Conformations simulations

Figure 3. Sugar pseudorotation phase angles in 400 conformations simulated by Monte Carlo. Left panels evolution of pseudorotation during simulation right panels distribution of pseudorotation. Pseudorotation angles of B- and A-forms are shown in thick lines for comparison.

Computational methods such as molecular mechanics (MM) and quantum theory calculations have become convenient and reliable techniques in the analysis of CD data. A common approach in chiral supramolecular structural study is to examine if a supramolecular conformation simulated by MM method is consistent with the observed CD spectrum of the sample. However, in order to use this approach, one needs to correlate the stereostructures and CD data by using, for example, exciton chirality method or reference CD spectra of analogs with known structures. Thus, it should be noted that the application of this method has some limitations for evaluation in supramolecular systems. 

Guenot, J., Kollman, P.A. Conformational and energetic effects of truncating nonbonded interactions in an aqueous protein dynamics simulation. J. Comput. Chem. 14 (1993) 295-311. 

The simulations also revealed that flapping motions of one of the loops of the avidin monomer play a crucial role in the mechanism of the unbinding of biotin. The fluctuation time for this loop as well as the relaxation time for many of the processes in proteins can be on the order of microseconds and longer (Eaton et al., 1997). The loop has enough time to fluctuate into an open state on experimental time scales (1 ms), but the fluctuation time is too long for this event to take place on the nanosecond time scale of simulations. To facilitate the exit of biotin from its binding pocket, the conformation of this loop was altered (Izrailev et al., 1997) using the interactive molecular dynamics features of MDScope (Nelson et al., 1995 Nelson et al., 1996 Humphrey et al., 1996). 

Schlitter et al., 1993] Schlitter, J., Engels, M., Kruger, P., Jacoby, E., and Wollmer, A. Targeted molecular dynamics simulation of conformational change - application to the t <- r transition in insulin. Molecular Simulation. 10 (1993) 291-308... 

Conformational Transitions of Proteins from Atomistic Simulations... 

Simulations of the dynamic motion of proteins aim at sampling relevant portions of the conformational space accessible to the proteins under the influence of environmental variables such as temperature, pressure, and pH. We... 

Molecular dynamics simulations ([McCammon and Harvey 1987]) propagate an atomistic system by iteratively solving Newton s equation of motion for each atomic particle. Due to computational constraints, simulations can only be extended to a typical time scale of 1 ns currently, and conformational transitions such as protein domains movements are unlikely to be observed. 

To facilitate conformational transitions in the before-mentioned adenylate kinase, Elamrani and co-workers scaled all atomic masses by a large factor thus allowing the use of a high effective simulation temperature of 2000K ([Elamrani et al. 1996]). To prevent protein unfolding, elements of secondary structure had to be constrained. 

The essential slow modes of a protein during a simulation accounting for most of its conformational variability can often be described by only a few principal components. Comparison of PGA with NMA for a 200 ps simulation of bovine pancreatic trypsic inhibitor showed that the variation in the first principal components was twice as high as expected from normal mode analy-si.s ([Hayward et al. 1994]). The so-called essential dynamics analysis method ([Amadei et al. 1993]) is a related method and will not be discussed here. 

Grubmiiller described a method to induce conformational transitions in proteins and derived rate constants for these ([Grubmiiller 1994]). The method employs subsequent modifications of the original potential function based on a principal component analysis of a short MD simulation. It is discussed in more detail in the chapter of Eichinger et al. in this volume. 

If both starting structure and target structure are known, the method of targeted molecular dynamics simulation can be used to enforce a conformational transition towards the given final structure during a given simulation time ([Schlitter et al. 1994]). 

The first term represents the forces due to the electrostatic field, the second describes forces that occur at the boundary between solute and solvent regime due to the change of dielectric constant, and the third term describes ionic forces due to the tendency of the ions in solution to move into regions of lower dielectric. Applications of the so-called PBSD method on small model systems and for the interaction of a stretch of DNA with a protein model have been discussed recently ([Elcock et al. 1997]). This simulation technique guarantees equilibrated solvent at each state of the simulation and may therefore avoid some of the problems mentioned in the previous section. Due to the smaller number of particles, the method may also speed up simulations potentially. Still, to be able to simulate long time scale protein motion, the method might ideally be combined with non-equilibrium techniques to enforce conformational transitions. 

Abstract. Molecular dynamics (MD) simulations of proteins provide descriptions of atomic motions, which allow to relate observable properties of proteins to microscopic processes. Unfortunately, such MD simulations require an enormous amount of computer time and, therefore, are limited to time scales of nanoseconds. We describe first a fast multiple time step structure adapted multipole method (FA-MUSAMM) to speed up the evaluation of the computationally most demanding Coulomb interactions in solvated protein models, secondly an application of this method aiming at a microscopic understanding of single molecule atomic force microscopy experiments, and, thirdly, a new method to predict slow conformational motions at microsecond time scales. 

As an example for an efficient yet quite accurate approximation, in the first part of our contribution we describe a combination of a structure adapted multipole method with a multiple time step scheme (FAMUSAMM — fast multistep structure adapted multipole method) and evaluate its performance. In the second part we present, as a recent application of this method, an MD study of a ligand-receptor unbinding process enforced by single molecule atomic force microscopy. Through comparison of computed unbinding forces with experimental data we evaluate the quality of the simulations. The third part sketches, as a perspective, one way to drastically extend accessible time scales if one restricts oneself to the study of conformational transitions, which arc ubiquitous in proteins and are the elementary steps of many functional conformational motions. 

The previous application — in accord with most MD studies — illustrates the urgent need to further push the limits of MD simulations set by todays computer technology in order to bridge time scale gaps between theory and either experiments or biochemical processes. The latter often involve conformational motions of proteins, which typically occur at the microsecond to millisecond range. Prominent examples for functionally relevant conformatiotial motions... 

Fig. 9. Two-dimensional sketch of the 3N-dimensional configuration space of a protein. Shown are two Cartesian coordinates, xi and X2, as well as two conformational coordinates (ci and C2), which have been derived by principle component analysis of an ensemble ( cloud of dots) generated by a conventional MD simulation, which approximates the configurational space density p in this region of configurational space. The width of the two Gaussians describe the size of the fluctuations along the configurational coordinates and are given by the eigenvalues Ai.

Step 1 A short conventional MD simulation (typically extending over a few lOOps) is performed to generate an ensemble of protein structures x 6 71 (each described by N atomic positions), which characterizes the initial conformational substate. The 2-dimensional sketch in Fig. 9 shows such an ensemble as a cloud of dots, each dot x representing one snapshot of the protein. 

Conformational Dynamics Simulations of Proteins molecular dynamics conformational flooding... 

Fig. 10. Conformational flooding accelerates conformational transitions and makes them accessible for MD simulations. Top left snapshots of the protein backbone of BPTI during a 500 ps-MD simulation. Bottom left a projection of the conformational coordinates contributing most to the atomic motions shows that, on that MD time scale, the system remains in its initial configuration (CS 1). Top right Conformational flooding forces the system into new conformations after crossing high energy barriers (CS 2, CS 3,. . . ). Bottom right The projection visualizes the new conformations they remain stable, even when the applied flooding potentials (dashed contour lines) is switched off.

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