Force field empirical

Empirical Force Field Models Molecular Mechanics... 

V S, C M Kelly and C R Landis 1991. SHAPES Empirical Force-Field - New Treatment of igular Potentials and Its Application to Square-Planar Transition-Metal Complexes. Journal of American Chemical Society 113 1-12. 

Dinur U and A T Hagler 1991. New Approaches to Empirical Force Fields. In K B Lipkowitz and D B Boyd (Editors). Reviews in Computational Chemistry Volmne 2. New York, VCH Publishers, pp. 99-164. 

The most ambitious approaches to the protein folding problem attempt to solve it from firs principles (ab initio). As such, the problem is to explore the coirformational space of th molecule in order to identify the most appropriate structure. The total number of possibl conformations is invariably very large and so it is usual to try to find only the very lowes energy structure(s). Some form of empirical force field is usually used, often augmente with a solvation term (see Section 11.12). The global minimum in the energy function i assumed to correspond to the naturally occurring structure of the molecule. 

II. Ab Initio, Semi-Empirical and Empirical Force Field Methods... 

Empirical force field (EFF) is a force field designed just for modeling hydrocarbons. It uses three valence terms, no electrostatic term and five cross terms. 

Molecula.rMecha.nics. Molecular mechanics (MM), or empirical force field methods (EFF), ate so called because they are a model based on equations from Newtonian mechanics. This model assumes that atoms are hard spheres attached by networks of springs, with discrete force constants. 

Empirical energy functions can fulfill the demands required by computational studies of biochemical and biophysical systems. The mathematical equations in empirical energy functions include relatively simple terms to describe the physical interactions that dictate the structure and dynamic properties of biological molecules. In addition, empirical force fields use atomistic models, in which atoms are the smallest particles in the system rather than the electrons and nuclei used in quantum mechanics. These two simplifications allow for the computational speed required to perform the required number of energy calculations on biomolecules in their environments to be attained, and, more important, via the use of properly optimized parameters in the mathematical models the required chemical accuracy can be achieved. The use of empirical energy functions was initially applied to small organic molecules, where it was referred to as molecular mechanics [4], and more recently to biological systems [2,3]. 

B. Optimization Procedures Used in Empirical Force Fields... 

Knowledge of the approaches and target data used in the optimization of an empirical force field aids in the selection of the appropriate force field for a given study and acts... 

Table 1 Types and Sources of Target Data Used m the Optimization of Empirical Force Field Parameters...

Tliroughout this chapter and in Table 1 the inclusion of QM results as target data is evident, with the use of such data in the optimization of empirical forces fields leading to many improvements. Use of QM data alone, however, is insufficient for the optimization of parameters for condensed phase simulations. This is due to limitations in the ability to perform QM calculations at an adequate level combined with limitations in empirical force fields. As discussed above, QM data are insufficient for the treatment of dispersion... 

The only problem with the foregoing approach to molecular interactions is that the accurate solution of Schrddinger s equation is possible only for very small systems, due to the limitations in current algorithms and computer power. Eor systems of biological interest, molecular interactions must be approximated by the use of empirical force fields made up of parametrized tenns, most of which bear no recognizable relation to Coulomb s law. Nonetheless the force fields in use today all include tenns describing electrostatic interactions. This is due at least in part to the following facts. 

Since empirical force fields do not accurately estimate the true interatomic forces, it is difficult a priori to say how accurate the fast multipole approximation to the exact Coulomb potential and forces (exact in terms of the sum over partial charges) should be. Probably a good rule is to make sure that at each atom the approximate electrostatic force is within a few percent relative error of the true electrostatic force, obtained by explicitly summing over all atom pairs, i.e., IF — FJ < 0.05 F , for all atoms i, where F is the... 

Central to the quality of any computational smdy is the mathematical model used to relate the structure of a system to its energy. General details of the empirical force fields used in the study of biologically relevant molecules are covered in Chapter 2, and only particular information relevant to nucleic acids is discussed in this chapter. 

A more practical approach for larger systems is molecular dynamics. In this method, the properties of bonds are determined through a combination of quantum-mechanical simulation and physical experiments, and stored in a database called a (semi-empirical) force field. Then a classical (non-quantum) simulation is done where bonds are modeled as spring-like interactions. Molecular... 

Eksterowicz J. E., Houk K. N. Transition-State Modeling With Empirical Force Fields Chem. Rev. (Washington, D. C.) 1993 93 2439-2461... 

It is dangerous to draw too many conclusions from the numerical results of molecular mechanics calculations. In this case, we wanted only to show that the two likely conformations for the E and G-rings of PbTX-1 are roughly equal in energy and that it is plausible that they could both exist in solution at room temperature. It would be very useful to be able to estimate the energy of activation required for the conversions between conformations. Unfortunately, estimation of the energy barrier is beyond the realm of the empirical force field method for all but the simplest cases. 

In the ONIOM(QM MM) scheme as described in Section 2.2, the protein is divided into two subsystems. The QM region (or model system ) contains the active-site selection and is treated by quantum mechanics (here most commonly the density functional B3LYP [31-34]). The MM region (referred to as the real system ) is treated with an empirical force field (here most commonly Amber 96 [35]). The real system contains the surrounding protein (or selected parts of it) and some solvent molecules. To analyze the effects of the protein on the catalytic reactions, we have in general compared the results from ONIOM QM MM models with active-site QM-only calculations. Such comparisons make it possible to isolate catalytic effects originating from e.g. the metal center itself from effects of the surrounding protein matrix. 

Keywords Empirical force field, Electronic polarization, Polarizability, Force field, Inducible dipoles,... 

Mackerell AD (2004) Empirical force fields for biological macromolecules Overview and issues. J Comput Chem 25(13) 1584-1604... 

Anisimov VM, Vorobyov IV, Roux B, MacKerell AD (2007) Polarizable empirical force field for the primary and secondary alcohol series based on the classical drude model. J Chem Theory Comput 3(6) 1927-1946... 

Lopes PEM, Lamoureux G, MacKerell AD, Polarizable Empirical Force Field for Nitrogen-containing Heteroaromatic Compounds Based on the Classical Drude Oscillator. Accepted for publication on J Comput Chem... 

Foloppe N, MacKerell AD (2000) All-atom empirical force field for nucleic acids I. Parameter optimization based on small molecule and condensed phase macromolecular target data. J Comput Chem 21 (2) 86-104... 

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