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Transmembrane Protein Docking with JabberDock
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Transmembrane Protein Docking with JabberDock
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Cite this: J. Chem. Inf. Model. 2021, 61, 3, 1493–1499
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https://doi.org/10.1021/acs.jcim.0c01315
Published February 26, 2021

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Abstract

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Transmembrane proteins act as an intermediary for a broad range of biological process. Making up 20% to 30% of the proteome, their ubiquitous nature has resulted in them comprising 50% of all targets in drug design. Despite their importance, they make up only 4% of all structures in the PDB database, primarily owing to difficulties associated with isolating and characterizing them. Membrane protein docking algorithms could help to fill this knowledge gap, yet only few exist. Moreover, these existing methods achieve success rates lower than the current best soluble proteins docking software. We present and test a pipeline using our software, JabberDock, to dock membrane proteins. JabberDock docks shapes representative of membrane protein structure and dynamics in their biphasic environment. We verify JabberDock’s ability to yield accurate predictions by applying it to a benchmark of 20 transmembrane dimers, returning a success rate of 75.0%. This makes our software very competitive among available membrane protein–protein docking tools.

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Introduction

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Transmembrane proteins play an essential role as a mediator for many functions critical to an organism’s survival. Situated within a lipid membrane that compartmentalizes two distinct biological regimes, their tasks include sensing, signaling, motility, endocytosis, and anchoring. Their malfunction is responsible for a multitude of diseases, (1) and consequently, they are a frequent target in drug design. The formation of complexes, wherein two or more transmembrane proteins will oligomerize into either helix bundles or β-barrels, is of vital significance to both the function and malfunction of these processes. Yet, of the ∼170,000 structures available on the PDB database, only ∼7000 (4%) are transmembrane proteins (2) despite them making up 20%–30% of the proteome and 50% of all known drug targets. (3) This relatively small number of available structures is primarily due to the greater technical difficulties associated with characterizing them compared to soluble proteins. A computational tool capable of accurately predicting complexes would therefore help address some of this knowledge gap, provide understanding to underlying biological mechanisms, and inform drug design.
A plethora of increasingly sophisticated protein–protein docking approaches have been developed to address the problem of protein assembly prediction. (4) These efforts are nucleated around the community-led CAPRI competition, which is used to identify the most reliable algorithms, promising methodologies and current hurdles. (5) However, the vast majority of these methods center around the docking of two or more soluble proteins. While docking transmembrane proteins is facilitated by limitations on the search space imposed by the lipid bilayer, membrane docking algorithms must consider the impact of the lipid bilayer on a protein’s recognition of a partner in tandem with the solvent. In this context, there are only a small number of tools currently available. MPDock, (6) utilizing existing Rosetta sampling and scoring methods in an integrative modeling context, found a successful high ranking pose in three out of five applied bound complexes. Hurwitz et al.’s program Memdock (7) uses a traditional rigid docking, refinement, reranking method, with energetic terms representing the membrane’s hydrophobic environment included in the final stage. Comparing the performance of Memdock and GRAMM-X (8) on 11 unbound complexes, the authors showed that the first yielded a success rate of 36.4% and the latter of 9.1%. Viswanath et al. used the DOCK/PIPER (9) docking algorithm with an additional reranking step that considered the membrane transfer energy, achieving a success rate of 36.6% for 26 unbound complexes. Testing other software on the same data set, the authors reported success rates of 30%, 46.6%, and 56.6% for ZDOCK+ZRANK, (10,11) CLUSPRO, (12) and GRAMM-X, (8) respectively. All of these approaches were only tested against cases featuring α-helical transmembrane proteins. Koukos et al., using HADDOCK (13) without any specific membrane protein optimization, achieved a blind docking success rate of 19.2% on their dimeric unbound data set of 26 complexes that included β-barrel, monotopic, and α-helix proteins. Of these 26 test cases, 11 featured a pair of integral proteins as binding partners, and only three of these were unbound-ligand-to-unbound-receptor docking. The latter achieved a success rate of 36.4%. HADDOCK has also very recently been combined as a refinement tool with the LightDock (14) docking algorithm and tested against 18 transmembrane-soluble protein complexes, (15) achieving a success rate of 61.1%. At the time of publication, MPDock was presented as a proof of concept, not yet designed for widespread use. The DOCK/PIPER membrane energy reranking tool is available for download, but it must be applied to models obtained independently. Memdock is usable as a web server, although requires input structures to have their solvent-exposed regions manually removed.
We recently released our protein–protein docking software, JabberDock, (16) after testing it against a standard benchmark of 226 soluble complexes developed by the CAPRI community. (17) It obtained a greater than 54% success rate, with the notable achievement that the flexibility of the individual structures made little difference to its overall success. JabberDock’s defining feature is its usage of a novel protein volumetric representation called spatial and temporal influence density (STID) maps, which are built from short molecular dynamics (MD) simulations. STID maps are generated via a physical model describing the protein’s shape and electrostatic and residue-level dynamics. Through a comprehensive benchmark, we identified an ideal cutoff value (isovalue) to transform STID volumetric maps into three-dimensional surfaces. JabberDock docks proteins represented by these shapes, attempting to maximize their surface complementarity. A key characteristic of STID maps is that the ideal isovalue to transform them into shapes emerges naturally from the MD simulation, specifically from the relationship between the solvent accessible surface area and the average STID value. Thus, crucially, it is environmentally independent. This property makes STID maps an attractive representation for membrane proteins, exposed to a biphasic environment. The STID map representative of a transmembrane protein can be obtained by independently simulating the preoriented partners immersed in an explicit lipid bilayer. Docking then requires maximizing the complementarity of two membrane protein surfaces, with the ligand’s translational motion perpendicular to the membrane and rotations into the plane of the bilayer constrained. Preliminary work in this endeavor yielded encouraging results: we predicted the transmembrane dimeric complex formed by bo3 oxidase with our top-scoring pose corroborating available mass photometry data. (18) Herein, we present and test our methodology to dock integral membrane protein dimers, now available in JabberDock as an automated pipeline.

Results

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JabberDock docks transmembrane proteins via a multistage process summarized by the flow diagram in Figure 1 and fully detailed in Methods. In short, JabberDock requires input protein structures to be aligned with the center of mass for the transmembrane region of the proteins at z = 0, where the z-axis is perpendicular to the bilayer plane. In our tests, we obtained these preorientated structures via the OPM server. (19) Structures are repaired where necessary using the Modeller package, (20) before being immersed in a POPE bilayer via the PACKMOL-memgen tool. (21) GROMACS (22) is then used to generate the simulation data using the Amber14SB (23) and SLipid (24) force fields, which enables the generation of STID maps. The maps of both binding partners are then converted into isosurfaces using a predetermined cutoff and docked such that their surface complementarity is maximized (16) (see SI and Figure S2). This surface-based scoring function is effective because it bypasses the need to explicitly handle packing of interfacial atoms, yielding smoother and gentler gradients compared to typical atomistic representations (see SI and Figure S3). Here, the search space is navigated using the particle swarm optimisation algorithm implemented in the POWer optimization engine. (25) On average, our full docking pipeline requires 3 days for simulation and 12 h for docking on our hardware (see details in SI).

Figure 1

Figure 1. JabberDock transmembrane protein docking pipeline. Full details of each step, including a convergence benchmark for Step 4, are available in Methods. This example’s target complex is the homodimer 1Q90 (BF), using 2ZT9 (A) as the ligand (blue) and receptor (red). Step 7 features a representation of the fifth best model; an intermediate success overlaid on the bound structure (gray).

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There does not yet exist a standard transmembrane protein docking benchmark equivalent to the soluble proteins one made available by the CAPRI community. (17) To test JabberDock, we selected all the unbound cases involving pairs of transmembrane proteins within Memdock, (7) HADDOCK, (13) and DOCK/PIPER (9) benchmarks. To avoid testing against similar examples, and thus biasing our statistics, we only selected one representative within test cases featuring greater than 80% sequence homology. This resulted in a diverse benchmark set featuring 20 α-helical complexes. We summarize our results for each test case in Table 1. Full details, including the three metrics used to define success by the CAPRI community (RMSD of the best pose, with its corresponding ratio of correct residue contacts (fnat.) and interfacial RMSD), are given in Table S1, spreadsheet.
Table 1. Results of Membrane Docking Benchmarka
TargetReceptorLigandRank of first successful modelQuality of best pose in top 10
1BL8 (AB)1K4D (C)1K4D (C)2∗∗
1EHK (AB)3S33 (A)3S33 (B)1∗
1H2S (CD)1GU8 (A)2F95 (B)1∗∗
2WIE (AB)3V3C (A)3V3C (A)1∗∗
1E12 (AC)3A7K (A)3A7K (A)2∗
1M56 (AC)3OMI (A)1QLE (C)X–
1Q90 (BF)2ZT9 (A)2ZT9 (A)5∗∗
1ZOY (CD)1YQ3 (C)1YQ3 (D)159–
2QJY (AD)1ZRT (C)1ZRT (C)3∗∗
3CHX (BJ)1YEW (B)1YEW (B)8∗
3KLY (AB)3KCU (A)3KCU (A)5∗∗
3OE0 (AB)3ODU (A)3ODU (A)X–
3RVY (AB)3RW0 (A)3RW0 (A)X–
4DKL (AB)4EA3 (A)4EA3 (A)1∗∗
2NRF (AB)2IC8 (A)2IC8 (A)1*
2VT4 (AB)2Y00 (A)2Y00 (B)8∗∗
3KCU (AB)3Q7K (A)3Q7K (A)1∗
1M0L (AC)1C8S (A)1C8S (A)7∗
2K9J (BA)2RMZ (A)2K1A (A)1∗
2KS1 (BA)2N2A (A)2M0B (A)135–
a

The target complex is provided with two composite chains (name indicated in parentheses), which the receptor and ligand correspond to respectively. The rank of the first successful model, either of acceptable (∗) or intermediate (∗∗) quality as determined by the CAPRI criteria (see Methods), is given along with the quality of the best pose found in the top 10 predictions. X indicates that no successful pose was found within the 300 models produced. See Table S1, spreadsheet, for details.

