Computational prediction of protein–protein binding affinities

“The weighted-histogram analysis method 127,128 or related algorithms are then used to calculate a potential of mean force (PMF) along the RC.”

“In most applications, this is achieved in discrete steps by adding a quadratic umbrella potential with reference values for the RC change in steps of 0.5 – 2 Å in case of a distance RC.”

“The changes in free energy can be calculated by integrating the generalized force along the switching pathway (thermodynamic integration [TI] 106 ), free energy perturbation (FEP) 107 or using alternative methods such as Bennett' acceptance ratio (BAR) method.”

“87 – 91 A very systematic study to predict the free energy of binding and to score docked complexes was recently performed by Chen et al. 89 The authors compared various force fields, protocols for performing MD simulations and using the Poisson – Boltzmann or the GB solvation model (not including…”

“Among the most common are geometric hashing methods to rapidly match geometric surface descriptors of proteins 38,39 and fast Fourier transform (FFT) correlation techniques 16,37,40,41 to efficiently locate overlaps between complementary protein surfaces.”

“The restriction of orientation and axial placement in the separated state can be calculated analytically whereas commonly a FEP approach is employed to obtain the corresponding contributions in the bound complex.”

“108 In order to obtain the effect of a mutation on binding affinity, the transformation needs to be performed in the complex and for the unbound solvated partner.”

“74,75 The majority of force field scoring potentials neglect any intramolecular energy changes of the binding partners and therefore do not include changes in intramolecular interactions or changes in conformational entropy (e.g., restriction of conformational fluctuations upon binding).”

“On the longer run, it is desired to create completely new protein partners with programmed surface properties to allow for new interactions with selected candidate partners.(8,9) Such efforts may form the basis for synthetic complexes that can act as designed molecular machines with a desired new function.”

“87,88 The most straight forward approach is then to start from separate protein molecules and follow binding during sufficiently long MD simulations.”

“Among the most common are geometric hashing methods to rapidly match geometric surface descriptors of proteins 38,39 and fast Fourier transform (FFT) correlation techniques 16,37,40,41 to efficiently locate overlaps between complementary protein surfaces.”

“133 Alternatively, it is possible to use Umbrella integration, 134 metadynamics, 135 – 137 or to apply an adaptive force (ABF) 135,136 along the RC to offset the effective interaction between partners.”

“For the latter cases, recent improvements of CryoEM (electron microscopy under cryogenic conditions) resulted in solving the structure of many new large and transient biomolecular assemblies achieving often atomic or near-atomic resolution.(17,18) The CryoEM method is limited to complexes above a certain size limit (~…”

“For example, Gohlke et al.(85,86) investigated the Ras–Raf and Ras–RalGDS complex and reported a binding free energy in good agreement with experiment, however, depending on how conformational entropy was estimated and with errors of about several kcal/mol.”

“11,13 Within this ensemble, there are structures close to the bound and unbound forms and the process of binding to partner molecules shifts the ensemble toward the bound form.”

“128 In this case, the bound and unbound states are characterized by different sets of distances that are included as distance restraints and a coupling parameter lambda is employed to transform between the sets of restraints.”

“120,121 It includes not only the sampling of the native binding but allows also the characterization of alternative and intermediate encounter binding states.”

“…of new starting configurations and addition of a biasing potential to promote also dissociation of the bound complex in Hamiltonian replica exchange (H-REMD) simulations 119 it was possible to sample sufficient association and dissociation events to generate a Markov model for the binding process.”

“79 For rapid evaluation of single complex structures, usually explicit solvent molecules are not included.”

“8,9 Such efforts may form the basis for synthetic complexes that can act as designed molecular machines with a desired new function.”

“The prediction of the binding affinity of putative protein–protein interactions is related to the computational modeling of the structure of protein–protein complexes and the ranking of possible predicted solutions.(30,34) Besides of experimentally determined complexes, one can distinguish two main computational techn…”

“101,102 For protein engineering, it is of significant interest to predict changes in binding affinity of protein – protein complexes due to mutations and to identify important residues for the interaction (hotspots).”

“111,129,130 Significant improvements can often be achieved by coupling Umbrella sampling with H-REMD allowing exchanges of sampled states between separate U.S. windows.”

“2,4 This also includes the effect of mutations in proteins that can modulate or even disrupt the binding to partner proteins.”

