Biomolecule modeling

The IE scheme is nonconservative, with the damping both frequency and timestep dependent [42, 43]. However, IE is unconditionally stable or A-stable, i.e., the stability domain of the model problem y t) = qy t), where q is a complex number (exact solution y t) = exp(gt)), is the set of all qAt satisfying Re (qAt) < 0, or the left-half of the complex plane. The discussion of IE here is only for future reference, since the application of the scheme is faulty for biomolecules. 

The LIN method (described below) was constructed on the premise of filtering out the high-frequency motion by NM analysis and using a large-timestep implicit method to resolve the remaining motion components. This technique turned out to work when properly implemented for up to moderate timesteps (e.g., 15 Is) [73] (each timestep interval is associated with a new linearization model). However, the CPU gain for biomolecules is modest even when substantial work is expanded on sparse matrix techniques, adaptive timestep selection, and fast minimization [73]. Still, LIN can be considered a true long-timestep method. 

Optimized potentials for liquid simulation (OPES) was designed for modeling bulk liquids. It has also seen significant use in modeling the molecular dynamics of biomolecules. OPLS uses five valence terms, one of which is an electrostatic term, but no cross terms. 

YETI is a force held designed for the accurate representation of nonbonded interactions. It is most often used for modeling interactions between biomolecules and small substrate molecules. It is not designed for molecular geometry optimization so researchers often optimize the molecular geometry with some other force held, such as AMBER, then use YETI to model the docking process. Recent additions to YETI are support for metals and solvent effects. 

The modeling of biomolecules is a very broad and sophisticated field. The description given in this chapter is only meant to provide the connections between the topics in this book and this field. Before embarking on a computational biochemical study, it is recommended that the researcher investigate the literature pertaining to this field more closely. The references provided below should provide a good starting point for such a survey. 

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]. 

Here,. Ai(X) is the partial SASA of atom i (which depends on the solute configuration X), and Yi is an atomic free energy per unit area associated with atom i. We refer to those models as full SASA. Because it is so simple, this approach is widely used in computations on biomolecules [96-98]. Variations of the solvent-exposed area models are the shell model of Scheraga [99,100], the excluded-volume model of Colonna-Cesari and Sander [101,102], and the Gaussian model of Lazaridis and Karplus [103]. Full SASA models have been used for investigating the thermal denaturation of proteins [103] and to examine protein-protein association [104]. 

The first dynamical simulation of a protein based on a detailed atomic model was reported in 1977. Since then, the uses of various theoretical and computational approaches have contributed tremendously to our understanding of complex biomolecular systems such as proteins, nucleic acids, and bilayer membranes. By providing detailed information on biomolecular systems that is often experimentally inaccessible, computational approaches based on detailed atomic models can help in the current efforts to understand the relationship of the strucmre of biomolecules to their function. For that reason, they are now considered to be an integrated and essential component of research in modern biology, biochemistry, and biophysics. 

One of the most thoroughly investigated examples of polymeric biomolecules in regard to the stabilization of ordered structures by hydration are the DNAs. Only shortly after establishing the double-helix model by Watson and Crick 1953 it became clear, that the hydration shell of DNA plays an important role in stabilizing the native conformation. The data obtained by the authors working in this field up until 1977 are reviewed by Hopfinger155>. 

Schwack W (1988) Photoinduced additions of pesticides to biomolecules. 2. Model reactions of DDT and methoxychlor with methyl oleate. J Agric Eood Chem 36 645-648. 

B. Krebs and G. Henkel, Transition metal thiolates — from molecular fragments of sulfidic solids to models of active centers in biomolecules. Angew. Chem. Int. Ed. 30 (1991) 769. 

Lamoureux G, Harder E, Vorobyov IV, Roux B, MacKerell AD (2006) A polarizable model of water for molecular dynamics simulations of biomolecules. Chem Phys Lett 418(l-3) 245-249... 

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