skip to main content


Title: Estimation of binding rates and affinities from multiensemble Markov models and ligand decoupling

Accurate and efficient simulation of the thermodynamics and kinetics of protein–ligand interactions is crucial for computational drug discovery. Multiensemble Markov Model (MEMM) estimators can provide estimates of both binding rates and affinities from collections of short trajectories but have not been systematically explored for situations when a ligand is decoupled through scaling of non-bonded interactions. In this work, we compare the performance of two MEMM approaches for estimating ligand binding affinities and rates: (1) the transition-based reweighting analysis method (TRAM) and (2) a Maximum Caliber (MaxCal) based method. As a test system, we construct a small host–guest system where the ligand is a single uncharged Lennard-Jones (LJ) particle, and the receptor is an 11-particle icosahedral pocket made from the same atom type. To realistically mimic a protein–ligand binding system, the LJ ϵ parameter was tuned, and the system was placed in a periodic box with 860 TIP3P water molecules. A benchmark was performed using over 80 µs of unbiased simulation, and an 18-state Markov state model was used to estimate reference binding affinities and rates. We then tested the performance of TRAM and MaxCal when challenged with limited data. Both TRAM and MaxCal approaches perform better than conventional Markov state models, with TRAM showing better convergence and accuracy. We find that subsampling of trajectories to remove time correlation improves the accuracy of both TRAM and MaxCal and that in most cases, only a single biased ensemble to enhance sampled transitions is required to make accurate estimates.

 
more » « less
NSF-PAR ID:
10364744
Author(s) / Creator(s):
 ;  
Publisher / Repository:
American Institute of Physics
Date Published:
Journal Name:
The Journal of Chemical Physics
Volume:
156
Issue:
13
ISSN:
0021-9606
Page Range / eLocation ID:
Article No. 134115
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. null (Ed.)
    A growing number of computational tools have been developed to accurately and rapidly predict the impact of amino acid mutations on protein-protein relative binding affinities. Such tools have many applications, for example, designing new drugs and studying evolutionary mechanisms. In the search for accuracy, many of these methods employ expensive yet rigorous molecular dynamics simulations. By contrast, non-rigorous methods use less exhaustive statistical mechanics, allowing for more efficient calculations. However, it is unclear if such methods retain enough accuracy to replace rigorous methods in binding affinity calculations. This trade-off between accuracy and computational expense makes it difficult to determine the best method for a particular system or study. Here, eight non-rigorous computational methods were assessed using eight antibody-antigen and eight non-antibody-antigen complexes for their ability to accurately predict relative binding affinities (ΔΔG) for 654 single mutations. In addition to assessing accuracy, we analyzed the CPU cost and performance for each method using a variety of physico-chemical structural features. This allowed us to posit scenarios in which each method may be best utilized. Most methods performed worse when applied to antibody-antigen complexes compared to non-antibody-antigen complexes. Rosetta-based JayZ and EasyE methods classified mutations as destabilizing (ΔΔG < -0.5 kcal/mol) with high (83–98%) accuracy and a relatively low computational cost for non-antibody-antigen complexes. Some of the most accurate results for antibody-antigen systems came from combining molecular dynamics with FoldX with a correlation coefficient (r) of 0.46, but this was also the most computationally expensive method. Overall, our results suggest these methods can be used to quickly and accurately predict stabilizing versus destabilizing mutations but are less accurate at predicting actual binding affinities. This study highlights the need for continued development of reliable, accessible, and reproducible methods for predicting binding affinities in antibody-antigen proteins and provides a recipe for using current methods. 
    more » « less
  2. null (Ed.)
    Protein–protein binding is fundamental to most biological processes. It is important to be able to use computation to accurately estimate the change in protein–protein binding free energy due to mutations in order to answer biological questions that would be experimentally challenging, laborious, or time-consuming. Although nonrigorous free-energy methods are faster, rigorous alchemical molecular dynamics-based methods are considerably more accurate and are becoming more feasible with the advancement of computer hardware and molecular simulation software. Even with sufficient computational resources, there are still major challenges to using alchemical free-energy methods for protein–protein complexes, such as generating hybrid structures and topologies, maintaining a neutral net charge of the system when there is a charge-changing mutation, and setting up the simulation. In the current study, we have used the pmx package to generate hybrid structures and topologies, and a double-system/single-box approach to maintain the net charge of the system. To test the approach, we predicted relative binding affinities for two protein–protein complexes using a nonequilibrium alchemical method based on the Crooks fluctuation theorem and compared the results with experimental values. The method correctly identified stabilizing from destabilizing mutations for a small protein–protein complex, and a larger, more challenging antibody complex. Strong correlations were obtained between predicted and experimental relative binding affinities for both protein–protein systems. 
    more » « less
  3. Abstract

    Understanding animal movement often relies upon telemetry and biologging devices. These data are frequently used to estimate latent behavioural states to help understand why animals move across the landscape. While there are a variety of methods that make behavioural inferences from biotelemetry data, some features of these methods (e.g. analysis of a single data stream, use of parametric distributions) may limit their generality to reliably discriminate among behavioural states.

