Understanding Chemistry and Biochemistry with Conceptual Models EVB Tutorial Fernanda Duartea, Miha Purgb a)EaStCHEM School of Chemistry, University of Edinburgh, Edinburgh EH9 3FJ, UK * [email protected] · : http://fduartegroup.org b)Department of Cell and Molecular Biology, Uppsala University, Uppsala, Sweden *[email protected]· : https://kamerlinlab.com 1. OVERVIEW 1 1.1 REQUIREMENTS & SOFTWARE 2 1.2. USEFUL REFERENCES 2 2. EVB THEORY 3 2.1 CHEMICAL REACTIONS WITH EVB 4 2.2 OBTAINING FREE ENERGIES 5 3. CASE STUDIES 6 3.1 SN2 REACTION 6 3.2. DFPASE 14 4. ADDENDUM 22 4.1 SOFTWARE INSTALLATION 22 1. Overview The aim of this tutorial is to Provide you with a general overview about how to Perform Free Energy Perturbation/ Umbrella SamPling (FEP/US) EmPirical Valence Bond (EVB) simulations of chemical reactions utilizing the software Q [5,7]. Due to the comPlexity of the task and time constraints, this tutorial will just cover the crucial asPects of the general Procedure, including toPology generation, FEP file generation, FEP/US simulations and grouP contribution calculations. Other asPects such as parameterization, structure processing, substrate docking, setting protonation states, equilibrations, etc. will not be covered and the reader is encouraged to master them if the aim is to use the aPProach in a scientific project. Below, we provide some reference that will helP the reader to gain a deePer understanding of comPlete protocol. By the end of this tutorial, you should be able to understand the fundamental concePts behind EVB calculations, the structure of Q Program and how to set uP and analyze FEP/US simulations yourself. 1 Understanding Chemistry and Biochemistry with Conceptual Models 1.1 Requirements & Software A functional understanding of the Unix/Linux environment and specifically the command line, is Prerequisite for successfully comPleting this tutorial, therefore we strongly recommend that those new to Unix/Linux acquaint themselves with the basics beforehand (examPle tutorial: http://www.ee.surrey.ac.uk/Teaching/Unix/unix1.html). Instructions regarding accessing the remote comPuter cluster will be Provided seParately. All FEP/US EVB simulations will be Performed using the software Package Q. this software allows the calculation of properties such as solvation free energies, binding affinities, and reaction free energies, which is the toPic of this tutorial, Q is develoPed and maintained by the Kamerlin and Åqvist grouPs at UpPsala University, it is an open source software (GPLv2) available free of charge from the online rePository GitHub. The Q manual will be Provided with the tutorial material. Please see Addendum for references and installation instructions. To comPlement the bare-bones nature of Q and make our lives a bit easier, we will also make use of the Python scriPts Provided in the software Package Qtools. These scriPts will simPlify the tasks required to successfully carry out this tutorial: Parameter conversion, inPut generation, simulation analysis, etc. Again, Please see Addendum for installation instructions. The final, but crucial software requirement is VMD (Visual Molecular Dynamics), allowing us to visualize and analyze our simulations. VMD can be obtained free of charge (registration required) here: http://www.ks.uiuc.edu/Research/vmd/. It will also be installed on the node The instructors will Provide you with access to a comPuter cluster where you will submit your calculations, as well as Provide you with the required material for this tutorial. Commands throughout the tutorial will be preceded by a dollar sign ($), and comments with a hash (#). Make sure you are able to connect to the cluster, and then download the Provided material to your remote account. e.g.: $ ssh [email protected] # Password: c5bS2A7wNH $ cp -r qmaterial YOURNAME # replace YOURNAME with your name # load the required software $ source /home/evb/bin/q_evb/load.sh 1.2. Useful References [1] A. Warshel, R.M. Weiss, J. Am. Chem. Soc., 1980, 102, 6218. [2] J. Åqvist, and A. Warshel Chem. Rev. 1993, 93, 2523. [3] Hong, G., Rosta, E. and Warshel, A. J. Phys. Chem B, 2006 110, 19570. 2 Understanding Chemistry and Biochemistry with Conceptual Models [4] Warshel, A. (1991). ComPuter Modeling of Chemical Reactions in Enzymes and Solutions (New York: Wiley). [5] . Marelius, K. Kolmodin, I. Feierberg, J. Åqvist, J. Mol. Graph. Mod. 1998, 16, 213. [6] P. Bauer, A. Barrozo, B. Amrein, M. Esguerra, P. B. Wilson, D. T. Major, J. Åqvist and S. C. L. Kamerlin, SoftwareX 2018 https://github.com/qusers/Q6 [7] F . Duarte, B. A. Amrein, D. Blaha-Nelson and S. C. L. Kamerlin, BBA - General Subjects 2015, 1850, 954. [8] F. Duarte, S. C. L. Kamerlin (Editors). From Physical Chemistry to Chemical Biology: Theory and APPlications of the EmPirical Valence Bond APProach. John Wiley & Sons. 2017. [9] Purg, M., Kamerlin, S.C.L., In review in Methods in Enzymology (Vol 607: PhosPhatases) [10] Purg, M., Elias, M. and Kamerlin, S.C.L. J. Am. Chem. Soc. 2017, 139, 17533. [11] Muegge, I., Tao, H. and Warshel, A.,. Protein engineering, 1997, 10, 1363. 