Interaction center

Although the folding of short proteins has been simulated at the atomic level of detail [159,160], a simplified protein representation is often applied. Simplifications include using one or a few interaction centers per residue [161] as well as a lattice representation of a protein [162]. Some methods are hierarchical in that they begin with a simplified lattice representation and end up with an atomistic detailed molecular dynamics simulation [163]. 

Interacting centers Proteins Quantitative study Refs. 

This example shows that dipolar interactions can produce unexpected effects in systems containing polynuclear clusters, so that their complete quantitative description requires a model in which the dipolar interactions between all the paramagnetic sites of the system are explicitly taken into account. Local spin models of this kind can provide a description of the relative arrangement of the interacting centers at atomic resolution and have been worked out for systems containing [2Fe-2S] and [4Fe-4S] clusters (112, 192). In the latter case, an additional complication arises due to the delocalized character of the [Fe(III), Fe(II)] mixed-valence pair, so that the magnetic moments carried by the two sites A and B of Fig. 8B must be written... 

A modification of the united-atom approach, called the anisotropic united-atom (AUA) model was the focus of extensive work by Karabomi et al. [362-365]. As in the other models of hydrocarbon chains described so far, the AUA approach to monolayers was preceded by work on alkanes [367]. hi the AUA model the interaction site is located at the geometrical mean of the valence electrons of the atoms it represents, while the pseudoatom itself is located at the carbon atom position. The movement of each interaction center depends on the conformation of the molecule as a whole. 

Theoretical studies aimed at rationalizing the interaction between the chiral modifier and the pyruvate have been undertaken using quantum chemistry techniques, at both ab initio and semi-empirical levels, and molecular mechanics. The studies were based on the experimental observation that the quinuclidine nitrogen is the main interaction center between cinchonidine and the reactant pyruvate. This center can either act as a nucleophile or after protonation (protic solvent) as an electrophile. In a first step, NH3 and NH4 have been used as models of this reaction center, and the optimal structures and complexation energies of the pyruvate with NH3 and NHa, respectively, were calculated [40]. The pyruvate—NHa complex was found to be much more stable (by 25 kcal/mol) due to favorable electrostatic interaction, indicating that in acidic solvents the protonated cinchonidine will interact with the pyruvate. 

First, we have modified the mono-mono term (now denoted Emono-mono ) to propose a functional form mimicking the three terms present in ab initio, namely the nucleus-nucleus repulsion, the electron-nucleus attraction and the electron-electron repulsion. For two interacting centers i and j, the modified mono-mono term is ... 

Analysis of calculation results has shown profound reconstruction of links between interacting centers that occurred in the chosen model. The most significant changes are observed in the first coordination sphere of central atom. In the process of interaction of Zn(CN)42" complex with IT and OH" particles, there is a tendency to destruction of the first coordination sphere of Zn atom with subsequent forming Zn(OH)2 complex and four molecules of HCN. Further HCN degradation in water solution under plasma action is running in accordance with the pattern below ... 

In a statistical Monte Carlo simulation the pair potentials are introduced by means of analytical functions. In the election of that analytical form for the pair potential, it must be considered that when a Monte Carlo calculation is performed, the more time consuming step is the evaluation of the energy for the different configurations. Given that this calculation must be done millions of times, the chosen analytic functions must be of enough accuracy and flexibility but also they must be fastly computed. In this way it is wise to avoid exponential terms and to minimize the number of interatomic distances to be calculated at each configuration which depends on the quantity of interaction centers chosen for each molecule. A very commonly used function consists of a sum of rn terms, r being the distance between the different interaction centers, usually, situated at the nuclei. In particular, non-bonded interactions are usually represented by an atom-atom centered monopole expression (Coulomb term) plus a Lennard-Jones 6-12 term, as indicated in equation (51). 

In this expression, i and j are the interaction centers in a and p molecules, respectively, Aj and Q are adjustable parameters that describe the interaction between i and j, q and q are the charges associated with centers i and j and, finally, q is the distance between i andj. The parameters, of whom pair potentials depend on, can be fitted to reproduce theoretical results, experimental data or a combination of both. 

Molecules having two reactive centers that are noninteracting or only weakly interacting, such as the carboxylate anions in malonate or succinate, are not considered to be ambident. The term bifunctional should be used to describe these compounds. If a molecule contains more than two interacting centers, the terms polydent or multident should be used. Examples of such nucleophiles include anions derived from malonic esters, /3-keto esters, /8-diketones, as well as phenoxide ions. 

Bandyopadhyay and Yashonath (31), in an extension of their work on MD studies of noble gas diffusion, presented MD results for methane diffusion in NaY and NaCaA zeolites. The zeolite models were the same as those used in the noble gas simulations (13, 15, 17, 18, 20, 28, 29) and the zeolite lattice was held rigid. The methane molecule was approximated as a single interaction center and the guest-host potential parameters were calculated from data of Bezus et al. (49) (for the dispersive term) and by setting the force on a pair of atoms equal to zero at the sum of their van der Waals radii (for the repulsive term). Simulations were run for 600 ps with a time step of 10 fs. 

In references [10, 12], the particular case was studied of the successive electron transfers of a molecule with n identical and non-interacting centers by following an... 

By inserting Eq. (6.45) in the expression of the surface concentrations (which are analogous to that given in Eq. (6.4)), the following expression for the particular case of n non-interacting centers is found ... 

Thus, Eqs. (6.44)-(6.51) clearly demonstrate that the whole current-potential curve corresponding to a molecule with n non-interacting centers is n times that corresponding to a molecule with only one redox center for the same concentration and diffusion coefficients and in any single or multipulse electrochemical technique, independently of the electrode geometry [12],... 

This expression is sufficient in the simplified simulation of magnetic susceptibility in polynuclear coordination compounds, where the case of very weakly interacting centers occurs. A non-trivial inquire is whether the HDVV is literaly valid for strongly bonded system—the present discussion having as implicit goal the corresponding answer. 

FIGURE 5. The cr-symmetry orbitals of a long, all-trans polysilane chain showing backbone orbitals (left), orbitals of the SiH bonds (right), and the result of their mutual interaction (center). (Reprinted from Ref. 63.)... 

MMGK (Molecular mechanics with Gillespie-Kepert terms) [193] is designed for application to coordination compounds. It is based on CHARMM, but an additional term describing repulsion of some effective interaction centers placed on the coordination bonds is added. 

Considering the highly processive mechanism of the protein degradation by the proteasome, a question naturally arises what is a mechanism behind such translocation rates Let us discuss one of the possible translocation mechanisms. In [52] we assume that the proteasome has a fluctuationally driven transport mechanism and we show that such a mechanism generally results in a nonmonotonous translocation rate. Since the proteasome has a symmetric structure, three ingredients are required for fluctuationally driven translocation the anisotropy of the proteasome-protein interaction potential, thermal noise in the interaction centers, and the energy input. Under the assumption that the protein potential is asymmetric and periodic, and that the energy input is modeled with a periodic force or colored noise, one can even obtain nonmonotonous translocation rates analytically [52]. Here we... 

Analytical results are possible if we assume collective oscillations of the peptide elements, e.g., F(t) = Acos(thermal fluctuations, represented by mutually uncorrelated white noise of intensity a2 fi(t) = where = u2[Pg.379]

Figure 4 The interaction model taken from LUDI consists of an interaction center and a spherical interaction surface describing distance and angle constraints of the interaction. An interaction occurs if the interaction center of the first group is located close to the interaction surface of the second group and vice versa.

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