Heavy proteins

Referring to figure Bl.8.5 the radii of the tliree circles are the magnitudes of the observed structure amplitudes of a reflection from the native protein, and of the same reflection from two heavy-atom derivatives, dl and d2- We assume that we have been able to detemiine the heavy-atom positions in the derivatives and hl and h2 are the calculated heavy-atom contributions to the structure amplitudes of the derivatives. The centres of the derivative circles are at points - hl and - h2 in the complex plane, and the three circles intersect at one point, which is therefore the complex value of The phases for as many reflections as possible can then be... 

Figure Bl.8.5. Pp Pdl and Fdl are the measured stnicture amplitudes of a reflection from a native protein and from two heavy-atom derivatives. and are the heavy atom contributions. The pomt at which the tliree circles intersect is the complex value of F. ...

In many cases the dynamical system consists of fast degrees of freedom, labeled x, and slow degrees of freedom, labeled y. An example is that of a fluid containing polyatomic molecules. The internal vibrations of the molecules are often very fast compared to their translational and orientational motions. Although this and other systems, like proteins, have already been treated using RESPA,[17, 34, 22, 23, 24, 25, 26] another example, and the one we focus on here, is that of a system of very light particles (of mass m) dissolved in a bath of very heavy particles (mass M).[14] The positions of the heavy particles are denoted y and the positions of the light particles rire denoted by X. In this case the total Liouvillian of the system is ... 

The principle of this test is as follows The liquid suspected of containing urea is treated with dilute acid or alkali until its pH is about 7. A solution of the enzyme is also made and its pH adjusted to 7. The two solutions are mixed and the resulting conversion of urea to ammonium carbonate causes the pH of the solution to rise to over 8 this change is noted by the use of a suitable indicator, phenol-red being the one usually employed. Proteins do not interfere with the test, but the reaction is inhibited by traces of heavy metals. 

In general, nonconventional protein foods must be competitive with conventional plant and animal protein sources on the bases of cost delivered to the consumer, nutritional value to humans or animals, functional value in foods, sensory quality, and social and cultural acceptability. Also, requirements of regulatory agencies in different countries for freedom from toxins or toxic residues in single-cell protein products, toxic glycosides in leaf protein products, pathogenic microorganisms, heavy metals and toxins in fish protein concentrates, or inhibitory or toxic peptide components in synthetic peptides must be met before new nonconventional food or feed protein products can be marketed. 

Because they are weak acids or bases, the iadicators may affect the pH of the sample, especially ia the case of a poorly buffered solution. Variations in the ionic strength or solvent composition, or both, also can produce large uncertainties in pH measurements, presumably caused by changes in the equihbria of the indicator species. Specific chemical reactions also may occur between solutes in the sample and the indicator species to produce appreciable pH errors. Examples of such interferences include binding of the indicator forms by proteins and colloidal substances and direct reaction with sample components, eg, oxidising agents and heavy-metal ions. 

Because of their zwitterionic nature, amino acids are generally soluble in water. Their solubility in organic solvents rises as the fat-soluble portion of the molecule increases. The likeliest impurities are traces of salts, heavy metal ions, proteins and other amino acids. Purification of these is usually easy, by recrystallisation from water or ethanol/water mixtures. The amino acid is dissolved in the boiling solvent, decolorised if necessary by boiling with Ig of acid-washed charcoal/lOOg amino acid, then filtered hot, chilled, and set aside for several hours to crystallise. The crystals are filtered off, washed with ethanol, then ether, and dried. 

Eor biomolecules, such as proteins, the fastest motions are the stretching vibrations of the bonds connecting hydrogen atoms to heavy atoms (X—H stretching). The frequency of these motions is in the vicinity of 3000 cm , which means periods of about 10 fs (1 X lO s). Thus, an appropriate time step for simulating biomolecules would be At =... 

Since the summation in Eq. (12) may be on any subset of atoms, it can be fine-tuned to best suit the problem at hand. The summation may be over the whole molecule, but it is very common to calculate conformational distances based only on non-hydrogen heavy atoms or, in the case of proteins, even based on only the backbone Ca atoms. Alternatively, in a study related to drug design one may consider, for example, focusing only on atoms that make up the pharmacophore region or that are otherwise known to be functionally important. 

The reaction center is built up from four polypeptide chains, three of which are called L, M, and H because they were thought to have light, medium, and heavy molecular masses as deduced from their electrophoretic mobility on SDS-PAGE. Subsequent amino acid sequence determinations showed, however, that the H chain is in fact the smallest with 258 amino acids, followed by the L chain with 273 amino acids. The M chain is the largest polypeptide with 323 amino acids. This discrepancy between apparent relative masses and real molecular weights illustrates the uncertainty in deducing molecular masses of membrane-bound proteins from their mobility in electrophoretic gels. 

Figure 15.14 Schematic representation of the specific interactions between phosphoryicholine (orange) and the protein side groups (green) in Fab. The binding cavity is in a cleft between the light and the heavy chains. Choiine binds in the interior while the phosphate group is toward the surface. (Adapted from E.A. Padlan et al., Immunochemistry 13 945-949, 1976.)...

MIR), requires the introduction of new x-ray scatterers into the unit cell of the crystal. These additions should be heavy atoms (so that they make a significant contribution to the diffraction pattern) there should not be too many of them (so that their positions can be located) and they should not change the structure of the molecule or of the crystal cell—in other words, the crystals should be isomorphous. In practice, isomorphous replacement is usually done by diffusing different heavy-metal complexes into the channels of preformed protein crystals. With luck the protein molecules expose side chains in these solvent channels, such as SH groups, that are able to bind heavy metals. It is also possible to replace endogenous light metals in metal-loproteins with heavier ones, e.g., zinc by mercury or calcium by samarium. 

Since such heavy metals contain many more electrons than the light atoms, H, N, C, O, and S, of the protein, they scatter x-rays more strongly. All diffracted beams would therefore increase in intensity after heavy-metal substitution if all interference were positive. In fact, however, some interference is negative consequently, following heavy-metal substitution, some spots measurably increase in intensity, others decrease, and many show no detectable difference. 

How do we find phase differences between diffracted spots from intensity changes following heavy-metal substitution We first use the intensity differences to deduce the positions of the heavy atoms in the crystal unit cell. Fourier summations of these intensity differences give maps of the vectors between the heavy atoms, the so-called Patterson maps (Figure 18.9). From these vector maps it is relatively easy to deduce the atomic arrangement of the heavy atoms, so long as there are not too many of them. From the positions of the heavy metals in the unit cell, one can calculate the amplitudes and phases of their contribution to the diffracted beams of the protein crystals containing heavy metals. 

How is that knowledge used to find the phase of the contribution from the protein in the absence of the heavy-metal atoms We know the phase and amplitude of the heavy metals and the amplitude of the protein alone. In addition, we know the amplitude of protein plus heavy metals (i.e., protein heavy-metal complex) thus we know one phase and three amplitudes. From this we can calculate whether the interference of the x-rays scattered by the heavy metals and protein is constructive or destructive (Figure 18.10). The extent of positive or negative interference plus knowledge of the phase of the heavy metal together give an estimate of the phase of the protein. 

Figure 18.10 The diffracted waves from the protein part (ted) and from the heavy metals (green) interfere with each other in crystals of a heavy-atom derivative. If this interference is positive as illustrated in (a), the intensity of the spot from the heavy-atom derivative (blue) crystal will be stronger than that of the protein (red) alone (larger amplitude). If the interference is negative as in (b). the reverse is true (smaller amplitude).

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