Edge Mapper for RBFE Calculations

A significant component of preclinical drug discovery involves optimizing the noncovalent binding between a target protein and ligands to improve affinity [Liu-2013]. To address this, many computational methods have been developed over the years; alchemical free energy methods are more expensive methods that target higher accuracy. These techniques can be used to compute either absolute binding affinities (ABFE) or relative binding affinities (RBFE). Although ABFE calculations are more attractive, RBFE calculations are more efficient and are therefore more widespread.

The RBFE approach requires a map of alchemical transformations between pairs of ligands; each transformation is known as an edge, and the entire set of transformations, or edges, must connect all the ligands together, forming a map that allows any ligand to be transformed into any other by following a path of edges (individual transformations). This map is generated prior to running the RBFE calculations. Starting from an Orion dataset of ligands, this tutorial uses the Edge Mapper for RBFE Calculations Floe in the MD Affinity Package to generate the map of edges needed for the RBFE calculations in the Nonequilibrium Switching Floe.

Given \(n\) ligands, out of all possible \(n(n-1)/2\) edges, the Mapper Floe selects a reasonable subset of the edges with the goal of keeping the computational demand low and providing a high probability of giving accurate RBFE calculations, considering each edge involves computational expense.

The Default map is principally rooted in the Lead Optimization Mapper (LOMAP) [Liu-2013]. The general consensus is that the more similar the ligands in the edge are, the more accurate the free energy difference estimation is. Thus, edges are selected based on a set of heuristics for chemical similarity measures, including the MCS, ROCS®, and the equal charge check. All ligands should be part of a ring (cycle of edges) to provide a minimal redundancy of pathways to increase the accuracy of the RBFE calculations.

In the Map Type parameter on the Job Form, two map types are available in addition to the Default map: a Star map with a center ligand (hub) and a Binary Star map with two center ligands and an axle edge. If Star map or Binary Star map is selected, you are expected to provide the name(s) of the hub (reference) ligand(s), or the hub(s) will be automatically selected based on the similarities to other ligands. If the specified hub ligand name(s) does not exist in the provided ligand set, it will also auto-select the hub(s).

The OpenEye Mapper Floe with its cubes and connections is shown in Figure 1.

OE Mapper

Figure 1. The Edge Mapper for RBFE Calculations Floe.

The Floe Inputs

To run the Mapper Floe, the usual input is an Orion dataset of posed ligands. The provided ligands must have reasonable 3D coordinates, all atoms specified, and correct chemistry such as bond orders and formal charges. This input ligand dataset could also be used as input for other protein-ligand MD floes such as the Bound Protein-Ligand MD, Short Trajectory MD with Analysis, or Ligand Bound and Unbound Equilibration for NES Floes; the output bound dataset produced by the Ligand Bound and Unbound Equilibration for NES Floe could also be used.

Optionally, you can also import an externally-generated map into the Mapper Floe to generate a Mapper output dataset of only those edges defined by the external map. In this case, the Mapper will not attempt to create the mapper graph, instead it simply translates the edges given in the user-defined file into the output dataset. However, the edge score is evaluated and displayed for the user-provided edges as well. The user-provided map must be a text file containing one edge per line in the following text format:

ligA >> ligB

The first field is the title of the starting ligand, followed by “>>”, and the third field is title of the final ligand. With the above example line, the Mapper will look in the input ligand dataset for a ligand titled “ligA” and another titled “ligB,” and it will generate an edge record in the Mapper output dataset defining the transformation of LigA into LigB. With user-defined maps, the ligand input dataset can contain ligands that are not used in any edge, but all user-defined edges must have ligands by that title in the input ligand dataset.

For this tutorial, the CDK2 receptor and sixteen ligands have been selected. The files can be downloaded below with the ligand mapping text file as well.

How to Use the Floe

Running the floe is straightforward. Figure 1 shows the Job Form for the Edge Mapper for RBFE Calculations Floe. Here, you can define the names of the job and the output datasets and select the Orion dataset of input ligands (for this tutorial, use the CDK receptor and ligand dataset you just downloaded). The Mapper will upload a .tar.gz file with useful information about selected edges as well as the edge information for all possible edges; you must specify this file name as well. In addition, you must set the name of the All Edges Mapper Dataset for all possible \(n(n-1)/2\) edges, which could be used in the Analyze page to select new sets of edges. If you want run the floe using an external map file, you can specify it with the Optional Ligand Edge Map File parameter. For this tutorial, you may use the CDK2 ligand mapping file downloaded above. When using an external map file, the Mapper will not attempt to connect “similar” ligands to create edges, but it will only form edges based on those defined in the input map file.

