Toward a quantitative theory of intrinsically disordered proteins and their function

Abstract

A large number of proteins are sufficiently unstable that their full 3D structure cannot be resolved. The origins of this intrinsic disorder are not well understood, but its ubiquitous presence undercuts the principle that a protein's structure determines its function. Here we present a quantitative theory that makes predictions regarding the role of intrinsic disorder in protein structure and function. In particular, we discuss the implications of analytical solutions of a series of fundamental thermodynamic models of protein interactions in which disordered proteins are characterized by positive folding free energies. We validate our predictions by assigning protein function by using the gene ontology classification--in which "protein binding", "catalytic activity", and "transcription regulator activity" are the three largest functional categories--and by performing genome-wide surveys of both the amount of disorder in these functional classes and binding affinities for both prokaryotic and eukaryotic genomes. Specifically, without assuming any a priori structure-function relationship, the theory predicts that both catalytic and low-affinity binding (K(d) greater, >or= 0(-7) M) proteins prefer ordered structures, whereas only high-affinity binding proteins (found mostly in eukaryotes) can tolerate disorder. Relevant to both transcription and signal transduction, the theory also explains how increasing disorder can tune the binding affinity to maximize the specificity of promiscuous interactions. Collectively, these studies provide insight into how natural selection acts on folding stability to optimize protein function.

Fig. 1.

Disorder distribution. Normalized histograms of the percentage of disordered residues (see Materials and Methods) in the sequence of human (H. sapiens), yeast (S. cerevisiae) and E. coli (K-12) proteins within the gene ontology (11) categories of “protein binding”, “catalytic activity”, and “transcription regulator activity”. The distributions after removing the overlap between the three categories are shown by the lower bars (shaded). All distributions are normalized to the total number of proteins in each category noted in the upper right corner of each frame. In humans, contrary to the bias of transcription and catalytic proteins to be significantly more disordered and ordered, respectively, binding proteins indicate that disorder is neither strongly favored nor disfavored. The statistical significance of these results, based on a Kolmogorov–Smirnov test (37), is P < 10⁻¹⁵⁰. In yeast, although binding and catalytic proteins show the same trend as occurs in higher eukaryotes, transcription proteins overall show no significant preference for order or disorder. In E. coli, all three functions show strikingly similar distributions favoring ordered structures. Similar distributions were found in other eukaryotic and prokaryotic genomes.

Fig. 2.

Binding and catalytic efficiency. (A) Ratio of complex concentration [FS]_bind as given by Eq. 3 to maximum concentration [FS]_bind^max (ΔG_f ≪ 0). c_p = c_s = 1 μM. Vertical dash-dotted lines indicate the folding free energy for 90% (dashed lines for 97%) binding efficiency ([FS]_bind/[FS]_bind^max with K_d^c = 10⁻⁵ and 10⁻¹⁰ M, respectively. To maintain high binding efficiency, weak binding requires negative ΔG_f (prefers order), whereas strong binding allows positive ΔG_f (tolerates disorder). (B) Fractional production rate for catalytic activity relative to maximum catalytic rate V_cat^max (ΔG_f ≪ 0) as given by Eq. 4 ([S] = 1 μM). The vertical dash-dotted line indicates the folding free energy for 90% (dashed line for 97%) catalytic efficiency (V_cat/V_cat^max) with all relevant K_m^c. To maintain high catalytic efficiency, negative ΔG_f (ordered structure) is required for the whole range of physiological parameters shown here. Note that to allow for fast conversion, enzyme–substrate interactions (characterized by the Michaelis constant K_m) are limited to much weaker interactions than those of binding proteins (K_d).

Fig. 3.

Maximum discrimination in binding to similar substrates. The solid curve shows the equilibrium complex concentration [FS]_bind (Eq. 3) normalized by the strong binding limit [FS]_bind^strong (K_d^exp → 0). c_p = c_s is used without losing generality. Each pair of vertical lines shows the relative amount of bound complex formed by two different substrates with a binding free energy difference of 1.5 kcal/mol. For strong binding, the complex concentration saturates, and there is almost no difference in the amount of complex formed by either substrate (dashed lines). On the other hand, decreasing the experimental binding affinity by destabilizing the folded state (F) enhances complex formation by the stronger binding substrate relative to the weaker one (dash-dotted lines).

Fig. 4.

Distributions of experimentally measured protein–ligand binding affinities. Data are taken from the PDBbind database (version 2007). The overall distributions are consistent with our hypothesis that the lack of disorder in prokaryotes could be due to their relatively weaker binding affinities (≳10⁻⁷ M).

Fig. 5.

Intrinsic disorder as a function of protein length for proteins with (nonoverlapping) binding, transcription, and catalytic function (large circles), and for proteins with more than one function, as indicated by the colored arrows from each individual functional category (smaller circles). For each polar coordinate plot, the radial and angular (counterclockwise) coordinates correspond to protein length in a log-scale and the percentage of residues that are classified as disordered for the protein (as in Fig. 1), respectively. For clarity, percent disorder and protein length are labeled only in transcription and catalysis plots, respectively. Indicated outside each circle is the percentage of proteins in each functional category relative to the total number of proteins for which the function has been annotated for each organism (i.e., 15,260, 5,900, and 1,362 for human, yeast and E. coli, respectively). The figure shows that disorder does not correlate with protein length for well-sampled functional categories. The analysis of disorder in multifunctional proteins also reveals interesting patterns. Specifically, binding does not seem to impact the level of disorder of either transcription or catalytic proteins, whereas disorder in proteins with both catalytic and transcription functionalities appear to follow either one of the patterns found for the individual functions.