Protein molecule

Protein molecules extracted from Escherichia coli ribosomes were examined by viscosity, sedimentation, and diffusion experiments for characterization with respect to molecular weight, hydration, and ellipticity. These dataf are examined in this and the following problem. Use Fig. 9.4a to estimate the axial ratio of the molecules, assuming a solvation of 0.26 g water (g protein)"V At 20°C, [r ] = 27.7 cm g" and P2 = 1.36 for aqueous solutions of this polymer. 

The forces in a protein molecule are modeled by the gradient of the potential energy V(s, x) in dependence on a vector s encoding the amino acid sequence of the molecule and a vector x containing the Cartesian coordinates of all essential atoms of a molecule. In an equilibrium state x, the forces (s, x) vanish, so x is stationary and for stability reasons we must have a local minimizer. The most stable equilibrium state of a molecule is usually the 

Therefore, modeling a protein molecule amounts to deciding on the atoms considered to be essential and to specifying the contribution of the various interactions to the potential. Since the work to find the global minimizer increases drastically (and possibly exponentially) with the dimension of x, it is customary to use for larger proteins a reduced description that treats only very few atoms in each amino acid as essential. 

Eample For protein molecules with motions occurring at a frequency of about 1 cm the vibrational period is about 30 ps. Clearly, simulations of hundreds of picoseconds are necessary to probe adequately the motions of this system. 

Hydrogen bonding stabilizes some protein molecules in helical forms, and disulfide cross-links stabilize some protein molecules in globular forms. We shall consider helical structures in Sec. 1.11 and shall learn more about ellipsoidal globular proteins in the chapters concerned with the solution properties of polymers, especially Chap. 9. Both secondary and tertiary levels of structure are also influenced by the distribution of polar and nonpolar amino acid molecules relative to the aqueous environment of the protein molecules. Nonpolar amino acids are designated in Table 1.3. 

Binding of Water in Cavities Inside Protein Molecules 

It is conventional to speak of three levels of structure in protein molecules  

Kondo A, Oku S and FllgashItanI K 1991 Structural changes In protein molecules adsorbed on ultrafine silica particles J. Colloid Interfaoe Sc/. 143 214-21 

Ermolina I V, Fedotov V D and Feldman Yu D 1998 Structure and dynamic behaviour of protein molecules in solution Physioa A 249 347-52 

Figure 1.10 Helical conformations in polymer molecules, (a) A vinyl polymer with R substituents has three repeat units per turn, (b) The a helix of the protein molecule is stabilized by hydrogen bonding. [From R. B. Corey and L. Pauling,/ end. Inst. Lombardo Sci. 89 10 (1955).]

Figure 9.4b shows a theoretical f/fQ contour for a value of this ratio equal to 1.45. As noted in the discussion of this figure in Sec. 9.3, the intersection of the f/fQ and [77] contours permits the state of solvation and ellipticity of such a protein molecule to be characterized uniquely. 

In favourable contrast to molecular dynamics, BD allows molecular movements of realistically long duration to be simulated. Nevertheless, the practical number of protein molecules which can be simulated is only two since collective phenomena are often of crucial importance in detennining the course of interaction events, other simulation teclmiques, such as cellular automata [115], need to be used to capture the behaviour of large numbers of particles. 

Rigid, unsolvated spheres. Stokes law, Eq. (9.5), provides a relationship between f and the radius of the particle. Since this structure is a reasonable model for some protein molecules, experimental D values can be interpreted, via f, to yield values of R for such systems. Note that this application can also yield a value for M, since M = N pj [(4/3)ttR ], where pj is the density of the unsolvated material. 

The method described here becomes less suitable as the size of the ligand molecule increases. The problem of computing the cratic term for formation of complexes of two protein molecules have been discussed by others [34] [35]. 

Hydroxylated amino acids (eg, 4-hydroxyproline, 5-hydroxylysine) and A/-methylated amino acids (eg, /V-methylhistidine) are obtained by the acid hydrolysis of proteins. y-Carboxyglutamic acid occurs as a component of some sections of protein molecules it decarboxylates spontaneously to L-glutamate at low pH. These examples are formed upon the nontranslational modification of protein and are often called secondary protein amino acids 

Neural networks have been applied to IR spectrum interpreting systems in many variations and applications. Anand [108] introduced a neural network approach to analyze the presence of amino acids in protein molecules with a reliability of nearly 90%. Robb and Munk [109] used a linear neural network model for interpreting IR spectra for routine analysis purposes, with a similar performance. Ehrentreich et al. [110] used a counterpropagation network based on a strategy of Novic and Zupan [111] to model the correlation of structures and IR spectra. Penchev and co-workers [112] compared three types of spectral features derived from IR peak tables for their ability to be used in automatic classification of IR spectra. 

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