Conformation free energies

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. 

Calculation of Conformational Free Energies for a Model of a Bilobal Enzyme Protein kinases catalyze the transfer of phosphate from adenosine triphosphate (ATP) to protein substrates and are regulatory elements of most known pathways of signal transduction. 

Free Energy Function The conformational free energy was estimated by the following energy expression ... 

The ranking of conformational free energies indicated that the closed state of cAPK is favored even in the absence of ligands, which is in contrast to experimental data that showed a preferred population of the open conformation. One reason for this discrepancy could be that the modelled intermediate ... 

Fig. 2. Conformational free energy of closed, intermediate and open protein kinase conformations. cAPK indicates the unbound form of cAMP-dependent protein kinase, cAPKiATP the binary complex of cAPK with ATP, cAPKiPKP the binary complex of cAPK with the peptide inhibitor PKI(5-24), and cAPK PKI ATP the ternary complex of cAPK with ATP and PKI(5-24). Shown are averaged values for the three crystal structures lATP.pdb, ICDKA.pdb, and ICDKB.pdb. All values have been normalized with respect to the free energy of the closed conformations.

Vorobjev, Y., Almagro, J. C., Hermans, J. Conformational free energy calculated by a new iiK thod from dynamics simulation and continuum dielectric... 

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... 

Table 3. Conformational free energy simulation of linear DPDPE. Changes in free energy and its components. Units kcal/mol...

K. Kuczera. One- and multidimensional conformational free energy simulations. J. Comp. Chem., 17 1726-1749, 1996. 

Y. Wang and K. Kuczera. Exploration of conformational free energy surface of helical Ala and Aibn peptides. J. Phys. Chem. B, 101 5205-5213, 1997. 

Y. Wang and K. Kuczera. Conformational free energy surface of the linear DPDPE peptide Cost of pre-organization for disulfide bond formation. J. Am. Chem. Soc., submitted, 1997. 

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... 

TaUe 3.6. Conformational Free Energies (—AG°) for Substituent Groups ... 

Table 3.8. Comparison of Conformational Free-Energy Values for Substituents on Tetrahydropyran, 1,3-Dioxane, and 1,3-Dithiane Rings with Those for Cyclohexane...

The steric parameters for the estimation of reactant state effects were chosen to be the conformational free energy differences for cyclohexane axial-equatorial equilibria (A-values) (8). In order to establish the methyl group as the standard size group, modified A-values (A ) for the various groups were used, by simply subtracting the A value for the methyl group (1.70) from the A values of the various substituents ... 

The conformation of macro- or polyions has been defined and discussed briefly in Section 4.1.1. The conformation of a polyion is determined by a balance between contractile forces, which depend on conformation free energy, and extension forces, which arise from electrical free energy. The extent of conformational change is determined by several factors. Changes are facilitated by the degree of flexibility of the polyion, and conformational change is greatest at low concentration of polyions. 

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