Exercise 2: Solvating the Structure HyperChem lets you place a molecular system in a periodic box of water molecules to simulate behavior in aqueous solution, as in a biological system. In this exercise, you solvate the alanine zwitterion you created in Exercise 1. Before you continue, follow these steps: 1. Remove labels from the display by using the default settings in the Labels dialog box. 2. Choose Periodic Box on the Setup menu to open the Periodic Box Options dialog box. Setting up Periodic Boundary Conditions To solvate a system with HyperChem you specify a rectangular box or cube of equilibrated water molecules. You define the dimensions of the box, place the solute in the center, and define the minimum distance between the solvent and solute atoms. HyperChem eliminates all water molecules with atoms that come closer to a solute atom than the specified distance. Specifying the Periodic Box Size There are several factors to consider when you define the size of

the periodic box. For example, it must be larger than the dimensions for the Smallest box enclosing solute that appear in the Periodic Box Options dialog box. Box dimensions at least twice the largest solute dimension avoid solute-solute interactions when using the default cutoffs. The solute- solute interactions can also be avoided with a smaller box by lessening the cutoff radius after solvation (so that the largest solute dimension plus the cutoff radius and range is less than the smallest box dimension). The reference cube of water is formed from an equilibrated cube of 18.70136Å and its nearest images, so you shouldn’t use dimensions larger than 56.10408Å. Dimensions that are multiples of 18.70136Å minimize initial bad contacts. To choose the periodic box size: 1. Specify a box size of 12.0 by 10.0 by 12.0 Ångstroms, as shown in the following illustration. Displaying the Solvated System 1. Choose Rendering on the Display menu. 2. Turn on Perspective in the Rendering/Sticks dialog box, and then choose OK. 3. Set the select level to Molecules. 4. Select a bond or atom of the alanine molecule, and rotate the whole system to look like this:

Adjusting Cutoffs and Dielectric Options When you use periodic boundary conditions, you need to check the options for cutoffs and dielectric in the Force Field Options dialog box. To check the options for cutoffs and dielectric: 1. Choose Molecular Mechanics on the Setup menu. 2. Choose Options to open the Force Field Options dialog box. 3. Look at the Cutoffs options at the right of the dialog box.

Optimizing the Solvated Molecule The next step is to optimize the solvated system using periodic boundary conditions. Since the alanine molecule has an optimum geometry (at least in isolation), the optimization primarily relaxes the solvent. Changes in alanine reflect the difference between isolated and in solution optimal structures. When the optimization is complete, remeasure the O-C’-O angle and the N-C⟨-C’-O torsion: O-C’-O angle= 123.9º N-Ca-C’-O torsions = -51 and 99 degreesº Recall that for the unoptimized structure, the O-C’-O angle measured 120 degrees and the N-C⟨-C’-O torsion angles measured ±60 degrees and ±120 degrees. Later in this lesson, you use the N-C⟨-C’-O angle to demonstrate molecular dynamics features of HyperChem, so save this angle as a named selection.

Setting up Averaging from Molecular Dynamics Molecular dynamics is often used to obtain macroscopic information by sampling a microscopic simulation over a long period of time. It is also useful to track energetic and geometric quantities as the simulation proceeds to see if the system has stabilized enough for sampling to be statistically valid or not. Note: When you start the Averaging function, HyperChem creates a file with the extension .csv in the current working directory (see page 173). However, if you are reading a snapshot file from a CD, the current directory is on the CD; you cannot create a file there. You will need to copy the snapshot file to your hard drive first. To set up averaging: 1. Choose Averages to open the Molecular Dynamics Averages dialog box.

Setting up Playback Dynamics The next step is to set up playback dynamics. Playback dynamics is convenient because it saves time-consuming dynamics simulations for you to analyze later. Molecular dynamics simulates the evolution of a system over time, producing a trajectory of atomic positions and velocities. These calculations can be very time consuming, and for statistically meaningful results, long simulation times corresponding to many thousands of time steps might be required. Often you’ll want to save the calculated trajectory for later playback or analysis, rather than having to repeat the simulation. To set up playback dynamics: 1. Choose Snapshots at the bottom of the Molecular Dynamics Options dialog box. The Molecular Dynamics Snapshots dialog box opens. 2. Enter ala-run as the filename. HyperChem generates two files with the prefix ala-run. One file, ala-run.hin, is a HIN file that contains a snapshot entry. Another file, ala-run.snp, is a binary file containing atomic coordinates and velocities. 3. Use a Snapshot period of 1 data step. 4. Choose OK to return to the Molecular Dynamics Options dialog box. Proceeding with Dynamics 1. Choose OK to return to the Molecular Dynamics Options dialog box, then choose Proceed to start dynamics. A graph titled Molecular Dynamics Results opens on the workspace. 2. Move the graph so that you can watch the simulation. While the calculation is running, you can change the view of the system by using the rotation, translation, zoom, and clip tools. You can also use applications in other windows, but this can slow down the simulation. 3. As the simulation continues, choose Rescale to rescale the values being plotted.

