Statistical potentials

Unfortunately, the approach of determining empirical potentials from equilibrium data is intrinsically limited, even if we assume complete knowledge of all equilibrium geometries and their energies. It is obvious that statistical potentials cannot define an energy scale, since multiplication of a potential by a positive, constant factor does not alter its global minimizers. But for the purpose of tertiary structure prediction by global optimization, this does not not matter. 

A. Ben-Naim, Statistical potentials extracted from protein structures Are these meaningful potentials J. Chem Phys. 107 (1997), 3698-3706. 

S. Sun, Reduced representation model of protein structure prediction statistical potential and genetic algorithms. Protein Sci. 2 (1993), 762-785. 

S. Sun, Reduced representation approach to protein tertiary structure prediction statistical potential and simulated annealing, J. Theor. Biol. 172 (1995), 13-32. 

P.D. Thomas and K.A. Dill, Statistical potentials extracted from protein structures How accurate are they J. Mol. Biol. 257 (1996), 457-469. 

The molecules in cmde oil include several basic stmctural types (Table 1, Fig. 1). Because they may contain from 1 to 100+ carbon atoms and may occur in combination, the statistical potential for isomeric stmctures is staggering. For example, whereas there are just 75 possible paraffinic stmctures for C q, there are >10 isomers for C2Q. A few stmctures tend to dominate the distributions of each isomer group, however. 

Another group of methods for testing 3D models that implicitly take into account many of the criteria listed above involve 3D profiles and statistical potentials [87,216]. These methods evaluate the environment of each residue in a model with respect to the expected environment as found in the high resolution X-ray structures. Programs implementing this approach include VERIFY3D [216], PROSA [217], HARMONY [218], and ANOLEA [120]. 

Melo F, Sanchez R, Sali A. 2002. Statistical potentials for fold assessment. Protein Sci 11(2) 430-448. 

Gohlke, H. and Klebe, G. Statistical potentials and scoring functions applied to protein-ligand binding. Curr. Opin. Strua. Bid. 2001, 11, 231-235. 

A domain wall under an external electric field moves in a statistical potential generated by their interaction with the lattice, point defects, dislocations, and neighboring walls. Reversible movement of the wall is regarded as a small displacement around a local minimum. When the driven field is high enough, irreversible jumps above the potential barrier into a neighboring local minimum occur (see Figure 1.23). 

In case of proteins, one of the most decisive facts was also the availability of the Protein Data Bank, a result of many-year extensive work of X-ray and NMR worldwide communities. Only thanks to the Protein Data Bank, it was possible to acquire gradually the necessary knowledge about what are and what decides the secondary structures, and to create the statistical potentials useful in such procedure as REFINER. The statistical potentials were able to compensate for our current lack of physical/chemical understanding of many-body interactions. Without a similar data base (in other domains of chemistry), it is difficult to imagine a proper calibration of theoretical tools. 

A. Ben-Naim,/. Chem. Phys., 107, 3698 (1997). Statistical Potentials Extracted from Protein... 

A useful extension of this method consists in assuming that the membrane acquires a Boltzmann-like distribution of type (B.5) even for an arbitrary, nonharmonic potential /( ), which has a minimum at u = 0 [24,25]. When an external pressure Peat is applied to the undulating membrane, the relevant statistical potential is the enthalpy hill) = /(ii) + pextu and the membrane distribution is provided by ... 

H. Gohlke and G. Klebe, Curr. Opin. Struct. Biol., 11, 231 (2001). Statistical Potentials and... 

Despite these limitations, statistical potentials provide a simple and effective alternative method to derive the interaction free energy from the structural information for complicated protein systems. In the past decades, the method has been significantly developed and used with considerable success in the fields of protein structure prediction, protein-protein interactions, and protein-ligand interactions [46]. 

Mooij, W.T., Verdonk, M.L. General and targeted statistical potentials for protein-ligand interactions. Proteins 2005, 61, 272-87. 

Samudrala and Moult described a method for handling context sensitivity of protein structure prediction, that is, simultaneous loop and side-chain modeling, using a graph theory method [198, 209] and an all-atom distance-dependent statistical potential energy function [199]. Their program RAMP is listed in Table 5.6. 

Thomas, P. D. Dill, K. A. (1996). Statistical potentials extracted from protein structures how accurate are they ... 

Lu, H., L. Lu, and J. Skolnick. 2003. Development of unified statistical potentials describing protein-protein interactions. Biophys J 84 1895-1901. 

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... 

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