Quantifying Protein Disorder through Measures of Excess Conformational Entropy

Abstract

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.

Tunable order–disorder continuum in protein–DNA interactions

“…The Wako–Saitô–Muñoz–Eaton (WSME) model ( 50 , 51 ) in its latest version includes contributions from intramolecular van der Waals interactions, electrostatics and solvation apart from conformational entropy ( 52 , 53 ) (see Supporting Methods ). In the current work, the basic WSME model terms of CytR DBD (PDB ID: 2L8N) are supplemented with an extra weighting term on residue j .…”

Towards a thermodynamic mechanistic model for the effect of temperature on arthropod vector competence for transmission of arboviruses

“…It is suggested here that through the S conf GP and S conf Cr terms in Equation 10, the IDRs in the GP and Cr molecules (Fong et al, 2009;Dolan et al, 2015) could control ΔS a_receptor and ΔS a_virus and hence dictate the temperature range over which K a is biologically significant. Thus, based on the estimated change in conformational entropy (ΔΔS conf ) of ∼ 6.1 J/mol/K per amino acid residue in an IDR of a protein (Rajasekaran et al, 2016), "adjusting" ΔS a_virus by ± 500 J/ mol/K would require a change in the order/disorder status of 82 amino acids in the VSV GP/Cr system. This is across seven VSV G proteins (Carneiro et al, 2002) and hence seven Cr molecules and would equate to ∼12 amino acid residues per GP/Cr pair.…”

Using thermodynamic parameters to calibrate a mechanistic dose-response for infection of a host by a virus

“…−4958 kJ/mol for VSV binding to PL bilayers (Carneiro et al, 2002) Entropy term, ΔS a Component entropy terms ΔS solvent Likely to be positive as disordering and hence entropy of water solvent molecules displaced from GP/Cr contact surfaces during binding may increase +401 J/mol/K for antibody binding to its antigen (Bostrom et al, 2011) ΔS conf Negative due to reduction in conformational mobility. Estimated to be −6.1 J/mol/K per amino acid for ordering of disordered regions of proteins (Rajasekaran et al, 2016) −301 J/mol/K for antibody binding to its antigen (Bostrom et al, 2011) ΔS rt Negative for all interactions when a particle is immobilised on a surface.…”

“…Many ligand binding proteins have intrinsically disordered regions (IDRs) which undergo a disorder-to-order transition on or near the interface on binding the ligand (Fong et al, 2009) decreasing the entropy such that ΔS conf is negative (Rajasekaran et al, 2016). Viral proteins are rich in intrinsic disorder (Dolan et al, 2015) and intrinsically disordered proteins serve as host cell receptors for viruses.…”

“…Thus increasing ΔS a by 20 J/mol/K (irrespective of the values of ΔH a and T) increases K a by 11-fold. A decrease in conformational entropy (ΔS conf ) due to steric hindrance of 20 J/mol/K represents the ordering of just four amino acid residues on the basis of the −6.1 J/ mol/K per residue proposed by Rajasekaran et al (2016) for disordered proteins. Therefore blocking the disordering of just four amino acids in the EBOV GP could explain the 10-fold decrease in infectivity of EBOV GP pseudoviruses with high GP densities.…”