Computational approach

Molecular mechanics are the most broadly applicable computational techniques as they can be used on small molecules as successfully as on proteins. The speed with which large numbers of simple calculations can be undertaken on even modest computers, together with the ease with which the method can be understood by non-specialists, engenders the broadest use of this technique. 

As this method is the most commonly encountered, and is often the basis for geometries used in higher-level calculations, it is worth describing the interactions in detail. The molecular mechanics method assumes that the total energy of the system may be broken down into the following components  

The best description of a bond stretch is a Morse function but, as this is computationally expensive, a simpler harmonic function is usually used in molecular modelling. Many force fields use extra terms in the equation to improve the accuracy of the function which, at its simplest, has the form  

The contribution which the bond energy makes to the overall structure is found by summing the energy for all bonds. Ideal values (Z0) are required for all types of bonds, thus C—C, C=C and C=C bonds will need a different set of parameters to describe their behaviour. 

Angles are treated in a similar way to bonds by using a harmonic function based on  

Before presenting results there is also a need to introduce the basic construction work behind the most common computational approaches used for predicting electrolyte and additive electrochemical stabilities. We will not cover the applied computational methods per se, since there are many excellent texts on computational chemistry, but outline the basic physical and chemical considerations behind the strategies chosen, methods apphed, and models used, for the particular aim of predictions of electrolyte and additive electrochemical stability. 

As much as there are many different aims with using predictive methods - there are many different sdategies employed, with sdong correlation to the way the scientist(s) in charge endeavour in the project. We simply here outline some of our observations of the field to show the vast variation in strategies. 

One strategy is to extensively attack a single, very specific, and hopefully from an experimental point-of-view well understood, reduction, or oxidation reaction with the aim of as accurately as possible obtain a computed numerical value for f ox and/ or Etei- The most typical example would be EC reduction [10-13]. The aim is not necessarily to obtain a prediction needed for rational development of electrolytes -but perhaps more to confirm and further develop the computational/experimental correlation for certain choices of methods and models or their combinations. 

If the method and model combination from studies such as those described above subsequently are applied to a larger variety of reactions - then this strategy has been developed into a predictive one with an orientation towards electrolyte technology field impact rather than an internal scientific. A typical example would be to assess the reduction stability of a variety of electrolyte solvents [14-18]. 

Yet another strategy is to correlate computational results for a wide variation of reactions in different electrolytes with the corresponding experimental observations, either in absolute or relative values. A typical example would here be the intrinsic stability of various anions in a variety of solvents [8,19, 20]. 

1 Hagenbuch, B. and Meier, P.J. (2003) The superfamily of organic anion transporting polypeptides. Biochimica et Biophysica Acta, 1609, 1-18. 

and Wright, M.W. (2002) Guidelines for human gene nomenclature. Genomics, 79, 464-470. 

4 Mikkaichi, T, Suzuki. T. Tanemoto, M., Ito, S., and Abe. T. (2004) The organic anion transporter (OATP) family. Drug Metabohsm and Pharmacokinetics, 19, 171-179. 

5 Meier, P.J. and Stieger, B. (2002) Bile salt transporters. Annual Review of Physiology, 64, 635-661. 

6 Tamai, L, Nezu, J., Uchino, H., Sai, Y., Oku, A., Shimane, M., and Tsuji, A. (2000) Molecular identification and characterization of novel members of the human organic anion transporter (OATP) family. Biochemical and Biophysical Research Communications, 273, 251—260. 

A recent publication and corresponding response [85, 86] provide an example of the ongoing debate surrounding ion-pairing. 

In concluding this section we hope we have shown that there is a clear need for more elaborated studies to understand how lipophilic ions interact with biological membranes - an aspect that may look deceptively simple, but which is not yet completely understood. 

The interaction energy of two particles at R and R with tensor electric suscep- 

Rj ) are the Green s functions for the full field equations. By letting r = and r = 2 coupled equations for the electric fields at the two 

02(01) = 0 suffice to express the zero-point energy shift the interacting 

VAN KAMPEN et al. [5.49] proposed that the interaction forces for macroscopic media could be calculated by considering only the surface-mode solutions of Maxwell s equations at all interfaces. This method was extended [5.44,45] and is used in various applications. For the original case of two half-spaces separated by a gap d, the solutions are sought to the equations of electrostatics subject to the conditions V - D = 0 and vxE = 0 with no spacial dielectric dispersion, but with boundary conditions at the interfaces. By matching boundary conditions and requiring vanishing solutions at infinity, the dispersion relation 

A particularly lucid treatment and comparison of the surface-mode and Lifshitz approaches to the calculation of the van der Waals interaction forces was given by 

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Tuckerman M E and Hughes A 1998 Path integral molecular dynamics a computational approach to quantum statistical mechanics Classical and Quantum Dynamics In Condensed Phase Simulations ed B J Berne, G Ciccotti and D F Coker (Singapore World Scientific) pp 311-57... 