Part 2: Monte Carlo Simulation The Monte Carlo method samples configurations from a Boltzmann- weighted distribution at a given temperature. At elevated temperatures, this technique may be used to move the molecular system of interest across potential energy barriers. In this exercise we employ the Monte Carlo method followed by geometry optimization as an additional conformational search technique. To set up the Monte Carlo simulation: 1. First retrieve the solvated alanine zwitterion system, which was saved as ala-liq.hin. 2. Choose Monte Carlo on the Compute menu. The Monte Carlo Options dialog box allows you to set up the Monte Carlo simulation parameters. In this example we will run a constant temperature simulation with 1000 steps. For some systems, it may be useful to add optional heat and cool phases. 3. Set the Run Steps to 1000. Set Heat and Cool steps to 0. 4. Set the maximum step size, Max Delta, to 0.05 Å. This sets the maximum trial atomic displacement. If it is too small only limited sampling of new configurations will occur. If it is too large, unphysical configurations may be generated. This reduces the efficiency of the simulation. 5. Set the Simulation Temperature to 300K. 6. Make sure that Periodic boundary conditions is on ( ). 7. Set the Data Collection period to 4 steps. Setting up Monte Carlo Playback 8. Set up a snapshot file, if desired. Playback of the Monte Carlo “trajectory” is set up in the same way as Dynamics playback. See “Setting up Playback Dynamics” on page 170. As with Dynamics, analysis of the simulation may be conveniently carried out at playback. For example, you can stop the playback at the point in a simulation where the potential energy falls, and save the structure at that point. You can also change the graphing and averaging selections before playing back a run. Setting up Averaging from Monte Carlo 9. Set up Averages and Graphing as desired. The Monte Carlo Averages setup is identical to Molecular Dynamics Averages setup. There is an additional parameter that you can monitor in Monte Carlo: the acceptance ratio. It appears as ACCR on the list of possible selections in the Monte Carlo Averages dialog box; DACCR, the rms deviation of ACCR from its mean, appears also. The acceptance ratio is a running average of the ratio of the number of accepted moves to attempted moves. Optimal values are close to 0.5. Varying the step size can have a large effect on the acceptance ratio. For a more detailed discussion, see the Monte Carlo section of the Computational Chemistry manual.

MOLECULAR DYNAMICS LABORATORY

Length of SimulationsHyperChem integrates the equations of motion using very small time steps (Δt). At each step, thealgorithm evaluates energy and forces of the molecular system. Use a time step of about 0.5 to 1.0

femtoseconds (fs) for an All Atom system or 1 to 2 fs for a United Atom system. Small time steps allowthe simulation to adequately integrate the highest frequency motions of the system, usually bond stretchingvibrations on the order of several picoseconds.

Adjust Δt for each molecular system to obtain energy conservation (see the next section).

One drawback to a molecular dynamics simulation is that the trajectory length calculated in a reasonabletime is several orders of magnitude shorter than any chemical process and most physical processes, whichoccur in nanoseconds or longer. This allows you to study properties that change within shorter time periods(such as energy fluctuations and atomic positions), but not long­term processes like protein folding.

Conservation of EnergyMolecular dynamics calculations use equations 25–27.

HyperChem integrates equations 26 and 27 to describe the motions of atoms. In the absence of temperatureregulation, there are no external sources or depositories of energy. That is, no other energy terms exist inthe Hamiltonian, and the total energy of the system is constant.

One way to test for success of a dynamics simulation and the length of the time step is to determine thechange in kinetic and potential energy between time steps. In the microcanonical ensemble (constantnumber, volume, and energy), the change in kinetic energy should be of the opposite sign and exactmagnitude as the change in potential energy. Though the total energy of the system should not changeduring the simulation, molecular dynamics simulations only approximate this condition. Energyconservation is difficult to achieve using computers with finite precision

Temperature ControlIn a molecular dynamics calculation, you can add a term to adjust the velocities, keeping the molecularsystem near a desired temperature.

During a constant temperature simulation, velocities are scaled at each time step. This couples the systemto a simulated heat bath at T0, with a temperature relaxation time of τ. The velocities are scaled by afactor  .λ

If the coupling parameter (the Bath relaxation constant in HyperChem), τ, is too “tight” (<0.1 ps), anisokinetic energy ensemble results rather than an isothermal (microcanonical) ensemble. The trajectory isthen neither canonical or microcanonical.

You cannot calculate true time­dependent properties or ensemble averages for this trajectory. You can usesmall values of  τ for these simulations:

• To obtain a minimum energy structure at 0K.• To reach equilibrium temperature quickly before starting theequilibration phase of a simulation.If the Bath relaxation constant, τ, is greater than 0.1 ps, you should be able to calculate dynamicproperties, like time correlation functions and diffusion constants.

Simulation PeriodsA molecular dynamics simulation can have three distinct time and temperature periods: heating, simulation(run), and cooling. If you want to measure equilibrium properties of a molecular system, you can dividethe simulation period into two parts: equilibration and data collection.

