VH‐VL interdomain dynamics observed by computer simulations and NMR

Abstract The relative orientation of the two variable domains, VH and VL, influences the shape of the antigen binding site, that is, the paratope, and is essential to understand antigen specificity. ABangle characterizes the VH‐VL orientation by using five angles and a distance and compares it to other known structures. Molecular dynamics simulations of antibody variable domains (Fvs) reveal fluctuations in the relative domain orientations. The observed dynamics between these domains are confirmed by NMR experiments on a single‐chain variable fragment antibody (scFv) in complex with IL‐1β and an antigen‐binding fragment (Fab). The variability of these relative domain orientations can be interpreted as a structural feature of antibodies, which increases the antibody repertoire significantly and can enlarge the number of possible binding partners substantially. The movements of the VH and VL domains are well sampled with molecular dynamics simulations and are in agreement with the NMR ensemble. Fast Fourier transformation of the ABangle metrics allows to assign timescales of 0.1‐10 GHz to the fastest collective interdomain movements. The results clearly show the necessity of dynamics to understand and characterize the favorable orientations of the VH and VL domains implying a considerable binding interface flexibility and reveal in all antibody fragments (Fab, scFv, and Fv) very similar VH‐VL interdomain variations comparable to the distributions observed for known X‐ray structures of antibodies. Significance Statement Antibodies have become key players as therapeutic agents. The binding ability of antibodies is determined by the antigen‐binding fragment (Fab), in particular the variable fragment region (Fv). Antigen‐binding is mediated by the complementarity‐determining regions consisting of six loops, each three of the heavy and light chain variable domain VH and VL. The relative orientation of the VH and VL domains influences the shape of the antigen‐binding site and is a major objective in antibody design. In agreement with NMR experiments and molecular dynamics simulations, we show a considerable binding site flexibility in the low nanosecond timescale. Thus we suggest that this flexibility and its implications for binding and specificity should be considered when designing and optimizing therapeutic antibodies.


Significance Statement
Antibodies have become key players as therapeutic agents. The binding ability of antibodies is determined by the antigen-binding fragment (Fab), in particular the variable fragment region (Fv). Antigen-binding is mediated by the complementaritydetermining regions consisting of six loops, each three of the heavy and light chain variable domain V H and V L . The relative orientation of the V H and V L domains influences the shape of the antigen-binding site and is a major objective in antibody design. In agreement with NMR experiments and molecular dynamics simulations, we show a considerable binding site flexibility in the low nanosecond timescale. Thus we suggest that this flexibility and its implications for binding and specificity should be considered when designing and optimizing therapeutic antibodies.

K E Y W O R D S
antibodies, molecular dynamics simulations, NMR, V H and V L domain orientation

| INTRODUCTION
Antibodies have become an important tool in therapeutics and clinical diagnostics. 1,2 This increasing relevance has motivated the development of computational techniques to study antibody structure and function. 3,4 The ability of antibodies to specifically recognize a broad variety of pathogenic molecules is determined by the antigen-binding fragment (Fab), in particular the variable fragment region (Fv). The Fab consists of a heavy and a light chain that can both be subdivided into a variable (Fv) and a constant region. Fab systems are relatively large and remain a challenge in molecular dynamics simulations. Therefore, various studies only consider the Fv fragment to describe and investigate antigen-binding. This reduces the system size and thereby decreases the computational time and costs. 5 The Fv fragment is the focal point of recombination and hypermutation events. [6][7][8][9][10][11] Antigen-binding is mediated by six loops of variable sequence and length denoted as the complementarity-determining regions (CDRs) which are distributed evenly over the heavy and light chain variable domains, V H and V L .
Besides lengths and sequence of the CDRs, the relative orientation of V H and V L is a third very important factor that determines the shape of the antigen-binding site. 12 The variability in orientation of the V H and V L domains to one another is an additional structural feature of antibodies, which directly increases the repertoire of antibody specificity. 13 Modifications of the V H -V L domain orientation directly change the binding site geometry and have an effect on the specificity of the paratope, the antigen-binding site, for target antigens. 14 It has been shown that reducing the system to the variable regions might not always be sufficient to characterize the antigen-binding process with molecular dynamics simulations, because of possible stabilization in the Fab by C H 1-C L . 5 Still, the characterization of the V H -V L domain orientation is crucial in understanding the antigen-binding process. Antibodyantigen binding can be understood in terms of the conformational selection mechanism. 15,16 This paradigm follows the idea of an ensemble of preexisting conformations with different probabilities from which the binding competent state is selected. Transitions between different states in this preexisting conformational space can occur on different timescales, and therefore characterization of the thermodynamics and kinetics is vital to understand their conformational diversity. 17 This work uses experimental Nuclear Magnetic Resonance (NMR) Nuclear Overhauser Effect (NOE) data in combination with molecular dynamics simulations to understand the V H -V L domain movements.
We compare the V H -V L domain orientation observed in our simulations to the NMR ensemble of a single-chain variable fragment 18 (scFv) and the corresponding antigen-binding fragment (Fab). The scFv is the smallest fragment to retain full binding activity and can bind a target protein the same way a Fab does. 19 The systems studied by simulations with and without NOE time-averaged restraints are shown in Figure 1. We analyzed this potential therapeutic antibody targeted at the cytokine IL-1β. 20 Human IL-1β is an active proinflammatory cytokine and is a key orchestrator in autoinflammatory and immune responses. 21 IL-1β signaling requires the assembly of a heterotrimeric complex consisting of the IL-1β, the interleukin-1 receptor type I (IL-1RI), and the interleukin-1 receptor accessory protein (IL-1RAcP). Neutralization of IL-1β can be achieved with a therapeutic antibody by interfering either with the binding to the IL-1RI or the interaction between IL-1β and IL-1RAcP. 22

