Molecular dynamics trajectories

As examples of applications, we present the overall accuracy of predicted ionization constants for about 50 groups in 4 proteins, changes in the average charge of bovine pancreatic trypsin inhibitor at pH 7 along a molecular dynamics trajectory, and finally, we discuss some preliminary results obtained for protein kinases and protein phosphatases. 

In molecular mechanics and molecular dynamics studies of proteins, assig-ment of standard, non-dynamical ionization states of protein titratable groups is a common practice. This assumption seems to be well justified because proton exchange times between protein and solution usually far exceed the time range of the MD simulations. We investigated to what extent the assumed protonation state of a protein influences its molecular dynamics trajectory, and how often our titration algorithm predicted ionization states identical to those imposed on the groups, when applied to a set of structures derived from a molecular dynamics trajectory [34]. As a model we took the bovine... 

Wlodek, S. T., Antosiewicz, J., McCammon, J. A. Prediction of titration properties of structures of a protein derived from molecular dynamics trajectories. Protein Sci. 6 (1997) 373-382. 

Once HyperChem calciilates potential energy, it can obtain all of th c forces on the n uclei at negligible addition a I expen se, I h is allows for rapid optimi/ation of equilibrium and tran sitiori-state geometries and th e possibility of com put in g force con stan ts, vibra-tiorial modes, and molecular dynamics trajectories. 

Quenched dynamics is a combination of high temperature molecular dynamics and energy minimization. This process determines the energy distribution of con formational families produced during molecular dynamics trajectories. To provide a better estimate of conformations, you should combine quenched dynamics with simulated annealing. 

Quantum mechanical calculation of molecular dynamics trajectories can sim ulate bon d breakin g and frtrm ation.. Although you dt) n ot see th e appearance or disappearan ce ofhonds, you can plot the distan ce between two bonded atom s.. A distan ce excccdi n g a theoretical bond length suggests bond breaking. 

This section desenhes a minimal theoretical background so you can understand the process of creating a classical molecular dynamics trajectory and use it to obtain a visual or statistical resn It. 

Aclassical molecular dynamics trajectory is simply a set of atoms with in itial condition s con sisiin g of the liX Cartesian coordinates ofX atoms and the iiX (. artesian velocities... 

A given molecular dynamics trajectory can be divided into three seqneiitlally-ordered phases ... 

Coordin ates of atom s can he set by n orm al translation orrotation of HyperCh cm molecules, fo set initial velocities, however, it is necessary to edit th e H l. file explicitly. The tin it o f velocity in the HIN file is. An gstrom s/picosecon d.. Areact.hin file and a script react.scr are in eluded with HyperChem to illustrate one simple reacting trajectory. In order to have these initial velocities used in a trajectory the Restart check box of the Molecular Dynamics Option s dialog box must he checked. If it is n ot, the in itial velocities in the HIN file will be ignored and a re-equilibration to the tern peratiire f of th e Molecular Dyn am ics Option s dialog box will occur. This destroys any imposed initial conditions on the molecular dynamics trajectory. 

Finite difference techniques are used to generate molecular dynamics trajectories with continuous potential models, which we will assume to be pairwise additive. The essential idea is that the integration is broken down into many small stages, each separated in time by a fixed time 6t. The total force on each particle in the configuration at a time t is calculated as the vector sum of its interactions with other particles. From the force we can determine the accelerations of the particles, which are then combined with the positions and velocities at a time t to calculate the positions and velocities at a time t + 6t. The force is assumed to be constant during the time step. The forces on the particles in their new positions are then determined, leading to new positions and velocities at time t - - 2St, and so on. 

Dauber-Osguthorpe P and D J Osguthorpe 1990. Analysis of Intramolecular Motions by Filterin Molecular Dynamics Trajectories. Journal of the American Chemical Society 112 7921-7935. 

Most potential energy surfaces are extremely complex. Fiber and Karplus analyzed a 300 psec molecular dynamics trajectory of the protein myoglobin. They estimate that 2000 thermally accessible minima exist near the native protein structure. The total number of conformations is even larger. Dill derived a formula to calculate the upper bound of thermally accessible conformations in a protein. Using this formula, a protein of 150 residues (the approx-... 

