Conformer selection and induced fit in flexible backbone protein-protein docking using computational and NMR ensembles

Accommodating backbone flexibility continues to be the most difficult challenge in computational docking of protein-protein complexes. Towards that end, we simulate four distinct biophysical models of protein binding in RosettaDock, a multiscale Monte-Carlo-based algorithm that uses a quasi-kinetic search process to emulate the diffusional encounter of two proteins and to identify low-energy complexes. The four binding models are as follows: (1) key-lock (KL) model, using rigid-backbone docking; (2) conformer selection (CS) model, using a novel ensemble docking algorithm; (3) induced fit (IF) model, using energy-gradient-based backbone minimization; and (4) combined conformer selection/induced fit (CS/IF) model. Backbone flexibility was limited to the smaller partner of the complex, structural ensembles were generated using Rosetta refinement methods, and docking consisted of local perturbations around the complexed conformation using unbound component crystal structures for a set of 21 target complexes. The lowest-energy structure contained > 30% of the native residue-residue contacts for 9, 13, 13, and 14 targets for KL, CS, IF, and CS/IF docking, respectively. When applied to 15 targets using nuclear magnetic resonance ensembles of the smaller protein, the lowest-energy structure recovered at least 30% native residue contacts in 3, 8, 4, and 8 targets for KL, CS, IF, and CS/IF docking, respectively. CS/IF docking of the nuclear magnetic resonance ensemble performed equally well or better than KL docking with the unbound crystal structure in 10 of 15 cases. The marked success of CS and CS/IF docking shows that ensemble docking can be a versatile and effective method for accommodating conformational plasticity in docking and serves as a demonstration for the CS theory—that binding-competent conformers exist in the unbound ensemble and can be selected based on their favorable binding energies.     

Refining conformational ensembles of flexible proteins against small-angle x-ray scattering data

Intrinsically disordered proteins and flexible regions in multidomain proteins display substantial conformational heterogeneity. Characterizing the conformational ensembles of these proteins in solution typically requires combining one or more biophysical techniques with computational modeling or simulations. Experimental data can either be used to assess the accuracy of a computational model or to refine the computational model to get a better agreement with the experimental data. In both cases, one generally needs a so-called forward model (i.e., an algorithm to calculate experimental observables from individual conformations or ensembles). In many cases, this involves one or more parameters that need to be set, and it is not always trivial to determine the optimal values or to understand the impact on the choice of parameters. For example, in the case of small-angle x-ray scattering (SAXS) experiments, many forward models include parameters that describe the contribution of the hydration layer and displaced solvent to the background-subtracted experimental data. Often, one also needs to fit a scale factor and a constant background for the SAXS data but across the entire ensemble. Here, we present a protocol to dissect the effect of the free parameters on the calculated SAXS intensities and to identify a reliable set of values. We have implemented this procedure in our Bayesian/maximum entropy framework for ensemble refinement and demonstrate the results on four intrinsically disordered proteins and a protein with three domains connected by flexible linkers. Our results show that the resulting ensembles can depend on the parameters used for solvent effects and suggest that these should be chosen carefully. We also find a set of parameters that work robustly across all proteins.     

A multidomain flexible docking approach to deal with large conformational changes in the modeling of biomolecular complexes

Binding-induced backbone and large-scale conformational changes represent one of the major challenges in the modeling of biomolecular complexes by docking. To address this challenge, we have developed a flexible multidomain docking protocol that follows a "divide-and-conquer" approach to model both large-scale domain motions and small- to medium-scale interfacial rearrangements: the flexible binding partner is treated as an assembly of subparts/domains that are docked simultaneously making use of HADDOCK's multidomain docking ability. For this, the flexible molecules are cut at hinge regions predicted using an elastic network model. The performance of this approach is demonstrated on a benchmark covering an unprecedented range of conformational changes of 1.5 to 19.5 ?. We show from a statistical survey of known complexes that the cumulative sum of eigenvalues obtained from the elastic network has some predictive power to indicate the extent of the conformational change to be expected.     

