Introduction

In this tutorial we will learn to use the strength of umbrella sampling (US) and metadynamics (MTD) together with temperature accelerated molecular dynamics/driven-adiabatic free energy dynamics (TAMD/d-AFED) for efficient sampling of high dimensional free energy landscape. Within this approach, the collective variables along which free energy surface is broad and unbound is sampled using US, the CV along which significantly high barriers are present is sampled using MTD and all the orthogonal CVs are sampled using TAMD/d-AFED. This tutorial follows the method used in the paper  OpenMM-UFEDMM 2023 paper, S. Awasthi,  N. N. Nair. J. Chem. Phys. 2017 .  It is recommended to read the d-AFED part of this tutorial for selection of extended space CV parameters. The basic form of Lagrangian used in this method is:

In this tutorial we will explore the free energy surface of alanine tripeptide in vacuo as a function of four backbone dihedral angles (Φ1, Ψ1, Φ2, Ψ2) using TASS. The first thing we need to do is build an initial structure using ff14SB force-field and relax this at 300K so that we can use this as the input for umbrella equilibration.  What we do is:

1. Umbrella equilibration 

2. TASS run and reweight  

Reweighting of TASS 

We are using  mean force approach to combine the umbrella windows. In this method, the one-dimensional projection of the free energy surface along the umbrella coordinate, s1, is computed first using numerical integration as, 

Here the A(t) is the time-dependent reweighting factor, which needs to be calculated based on the bias potentials applied to the auxiliary variables. See the tutorial on UFED for the equations for well-tempered metadynamics bias reweighting.

In the above, the unbiased probability distribution has to be also obtained by appropriate reweighting.

For more details see, A. Pal, S. Pal, S. Verma, M. Shiga, N. N. Nair, J. Comput. Chem. 2021