All-atom representation

Levitt Warshel [17, 18] were the first to show that reduced representations may work they used Ca atoms and virtual atoms at side chain centroids. OOBATAKE Crippen [24] simplified further by only considering the Ca atoms. This is snfficient since there are reasonably reliable methods (Holm Sander [11, 12]) that compute a full atom geometry from the geometry of the Ca atoms. (All atom representations are used as well, but limited to the prediction of tiny systems such as enkephalin.)... 

Presently, only the molecular dynamics approach suffers from a computational bottleneck [58-60]. This stems from the inclusion of thousands of solvent molecules in simulation. By using implicit solvation potentials, in which solvent degrees of freedom are averaged out, the computational problem is eliminated. It is presently an open question whether a potential without explicit solvent can approximate the true potential sufficiently well to qualify as a sound protein folding theory [61]. A toy model study claims that it cannot [62], but like many other negative results, it is of relatively little use as it is based on numerous assumptions, none of which are true in all-atom representations. 

In the study of the dynamic properties of phospholipids, two main levels of detail are used mean field and all-atom representation of the system. Likewise, there are two main simulation techniques Monte Carlo (MC) and molecular dynamics (MD) simulations. 

The representation of the biomolecule can be simplified from an all-atom representation to a representation in which each amino-acid residue is represented by one [68] or a few centres [69, 70]. Such models have been used... 

Figure 2. Transformation of the all atom representation of a protein fragment to the residue-based, or bead model employed to simulate protein folding.

C. dementi, A. E. Garcia, J. N. Onuchic (2003) Interplay among tertiary contacts, secondary structure formation and side-chain packing in the protein folding mechanism All-atom representation study of protein L. J. Mol. Biol. 326, pp. 933-954... 

Fig. 20. a Active site of E. coli amine oxidase. The polypeptide backbone is shown as a continuous coil, colored white for subunit A and grey for subunit B. Conserved residues are shown in all-atom representation, and the copper is shown as a green van der Waals dot surface. The position of TPQ in crystal form I is illustrated in green, coordinated to the copper. The precise location and orientation of the TPQ ring are not completely determined at the resolution of the current studies of crystal form II, and its general location is indicated by a yellow phenyl ring, close to the putative catalytic base Asp 383 (red). In crystal form II, TPQ is not a copper ligand, and the copper coordination is completed by two water molecules, shown in yellow (with permission from [28])... 

The next stage of realism beyond a lattice model is a continuum bead model, where atoms are grouped together into beads, and the beads are allowed to move continuously in space. Typically, one bead represents a single amino acid in a protein. All-atom representations of biomolecules constitute a further level of sophistication. In this final section of our review we investigate the potential energy surfaces of a continuum bead heteropolymer and a tetrapeptide modeled by an all atom potential. Disconnectivity graphs immediately provide a visual distinction between frustrated and unfrustrated systems in both cases. 

For example, larger side chains could be represented by two united atoms [138]. Alternatively, an all-atom representation of the main chain could be employed with a reduced representation of the side chains [28]. Using this kind of representation and more elaborate statistical potentials, the structure of short peptides such as melittin, pancreatic polypeptide inhibitor, apamin [28], PPT, and PTHrP [138] have been predicted with an accuracy ranging from 1.7-A root-mean-square deviation, (RMSD) (measured for the a-carbon positions) for the small single helix of melittin to... 

An interesting hierarchical Monte Carlo procedure for the prediction of protein structures has been proposed recently by Rose et al. [209]. Their model employs an all-atom representation of the main chain and a crude representation of the side groups interacting via a simple contact potential. The method seems to be quite accurate in the prediction of protein secondary and supersecondary structure however, the overall global accuracy of the folded structures is rather low. 

Note that any Ht satisfies Equation 10.5 and H nm satisfies Equation 10.2. Einally, the eigenvectors of MNM (in the same form as those of RTB) can be transformed to the all-atom representation by Equation 10.1. 

RNA structure prediction models that predominantly rely upon molecular mechanics techniques such as molecular dynamics (MD) are referred to here as physics-based (PB) models. These models are based on the classical all-atom MD simulation technique, which employs a parameterized force field, a set of energy rules, to emulate atom interactions. In order to decrease computational expense from the all-atom representation, CG models group multiple atoms into beads or pseudoatoms. In a similar sense, the all-atom MD force field must be converted to depict feasible interactions between these pseudoatoms. 

In an FEP study, Rao and Singh used AMBER 3.3 to determine the relative binding free enei of pepstatin and its derivatives to Rhizopus pepsin. A united-atom and an all-atom representation were used for the residues of the enzyme and for the inhibitors, respectively. The pepstatin-Rhizopus pepsin complex was modeled starting from the high resolution crystal structure, where the inhibitor was in the reduced form. All pepstatin derivatives studied had modifications made on statine. The AAGlfia mutation of... 

Tertiary Contacts, Secondary Structure Formation and Side-chain Packing in the Protein Folding Mechanism All-atom Representation Study of Protein L. 

Boundaries between atomistic and coarse-grained simulation approaches are floating. Atomistic simulations of ionomer systems typically employ all-atom representations of water molecules, anionic head groups, and protons. For the remaining components, the use of a coarse-grained or united-atom representation for the CF , groups in both the fluorocarbon backbone and the sidechains could markedly improve the computational efficiency of atomistic simulations. United-atom force fields permit simulations of substantially larger systems compared to all-atom force fields. For instance, Urata et al. (2005) have employed a united-atom representation of CF , ... 

The minimization of the model can proceed ad hoc guided by chemical intuition. Alternatively, minimal models may be derived by a well-defined coaise-graining transformation, beginning with an all-atom representation of the system. They may also be empirically derived by proposing a general functional form and performing a non-linear fit of the parameters of the function to a set of experimental data. These models are attractive in that the number of degrees of freedom and possible conformations is far fewer than the number of conformations accessible to an all-atom model. 

Methods in which systems ate represented in a less than allatom level. For example, an amino acid in a protein may be represented with a single interaction center for the side chain or each residue in an RNA may be represented with two interaction points. These methods are used for very large systems where the resolution does not warrant an all-atom representation. 

The individual components of a force field reflect established physical principles, such as representing bond lengths and angles as harmonic oscillators, and using Lennard-Jones 12-6 and Coulomb-type functions for the van der Waals and electrostatic nonbonding interactions, respectively. FIow-ever, the force fields are not independent of the protein models used. Each force field has associated with it atomic and molecular definitions and parameters, definitions that will differ between united atom and all-atom representations, for example. Similarly, water models are parameterized for use with certain force fields and are not necessarily interchangeable. ... 

Effective noncovalent interactions and nanoscopic modeling Toward a semiclassical all-atom representation... 

---