Function of residuals

Sulfur content and specific gravity as a function of residue yield. 

Each food or food ingredient shows a characteristic equiHbrium relative humidity at a given moisture content and temperature. Thus as a food is dried and its moisture content is reduced from its fresh value where water activity is generally 1.0, to lower and lower values, the equiHbrium water activity of the food decreases as a complex function of residual moisture. The shape of the equiHbrium relative humidity—moisture content curve is set by the chemistry of the food. Foods high ia fmctose, for example, biad water and thus show lower water activities at high moisture contents. Dried pmnes and raisias are examples. Drying can be terminated at any desired moisture content and hence any water activity. 

Slopes BC and CD = function of elastic recovery Lines OC and OE = function of (residual die wall force) RDWF... 

Fig. 3. Secondary chemical shifts for 13C , 13CO, H , and 13C as a function of residue number in apomyoglobin at pH 4.1. Bars at the top of the figure indicate the presence of NOEs the smaller bars indicate that the NOE was ambiguous due to resonance overlap. Black rectangles at the base of the top panel indicate the locations of helices in the native holomyoglobin structure (Kuriyan et al, 1986). Hashed rectangles indicate putative boundaries for helical regions in the pH 4 intermediate, based on the chemical shift and NOE data. Reproduced from Eliezer et al (2000). Biochemistry 39, 2894-2901, with permission from the American Chemical Society.

Fig. 5. Physical-chemical parameters as a function of residue number for hamster PrP (Inouye and Kirschner, 1998). The parameters (arbitrary scale) are charge at pH 7 hydrophobicity a-helix (solid), /8-strand (dashed) turn (solid), coil (dashed) a-helical (solid) and /8-strand amphiphilicity (dashed). The predicted helices (Huang et al., 1994) are labeled HI, H2, H3, and H4, and the NMR-observed helices and /8-strands are A-C and SI, S2, respectively (James et al., 1997).

Figure 17.12. Ratio of volumes of an n-stage CSTR battery and a plug flow reactor as a function of residual concentration ratio C/C0 with a rate equation r = kC2.

Figure 2. Residues of carbaryl found on thinners hands (Y) as a function of residues found on leaves (X) for 0.5 and 1.0 lb/100 gal application rates (2.0 lb AI and 4.0 lb Al/acre) (Y — 690X — 45 correlation coefficient (r) = 0.99).

Kijowski, J., Lesnierowski, G., and Fabisz-Kijowska, A. 1999. Lysozyme polymer formation and functionality of residuals after lysozyme extraction. In Egg Nutrition and Biotechnology (J.S. Sim, S. Nakai, and W. Guenter, eds), pp. 269-285. CABI Publishing, Wallingford, UK. 

Determination of the adsorption isotherm is important, since it allows establishing of the basic relationship between the adsorbed amounts of ODN onto colloidal particles as a function of residual ODN concentration (equilibrium ODN concentration). Two major pieces of information can be deduced from the adsorption isotherm (i) the affinity between the ODN and the particles revealed... 

Fig. 1.3. Paramagnetic relaxation enhancement profiles for apomyoglobin unfolded at pH 2.3 in the presence (left panels) and absence (right panels) of 8M urea. Data for spin labels attached at residues 18 and 77 is shown. The plots show the ratio of HSQC cross-peak intensity with the spin label oxidized (paramagnetic) and reduced (diamagnetic) as a function of residue number. The solid lines in the left panels represent the broadening profile expected for a random coil polypeptide. The figure is adapted from data reported in [14]. The positions of the helices in holomyoglobin are shown by the bars at the top of the figure...

Figure 6. Adsorption isotherm for 2,4,5-T Capacity for adsorption of 2,4,5-T on 273-micron Columbia LC carbon at 25°C. is plotted as a function of residual concentration, C q, at equilibrium. The left ordinate gives capacity in units of fimoles of solute per gram of carbon and the right ordinate in units of milligrams of solute per gram of carbon. The points represent experimental data the line drawn through the data is the calculated Langmuir isotherm.

Tab. 5. Orders of reactivity of single and grouped humic acids, expressed as a function of residual free spin concentration percentages (in parentheses) in the interaction products, for homogeneous classes of phenoxy compounds ... 

Partial residuals are produced with GAM, and not the usual residual plots. Plots of residuals and functions of residuals are useful particularly for identifying patterns in the data that may suggest heterogeneity of variance or bias due to deterministic model misspecification or misspecifications of the regression variables. One particular form of bias that may exist occurs when a predictor variable is included in the model in a linear form when it actually has a curvilinear or nonlinear relationship with the response variable. A plot used by Ezekiel (23) and later referred to as a partial residual plot by Larsen and McCleary (24) is useful for this purpose. Partial residuals are defined as... 

Zhang, K. Y. and D. Eisenberg, The three-dimensional profile method using residue preference as a continuous function of residue environment. Protein Sci, 1994. 3(4) p. 687-95. 

Figure 13. Calculated and experimental rms fluctuations of lysozyme. Backbone averages are shown as a function of residue number, and were obtained (a) from a molecular dynamics simulation and (b) from X-ray temperature factors without correcting for disorder contributions. (From Ref. 192.)...

Figure 15. Root-mean-square displacement subaverages as a function of residue number for the C" atoms (TAV = 0.2, 0.5, 1, 2, and 5 ps).

The results for the mainchain and sidechain averages for each residue as a function of residue number are given. For the mainchain fluctuations, the molecular dynamics and normal-mode values are very similar for the side-chains, there is some correspondence, although the differences are considerably more pronounced. This is in accord with the results on anharmonicity found in the molecular dynamic simulations (see above). 

Folkertsma, S., van Noort, P., Van Durme, J., Joosten, H.J., Bettler, E., Fleuren, W., Oliveira, L., Horn, F., de Vlieg, J. and Vriend, G. (2004) A family-based approach reveals the function of residues in the nuclear receptor ligand-binding domain. Journal of Molecular Biology, 341, 321-335. 

Fig. 4.7. Adsorption isotherm of polyacrylamide on Na-kaolinite as a function of residual polymer concentration and the corresponding Langmuirian plot.

Figure 3. Specific conductivity (ohm 1 cm 1) as a function of residual Na+ content at 1000 Hz...

Figure 3, Longitudinal shrinkage ratio of old and recent wood as a function of residual density, from the data of Table IV.

Figure 1. Residual compression strength parallel to grain as a function of residual density, based on data in Table V.

FIGURE 8.6 Local diffusion constants as a function of residue number for GB3 simulation date from [13], and experimental values are from [51]. 

---