BFEE: A User-Friendly Graphical Interface Facilitating Absolute Binding Free-energy Calculations

Abstract

Quantifying protein-ligand binding has attracted the attention of both theorists and experimentalists for decades. Many methods for estimating binding free energies in silico have been reported in recent years. Proper use of the proposed strategies requires, however, adequate knowledge of the protein-ligand complex, the mathematical background for deriving the underlying theory, and time for setting up the simulations, bookkeeping and post-processing. Here, to minimize human intervention, we propose a toolkit aimed at facilitating the accurate estimation of standard binding free energies using a geometrical route, coined binding free-energy estimator (BFEE), and introduced as a plug-in of the popular visualization program VMD. Benefit from recent developments in new collective variables, BFEE can be used to generate the simulation input files, based solely on the structure of the complex. Once the simulations are completed, BFEE can also be utilized to perform the post-treatment of the free-energy calculations, allowing the absolute binding free energy to be estimated directly from the one dimensional potentials of mean force in simulation outputs. The minimal amount of human intervention required during the whole process combined with the ergonomic graphical interface makes BFEE a very effective and practical tool for the end-user.

Graphical abstract

INTRODUCTION

The importance of accurate binding free-energy calculations of protein-ligand complexes is a truism.¹ The most serious difficulty of in silico estimation of the binding affinity resides in capturing the change in configurational entropy associated to protein-ligand association, which requires adequate sampling of all the relevant movements of the ligand with respect to the protein.^2,3 Approximate methods, on the one hand, such as molecular mechanics/Poisson-Boltzmann surface area,⁴ usually ignore part of the entropic contribution to the binding free energy. Strategies for the accurate evaluation of this contribution, on the other hand, involve a rather elaborate workflow. For example, the confine-and-release method⁵ uses extensive potential of mean force (PMF) calculations to search for the metastable states of the complex and add corrections arising from geometrical restraints to the binding affinity obtained by an alchemical route. The attach-pull-release strategy⁶ decomposes the absolute binding free energy into the reversible work of connecting an artificial spring to the host, adjusting the spring to extract the host from the guest, and ultimately releasing the spring. We also purposed a geometrical route, in which protein-ligand binding is decomposed into several independent subprocesses, each of which describes the sampling of one degree of freedom at a time. Restraints are added to these degrees of freedom, the contributions of which are evaluated in PMF calculations (Figure 1).^7–9

Figure 1.

Left: Workflow of the BFEE plug-in. Right: Degrees of freedom considered in the binding free energy calculation strategy. The isomerization of the ligand is considered by characterizing its RMSD with respect to the conformation of the ligand in the bound state, but this variable is not shown in the figure for clarity.

As one can easily expect, setting up an absolute binding free-energy calculation using the latter strategy can require substantial human intervention, i.e., from building the simulation assays to choosing the proper simulation parameters. Attempts to automate the setup have been made, e.g., using the CharmmGUI server.^10,11 This approach, however, selects groups of atoms to define the relative orientation and position of the ligand with respect to the protein, which can be problematic for unusual geometries of the host or the guest. Moreover, this tool only helps users to generate input files. The more taxing aspect of the stepwise strategy of the geometric route is without a doubt the bookkeeping of the different PMF calculations, in particular their post-treatment and the evaluation of the configurational integrals that appear in the expression of the binding constant, K_eq (Equation 1). Some other codes, like mmpbsa.py¹² in Ambertools,¹³ analyze the results of a binding free energy estimation using the approximate MM-PBSA method. Development of an automated tool for the setup and the post-treatment of accurate free-energy calculations is, therefore, highly desirable.

With the objective of minimizing human intervention in the estimation of protein-ligand binding affinities, we present in this contribution a plug-in for the visualization program VMD¹⁴ coined binding free-energy estimator (BFEE). This plug-in can automatically set up and analyze absolute binding free-energy calculations carried out with the popular molecular dynamics engine NAMD,¹⁵ eliminating tedious and repetitive file preparation and bookkeeping, as shown in Figure 1.