JabberDock was successful (i.e., yielding at least one acceptable model or better among its top 10 candidates) in 75% of the cases in our benchmark set, producing an intermediate quality success in 40% of cases (see Figure 2, Figure S5 and Table S1). This remarkable performance is explained by JabberDock’s ability to identify the binding interface correctly, primarily due to its sensitivity to the dynamics of individual amino acids. Indeed, as shown in Figure 2a, in nearly every test case, at least one prediction in the top 10 results features a correctly identified binding interface. We also notice that results obtained here are superior to those we reported for JabberDock against soluble proteins (54%). Given that our STID map-based scoring function performs comparatively in a water and membrane environment (see Figure S2), this substantial increase can be explained by the added benefit of a priori knowledge about the orientation of the proteins with respect to the bilayer, coupled with the strict constraints imposed by the lipid membrane.

Figure 2

Figure 2. (a) Quality of best models within the top 10 results for every docking case. For each case, the lowest α-carbon RMSD between the prediction and crystallized homologue is presented against the associated native residue fraction (fnat.). The dark- to light-shaded regions represent the criteria for high to acceptable quality results. Thus, a point landing in one of these regions indicates a success. (b) Percentage of cases yielding an acceptable (purple) and intermediate (pink) success as a function of the number of ranked structures considered as candidate models. The region corresponding to the top 10 models is shaded and magnified in the inset.

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Expanding the pool of candidate structures to the whole 300 models returned by JabberDock does little to improve its overall success rate (with a successful model produced in 85.0% of cases, see Figure 2b), in contrast to other protein docking software and the soluble benchmark. This is because JabberDock returned a top 10 successful model for the majority of cases it dealt with (15 out of 20). The few unsuccessful cases, also challenging for other docking algorithms, possess similar structural features to those complexes in the soluble benchmark that JabberDock found problematic. The NavAb voltage-gated sodium channel (PDB: 3RVY) features an interlocked arrangement where, following the unbound MD simulation, the binding site closed up, preventing the ligand STID surface from navigating into the binding pocket. The wild type cytochrome c oxidase (PDB: 1M56) lacks characteristic surface features (i.e., it is relatively smooth), making it difficult for JabberDock to differentiate between nonbinding and binding regions (see Figure S4). All remaining cases that were not successful featured either, individually or as a combination, surfaces devoid of feature-rich regions (see SI and Figure S4), or relatively small binding interfaces, particularly demanding to identify given the goal of the optimizer to maximize surface complementarity.
Some proteins can form multiple complexes by interacting with different binding partners. In our previous work, (16) we observed that knowledge of a protein’s bound state with a specific partner may facilitate its docking with a different one; i.e., the bound state of the native complex from which the ligand or receptor is sourced can be used as a surrogate for the target complex. Here, we tested this approach with the 1M56 test case, comprised of two binding partners that have had their structures solved as part of an alternative complex. As reported in Table S1, when docking STID maps generated from MD simulations of monomeric binding partners (i.e., extracted from their existing complexes and simulated in the unbound state), none of the 300 candidate models were successful. In contrast, docking STID maps generated from surrogate bound-state conformations (i.e., from simulations of alternative complexes) yielded eight successful poses, the best one at rank 51. This improvement, although not featuring a top 10 successful result, indicates that membrane protein docking may benefit from STID maps representing bound dynamics extracted from other known complexes these membrane proteins are involved with.

Discussion and Conclusion

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We have presented a pipeline enabling our blind soluble protein–protein docking software, JabberDock, to successfully tackle cases involving integral membrane protein dimers. This success is due to the molecular representation we adopt to dock proteins (STID maps), casting electrostatics, dynamics, and the protein’s shape into a single volumetric representation. The preliminary stages in the building of a STID map require an MD simulation; thus, the different characteristics expressed by the protein in both the soluble and lipid environments are encapsulated in the isosurface’s topography. Consequently, other than an extended MD simulation, one only needs to restrict the search space of the ligand in the docking protocol to regions occupied by the lipid membrane. The problem is, therefore, more manageable overall than a soluble protein docking one.
As no standard transmembrane protein docking benchmark exists, we applied JabberDock to an unbound benchmark of 20 transmembrane α-helix proteins taken from three other benchmarks, (7,9,13) which returned a success rate of 75%. These results correspond to correctly identifying seven versus DOCK/PIPER’s two out of eight cases, (9) eight versus Memdock’s four out of eleven cases, (7) and one versus HADDOCK’s one out of three cases (13) (note that two cases were tested by more than one of these methods, hence, 22 individual comparisons from 20 cases). Applying the same difficulty classification method employed by CAPRI to soluble protein docking (see Methods), we see that acceptable models within the top 10 candidates were obtained even for some of the most flexible cases. Unsuccessful cases were primarily those where the STID maps featured flat interfaces, a similar issue encountered with the soluble benchmark set. In this context, we have observed that docking binding partners using STID maps generated from alternative complexes could improve the docking quality of an otherwise unsuccessful docking case. The observed increase in docking accuracy was less significant than what we previously observed for globular proteins, where the improvement yielded several successful complexes in the top 10 predictions. This difference is potentially because the change in dynamics from switching a binding interface from lipids to a protein is smaller than the equivalent with a water solvent. It nevertheless demonstrates that there is scope for increasing JabberDock success rate by refining our STID map representation. Given the success of the results presented here and that previously demonstrated with globular proteins, we expect JabberDock to also perform well with transmembrane-solvent proteins, regardless of whether the ligand is extracellular, periplasmic, or cytoplasmic.

Availability

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JabberDock is available for download under GPL license at https://github.com/degiacom/JabberDock, along with input and target structures used in our benchmark. Authors will release the atomic coordinates of all produced models upon article publication using Durham Research Online Data sets Archive (DRO–DATA).

Methods

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System Building

Here, we detail the operations required to prepare the binding partners, corresponding to steps 1 and 2 of Figure 1. Proteins must be preoriented before input; i.e., the center of the transmembrane domain of both binding partners is at the origin with the appropriate orientation given that the bilayer will be built parallel to the x–y plane. Such prealignment comes as standard for structures downloaded from the OPM server. (19)
(1)

Structures are initially checked and, where necessary, repaired using the Modeller program. (20) Specifically, the FASTA sequence of the protein is downloaded from the PDB database (2) (placing the FASTA file in the folder is enough if there is no connection to the Internet), and this is used to patch up to 15 consecutive missing residues. Modeller will also place missing atoms. In its current form, the patching code can only handle two chains at most. This step can be skipped, but it is necessary for a complete simulation.

(2)

The protein is immersed in a POPE bilayer and solvated via the PACKMOL-memgen tool (21) available through the AmberTools(v.18+) package. Lipid and TIP3P water molecules are placed using a random seed, and 80 loops are performed during PACKMOL’s GENCAN routine to improve packing with a total of 120 nloops used for all-together packing. A tolerance of 2.4 Å is used to detect clashes between molecules. POPE residue names are then corrected to reflect the SLipid (24) nomenclature before the topology files are generated through GROMACS. (22) Since the SLipid and Amber14SB (23) force fields use different angle and dihedral descriptions, a small fix is applied to allow the two to work in conjunction after this step. Finally, the system is neutralized by swapping water molecules for the appropriate number of Na+ or Cl– counterions.

Molecular Dynamics

Here, we provide details on the MD protocol used to simulate the binding partners, corresponding to step 3 of Figure 1. All simulations are run on the GROMACS (22) MD engine, with Amber14SB (23) and SLipid (24) force fields used for the protein and lipids, respectively. The system is energy minimized using a steepest descent algorithm, with a tolerance threshold set to 200 kJ mol–1 nm–1. The initial step size is set to 1 pm and the maximum number of allowed steps to 5 × 106. The cutoffs for both Coulombic and van der Waals interactions are set to 1.2 nm.
The protein is then equilibrated for 20 ns within an isothermal–isobaric ensemble; T is set to 310.15 K and pressure to 1 bar with a 2 fs step size. The constraint algorithm LINCS (26) is applied to the bonds. A particle mesh Ewald summation is used to treat long-range interactions, and a velocity-rescale temperature with a coupling constant of 0.1 ps is applied separately to protein, lipids, and water/ions. A Berendsen pressure coupling method implemented semi-isotropically maintains the pressure with a coupling constant of 1.0 ps and compressibility of 4.5 × 10–5 bar–1. Velocities are randomly assigned from a Boltzmann distribution at T. A second equilibration stage is then run for 40 ns with the same settings but with all constraints removed. Finally, production occurs over a 10 ns time scale, for reasons shown in Figure S1, again in an isothermal–isobaric ensemble with the same settings as the equilibration. Atomic coordinates are saved every 5 ps and used to generate a STID map following the procedure outlined by Rudden and Degiacomi. (16)

Homology Modeling

Several test cases only had their ligand and/or receptor starting structure known from a homologue, sometimes bound to an alternative binding partner. For these cases, receptor and ligand crystal structures were mutated into their target counterparts via the Modeler program. (20) Motifs up to 15 residues long were permitted to be patched if they were missing from the structure, and structures were kept frozen to prevent optimization of models. The roto-translations returned by JabberDock were applied to these structures to yield the final predicted complexes. Table S1 reports on the sequence identity between homologues and the target structure. Their RMSD, determining case difficulty (see below), is also provided. We note that three benchmark cases (1ZOY, 2VT4, and 1EHK) feature binding partners extracted from a known complex that is a homologue to the target. Although not a real-world test case, these are suitable benchmark cases as the conformations of subunits in the two dimers differ.