OE Mapper Input Output

Figure 1. Job Form for the OE Mapper Floe.

At the end of the run, a Floe Report is produced with the generated map shown in Figure 2.

OE Mapper Graph Output

Figure 2. Map created by the Mapper tutorial.

Each edge in the graph is represented by a pair of ligands connected with a blue line. The float value with each line is the score computed by the Mapper for that edge. These scores are numbers in the range [0, 1] where zero is worst (i.e., this edge is unlikely to succeed) and 1 is best (likely to succeed). In addition to the graph diagram, two files are produced:

  • A map text file where each edge is tabulated according to the map file grammar previously described. This file can be downloaded and customized by adding or removing edges to make a user-defined input for a subsequent mapper run to make a custom map.

  • A .tar.gz file containing several edge information files: edges_by_ligand.csv, which contains lists of ligands connected to each ligand; LigA_LigB_edge_matrix.csv, which contains edges scores for all \(n(n-1)/2\) possible edges, Orion_record_fields_key.txt, which contains lists of fields of the output records; and lastly, the Floe report in a ZIP archive format. This could be useful in deciding which edges to add or remove in customizing the map. An example of the uploaded file can downloaded here:

How to Edit the Mapper Edges

In this part of the tutorial, we modify the Mapper edges for CDK2 by removing the edge involving the compounds 1oiu – 22 and adding two new edges, 1oiu – 32 and 1oiu – 30. To this end, we need to choose edges from the dataset containing all the \(n(n-1)/2\) possible edges that were produced along the Mapper Floe. After selecting this dataset, its main content can be seen in the Spreadsheet Panel on the Analyze page, as shown here in Figure 3.

Orion Analyze page spreadsheet

Figure 3. Analyze page spreadsheet for the Mapper Floe.

The spreadsheet shows all 120 edges in our example. Since we want to modify the edges generated by the Mapper, the first step is to select these edges. We can filter the data on the spreadsheet based on the Chosen_OPLMD column. On the Active Data Bar, select the ‘Filters’ drop-down menu. Click the caret in the Choose a Filter search box. The columns from the spreadsheet will be listed. Choose the Chosen_OPLMD column option. Indeed, the Mapper edges have a value of 1 in this field and 0 otherwise. The filter selection process is shown here in Figure 4.

Orion Analyze page spreadsheet

Figure 4. How to filter the data in the spreadsheet.

After the filter is applied to effectively select the records from the spreadsheet, we next need to go to the Plot Panel. In the scatter plot, use the Normal Selection box from the ‘Tools’ drop-down to enclose and select the desired plot points within the box, as shown in Figure 5 below. Alternatively, you can use the spreadsheet itself to select the points; use the Alt key + mouse click or Ctrl key + mouse click to highlight the points. Points may also be selected singly on the plot.

Orion Analyze page spreadsheet

Figure 5. How to select data points on the plot.

All the spreadsheet rows and data points should be highlighted as shown below.

Orion Analyze page spreadsheet

Figure 6. Selected rows in the spreadsheet.

Since we want to remove the 1oiu – 22 edge from the set, we need to find this edge and deselect it.

Orion Analyze page spreadsheet

Figure 7. Deselecting an edge.

At this point, we can add two new edges that were not present in the generated Mapper set. Therefore, we need to remove the “Chosen_OPLMD” column filter. All the edges will be displayed again in the spreadsheet, with the selected edges still marked. In the spreadsheet, scroll to find the 1oiu – 32 and 1oiu – 30 edges and add them to the selection by using the Ctrl key + mouse click combination.

Orion Analyze page spreadsheet

Figure 8. Adding new edges.

Finally, using the ‘Selected’ drop-down from the Active Data Bar, save the selected records with the new edges in a dataset that can be used in other NES floes.

Orion Analyze page spreadsheet

Figure 9. How to save the new dataset.