Advanced ensemble modelling of flexible macromolecules using X-ray solution scattering

Abstract

Dynamic ensembles of macromolecules mediate essential processes in biology. Understanding the mechanisms driving the function and molecular interactions of 'unstructured' and flexible molecules requires alternative approaches to those traditionally employed in structural biology. Small-angle X-ray scattering (SAXS) is an established method for structural characterization of biological macromolecules in solution, and is directly applicable to the study of flexible systems such as intrinsically disordered proteins and multi-domain proteins with unstructured regions. The Ensemble Optimization Method (EOM) [Bernadó et al. (2007 ▶). J. Am. Chem. Soc. 129, 5656-5664] was the first approach introducing the concept of ensemble fitting of the SAXS data from flexible systems. In this approach, a large pool of macromolecules covering the available conformational space is generated and a sub-ensemble of conformers coexisting in solution is selected guided by the fit to the experimental SAXS data. This paper presents a series of new developments and advancements to the method, including significantly enhanced functionality and also quantitative metrics for the characterization of the results. Building on the original concept of ensemble optimization, the algorithms for pool generation have been redesigned to allow for the construction of partially or completely symmetric oligomeric models, and the selection procedure was improved to refine the size of the ensemble. Quantitative measures of the flexibility of the system studied, based on the characteristic integral parameters of the selected ensemble, are introduced. These improvements are implemented in the new EOM version 2.0, and the capabilities as well as inherent limitations of the ensemble approach in SAXS, and of EOM 2.0 in particular, are discussed.

Keywords: hybrid methods; macromolecular dynamics; proteins; small-angle scattering; symmetric oligomers; unstructured biology.

Figure 1

(i) Different views of an example multi-domain protein composed of two domains [solved by MX: (a) grey and (b) yellow], connected by a disordered linker 30 amino acids long (transparent red spheres, left area). (ii) Multiple inter-domain linker reconstructions (multiple colours) computed with EOM (upper-right area). (iii) Different views of multiple inter-domain linker reconstructions computed with EOM 2.0 using the new possibility to fix domain positions in three-dimensional coordinates (bottom-right area).

Figure 2

Different views of a hexameric multi-domain protein with a symmetric oligomeric core. Each monomer is composed of two domains connected by a flexible linker and with disordered N- and C-termini. (a) Generated full-length hexamer where P6 symmetry is applied to the core and to the disordered regions. (b) Asymmetric modelling where the generated chains are independent of each other and the symmetry is present in the core only.

Figure 3

Qualitative characterization of particle flexibility from various characteristic R _g distributions. (a) Pool (black), which represents the case of complete randomness; EOM(1) (purple), EOM(2) (orange), EOM(3) (pink) and EOM(4) (dark green) which represent the real outcome of independent EOM 2.0 runs in terms of R _g distributions; uniform (cyan), compact (light blue), bimodal (red) which represent extreme (theoretical) cases. (b) H _b(S) values computed from the distributions in (a). (c) Combination of R _flex values for all the distributions (and compared to the threshold of randomness computed from the pool, in brackets, ∼89%) with the associated R _σ values. The last example (red curve) indicates a potentially inconsistent result.

Figure 4

Distribution of end-to-end distances computed from pools containing 10 000 structures of 100 and 500 amino-acid chains and compared with the expected normal distribution having the same mean and standard deviation values.

Figure 5

Distributions of R _g pools (blue) and selected ensembles (red) for determination of open and closed conformations of calmodulin using three different lengths of inter-domain disordered linkers (zero, six and 12 amino acids) for the pool generation. Violet and light blue triangles show R _g for closed and open conformations, respectively.

Figure 6

Comparison of R _g distributions showing that subpopulations of conformers can be identified from a large ensemble if the difference between their mean R _g is greater than approximately two times the standard deviations of the original pool (bottom left). The R _g values of the two subpopulations are indicated as vertical lines on each plot.

Figure 7

Characterization of the flexibility of uPAR^WT and the mutated uPAR^H47C-N259C using EOM 2.0. (a) Size distributions (R _g) of uPAR^WT and uPAR^H47C-N259C, providing only a qualitative assessment through direct comparison of the distributions of the selected ensembles and the pool. (b) The metrics R _flex and R _σ enable characterization of the flexibility quantitatively, with R _flex = ∼82% and R _flex = ∼45%, for uPAR^WT and uPAR^H47C-N259C, respectively, reflecting a significant change in compactness of the particle upon mutation (with a threshold of randomness of ∼85% calculated from the pool).