Protein Docking

Here, we provide details on the docking process of protein surfaces generated from STID maps, corresponding to steps 5, 6, and 7 of Figure 1. An initial starting point with the two input monomers’ transmembrane region centers of mass centered at the origin is used prior to generating any models. JabberDock uses a seven-dimensional space for implementation comfort when roto-translating the STID maps. Three dimensions define ligand translation in the Cartesian space. Three dimensions define an axis of rotation for this ligand, and one dimension defines a rotation angle around this axis. The x and y translation values are limited by the size of the receptor, and the ligand is only allowed to move ±5 Å along the z-axis. The axis of rotation is the z-axis, which is permitted to precess by up to 0.157 radians (9°) into the x–y plane. Possible rotation angles in radians range between 0 and 2π.
To navigate the potential energy surface (PES) associated with the scoring function and produce an ensemble of possible docked poses, JabberDock leverages a distributed heuristic global optimization algorithm featured in the POWer optimization environment–particle swarm optimization “kick and reseed” (PSO-KaR). (25) PSO-KaR is used to explore the PES over 300 iterations using 80 randomly initialized agents (“particles”). According to the “kick and reseed” procedure, particles converging to a local minimum (i.e., with a velocity decaying to less than 4% of the search space dimension in each direction) are randomly restarted, and a repulsion potential is placed at their convergence location. The whole optimization process is repeated three times, with the memory of previous repulsion potentials retained from one repetition to the next. In summary, this docking procedure requires the evaluation of 72,000 docking poses. To obtain a diverse ensemble of solutions, 300 poses were finally selected as representatives from the pool of poses having a positive score using a K-means clustering algorithm on the 7-dimensional coordinates associated with each model.

Assessment of Models Accuracy

Following the CAPRI guidelines, we used three metrics to determine the quality of a model: the ratio of correct contact residues (a valid contact defined as an atom within 5 Å of the binding partner) to the number of residues in the predicted complex, fnat, the RMSD between the alpha carbons of the known crystal pose and the predicted pose, and the RMSD of the two poses between the α-carbons at the interface (defined as within 10 Å of the binding partner). CAPRI guidelines specify four levels of possible success criteria: (1) incorrect, where RMSD > 10.0 Å and interfacial RMSD > 4.0 Å OR fnat < 0.1, (2) acceptable quality, where RMSD ≤ 10.0 Å or interfacial RMSD ≤ 4.0 Å and 0.1 ≤ fnat < 0.3 OR fnat ≥ 0.3 and RMSD > 5.0 Å and interfacial RMSD > 2.0 Å, (3) intermediate quality, where RMSD ≤ 5.0 Å or interfacial RMSD ≤ 2 Å and 0.3 ≤ fnat < 0.5 OR fnat ≥ 0.5 and RMSD > 1.0 Å and interfacial RMSD > 1.0 Å, and (4) high quality, where RMSD ≤ 1.0 Å or interfacial RMSD ≤ 1.0 Å and fnat ≥ 0.5. The protocol for applying this list of inequalities follows the order provided, beginning with defining the incorrect predictions. In the text, we qualify the result of a test as of high, intermediate, or acceptable quality if at least one in the top 10 ranked models matches the criteria above.

Case Difficulty Classification

Docking cases are classified under three levels of difficulty associated with their flexibility, which we quantify via the RMSD difference between the Cα atoms at the interface after superposing the bound and unbound interfaces. Cases can be classified as either rigid-body (or easy), medium, or difficult. Easy cases are those with a minimal difference between the unbound crystallized structures and the bound: less than 1 Å difference. In medium cases, the RMSD difference is between 1 and 2.5 Å. Finally, difficult cases can be anything greater than 2.5 Å. Thus, the difficult cases are accordingly significantly more challenging than the other two, particularly given that the requirements for an acceptable success are close to the upper boundaries that define the difficult cases. Our benchmark set featured two easy, 15 medium and three difficult cases, as detailed in Table S1, spreadsheet. The RMSDs reported in Table S1, spreadsheet refer to those between target structures and crystal structures, either of the unbound molecule or mutated structure from the homologue.

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Author Information

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  • Corresponding Author
  • Author
    • Lucas S. P. Rudden - Department of Physics, Durham University, South Road, DH1 3LE Durham, United Kingdom
  • Notes
    The authors declare no competing financial interest.

Acknowledgments

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We wish to thank Durham University for computer time on its HPC facility, Hamilton. The work was supported by the Engineering and Physical Sciences Research Council (Grant EP/P016499/1).

