A fundamental question in protein folding is whether the coil to globule collapse transition occurs during the initial stages of folding (burst-phase) or simultaneously with the protein folding transition. Single molecule fluorescence resonance energy transfer (FRET) and small angle X-ray scattering (SAXS) experiments disagree on whether Protein L collapse transition occurs during the burst-phase of folding. We study Protein L folding using a coarse-grained model and molecular dynamics simulations. The collapse transition in Protein L is found to be concomitant with the folding transition. In the burst-phase of folding, we find that FRET experiments overestimate radius of gyration, R g , of the protein due to the application of Gaussian polymer chain end-to-end distribution to extract R g from the FRET efficiency. FRET experiments estimate ≈ 6Å decrease in R g when the actual decrease is ≈ 3Å on Guanidinium Chloride denaturant dilution from 7.5M to 1M, and thereby suggesting pronounced compaction in the protein dimensions in the burst-phase.The ≈ 3Å decrease is close to the statistical uncertainties of the R g data measured from SAXS experiments, which suggest no compaction, leading to a disagreement with the FRET experiments.

Theory and simulations predicted sometime ago that the sizes of unfolded states of globular proteins should decrease continuously as the denaturant concentration is shifted from a high to a low value. However, small angle X-ray scattering (SAXS) data were used to assert the opposite, while interpretation of single molecule Forster resonance energy transfer experiments (FRET) supported the theoretical predictions. The disagreement between the two experiments is the SAXS-FRET controversy. By harnessing recent advances in SAXS and FRET experiments and setting these findings in the context of a general theory and simulations, we establish that compaction of unfolded states is universal. The theory also predicts that proteins rich in β-sheets are more collapsible than α-helical proteins. Because the extent of compaction is small, experiments have to be accurate and their interpretations should be as model free as possible. Theory also suggests that collapsibility itself could be a physical restriction on the evolution of foldable sequences, and provides a physical basis for the origin of multi-domain proteins.

Recent fluorescence spectroscopy measurements of the turnover time distribution of single-enzyme turnover kinetics of β-galactosidase provide evidence of Michaelis-Menten kinetics at low substrate concentration. However, at high substrate concentrations, the dimensionless variance of the turnover time distribution shows systematic deviations from the Michaelis-Menten prediction. This difference is attributed to conformational fluctuations in both the enzyme and the enzyme-substrate complex and to the possibility of both parallel- and off-pathway kinetics. Here, we use the chemical master equation to model the kinetics of a single fluctuating enzyme that can yield a product through either parallel- or off-pathway mechanisms. An exact expression is obtained for the turnover time distribution from which the mean turnover time and randomness parameters are calculated. The parallel- and off-pathway mechanisms yield strikingly different dependences of the mean turnover time and the randomness parameter on the substrate concentration. In the parallel mechanism, the distinct contributions of enzyme and enzyme-substrate fluctuations are clearly discerned from the variation of the randomness parameter with substrate concentration. From these general results, we conclude that an off-pathway mechanism, with substantial enzyme-substrate fluctuations, is needed to rationalize the experimental findings of single-enzyme turnover kinetics of β-galactosidase.

Salts differ in their ability to stabilize protein conformations, thereby affecting the thermodynamics and kinetics of protein folding. We developed a coarse-grained protein model that can predict salt-induced changes in protein properties by using the transfer free-energy data of various chemical groups from water to salt solutions. Using this model and molecular dynamics simulations, we probed the effect of seven different salts on the folding thermodynamics of the DNA binding domain of lac repressor protein ( lac-DBD) and N-terminal domain of ribosomal protein (NTL9). We show that a salt can act as a protein stabilizing or destabilizing agent depending on the protein sequence and folded state topology. The computed thermodynamic properties, especially the m values for various salts, which reveal the relative ability of a salt to stabilize the protein folded state, are in quantitative agreement with the experimentally measured values. The computations show that the degree of protein compaction in the denatured ensemble strongly depends on the salt identity, and for the same variation in salt concentration, the compaction in the protein dimensions varies from ∼4% to ∼30% depending on the salt. The transition-state ensemble (TSE) of lac-DBD is homogeneous and polarized, while the TSE of NTL9 is heterogeneous and diffusive. Salts induce subtle structural changes in the TSE that are in agreement with Hammond's postulate. The barrier to protein folding tends to disappear in the presence of moderate concentrations (∼3-4 m) of strongly stabilizing salts.

Salts modulate the behavior of intrinsically disordered proteins (IDPs) and influence the formation of membraneless organelles through liquid−liquid phase separation (LLPS). In low ionic strength solutions, IDP conformations are perturbed by the screening of electrostatic interactions, independent of the salt identity. In this regime, insight into the IDP behavior can be obtained using the theory for salt-induced transitions in charged polymers. However, salt-specific interactions with the charged and uncharged residues, known as the Hofmeister effect, influence IDP behavior in high ionic strength solutions. There is a lack of reliable theoretical models in high salt concentration regimes to predict the salt effect on IDPs. We propose a simulation methodology using a coarse-grained IDP model and experimentally measured water to salt solution transfer free energies of various chemical groups that allowed us to study the saltspecific transitions induced in the IDPs conformational ensemble. We probed the effect of three different monovalent salts on five IDPs belonging to various polymer classes based on charged residue content. We demonstrate that all of the IDPs of different polymer classes behave as self-avoiding walks (SAWs) at physiological salt concentration. In high salt concentrations, the transitions observed in the IDP conformational ensembles are dependent on the salt used and the IDP sequence and composition. Changing the anion with the cation fixed can result in the IDP transition from a SAW-like behavior to a collapsed globule. An important implication of these results is that a suitable salt can be identified to induce condensation of an IDP through LLPS.