Loop entropy

Abstract: To explore the plasticity and structural constraints of the protein-folding nucleus we have constructed through circular permutation four topological variants of the ribosomal protein S6. In effect, these topological variants represent entropy mutants with maintained spatial contacts. The proteins were characterized at two complementary levels of detail: by φ-value analysis estimating the extent of contact formation in the transition-state ensemble and by Hammond analysis measuring the site-specific growth of the folding nucleus. The results show that, although the loop-entropy alterations markedly influence the appearance and structural location of the folding nucleus, it retains a common motif of one helix docking against two strands. This nucleation motif is built around a shared subset of side chains in the center of the hydrophobic core but extends in different directions of the S6 structure following the permutant-specific differences in local loop entropies. The adjustment of the critical folding nucleus to alterations in loop entropies is reflected by a direct correlation between the φ-value change and the accompanying change in local sequence separation.

Abstract: Conformational entropy makes important contribution to the stability and folding of RNA molecule, but it is challenging to either measure or compute conformational entropy associated with long loops. We develop optimized discrete k-state models of RNA backbone based on known RNA structures for computing entropy of loops, which are modeled as self-avoiding walks. To estimate entropy of hairpin, bulge, internal loop, and multibranch loop of long length (up to 50), we develop an efficient sampling method based on the sequential Monte Carlo principle. Our method considers excluded volume effect. It is general and can be applied to calculating entropy of loops with longer length and arbitrary complexity. For loops of short length, our results are in good agreement with a recent theoretical model and experimental measurement. For long loops, our estimated entropy of hairpin loops is in excellent agreement with the Jacobson–Stockmayer extrapolation model. However, for bulge loops and more complex secondary structures such as internal and multibranch loops, we find that the Jacobson–Stockmayer extrapolation model has large errors. Based on estimated entropy, we have developed empirical formulae for accurate calculation of entropy of long loops in different secondary structures. Our study on the effect of asymmetric size of loops suggest that loop entropy of internal loops is largely determined by the total loop length, and is only marginally affected by the asymmetric size of the two loops. Our finding suggests that the significant asymmetric effects of loop length in internal loops measured by experiments are likely to be partially enthalpic. Our method can be applied to develop improved energy parameters important for studying RNA stability and folding, and for predicting RNA secondary and tertiary structures. The discrete model and the program used to calculate loop entropy can be downloaded at http://gila.bioengr.uic.edu/resources/RNA.html.

Abstract: Long insertions into a loop of a folded host protein are expected to have destabilizing effects because of the entropic cost associated with loop closure unless the inserted sequence adopts a folded structure with amino- and carboxy-termini in close proximity. A loop entropy reduction screen based on this concept was used in an attempt to retrieve folded sequences from random sequence libraries. A library of long random sequences was inserted into a loop of the SH2 domain, displayed on the surface of M13 phage, and the inserted sequences that did not disrupt SH2 function were retrieved by panning using beads coated with a phosphotyrosine containing SH2 peptide ligand. Two sequences of a library of 2 × 108 sequences were isolated after multiple rounds of panning, and were found to have recovery levels similar to the wild-type SH2 domain and to be relatively intolerant to further mutation in PCR mutagenesis experiments. Surprisingly, although these inserted sequences exhibited little nonrandom structure, they do not significantly destabilize the host SH2 domain. Additional insertion variants recovered at lower levels in the panning experiments were also found to have a minimal effect on the stability and peptide-binding function of the SH2 domain. The additional level of selection present in the panning experiments is likely to involve in vivo folding and assembly, as there was a rough correlation between recovery levels in the phage-panning experiments and protein solubility. The finding that loop insertions of 60–80 amino acids have minimal effects on SH2 domain stability suggests that the free energy cost of inserting long loops may be considerably less than polymer theory estimates based on the entropic cost of loop closure, and, hence, that loop insertion may have provided an evolutionary route to multidomain protein structures.

Abstract: The distribution of one-disulfide bonds in the two-disulfide intermediates in the oxidative refolding of bovine pancreatic ribonuclease A has been characterized. These two-disulfide intermediates were formed from the fully reduced denatured protein by oxidation with dithiothreitol, then blocked with AEMTS, purified by cation-exchange chromatography, enzymatically digested, and analyzed by reversed-phase high-performance liquid chromatography and mass spectrometry. The relative concentration of each of the 28 possible one-disulfide bonds in the two-disulfide ensemble was determined. Comparison with a statistical mechanical treatment of loop formation shows that the two-disulfide intermediates are probably compact. All 28 disulfide bonds were observed, demonstrating the absence of specific long-range interactions in these intermediates. Thermodynamic arguments suggest that the absence of such specific long-range interactions in the two-disulfide species may elevate the concentration of kinetically important three-disulfide intermediates and thereby increase the folding rate. Bond [65-72] was found to make up approximately 27% of the disulfide bonds of the two-disulfide species, significantly more than all other disulfides, because of stabilization by loop entropy factors and an energetically favorable beta-turn. This turn may be one of several chain-folding initiation sites, accelerating folding by decreasing the dimensionality of the conformational space that has to be searched.