References

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    Membrane proteins structures: A review on computational modeling tools
    Almeida, Jose G.; Preto, Antonio J.; Koukos, Panagiotis I.; Bonvin, Alexandre M. J. J.; Moreira, Irina S.
    Biochimica et Biophysica Acta, Biomembranes (2017), 1859 (10), 2021-2039CODEN: BBBMBS; ISSN:0005-2736. (Elsevier B.V.)
    A review. Membrane proteins (MPs) play diverse and important functions in living organisms. They constitute 20% to 30% of the known bacterial, archaean and eukaryotic organisms' genomes. In humans, their importance is emphasized as they represent 50% of all known drug targets. Nevertheless, exptl. detn. of their three-dimensional (3D) structure has proven to be both time consuming and rather expensive, which has led to the development of computational algorithms to complement the available exptl. methods and provide valuable insights. This review highlights the importance of membrane proteins and how computational methods are capable of overcoming challenges assocd. with their exptl. characterization. It covers various MP structural aspects, such as lipid interactions, allostery, and structure prediction, based on methods such as Mol. Dynamics (MD) and Machine-Learning (ML). Recent developments in algorithms, tools and hybrid approaches, together with the increase in both computational resources and the amt. of available data have resulted in increasingly powerful and trustworthy approaches to model MPs. Even though MPs are elementary and important in nature, the detn. of their 3D structure has proven to be a challenging endeavor. Computational methods provide a reliable alternative to exptl. methods. In this review, we focus on computational techniques to det. the 3D structure of MP and characterize their binding interfaces. We also summarize the most relevant databases and software programs available for the study of MPs.
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  4. 4
    Pagadala, N. S.; Syed, K.; Tuszynski, J. Software for Molecular Docking: A Review. Biophys. Rev. 2017, 9 (2), 91– 102,  DOI: 10.1007/s12551-016-0247-1
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    4
    Software for molecular docking: a review
    Pagadala, Nataraj S.; Syed, Khajamohiddin; Tuszynski, Jack
    Biophysical Reviews (2017), 9 (2), 91-102CODEN: BRIECG; ISSN:1867-2450. (Springer)
    Mol. docking methodol. explores the behavior of small mols. in the binding site of a target protein. As more protein structures are detd. exptl. using X-ray crystallog. or NMR (NMR) spectroscopy, mol. docking is increasingly used as a tool in drug discovery. Docking against homol.-modeled targets also becomes possible for proteins whose structures are not known. With the docking strategies, the druggability of the compds. and their specificity against a particular target can be calcd. for further lead optimization processes. Mol. docking programs perform a search algorithm in which the conformation of the ligand is evaluated recursively until the convergence to the min. energy is reached. Finally, an affinity scoring function, ΔG [U total in kcal/mol], is employed to rank the candidate poses as the sum of the electrostatic and van der Waals energies. The driving forces for these specific interactions in biol. systems aim toward complementarities between the shape and electrostatics of the binding site surfaces and the ligand or substrate.
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  5. 5
    Lensink, M. F.; Velankar, S.; Wodak, S. J. Modeling Protein–Protein and Protein–Peptide Complexes: CAPRI. Proteins: Struct., Funct., Genet. 2017, 85 (3), 359– 377,  DOI: 10.1002/prot.25215
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  6. 6
    Alford, R. F.; Koehler Leman, J.; Weitzner, B. D.; Duran, A. M.; Tilley, D. C.; Elazar, A.; Gray, J. J. An Integrated Framework Advancing Membrane Protein Modeling and Design. PLoS Comput. Biol. 2015, 11 (9), e1004398,  DOI: 10.1371/journal.pcbi.1004398
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    An integrated framework advancing membrane protein modeling and design
    Alford, Rebecca F.; Leman, Julia Koehler; Weitzner, Brian D.; Duran, Amanda M.; Tgilley, Drew C.; Elazar, Assaf; Gray, Jeffrey J.
    PLoS Computational Biology (2015), 11 (9), e1004398/1-e1004398/23CODEN: PCBLBG; ISSN:1553-7358. (Public Library of Science)
    Membrane proteins are crit. functional mols. in the human body, constituting more than 30% of open reading frames in the human genome. Unfortunately, a myriad of difficulties in overexpression and reconstitution into membrane mimetics severely limit our ability to det. their structures. Computational tools are therefore instrumental to membrane protein structure prediction, consequently increasing our understanding of membrane protein function and their role in disease. Here, we describe a general framework facilitating membrane protein modeling and design that combines the scientific principles for membrane protein modeling with the flexible software architecture of Rosetta3. This new framework, called RosettaMP, provides a general membrane representation that interfaces with scoring, conformational sampling, and mutation routines that can be easily combined to create new protocols. To demonstrate the capabilities of this implementation, we developed four proof-of-concept applications for (1) prediction of free energy changes upon mutation; (2) high-resoln. structural refinement; (3) protein-protein docking; and (4) assembly of sym. protein complexes, all in the membrane environment. Preliminary data show that these algorithms can produce meaningful scores and structures. The data also suggest needed improvements to both sampling routines and score functions. Importantly, the applications collectively demonstrate the potential of combining the flexible nature of RosettaMP with the power of Rosetta algorithms to facilitate membrane protein modeling and design.
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  7. 7
    Hurwitz, N.; Schneidman-Duhovny, Di; Wolfson, H. J. Memdock: An α-Helical Membrane Protein Docking Algorithm. Bioinformatics 2016, 32 (16), 2444– 2450,  DOI: 10.1093/bioinformatics/btw184
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    Memdock: an α-helical membrane protein docking algorithm
    Hurwitz, Naama; Schneidman-Duhovny, Dina; Wolfson, Haim J.
    Bioinformatics (2016), 32 (16), 2444-2450CODEN: BOINFP; ISSN:1367-4803. (Oxford University Press)
    Motivation: A wide range of fundamental biol. processes are mediated by membrane proteins. Despite their large no. and importance, less than 1% of all 3D protein structures deposited in the Protein Data Bank are of membrane proteins. This is mainly due to the challenges of crystg. such proteins or performing NMR spectroscopy analyses. All the more so, there is only a small no. of membrane protein-protein complexes with known structure. Therefore, developing computational tools for docking membrane proteins is crucial. Numerous methods for docking globular proteins exist, however few have been developed esp. for membrane proteins and designed to address docking within the lipid bilayer environment. Results: We present a novel algorithm, Memdock, for docking α-helical membrane proteins which takes into consideration the lipid bilayer environment for docking as well as for refining and ranking the docking candidates. We show that our algorithm improves both the docking accuracy and the candidates ranking compared to a std. protein-protein docking algorithm.
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  8. 8
    Tovchigrechko, A.; Vakser, I. A. Development and Testing of an Automated Approach to Protein Docking. Proteins: Struct., Funct., Genet. 2005, 60, 296– 301,  DOI: 10.1002/prot.20573
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    Viswanath, S.; Dominguez, L.; Foster, L. S.; Straub, J. E.; Elber, R. Extension of a Protein Docking Algorithm to Membranes and Applications to Amyloid Precursor Protein Dimerization. Proteins: Struct., Funct., Genet. 2015, 83 (12), 2170– 2185,  DOI: 10.1002/prot.24934
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  10. 10
    Chen, R.; Li, L.; Weng, Z. ZDOCK: An Initial-Stage Protein-Docking Algorithm. Proteins: Struct., Funct., Genet. 2003, 52 (1), 80– 87,  DOI: 10.1002/prot.10389
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    ZDOCK: An initial-stage protein-docking algorithm
    Chen, Rong; Li, Li; Weng, Zhiping
    Proteins: Structure, Function, and Genetics (2003), 52 (1), 80-87CODEN: PSFGEY; ISSN:0887-3585. (Wiley-Liss, Inc.)
    The development of scoring functions is of great importance to protein docking. Here we present a new scoring function for the initial stage of unbound docking. It combines our recently developed pairwise shape complementarity with desolvation and electrostatics. We compare this scoring function with three other functions on a large benchmark of 49 nonredundant test cases and show its superior performance, esp. for the antibody-antigen category of test cases. For 44 test cases (90% of the benchmark), we can retain at least one near-native structure within the top 2000 predictions at the 6° rotational sampling d., with an av. of 52 near-native structures per test case. The remaining five difficult test cases can be explained by a combination of poor binding affinity, large backbone conformational changes, and our algorithm's strong tendency for identifying large concave binding pockets. All four scoring functions have been integrated into our Fast Fourier Transform based docking algorithm ZDOCK, which is freely available to academic users at http://zlab.bu.edu/∼rong/dock.
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  11. 11
    Pierce, B.; Weng, Z. ZRANK: Reranking Protein Docking Predictions with an Optimized Energy Function. Proteins: Struct., Funct., Genet. 2007, 67 (4), 1078– 1086,  DOI: 10.1002/prot.21373
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    11
    ZRANK: reranking protein docking predictions with an optimized energy function
    Pierce, Brian; Weng, Zhiping
    Proteins: Structure, Function, and Bioinformatics (2007), 67 (4), 1078-1086CODEN: PSFBAF ISSN:. (Wiley-Liss, Inc.)
    Protein-protein docking requires fast and effective methods to quickly discriminate correct from incorrect predictions generated by initial-stage docking. The authors have developed and tested a scoring function that utilizes detailed electrostatics, van der Waals, and desolvation to rescore initial-stage docking predictions. Wts. for the scoring terms were optimized for a set of test cases, and this optimized function was then tested on an independent set of nonredundant cases. This program, named ZRANK, is shown to significantly improve the success rate over the initial ZDOCK rankings across a large benchmark. The amt. of test cases with No. 1 ranked hits increased from 2 to 11 and from 6 to 12 when predictions from two ZDOCK versions were considered. ZRANK can be applied either as a refinement protocol in itself or as a preprocessing stage to enrich the well-ranked hits prior to further refinement.
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  12. 12
    Kozakov, D.; Hall, D. R.; Beglov, D.; Brenke, R.; Comeau, S. R.; Shen, Y.; Li, K.; Zheng, J.; Vakili, P.; Paschalidis, I. C.; Vajda, S. Achieving Reliability and High Accuracy in Automated Protein Docking: ClusPro, PIPER, SDU, and Stability Analysis in CAPRI Rounds 13–19. Proteins: Struct., Funct., Genet. 2010, 78 (15), 3124– 3130,  DOI: 10.1002/prot.22835
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    Koukos, P. I.; Faro, I.; van Noort, C. W.; Bonvin, A. M. J. J. A Membrane Protein Complex Docking Benchmark. J. Mol. Biol. 2018, 430 (24), 5246– 5256,  DOI: 10.1016/j.jmb.2018.11.005
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    13
    A Membrane Protein Complex Docking Benchmark
    Koukos, Panagiotis I.; Faro, Inge; van Noort, Charlotte W.; Bonvin, Alexandre M. J. J.
    Journal of Molecular Biology (2018), 430 (24), 5246-5256CODEN: JMOBAK; ISSN:0022-2836. (Elsevier Ltd.)
    The authors report the first membrane protein-protein docking benchmark consisting of 37 targets of diverse functions and folds. The structures were chosen based on a set of parameters such as the availability of unbound structures, the modeling difficulty and their uniqueness. They have been cleaned and consistently numbered to facilitate their use in docking. Using this benchmark, the authors establish the baseline performance of HADDOCK, without any specific optimization for membrane proteins, for two scenarios: true interface-driven docking and ab initio docking. Despite the fact that HADDOCK has been developed for sol. complexes, it shows promising docking performance for membrane systems, but there is clearly room for further optimization. The resulting set of docking decoys, together with anal. scripts, is made freely available. These can serve as a basis for the optimization of membrane complex-specific scoring functions.
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  14. 14
