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Continuous Interdomain Orientation Distributions Reveal Components of Binding Thermodynamics

Abstract

The flexibility of biological macromolecules is an important structural determinant of function. Unfortunately, the correlations between different motional modes are poorly captured by discrete ensemble representations. Here, we present new ways to both represent and visualize correlated interdomain motions. Interdomain motions are determined directly from residual dipolar couplings, represented as a continuous conformational distribution, and visualized using the disk-on-sphere representation. Using the disk-on-sphere representation, features of interdomain motions, including correlations, are intuitively visualized. The representation works especially well for multidomain systems with broad conformational distributions.This analysis also can be extended to multiple probability density modes, using a Bingham mixture model. We use this new paradigm to study the interdomain motions of staphylococcal protein A, which is a key virulence factor contributing to the pathogenicity of Staphylococcus aureus . We capture the smooth transitions between important states and demonstrate the utility of continuous distribution functions for computing the reorientational components of binding thermodynamics. Such insights allow for the dissection of the dynamic structural components of functionally important intermolecular interactions.

Introduction

Dynamics of biological macromolecules over various spatial and time scales are essential for biological functions such as molecular recognition, catalysis, and signaling. Multiple studies have demonstrated that interdomain motions are a crucial component of the dynamics associated with molecular recognition [1], [2], [3]. Protein and RNA molecules can rearrange interdomain orientations upon binding, thereby enabling adaptive conformational changes that are accompanied by contributions to the free energy, internal energy, and entropy of binding. Despite the recent interest in studying interdomain motions, one challenge of studying such motions is the lack of effective representations. Using the discrete ensemble representation, correlations between different motional modes are not directly captured. Here, we present a new paradigm to represent and visualize correlated interdomain motions. We represent interdomain motions as a continuous distribution on SO(3) (3D rotational space) and parameterize the correlations directly. By using the continuous representation, correlations are quantified directly from experimental observables. In addition, this continuous representation enables the computation of the re-orientational components of the free energy, internal energy, and entropy of binding. We also design a visualization method called the disk-on-sphere (DoS) drawing to visualize the spatial dynamic information (see Fig. 1). Features of the interdomain motions, including geometry and correlations of these motions, are effectively represented in the DoS visualization. Finally, unlike discrete ensemble representations, the continuous representation of orientational distributions is not over-fit, requires no non-physical assumptions, and can be computed directly from the measured RDCs (see section "Interdomain orientations can be represented as a continuous distribution").

Staphylococcal protein A (SpA) is a key virulence factor that supports the invasion of Staphylococcus aureus into the human body. SpA binds to an array of targets in the host to disarm the immune system, facilitate the colonization, and consequently contribute to the pathogenicity of S. aureus. The emergence of antibiotic-resistant S. aureus strains has driven the search for vaccines with high efficacy to counteract several virulence factors, including SpA [6]. Targeting virulence as opposed to bacterial cell growth may be a more effective way to avoid the emergence of resistant strains. Structural studies of SpA and its interaction with host proteins would support rational design of improved vaccines or other therapeutics to diminish S. aureus virulence. The binding targets of SpA include the Fc region of antibodies, the Fab region of VH3 antigen receptors (e.g., IgM) on B cells, TNFR1, and EGFR [7], [8], [9]. There are five tandem functional domains in the N-terminal half of SpA (SpA-N). The five domains share a high sequence identity and they are structurally and functionally similar [8], [10], [11]. Recent studies indicate a correlation between the functional plasticity and the structural flexibility of SpA-N [10], [12], [13].

Given the limited current knowledge of SpA-N interdomain motions, we undertook an NMR study as an initial effort to understand the link between structural flexibility and functional plasticity. NMR spin relaxation experiments identified a 6-residue flexible interdomain linker and interdomain motions. To obtain spatial dynamic information, we measured residual dipolar couplings (RDCs) from two SpA-N domains with multiple alignments. The interdomain motions of SpA-N were analyzed using the new paradigm. Significant correlations were observed in the orientational distribution, indicating that the motion populates some interdomain orientations more than others. A novel statistical thermodynamic analysis of the observed orientational distribution suggests that it is among the energetically most favorable orientational distributions for binding to antibodies. Thus, the affinity is enhanced by an orientationally pre-posed distribution of interdomain orientations while maintaining the flexibility is presumably required for function.

Section snippets

The linkers between SpA-N tandem domains are highly flexible

SpA-N has five tandem domains (E–D–A–B–C). Each domain is a three-helix bundle. NMR structural studies suggest that there are unstructured regions between domains, each consisting of 6 to 10 residues [14]. However, the flexibility of these unstructured regions has not been directly measured. Hence, we conducted NMR spin relaxation experiments to measure the flexibility at picosecond to nanosecond timescale. Instead of using the five domains of SpA-N, we replaced E/D/A/C domains with B domain

Discussion

Previous studies have shown that calculations in structural biology that rely on discrete conformational ensembles are brittle. Instead, the continuous nature of proteins must be taken into account in order to avoid overtting and brittle changes in energetics as one moves between discrete structures. Only in the limit can a discrete ensemble approximate a continuous distribution adequately, and this limiting case is far too expensive for any computer. In the absence of a continuous model,

Molecular cloning and protein preparation

The 5B and Z-I2LBT-mutA-C genes were synthesized by GENEWIZ, Inc. and then cloned into pAED4. The design of Z-I2LBT-mutA-C was based on the Z-I2LBT-mutA construct [19]. The amino acid sequence of Z-I2LBT-mutA-C is "MVDNKFNKEQQNAFYEILHLPNLNEEQRNAFIQSLKDYIDTNNDGAYEGDELQSANLLAEAKKLNDAQAPKADNKFNKEQQNAFYEILHLPNLTEEQRNGFIQSLKDDPSVSKEILAEAKKLNDAQAPK." The NHis-Z-I2LBT-mutA-C gene (Z-I2LBT-mutA-C with a 6   × His tag fused to the N-terminus) was constructed by inserting the Z-I2LBT-mutA-C into pET28a

Acknowledgments

We thank Drs. Hashim Al-Hashimi, Mark Hallen, Swati Jain, Pablo Gainza, James Prestegard, and Ken Dill, Mr. Hunter Nisonoff, and Ms. Rachel Kositsky for their helpful discussions. A portion of this work was conducted at Duke NMR center. We would like to thank Dr. Ronald Venters, Dr. Anthony Ribeiro, and Mr. Donald Mika for their constant help. The work was supported by NIH grants R01-GM-78031 (to B.R.D.), R01-GM-118543 (to B.R.D.), and R01-GM-081666 (to T.G.O.).

Author Contributions: Y.Q.,

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