Overview. For this we will use the Q program ( for carrying out EVB calculations.

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1 EVB Tutorial: S N 2 Reaction in Gas Phase and Solution Overview The objective of this tutorial is to give a glimpse into the main features of the Empirical Valence Bond (EVB) method. We will study a simple system: The uncatalyzed S N 2 reaction in gas and aqueous phase. Maybe, if you have some time, we could also look at the dehalogenation that occurs in the haloalkane dehalogenase (DhlA). For this we will use the Q program ( for carrying out EVB calculations. The tutorial per se does not contain all the information regarding the theory behind the methodologies used herein. For a good overview about the EVB method, see references at the end of this file. This tutorial will guide you through several steps, from the setup of the system to be studied, to the analysis of the calculations. It will be divided into five parts: Setting up the systems Partial charge calculations Relaxing of the systems Calibration of EVB parameters Effects of a mutation By the end of the tutorial, the participants should be able to understand the fundamental concepts behind EVB calculations, the structure of Q program and how to set up simulations, as well as how to analyze mutation effects in enzymes using the method.

2 1. Setting Up The Systems Let us start setting up our systems. Go to the folder 0-top. There you will find two subfolders and one input file. If you type ls (or ll -t), you will be able to see all the files (folders are in bold) in this folder: 0-ff prep.inp probr_cl.pdb Take a look at the PDB file called probr_cl.pdb. It contains the xyz coordinates of the system and residue/atom names. It is essential to have the correct order of the atoms in order for the program to match them to the corresponding parameters of the force field. These parameters can be find in the folder 0-ff (extension.lib and.prm) We will use the qprep5 program to set up our system. The input file (prep.inp), contains the instructions that will be given to qprep5 to create a topology file. Here is an example of the input file to be used for this task: readlib./0-ff/qoplsaa.lib readlib./0-ff/prb.lib readlib./0-ff/cl-.lib readprm./0-ff/qoplsaa_prb_cl-.prm readpdb probr_cl.pdb boundary sphere 1:C1 20 #solvate 1:C HOH maketop probr_cl.top writetop probr_cl.top writepdb probr_cl_start.pdb y quit It tells the program which starting structure to use (readpdb probr_cl.pdb) and where to find the parameters (readlib/readprm) It also contains instruction for solvation the system. In this case, that line is commented and the generated topology (.top) will not contain any solvent. Finally, the input will write the topology file and a new PDB file You can open the new PDB in a molecular visualization software to see that no solvation has been included (you can also uncomment that line ) In order to use qprep5, use the following command: qprep5 prep.inp >prep.log You will see that three new files (prep.log; probr_cl_start.pdb and probr_cl.top) have been created. Take a look at the log file to check that everything has run smoothly.

3 2. Relaxing the Systems Now we will perform a procedure called relaxation. It basically consists of running MD simulations to allow our system to find a minimum in its potential energy at the temperature we wish to study. We will go to folder 1-relax and perform a set of MD runs, going from 1 K up to 300 K. From the Setting Up the Systems section, we created a topology file (.top extension). This topology file will be used all the way until the end of this tutorial, so make sure to always have it whichever directory you are running your simulations. Copy the topology from where you created it (0-top to the 1-relax directory. Within this directory, you will find three input files. Each of them refers to a step in the heating procedure ( ). Let us take a look at relax003.inp: [md] steps temperature 300 stepsize 1 bath_coupling 100 [cut-offs] q_atom 99 [files] topology restart final trajectory fep probr_cl.top relax_002.re relax_003.re relax_003.dcd probr_cl.fep [lambdas] [sequence_restraints] [distance_restraints] We will go through some of these sections. Steps stands for the total number of MD steps to be performed, stepsize is the size of the step in fs, temperature is in K, bath-coupling and separate_scaling are related to the thermostat used to ensure constant temperature. At the [files] section, we specify what topology and FEP file (more about it later) should be used, and what will be the names for the trajectory (.dcd) and restart (.re) files to be written. The restart files are important, as we can divide the simulation into several steps. Then, we have the section called lambdas, which is related to the free energy perturbation calculation to be performed between the reactant and the product state stands for the system 100 % at the state 1 (reactant), and 0 % at the state two (product). Finally, sets of position restraints are used to ensure that the heating is made in a smooth manner. The first two numbers correspond to the atom

