Deciphering hierarchical features in the energy landscape of adenylate kinase folding/unfolding

Abstract

Hierarchical features of the energy landscape of the folding/unfolding behavior of adenylate kinase, including its dependence on denaturant concentration, are elucidated in terms of single-molecule fluorescence resonance energy transfer (smFRET) measurements in which the proteins are encapsulated in a lipid vesicle. The core in constructing the energy landscape from single-molecule time-series across different denaturant concentrations is the application of rate-distortion theory (RDT), which naturally considers the effects of measurement noise and sampling error, in combination with change-point detection and the quantification of the FRET efficiency-dependent photobleaching behavior. Energy landscapes are constructed as a function of observation time scale, revealing multiple partially folded conformations at small time scales that are situated in a superbasin. As the time scale increases, these denatured states merge into a single basin, demonstrating the coarse-graining of the energy landscape as observation time increases. Because the photobleaching time scale is dependent on the conformational state of the protein, possible nonequilibrium features are discussed, and a statistical test for violation of the detailed balance condition is developed based on the state sequences arising from the RDT framework.

Single-molecule FRET methods to study the dynamics of proteins at work

“…Taylor et al [58] introduced a sophisticated analysis tool on the basis of information theory and soft clustering to construct free energy landscapes in the form of disconnectivity graphs. They demonstrated the utility of their technique by analyzing experimental results on the dynamics of a glutamate receptor [58] and on the folding of a multidomain protein [59].…”

Raman spectroscopic histology using machine learning for nonalcoholic fatty liver disease

“…To identify groups of spectra having similar Raman information, we performed unsupervised clustering of the spectra with rate–distortion theory (RDT) , which has demonstrated good performance in situations involving detection noise and overlap among clusters . The details of RDT clustering are explained in Appendix S2.…”

“…The details of RDT clustering are explained in Appendix S2. To select an appropriate number of clusters, we identify the simplest model in which each of the clusters contains similar Raman characteristics with differences within clusters that are comparable to those that may arise from Poisson error otherwise being overfitted . The details are explained in Appendix S3.…”

Moving beyond static snapshots: Protein dynamics and the Protein Data Bank

“…At present there are over 1200 papers with adenylate kinase in the title via PubMed. Enzymology (34,35), genetics (36), crystallography (37)(38)(39)(40), solution scattering (41), NMR (42,43), MD simulations (44,45), thermodynamics and unfolding (46,47), single molecule studies (48,49), hydrogen exchange mass spectrometry (43), various spectroscopies, mutagenesis (50,51), evolution (52,53), phylogeny (54), and bioinformatics (55), and others have all been employed to gain insight regarding the connections between structure, dynamics, and function. There is not a single model for a pathway commensurate with all the studies.…”