Once HyperChem calculates potential energy, it can obtain all of the forces on the nuclei at negligible additional expense. This allows for rapid optimization of equilibrium and transition-state geometries and the possibility of computing force constants, vibrational modes, and molecular dynamics trajectories. 

The acceleration is determined and the cycle renewed. In the subsequent steps, the velocities advance from t-1/2 At to t-tl/2 At. The resulting set of positions and velocities is the molecular dynamics trajectory. 

HyperChem runs the molecular dynamics trajectory, averaging and analyzing a trajectory and creating the Cartesian coordinates and velocities. The period for reporting these coordinates and velocities is the data collection period At2. It is a multiple of the basic time step, At2 = n2 Atj, and is also referred to as a data step. The value n2 is set in the Molecular Dynamics options dialog box. 

An important issue, the significance of which is sometime underestimated, is the analysis of the resulting molecular dynamics trajectories. Clearly, the value of any computer simulation lies in the quality of the information extracted from it. In fact, it is good practice to plan the analysis procedure before starting the simulation, as the goals of the analysis will often detennine the character of the simulation to be performed. 

The distance matrix A, which holds the relative distances (by whatever similarity measure) between the individual confonnations, is rarely informative by itself. For example, when sampling along a molecular dynamics trajectory, the A matrix can have a block diagonal form, indicating that the trajectory has moved from one conformational basin to another. Nonetheless, even in this case, the matrix in itself does not give reliable information about the size and shape of the respective basins. In general, the distance matrix requires further processing. 

JM Troyer, EE Cohen. Protein conformational landscapes Energy minimization and clustering of a long molecular dynamics trajectory. Proteins 23 97-110, 1995. 

One of the main attractions of normal mode analysis is that the results are easily visualized. One can sort the modes in tenns of their contributions to the total MSF and concentrate on only those with the largest contributions. Each individual mode can be visualized as a collective motion that is certainly easier to interpret than the welter of information generated by a molecular dynamics trajectory. Figure 4 shows the first two normal modes of human lysozyme analyzed for their dynamic domains and hinge axes, showing how clean the results can sometimes be. However, recent analytical tools for molecular dynamics trajectories, such as the principal component analysis or essential dynamics method [25,62-64], promise also to provide equally clean, and perhaps more realistic, visualizations. That said, molecular dynamics is also limited in that many of the functional motions in biological molecules occur in time scales well beyond what is currently possible to simulate. 

The highest probability paths will make the argument of the exponential small. That will be true for paths that follow Newtonian dynamics where mr = F(r). Olender and Elber [45] demonstrated how large values of the time step ht can be used in a way that projects out high frequency motions of the system and allows for the simulation of long-time molecular dynamics trajectories for macromolecular systems. 

Figure 3 Calculated X-ray diffuse scattering patterns from (a) a full molecular dynamics trajectory of orthorhombic hen egg white lysozyme and (b) a trajectory obtained by fitting to the full trajectory rigid-body side chains and segments of the backbone. A full description is given in Ref. 13.

Another principal difficulty is that the precise effect of local dynamics on the NOE intensity cannot be determined from the data. The dynamic correction factor [85] describes the ratio of the effects of distance and angular fluctuations. Theoretical studies based on NOE intensities extracted from molecular dynamics trajectories [86,87] are helpful to understand the detailed relationship between NMR parameters and local dynamics and may lead to structure-dependent corrections. In an implicit way, an estimate of the dynamic correction factor has been used in an ensemble relaxation matrix refinement by including order parameters for proton-proton vectors derived from molecular dynamics calculations [72]. One remaining challenge is to incorporate data describing the local dynamics of the molecule directly into the refinement, in such a way that an order parameter calculated from the calculated ensemble is similar to the measured order parameter. 

Methods for simulating restrained x>ray refinement data from molecular dynamics trajectories. 

There are therefore four adjustable parameters per atom in the refinement (xy, yy, Zj, By). In the computer experiments we have carried out to test the assumptions of the nucleic acid refinement model we have generated sets of observed structure factors F (Q), from the Z-DNA molecular dynamics trajectories. The thermal averaging implicit in Equation III.3 is accomplished by averaging the atomic structure factors obtained from coordinate sets sampled along the molecular dynamics trajectories at each temperature ... 

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