The examples of modelling discussed in section C2.5.2 and section C2.5.3 are meant to illustrate tlie ideas behind tlie tlieoretical and computational approaches to protein folding. It should be borne in mind tliat we have discussed only a very limited aspect of tlie rich field of protein folding. The computations described in section C2.5.3 can be carried out easily on a desktop computer. Such an exercise is, perhaps, tlie best of way of appreciating tlie simple approach to get at tlie principles tliat govern tlie folding of proteins. 

Wang J and Wang W 1999 A computational approach to simplifying the protein folding alphabet Natur. Struct. Biol. 6 1033-8... 

In summary, the techniques outlined in this work represent the first step on a path that will lead to increased understanding of, and more accurate computational approaches for treating, nonadiabatic processes in which relativistic effects cannot be neglected. 

In Chapter VI, Ohm and Deumens present their electron nuclear dynamics (END) time-dependent, nonadiabatic, theoretical, and computational approach to the study of molecular processes. This approach stresses the analysis of such processes in terms of dynamical, time-evolving states rather than stationary molecular states. Thus, rovibrational and scattering states are reduced to less prominent roles as is the case in most modem wavepacket treatments of molecular reaction dynamics. Unlike most theoretical methods, END also relegates electronic stationary states, potential energy surfaces, adiabatic and diabatic descriptions, and nonadiabatic coupling terms to the background in favor of a dynamic, time-evolving description of all electrons. 

The classical microscopic description of molecular processes leads to a mathematical model in terms of Hamiltonian differential equations. In principle, the discretization of such systems permits a simulation of the dynamics. However, as will be worked out below in Section 2, both forward and backward numerical analysis restrict such simulations to only short time spans and to comparatively small discretization steps. Fortunately, most questions of chemical relevance just require the computation of averages of physical observables, of stable conformations or of conformational changes. The computation of averages is usually performed on a statistical physics basis. In the subsequent Section 3 we advocate a new computational approach on the basis of the mathematical theory of dynamical systems we directly solve a... 

Y. Wang. Computational Approach to the Influence of the Distdfl.dc Bond on Peptide Properties. PhD thesis. University of Kansas, 1997. 

The first chapter, on Conformational Dynamics, includes discussion of several rather recent computational approaches to treat the dominant slow modes of molecular dynamical systems. In the first paper, SCHULTEN and his group review the new field of steered molecular dynamics (SMD), in which large external forces are applied in order to be able to study unbinding of ligands and conformation changes on time scales accessible to MD... 

Hiir.l D M 1990. A Computational Approach to Chemistry. Oxford, Blackwell Scientific. 

I. Shavitt, Advanced Theories and Computational Approaches to the Electronic Structure... 

I. Shavitt, Advanced Theories and Computational Approaches to the Electronic Structure of Molecules C. E. Dykstra, Ed., 185, Reidel, Dordrecht (1984). 

G.R. Johnson, R.A. Stryk, and M.E. Nixon, Two- and Three-Dimensional Computational Approaches for Steel Projectiles Impacting Concrete Targets, Proc. Post-SM RT Seminar on Impact, Lausanne, Switzerland, 1987. 

For reasons of space and because of their prime importance, we focus here on free energy calculations based on detailed molecular dynamics (MD) or Monte Carlo (MC) simulations. However, several other computational approaches exist to calculate free energies, including continuum dielectric models and integral equation methods [4,14]. 

R Stanton, S Dixon, K Merz Jr. In A Warshel, G Naray-Szabo, eds. Computational Approaches to Biochemical Reactivity. New York Kluwer, 1996. 

The best computational approach to the study of chemical reactions uses quantum mechanics however, in practice the size of the enzyme system precludes the use of tradi-... 

III. COMPUTATIONAL APPROACHES TO MODELING LIGAND-RECEPTOR INTERACTIONS... 

Naturally, the pivotal role of protein folding in biophysics and biochemistry has yielded a very large body of research. In this chapter we focus primarily on the different theoretical and computational approaches that have contributed to the current understand-... 

Computational studies of nucleic acids offer the possibility to enliance and extend the infonnation available from experimental work. Computational approaches can facilitate the experimental detennination of DNA and RNA structures. Dynamic information. 

RNA structures, compared to the helical motifs that dominate DNA, are quite diverse, assuming various loop conformations in addition to helical structures. This diversity allows RNA molecules to assume a wide variety of tertiary structures with many biological functions beyond the storage and propagation of the genetic code. Examples include transfer RNA, which is involved in the translation of mRNA into proteins, the RNA components of ribosomes, the translation machinery, and catalytic RNA molecules. In addition, it is now known that secondary and tertiary elements of mRNA can act to regulate the translation of its own primary sequence. Such diversity makes RNA a prime area for the study of structure-function relationships to which computational approaches can make a significant contribution. 

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. 

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