CIRSE: a solvation energy estimator compatible with flexible protein docking and design applications

We present the Coordinate Internal Representation of Solvation Energy (CIRSE) for computing the solvation energy of protein configurations in terms of pairwise interactions between their atoms with analytic derivatives. Currently, CIRSE is trained to a Poisson/surface-area benchmark, but CIRSE is not meant to fit this benchmark exclusively. CIRSE predicts the overall solvation energy of protein structures from 331 NMR ensembles with 0.951+/-0.047 correlation and predicts relative solvation energy changes between members of individual ensembles with an accuracy of 15.8+/-9.6 kcal/mol. The energy of individual atoms in any of CIRSE's 17 types is predicted with at least 0.98 correlation. We apply the model in energy minimization, rotamer optimization, protein design, and protein docking applications. The CIRSE model shows some propensity to accumulate errors in energy minimization as well as rotamer optimization, but these errors are consistent enough that CIRSE correctly identifies the relative solvation energies of designed sequences as well as putative docked complexes. We analyze the errors accumulated by the CIRSE model during each type of simulation and suggest means of improving the model to be generally useful for all-atom simulations.     

SPEACH_AF: Sampling protein ensembles and conformational heterogeneity with Alphafold2

The unprecedented performance of Deepmind’s Alphafold2 in predicting protein structure in CASP XIV and the creation of a database of structures for multiple proteomes and protein sequence repositories is reshaping structural biology. However, because this database returns a single structure, it brought into question Alphafold’s ability to capture the intrinsic conformational flexibility of proteins. Here we present a general approach to drive Alphafold2 to model alternate protein conformations through simple manipulation of the multiple sequence alignment via in silico mutagenesis. The approach is grounded in the hypothesis that the multiple sequence alignment must also encode for protein structural heterogeneity, thus its rational manipulation will enable Alphafold2 to sample alternate conformations. A systematic modeling pipeline is benchmarked against canonical examples of protein conformational flexibility and applied to interrogate the conformational landscape of membrane proteins. This work broadens the applicability of Alphafold2 by generating multiple protein conformations to be tested biologically, biochemically, biophysically, and for use in structure-based drug design.     

A combinatorial approach to protein docking with flexible side chains.

Rigid-body docking approaches are not sufficient to predict the structure of a protein complex from the unbound (native) structures of the two proteins. Accounting for side chain flexibility is an important step towards fully flexible protein docking. This work describes an approach that allows conformational flexibility for the side chains while keeping the protein backbone rigid. Starting from candidates created by a rigid-docking algorithm, we demangle the side chains of the docking site, thus creating reasonable approximations of the true complex structure. These structures are ranked with respect to the binding free energy. We present two new techniques for side chain demangling. Both approaches are based on a discrete representation of the side chain conformational space by the use of a rotamer library. This leads to a combinatorial optimization problem. For the solution of this problem, we propose a fast heuristic approach and an exact, albeit slower, method that uses branch-and-cut techniques. As a test set, we use the unbound structures of three proteases and the corresponding protein inhibitors. For each of the examples, the highest-ranking conformation produced was a good approximation of the true complex structure.     

Internal estimation and controlled selection with applications to sheep

Summary This paper examines the relationship of economic weights, a _i, with a general economic value surface. It is inferred that the a _i may vary across the population, as they can depend on the mean vector for the characters of interest. It is shown how these ideas extend to provide simple mechanisms for controlled selection. The problem of estimation is raised, and it is suggested that the procedures can be efficiently implemented, even in small populations, by a system of internal parameter estimation. This makes the entire selection programme independent of externally generated estimates of genetic parameters.     

