Protein molecule, average number

Gerstein and Chothia [137] studied 22 proteins, the average number of surface atoms of per molecule of which was 420, and found them to be 47% hydrated, that is, in contact with water molecules. The peripheral hydrating water molecules had a molecular volume of 0.0245 nm compared with the molecular volume of bulk water, V"/Nj = 0.0300 nm at room temperature, that is, they were compressed by 22% with respect to it. 

For a polypeptide chain of 100 residues in length, a rather modest size, the number of possible sequences is 20 , or because 20 = lO, lO unique possibilities. These numbers are more than astronomical Because an average protein molecule of 100 residues would have a mass of 13,800 daltons (average molecular mass of an amino acid residue = 138), lO such molecules would have amass of 1.38 X lO " daltons. The mass of the observable universe is estimated to be 10 proton masses (about 10 daltons). Thus, the universe lacks enough material to make just one molecule of each possible polypeptide sequence for a protein only 100 residues in length. 

With applications to protein solution thermodynamics in mind, we now present an alternative derivation of the potential distribution theorem. Consider a macroscopic solution consisting of the solute of interest and the solvent. We describe a macroscopic subsystem of this solution based on the grand canonical ensemble of statistical thermodynamics, accordingly specified by a temperature, a volume, and chemical potentials for all solution species including the solute of interest, which is identified with a subscript index 1. The average number of solute molecules in this subsystem is... 

The main component of E. coli—as in all cells—is water (70%). The other components are macromolecules (proteins, nucleic acids, polysaccharides), small organic molecules, and inorganic ions. The majority of the macromolecules are proteins, which represent ca. 55% of the dry mass of the cell. When a number of assumptions are made about the distribution and size (average mass 40 kDa) of proteins, it can be estimated that there are approximately 250000 protein molecules in the cytoplasm of an E. coli cell. In eukaryotic cells, which are about a thousand times larger, it is estimated that the number of protein molecules is in the order of several billion. 

Fig. 4. Oxygenation curves for myoglobin and hemoglobin. The average number of oxygen molecules bound per protein molecule, n, is plotted vs. the partial pressure of O2. For hemoglobin the oxygenation curve is given at three different partial pressures of carbon dioxide...

Careful analysis of electron-density maps usually reveals many ordered water molecules on the surface of crystalline proteins (Plate 4). Additional disordered water is presumed to occupy regions of low density between the ordered particles. The quantity of water varies among proteins and even among different crystal forms of the same protein. The number of detectable ordered water molecules averages about one per amino-acid residue in the protein. Both the ordered and disordered water are essential to crystal integrity, and drying destroys the crystal structure. For this reason, protein crystals are subjected to X-ray analysis in a very humid atmosphere or in a solution that will not dissolve them, such as the mother liquor. 

A simple calculation is instructive. Consider reaction with one type of side chain of which there are, say, dozens on each protein molecule (in identical environments) and suppose we wish to have an average of one chelator per protein molecule. Poisson statistics are appropriate to describe a situation like this (23), where the number of labeled side chains will be a small fraction of the number of available side chains. 

This simple example shows that even though only 26% of the protein molecules contain more than one chelating group, 63% of the signal will come from these multiply labeled molecules Refinements in the mathematical model will not change this conclusion qualitatively. Since the more chelators the product contains, the less it resembles the unmodified protein, it is evident that with a nonselective reagent the average number of chelators per protein must be kept well below 1.0 if the labeled product is to retain its native properties. 

The total protein concentration is simply E (PH,), the sum extending from y = 0to = wso that the average number of bound protons per molecule ( ) is... 

Throughout this paper we have so far discussed only the average number of hydrogen ions bound to or dissociated from a protein molecule at any pH. It should be pointed out that individual protein molecules may at any given instant have Zh values which can be larger or smaller than the average value Zu Edsall (1943) has shown for example that in hemoglobin at pH 6.4, where — 0, 4% of all molecules have Zs = -f3, 9% have Zh = -f2, 17% have Z = +1, 22% have Z = 0, 21 % have... 

E. coli is a rod-shaped bacterium about 2 long and 1 /a in diameter. The average density of a cell is 1.28 g/ml. Approximately 13.5% of the wet weight of E. coli is soluble protein. Estimate the number of molecules of a particular enzyme per cell if the enzyme has a MW of 100,000 and represents 0.1% of the total soluble protein. 

The average hydrophobicity (Ftav) of a protein can be estimated as Ftav = XFta/n, where n is the number of a.a. residues in the protein molecule. 

In RPLC, the influence of pressure on the chromatographic behavior is related to the hydrophobic interactions involved in the retention mechanism and to the change upon adsorption in the numbers of acetonitrile and water molecules in the solvent shells of the protein molecule and of the bonded layer. The importance of the changes in the retention factor and the saturation capacity with a change in the average column pressure will thus depend on the retention mode used and will vary with the hydrophobicity of the molecule [128]. In RPLC, it is larger with polymeric than with monomeric bonded phases [126]. 

As stated earlier, we hope to determine complex stoichiometry through the use of the Hummel-Dreyer technique. A calculation of stoichiometry at the point of polymer saturation will provide the average number of binding sites per polymer molecule, from which an intrinsic dissociation constant may be estimated. Currently, calculations of complexation stoichiometries have been hampered by a chromatographic overlap of the protein peak with that of the complex, and also by the extremely high polydispersity of the PDMDAAC samples. 

FIGURE 7.15 Association of /1-caseinate (expressed as the average number of molecules in an aggregate) as a function of protein concentration at various temperatures (indicated, °C) at pH 7.0. Ionic strength 0.2 molar (full lines) or 0.05 molar (broken line). 

Next we might ask how many protein molecules a cell needs to operate and maintain Itself. To estimate this number, let s take a typical eukaryotic cell, such as a hepatocyte (liver cell). This cell, roughly a cube 15 jxm (0.0015 cm) on a side, has a volume of 3.4 X 10 cm (or milliliters). Assuming a cell density of 1.03 g/ml, the cell would weigh 3.5 X 10 g. Since protein accounts for approximately 20 percent of a cell s weight, the total weight of cellular protein is 7 X 10 g. The average yeast protein has a mo-... 

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