“133 Alternatively, it is possible to use Umbrella integration, 134 metadynamics, 135 – 137 or to apply an adaptive force (ABF) 135,136 along the RC to offset the effective interaction between partners.”

“122,123 Briefly, in this technique, the space along one or more RCs is discretized in intervals and simulations are distributed along the coordinates such that each interval is populated by a fixed number of simulations.”

“87 – 91 A very systematic study to predict the free energy of binding and to score docked complexes was recently performed by Chen et al. 89 The authors compared various force fields, protocols for performing MD simulations and using the Poisson – Boltzmann or the GB solvation model (not including…”

“are mediated by the assembly of proteins to form transient dimers or oligomers in order to act as enzymes, transporters, or to stabilize the shape of the cell.(1,2) Numerous interactions between proteins in a cell are in principle possible but only a fraction of putative complexes and assemblies is indeed formed and o…”

“95,97,98 In a recent study of Sun et al., 97 entropy effects on the performance of endpoint methods of over 1,500 protein – ligand systems were assessed.”

“133 Alternatively, it is possible to use Umbrella integration, 134 metadynamics, 135 – 137 or to apply an adaptive force (ABF) 135,136 along the RC to offset the effective interaction between partners.”

“80,81 More frequently, approaches are used that involve a reevaluation of explicit solvent MD trajectories after replacement of the surrounding environment by an implicit solvent model (see next paragraph).”

“95,97,98 In a recent study of Sun et al., 97 entropy effects on the performance of endpoint methods of over 1,500 protein – ligand systems were assessed.”

“12,48,49”

“101,102 For protein engineering, it is of significant interest to predict changes in binding affinity of protein – protein complexes due to mutations and to identify important residues for the interaction (hotspots).”

“In direct methods, complex formation can be detected by changes in heat capacity of the solution upon varying partner concentration (e.g., in isothermal titration calorimetry 27 ) or optically using for example an associated change in absorbance or fluorescence.”

“138,140,141 These examples indicate that the methodology, in principle, allow accurate calculation of protein – protein binding free energies if the bound complex structure is known.”

“44 If experimental data or data based on bioinformatics analysis are available, this information can be included either directly during the docking search, for example, in the HADDOCK, 45 ATTRACT, 43 or RosettaDock 46,47 approaches, or can be used to screen and rerank the docking solutions obtained from rapid FFT-base…”

“118 With a further adaptive selection of new starting configurations and addition of a biasing potential to promote also dissociation of the bound complex in Hamiltonian replica exchange (H-REMD) simulations 119 it was possible to sample sufficient association and dissociation events to generate a…”

“In most applications, this is achieved in discrete steps by adding a quadratic umbrella potential with reference values for the RC change in steps of 0.5 – 2 Å in case of a distance RC.”

“44 If experimental data or data based on bioinformatics analysis are available, this information can be included either directly during the docking search, for example, in the HADDOCK, 45 ATTRACT, 43 or RosettaDock 46,47 approaches, or can be used to screen and rerank the docking solutions obtained from rapid FFT-base…”

“5,6 Within different protein families, these domains can differ in sequence resulting in different binding specificities and in different combinations of possible interactions.”

“31,54 More sophisticated physics-based or knowledge-based approaches often result in correlation coefficients that are not much larger.”

“15,16,25,35 In addition, the de novo design of protein – protein interactions requires docking or modeling of new protein – protein interfaces.”

“Databases of protein domain – domain interactions such as 3DiD, 22 SCOPPI, 23 or PIBASE 24 are available that allow identification of interfaces and are helpful to predict the range of binding affinities for domain-mediated protein complexes.”

“19,20 In addition, several NMR techniques can be used to quantify protein – protein affinity and also help in modeling complexes if the structure of partner proteins is known.”

“19,20 In addition, several NMR techniques can be used to quantify protein – protein affinity and also help in modeling complexes if the structure of partner proteins is known.”

“59 64 The potentials differ in the resolution of the interface description.”

“32,49 For the purpose of ranking, various terms of the force field are weighted to give an optimal correlation with respect to experimental data on a training set of complexes.”

“15,16,25,35 In addition, the de novo design of protein – protein interactions requires docking or modeling of new protein – protein interfaces.”

