Contribution of secondary structure to the heat capacity and enthalpy distribution of the unfolded state in proteins

Energy landscapes and heat capacity signatures for peptides correlate with phase separation propensity

Phase separation plays an important role in the formation of membraneless compartments within the cell and intrinsically disordered proteins with low-complexity sequences can drive this compartmentalisation. Various intermolecular forces, such as aromatic-aromatic and cation-aromatic interactions, promote phase separation. However, little is known about how the ability of proteins to phase separate under physiological conditions is encoded in their energy landscapes and this is the focus of the present investigation. Our results provide a first glimpse into how the energy landscapes of minimal peptides that contain - and cation- interactions differ from the peptides that lack amino acids with such interactions. The peaks in the heat capacity () as a function of temperature report on alternative low-lying conformations that differ significantly in terms of their enthalpic and entropic contributions. The analysis and subsequent quantification of frustration of the energy landscape suggest that the interactions that promote phase separation lead to features (peaks or inflection points) at low temperatures in . More features may occur for peptides containing residues with better phase separation propensity and the energy landscape is more frustrated for such peptides. Overall, this work links the features in the underlying single-molecule potential energy landscapes to their collective phase separation behaviour and identifies quantities ( and frustration metric) that can be utilised in soft material design.

Unraveling the Thermodynamics of Ultra-tight Binding of Intrinsically Disordered Proteins

Protein interactions mediated by the intrinsically disordered proteins (IDPs) are generally associated with lower affinities compared to those between globular proteins. Here, we characterize the association between the intrinsically disordered HigA2 antitoxin and its globular target HigB2 toxin from Vibrio cholerae using competition ITC experiments. We demonstrate that this interaction reaches one of the highest affinities reported for IDP-target systems (K_D = 3 pM) and can be entirely attributed to a short, 20-residue-long interaction motif that folds into α-helix upon binding. We perform an experimentally based decomposition of the IDP-target association parameters into folding and binding contributions, which allows a direct comparison of the binding contribution with those from globular ultra-high affinity binders. We find that the HigA2-HigB2 interface is energy optimized to a similar extent as the interfaces of globular ultra-high affinity complexes, such as barnase-barstar. Evaluation of other ultra-high affinity IDP-target systems shows that a strategy based on entropy optimization can also achieve comparably high, picomolar affinities. Taken together, these examples show how IDP-target interactions achieve picomolar affinities either through enthalpy optimization (HigA2-HigB2), resembling the ultra-high affinity binding of globular proteins, or via bound-state fuzziness and entropy optimization (CcdA-CcdB, histone H1-prothymosin α).

Empirical protein partition functions

In the present paper, we outline how to construct the partition function for a protein using empirical heat capacity data. The procedure is based on the calculation of a set of energy moments from the temperature dependence of the heat capacity. Given a set of energy moments, one can then use the maximum-entropy method to calculate an approximate energy distribution for the protein; the more energy moments one has, the better the approximation. The energy distribution can then be used to calculate the probability that the molecule is in a given energy level, which, using standard statistical mechanics, gives the degeneracy of the particular energy level. The degeneracy as a function of energy is the central ingredient in the construction of the partition function. Given the partition function, one can calculate all of the thermodynamic functions of the protein (free energy, energy, entropy, heat capacity, and energy probability distribution) as a function of temperature. The three-dimensional plot of the probability that the protein has a given energy at a given temperature tells one graphically (without imposing the assumption) whether or not it is a good approximation to divide the terms in the partition function into two or more groups, reflecting, for example, the presence of distinct native and denatured species.

Energy and Enthalpy Distribution Functions for a Few Physical Systems

The present work is devoted to extracting the energy or enthalpy distribution function of a physical system from the moments of the distribution using the maximum entropy method. This distribution theory has the salient traits that it utilizes only the experimental thermodynamic data. The calculated distribution functions provide invaluable insight into the state or phase behavior of the physical systems under study. As concrete evidence, we demonstrate the elegance of the distribution theory by studying first a test case of a two-dimensional six-state Potts model for which simulation results are available for comparison, then the biphasic behavior of the binary alloy Na-K whose excess heat capacity, experimentally observed to fall in a narrow temperature range, has yet to be clarified theoretically, and finally, the thermally induced state behavior of a collection of 16 proteins.

HEAT CAPACITY IN PROTEINS

Heat capacity (Cp) is one of several major thermodynamic quantities commonly measured in proteins. With more than half a dozen definitions, it is the hardest of these quantities to understand in physical terms, but the richest in insight. There are many ramifications of observed Cp changes: The sign distinguishes apolar from polar solvation. It imparts a temperature (T) dependence to entropy and enthalpy that may change their signs and which of them dominate. Protein unfolding usually has a positive deltaCp, producing a maximum in stability and sometimes cold denaturation. There are two heat capacity contributions, from hydration and protein-protein interactions; which dominates in folding and binding is an open question. Theoretical work to date has dealt mostly with the hydration term and can account, at least semiquantitatively, for the major Cp-related features: the positive and negative Cp of hydration for apolar and polar groups, respectively; the convergence of apolar group hydration entropy at T approximately 112 degrees C; the decrease in apolar hydration Cp with increasing T; and the T-maximum in protein stability and cold denaturation.

Glutamine 53 is a gatekeeper residue in the FK506 binding protein

The effect of non-random conformational averaging in the urea-unfolded state on the folding pathway has been investigated in a variant of the FK506 binding protein with three additional residues at the amino terminus (FKBP(*)). Three mutations (asparagine, aspartate, and threonine) were introduced into position Q53 to enhance formation of non-native helix observed in this part of the protein in the urea-unfolded state. NMR analysis showed minor structural changes in the native state of each mutant, but additional medium-range alphaN(i,i+2) of each mutant nuclear Overhauser enhancements were observed in the urea-unfolded state that were not in FKBP(*), indicating that the mutations had a more substantial effect on the unfolded state ensemble than on the native state ensemble. Isothermal equilibrium denaturation measurements showed that the Q53T and Q53D mutants were destabilized, whereas the Q53N mutant was stabilized relative to FKBP(*) with little change in the equilibrium m values. The unfolding rates of Q53N and Q53T were similar to that of FKBP(*), but Q53D unfolded twice as fast as FKBP(*). In contrast, the mutations had a more pronounced effect on the refolding kinetics. Q53N refolded slightly faster and exhibited a kinetic folding intermediate similar to that of FKBP(*). The Q53D and Q53T mutants also refolded faster than FKBP(*) but lacked the folding intermediate, indicating that these mutants experienced a different folding trajectory and transition state than FKBP(*) and Q53N. The refolding kinetic Phi values were 0.74, 1.4 and 7.9 for Q53N, Q53T, and Q53D, respectively. The data point to Q53 functioning as a gatekeeper residue in the folding of FKBP(*). This study shows that perturbing the unfolded state ensemble via mutagenesis can provide insights into residues that play important roles in the folding pathway, and represents an attractive strategy for mapping the high-energy portions of the folding energy landscape.