    Jiménez-García, B.; Roel-Touris, J.; Romero-Durana, M.; Vidal, M.; Jiménez-González, D.; Fernández-Recio, J. LightDock: A New Multi-Scale Approach to Protein–Protein Docking. Bioinformatics 2018, 34 (1), 49– 55,  DOI: 10.1093/bioinformatics/btx555
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    LightDock: a new multi-scale approach toprotein-protein dockingz
    Jimenez-Garcia, Brian; Roel-Touris, Jorge; Romero-Durana, Miguel; Vidal, Miquel; Jimenez-Gonzalez, Daniel; Fernandez-Recio, Juan
    Bioinformatics (2018), 34 (1), 49-55CODEN: BOINFP; ISSN:1367-4811. (Oxford University Press)
    Computational prediction of protein-protein complex structure by docking can provide structural and mechanistic insights for protein interactions of biomedical interest. However, current methods struggle with difficult cases, such as those involving flexible proteins, low-affinity complexes or transient interactions. A major challenge is how to efficiently sample the structural and energetic landscape of the assocn. at different resoln. levels, given that each scoring function is often highly coupled to a specific type of search method. Thus, new methodologies capable of accommodating multi-scale conformational flexibility and scoring are strongly needed. We describe here a new multi-scale protein-protein docking methodol., LightDock, capable of accommodating conformational flexibility and a variety of scoring functions at different resoln. levels. Implicit use of normal modes during the search and at./coarse-grained combined scoring functions yielded improved predictive results with respect to state-of-the-art rigidbody docking, especiallyin flexible cases.
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  15. 15
    Roel-Touris, J.; Jiménez-García, B.; Bonvin, A. Integrative Modeling of Membrane-Associated Protein Assemblies. Nat. Commun. 2020, 11 (1), 6210,  DOI: 10.1038/s41467-020-20076-5
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    15
    Integrative modeling of membrane-associated protein assemblies
    Roel-Touris, Jorge; Jimenez-Garcia, Brian; Bonvin, Alexandre M. J. J.
    Nature Communications (2020), 11 (1), 6210CODEN: NCAOBW; ISSN:2041-1723. (Nature Research)
    Membrane proteins are among the most challenging systems to study with exptl. structural biol. techniques. The increased no. of deposited structures of membrane proteins has opened the route to modeling their complexes by methods such as docking. Here, we present an integrative computational protocol for the modeling of membrane-assocd. protein assemblies. The information encoded by the membrane is represented by artificial beads, which allow targeting of the docking toward the binding-competent regions. It combines efficient, artificial intelligence-based rigid-body docking by LightDock with a flexible final refinement with HADDOCK to remove potential clashes at the interface. We demonstrate the performance of this protocol on eighteen membrane-assocd. complexes, whose interface lies between the membrane and either the cytosolic or periplasmic regions. In addn., we provide a comparison to another state-of-the-art docking software, ZDOCK. This protocol should shed light on the still dark fraction of the interactome consisting of membrane proteins.
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  16. 16
    Rudden, L. S. P.; Degiacomi, M. T. Protein Docking Using a Single Representation for Protein Surface, Electrostatics, and Local Dynamics. J. Chem. Theory Comput. 2019, 15 (9), 5135– 5143,  DOI: 10.1021/acs.jctc.9b00474
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    16
    Protein Docking Using a Single Representation for Protein Surface, Electrostatics, and Local Dynamics
    Rudden, Lucas S. P.; Degiacomi, Matteo T.
    Journal of Chemical Theory and Computation (2019), 15 (9), 5135-5143CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
    Predicting the assembly of multiple proteins into specific complexes is crit. to understanding their biol. function in an organism and thus the design of drugs to address their malfunction. Proteins are flexible mols., which inherently pose a problem to any protein docking computational method, where even a simple rearrangement of the side chain and backbone atoms at the interface of binding partners complicates the successful detn. of the correct docked pose. Herein, we present a means of representing protein surface, electrostatics, and local dynamics within a single volumetric descriptor. We show that our representations can be phys. related to the surface-accessible solvent area and mass of the protein. We then demonstrate that the application of this representation into a protein-protein docking scenario bypasses the need to compensate for, and predict, specific side chain packing at the interface of binding partners. This representation is leveraged in our de novo protein docking software, JabberDock, which can accurately and robustly predict difficult target complexes with an av. success rate of >54%, which is comparable to or greater than the currently available methods.
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  17. 17
    Vreven, T.; Moal, I. H.; Vangone, A.; Pierce, B. G.; Kastritis, P. L.; Torchala, M.; Chaleil, R.; Jiménez-García, B.; Bates, P. A.; Fernandez-Recio, J.; Bonvin, A. M. J. J.; Weng, Z. Updates to the Integrated Protein–Protein Interaction Benchmarks: Docking Benchmark Version 5 and Affinity Benchmark Version 2. J. Mol. Biol. 2015, 427 (19), 3031– 3041,  DOI: 10.1016/j.jmb.2015.07.016
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    17
    Updates to the Integrated Protein-Protein Interaction Benchmarks: Docking Benchmark Version 5 and Affinity Benchmark Version 2
    Vreven, Thom; Moal, Iain H.; Vangone, Anna; Pierce, Brian G.; Kastritis, Panagiotis L.; Torchala, Mieczyslaw; Chaleil, Raphael; Jimenez-Garcia, Brian; Bates, Paul A.; Fernandez-Recio, Juan; Bonvin, Alexandre M. J. J.; Weng, Zhiping
    Journal of Molecular Biology (2015), 427 (19), 3031-3041CODEN: JMOBAK; ISSN:0022-2836. (Elsevier Ltd.)
    The authors present an updated and integrated version of the authors' widely used protein-protein docking and binding affinity benchmarks. The benchmarks consist of non-redundant, high-quality structures of protein-protein complexes along with the unbound structures of their components. Fifty-five new complexes were added to the docking benchmark, 35 of which have exptl. measured binding affinities. These updated docking and affinity benchmarks now contain 230 and 179 entries, resp. In particular, the no. of antibody-antigen complexes has increased significantly, by 67% and 74% in the docking and affinity benchmarks, resp. The authors tested previously developed docking and affinity prediction algorithms on the new cases. Considering only the top 10 docking predictions per benchmark case, a prediction accuracy of 38% is achieved on all 55 cases and up to 50% for the 32 rigid-body cases only. Predicted affinity scores correlate with exptl. binding energies up to r = 0.52 overall and r = 0.72 for the rigid complexes.
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  18. 18
    Olerinyova, A.; Sonn-Segev, A.; Gault, J.; Eichmann, C.; Schimpf, J.; Kopf, A. H.; Rudden, L. S.P.; Ashkinadze, D.; Bomba, R.; Frey, L.; Greenwald, J.; Degiacomi, M. T.; Steinhilper, R.; Killian, J. A.; Friedrich, T.; Riek, R.; Struwe, W. B.; Kukura, P. Mass Photometry of Membrane Proteins. Chem 2021, 7, 224– 236,  DOI: 10.1016/j.chempr.2020.11.011
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    18
    Mass Photometry of Membrane Proteins
    Olerinyova, Anna; Sonn-Segev, Adar; Gault, Joseph; Eichmann, Cedric; Schimpf, Johannes; Kopf, Adrian H.; Rudden, Lucas S. P.; Ashkinadze, Dzmitry; Bomba, Radoslaw; Frey, Lukas; Greenwald, Jason; Degiacomi, Matteo T.; Steinhilper, Ralf; Killian, J. Antoinette; Friedrich, Thorsten; Riek, Roland; Struwe, Weston B.; Kukura, Philipp
    Chem (2021), 7 (1), 224-236CODEN: CHEMVE; ISSN:2451-9294. (Cell Press)
    Integral membrane proteins (IMPs) are biol. highly significant but challenging to study because they require maintaining a cellular lipid-like environment. Here, we explore the application of mass photometry (MP) to IMPs and membrane-mimetic systems at the single-particle level. We apply MP to amphipathic vehicles, such as detergents and amphipols, as well as to lipid and native nanodiscs, characterizing the particle size, sample purity, and heterogeneity. Using methods established for cryogenic electron microscopy, we eliminate detergent background, enabling high-resoln. studies of membrane-protein structure and interactions. We find evidence that, when extd. from native membranes using native styrene-maleic acid nanodiscs, the potassium channel KcsA is present as a dimer of tetramers-in contrast to results obtained using detergent purifn. Finally, using lipid nanodiscs, we show that MP can help distinguish between functional and non-functional nanodisc assemblies, as well as det. the crit. factors for lipid nanodisc formation.
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    Lomize, M. A.; Lomize, A. L.; Pogozheva, I. D.; Mosberg, H. I. OPM: Orientations of Proteins in Membranes Database. Bioinformatics 2006, 22 (5), 623– 625,  DOI: 10.1093/bioinformatics/btk023
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    OPM: Orientations of Proteins in Membranes database
    Lomize, Mikhail A.; Lomize, Andrei L.; Pogozheva, Irina D.; Mosberg, Henry I.
    Bioinformatics (2006), 22 (5), 623-625CODEN: BOINFP; ISSN:1367-4803. (Oxford University Press)
    The Orientations of Proteins in Membranes (OPM) database provides a collection of transmembrane, monotopic, and peripheral proteins from the Protein Data Bank whose spatial arrangements in the lipid bilayer have been calcd. theor. and compared with exptl. data. The database allows anal., sorting, and searching of membrane proteins based on their structural classification, species, destination membrane, nos. of transmembrane segments and subunits, nos. of secondary structures, and the calcd. hydrophobic thickness or tilt angle with respect to the bilayer normal. All coordinate files with the calcd. membrane boundaries are available for downloading. The Internet site for the database is: http://opm.phar.umich.edu.
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    Fiser, A.; Sali, A. ModLoop: Automated Modeling of Loops in Protein Structures. Bioinformatics 2003, 19 (18), 2500– 2501,  DOI: 10.1093/bioinformatics/btg362
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    20
    ModLoop: automated modeling of loops in protein structures
    Fiser, Andras; Sali, Andrej
    Bioinformatics (2003), 19 (18), 2500-2501CODEN: BOINFP; ISSN:1367-4803. (Oxford University Press)
    Summary: ModLoop is a web server for automated modeling of loops in protein structures. The input is the at. coordinates of the protein structure in the Protein Data Bank format, and the specification of the starting and ending residues of one or more segments to be modeled, contg. no more than 20 residues in total. The output is the coordinates of the non-hydrogen atoms in the modeled segments. A user provides the input to the server via a simple web interface, and receives the output by e-mail. The server relies on the loop modeling routine in MODELLER that predicts the loop conformations by satisfaction of spatial restraints, without relying on a database of known protein structures. For a rapid response, ModLoop runs on a cluster of Linux PC computers.
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    Schott-Verdugo, S.; Gohlke, H. PACKMOL-Memgen: A Simple-To-Use, Generalized Workflow for Membrane-Protein-Lipid-Bilayer System Building. J. Chem. Inf. Model. 2019, 59 (6), 2522– 2528,  DOI: 10.1021/acs.jcim.9b00269
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    21
    PACKMOL-Memgen: A Simple-To-Use, Generalized Workflow for Membrane-Protein-Lipid-Bilayer System Building
    Schott-Verdugo, Stephan; Gohlke, Holger
    Journal of Chemical Information and Modeling (2019), 59 (6), 2522-2528CODEN: JCISD8; ISSN:1549-9596. (American Chemical Society)
    We present PACKMOL-Memgen, a simple-to-use, generalized workflow for automated building of membrane-protein-lipid-bilayer systems based on open-source tools including Packmol, memembed, pdbremix, and AmberTools. Compared with web-interface-based related tools, PACKMOL-Memgen allows setup of multiple configurations of a system in a user-friendly and efficient manner within minutes. The generated systems are well-packed and thus well-suited as starting configurations in MD simulations under periodic boundary conditions, requiring only moderate equilibration times. PACKMOL-Memgen is distributed with AmberTools and runs on most computing platforms, and its output can also be used for CHARMM or adapted to other mol.-simulation packages.
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    Berendsen, H. J. C.; van der Spoel, D.; van Drunen, R. GROMACS: A Message-Passing Parallel Molecular Dynamics Implementation. Comput. Phys. Commun. 1995, 91 (1–3), 43– 56,  DOI: 10.1016/0010-4655(95)00042-E
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    GROMACS: A message-passing parallel molecular dynamics implementation
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  • Abstract