“12,49”

“37 A variety of computational methods exists to efficiently generate a large number of putative binding geometries typically with an initial systematic docking search keeping partner structures rigid.”

“138,140,141 These examples indicate that the methodology, in principle, allow accurate calculation of protein – protein binding free energies if the bound complex structure is known.”

“59 64 The potentials differ in the resolution of the interface description.”

“125 It is also possible to extract kinetics and binding free energies from these simulations.”

“80,81 More frequently, approaches are used that involve a reevaluation of explicit solvent MD trajectories after replacement of the surrounding environment by an implicit solvent model (see next paragraph).”

“36 Hence, many interactions especially those mediated by reoccurring protein domains can be modeled based on similarity to an already known interaction.”

“…based on bioinformatics analysis are available, this information can be included either directly during the docking search, for example, in the HADDOCK, 45 ATTRACT, 43 or RosettaDock 46,47 approaches, or can be used to screen and rerank the docking solutions obtained from rapid FFT-based methods.”

“111,129,130 Significant improvements can often be achieved by coupling Umbrella sampling with H-REMD allowing exchanges of sampled states between separate U.S. windows.”

“Databases of protein domain – domain interactions such as 3DiD, 22 SCOPPI, 23 or PIBASE 24 are available that allow identification of interfaces and are helpful to predict the range of binding affinities for domain-mediated protein complexes.”

“Alternatively, molecular dynamics (MD), Brownian dynamics, Monte Carlo, or multistart energy minimization can be used to generate locally optimized protein–protein docking complexes.(16) To enhance the speed, often coarse-grained (CG) instead of atomistic protein models are used.”

“44 If experimental data or data based on bioinformatics analysis are available, this information can be included either directly during the docking search, for example, in the HADDOCK, 45 ATTRACT, 43 or RosettaDock 46,47 approaches, or can be used to screen and rerank the docking solutions obtained…”

“109 – 114 Although typically performed in explicit solvent, it is also possible to perform alchemical transformations in implicit solvent 115 with computational costs similar to MM/PBSA but avoiding the endpoint approximations inherent to endpoint ensemble approaches.”

“The WE technique allows eventually the extraction of both kinetic and thermodynamic data along the binding RC. 123 Although so far only applied to study small-ligand binding to proteins, 123,124 in principle, it could also be used to study protein – protein binding.”

“Aldeghi et al. 99 also found a higher sensitivity of the IE term to the simulated ensemble than the other MM-PBSA terms for three sets of bromodomain-inhibitor pairs.”

“117 However, such association simulations do not allow direct extraction of the associated binding free energy.”

“11,13 Within this ensemble, there are structures close to the bound and unbound forms and the process of binding to partner molecules shifts the ensemble toward the bound form.”

“Among the most common are geometric hashing methods to rapidly match geometric surface descriptors of proteins 38,39 and fast Fourier transform (FFT) correlation techniques 16,37,40,41 to efficiently locate overlaps between complementary protein surfaces.”

“Numerous interactions between proteins in a cell are in principle possible but only a fraction of putative complexes and assemblies is indeed formed and of functional relevance.(3) The associated binding free energy of protein–protein interactions determines the stability of association and the conditions for complex…”

“55 In an extension of the BSA approach for binding prediction, Vangone and Bonvin 56 suggested a contact-based scoring with optimal weights on various types of contacts at an interface (e.g., polar – polar, polar – nonpolar, etc.) that showed improved correlation with experimental binding affinity…”

“33 In the second and third sections, we will focus on rapid approaches to rank predicted complexes and to estimate binding affinities based on single complex structures or ensembles of structures with a focus on force field-based methods.”

“30 – 32 These sets can serve as references for evaluating computational efforts; however, one should always be aware of experimental conditions and the method for binding affinity determination compared to the computational setup.”

“IE has been successfully applied in studies in combination with MM-PBSA and MM-GBSA calculations of protein – protein 96,97 or protein – ligand 95,97 binding affinities.”

“144,145 Finally, with increasing computational resources and development of improved advanced sampling methods, the option to directly follow protein – protein association and dissociation offers the opportunity for an in depth understanding of transient nonspecific and specific binding.”

“Some approaches included conformational changes during docking already during the initial search including soft collective normal mode (NM) directions as additional variables during docking by energy minimization 42,43 or in using swarm optimization.”