Initial Conditions and HeatingA molecular dynamics simulation usually starts with a molecular structure refined by geometryoptimization, but without atomic velocities. To completely describe the dynamics of a classical systemcontaining N atoms, you must define 6N variables. These correspond to 3N geometric coordinates (x, y,and z) and 3N variables for the velocities of each atom in the x, y, and z directions.

To begin a molecular dynamics simulation from this static structure, HyperChem assigns velocity valuesthat are realistic for the molecular system at a designated temperature.

Since HyperChem­constructed molecular systems are near 0 K (the atoms have zero velocity), a simulationusually begins by adjusting the system to a higher temperature during a heating step. Heating can takeplace in one step (from near 0 K to simulation temperature), but it is better to heat to the simulationtemperature slowly, in small temperature increments.

Equilibration and Data CollectionIn many molecular dynamics simulations, equilibration is a separate step that precedes datacollection. Equilibration is generally necessary to avoid introducing artifacts during the heating step and toensure that the trajectory is actually simulating equilibrium properties. The period required forequilibration depends on the property of interest and the molecular system. It may take about 100 ps for thesystem to approach equilibrium, but some properties are fairly stable after 10–20 ps.18 Suggested timesrange from 5 ps to nearly 100 ps for medium­sized proteins.

Tests for EquilibrationTo determine when a molecular system reaches equilibrium, you can monitor fluctuations in temperature,kinetic energy, total energy, number of hydrogen bonds or nonbond contacts, or the number of times aparticular configuration occurs. If you plot potential energy against time during a constant temperature run,then equilibration is close when average potential energy is constant.

Other properties of the molecular system may also become constant unless a major conformational changeoccurs.

Solvent SimulationsOften you need to add solvent molecules to a solute before running a molecular dynamics simulation (seealso “Solvation and Periodic Boundary Conditions” on page 65). In HyperChem, choose Periodic Box onthe Setup menu to enclose a solute in a periodic box filled appropriately with TIP3P models of watermolecules.

Choice of Dielectric ConstantBefore running a molecular dynamics simulation with solvent and a molecular mechanics method, choosethe appropriate dielectric constant. You specify the type and value of the dielectric constant in the ForceField Options dialog box. The dielectric constant defines the screening effect of solvent molecules onnonbonded (electrostatic) interactions.

Use a constant dielectric of 1.0 with TIP3P water molecules in a periodic box. Because of theparameterization of TIP3P molecules, using a distance­dependent dielectric or a value other than 1.0 givesunnatural results.

Constant Energy SimulationsYou can check the success of a simulation by studying averages ofthe energy terms and their deviations. Since energy is conserved ina constant energy simulation, you can monitor the equilibrationby dividing the deviation of the total energy (D ETOT) by the averagetotal energy (ETOT). The data to calculate these averages is inthe CSV file. This is a convenient way to obtain the averages for amolecular dynamics run:4. Before starting a molecular dynamics simulation, L­click onAverages in the Molecular Dynamics Options dialog box.5. Choose D ETOT and Add to average this value. Repeat this processfor ETOT. L­click OK.6. Set options for the simulation and L­click Proceed.7. After a molecular dynamics simulation or the playback of asimulation, L­click on Averages in the Molecular DynamicsOptions dialog box.8. L­click on D ETOT. The average appears below, after Value.Write down this number. Repeat for ETOT. This averagereplaces the previous average.9. Calculate the ratio.For simulations of liquids, the generally accepted upper limit forthe ratio is 0.0001.

Time StepWhen the friction coefficient is set to zero, HyperChem performs regular molecular dynamics, and oneshould use a time step that is appropriate for a molecular dynamics run. With larger values of the frictioncoefficient, larger time steps can be used. This is because the solution to the Langevin equation in effectseparates the motions of the atoms into two time scales: the short­time (fast) motions, like bond stretches,which are approximated, and longtime (slow) motions, such as torsional motions, which are accuratelyevaluated. As one increases the friction coefficient, the short­time motions become more approximate, andthus it is less important to have a small timestep.

Monte Carlo SimulationsIntroductionMonte Carlo simulations are commonly used to compute the average thermodynamic properties of amolecule or a system of molecules, and have been employed extensively in the study of the structure andequilibrium properties of liquids and solutions.

Monte Carlo methods have also been used to conduct conformational searches under non­equilibriumconditions.

Step Size and Acceptance RatioThe step size, Δ r, is the maximum allowed atomic displacement used in the generation of trialconfigurations. The default value of r in HyperChem is 0.05 Ã…ngstroms. For most organic molecules,

this will result in an acceptance ratio of about 0.5, which means that about 50% of all moves are accepted.

Increasing the size of the trial displacements may lead to more complete searching of configuration space,but the acceptance ratio will, in general, decrease. Smaller displacements generally lead to higheracceptance ratios but result in more limited sampling.

There has been little research to date on what the optimum value of the acceptance ratio should be. Mostresearchers tend to try for an average value around 0.5; smaller values may be appropriate when longerruns are acceptable and more extensive sampling is necessary.