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    Figure 1

    Figure 1. JabberDock transmembrane protein docking pipeline. Full details of each step, including a convergence benchmark for Step 4, are available in Methods. This example’s target complex is the homodimer 1Q90 (BF), using 2ZT9 (A) as the ligand (blue) and receptor (red). Step 7 features a representation of the fifth best model; an intermediate success overlaid on the bound structure (gray).

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    Figure 2

    Figure 2. (a) Quality of best models within the top 10 results for every docking case. For each case, the lowest α-carbon RMSD between the prediction and crystallized homologue is presented against the associated native residue fraction (fnat.). The dark- to light-shaded regions represent the criteria for high to acceptable quality results. Thus, a point landing in one of these regions indicates a success. (b) Percentage of cases yielding an acceptable (purple) and intermediate (pink) success as a function of the number of ranked structures considered as candidate models. The region corresponding to the top 10 models is shaded and magnified in the inset.

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  • References

    This article references 26 other publications.

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      A review. Membrane proteins (MPs) play diverse and important functions in living organisms. They constitute 20% to 30% of the known bacterial, archaean and eukaryotic organisms' genomes. In humans, their importance is emphasized as they represent 50% of all known drug targets. Nevertheless, exptl. detn. of their three-dimensional (3D) structure has proven to be both time consuming and rather expensive, which has led to the development of computational algorithms to complement the available exptl. methods and provide valuable insights. This review highlights the importance of membrane proteins and how computational methods are capable of overcoming challenges assocd. with their exptl. characterization. It covers various MP structural aspects, such as lipid interactions, allostery, and structure prediction, based on methods such as Mol. Dynamics (MD) and Machine-Learning (ML). Recent developments in algorithms, tools and hybrid approaches, together with the increase in both computational resources and the amt. of available data have resulted in increasingly powerful and trustworthy approaches to model MPs. Even though MPs are elementary and important in nature, the detn. of their 3D structure has proven to be a challenging endeavor. Computational methods provide a reliable alternative to exptl. methods. In this review, we focus on computational techniques to det. the 3D structure of MP and characterize their binding interfaces. We also summarize the most relevant databases and software programs available for the study of MPs.
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      Mol. docking methodol. explores the behavior of small mols. in the binding site of a target protein. As more protein structures are detd. exptl. using X-ray crystallog. or NMR (NMR) spectroscopy, mol. docking is increasingly used as a tool in drug discovery. Docking against homol.-modeled targets also becomes possible for proteins whose structures are not known. With the docking strategies, the druggability of the compds. and their specificity against a particular target can be calcd. for further lead optimization processes. Mol. docking programs perform a search algorithm in which the conformation of the ligand is evaluated recursively until the convergence to the min. energy is reached. Finally, an affinity scoring function, ΔG [U total in kcal/mol], is employed to rank the candidate poses as the sum of the electrostatic and van der Waals energies. The driving forces for these specific interactions in biol. systems aim toward complementarities between the shape and electrostatics of the binding site surfaces and the ligand or substrate.
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      Motivation: A wide range of fundamental biol. processes are mediated by membrane proteins. Despite their large no. and importance, less than 1% of all 3D protein structures deposited in the Protein Data Bank are of membrane proteins. This is mainly due to the challenges of crystg. such proteins or performing NMR spectroscopy analyses. All the more so, there is only a small no. of membrane protein-protein complexes with known structure. Therefore, developing computational tools for docking membrane proteins is crucial. Numerous methods for docking globular proteins exist, however few have been developed esp. for membrane proteins and designed to address docking within the lipid bilayer environment. Results: We present a novel algorithm, Memdock, for docking α-helical membrane proteins which takes into consideration the lipid bilayer environment for docking as well as for refining and ranking the docking candidates. We show that our algorithm improves both the docking accuracy and the candidates ranking compared to a std. protein-protein docking algorithm.
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      The development of scoring functions is of great importance to protein docking. Here we present a new scoring function for the initial stage of unbound docking. It combines our recently developed pairwise shape complementarity with desolvation and electrostatics. We compare this scoring function with three other functions on a large benchmark of 49 nonredundant test cases and show its superior performance, esp. for the antibody-antigen category of test cases. For 44 test cases (90% of the benchmark), we can retain at least one near-native structure within the top 2000 predictions at the 6° rotational sampling d., with an av. of 52 near-native structures per test case. The remaining five difficult test cases can be explained by a combination of poor binding affinity, large backbone conformational changes, and our algorithm's strong tendency for identifying large concave binding pockets. All four scoring functions have been integrated into our Fast Fourier Transform based docking algorithm ZDOCK, which is freely available to academic users at http://zlab.bu.edu/∼rong/dock.
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      11
      ZRANK: reranking protein docking predictions with an optimized energy function
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      Proteins: Structure, Function, and Bioinformatics (2007), 67 (4), 1078-1086CODEN: PSFBAF ISSN:. (Wiley-Liss, Inc.)
      Protein-protein docking requires fast and effective methods to quickly discriminate correct from incorrect predictions generated by initial-stage docking. The authors have developed and tested a scoring function that utilizes detailed electrostatics, van der Waals, and desolvation to rescore initial-stage docking predictions. Wts. for the scoring terms were optimized for a set of test cases, and this optimized function was then tested on an independent set of nonredundant cases. This program, named ZRANK, is shown to significantly improve the success rate over the initial ZDOCK rankings across a large benchmark. The amt. of test cases with No. 1 ranked hits increased from 2 to 11 and from 6 to 12 when predictions from two ZDOCK versions were considered. ZRANK can be applied either as a refinement protocol in itself or as a preprocessing stage to enrich the well-ranked hits prior to further refinement.
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      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2sXlsFSjsrc%253D&md5=1411a3702d465d70a46b8edf8e7e300a
    12. 12
      Kozakov, D.; Hall, D. R.; Beglov, D.; Brenke, R.; Comeau, S. R.; Shen, Y.; Li, K.; Zheng, J.; Vakili, P.; Paschalidis, I. C.; Vajda, S. Achieving Reliability and High Accuracy in Automated Protein Docking: ClusPro, PIPER, SDU, and Stability Analysis in CAPRI Rounds 13–19. Proteins: Struct., Funct., Genet. 2010, 78 (15), 3124– 3130,  DOI: 10.1002/prot.22835
      There is no corresponding record for this reference.
    13. 13
      Koukos, P. I.; Faro, I.; van Noort, C. W.; Bonvin, A. M. J. J. A Membrane Protein Complex Docking Benchmark. J. Mol. Biol. 2018, 430 (24), 5246– 5256,  DOI: 10.1016/j.jmb.2018.11.005
      13
      A Membrane Protein Complex Docking Benchmark
      Koukos, Panagiotis I.; Faro, Inge; van Noort, Charlotte W.; Bonvin, Alexandre M. J. J.
      Journal of Molecular Biology (2018), 430 (24), 5246-5256CODEN: JMOBAK; ISSN:0022-2836. (Elsevier Ltd.)
      The authors report the first membrane protein-protein docking benchmark consisting of 37 targets of diverse functions and folds. The structures were chosen based on a set of parameters such as the availability of unbound structures, the modeling difficulty and their uniqueness. They have been cleaned and consistently numbered to facilitate their use in docking. Using this benchmark, the authors establish the baseline performance of HADDOCK, without any specific optimization for membrane proteins, for two scenarios: true interface-driven docking and ab initio docking. Despite the fact that HADDOCK has been developed for sol. complexes, it shows promising docking performance for membrane systems, but there is clearly room for further optimization. The resulting set of docking decoys, together with anal. scripts, is made freely available. These can serve as a basis for the optimization of membrane complex-specific scoring functions.
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    14. 14
      Jiménez-García, B.; Roel-Touris, J.; Romero-Durana, M.; Vidal, M.; Jiménez-González, D.; Fernández-Recio, J. LightDock: A New Multi-Scale Approach to Protein–Protein Docking. Bioinformatics 2018, 34 (1), 49– 55,  DOI: 10.1093/bioinformatics/btx555
      14
      LightDock: a new multi-scale approach toprotein-protein dockingz
      Jimenez-Garcia, Brian; Roel-Touris, Jorge; Romero-Durana, Miguel; Vidal, Miquel; Jimenez-Gonzalez, Daniel; Fernandez-Recio, Juan
      Bioinformatics (2018), 34 (1), 49-55CODEN: BOINFP; ISSN:1367-4811. (Oxford University Press)