    To address some of the limitations of existing behavioural state estimation models, we introduce a nonparametric Bayesian framework called the mixed‐membership method for movement (M4), which is available within the open‐sourcebayesmoveR package. This framework can analyse multiple data streams (e.g. step length, turning angle, acceleration) without relying on parametric distributions, which may capture complex behaviours more successfully than current methods. We tested our Bayesian framework using simulated trajectories and compared model performance against two segmentation methods (behavioural change point analysis (BCPA) and segclust2d), one machine learning method [expectation‐maximization binary clustering (EMbC)] and one type of state‐space model [hidden Markov model (HMM)]. We also illustrated this Bayesian framework using movements of juvenile snail kitesRostrhamus sociabilisin Florida, USA.

    The Bayesian framework estimated breakpoints more accurately than the other segmentation methods for tracks of different lengths. Likewise, the Bayesian framework provided more accurate estimates of behaviour than the other state estimation methods when simulations were generated from less frequently considered distributions (e.g. truncated normal, beta, uniform). Three behavioural states were estimated from snail kite movements, which were labelled as ‘encamped’, ‘area‐restricted search’ and ‘transit’. Changes in these behaviours over time were associated with known dispersal events from the nest site, as well as movements to and from possible breeding locations.

    Our nonparametric Bayesian framework estimated behavioural states with comparable or superior accuracy compared to the other methods when step lengths and turning angles of simulations were generated from less frequently considered distributions. Since the most appropriate parametric distributions may not be obvious a priori, methods (such as M4) that are agnostic to the underlying distributions can provide powerful alternatives to address questions in movement ecology.

     
    more » « less
  4. Metabotropic glutamate receptors (mGluRs) play an important role in regulating glutamate signal pathways, which are involved in neuropathy and periphery homeostasis. mGluR4, which belongs to Group III mGluRs, is most widely distributed in the periphery among all the mGluRs. It has been proved that the regulation of this receptor is involved in diabetes, colorectal carcinoma and many other diseases. However, the application of structure-based drug design to identify small molecules to regulate the mGluR4 receptor is limited due to the absence of a resolved mGluR4 protein structure. In this work, we first built a homology model of mGluR4 based on a crystal structure of mGluR8, and then conducted hierarchical virtual screening (HVS) to identify possible active ligands for mGluR4. The HVS protocol consists of three hierarchical filters including Glide docking, molecular dynamic (MD) simulation and binding free energy calculation. We successfully prioritized active ligands of mGluR4 from a set of screening compounds using HVS. The predicted active ligands based on binding affinities can almost cover all the experiment-determined active ligands, with only one ligand missed. The correlation between the measured and predicted binding affinities is significantly improved for the MM-PB/GBSA-WSAS methods compared to the Glide docking method. More importantly, we have identified hotspots for ligand binding, and we found that SER157 and GLY158 tend to contribute to the selectivity of mGluR4 ligands, while ALA154 and ALA155 could account for the ligand selectivity to mGluR8. We also recognized other 5 key residues that are critical for ligand potency. The difference of the binding profiles between mGluR4 and mGluR8 can guide us to develop more potent and selective modulators. Moreover, we evaluated the performance of IPSF, a novel type of scoring function trained by a machine learning algorithm on residue–ligand interaction profiles, in guiding drug lead optimization. The cross-validation root-mean-square errors (RMSEs) are much smaller than those by the endpoint methods, and the correlation coefficients are comparable to the best endpoint methods for both mGluRs. Thus, machine learning-based IPSF can be applied to guide lead optimization, albeit the total number of actives/inactives are not big, a typical scenario in drug discovery projects. 
    more » « less
  5. ABSTRACT

    Protein‐protein interactions are either through direct contacts between two binding partners or mediated by structural waters. Both direct contacts and water‐mediated interactions are crucial to the formation of a protein‐protein complex. During the recent CAPRI rounds, a novel parallel searching strategy for predicting water‐mediated interactions is introduced into our protein‐protein docking method, MDockPP. Briefly, a FFT‐based docking algorithm is employed in generating putative binding modes, and an iteratively derived statistical potential‐based scoring function, ITScorePP, in conjunction with biological information is used to assess and rank the binding modes. Up to 10 binding modes are selected as the initial protein‐protein complex structures for MD simulations in explicit solvent. Water molecules near the interface are clustered based on the snapshots extracted from independent equilibrated trajectories. Then, protein‐ligand docking is employed for a parallel search for water molecules near the protein‐protein interface. The water molecules generated by ligand docking and the clustered water molecules generated by MD simulations are merged, referred to as the predicted structural water molecules. Here, we report the performance of this protocol for CAPRI rounds 28–29 and 31–35 containing 20 valid docking targets and 11 scoring targets. In the docking experiments, we predicted correct binding modes for nine targets, including one high‐accuracy, two medium‐accuracy, and six acceptable predictions. Regarding the two targets for the prediction of water‐mediated interactions, we achieved models ranked as “excellent” in accordance with the CAPRI evaluation criteria; one of these two targets is considered as a difficult target for structural water prediction. Proteins 2017; 85:424–434. © 2016 Wiley Periodicals, Inc.

     
    more » « less