Karplus calculations

A. Warshel and M. Karplus, Calculation of ground and excited state potential surfaces of conjugated molecules. I. Formulation and parametrization, J. Am. Chem. Soc., 94 (1972) 5612-5625. 

Bernhard R. Brooks, Robert E. Bruccoleri, Barry D. Olafson, David J. States, S. Swaminathan, and Martin Karplus. CHARMM A program for macro-molecular energy, minimization, and dynamics calculations. J. Comp. Chem., 4(2) 187-217, 1983. 

Bashford, D., Karplus, M. Multiple-site titration curves of proteins an analysis of exact and approximate methods for their calculation. J. Phys. Chem. 95 (1991) 9556-9561. 

J G 1994. Extended Electron Distributions Applied to the Molecular Mechanics of Some termolecular Interactions. Journal of Computer-Aided Molecular Design 8 653-668. el A and M Karplus 1972. Calculation of Ground and Excited State Potential Surfaces of anjugated Molecules. 1. Formulation and Parameterisation. Journal of the American Chemical Society 1 5612-5622. 

Most potential energy surfaces are extremely complex. Fiber and Karplus analyzed a 300 psec molecular dynamics trajectory of the protein myoglobin. They estimate that 2000 thermally accessible minima exist near the native protein structure. The total number of conformations is even larger. Dill derived a formula to calculate the upper bound of thermally accessible conformations in a protein. Using this formula, a protein of 150 residues (the approx-... 

MJ Field, M Karplus. CRYSTAL Program for Crystal Calculations in CHARMM. Cambridge, MA Harvard University, 1992. 

BR Brooks, RE Bmccoleri, BD Olafson, DJ States, S Swammathan, M Karplus. CFIARMM A program for macromolecular energy, minimization, and dynamics calculations. I Comput Chem 4 187-217, 1983. 

T Lazaridis, G Archontis, M Karplus. Enthalpic contribution to protein stability Atom-based calculations and statistical mechanics. Adv Protein Chem 47 231-306, 1995. 

Similar calculations have been applied to the 3-substituted thietane dioxide series (i.e. 188(1 -3))198, assuming that only the constant C in the Karplus equation should be significantly affected by the substituents and by the oxidation state of sulfur. The results thus obtained were in poor agreement with X-ray data. 

It is difficult to decide whether the discrepancy between the calculated and experimental data is due to a different conformational preference of the thietane dioxides in the liquid and the solid phase, or to the crude approximations included in the Karplus-Barfield equation. However, the relationship between vicinal coupling constants and dihedral angles appears qualitatively valid in thietane oxides and dioxides, particularly if trends instead of exact values are discussed . At any rate thietane dioxides, 1,3-dithietane dioxides and tetroxides maintain either planarity or a slightly distorted average vibrating conformation with a low barrier to ring planarity . 

Raimondi, M., Campion, W. and Karplus, M. (1977) Convergence of the valence bond calculations... 

Brooks R, Bruccoleri RE, Olafson BD, States DJ, Swaminathan S, Karplus M (1983) Charmm A program for macromolecular energy minimization and dynamics calculations. J Comput Chem 4 187-217. 

Lim C, Bashford D, Karplus M (1991) Absolute pKa calculations with continuum dielectric methods. JPhys Chem 95 5610-5620. 

With collection for kinetic shift, the two lowest frequencies are 30 cm"1 for both K and Na complexes. With correction for kinetic shift, the two lowest frequencies are 10 cm"1 for Na complexes and 5 cm"1 for K complexes. This set is considered to be the best. For a discussion, see Klassen et al.64 Experimental determinations based on ion-molecule equilibria, Sunner et al.94 Theoretical calculations, HF/6-31G, combined with a semiempirical correction. Roux and Karp us.,5c Theoretical calculations, HF/6-31G, combined with a semiempirical correction. Roux and Karplus.,5c Theoretical calculations, 6-31+G(2d) MP2, Jensen.93 Succinamide. 

Four years later, Christian Bartels and Martin Karplus [55] used the WHAM equations as the core of their adaptive US approach, in which the efficiency of free energy calculations was improved through refinement of the biasing potentials as the simulation progressed. Efforts to develop adaptive US techniques had, however, started even before WHAM was developed. They were pioneered by Mihaly Mezei [56], who used a self-consistent procedure to refine non-Boltzmann biases. 

Simonson, T. Archontis, G. Karplus, M., Continuum treatment of long-range interactions in free energy calculations. Application to protein-ligand binding, J. Phys. Chem. B 1997, 101, 8349-8362... 

Boresch, S. Karplus, M., The role of bonded terms in free energy simulations II. Calculation of their influence on free energy differences of solvation, J. Phys. Chem. A 1999,103, 119-136... 

Archontis, G. Simonson, T. Karplus, M., Binding free energies and free energy components from molecular dynamics and Poisson-Boltzmann calculations. Application to amino acid recognition by aspartyl-tRNA synthetase, J. Mol. Biol. 2001, 306, 307-327... 

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