Grained Protein Models

Lattice models were first used to study proteins by Go et who 

In addition to the HP model, several other low-resolution protein models have been developed to provide insight into the nature of protein folding. The AB model, used in the studies mentioned by Shakhnovich et al. and studied extensively by Socci and Onuchic, is similar in spirit to the HP model. The AB model is a three-dimensional lattice protein with 27 monomers. Each monomer is either of type A or type B, and the interaction energy between two nearest-neighbor, nonbonded monomers is Ec for an AA or BB pair, and E for an AB pair, where Ei E 0. In this scheme, like contacts are favored over unlike contacts, and there is an overall driving energy toward 

Boltzmann s constant is set equal to 1. Regardless of whether a move is accepted or rejected, one unit of time (one Monte Carlo step) is considered to have passed. This probabilistic acceptance criterion is known as the Metropolis Monte Carlo algorithm. Although no connection exists between physically relevant time scales and Monte Carlo time steps, Monte Carlo simulations can estimate the relative time scales of protein folding versus simulation time, as well as the time needed to reach equilibrium at a given temperature. Keep in mind, however, that any time scale extracted from a Monte Carlo simulation depends on the move set used. Even so, useful information can be extracted from such a simulation, such as relative transition times for two different sequences. 

The lattice models mentioned above were among the first to test the predictions of energy landscape theory as well as to show that many important features in protein folding could be captured by simple physical principles. In other studies, lattice models have been extended to include side-chain elements,side-chain-only models, and diamond, body-centered cubic (bcc) and face-centered cubic (fee) lattices. These models, while maintaining their simplicity and computational tractability, are much more realistic than those discussed above, and will likely provide further insight into the interactions that drive protein folding. For an excellent review on reduced protein models, we refer the reader to Kolinski and Skolnick and the extensive references therein.  

Off-lattice minimalist models are similar to the lattice models in that they generally use a simplified amino acid representation. Rather than being confined to a lattice, the protein is free to move in continuous space. As with lattice models, many different off-lattice models have been studied. Some are meant to be reduced models of specific proteins,whereas others are meant to capture a specific secondary structure motif, such as an a-helix, a p-sheet, or an a-p sandwich (see citations in Ref. 81). As before, we will focus on a few representative models and provide appropriate references about the others. 

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This work reports our eff ort to develop a coarse-grained protein model that can be used to smdy protein-protein interactions in multi-protein systems via DMD simulations. We deploy a two-bead-per-residue protein model one bead for the backbone and the other for the sidechain. The parameters of our protein model are obtained by coarse-graining atomistic simulation results for backbone-backbone, backbone-sidechain, and sidechain-sidechain interactions in explicit water. The rest of the paper is organized as follows. Section 2 describes the protein model in detail Sect. 3 describes the atomistic and DMD simulations Sect. 4 discusses the analysis leading to the final choice of model parameters and Sect. 5 summarizes the current status of the model. 

Fig. 6.31 Normalised intermediate scattering function from C-phycocyanin (CPC) obtained by spin-echo [335] compared to a full MD simulation (solid line) exhibiting a good quantitative matching. In contrast the MD results from simplified treatments as from protein without solvent (long dash-short dash /me), with point-like residues (Cpt-atoms) (dashed line) or coarse grained harmonic model (dash-dotted line) show similar slopes but deviate in particular in terms of the amplitude of initial decay. The latter deviation are (partly) explained by the employed technique of Fourier transformation. (Reprinted with permission from [348]. Copyright 2002 Elsevier)...

The fastest proteins fold amazingly quickly some as fast as a millionth of a second. While this time is very fast on a person s timescale, it is remarkably long for computers to simulate. In fact, there is about a 1000-fold gap between the simulation timescales and the times at which the fastest proteins fold. This is why the simulation of collapse kinetics is extremely computationally demanding. Thus, the current challenge lies in understanding how particular chemical sequences in coarse-grained copolymer models lead to particular collapse features. This is a fundamental issue in the problem. 

We use a coarse-grained, off-lattice three-color, 46-bead protein model [29,56,57] as an illustrative vehicle of multibasin transitions [41]. This model is composed of hydrophilic (L), hydrophobic (B), and neutral (N) beads, interacting with the following potential ... 

Protein models can be classified broadly into two types all-atom if they describe every atom in the protein explicitly and coarse-grained if they group several atoms into one interactive site. All-atom force fields such as CHARMM [4], AMBER [5],... 

Electrostatic Interactions between RNA and Protein Capsid in Cowpea Chlorotic Mottle Virus Simulated by a Coarse-grain RNA Model and Monte Carlo Approach. 

A step closer toward realism is taken by off-lattice models in which the backbone is specified in some detail, while side chains, if they are represented at all, are taken to be single, unified spheres [44-50]. One indication that this approach is too simplistic was given in [51], which proved that for a backbone representation in which only Ca carbons were modeled, no contact potential could stabilize the native conformation of a single protein against its nonnative ( decoy ) conformations. However, Irback and co-workers were able to fold real protein sequences, albeit short ones, using a detailed backbone representation, with coarse-grained side chains modeled as spheres [49, 52-54]. 

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