“Using an extension of the MM/PBSA method with residue specific dielectric constants, Petukh et al. 105 achieved a high correlation (correlation coefficient of − 0.62) with experiment for a set of 1,300 mutations in 43 protein – protein complexes (several other applications are reviewed in Reference 79).”

“116”

“50 In fact, it has been found that the majority of stable natural protein – protein interactions can in principle be modeled by a template-based approach.”

“26 Methods based on separation of complex and unbound partners require long lifetimes of the complex (small dissociation rate constants) beyond the time scale of the experiment.”

“90 The inclusion of an explicit water model has been proven to give good results in various protein – protein binding affinity predictions for single complexes (e.g., Ulucan et al. 93 ).”

“26,28 In the surface plasmon resonance technique, one partner is immobilized on a sensor surface.”

“5,6 Within different protein families, these domains can differ in sequence resulting in different binding specificities and in different combinations of possible interactions.”

“Besides of using knowledge-based statistical potentials for ranking of docked complexes, it can also be based on a molecular mechanics (MM) type force field description of binding partners.(45,46,73) Similar to the statistical potentials discussed above, these scoring potentials are mostly used to provide a relative r…”

“143 The calculated binding free energies for the near-native complex geometries were in reasonable agreement with experiment.”

“17,18 The CryoEM method is limited to complexes above a certain size limit (~100 kD) to achieve sufficient contrast of the image relative to a noisy background but no crystals of the complex are necessary.”

“29 With the method, it is also possible to analyze the time dependence of binding and to determine kinetic constants of protein – protein association and dissociation.”

“Methods have also been developed to just obtain the change in translational and orientational (external) entropy of one partner with respect to the other.(83,84) MM-GBSA and MM-PBSA have been used both for the calculation of absolute protein–protein binding affinities and to evaluate docked protein–protein complex str…”

“The ensemblesbased MM/PBSA or MM/GBSA approaches can also be used to identify hot spots and to calculate the change in the binding free energy upon mutation of interface residues.(104) The hot spots of 15 protein–protein complexes were calculated recently with MM/PBSA using residue type specific dielectric constants (…”

“142 However, one should keep in mind that a CG model misses many details of intermolecular interactions such as hydrogen bonds and several conformational degrees of freedom are merged into effective interaction potentials.”

“15,16,25,35 In addition, the de novo design of protein – protein interactions requires docking or modeling of new protein – protein interfaces.”

“Among the most common are geometric hashing methods to rapidly match geometric surface descriptors of proteins 38,39 and fast Fourier transform (FFT) correlation techniques 16,37,40,41 to efficiently locate overlaps between complementary protein surfaces.”

“14 However, every conformation is, in principle, accessible even in the unbound state albeit with a potentially very low statistical weight.”

“10,11 During binding, proteins appear to induce conformational changes in the partners that are a prerequisite for specific complex formation.”

“Furthermore, an external entropy correction alone has been shown to not necessarily improve the correlation to experimental binding affinities for protein–ligand systems.(100)”

“138,140,141 These examples indicate that the methodology, in principle, allow accurate calculation of protein – protein binding free energies if the bound complex structure is known.”

“7 Second, for the majority of natural stable protein – protein interactions one often finds homologous complex geometries in the data base of experimentally determined complexes.”

“111,129,130 Significant improvements can often be achieved by coupling Umbrella sampling with H-REMD allowing exchanges of sampled states between separate U.S. windows.”

“90 The inclusion of an explicit water model has been proven to give good results in various protein – protein binding affinity predictions for single complexes (e.g., Ulucan et al. 93 ).”

“133 Alternatively, it is possible to use Umbrella integration, 134 metadynamics, 135 – 137 or to apply an adaptive force (ABF) 135,136 along the RC to offset the effective interaction between partners.”

“129,131,132 Another possibility is to calculate first an approximate PMF and add this to bias the simulations along the RC to smooth the effective interaction for calculating a precise PMF in a second step or iteratively in several steps.”

“On a smaller test set of four proteins, crystal water molecules were added in the evERdock approach that improved water mediated contacts so that the identification of near-native binding decoys could be improved.(94) SIEBENMORGEN AND ZACHARIAS 7 of 18”

“95,97,98 In a recent study of Sun et al., 97 entropy effects on the performance of endpoint methods of over 1,500 protein – ligand systems were assessed.”

