Domains, free energy

The free energy of a monolayer domain in the coexistence region of a phase transition can be described as a balance between the dipolar electrostatic energy and the line tension between the two phases. Following the development of McConnell [168], a monolayer having n circular noninteracting domains of radius R has a free energy... 

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. 

Mesoscale simulations model a material as a collection of units, called beads. Each bead might represent a substructure, molecule, monomer, micelle, micro-crystalline domain, solid particle, or an arbitrary region of a fluid. Multiple beads might be connected, typically by a harmonic potential, in order to model a polymer. A simulation is then conducted in which there is an interaction potential between beads and sometimes dynamical equations of motion. This is very hard to do with extremely large molecular dynamics calculations because they would have to be very accurate to correctly reflect the small free energy differences between microstates. There are algorithms for determining an appropriate bead size from molecular dynamics and Monte Carlo simulations. 

As we have already pointed out, the theoretical basis of free energy calculations were laid a long time ago [1,4,5], but, quite understandably, had to wait for sufficient computational capabilities to be applied to molecular systems of interest to the chemist, the physicist, and the biologist. In the meantime, these calculations were the domain of analytical theories. The most useful in practice were perturbation theories of dense liquids. In the Barker-Henderson theory [13], the reference state was chosen to be a hard-sphere fluid. The subsequent Weeks-Chandler-Andersen theory [14] differed from the Barker-Henderson approach by dividing the intermolecular potential such that its unperturbed and perturbed parts were associated with repulsive and attractive forces, respectively. This division yields slower variation of the perturbation term with intermolecular separation and, consequently, faster convergence of the perturbation series than the division employed by Barker and Henderson. 

Fig. 9.1. Left panel A model zinc finger obtained using the second domain of the transcription factor IIIA. The zinc ion (gray sphere) is coordinated tetrahedrally by two histidine (H) and two cysteine (C) residues. Right panel Results showing the free energy change for displacing Zn2+ by other comparable ions Fe2+ and Co2+ from different binding motifs CCHH, CCHC, and CCCC, respectively...

Compared to US and its subsequent variants, the ABF method obviates the a priori knowledge of the free energy surface. As a result, exploration of is only driven by the self-diffusion properties of the system. It should be clearly understood, however, that while the ABF helps progression along the order parameter, the method s efficiency depends on the (possibly slow) relaxation of the collective degrees of freedom orthogonal to . This explains the considerable simulation time required to model the dimerization of the transmembrane domain of glycophorin A in a simplified membrane [54],... 

Here scalar order parameter, has the interpretation of a normalized difference between the oil and water concentrations go is the strength of surfactant and /o is the parameter describing the stability of the microemulsion and is proportional to the chemical potential of the surfactant. The constant go is solely responsible for the creation of internal surfaces in the model. The microemulsion or the lamellar phase forms only when go is negative. The function/(<))) is the bulk free energy and describes the coexistence of the pure water phase (4> = —1), pure oil phase (4> = 1), and microemulsion (< ) = 0), provided that/o = 0 (in the mean-held approximation). One can easily calculate the correlation function (4>(r)(0)) — (4>(r) (4>(0)) in various bulk homogeneous phases. In the microemulsion this function oscillates, indicating local correlations between water-rich and oil-rich domains. In the pure water or oil phases it should decay monotonically to zero. This does occur, provided that g2 > 4 /TT/o — go- Because of the < ), —<(> (oil-water) symmetry of the model, the interface between the oil-rich and water-rich domains is given by... 

Studies using free energy calculations for the design and analysis of potential drug candidates are reviewed in section five. The chapters in this section cover drug discovery programs targeting fructose 1,6-bisphosphatase (diabetes), COX-2 (inflammation), SRC SH2 domain (osteoporosis and cancer), HIV reverse transcriptase (AIDS), HIV-1 protease (AIDS), thymidylate synthase (cancer), dihydrofolate reductase (cancer) and adenosine deaminase (immunosuppression, myocardial ischemia). 

It is customary [129] to define u0 independent of T, whilst r0 = a0t. In thermodynamic equilibrium the free energy must be a minimum as a function of m and m is assumed to have the mean-field value of m = /V. By this assumption the internal field acting at each point in the domain is the same,... 

Many other interesting examples of spontaneous reflection symmetry breaking in macroscopic domains, driven by boundary conditions, have been described in LC systems. For example, it is well known that in polymer disperse LCs, where the LC sample is confined in small spherical droplets, chiral director structures are often observed, driven by minimization of surface and bulk elastic free energies.24 We have reported chiral domain structures, and indeed chiral electro-optic behavior, in cylindrical nematic domains surrounded by isotropic liquid (the molecules were achiral).25... 

The free energy of the phosphorylated histidine (P His) or cysteine (P Cys) is comparable with the free energy of PEP (AG° = — 61.5 kJ mol ). The reactions (1) to (4) are therefore fully reversible under physiological conditions, whereas reaction (5) is irreversible. The substrate when bound to the domain IIC (or IID) obtains the phosphoryl group from the unit IIB, via unit IIA, which is rephosphorylated by P HPr. Efficient translocation of carbohydrates depends on the phosphorylated IIB domain. The release of the phosphorylated substrate terminates the uptake process. 

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