Gaussian functions/distribution proteins

Gaussian curves (normal distribution functions) can sometimes be used to describe the shape of the overall envelope of the many vibrationally induced subbands that make up one electronic absorption band, e.g., for the absorption spectrum of the copper-containing blue protein of Pseudomonas (Fig. 23-8) Gaussian bands are appropriate. They permit resolution of the spectrum into components representing individual electronic transitions. Each transition is described by a peak position, height (molar extinction coefficient), and width (as measured at the halfheight, in cm-1). However, most absorption bands of organic compounds are not symmetric but are skewed... 

The energy-conserving delta function is actually where the protein seems to play its major role. Because the transfer of charge in this model is sudden, the electron transition is between states of constant atomic position (a nonadiabatic transition). The atoms from which this transfer occurs are bound harmonically to the lattice and when in thermal equilibrium have a Gaussian distribution around the center of the potential ... 

Equation (9-114) corresponds to a Gaussian distribution function (see also Section 8.3.2.1). The molar mass can be calculated from the position of the inflection point of the function c = /(r — r ). For proteins in CsCl/ H2O, the lower molar mass limit giving a meaningful measurement is 10 000-50 000 g/mol molecule. The limit is essentially governed by the length of the ultracentrifuge cell ( 1.2 cm) and the optimal values of r — for this length. 

Figure 7. The probability distribution function of the Z sctn-es computed for the population of false positives. A set of 47 sequences from the 547 set of proteins with known structures without homologs in the HL set is used to sample the distribution of Z scores for false positives. Each of the sequences is aligned to all the structures included in HL set. Hie Z semes are calculated far the 200 best matches (according to energy) using 100 shuffled sequences. The observed distribution of Z scores is represented by +. The dashed line shows the attempted analytical fit to a Gaussian distribution, whereas the solid line the analytical fit to the expected extreme value (double exponential) distribution. Note the significant tail to the right, which is the probability of obtaining a relatively large Z score by chance. See text far mote details.

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