Sizes, conformational fluctuations, and <scp>SAXS</scp> profiles for intrinsically disordered proteins

The preponderance of intrinsically disordered proteins (IDPs) in the eukaryotic proteome, and their ability to interact with each other, and with folded proteins, RNA, and DNA for functional purposes, have made it important to quantitatively characterize their biophysical properties. Toward this end, we developed the transferable self-organized polymer (SOP-IDP) model to calculate the properties of several IDPs. The values of the radius of gyration ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>R</mml:mi> <mml:mi>g</mml:mi></mml:msub> </mml:mrow> <mml:annotation>$$ {R}_g $$</mml:annotation></mml:semantics> </mml:math> ) obtained from SOP-IDP simulations are in excellent agreement (correlation coefficient of 0.96) with those estimated from SAXS experiments. For AP180 and Epsin, the predicted values of the hydrodynamic radii ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>R</mml:mi> <mml:mi>h</mml:mi></mml:msub> <mml:mi>s</mml:mi></mml:mrow> <mml:annotation>$$ {R}_h\mathrm{s} $$</mml:annotation></mml:semantics> </mml:math> ) are in nearly quantitative agreement with those from fluorescence correlation spectroscopy (FCS) experiments. Strikingly, the calculated SAXS profiles for 36 IDPs are also nearly superimposable on the experimental profiles. The dependence of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>R</mml:mi> <mml:mi>g</mml:mi></mml:msub> </mml:mrow> <mml:annotation>$$ {R}_g $$</mml:annotation></mml:semantics> </mml:math> and the mean end-to-end distance ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>R</mml:mi> <mml:mi>ee</mml:mi></mml:msub> </mml:mrow> <mml:annotation>$$ {R}_{ee} $$</mml:annotation></mml:semantics> </mml:math> ) on chain length, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>N</mml:mi></mml:mrow> <mml:annotation>$$ N $$</mml:annotation></mml:semantics> </mml:math> , follows Flory's scaling law, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>R</mml:mi> <mml:mi>α</mml:mi></mml:msub> <mml:mo>≈</mml:mo> <mml:msub><mml:mi>a</mml:mi> <mml:mi>α</mml:mi></mml:msub> <mml:msup><mml:mi>N</mml:mi> <mml:mn>0.588</mml:mn></mml:msup> </mml:mrow> <mml:annotation>$$ {R}_{\alpha}\approx {a}_{\alpha }{N}^{0.588} $$</mml:annotation></mml:semantics> </mml:math> ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>α</mml:mi> <mml:mo>=</mml:mo> <mml:mi>g</mml:mi> <mml:mo>,</mml:mo></mml:mrow> <mml:annotation>$$ \alpha =g, $$</mml:annotation></mml:semantics> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>e</mml:mi></mml:mrow> <mml:annotation>$$ e $$</mml:annotation></mml:semantics> </mml:math> ), suggesting that globally IDPs behave as synthetic polymers in a good solvent. This finding depends on the solvent quality, which can be altered by changing variables such as pH and salt concentration. The values of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>a</mml:mi> <mml:mi>g</mml:mi></mml:msub> </mml:mrow> <mml:annotation>$$ {a}_g $$</mml:annotation></mml:semantics> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>a</mml:mi> <mml:mi>e</mml:mi></mml:msub> </mml:mrow> <mml:annotation>$$ {a}_e $$</mml:annotation></mml:semantics> </mml:math> are 0.20 and 0.48 nm, respectively. Surprisingly, finite size corrections to scaling, expected on theoretical grounds, are negligible for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>R</mml:mi> <mml:mi>g</mml:mi></mml:msub> </mml:mrow> <mml:annotation>$$ {R}_g $$</mml:annotation></mml:semantics> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>R</mml:mi> <mml:mi>ee</mml:mi></mml:msub> </mml:mrow> <mml:annotation>$$ {R}_{ee} $$</mml:annotation></mml:semantics> </mml:math> . In contrast, only by accounting for the finite sizes of the IDPs, the dependence of experimentally measurable <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>R</mml:mi> <mml:mi>h</mml:mi></mml:msub> </mml:mrow> <mml:annotation>$$ {R}_h $$</mml:annotation></mml:semantics> </mml:math> on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>N</mml:mi></mml:mrow> <mml:annotation>$$ N $$</mml:annotation></mml:semantics> </mml:math> can be quantitatively explained using <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics><mml:mrow><mml:mi>ν</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0.588</mml:mn></mml:mrow> <mml:annotation>$$ \nu =0.588 $$</mml:annotation></mml:semantics> </mml:math> . Although Flory scaling law captures the estimates for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>R</mml:mi> <mml:mi>g</mml:mi></mml:msub> </mml:mrow> <mml:annotation>$$ {R}_g $$</mml:annotation></mml:semantics> </mml:math> , <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>R</mml:mi> <mml:mi>ee</mml:mi></mml:msub> </mml:mrow> <mml:annotation>$$ {R}_{ee} $$</mml:annotation></mml:semantics> </mml:math> , and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow><mml:msub><mml:mi>R</mml:mi> <mml:mi>h</mml:mi></mml:msub> </mml:mrow> <mml:annotation>$$ {R}_h $$</mml:annotation></mml:semantics> </mml:math> accurately, the spread of the simulated data around the theoretical curve is suggestive of of sequence-specific features that emerge through a fine-grained analysis of the conformational ensembles using hierarchical clustering. Typically, the ensemble of conformations partitions into three distinct clusters, having different equilibrium populations and structural properties. Without any further readjustments to the parameters of the SOP-IDP model, we also obtained nearly quantitative agreement with paramagnetic relaxation enhancement (PRE) measurements for α-synuclein. The transferable SOP-IDP model sets the stage for several applications, including the study of phase separation in IDPs and interactions with nucleic acids.