Pseudo-energy term

As described in the Introduction, it is usually possible to consider the modeling of experimental data separately from the scheme actually used to move atoms about. Ideally, the different models should be able to be used in the different minimization or dynamics schemes. Thus, the subsequent sections describe the kind of data offered by NMR and the kinds of penalty functions or pseudo-energy terms that can be used to represent them. For convenience, we use nomenclature common to force field-based approaches where one refers to a distance constraint potential Vdc r) as a function of intemudear distance. 

Rather than simply adjusting a power term, Scarsdale et al.47 noted that the pseudo-energy term was being based on a distance r, but what was measured was more directly related to r 6. With this reasoning, they used a term of the form... 

A more difficult question is the relative balance between the conventional force field and the pseudo-energy terms representing experimental data.81 If... 

When making such a decision, some considerations should be borne in mind. First, if one is using a refinement scheme that produces a known distribution of structures, then one can calculate the likely deviation that the pseudo-energy terms will permit. For example, if an MD refinement is used, structures will be able to cross barriers of about BT. Then, if one is using a quadratic form to enforce distance restraints, one could recast Eq. [9] as follows to get an idea of the violations that would be permitted for a given force constant and temperature ... 

To account for experimental constraints, in most calculations the following pseudo-energy term is added to the total energy ... 

To predict proton chemical shifts, methods had been developed using theoretically derived formulae with an empirical parametrization (see Section 4.6). Despite the relatively large scatter of the predictions when plotted versus the experimental values, it was found that the deviations were reduced when calculating the shifts from better refined structures. Proton chemical shifts were thus included as target functions into force field calculations. Kuszewski et included a harmonic pseudo-energy term into XI LOR. " The ll... 

Although the work was in the form of pseudo-equilibrium in the presence of irradiation, and did not take into account the effect of kinetics, it nevertheless gives a clear indication of an additional energy term due to irradiation. Similar studies were done by Kaufman et al. (1978) to show the magnitude of the Gibbs energy necessary to prevent [Pg.417]

Other forms for the pseudo-energy penalty term have also been investigated (61,62). In any case, pseudo-energy penalty term acts as a constraint on the overall energy of the system, which is a balance between favorable conformational energies and overall molecular alignment as measured by field-based similarity (dissimilarity). 

Near-degenerate states lead to oppositely signed terms that occur at nearly the same energy leading to a overall spectral feature that looks like an A term and is called a pseudo-A term (11). In many cases it may be that a quick SOS calculation may be sufficient to describe a pseudo-A term. We have had some success in describing the MCD spectra of furan, pyrrole, and related compounds through this approach (98). 

The rate constant for this dissociation is ki = A k exp( Ei/RT). The preexponential term (A2T) for these rate constants is one of the largest observed pseudo-Arrhenius terms. Activation energies as large as 40 kcal/mole have been measured in the ECD for fluoronitrobenzenes [5]. 

Restraints can also be incorporated into an annealed molecular dynamics protocol, performing simulations at decreasing temperatures. This approach has been used to generate protein structures consistent with NMR constraints and has recently attracted much attention for its use in solving crystal structures. In this latter application, information from the diffraction data (e.g., structure factors and phases) is incorporated as appropriate pseudo-eneigy terms in the potential energy function. 

Witmer-Witmer spin-spatial correlation rules can in principle be satisfied via pseudo-one-body energy terms. Thus, eqn (17.3) is best written as ... 

B-terms arise from field induced mixing of excited and ground states to other states with Zeeman interaction [10]. States with similar energy are prone to mix more. These transitions have absorption-band shape and are temperature independent. However, if the two mixed states are degenerate in energy, an A-term is observed. When the states are similar in energy then a derivative shaped signal is observed (pseudo A-term) [10]. 

For the determination of the unique fold of a protein it is necessary to obtain experimental information that is specific for the given molecule, e.g., from NMR experiments, and to enforce the resulting constraints by terms collected in a pseudo-energy , Enmr- As discussed above, two types of contributions for this term are normally used constraints on interatomic distances collected in Edist, and allowed ranges on torsion angles collected in Etors ... 

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