THEORETICAL BACKGROUND

The detail of the theoretical background of the binding free-energy calculation can be found elsewhere.^9,16 Here, we simply recall the expression of K_eq, utilized in the post-treatment of the PMF calculations,

$$K_{\text{eq}}=\frac{{\displaystyle {\int }_{\text{site}}\mathrm{d}\mathbf{1}}{\displaystyle \int \mathrm{d}\mathbf{x}{\mathrm{e}}^{-\beta U}}}{{\displaystyle {\int }_{\mathit{bulk}}\mathrm{d}\mathbf{1}}\delta \left({\mathbf{x}}_1-{\mathbf{x}}_1^{\ast }\right){\displaystyle \int \mathrm{d}\mathbf{x}{\mathrm{e}}^{-\beta U}}}=\frac{{\displaystyle {\int }_{\text{site}}\mathrm{d}\mathbf{1}}{\displaystyle \int \mathrm{d}\mathbf{x}{\mathrm{e}}^{-\beta U}}}{{\displaystyle {\int }_{\text{site}}\mathrm{d}\mathbf{1}}{\displaystyle \int \mathrm{d}\mathbf{x}{\mathrm{e}}^{-\beta \left(U+u_c\right)}}}\times \frac{{\displaystyle {\int }_{\text{site}}\mathrm{d}\mathbf{1}}{\displaystyle \int \mathrm{d}\mathbf{x}{\mathrm{e}}^{-\beta \left(U+u_c\right)}}}{{\displaystyle {\int }_{\text{site}}\mathrm{d}\mathbf{1}}{\displaystyle \int \mathrm{d}\mathbf{x}{\mathrm{e}}^{-\beta \left(U+u_c+u_o\right)}}}\times \frac{{\displaystyle {\int }_{\text{site}}\mathrm{d}\mathbf{1}}{\displaystyle \int \mathrm{d}\mathbf{x}{\mathrm{e}}^{-\beta \left(U+u_c+u_o\right)}}}{{\displaystyle {\int }_{\text{site}}\mathrm{d}\mathbf{1}}{\displaystyle \int \mathrm{d}\mathbf{x}{\mathrm{e}}^{-\beta \left(U+u_c+u_o+u_a\right)}}}\times \frac{{\displaystyle {\int }_{\text{site}}\mathrm{d}\mathbf{1}}{\displaystyle \int \mathrm{d}\mathbf{x}{\mathrm{e}}^{-\beta \left(U+u_c+u_o+u_a\right)}}}{{\displaystyle {\int }_{\text{bulk}}\mathrm{d}\mathbf{1}}\delta \left({\mathbf{x}}_1-{\mathbf{x}}_1^{\ast }\right){\displaystyle \int \mathrm{d}\mathbf{x}{\mathrm{e}}^{-\beta \left(U+u_c+u_o\right)}}}\times \frac{{\displaystyle {\int }_{\text{bulk}}\mathrm{d}\mathbf{1}}\delta \left({\mathbf{x}}_1-{\mathbf{x}}_1^{\ast }\right){\displaystyle \int \mathrm{d}\mathbf{x}{\mathrm{e}}^{-\beta \left(U+u_c+u_o\right)}}}{{\displaystyle {\int }_{\text{bulk}}\mathrm{d}\mathbf{1}}\delta \left({\mathbf{x}}_1-{\mathbf{x}}_1^{\ast }\right){\displaystyle \int \mathrm{d}\mathbf{x}{\mathrm{e}}^{-\beta \left(U+u_c\right)}}}\times \frac{{\displaystyle {\int }_{\text{bulk}}\mathrm{d}\mathbf{1}}\delta \left({\mathbf{x}}_1-{\mathbf{x}}_1^{\ast }\right){\displaystyle \int \mathrm{d}\mathbf{x}{\mathrm{e}}^{-\beta \left(U+u_c\right)}}}{{\displaystyle {\int }_{\text{bulk}}\mathrm{d}\mathbf{1}}\delta \left({\mathbf{x}}_1-{\mathbf{x}}_1^{\ast }\right){\displaystyle \int \mathrm{d}\mathbf{x}{\mathrm{e}}^{-\beta U}}}={\mathrm{e}}^{-\beta (\mathrm{\Delta }{G}_c^{\text{site}}+\mathrm{\Delta }{G}_o^{\text{site}}+\mathrm{\Delta }{G}_a^{\text{site}}-\frac{1}{\beta }\text{ln}(S\ast I\ast C°)+\mathrm{\Delta }{G}_o^{\text{bulk}}+\mathrm{\Delta }{G}_c^{\text{bulk}})}$$ (1)