2. EVB Theory Thie EVB apProach uses a fully classical descriPtion of the different VB configurations along a chemical reaction. The advantages of this apProach are that it is fast, allowing for extensive conformational samPling and a quantitative descriPtion of the effect of different environments on the activation free energy In Practice, this mean comParing a chemical reaction in the gas Phase versus that in solution, or a reaction in aqueous solution to that in an enzyme (i.e. catalytic Power), or even comParing a reaction in wild-tyPe enzyme to that of a mutant variant. The former is usually called “reference reaction”, as it is used to calibrate the EVB Potential to reProduce exPerimental or ab initio data. ‡ H3C H3C H3C CH2 CH2 CH2 Cl + C Cl C Br C + Br H Br Cl H H H H H Figure 1. SN2 reaction between 1-bromopropane and chloride ion. Reactive region is colored in black and surroundings in grey. To make the model transferable between different environments, the system is sPlit into two regions - the reactive (also known as Q or EVB), which contains all the chemically relevant grouPs involved on the reaction and surrounding region, which contain the rest of the system (Figure 1). Note that the reactive region is treated in the exact same manner in all mediums. The Hamiltonian can thus be written as the sum of interactions of the reactive region (Hr), the surrounding region (Hs) and the interactions between the two regions (Hrs) [1,2]: 3 Understanding Chemistry and Biochemistry with Conceptual Models �!"! = �! + �!" + �! (1) 2.1 Chemical Reactions with EVB We will describe the chemical reaction studied here using a simPle two-state EVB model, where the system is described by considering the two lowest energy VB states only. These states have a direct Physical meaning, namely, they describe the diabatic states of the reactants and Products (Figure 2). The wavefunction is then: � = �!�! + �!�! (2) where indices 1 and 2 denote the reactant and Product VB states, resPectively. By solving the secular equation, we obtain as the lowest eigenvalue, the analytical EVB ground-state Potential energy function [1] (Figure 1A): ! � = � + � − (� − � )! + 4�! (3) ! ! !! !! !! !! !" where the matrix elements H11, H22 and H12 are somewhat comPlex integrals of the form ∗ �!" = �!��! �τ. It is at this Point that we introduce the empirical part of Empirical Valence Bond, by approximating H11 and H22 with analytical molecular mechanics (MM) potential functions, acknowledging that H11 and H22 have a clear physical meaning - they rePresent the energies of the two states. With the exception of reactive bonds, which are modeled with Morse potentials, the interactions in the individual states are described using tyPical force-field functions (harmonic Potential, coulomb, Lenard-Jones, etc.). Figure 1: A) Schematic representation of potential energy functions Eg, H11, H22 and H12. B) ExamPle of configurational samPling of Eg using the biased potential Em(λ). The off-diagonal element H12 is the quantum couPling of states, and unlike the diagonal counterParts, does not have a classical analogy, and is thus typically aPProximated by an exPonential or Gaussian function, or as in our case, by a constant value. It has been shown to be indePendent of the environment [3]. 4 Understanding Chemistry and Biochemistry with Conceptual Models We now return to the concePt of the reference reaction. The reference reaction is a reaction in an environment (tyPically in the gas Phase or aqueous solution), for which the energetics are known either from exPeriment or from accurate quantum chemical calculations, and it is used to calibrate the unknown EVB Parameters in the EVB model. In a 2-state, constant H12 EVB model, the calibration involves fitting of two Parameters - H12, and the so-called gas- shift (energy difference of diabatic states in the gas Phase). Two known values on the energy profile are thus required to obtain a ProPer fit, a common choice in the field being the activation ≠ and reaction free energies (ΔG and ΔG0). The EVB Potential is then calibrated by varying H12 and ≠ gas-shift until the calculated ΔG and ΔG0 coincide with the reference values. The same parameters can then be used in a different environment. 2.2 Obtaining Free Energies While Potential energy surfaces at zero Kelvin obtained using the above methodology can be interesting on their own, they are not Particularly relatable to typical experimental conditions involving enzymatic reactions. Instead, we would like to account for the many loose degrees of freedom in our system, i.e. the entroPic contribution, and do configurational samPling (e.g. using molecular dynamics simulations) to calculate free energies. The activation free energy of a reaction can for examPle then be directly related to exPerimentally determined rate constants via transition state theory (Eyring-Polanyi equation): !!!‡ !!! � = � � !!! (4) ! A convenient approach for obtaining reaction free energy profiles in the context of EVB, is the maPPing aPProach, also known as the free energy Perturbation/umbrella samPling (FEP/US) aPProach.