Polymer scaling laws of unfolded and intrinsically disordered proteins quantified with single-molecule spectroscopy

Abstract

The dimensions of unfolded and intrinsically disordered proteins are highly dependent on their amino acid composition and solution conditions, especially salt and denaturant concentration. However, the quantitative implications of this behavior have remained unclear, largely because the effective theta-state, the central reference point for the underlying polymer collapse transition, has eluded experimental determination. Here, we used single-molecule fluorescence spectroscopy and two-focus correlation spectroscopy to determine the theta points for six different proteins. While the scaling exponents of all proteins converge to 0.62 AE 0.03 at high denaturant concentrations, as expected for a polymer in good solvent, the scaling regime in water strongly depends on sequence composition. The resulting average scaling exponent of 0.46 AE 0.05 for the four foldable protein sequences in our study suggests that the aqueous cellular milieu is close to effective theta conditions for unfolded proteins. In contrast, two intrinsically disordered proteins do not reach the Θ-point under any of our solvent conditions, which may reflect the optimization of their expanded state for the interactions with cellular partners. Sequence analyses based on our results imply that foldable sequences with more compact unfolded states are a more recent result of protein evolution.protein folding | single-molecule FRET | coil-globule transition | polymer theory I t has become increasingly clear that the structure and dynamics of unfolded proteins are essential for understanding protein folding (1-3) and the functional properties of intrinsically disordered proteins (IDPs) (4-6). Theoretical concepts from polymer physics (7-9) have frequently been used to describe the properties of unfolded polypeptide chains (4, 10, 11) with the goal to establish the link between protein folding and collapse (12-15). However, the methodology to test many of these concepts experimentally has only become available rather recently (2,16,17). A considerable body of experimental and theoretical work suggests that the dimensions of unfolded proteins depend on parameters such as amino acid composition (4), temperature (18), and solvent quality (3,10,15,19). The continuous collapse of polymers has been treated exhaustively by a number of theories (20-24) based on general principles that relate the dimensions and the length of a chain to its free energy. However, a prerequisite for the quantitative application of these theories and their comparison to experimental results is that the dimensions of the Θ-state are known, which serves as an essential reference state. At the Θ-point*, chain-chain and chain-solvent interactions balance such that the polymer is at a critical point, at which the thermodynamic phase boundaries disappear. As a result, the polypeptide chain obeys the same length scaling as an ideal chain without excluded volume and intrachain interactions. However, the Θ-conditions for protein chains are unknown. Besides its importance for obtaining the corre...

Single-molecule spectroscopy of the unexpected collapse of an unfolded protein at low pH

“…1(b)). This effect has been observed for a broad variety of proteins and peptides 2,4,8,9,[12][13][14]35 and can be described as a continuous expansion of the chain on transfer to good solvent. 25 The interesting question here is how mixtures of denaturants 36 and drastic changes in pH will affect the dimensions of the unfolded state.…”

“…These forces determine the dimensions of unfolded and disordered proteins and have been suggested to impact processes such as the coupled binding and folding of IDPs, 5 or the rate of protein folding reactions. [6][7][8] However, the dimensions of unfolded proteins and IDPs also depend critically on solution conditions such as ionic strength, 4,9 temperature, 10 osmolytes, 11 or denaturants, 2,[12][13][14] implying that the complex interplay between chain-chain and chainsolvent interactions has to be unraveled before quantitative predictions of the size of unstructured polypeptide chains and their effect on folding or binding will be possible.…”

“…4,[12][13][14] However, a prerequisite for their application is knowledge of the -state, which serves as a reference state for the coil-to-globule transition. At thepoint, chain-chain and chain-solvent interactions balance, and the chain obeys the length scaling of an ideal chain.…”

“…At thepoint, chain-chain and chain-solvent interactions balance, and the chain obeys the length scaling of an ideal chain. Based on the length scaling of unfolded proteins obtained from smallangle X-ray scattering (SAXS), 22 and the length scaling of folded globular proteins, 14,23 we recently obtained an approximate expression for the radius of gyration of unfolded proteins at the -point, 14 which allows the calculation of mean-field interaction free energies between the amino acids in unfolded proteins. 14 Although we found a close correspondence of these mean-field free energies with the free energy of solvation of the individual amino acids, 14,24 the description of unfolded proteins by one mean-field interaction parameter remains incomplete.…”

“…Proteins are heteropolymers of complex composition, consisting of 20 different types of amino acids. Averaging over all possible types of interactions by extracting one mean-field interaction as done in the past 14,25 is a crucial first step for understanding the behavior of polypeptide chains but will not be able to provide structural details. In the past, heteropolymer theories based on replica approaches, 26 the random energy approximation (REM) in spin-glass theory, 27 and Flory-Huggins theory of mixing 28,29 have been developed.…”