4 numbers in the PDB generated at the setup step. For further information, please refer to the Q manual. A weak distance restraint is also used to ensure the fragments are kept in the center of the sphere. Now let us take a look at some parts of the FEP file: Here we identify the atoms that should be treated as reacting fragments. Those will be the ones changing bonds, angles, torsions, charges and vdw parameters. The first section indicates the number of sates to be used and the atom to be part of the Q-region (first Q-atom ID and second PDB number of the atom). [FEP] states 2 [atoms] #Q index PDB index The next section gives the name of each atom type, vdw (columns two and three), soft pair (columns four and five), the 1-4 interactions (columns six and seven), and the mass of the atom. The soft pair interaction is used between reacting fragments, in order to reduce the high repulsion from the Lennard-Jones potential as the atoms come close together to form bonds. Details about it can be found at the Q manual. [atom_types] prb_c prc_cl cl-_cl Then the partial charges corresponding to the states 1 (reactant) and 2 (product) for the EVB calculation are indicated. The first column contains the Q-atom ID, and the last two columns are the charges for the EVB states 1 and 2. [change_charges] # PRB.C1 dq= # PRB.H2 dq= # PRB.H3 dq= Sometimes atoms can change their orbital properties, as it happens between sp2 and sp3 C atoms, or bonded and unbounded halogens. Their vdw properties will change, and it is here where we account for this. It works like the change in charges. [change_atoms] 1 prb_c1 prc_c1 # PRB.C1! 7 prb_br11 br-_br1 # PRB.Br11! 8 cl-_cl1 prc_cl11 # CL-.Cl1!

5 Then we add the pair of atoms where the soft potential will act. Again, we are using the Q-atom IDs. Note that here we are only using the atoms that breaking or forming bonds. [soft_pairs] 1 7 # prb_c1-prb_br # prc_c1-prc_cl11 [bond_types] # prb_c1-prb_br # prc_c1-prc_cl11 [change_bonds] # 1.C1-1.Br11 prb_c1-prb_br11 None # 1.C1-2.Cl1 None prc_c1-prc_cl11 These two sections are related to bond modifications. The bond types with three columns have changes in the spring constant (second column) and length (third column, in Å) of a covalent bond, and they are represented by a harmonic potential. The four columns in the bond type section provide the parameters for a Morse potential, which we use to represent the cleavage and formation of bonds. On the following section, we assign the type of bonds for every pair of atoms we are interested in. This time we use the PDB-atom ID for the pair of atoms, and two more columns, representing which type of bond will be used for the two states. Note that for cases where a bond is inexistent a zero is used. By analyzing the FEP file, can you tell which bond is being broken, and which one is being formed? For the angles and torsions, the procedure is analogous. The shape of the potentials follow the OPLS-AA force field convention. If you would like to know more, please refer to the Q manual. Finally, although being an old command, this part enables the printing of distances between two atoms in the output file. Here, the columns three and four have the Q-atom IDs of the atoms we would like information about. [off_diagonals] # prb_c1-prb_br # prc_c1-prc_cl11 Now, time for our MD simulations. In the 1-relax directory, you will see that there are three.inp files (relax_00x.inp). Those are the inputs used for the full relaxation procedure, and should be run sequentially. To run one of the input files, we will use the qdyn5_r8 or qdyn5p. Then run: batch run_relax_q.sh At the end of your relaxation process (three OK should appear), you should have three.log,.dcd and.re files. relax_003.re file will be used to launch your EVB calculations. In order to make sure that all relaxation process was accomplished, check the output file from your last input. At the end of the file you should have that Q terminated normally. If this is the case, time to go for the EVB runs. You can visualize the files in vmd (load the pdb and then the dcd file)

6 3. EVB calculations 3.1 Setting Up Your Calculation Once our systems are relaxed, we can now begin the EVB calculations. Go to the 2-fep folder. You will see that there are three directories. 1-RS_000 2-TS_000 3-PS_000 Each directory contains 51 input files corresponding to the EVB run. As you have learned from the lecture, EVB is a FEP procedure in which the energies used for the free energy calculation are a mix between the energies of the two or more states. The difference between these files is from where one starts the perturbation (from reactants, TS, or products). In order to run such calculation, we need to have the FEP, topology file and the necessary restart files from the relaxation step: cp../../1-relax/relax_003.re cont_relax_003.re cp../../1-relax/relax_003.re cont_relax_003.re.rest cp../../1-relax/*top. The files must be executed sequentially, starting with equil_000_1.000 and then followed by the fep*inp files (from fep_000_1.000.inp, which corresponds to our reactant state (lambdas set as 1.0 and 0.0), going all the way to fep_050_0.000.inp, the file corresponding to the product state (lambdas 0.0 and 1.0). Use the submission script available at each of the folders. bash run_feps_q.sh Running equilibration step equil_000_1.000 ( OK ) Running equilibration step equil_001_1.000 ( OK ) Running equilibration step fep_000_1.000 ( OK ) Running equilibration step fep_001_0.980 ( OK ) 4.2 Analyzing Our EVB Run and Calibrating the Parameters There is one type of file that has not being mentioned yet: the.en files. Those files contain a summary of the energies measured during every calculation, whether it is a MD or an EVB run. In order for us to be able to extract useful information from these energies, we will use another tool from Q: qfep5. To run it, you need an input file, which has been provided (qfep.inp). Such input looks like this: 51 # number of files/frames 2 0 # number of states and off-diagonals # kt and number of points to skip 51 # number of bins 10 # minimum points for bin