| METHODS
The NOEs and suggested structures for the scFv complex and the Fab were provided by the group of Mark Carr at University Leicester. 19,23 The first structure of the NMR ensemble of the scFv-IL-1β complex with the Protein Data Bank (PDB) Code (2KH2) was used as a starting structure for further simulations. The published NMR ensemble of the complex scFv will be referred to as "minimized NMR ensemble". In contrast to this, simulations performed with NOE restraints will be referred to as "simulated NMR ensemble." In addition, we removed IL-1β and the glycine-serine linker (G4S) and simulated the scFv and the Fv to understand the influence of complexation and the linker on the flexibility in these angles.
All structures were prepared in MOE (Molecular Operating Environment, Montreal, QC, Canada: 2018) 23 using the Protonate 3D 24 tool. The C-termini of the Fv structures were capped with N-methylamine. With the tleap tool of the AmberTools16 25 package, the two systems were placed into cubic water boxes of TIP3P 26 water molecules with a minimum wall distance to the protein of 10 Å. Parameters for all antibody simulations were derived from the AMBER force field 14SB. 27 To neutralize the charges, we used uniform background charges. Each system was carefully equilibrated using a multistep equilibration protocol. 28

| Molecular dynamics simulations
The scFv with and without IL-1β, Fv, and the Fab structures were simulated for 1 μs using molecular dynamics as implemented in the AMBER 18 simulation package. 29 Molecular dynamics simulations were performed in an NpT ensemble using pmemd.cuda. 30 Bonds involving hydrogen atoms were restrained by applying the SHAKE algorithm, 31 allowing a time step of 2.0 fs. Atmospheric pressure of the system was preserved by weak coupling to an external bath using the Berendsen algorithm. 32 The Langevin thermostat was used to maintain the temperature at 300K during simulations. 33

| NOE restraints simulations-NMR ensemble
The NOE distances are intramolecular NOEs and define the distances between amide protons. 34 The NOE values were converted on the basis of peak intensities into distances with upper limits of 5.0 Å (strong), 6.5 Å (medium), and 8.0 Å (weak). The structures were minimized, equilibrated, and then simulated for 1 μs using the NOE distance restraints (1141 for the complex scFv and 556 for the Fab) including time-averaged constraints 34,35 in an NpT ensemble using pmemd.cuda, 30 following the same parameters as described in Section 2.1. A time constant for the memory function for the distance restraints of 100 ns was chosen.  Figure S3. To obtain a simulated NMR ensemble, the provided NOEs of the scFv complex were used and the results are shown in Figure 3. Figure 3 shows in all metrics a very similar distribution as observed without linker, without NOE distance restraints, without the presence of antigen and confirms the high variability in the relative domain orientations. The overlay of the HL distribution of the scFv with the Fv is illustrated in Figure S7 and reveals a very similar distribution. To underline very similar distributions, Figure 4 compares the simulations with and without the presence of IL-1β and with and without NOE distance restraints. It clearly shows that the relative interdomain dynamics captured without antigen follow the conformational selection paradigm, because we seem to find the dynamics involved in antigen binding. Figure S6 Figure 7D, while the dynamics slower than 10 ns are displayed in Figure 7B.  17,44 Understanding the role of the C H 1 and C L domains is crucial in characterizing the antigen-binding process and has therefore been targeted by various experimental and computational studies. 45 The presence of the constant domains C H 1 and C L in the Fab has been discussed to have stability benefits in terms of interdomain orientation; 5 however, this also might be a consequence of too short timescales considered.

| ABangle
NMR experiments directly compared the complexed scFv with a Fab  Figure S5 and Figure S9) is dominated by dynamics occurring on frequencies <0.1 GHz. Thus this could be the functionally relevant dynamics, whereas faster motions are harmonic fluctuations that can or cannot be coupled to slower dynamics. Figure S9 clearly points out that in terms of frequencies of motions, the HL angle distribution is again dominated by movements slower than 10 ns, although no substantial differences in amplitude with and without experimental restraints and upon binding could be identified.

| CONCLUSION
In this study, the combination of experimental NOE data with molec-

AUTHOR CONTRIBUTIONS
The manuscript was discussed and written through contributions of all authors. All authors have given approval to the final version of the manuscript.