“An approach using a restraining potential to avoid trapping of protein–protein complexes in nonspecific transient states but at the same time restraining the partners not to separate has been introduced to refine docked complexes.(126) Different levels of the biasing potential are applied in an H-REMD simulation with…”

“109 – 114 Although typically performed in explicit solvent, it is also possible to perform alchemical transformations in implicit solvent 115 with computational costs similar to MM/PBSA but avoiding the endpoint approximations inherent to endpoint ensemble approaches.”

“69 – 72 The potentials also vary in the number of atom or pseudo atom types or the reference state from which the expected contact or distance probability for atom-pairs are derived.”

“109 – 114 Although typically performed in explicit solvent, it is also possible to perform alchemical transformations in implicit solvent 115 with computational costs similar to MM/PBSA but avoiding the endpoint approximations inherent to endpoint ensemble approaches.”

“While this method has been known to overestimate energies, it performs reasonably well for relative comparison of binding strength (41, 42).”

“However, more rigorous strategies are available to predict both the effect of mutations on the folding free energy and the binding free energy (Benedix et al., 2009; Kumari et al., 2014b; Seeliger & de Groot, 2010; Siebenmorgen & Zacharias, 2020).”

“…the context of AI for DD it is of utmost importance to train the models on a dataset structure-based DD include semi-empirical quantum mechanical (QM) methods 5 , molecular dynamics (MD) simulations 6,7 , docking 8 and coarse-grained simulations 9 , which can also be combined to be more efficient.”

“Supervised machine-learning is applied for developing protein-targeted scoring functions for the prediction of binding affinity 41,42 (for an extensive description of recent docking methods, see Reference 40 and references therein).”

“Combining equations (5) and (7), we have:”

“(1) In the potential of mean force methods, a complex is dissociated by forcing one of the binding partners to move relative to the other along a userdefined path.”

“On the one hand, for example, alchemical calculations are quite accurate, but they are still very challenging for protein-protein complexes (Gapsys et al., 2016; Mey et al., 2020; Siebenmorgen and Zacharias, 2020).”

“…thermodynamics and kinetics play foundational roles in regulating biological processes [1–4], such as the processes of protein–protein interactions [5], protein-metabolite recognitions [6] and protein-nucleic acids interactions [7, 8], where binding free energy between the systems controls the…”

“However, it is known that proteins are dynamic objects and their structure undergoes conformational changes, both under the natural effect of thermal noise and as a result of binding with a molecular partner [34].”

“There are several great reviews on using computational methods to studymembrane dynamic interactions (Corradi et al., 2019; Muller et al., 2019; Siebenmorgen and Zacharias, 2020).”

“Some of these methods rely on atomistic molecular dynamics (MD) simulations to produce configurational ensembles (Siebenmorgen and Zacharias, 2020).”

“221”

“A few papers that discuss, both, refinement of poses and scoring of PPIs have already been discussed in the previous paragraph [50–53 , 61 ] In an early study, Cuendet et al. studied the binding free energy of two protein-protein complexes that differ only by a single mutation [62].”

“Binding affinity (∆G) and the dissociation constant (Kd) were to determined accordingly [44,45].”

“Because Kd1/Kd2 cannot yet be predicted precisely for a given reference–variant pair (55, 56), the model’s estimates were expected to be imprecise for any given pair of antibodies or TCRs; however, the law of large numbers—on the order of 10(10) pairwise comparisons per repertoire—provides for accuracy of the desired…”

“Binding Free Energy Calculations using MM/PBSA and MM/GBSA Method The free intermolecular binding energy of C-Raf with RKIP and its variants was estimated using Molecular Mechanics/Poisson Boltzmann Surface Area (MM/PBSA) and Molecular Mechanics/ Generalized Born Surface Area (MM/GBSA) methodology (Chen et al., 2016;…”

“It has superior performance predicting binding free energy with respect to computation time in comparison with other free energy perturbation methods, hence MMGBSA-based free energy approach was utilized (Siebenmorgen & Zacharias, 2020; Su et al., 2015; Su et al., 2015; Wang et al., 2019).”

“The aim of these methods are various, varying from binding site identification [5, 6] to binding affinity prediction [7, 8] or protein-protein docking guide [9–12].”