7 2.345 # gas phase shift 1 # number of diagonal elements # st 1 and 2,Aij,mu=eta=r0= # linear comb. of states (E=e1-e2) fep_000_1.000.en fep_001_0.980.en fep_050_0.000.en stop The first line corresponds to the number of.en files (51) to be read for the mapping procedure (which are then listed below). We then have the total number of EVB states (2), the value of k B T, number of bins, and the minimum number of points per bin. We will discuss about the bins and points in a while. The next line, where α is located (2.345), is the first of the empirical parameters: the gas-phase shift. The other empirical parameters are denoted by Aij and µ, those being related to the coupling between the wavefunctions for the two EVB states. The remaining empirical parameters were set to zero. Note that the wavefunction coupling, or non-diagonal elements of the Hamiltonian, is of the form Aij=exp( µr ij ), where r ij is the distance between the atoms composing the two extremes of the reaction (in our case, the departing Br atom and the nucleophilic Cl atom). To perform the mapping, use the following command: qfep5 <map_fep.inp >map_fep.log Parts of the output file produced are shown below: # Part 0: Average energies for all states in all files # file state pts lambda EQtot EQbond EQang EQtor EQimp EQel EQvdW Eel_qq EvdW_qq Eel_qp EvdW_qp --> Name of file number 1: fep_000_1.000.en fep_000_1.000.en Name of file number 2: fep_001_0.980.en The Part 0 shows a summary of the energy contributions from different sources, from bond to van der Waals contributions, for both states at different stages of the FEP procedure (i.e. different lambdas). # Part 1: Free energy perturbation summary: # Calculation for full system # lambda(1) dgf sum(dgf) dgr sum(dgr) <dg>

8 The Part 1 starts showing relevant information regarding free energies. It shows how the free energy starts being built, both summing from lambda 1.00 to 0.00 (and backwards, dgf and dgb respectively. On the last column we can see the average between the forward and backward profile of the free energies. Here you can spot where the transition state (TS) is. Often the TS is at the lambda , although this is not necessarily a rule. Later we will analyze the geometry of our system at the TS. Thus, keep in mind that you will find which lambda, and consequently which fep_xxx.log, we should look in order to get the TS distances. # Part 2: Reaction free energy summary: # Lambda(1) bin Energy gap dga dgb dgg # pts c1**2 c2** The Part 2 gives information for the relationship between the lambdas, the number of bin to build the plot of the parabola, the energy gap between the states 1 and 2 for every lambda, the value of the free energy parabola, number of points per bin, and finally the constants c 2 1 and c 2 2, which correspond to the constants of the mixing of the wavefunctions of the states 1 and 2 (ψ g = c 1 ψ 1 + c 2 ψ 2 ). # Part 3: Bin-averaged summary: # bin energy gap <dgg> <dgg norm> pts <c1**2> <c2**2> <r_xy> In this last part, we can extract the free energy profile (dgg norm) plotted against the energy gap as the reaction coordinate. From here you can extract the activation free energy, as well as the free energy difference between reactant and product states. Moreover, we also see the bins and their corresponding center in the energy gap axis. There are plenty of new concepts, so don t worry you could not grasp all of them. It is just a matter of experience. Now, check that you finished your calculation. Once they are done, we can start calibrating the empirical parameters. 3.3 Calibrating Your EVB Parameters Now we come to the final part of the EVB calculation. We need to calibrate the three empirical parameters to reproduce the G and G0 of a reference reaction. In this case I have performed G2 calculations in gas phase to obtain an accurate estimate of the energetics. In some cases, when experimental data of similar systems are available one can also use them and obtain the corresponding activation barriers from the rate constants. Then it is a matter to find a set of empirical parameters that can adjust our EVB parabola to reproduce the results from such studies. Our values are: G = 13.0 kcal/mol and G 0 = -5.4

9 kcal/mol. Calibrating three parameters at the same time is not a trivial task. Every reaction has its peculiarities. Some reactions might be independent of the exponential factor of the non-diagonal terms in the Hamiltonian, while some will need it. In our case, we will set the exponential factor equals to 0. Then you will play with the other two values and try to reproduce the experimental values for the water reaction. Once you find a set that allows you to obtain the desired energetics, you will use the same values for the enzyme reaction and map the energies. You can visualize your trajectory in vmd: vmd../../0-topol/probr_cl_start.pdb fep_0*dcd Also you can extract your activation barrier fro part 3 of the output: If you have some time left, try to include solvent in your simulation and see its effect on the activation barrier. Is that in line with your expectation? References [1] Warshel, A., Weiss, R.M. (1980). An Empirical Valence Bond Approach for Comparing Reactions in Solutions and in Enzymes. Journal of the American Chemical Society 102, [2] Warshel, A. (1991). Computer Modeling of Chemical Reactions in Enzymes and Solutions (New York: Wiley). [3] Marelius, J., Kolmodin, K., Feierberg, I., Åqvist, J. (1998). Q: A Molecular Dynamics Program for Free Energy Calculations and Empirical Valence Bond Simulations in Biomolecular Systems. Journal Molecular Graphics Modelling 16, [4] Duarte, F. & Kamerlin SCL (2016) Theory and Applications of the Empirical Valence Bond Approach: From Physical Chemistry to Chemical Biology. (New York: Wiley).