# Computing the Dissociation Constant from Molecular Dynamics Simulations with Corrections for the Large Pressure Fluctuations—Aquaglyceroporins Have High Affinity for Their Substrate Glycerol

## TL;DR

This paper shows that correcting pressure fluctuations in simulations reveals glycerol has high affinity for aquaglyceroporin proteins.

## Contribution

A novel correction factor for pressure fluctuations in MD simulations is derived and applied to compute accurate ligand–protein binding affinities.

## Key findings

- Without correction, glycerol's affinity for aquaglyceroporins appears very low (~1/M).
- With correction, glycerol's affinity is in the 1/mM to 1/µM range, indicating high binding affinity.
- The correction factor depends on volume changes between bound and unbound states of the ligand.

## Abstract

In this paper, we consider the inevitable large fluctuations of pressure in typical molecular dynamics (MD) simulations of ligand–protein binding problems. In simulations under the constant pressure of one bar, the pressure artifactually fluctuates over the range of ±100 bars or more. This artifact can cause gross inaccuracy in the apparent binding affinity computed as the ratio of the probability for the ligand to be bound inside the protein and the probability for the ligand to be outside the protein. Based on statistical thermodynamics, we derive a correction factor for the ligand–protein binding affinity to compensate for the artifactual pressure fluctuations. The correction factor depends on the change in the system volume between the bound and the unbound states of the ligand. We conducted four sets of MD simulations for glycerol affinities with four aquaglyceroporins: AQP10, AQP3, AQP7, and GlpF. Without the correction factor, the apparent affinity of glycerol with each of these four aquaglyceroporins is computed directly from the simulations to be very low (~1/M). With the correction factor applied, glycerol’s affinity is computed to be 1/mM to 1/µM. In conclusion, glycerol has high affinity for its native facilitator aquaglyceroporins, which is in contrast to the current literature not correcting the artifactual consequences of the large pressure fluctuations in typical in silico experiments.