Other Potential Functions

A number of empirical potential functions have been suggested that can be fitted to various molecular interactions as well as to various solids. These will be reviewed in this section. 

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The spectrum of pleiotropic functions of different HI variants in different taxa has yet to be established. With respect to interactions within chromatin, the elucidation of the role of linker histones in transmitting or enhancing the effects of other non-histone proteins will be of particular interest. Given the dynamic behavior of HI in the nucleus, the possibility of auxiliary extrachromosomal functions performed by the free HI pool should be explored. An example of such a function is the recent finding that free HI is involved in the import of adenovirus DNA into the nucleus [158]. Other potential functions, especially at the period of maximum chromatin condensation, could depend on the gradient of free HI around the chromosomes. 

Other potential functions differ in the way the potential is partitioned into various contributions representing intra and intermolecular interactions. Cornell and collaborators 300 proposed an approach to determine the force field parameters based as much as possible on ab initio calculations. In this work each biomolecular system is divided into small residua, for which geometry optimization can be performed by an ab initio method. Ab initio calculations give partial atomic charges on atoms and the equilibrium geometry, i.e. the equilibrium values for the bond lengths, and planar and dihedral angles. 

The Rosato et al copper potential [33,34], combined with the constant-temperature/constant-pressure and periodic boundary capabilities in CHARMM, provides a good description of the properties of copper at 300 K and at 1000 K. This methodology, in conjunction with other potential functions relevant to metal-metal interactions, should prove satisfactory for the simulation of alloys. 

There exist several linkages of the SBUs which should be avoided, for example, the short separation of two metal atoms (M Mj), one ligand atom and one bridging atom (Lj Bj), and L Mj in SBUs unlinked. To prevent these undesirable linkages, other potential functions have to be considered, including the repulsive potential between Mj Mj pairs, the attractive potential between L, - - - Mj pairs, and the repulsive potential between Lj Bj pairs. A repulsive potential between Mr Mj pairs prevents SBUs from overlapping with each other. The distance between the Mr Mj pair is limited to 3.4 A for D4R. The Lennard-Jones potential parameters used in assembling the D4R are provided in Table 7.2. 

In addition to the E2F proteins, a number of other signaling proteins have been reported to interact with pRb, and it is assumed that pRb is also involved in processes other than the Gx/S control. However, these other potential functions of pRb are not well defined. The MDM2 protein has been identified as a further control element that... 

The (two-dimensional) model for a relatively stiff molecule subjected to a simple shear flow, on the one hand, shows many features observed in NEMD simulations of finitely extendible nonlinear elastic (FENE) chain molecules. On the other hand, the dynamics found for the simple model is intriguingly complex and it deserved a careful study on its own. It seems appropriate also to analyse the system at higher temperatures. Furthermore, the model provides a convenient test bed for various thermostats other and additional thermostats, e.g. based on deterministic scattering [22] should be tested. Obvious extensions of the present model may involve other potential functions of nonlinear elastic type such as = (1/2) -I- (1/4) or = (1/4) (1 — r ) as well as... 

A monolayer can be regarded as a special case in which the potential is a square well however, the potential well may take other forms. Of particular interest now is the case of multilayer adsorption, and a reasonable assumption is that the principal interaction between the solid and the adsorbate is of the dispersion type, so that for a plane solid surface the potential should decrease with the inverse cube of the distance (see Section VI-3A). To avoid having an infinite potential at the surface, the potential function may be written... 

Clearly, it is more desirable somehow to obtain detailed structural information on multilayer films so as perhaps to settle the problem of how properly to construct the potential function. Some attempts have been made to develop statistical mechanical other theoretical treatments of condensed layers in a potential field success has been reasonable (see Refs. 142, 143). 

This situation, despite the fact that reliability is increasing, is very undesirable. A considerable effort will be needed to revise the shape of the potential functions such that transferability is greatly enhanced and the number of atom types can be reduced. After all, there is only one type of carbon it has mass 12 and charge 6 and that is all that matters. What is obviously most needed is to incorporate essential many-body interactions in a proper way. In all present non-polarisable force fields many-body interactions are incorporated in an average way into pair-additive terms. In general, errors in one term are compensated by parameter adjustments in other terms, and the resulting force field is only valid for a limited range of environments. 

While this is disappointing, the nonuniqueness theorem also shows that if some empirical potential is able to predict correct protein folds then many other empirical potentials will do so, too. Thus, the construction of empirical potentials for fold prediction is much less constrained than one might think initially, and one is justified in using additional qualitative theoretical assumptions in the derivation of an appropriate empirical potential function. 

Ithough knowledge-based potentials are most popular, it is also possible to use other types potential function. Some of these are more firmly rooted in the fundamental physics of iteratomic interactions whereas others do not necessarily have any physical interpretation all but are able to discriminate the correct fold from decoy structures. These decoy ructures are generated so as to satisfy the basic principles of protein structure such as a ose-packed, hydrophobic core [Park and Levitt 1996]. The fold library is also clearly nportant in threading. For practical purposes the library should obviously not be too irge, but it should be as representative of the different protein folds as possible. To erive a fold database one would typically first use a relatively fast sequence comparison lethod in conjunction with cluster analysis to identify families of homologues, which are ssumed to have the same fold. A sequence identity threshold of about 30% is commonly... 

The potential of mean force is a useful analytical tool that results in an effective potential that reflects the average effect of all the other degrees of freedom on the dynamic variable of interest. Equation (2) indicates that given a potential function it is possible to calculate the probabihty for all states of the system (the Boltzmann relationship). The potential of mean force procedure works in the reverse direction. Given an observed distribution of values (from the trajectory), the corresponding effective potential function can be derived. The first step in this procedure is to organize the observed values of the dynamic variable, A, into a distribution function p(A). From this distribution the effective potential or potential of mean force, W(A), is calculated from the Boltzmann relation ... 

Eq. (1) would correspond to a constant energy, constant volume, or micro-canonical simulation scheme. There are various approaches to extend this to a canonical (constant temperature), or other thermodynamic ensembles. (A discussion of these approaches is beyond the scope of the present review.) However, in order to perform such a simulation there are several difficulties to overcome. First, the interactions have to be determined properly, which means that one needs a potential function which describes the system correctly. Second, one needs good initial conditions for the velocities and the positions of the individual particles since, as shown in Sec. II, simulations on this detailed level can only cover a fairly short period of time. Moreover, the overall conformation of the system should be in equilibrium. 

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