      Computational prediction of protein-protein complex structure by docking can provide structural and mechanistic insights for protein interactions of biomedical interest. However, current methods struggle with difficult cases, such as those involving flexible proteins, low-affinity complexes or transient interactions. A major challenge is how to efficiently sample the structural and energetic landscape of the assocn. at different resoln. levels, given that each scoring function is often highly coupled to a specific type of search method. Thus, new methodologies capable of accommodating multi-scale conformational flexibility and scoring are strongly needed. We describe here a new multi-scale protein-protein docking methodol., LightDock, capable of accommodating conformational flexibility and a variety of scoring functions at different resoln. levels. Implicit use of normal modes during the search and at./coarse-grained combined scoring functions yielded improved predictive results with respect to state-of-the-art rigidbody docking, especiallyin flexible cases.
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    15. 15
      Roel-Touris, J.; Jiménez-García, B.; Bonvin, A. Integrative Modeling of Membrane-Associated Protein Assemblies. Nat. Commun. 2020, 11 (1), 6210,  DOI: 10.1038/s41467-020-20076-5
      15
      Integrative modeling of membrane-associated protein assemblies
      Roel-Touris, Jorge; Jimenez-Garcia, Brian; Bonvin, Alexandre M. J. J.
      Nature Communications (2020), 11 (1), 6210CODEN: NCAOBW; ISSN:2041-1723. (Nature Research)
      Membrane proteins are among the most challenging systems to study with exptl. structural biol. techniques. The increased no. of deposited structures of membrane proteins has opened the route to modeling their complexes by methods such as docking. Here, we present an integrative computational protocol for the modeling of membrane-assocd. protein assemblies. The information encoded by the membrane is represented by artificial beads, which allow targeting of the docking toward the binding-competent regions. It combines efficient, artificial intelligence-based rigid-body docking by LightDock with a flexible final refinement with HADDOCK to remove potential clashes at the interface. We demonstrate the performance of this protocol on eighteen membrane-assocd. complexes, whose interface lies between the membrane and either the cytosolic or periplasmic regions. In addn., we provide a comparison to another state-of-the-art docking software, ZDOCK. This protocol should shed light on the still dark fraction of the interactome consisting of membrane proteins.
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    16. 16
      Rudden, L. S. P.; Degiacomi, M. T. Protein Docking Using a Single Representation for Protein Surface, Electrostatics, and Local Dynamics. J. Chem. Theory Comput. 2019, 15 (9), 5135– 5143,  DOI: 10.1021/acs.jctc.9b00474
      16
      Protein Docking Using a Single Representation for Protein Surface, Electrostatics, and Local Dynamics
      Rudden, Lucas S. P.; Degiacomi, Matteo T.
      Journal of Chemical Theory and Computation (2019), 15 (9), 5135-5143CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      Predicting the assembly of multiple proteins into specific complexes is crit. to understanding their biol. function in an organism and thus the design of drugs to address their malfunction. Proteins are flexible mols., which inherently pose a problem to any protein docking computational method, where even a simple rearrangement of the side chain and backbone atoms at the interface of binding partners complicates the successful detn. of the correct docked pose. Herein, we present a means of representing protein surface, electrostatics, and local dynamics within a single volumetric descriptor. We show that our representations can be phys. related to the surface-accessible solvent area and mass of the protein. We then demonstrate that the application of this representation into a protein-protein docking scenario bypasses the need to compensate for, and predict, specific side chain packing at the interface of binding partners. This representation is leveraged in our de novo protein docking software, JabberDock, which can accurately and robustly predict difficult target complexes with an av. success rate of >54%, which is comparable to or greater than the currently available methods.
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    17. 17
      Vreven, T.; Moal, I. H.; Vangone, A.; Pierce, B. G.; Kastritis, P. L.; Torchala, M.; Chaleil, R.; Jiménez-García, B.; Bates, P. A.; Fernandez-Recio, J.; Bonvin, A. M. J. J.; Weng, Z. Updates to the Integrated Protein–Protein Interaction Benchmarks: Docking Benchmark Version 5 and Affinity Benchmark Version 2. J. Mol. Biol. 2015, 427 (19), 3031– 3041,  DOI: 10.1016/j.jmb.2015.07.016
      17
      Updates to the Integrated Protein-Protein Interaction Benchmarks: Docking Benchmark Version 5 and Affinity Benchmark Version 2
      Vreven, Thom; Moal, Iain H.; Vangone, Anna; Pierce, Brian G.; Kastritis, Panagiotis L.; Torchala, Mieczyslaw; Chaleil, Raphael; Jimenez-Garcia, Brian; Bates, Paul A.; Fernandez-Recio, Juan; Bonvin, Alexandre M. J. J.; Weng, Zhiping
      Journal of Molecular Biology (2015), 427 (19), 3031-3041CODEN: JMOBAK; ISSN:0022-2836. (Elsevier Ltd.)
      The authors present an updated and integrated version of the authors' widely used protein-protein docking and binding affinity benchmarks. The benchmarks consist of non-redundant, high-quality structures of protein-protein complexes along with the unbound structures of their components. Fifty-five new complexes were added to the docking benchmark, 35 of which have exptl. measured binding affinities. These updated docking and affinity benchmarks now contain 230 and 179 entries, resp. In particular, the no. of antibody-antigen complexes has increased significantly, by 67% and 74% in the docking and affinity benchmarks, resp. The authors tested previously developed docking and affinity prediction algorithms on the new cases. Considering only the top 10 docking predictions per benchmark case, a prediction accuracy of 38% is achieved on all 55 cases and up to 50% for the 32 rigid-body cases only. Predicted affinity scores correlate with exptl. binding energies up to r = 0.52 overall and r = 0.72 for the rigid complexes.
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    18. 18
      Olerinyova, A.; Sonn-Segev, A.; Gault, J.; Eichmann, C.; Schimpf, J.; Kopf, A. H.; Rudden, L. S.P.; Ashkinadze, D.; Bomba, R.; Frey, L.; Greenwald, J.; Degiacomi, M. T.; Steinhilper, R.; Killian, J. A.; Friedrich, T.; Riek, R.; Struwe, W. B.; Kukura, P. Mass Photometry of Membrane Proteins. Chem 2021, 7, 224– 236,  DOI: 10.1016/j.chempr.2020.11.011
      18
      Mass Photometry of Membrane Proteins
      Olerinyova, Anna; Sonn-Segev, Adar; Gault, Joseph; Eichmann, Cedric; Schimpf, Johannes; Kopf, Adrian H.; Rudden, Lucas S. P.; Ashkinadze, Dzmitry; Bomba, Radoslaw; Frey, Lukas; Greenwald, Jason; Degiacomi, Matteo T.; Steinhilper, Ralf; Killian, J. Antoinette; Friedrich, Thorsten; Riek, Roland; Struwe, Weston B.; Kukura, Philipp
      Chem (2021), 7 (1), 224-236CODEN: CHEMVE; ISSN:2451-9294. (Cell Press)
      Integral membrane proteins (IMPs) are biol. highly significant but challenging to study because they require maintaining a cellular lipid-like environment. Here, we explore the application of mass photometry (MP) to IMPs and membrane-mimetic systems at the single-particle level. We apply MP to amphipathic vehicles, such as detergents and amphipols, as well as to lipid and native nanodiscs, characterizing the particle size, sample purity, and heterogeneity. Using methods established for cryogenic electron microscopy, we eliminate detergent background, enabling high-resoln. studies of membrane-protein structure and interactions. We find evidence that, when extd. from native membranes using native styrene-maleic acid nanodiscs, the potassium channel KcsA is present as a dimer of tetramers-in contrast to results obtained using detergent purifn. Finally, using lipid nanodiscs, we show that MP can help distinguish between functional and non-functional nanodisc assemblies, as well as det. the crit. factors for lipid nanodisc formation.
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    19. 19
      Lomize, M. A.; Lomize, A. L.; Pogozheva, I. D.; Mosberg, H. I. OPM: Orientations of Proteins in Membranes Database. Bioinformatics 2006, 22 (5), 623– 625,  DOI: 10.1093/bioinformatics/btk023
      19
      OPM: Orientations of Proteins in Membranes database
      Lomize, Mikhail A.; Lomize, Andrei L.; Pogozheva, Irina D.; Mosberg, Henry I.
      Bioinformatics (2006), 22 (5), 623-625CODEN: BOINFP; ISSN:1367-4803. (Oxford University Press)
      The Orientations of Proteins in Membranes (OPM) database provides a collection of transmembrane, monotopic, and peripheral proteins from the Protein Data Bank whose spatial arrangements in the lipid bilayer have been calcd. theor. and compared with exptl. data. The database allows anal., sorting, and searching of membrane proteins based on their structural classification, species, destination membrane, nos. of transmembrane segments and subunits, nos. of secondary structures, and the calcd. hydrophobic thickness or tilt angle with respect to the bilayer normal. All coordinate files with the calcd. membrane boundaries are available for downloading. The Internet site for the database is: http://opm.phar.umich.edu.
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    20. 20
      Fiser, A.; Sali, A. ModLoop: Automated Modeling of Loops in Protein Structures. Bioinformatics 2003, 19 (18), 2500– 2501,  DOI: 10.1093/bioinformatics/btg362
      20
      ModLoop: automated modeling of loops in protein structures
      Fiser, Andras; Sali, Andrej
      Bioinformatics (2003), 19 (18), 2500-2501CODEN: BOINFP; ISSN:1367-4803. (Oxford University Press)
      Summary: ModLoop is a web server for automated modeling of loops in protein structures. The input is the at. coordinates of the protein structure in the Protein Data Bank format, and the specification of the starting and ending residues of one or more segments to be modeled, contg. no more than 20 residues in total. The output is the coordinates of the non-hydrogen atoms in the modeled segments. A user provides the input to the server via a simple web interface, and receives the output by e-mail. The server relies on the loop modeling routine in MODELLER that predicts the loop conformations by satisfaction of spatial restraints, without relying on a database of known protein structures. For a rapid response, ModLoop runs on a cluster of Linux PC computers.
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    21. 21
      Schott-Verdugo, S.; Gohlke, H. PACKMOL-Memgen: A Simple-To-Use, Generalized Workflow for Membrane-Protein-Lipid-Bilayer System Building. J. Chem. Inf. Model. 2019, 59 (6), 2522– 2528,  DOI: 10.1021/acs.jcim.9b00269