where 1 denotes the ligand, x₁ the position of its center of mass, and x₁* an arbitrary location in the solution, sufficiently far from the binding site. U represents the potential energy of the whole protein-ligand assembly, u_o = u_Θ + u_Φ + u_Ψ is the restraining potential for the three Euler angles, Θ, Φ, and Ψ, and u_a = u_θ + u_ϕ is that for the spherical angles, θ and ϕ (see Figure 1). Under these premises, the standard binding free energy is given by

$$\mathrm{\Delta }{G}_{\text{bind}}^{°}=k_{\mathrm{B}}T\times \ln K_{\text{eq}}C°$$

As made clear by Equation 1, one needs to run eight individual one-dimensional PMF calculations, seven of which involve the protein-ligand complex, using in a sequential order the distance root-mean-square deviation (RMSD) with respect to the native conformation of the ligand in the bound state, the three Euler angles, Θ, Φ, and Ψ, the two spherical angles, θ and ϕ, and the distance between the centers of mass of the protein and the ligand. The remaining PMF calculation describes the change in the distance RMSD of the ligand in the unbound state. The corresponding restraints, namely u_c, u_o and u_a, are introduced as described in Equation 1.

METHOD

Implementation Details

BFEE is implemented as a Tcl plug-in in VMD,¹⁴ which is available for Microsoft Windows, Linux and macOS operating systems. Although BFEE is designed for PMF calculations applying the extended adaptive biasing force (eABF) method with an unbiased estimator^17,18 provided in the Colvars¹⁹ module of NAMD¹⁵, there is no technical barrier preventing one from porting this toolkit to other molecular dynamics engines. For example, by integrating TopoTools²⁰ or charmm2lammps.pl,²¹ one can easily generate LAMMPS²² input files with BFEE. The source code of this plug-in is provided in the Supporting Information. The most updated version of BFEE will be always released together with VMD.¹⁴

Functional Demonstration

BFEE is shown in Figure 2. We now detail the usage of the plug-in.

Figure 2.

Graphical user interface and functional demonstration of the BFEE plug-in.

Preparing the input files for the PMF calculations

Users are expected to be familiarized with NAMD¹⁵ and have successfully equilibrated the protein-ligand complex in bulk water. In order to set up the different simulations involved in the geometric route for standard binding free-energy determination, BFEE requires the structure file of the complex in bulk water ( psf file), the binary coordinates ( coor file), the binary velocities ( vel file), the periodic-cell dimensions (xsc file) and the force-field parameters (usually, prm or str files) as inputs. All of these files should already exist or be generated through an equilibrium simulation. The input files required for the eight individual PMF calculations are then automatically generated by clicking the “Generate Inputs” button, as shown in Figure 2.

Running the simulations

Ideally, one can submit the configuration files directly to the NAMD program without any modification. It might be, however, desirable to tailor the range of values sampled in the PMF calculations, as well as the center of the harmonic restraints as a function of the protein-ligand complex at hand. For the simulations characterizing the change in the RMSDs of the ligand (both in the bound and in the unbound states), in the Euler angles and in the spherical angles, we suggest choosing a range of values that satisfies ΔG(max)-ΔG(min) ≥ 5 kcal/mol (by default, BFEE sets the center of the angular harmonic restraints to their equilibrium value in the native complex, and samples a range of ±10° around this value in the PMF calculations). A short preliminary simulation for each angle can be performed to refine the range of values that ought to be covered in the different free-energy calculations. In addition, the center of each angular harmonic restraint acting on Θ, Φ, Ψ, θ, or ϕ may need to be adapted to reflect the corresponding free-energy minimum. These fine-tunings constitute the only human intervention needed during the entire binding free-energy calculation workflow. In practice, due to the inherent complexity of protein-ligand binding, one may turn to use a staging, or stratification strategy in PMF calculations rather than a single-window simulation (by default) for an improved convergence rate (see the Supporting Information for examples).

