Conformer constants

Figure 4.11 (a) The folded or bent conformation of cyclobutane, (b) The bent or envelop form of cyclopentane. In this structure the front carbon atom is bent upward. In actuality, the molecule is flexible and shifts conformations constantly... 

On comparing the curves with similar values for constants Ks and Kt and moderate interactions between B conformations, that is, ifaB = to, it can be seen that the steepness of the curve increases as the total number of subunit interactions increases, that is, linear < square < tetrahedral. Moreover, the midpoint of the JVs-log[S] curve shifts to lower S concentrations, that is, for the same binding and conformation constants, less ligand concentration is required for the half-saturation of enz5mie or a protein. Although the different geometries give different saturation curves if the same intrinsic constants are chosen, the curves stiU can be made to coincide closely by the proper selection of the various equihbrium constants. 

Grubmiiller described a method to induce conformational transitions in proteins and derived rate constants for these ([Grubmiiller 1994]). The method employs subsequent modifications of the original potential function based on a principal component analysis of a short MD simulation. It is discussed in more detail in the chapter of Eichinger et al. in this volume. 

The first term represents the forces due to the electrostatic field, the second describes forces that occur at the boundary between solute and solvent regime due to the change of dielectric constant, and the third term describes ionic forces due to the tendency of the ions in solution to move into regions of lower dielectric. Applications of the so-called PBSD method on small model systems and for the interaction of a stretch of DNA with a protein model have been discussed recently ([Elcock et al. 1997]). This simulation technique guarantees equilibrated solvent at each state of the simulation and may therefore avoid some of the problems mentioned in the previous section. Due to the smaller number of particles, the method may also speed up simulations potentially. Still, to be able to simulate long time scale protein motion, the method might ideally be combined with non-equilibrium techniques to enforce conformational transitions. 

The hydration shell is formed with the increasing of the water content of the sample and the NA transforms from the unordered to A- and then to B form, in the case of DNA and DNA-like polynucleotides and salt concentrations similar to in vivo conditions. The reverse process, dehydration of NA, results in the reverse conformational transitions but they take place at the values of relative humidity (r.h.) less than the forward direction [12]. Thus, there is a conformational hysteresis over the hydration-dehydration loop. The adsorption isotherms of the NAs, i.e. the plots of the number of the adsorbed water molecules versus the r.h. of the sample at constant temperature, also demonstrate the hysteresis phenomena [13]. The hysteresis is i( producible and its value does not decrease for at least a week. 

We consider a finite space, which contains the NA sample and is in contact with a bath of water or water vapor. That allows one to maintain the r.h. in the experimental space at a constant level and change it when necessary. Such a scheme corresponds to the real experiments with wet NA samples. A NA molecule is simulated by a sequence of units of the same type. Thus, in the present study, we consider the case of a homogeneous NA or the case where averaging over the unit type is possible. Every unit can be found in the one of three conformational states unordered. A- or B- conformations. The units can reversibly change their conformational state. A unit corresponds to a nucleotide of a real NA. We assume that the NA strands do not diverge during conformational transitions in the wet NA samples [18]. The conformational transitions are considered as cooperative processes that are caused by the unfavorable appearance of an interface between the distinct conformations. 

However, the B.E.T. and modificated B.E.T as well as isotherm of d Arcy and Watt fit the experimental data only in some range of the relative humidities up to about 80-85%. At the same time the adsorption in the interval 90-100% is of great interest for in this interval the A— B conformational transition, which is of biological importance, takes place [17], [18]. This disagreement can be the result of the fact that the adsorbed water molecules can form a regular lattice, structure of which depends on the conformation of the NA. To take into account this fact we assume that the water binding constants depend on the conformational variables of the model, i.e ... 

Conformational free energy simulations are being widely used in modeling of complex molecular systems [1]. Recent examples of applications include study of torsions in n-butane [2] and peptide sidechains [3, 4], as well as aggregation of methane [5] and a helix bundle protein in water [6]. Calculating free energy differences between molecular states is valuable because they are observable thermodynamic quantities, related to equilibrium constants and... 

Tree representation of the conformation search problem for hexane. Unlike the tree in Figure 9.4 the path gth from the root node to any of the terminal nodes is constant. 

Ihe allure of methods for calculating free energies and their associated thermod)mai values such as equilibrium constants has resulted in considerable interest in free ene calculations. A number of decisions must be made about the way that the calculatior performed. One obvious choice concerns the simulation method. In principle, eit Monte Carlo or molecular dynamics can be used in practice, molecular dynamics almost always used for systems where there is a significant degree of conformatio flexibility, whereas Monte Carlo can give very good results for small molecules which either rigid or have limited conformational freedom. 

Coupling constants (]) are a weighted average of various conformations. 

The furanose rings of the deoxyribose units of DNA are conformationally labile. All flexible forms of cyclopentane and related rings are of nearly constant strain and pseudorotations take place by a fast wave-like motion around the ring The flexibility of the furanose rings (M, Levitt, 1978) is presumably responsible for the partial unraveling of the DNA double helix in biological processes. 

The log(k/ko) value for 4-isopropyl-2,5-dimethylthiazole is twice that expected if the curve were linear, which implies a rate constant 6.5 times smaller than expected. This result can be explained by the existence of a privileged conformation, induced by the presence of the methyl group in the 5-position and that has a lower reactivity (258). This result also leads to a limitation in the use of Tafts Eg parameter to cases where the environment of a substituent does not induce particular conformation for this latter (258). 

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