“This is consistent with previous findings that there is poor correlation between number of contacts and affinity.(31) For the A6_c134 TCR, although our MD simulations suggested a smaller increase in the average number of contacts compared to the analysis of the crystal structure, increases were observed in the region…”

“…interactions or protein–protein inter-© actions (PPIs) Geng et al. (2019); Pandurangan and Blundell (2020); Geng et al. (2019); Li et al. (2021), Siebenmorgen and Zacharias (2020); Dehouck et al. (2013); Romero-Molina et al. (2022); Xue et al. (2016); Yang et al. (2023); Wang et al. (2020).”

“Protein domains frequently mediate protein-protein interactions; mutations in these domains can change a protein ’ s capacity to interact with other proteins [93].”

“[1] for a review of the underlying theory).”

“They include molecular dynamics simulations reaching very accurate estimations, but requiring extensive computational resources which limit their large-scale application (Siebenmorgen and Zacharias, 2020).”

“Beyond predicting inter-protein contacts, accurately identifying interface residues is essential for understanding complex formation, signaling, and functional regulation of protein assemblies 46 .”

“This can be done by analyzing the details of fusion protein-receptor interactions using molecular docking or molecular dynamics simulations coupled with free energy calculations [50 – 52].”

“During the past two decades, three general classes of computational approaches have been used to predict BA [11,12]: (1) physics-based ab-initio methods such as free energy perturbation and thermodynamics integration [13,14]; (2) knowledge-based statistical potentials such as DFIRE [15,16] or other empirical scoring f…”

“S6) (43, 44).”

“…in machine learning (ML) have begun to reshape the landscape of protein engineering, offering data-driven strategies to predict relevant properties, including protein stability (Musil et al., 2024), binding affinities (Siebenmorgen and Zacharias, 2020), and catalytic properties (Chen et al., 2022).”

“MD has been used to investigate a wide range of biologically important properties, such as the role of single-point mutations on enzyme structure [3,4] or activity [5,6] and the quantitative determination of binding energies for both protein-ligand [7,8] and protein - protein complexes [9].”

“…nuclear magnetic resonance (NMR), or cryo-electron microscopy (cryo-EM), the interaction partner of frhAGB -encoded hydrogenase could have been easily predicted using computational methods such as protein–protein docking, based entirely on three-dimensional protein structures (36, 37).”

“MM-PBSA/GBSA has been used recently to estimate protein-protein binding affinities in molecular complexes ( 47 , 106 , 107 ).”

“Transient interactions are also often mediated by disordered protein segments, small linear motifs and can require posttranslational modifications (PTMs),(37,39) complicating even further the understanding of their binding mechanisms.(10) Additionally, PTMs at functional sites can create new binding sites within trans…”

“Based on this alignment, a 3D model of the target protein can be constructed (Figure 3A) [56,57].”

“Wealso calculated the interaction energies of protein– protein interaction (Siebenmorgen and Zacharias, 2020).”

“However, most of these applications focused on the binding of biological macromolecules to drug, ion, or other small organic molecules (Siebenmorgen and Zacharias 2020).”

“model (MMGBSA: Molecular Mechanics Generalized Born Surface Area method).(35,36) To avoid large conformational changes during the simulation's weak positional restraints on the structures were included, assuming that the mutations do not alter the structure sig-”

“Despite decades of research, efficient and accurate computational prediction of binding free energies is still a challenge [30, 39, 42, 50, 54].”

“Machine-learning based scoring functions have been developed for the approximation of binding specificity [7, 8], however, they often do not include routines for preparing mutated structural models or ensembles of models.”

“Despite decades of theoretical and computational advancements in predicting protein-protein binding affinity, as reviewed by Siebenmorgen et al. [11], the problem remains highly complex and unsolved.”

“For this MM-GBSA 54 calculations employing the “single trajectory approach” in MMPBSA.py of AMBER22 80 , considering gas-phase energies and solvation free energies but not configurational entropies 55 , were performed.”

“The use of technical computers increases our knowledge about mechanisms of interaction, 3D-structural information of protein–protein complex, and prediction-binding affinity [30].”

“Mutations in protein sequences modulate or often disrupt protein interactions by changing associated binding affinity which may forbid normal protein function and cause disease (Cargill et al., 1999; Li et al., 2016; Siebenmorgen and Zacharias, 2019).”