Quantifying Protein Disorder through Measures of Excess Conformational Entropy

Intrinsically disordered proteins (IDPs) and proteins with a large degree of disorder are abundant in the proteomes of eukaryotes and viruses, and play a vital role in cellular homeostasis and disease. One fundamental question that has been raised on IDPs is the process by which they offset the entropic penalty involved in transitioning from a heterogeneous ensemble of conformations to a much smaller collection of binding-competent states. However, this has been a difficult problem to address, as the effective entropic cost of fixing residues in a folded-like conformation from disordered amino acid neighborhoods is itself not known. Moreover, there are several examples where the sequence complexity of disordered regions is as high as well-folded regions. Disorder in such cases therefore arises from excess conformational entropy determined entirely by correlated sequence effects, an entropic code that is yet to be identified. Here, we explore these issues by exploiting the order-disorder transitions of a helix in Pbx-Homeodomain together with a dual entropy statistical mechanical model to estimate the magnitude and sign of the excess conformational entropy of residues in disordered regions. We find that a mere 2.1-fold increase in the number of allowed conformations per residue (∼0.7kBT favoring the unfolded state) relative to a well-folded sequence, or ∼2(N) additional conformations for a N-residue sequence, is sufficient to promote disorder under physiological conditions. We show that this estimate is quite robust and helps in rationalizing the thermodynamic signatures of disordered regions in important regulatory proteins, modeling the conformational folding-binding landscapes of IDPs, quantifying the stability effects characteristic of disordered protein loops and their subtle roles in determining the partitioning of folding flux in ordered domains. In effect, the dual entropy model we propose provides a statistical thermodynamic basis for the relative conformational propensities of amino acids in folded and disordered environments in proteins. Our work thus lays the foundation for understanding and quantifying protein disorder through measures of excess conformational entropy.