The concept of the protein transition state ensemble (TSE), a collection of the conformations that have 50% probability to convert rapidly to the folded state and 50% chance to rapidly unfold, constitutes the basis of the modern interpretation of protein engineering experiments. It has been conjectured that conformations constituting the TSE in many proteins are the expanded and distorted forms of the native state built around a specific folding nucleus. This view has been supported by a number of on-lattice and off-lattice simulations. Here we report a direct observation and characterization of the TSE by molecular dynamic folding simulations of the C-Src SH3 domain, a small protein that has been extensively studied experimentally. Our analysis reveals a set of key interactions between residues, conserved by evolution, that must be formed to enter the kinetic basin of attraction of the native state.
RNA-Puzzles is a collective endeavor dedicated to the advancement and improvement of RNA 3D structure prediction. With agreement from crystallographers, the RNA structures are predicted by various groups before the publication of the crystal structures. We now report the prediction of 3D structures for six RNA sequences: four nucleolytic ribozymes and two riboswitches. Systematic protocols for comparing models and crystal structures are described and analyzed. In these six puzzles, we discuss (i) the comparison between the automated web servers and human experts; (ii) the prediction of coaxial stacking; (iii) the prediction of structural details and ligand binding; (iv) the development of novel prediction methods; and (v) the potential improvements to be made. We show that correct prediction of coaxial stacking and tertiary contacts is essential for the prediction of RNA architecture, while ligand binding modes can only be predicted with low resolution and simultaneous prediction of RNA structure with accurate ligand binding still remains out of reach. All the predicted models are available for the future development of force field parameters and the improvement of comparison and assessment tools.
Diverse proteins with similar structures are grouped into families of homologs and analogs, if their sequence similarity is higher or lower, respectively, than 20%-30%. It was suggested that protein homologs and analogs originate from a common ancestor and diverge in their distinct evolutionary time scales, emerging as a consequence of the physical properties of the protein sequence space. Although a number of studies have determined key signatures of protein family organization, the sequence-structure factors that differentiate the two evolution-related protein families remain unknown. Here, we stipulate that subtle structural changes, which appear due to accumulating mutations in the homologous families, lead to distinct packing of the protein core and, thus, novel compositions of core residues. The latter process leads to the formation of distinct families of homologs. We propose that such differentiation results in the formation of analogous families. To test our postulate, we developed a molecular modeling and design toolkit, Medusa, to computationally design protein sequences that correspond to the same fold family. We find that analogous proteins emerge when a backbone structure deviates only 1-2 Å root-mean-square deviation from the original structure. For close homologs, core residues are highly conserved. However, when the overall sequence similarity drops to ;25%-30%, the composition of core residues starts to diverge, thereby forming novel families of protein homologs. This direct observation of the formation of protein homologs within a specific fold family supports our hypothesis. The conservation of amino acids in designed sequences recapitulates that of the naturally occurring sequences, thereby validating our computational design methodology.
We study traveling time and traveling length for tracer dispersion in two-dimensional bond percolation, modeling flow by tracer particles driven by a pressure difference between two points separated by Euclidean distance r. We find that the minimal traveling time t(min) scales as t(min) approximately r(1.33), which is different from the scaling of the most probable traveling time, t* approximately r(1.64). We also calculate the length of the path corresponding to the minimal traveling time and find l(min) approximately r(1.13) and that the most probable traveling length scales as l* approximately r(1.21). We present the relevant distribution functions and scaling relations.
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