Classifying Protein-Protein Binding Affinity with Free-Energy Calculations and Machine Learning Approaches.

Understanding the intricate phenomenon of neuronal wiring in the brain is of great interest in neuroscience. In the fruit fly, Drosophila melanogaster, the Dpr-DIP interactome has been identified to play an important role in this process. However, experimental data suggest that a merely limited subset of complexes, essentially 57 out of a total of 231, exhibit strong binding affinity. In this work, we sought to identify the residue-level molecular basis underlying the difference in binding affinity using a state-of-the-art methodology consisting of standard binding free-energy calculations with a geometrical route and machine learning (ML) techniques. We determined the binding affinity for two complexes using statistical mechanics simulations, achieving an excellent reproduction of the experimental data. Moreover, we predicted the binding free energy for two additional low-affinity complexes, devoid of experimental estimation, while simultaneously identifying key residues for the binding. Furthermore, through the use of ML algorithms, linear discriminant analysis, and random forest, we achieved remarkable accuracy, as high as 0.99, in discerning between strong (cognate) and weak (noncognate) binders. The presented ML approach encompasses easily transferable input features, enabling its broad application to any interactome while facilitating the identification of pivotal residues critical for binding interactions. The predictive power of the generated model was probed on similar protein families from 13 diverse species. Our ML model exhibited commendable performance on these additional data sets, showcasing its reliability and robustness across the species barrier.

Improving Speed and Affordability without Compromising Accuracy: Standard Binding Free-Energy Calculations Using an Enhanced Sampling Algorithm, Multiple-Time Stepping, and Hydrogen Mass Repartitioning.

Accurate evaluation of protein-ligand binding free energies in silico is of paramount importance for understanding the mechanisms of biological regulation and providing a theoretical basis for drug design and discovery. Based on a series of atomistic molecular dynamics simulations in an explicit solvent, using well-tempered metadynamics extended adaptive biasing force (WTM-eABF) as an enhanced sampling algorithm, the so-called "geometrical route" offers a rigorous theoretical framework for binding affinity calculations that match experimental values. However, although robust, this strategy remains expensive, requiring substantial computational time to achieve convergence of the simulations. Improving the efficiency of the geometrical route, while preserving its reliability through improved ergodic sampling, is, therefore, highly desirable. In this contribution, having identified the computational bottleneck of the geometrical route, to accelerate the calculations we combine (i) a longer time step for the integration of the equations of motion with hydrogen-mass repartitioning (HMR), and (ii) multiple time-stepping (MTS) for collective-variable and biasing-force evaluation. Altogether, we performed 50 independent WTM-eABF simulations in triplicate for the "physical" separation of the Abl kinase-SH3 domain:p41 complex, following different HMR and MTS schemes, while tuning, in distinct protocols, the parameters of the enhanced-sampling algorithm. To demonstrate the consistency and reliability of the results obtained with the best-performing setups, we carried out quintuple simulations. Furthermore, we demonstrated the transferability of our method to other complexes by triplicating a 200 ns separation simulation of nine chosen protocols for the MDM2-p53:NVP-CGM097 complex. [Holzer et al. J. Med. Chem. 2015, 58, 6348-6358.] Our results, based on an aggregate simulation time of 14.4 µs, allowed an optimal set of parameters to be identified, able to accelerate convergence by a factor of three without any noticeable loss of accuracy.

Hazardous Shortcuts in Standard Binding Free Energy Calculations.

Calculating the standard binding free energies of protein-protein and protein-ligand complexes from atomistic molecular dynamics simulations in explicit solvent is a problem of central importance in computational biophysics. A rigorous strategy for carrying out such calculations is the so-called "geometrical route". In this method, two molecular objects are progressively separated from one another in the presence of orientational and conformational restraints serving to control the change in configurational entropy that accompanies the dissociation process, thereby allowing the computations to converge within simulations of affordable length. Although the geometrical route provides a rigorous theoretical framework, a tantalizing computational shortcut consists of simply leaving out such orientational and conformational degrees of freedom during the separation process. Here the accuracy and convergence of the two approaches are critically compared in the case of two protein-ligand complexes (Abl kinase-SH3:p41 and MDM2-p53:NVP-CGM097) and three protein-protein complexes (pig insulin dimer, SARS-CoV-2 spike RBD:ACE2, and CheA kinase-P2:CheY). The results of the simulations that strictly follow the geometrical route match the experimental standard binding free energies within chemical accuracy. In contrast, simulations bereft of geometrical restraints converge more poorly, yielding inconsistent results that are at variance with the experimental measurements. Furthermore, the orientational and positional time correlation functions of the protein in the unrestrained simulations decay over several microseconds, a time scale that is far longer than the typical simulation times of the geometrical route, which explains why those simulations fail to sample the relevant degrees of freedom during the separation process of the complexes.

Accurate determination of protein:ligand standard binding free energies from molecular dynamics simulations.

Designing a reliable computational methodology to calculate protein:ligand standard binding free energies is extremely challenging. The large change in configurational enthalpy and entropy that accompanies the association of ligand and protein is notoriously difficult to capture in naive brute-force simulations. Addressing this issue, the present protocol rests upon a rigorous statistical mechanical framework for the determination of protein:ligand binding affinities together with the comprehensive Binding Free-Energy Estimator 2 (BFEE2) application software. With the knowledge of the bound state, available from experiments or docking, application of the BFEE2 protocol with a reliable force field supplies in a matter of days standard binding free energies within chemical accuracy, for a broad range of protein:ligand complexes. Limiting undesirable human intervention, BFEE2 assists the end user in preparing all the necessary input files and performing the post-treatment of the simulations towards the final estimate of the binding affinity.