      21
      PACKMOL-Memgen: A Simple-To-Use, Generalized Workflow for Membrane-Protein-Lipid-Bilayer System Building
      Schott-Verdugo, Stephan; Gohlke, Holger
      Journal of Chemical Information and Modeling (2019), 59 (6), 2522-2528CODEN: JCISD8; ISSN:1549-9596. (American Chemical Society)
      We present PACKMOL-Memgen, a simple-to-use, generalized workflow for automated building of membrane-protein-lipid-bilayer systems based on open-source tools including Packmol, memembed, pdbremix, and AmberTools. Compared with web-interface-based related tools, PACKMOL-Memgen allows setup of multiple configurations of a system in a user-friendly and efficient manner within minutes. The generated systems are well-packed and thus well-suited as starting configurations in MD simulations under periodic boundary conditions, requiring only moderate equilibration times. PACKMOL-Memgen is distributed with AmberTools and runs on most computing platforms, and its output can also be used for CHARMM or adapted to other mol.-simulation packages.
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      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXhtVWqtrvI&md5=5b4477eb5d8f6e330832ca484d7c445e
    22. 22
      Berendsen, H. J. C.; van der Spoel, D.; van Drunen, R. GROMACS: A Message-Passing Parallel Molecular Dynamics Implementation. Comput. Phys. Commun. 1995, 91 (1–3), 43– 56,  DOI: 10.1016/0010-4655(95)00042-E
      22
      GROMACS: A message-passing parallel molecular dynamics implementation
      Berendsen, H. J. C.; van der Spoel, D.; van Drunen, R.
      Computer Physics Communications (1995), 91 (1-3), 43-56CODEN: CPHCBZ; ISSN:0010-4655. (Elsevier)
      A parallel message-passing implementation of a mol. dynamics (MD) program that is useful for bio(macro)mols. in aq. environment is described. The software has been developed for a custom-designed 32-processor ring GROMACS (Groningen MAchine for Chem. Simulation) with communication to and from left and right neighbors, but can run on any parallel system onto which a a ring of processors can be mapped and which supports PVM-like block send and receive calls. The GROMACS software consists of a preprocessor, a parallel MD and energy minimization program that can use an arbitrary no. of processors (including one), an optional monitor, and several anal. tools. The programs are written in ANSI C and available by ftp (information: [email protected]). The functionality is based on the GROMOS (Groningen Mol. Simulation) package (van Gunsteren and Berendsen, 1987; BIOMOS B.V., Nijenborgh 4, 9747 AG Groningen). Conversion programs between GROMOS and GROMACS formats are included.The MD program can handle rectangular periodic boundary conditions with temp. and pressure scaling. The interactions that can be handled without modification are variable non-bonded pair interactions with Coulomb and Lennard-Jones or Buckingham potentials, using a twin-range cut-off based on charge groups, and fixed bonded interactions of either harmonic or constraint type for bonds and bond angles and either periodic or cosine power series interactions for dihedral angles. Special forces can be added to groups of particles (for non-equil. dynamics or for position restraining) or between particles (for distance restraints). The parallelism is based on particle decompn. Interprocessor communication is largely limited to position and force distribution over the ring once per time step.
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    23. 23
      Maier, J. A.; Martinez, C.; Kasavajhala, K.; Wickstrom, L.; Hauser, K. E.; Simmerling, C. Ff14SB: Improving the Accuracy of Protein Side Chain and Backbone Parameters from Ff99SB. J. Chem. Theory Comput. 2015, 11 (8), 3696– 3713,  DOI: 10.1021/acs.jctc.5b00255
      23
      ff14SB: Improving the Accuracy of Protein Side Chain and Backbone Parameters from ff99SB
      Maier, James A.; Martinez, Carmenza; Kasavajhala, Koushik; Wickstrom, Lauren; Hauser, Kevin E.; Simmerling, Carlos
      Journal of Chemical Theory and Computation (2015), 11 (8), 3696-3713CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
      Mol. mechanics is powerful for its speed in atomistic simulations, but an accurate force field is required. The Amber ff99SB force field improved protein secondary structure balance and dynamics from earlier force fields like ff99, but weaknesses in side chain rotamer and backbone secondary structure preferences have been identified. Here, we performed a complete refit of all amino acid side chain dihedral parameters, which had been carried over from ff94. The training set of conformations included multidimensional dihedral scans designed to improve transferability of the parameters. Improvement in all amino acids was obtained as compared to ff99SB. Parameters were also generated for alternate protonation states of ionizable side chains. Av. errors in relative energies of pairs of conformations were under 1.0 kcal/mol as compared to QM, reduced 35% from ff99SB. We also took the opportunity to make empirical adjustments to the protein backbone dihedral parameters as compared to ff99SB. Multiple small adjustments of φ and ψ parameters were tested against NMR scalar coupling data and secondary structure content for short peptides. The best results were obtained from a phys. motivated adjustment to the φ rotational profile that compensates for lack of ff99SB QM training data in the β-ppII transition region. Together, these backbone and side chain modifications (hereafter called ff14SB) not only better reproduced their benchmarks, but also improved secondary structure content in small peptides and reprodn. of NMR χ1 scalar coupling measurements for proteins in soln. We also discuss the Amber ff12SB parameter set, a preliminary version of ff14SB that includes most of its improvements.
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    24. 24
      Jämbeck, J. P. M.; Lyubartsev, A. P. Derivation and Systematic Validation of a Refined All-Atom Force Field for Phosphatidylcholine Lipids. J. Phys. Chem. B 2012, 116 (10), 3164– 3179,  DOI: 10.1021/jp212503e
      24
      Derivation and systematic validation of a refined all-atom force field for phosphatidylcholine lipids
      Jambeck Joakim P M; Lyubartsev Alexander P
      The journal of physical chemistry. B (2012), 116 (10), 3164-79 ISSN:.
      An all-atomistic force field (FF) has been developed for fully saturated phospholipids. The parametrization has been largely based on high-level ab initio calculations in order to keep the empirical input to a minimum. Parameters for the lipid chains have been developed based on knowledge about bulk alkane liquids, for which thermodynamic and dynamic data are excellently reproduced. The FFs ability to simulate lipid bilayers in the liquid crystalline phase in a tensionless ensemble was tested in simulations of three lipids: 1,2-diauroyl-sn-glycero-3-phospocholine (DLPC), 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC), and 1,2-dipalmitoyl-sn-glycero-3-phospcholine (DPPC). Computed areas and volumes per lipid, and three different kinds of bilayer thicknesses, have been investigated. Most importantly NMR order parameters and scattering form factors agree in an excellent manner with experimental data under a range of temperatures. Further, the compatibility with the AMBER FF for biomolecules as well as the ability to simulate bilayers in gel phase was demonstrated. Overall, the FF presented here provides the important balance between the hydrophilic and hydrophobic forces present in lipid bilayers and therefore can be used for more complicated studies of realistic biological membranes with protein insertions.
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    25. 25
      Degiacomi, M. T.; Dal Peraro, M. Macromolecular Symmetric Assembly Prediction Using Swarm Intelligence Dynamic Modeling. Structure 2013, 21 (7), 1097– 1106,  DOI: 10.1016/j.str.2013.05.014
      25
      Macromolecular Symmetric Assembly Prediction Using Swarm Intelligence Dynamic Modeling
      Degiacomi, Matteo T.; Dal Peraro, Matteo
      Structure (Oxford, United Kingdom) (2013), 21 (7), 1097-1106CODEN: STRUE6; ISSN:0969-2126. (Elsevier Ltd.)
      Proteins often assemble in multimeric complexes to perform a specific biol. function. However, trapping these high-order conformations is difficult exptl. Therefore, predicting how proteins assemble using in silico techniques can be of great help. The size of the assocd. conformational space and the fact that proteins are intrinsically flexible structures make this optimization problem extremely challenging. Nonetheless, known exptl. spatial restraints can guide the search process, contributing to model biol. relevant states. We present here a swarm intelligence optimization protocol able to predict the arrangement of protein sym. assemblies by exploiting a limited amt. of exptl. restraints and steric interactions. Importantly, within this scheme the native flexibility of each protein subunit is taken into account as extd. from mol. dynamics (MD) simulations. We show that this is a key ingredient for the prediction of biol. functional assemblies when, upon oligomerization, subunits explore activated states undergoing significant conformational changes.
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    26. 26
      Hess, B.; Bekker, H.; Berendsen, H. J. C.; Fraaije, J. G. E. M. LINCS: A Linear Constraint Solver for Molecular Simulations. J. Comput. Chem. 1997, 18 (12), 1463– 1472,  DOI: 10.1002/(SICI)1096-987X(199709)18:12<1463::AID-JCC4>3.0.CO;2-H
      26
      LINCS: a linear constraint solver for molecular simulations
      Hess, Berk; Bekker, Henk; Berendsen, Herman J. C.; Fraaije, Johannes G. E. M.
      Journal of Computational Chemistry (1997), 18 (12), 1463-1472CODEN: JCCHDD; ISSN:0192-8651. (Wiley)
      We present a new LINear Constraint Solver (LINCS) for mol. simulations with bond constraints using the enzyme lysozyme and a 32-residue peptide as test systems. The algorithm is inherently stable, as the constraints themselves are reset instead of derivs. of the constraints, thereby eliminating drift. Although the derivation of the algorithm is presented in terms of matrixes, no matrix matrix multiplications are needed and only the nonzero matrix elements have to be stored, making the method useful for very large mols. At the same accuracy, the LINCS algorithm is 3-4 times faster than the SHAKE algorithm. Parallelization of the algorithm is straightforward.
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