BioSimSpace diaries: funnel metadynamics simulations

Funnel metadynamics

BioSimSpace supports a variety of protein-ligand binding free energy calculation methodologies, previous posts have covered alchemical approaches (RBFE variants and ABFE variants). Pathway based free energy methods offer an alternative ”geometric” route to estimate protein-ligand binding free energies. Additionally, inspection of the free energy profile as a ligand progresses from an unbound state to a bound state can provide insights into the binding mechanism, potentially revealing intermediate binding sites that may influence the course of a structure-based drug design campaign.

Pathway-based binding free energy methods typically require the definition of a collective variable, a low dimensionality descriptor that maps the transition of the ligand from a bound state to an unbound state. BioSimSpace supports the popular funnel metadynamics methodology originally developed by Limogelli et al. . In this approach a funnel-shaped collective variable guides the ligand from a target binding site to bulk solvent, and metadynamics calculations are performed using this collective variable to obtain a potential of mean force from which a standard binding free energy can be derived. Originally funnels had to be derived using a laborious and error-prone procedure.

Setting up the funnel

We can use the makeFunnel method from the module BioSimSpace.Metadynamics.CollectiveVariables to automatically generate funnel parameters. makeFunnel takes as input a system. It the user provides no further detail, the receptor (protein) is assumed to be the largest molecule, and the host (ligand) is assumed to be the second largest molecule. The ligand is assumed to be bound to the binding site of interest. Once the parameters have been derived, a funnel CV can be instantiated . We can view the funnel overlaid on the system to check that the procedure generated a suitable funnel.

 

funnel metadynamics

We see that the funnel (white spheres) is wider around the ligand (space fill)  in the protein surface (cartoon). The funnel narrows down as it goes further away from the protein surface. This is prevents the ligand from drifting around the simulation box when it is unbound, which would slow down convergence of the free energy estimates.

Running  a funnel metadynamics simulation

To run a funnel metadynamics simulation we can use BSS.Protocol.Metadynamics, passing funnel_cv as the collective variable of interest. BioSimSpace supports metadynamics calculations with a variety of backends, here we use OpenMM.

 

 

It’s as simple as that. In practice to obtain  reproducible free energy estimates it is necessary to run MD simulations  with a duration of several hundreds of nanoseconds.

 

Analysing a funnel metadynamics simulation

To verify whether a funnel metadynamics simulation was sufficiently long we can use BSS.Notebook to plot the funnel parameters (projection and extent) which describe the position of the centre of geometry of the ligand over time.

In the above plot we see that over  a simulation of 100 ns the ligand hits extrema values of the funnel parameter projection multiple times which is a necessary condition to obtain accurate free energy profiles. We can also plot the 2D free energy surface.

To obtain the absolute binding free energy of the ligand we must compute a standard state correction term.

Finally it is useful to plot how the absolute binding free energy estimates fluctuate over time for several replicates. The code below produces a visualisation for 5 replicates simulations of 100 ns each. The plot shows that there are substantial fluctuations between replicates but the mean across the five replicates oscillates within 1 kcal.mol-1 of the experimental binding affinity of the ligand (red dashed line).

 

If you want to try this out for yourself, check out our detailed funnel metadynamics tutorials by logging in to our JupyterHub server at try.openbiosim.org (GitHub account required) and following the instructions in the file TUTORIALS.txt.

This post was written  by Julien Michel by adapting materials produced by Dominykas Lukauskis.