A flexible docking scheme to explore the binding selectivity of PDZ domains

Modeling of protein binding site flexibility in molecular docking is still a challenging problem due to the large conformational space that needs sampling. Here, we propose a flexible receptor docking scheme: A dihedral restrained replica exchange molecular dynamics (REMD), where we incorporate the normal modes obtained by the Elastic Network Model (ENM) as dihedral restraints to speed up the search towards correct binding site conformations. To our knowledge, this is the first approach that uses ENM modes to bias REMD simulations towards binding induced fluctuations in docking studies. In our docking scheme, we first obtain the deformed structures of the unbound protein as initial conformations by moving along the binding fluctuation mode, and perform REMD using the ENM modes as dihedral restraints. Then, we generate an ensemble of multiple receptor conformations (MRCs) by clustering the lowest replica trajectory. Using ROSETTA LIGAND , we dock ligands to the clustered conformations to predict the binding pose and affinity. We apply this method to postsynaptic density‐95/Dlg/ZO‐1 (PDZ) domains; whose dynamics govern their binding specificity. Our approach produces the lowest energy bound complexes with an average ligand root mean square deviation of 0.36 Å. We further test our method on (i) homologs and (ii) mutant structures of PDZ where mutations alter the binding selectivity. In both cases, our approach succeeds to predict the correct pose and the affinity of binding peptides. Overall, with this approach, we generate an ensemble of MRCs that leads to predict the binding poses and specificities of a protein complex accurately.     

Selection and flexible optimization of binding modes from conformation ensembles

This paper describes a new semi-flexible docking approach named Fado (flexible alignment and docking), which incorporates flexibility by using an ensemble of precomputed ligand conformers. A primary ligand is defined as a linear combination over all input conformers. An optimization with regard to the linear coefficients makes the ligand flexible. Initially, a point matching problem utilizing the Merck Molecular Force Field (MMFF) is modeled in order to compute the correct orientation of the ligand with respect to the target. The problem is then solved through a local optimization approach (RPROP). This is done for 20 randomized ligand orientations, yielding 20 binding modes per complex. Evaluating these modes illustrates that our method is able to reproduce the binding modes of molecules within a few minutes of CPU time. A representative dataset of diverse protein-ligand complexes could be reproduced with 78% accuracy below 2A RMSD distance to the reference crystal structure. Fado is available upon request to the authors (see also http://www.zib.eu/Numerik/projects/docking/projectlong.en.html).     

Quantum clustering and network analysis of MD simulation trajectories to probe the conformational ensembles of protein-ligand interactions

In this article, we present a novel application of a quantum clustering (QC) technique to objectively cluster the conformations, sampled by molecular dynamics simulations performed on different ligand bound structures of the protein. We further portray each conformational population in terms of dynamically stable network parameters which beautifully capture the ligand induced variations in the ensemble in atomistic detail. The conformational populations thus identified by the QC method and verified by network parameters are evaluated for different ligand bound states of the protein pyrrolysyl-tRNA synthetase (DhPylRS) from D. hafniense. The ligand/environment induced re-distribution of protein conformational ensembles forms the basis for understanding several important biological phenomena such as allostery and enzyme catalysis. The atomistic level characterization of each population in the conformational ensemble in terms of the re-orchestrated networks of amino acids is a challenging problem, especially when the changes are minimal at the backbone level. Here we demonstrate that the QC method is sensitive to such subtle changes and is able to cluster MD snapshots which are similar at the side-chain interaction level. Although we have applied these methods on simulation trajectories of a modest time scale (20 ns each), we emphasize that our methodology provides a general approach towards an objective clustering of large-scale MD simulation data and may be applied to probe multistate equilibria at higher time scales, and to problems related to protein folding for any protein or protein-protein/RNA/DNA complex of interest with a known structure.     

