHMe from the database of local minima and compare with previous studies.
Alanine/chemistry , Oligopeptides/chemistry , Hydrogen Bonding , Models, Molecular , Protein Structure, Secondary , Stereoisomerism , Thermodynamics
We model the deposition and growth of MgF(2) on a sapphire substrate as it occurs in a low-temperature atom-beam-deposition experiment. In the experiment, an (X-ray) amorphous film of MgF(2) is obtained at low temperatures of 170-180 K, and upon heating, this transforms to the expected rutile phase via the CaCl(2)-type structure. We confirm this from our simulations and propose a mechanism for this transformation. The growth process is analyzed as a function of the synthesis parameters, which include the substrate temperature, deposition rate of clusters, and types of clusters deposited. Upon annealing an initially amorphous deposit, we observe the formation of two competing nanocrystalline modifications during this process, which exhibit the CaCl(2) and CdI(2) structure types, respectively. We argue that this joint growth of the two nanocrystalline polymorphs stabilizes the kinetically unstable CaCl(2)-type structure on the macroscopic level long enough to be observed in the experiment.
