Conformational equilibria free energy

Conformational Equilibria (Free Energy Differences, AG°/kcal mol ) of Disubstituted Oxanes... 

The equilibrium free energy difference between XX and XXI is assumed to be quite small because the energy difference values between the equatorial and axial conformers for the methyl (AG = 6.3-7.9 kJ/mol) and the two methoxy (AG = 2.1-2.9 kJ/mol) substituents of the cyclohexane ring are almost equal645. 

AMBER/OPLS united atom force field ° °" and with an implicit GB/SA solvent model.The SDE method does not yield equilibrium-free energy surfaces for folding. It does, however, allow for a study of the direct sequence of events connecting an unfolded conformation to the folded state. 

Although F inthe variational theory is the same as in SCFT (cf Eq. (6.128)), other contributions involving the free ions, the chain entropy, and so on (that means Ff) differ significantly in terms of computational details. In SCFT, Ff is computed after solving for fields experienced by different components in the system, which arise as a result of interactions of a particular component with the others. On the other hand, in variational calculations [1], a single polyelectrolyte chain, whose monomers interact with the excluded volume and the electrostatic interactions in the presence of the small ions is approximated by an effective Gaussian chain, whose conformational statistics depend on the different kinds of interactions in the system. To compute the equilibrium free energy, its variational ansatz is minimized with respect to the... 

We have previously calculated conformational free energy differences for a well-suited model system, the catalytic subunit of cAMP-dependent protein kinase (cAPK), which is the best characterized member of the protein kinase family. It has been crystallized in three different conformations and our main focus was on how ligand binding shifts the equilibrium among these ([Helms and McCammon 1997]). As an example using state-of-the-art computational techniques, we summarize the main conclusions of this study and discuss a variety of methods that may be used to extend this study into the dynamic regime of protein domain motion. 

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... 

The free energy differences obtained from our constrained simulations refer to strictly specified states, defined by single points in the 14-dimensional dihedral space. Standard concepts of a molecular conformation include some region, or volume in that space, explored by thermal fluctuations around a transient equilibrium structure. To obtain the free energy differences between conformers of the unconstrained peptide, a correction for the thermodynamic state is needed. The volume of explored conformational space may be estimated from the covariance matrix of the coordinates of interest, = ((Ci [13, lOj. For each of the four selected conform-... 

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. 

When two conformations of a molecule are m equilibrium with each other the one with the lower free energy predominates Why is equatorial methylcyclohexane more sta ble than axial methylcyclohexane ... 

A prototype of such phenomena can be seen in even the simplest carboxylic acid, acetic acid (CH3CHOOH). Acidity is determined by the energy or free energy difference between the dissociated and nondissociated forms, whose energetics usually depend significantly on their conformation, e.g., the syn/anti conformational change of the carboxyl-ate group in the compound substantially affects the acid-base equilibrium. The coupled conformation and solvent effects on acidity is treated in Ref. 20. 

The free-energy difference between conformers is referred to as the conformational free energy. For substituted cyclohexanes, it is conventional to specify the value of — AC ° for the equilibrium... 

Polypeptide chains exist in an equilibrium between different conformations as a function of environment (solvent, other solutes, pH) and thermodynamic (temperature, pressure) conditions. If a polypeptide adopts a structurally ordered, stable conformation, one speaks of an equilibrium between a folded state, represented by the structured, densely populated conformer, and an unfolded state, represented by diverse, sparsely populated conformers. Although this equilibrium exists for polypeptide chains of any size, its thermodynamics and kinetics are typically different for oligopeptides and proteins. This can be broadly explained with reference to the different dimensionalities of the free-energy hypersurfaces of these two types of molecules. 

Conformational Equilibria. The solvent effect on the conformational equilibria represents a typical problem studied using the DFT/SCRF methods. The presence of the environment may affect the free energy of a given conformer, its equilibrium conformation or even destabilize a particular conformation. The DFT/SCRF calculations have been applied to study such effects using various KS methods as well as different techniques for calculating [Pg.112]

The study of receptor-ligand binding is one of the most important applications of free energy simulations [1]. To approach this problem theoretically, one must first partition the conformational space into bound and unbound states. There is no unique way to do this, but in practical situations there is often a natural choice. The equilibrium binding constant is... 

The function U fXj is called the PMF it was first introduced by Kirkwood to describe the structure of liquids [61]. It plays the role of a free energy surface for the solute. Notice that the dynamics of the solute on the free energy surface W(X) do not correspond to the true dynamics. Rather, an MD simulation on 1T(X) should be viewed as a method to sample conformational space and to obtain equilibrium, thermally averaged properties. 

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