Lysozyme calculations

Fig. 10.2. Isosurface representation of the 3D distribution function g(r) of water oxygen around lysozyme calculated by the 3D-RISM theory. Green surfaces or spots show the area where the distribution function is larger than 2 (left), 4 (center), and 8 (right)...

Smith, P., R. Brunne, A. Mark and W. vanGunsteren. (1993). Dielectric properties of trypsin inhibitor and lysozyme calculated from molecular dynamics simulations. Journal of Physical Chemistry. 97 2009-2014. 

Takahashi, T., Nakamura, H., Wada, A. Electrostatic forces in two lysozymes Calculations and measurements of histidine pKa values. Biopolymers 1992,32,897-909. 

The presented algorithm was applied to 4 proteins (lysozyme, ribonuclease A, ovomucid and bovine pancreatic trypsin inhibitor) containing 51 titratable residues with experimentally known pKaS [32, 33]. Fig. 2 shows the correlation between the experimental and calculated pKaS. The linear correlation coefficient is r = 0.952 the slope of the line is A = 1.028 and the intercept is B = -0.104. This shows that the overall agreement between the experimental and predicted pKaS is good. 

Figure 3 Calculated X-ray diffuse scattering patterns from (a) a full molecular dynamics trajectory of orthorhombic hen egg white lysozyme and (b) a trajectory obtained by fitting to the full trajectory rigid-body side chains and segments of the backbone. A full description is given in Ref. 13.

At best, van der Waals interactions are weak and individually contribute 0.4 to 4.0 kj/mol of stabilization energy. ITowever, the sum of many such interactions within a macromolecule or between macromolecules can be substantial. For example, model studies of heats of sublimation show that each methylene group in a crystalline hydrocarbon accounts for 8 k[, and each C—IT group in a benzene crystal contributes 7 k[ of van der Waals energy per mole. Calculations indicate that the attractive van der Waals energy between the enzyme lysozyme and a sugar substrate that it binds is about 60 k[/mol. 

FIGURE 6.10. Comparing the energetics of the EVB configurations in solution and in the active site of lysozyme. The calculations were done by using the PDLD and related models (Refs. 6 and 7) and they represent a study of a stepwise mechanism. The energetics of a more concerted pathway (e.g., that of Fig. 6.9) is almost identical to that of the stepwise mechanism and correlated in a similar way with the electrostatic effect of the protein. 

For what is probably the earliest microscopic calculations of thermodynamic cycles in proteins see Ref. 12, that reported a PDLD study of the pKtt s of some groups in lysozyme. The use of FEP approaches for studies of proteins is more recent and early studies of catalysis and binding were reported in Refs. 11, 12, and 13 of Chapter 4. 

The discrete protonation states methods have been tested in pKa calculations for several small molecules and peptides, including succinic acid [4, 25], acetic acid [93], a heptapeptide derived from ovomucoid third domain [27], and decalysine [61], However, these methods have sofar been tested on only one protein, the hen egg lysozyme [16, 61, 71], While the method using explicit solvent for both MD and MC sampling did not give quantitative agreement with experiment due to convergence difficulty [16], the results using a GB model [71] and the mixed PB/explicit... 

Del Buono GS, Figueirido FE, Levy RM (1994) Intrinsic pKas of ionizable residues in proteins An explicit solvent calculation for lysozyme. Proteins 20 85-97. 

Dang, L. X. Merz, K. M. Kollman, P. A., Free-energy calculations on protein stability - Thr1B7-Val157 Mutation of T4 lysozyme, J. Am. Chem. Soc. 1989, 111, 8505-8508. 

Figure 1. Site energies (kcal/mole) of (GlcNAc)g bound to lysozyme. The total potential energy per site for residues A through F of (GlcNAc)g was calculated for the initial structure from X-ray and model building, E ) (A) for the average...

Normalized cross-correlations in the atomic fluctuations between substrate and lysozyme atoms were calculated from... 

Deng, Y. and Roux, B. (2006) Calculation of standard binding free energies Aromatic molecules in the T4 lysozyme L99A mutant. Journal of Chemical Theory and Computation, 2, 1255-1273. 

An anesthetic drug, Richlocaine, developed jointly by scientists from Kazakhstan and Russia, and commercially available biologically active substances bovine serum albumin, lysozyme, and catalase were used. Hydrogels of acrylamide and acrylic acid copolymer(AA-AAc),poly(N-isopropylacrylamide)(PNIPA),N-isopropylacrylamide and acrylic acid copolymer (NlPA-AAc), N-isopropylacrylamide and 2-(acrylamido)-2-propanesulfonic acid copolymer (NIPA-APSA) were synthesized. Diffusion parameters of bioactive substances into hydrogel matrices were calculated using Eq. (19.1) ... 

Fig. 2. Agreement between experimental distances of nuclei of lysozyme, from the bound Gd(III) (obtained from the sixth root of the observed nmr broadening in solution) and the distances calculated from the X-ray structure. The numbers in this and Figs. 3 and 4 refer to the residues in the sequence (see Ref. 5). 

Fig. 3. Experimental dipolar shift ratios [for Pr(III)] of lysozyme nuclei plotted against values calculated from the X-ray structure, for a defined direction of the magnetic symmetry axis (see Ref. 5).

Fig. 4. Experimentally measured ring current shifts for lysozyme resonances plotted against ring current shifts calculated from the X-ray structure. The poor agreement for these data, compared to those in Figs. 2 and 3, reflects the theoretical uncertainty in the calculated values (see Ref. 5).

Similar results obtained with lysozyme (a protein of molecular weight 14,600) in a 75% ethanol-25 % water solution are shown in Figure 5. The vertical bars indicate the repelling voltage required to stop singly charged monomers, dimers, and trimers of lysozyme traveling at the calculated beam velocity of 754 meters/sec. Sharp dropoffs are seen to... 

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