Methods for calculating Potentials of Mean Force

1 School of PhysicsGeorgia Institute of TechnologyUniversity of Illinois at Urbana-ChampaignBeckman Institute for Advanced Science and TechnologyTheoretical and Computational Biophysics GroupMethods for calculatingPotentials of Mean ForceAnthony HazelJames C. GumbartSept. 2017A current version of this tutorial is available list for additional Required programs.. Getting started.. 52 Exploring the pathway with Steered Setting up and running the SMD simulation.. Analysis of the SMD simulation.. 93 Determining the PMF with Adaptive Biasing Setting up and running the ABF simulation.

2 Analysis of the ABF simulations.. 134 Determining the PMF with Umbrella Umbrella sampling.. Replica exchange molecular dynamics.. Setting up the US windows.. Preparing the simulations.. Running the simulations.. Analyzing the simulations.. Sampling of reaction coordinate space.. 221 INTRODUCTION31 IntroductionLiving cells are de ned in part by the possession of a membrane barrier sur-rounding their perimeter, thereby delineating the border between the insideand the outside. The existence of this barrier, as well as the proteins that me-diate exchange of ions and other substrates across it, leads immediately to thequestion of how transport across the membrane, whether it be active or passive,is achieved and, in particular, how its done selectively.

3 Although some commonmechanisms exist, each protein has evolved speci c features to optimally trans-port its particular substrate. The transport process is characterized typically bya substrate pathway along with associated conformational changes in the pro-tein. These changes are often small or even non-existent for passive channels,but can be quite large for active transporters. The substrate pathway can alsobe characterized by the substrate's free energy along it, known as the potentialof mean Force (PMF), which dictates the speed of transport and the X-ray crystallography and other experimental structural techniquescan provide snapshots of membrane proteins, even in multiple states, they can-not display the dynamics connecting those states.

4 Computational Methods ,namely molecular dynamics (MD) simulations, provide a means of animatingthe static structures, allowing for, , the visualization of an entire permeationevent of a substrate through a channel or transporter. However, the relevanttime scales for many transport processes is beyond that afforded by MD, whichis typically limited to a few microseconds currently. As such, Methods to accel-erate the process of interest in a simulation have been developed. One exampleis steered molecular dynamics (SMD) (1,2), a method in which forces are ap-plied to part of the system, , the substrate, to drive it along a prede neddirection.

5 Commonly implemented using a constant Force or a constant veloc-ity, this method is useful for exploring possible permeation pathways through amembrane protein. However, because the forces imposed are usually orders ofmagnitude greater than would be experienced in a living system, interpretationof the results is often limited to a qualitative description of the possible behaviorof the substrate and protein. For a quantitative picture of transport, one mustturn to more advanced Methods . For example, the results of multiple SMD sim-ulations combined through application of Jarzynski's equality provides a meansof recovering an equilibrium PMF from non-equilibrium events (3{7).}

6 Alterna-tively, adaptive biasing forces (ABF) can generate quasi-equilibrium trajectoriesfrom which the PMF can be deduced (8{11).Numerous channels and transporters have been studied using MD-basedmethods. SMD has been used to address substrate binding and/or transport inthe water channel aquaporin (12{15), the ADP/ATP carrier AAC (16), neuro-transmitter transporters LeuT (17), the sugar transporter LacY (18,19), andmany others. In addition, SMD has been used to probe the conformationalchanges underlying function for many membrane proteins, such as the vitaminB12transporter BtuB (20) and the protein-conducting channel SecY (21{23).}}}

7 ABF has been used to nd the free-energy pro le for, , glycerol in the channelGlpF (24), ADP in AAC (25), and ions in the nicotinic acetylcholine and glycine1 INTRODUCTION4 Figure 1:Crystal structure of AmtB. The top of the gure is the extracellular side ofthe channel and the bottom is the cytoplasmic side. The four crystallographically resolvedNH3/NH+4molecules, denoted Am1 to Am4 from top to bottom, are also seen in (26). Both Methods , SMD and ABF, are clearly well established, butstill require care to ensure their proper this tutorial, applications of SMD and ABF to the ammonium transporterAmtB will be explored (see ).

8 AmtB has been well studied by computa-tional Methods , including those used to calculate free energies (27{32). SMDwill be used rst to gain an approximate knowledge of the permeation pathwayand the barriers along it. Then the PMF for ammonia in the central region ofthe channel will be calculated using ABF. The appropriate choice of parametersand potential difficulties will also be reader of this tutorial is assumed to be familiar with the use of NAMDto perform \standard" calculations, including energy minimization and MD sim-ulations.}

9 General documentation, tutorials and templates of NAMD con gura-tion les are available from the Documentation section of the NAMD web of the simulations in this tutorial can, out of necessity, takea signi cant amount of time to run on a single processor. If thistime becomes prohibitive to completing the tutorial, example outputis provided throughout to enable the reader to still carry out thedesired INTRODUCTION5 The investigations of AmtB described below will utilize the A struc-ture solved in 2004 (33). Prior to carrying out SMD and ABF simulations, amembrane-water system containing AmtB should be built and Required programs1 VMD:Available (for all platforms)2 NAMD (ver.)

10 Or higher compiled with thereplicaoption):Available (for all platforms)3 Plotting program:The free program xmgrace (unix) is recommended. It can be downloaded Other useful graphing programs areMathematica, , Matlab, ,and gnuplot, For Windows, Microsoft Excel can alsobe wham:Available (for Linux andsimilar variants) Getting started1A fully built and equilibrated system is required for the tutorial. The nec-essary les are provided inchannel-tutorial-files/common/, or can bedownloaded input les for running the simulation as well as output are build the system from scratch using the tools within VMD, beginby downloading the structure of AmtB from the Protein Data Bank (PDB code:1U7G).