Post-treatment

BFEE calculates the binding free energy as well as the contribution of each degree of freedom automatically. As shown in Figure 2, only the free-energy profile at each step of the workflow (usually czar.pmf. See the Supporting Information for the difference between pmf and czar.pmf files) is needed as input if default force constants (listed below in the same window) are used for the geometric restraints. The results of the free-energy calculation will be shown after clicking the button “Compute Binding Free Energy”, as depicted in Figure 3, which shows the affinity of ligand p41 binding to SH3 domain of Abl kinase. Although to reach this degree of convergence required a stratification strategy, an example using single-window simulations produced a result within ~1 kcal/mol. This example and others are provided in the Supporting Information.

Figure 3.

Results shown in a message box of BFEE. The data were obtained from the case of ligand p41 binding to SH3 domain of Abl kinase. The initial coor, vel, xsc and force field files of the molecular system are provided in the Supporting Information as a test example of the BFEE plug-in. See ref. ¹² for more information about the molecular assembly.

Error Estimation

Error estimation is extremely important in binding free-energy calculations. The recommended way to estimate the error using BFEE is to run parallel simulations independently, with different seeds, and then calculate the standard deviation over the different binding free energies. Since BFEE handles all the generation of inputs and analysis of outputs, almost no additional human intervention is needed in the error calculation, unlike the determination of the precision of the calculation, which requires an estimation of the correlation length of the time series.²³

Additionally, it is crucial to guarantee that each step of the PMF calculation is converged when evaluating the reliability of binding free-energy estimates. This evaluation can be done by monitoring the time evolution of individual free-energy landscape ( hist.czar.pmf file). If a PMF calculation is converged, the free-energy and gradient profiles should remain unchanged with respect to the simulation time. We have an in-house script to perform this task, and we will make it available with the formal release of BFEE. (Currently, this script can be found at https://github.com/fhh2626/eABF-analyzer-for-NAMD)

CONCLUSION AND PERSPECTIVE

Motivated by the idea that to be truly useful beyond the academic walls, accurate binding free-energy estimation ought to be automated to reduce human intervention as much as possible, in a continuing effort we have designed a “parameterless” computational workflow¹⁶ and an ergonomic graphical user-friendly interface for the setup and post-treatment of the different simulations. With these objectives in mind, we introduce a new plug-in, BFEE, for accurate standard binding free-energy calculations, based on a strategy recently put forth,^9,16 making use of geometric transformations. The rapid setup and post-treatment of the simulations by BFEE make the latter a very attractive option for the non-expert in the field of advanced statistical-mechanics simulations.

At the design level, BFEE offers a sufficiently general and easy way to investigate any recognition-and-association process relevant to chemistry and biology. In practice, however, there are at least two cases for which usage of BFEE is ill-advised, namely, (i) when the guest is deeply buried in the host molecule, rendering the PMF calculation of the separation nearly intractable over common timescales, and (ii) in protein-protein complexes, where the interaction network at the interface is intricate, necessitating the introduction of additional restraints.²⁴ Possible workarounds consist of (i) turning to an alchemical approach as an alternative to the geometric route, with the corresponding input files generated automatically by BFEE (which is currently under development as an extension) and (ii) generalizing the plug-in to protein-protein binding to account for the complexity of the interfacial interactions through harmonic restraints acting on the participating amino-acid side chains. In its present version, BFEE provides a very convenient, user-friendly framework for investigating protein-ligand binding. Future developments include an extension of the plug-in to address virtually any problem relevant to recognition and association applied to arbitrary host-guest complexes, such as protein-protein and protein-membrane molecular assemblies.