Automated docking of ligands to antibodies: methods and applications

Many approaches to studying protein-ligand interactions by computational docking are currently available. Given the structures of a protein and a ligand, the ultimate goal of all docking methods is to predict the structure of the resulting complex. This requires a suitable representation of molecular structures and properties, search algorithms to efficiently scan the configuration space for favorable interaction geometries, and accurate scoring functions to evaluate and rank the generated orientations. For many of the available methods, tests on experimentally known antibody-antigen or antibody-hapten complexes have appeared in the literature. In addition, some of them have been used in predictive studies on antibody-ligand interactions to provide structural insights where adequate experimental information is missing. The AutoDock program is presented as example of a method for flexibly docking ligands to antibodies. Applying parameters of the second-generation AMBER force field, three antibody-hapten complexes (AN02, DB3, NC6.8) are used as new test cases to analyze the ability of the method to reproduce experimental findings. The X-ray structures could be reconstituted and the corresponding solutions were ranked with best energy score in all cases. Docking to the free instead of the complexed NC6.8 structure indicated the limits of the rigid protein treatment, although fairly good guesses about the location of the binding site and the contact residues could still be obtained if conformational flexibility was allowed at least in the ligand.     

Peptide binding to the PDZ3 domain by conformational selection

The PDZ domains, a large family of peptide recognition proteins, bind to the C‐terminal segment of membrane ion channels and receptors thereby mediating their localization. The peptide binding process is not known in detail and seems to differ among different PDZ domains. For the third PDZ domain of the synaptic protein PSD‐95 (PDZ3), a lock‐and‐key mechanism was postulated on the basis of the almost perfect overlap of the crystal structures in the presence and absence of its peptide ligand. Here, peptide binding to PDZ3 is investigated by explicit solvent molecular dynamics (MD) simulations (for a total of 1.3 μs) and the cut‐based free energy profile method for determining free energy barriers and basins. The free energy landscape of apo PDZ3 indicates that there are multiple basins within the native state. These basins differ by the relative orientation of the α2 helix and β2 strand, the two secondary structure elements that make up the peptide binding site. Only the structure with the smallest aperture of the binding site is populated in the MD simulations of the complex whose analysis reveals that the peptide ligand binds to PDZ3 by selecting one of three conformations. Thus, the dynamical information obtained by the atomistic simulations increment the static, that is, partial, picture of the PDZ3 binding mechanism based on the X‐ray crystallography data. Importantly, the simulation results show for the first time that conformational selection is a possible mechanism of peptide binding by PDZ domains in general. Proteins 2012. © 2012 Wiley Periodicals, Inc.     

Modeling of the bacterial luciferase-flavin mononucleotide complex combining flexible docking with structure-activity data

Although the crystal structure of Vibrio harveyi luciferase has been elucidated, the binding sites for the flavin mononucleotide and fatty aldehyde substrates are still unknown. The determined location of the phosphate-binding site close to Arg 107 on the alpha subunit of luciferase is supported here by point mutagenesis. This information, together with previous structure-activity data for the length of the linker connecting the phosphate group to the isoalloxazine ring represent important characteristics of the luciferase-bound conformation of the flavin mononucleotide. A model of the luciferase-flavin complex is developed here using flexible docking supplemented by these structural constraints. The location of the phosphate moiety was used as the anchor in a flexible docking procedure performed by conformation search by using the Monte Carlo minimization approach. The resulting databases of energy-ranked feasible conformations of the luciferase complexes with flavin mononucleotide, omega-phosphopentylflavin, omega-phosphobutylflavin, and omega-phosphopropylflavin were filtered according to the structure-activity profile of these analogs. A unique model was sought not only on energetic criteria but also on the geometric requirement that the isoalloxazine ring of the active flavin analogs must assume a common orientation in the luciferase-binding site, an orientation that is also inaccessible to the inactive flavin analog. The resulting model of the bacterial luciferase-flavin mononucleotide complex is consistent with the experimental data available in the literature. Specifically, the isoalloxazine ring of the flavin mononucleotide interacts with the Ala 74-Ala 75 cis-peptide bond as well as with the Cys 106 side chain in the alpha subunit of luciferase. The model of the binary complex reveals a distinct cavity suitable for aldehyde binding adjacent to the isoalloxazine ring and flanked by other key residues (His 44 and Trp 250) implicated in the active site.