MD Simulations in vacuo

In a complementary approach the backbones of dendrimers are jacketed as tightly as possible with dendrons of the largest possible space demand. Here the dendrons serve as space filling parts to implement sufficient strain to the dendrimers backbone in order to stretch it to the extreme. A good example for this is dendrimer 22a with its third generation dendrons [15b]. The molecular dimensions obtained from MD-simulations in vacuo show that (a) it attains an almost stretched conformation, (b) the dendritic layer around the PPP backbone... 

P. Beudaert, V. Lamare, J. F. Dozol, L. Troxler, and G. Wipff. Theoretical studies on tri-n-butyl phosphate Md simulations in vacuo, in water, in chloroform, and at a water/ chloroform interface. Solvent Extr. Ion Exch., 16(2) 597-618, 1998. 

These investigators employed the CHARMm force field with the carbohydrate parameters of Ha et al. jn j s MD simulations in vacuo. They note particularly, as have others, >135 that the use of the isolated spin pair approximation (ISPA), which is often used to convert NOE intensities into interproton distances, can be extremely inaccurate. Within ISPA, the assumption is made that the NOE intensity NOEfj) between two protons arises only from spin relaxation between the two protons. This approximation neglects the effects of spin diffusion and internal motion. Taking for calibration a known interproton distance (r f) and its associated NOE (NO f), the ISPA distance two protons i and j) may be derived from Eq. [14].i35... 

Figure 2. Inversion of chirality at C-12 from if to S during MD simulation in vacuo (55). Charts a) and b) represent distances from Hb-10 to H-7, and from H-4 to Hb-6, respectively, when started from serratezomine A (40) (S at C-12). Charts c) and d) represent those started from the isomer (if at C-12).

As it was mentioned in Section 9.4.1, 3D structures generated by DG have to be optimized. For this purpose, MD is a well-suited tool. In addition, MD structure calculations can also be performed if no coarse structural model exists. In both cases, pairwise atom distances obtained from NMR measurements are directly used in the MD computations in order to restrain the degrees of motional freedom of defined atoms (rMD Section 9.4.2.4). To make sure that a calculated molecular conformation is rehable, the time-averaged 3D structure must be stable in a free MD run (fMD Sechon 9.4.2.5J where the distance restraints are removed and the molecule is surrounded by expMcit solvent which was also used in the NMR measurement Before both procedures are described in detail the general preparation of an MD run (Section 9.4.2.1), simulations in vacuo (Section 9.4.2.2) and the handling of distance restraints in a MD calculation (Section 9.4.2.3) are treated. Finally, a short overview of the SA technique as a special M D method is given in Sechon 9.4.2.6. 

Collective motions of secondary and supersecondary structures in proteins are important for understanding functionality. A unique collective motion has been detected by molecular dynamics dynamics simulations of the carboxy terminal fragment (CTF) of the L7/L12 ribosomal protein [79]. In the crystal state, the unit cell embodies eight units of CTF. A dimer has been proposed as a functional significant structure. MD simulations of the dimer [80] and of CTF immersed in a bath of 2352 SPC water molecules carried out in our laboratory, have shown that protein collective motions are not damped down. For this particular case, the simulations in vacuo are good enough for reproducing structural features and the dynamical behavior of the whole protein. 

In order to apply the techniques discussed above to the MD simulation o biomolecules, one takes the Liouville operator for a macromolecule in vacuo containing N atoms to be... 

The X-ray structure of the L-Sr(Picrate)2 (L = p-tert-butyl-calix[4]arene-tetra(diethylamide)) is reported, as well as MD simulations on the L M2+ complexes in vacuo, in water, and in acetonitrile solutions for alkaline earth cations with a comparison of converging and diverging conformers.130 In the simulated and solid-state structures of the L M2+ complex, the ligand wraps around the complexed cations M2+ (more than it does with alkaline cations), which are completely encapsulated within the polar pseudo-cavity of L, without coordination to its counterion in the crystal or to solvent molecules in solution. In contrast to alkali cation complexes, which display conformational flexibility in solution, computations show that the alkaline earth cation complexes are of the converging type in water and in acetonitrile. Subtle structural changes from Mg2+ to Ba2+ are observed in the gas phase and in solution. Based on FBP calculations, a binding sequence of alkaline earth cations was determined Mg2+ displays the weakest affinity for L, while Ca2+ and Sr2+ are the most stable complexes, which is in agreement with the experiment. 

Figure 1.10 Vibrational spectra (frequencies in cm 1j of the phenoxide molecule in vacuo and in solution obtained by the MD simulation. The intensities were scaled in order to fit on the same scale.

Some investigators would argue that the results of distance geometry are only initial structures and that biases should disappear after thorough MD or other energetic refinement. In this case, one should bear in mind that one may then suffer from biases in the molecular mechanics force field. The most serious of these is the tendency for structures to become too compact if simulations are conducted in vacuo. The obvious solution here is to perform simulations in the presence of explicit solvent, although this is computationally expensive. 

The two most eommonly nsed methods in the literatnre for stndying flexible ligands sueh as AA and AEA have been the Monte Carlo and molecnlar dynamics (MD) techniques. In their Monte Carlo study, Rabinovich and Ripatti (Rabinovich and Ripatti, 1991) foimd that polyimsaturated fatty acids whose double bonds are separated by one methylene carbon assume an extended (angle-iron) conformation when all molecnles are efficiently packed below the phase-transition temperature. MD or molecular dynamics/simulated annealing (MD/SA) studies (in vacuo) of AA (9) and of other polyimsaturated fatty acids related to AA have been published by several groups... 

In 1993 Rutherford et al. suggested that the poor performance of the Homans parameter set may reflect weaknesses of the computational method. 131 Despite the seemingly logical combination of parameters employed by Homans, after several attempts to reproduce experimental NOE intensities, Rutherford et al. concluded that the parameters were unsuitable for application in unrestrained MD simulations of oligosaccharides. 31 Moreover, those authors noted that the poor agreement with experiment was independent of the presence or absence of the exo-anomeric torsional terms. These conclusions were based on comparatively long trajectories of up to 1 ns performed in vacuo on a model mannobioside, a-D-Man(l-3)a-D-Man-OMe (8). However, the possibility remains that the poor performance was related to the short durations of the solvated simulations. No MD simulations with Homans parameters have been reported that approach the nanosecond time scale in the presence of explicit solvation. Recent MD simulations with explicit solvation indicate that conformational equilibration may not be achieved before 50—100 ps and that accurate ensemble averages may not be reached before 500 ps. > 3... 

In slightly more than 10 years since the original protein MD simulation, a number of detailed MD simulations of globular proteins in vacuo, in solution, and in hydrated crystals have been performed. More recently, MD simulations for nucleic acids (DNA and tRNA) have appeared in the literature. °" Nucleic acid simulations can be particularly diallenging due to the complex hydration and polyelectrolyte properties of these molecules, as well as the limited experimental structural data available for these systems. MD simulations of model lipid bilayers and micelles are even less common, " due mainly to the size and complex behavior of these systems. As resources and the sophistication of simulation methods and models continue to improve, MD simulations of larger and more complex biomolecular systems will become commonplace. 

One possible rapid and simple MD simulation protocol for use in verifying designed molecules is to use a model of the receptor with only a few flexible residues or side chains. The system would be studied either in vacuo or with only a small number of water molecules. The ligand is first minimized, and... 

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