Small form factor function

Figure 2.19 Organization of polypeptide chains into domains. Small protein molecules like the epidermal growth factor, EGF, comprise only one domain. Others, like the serine proteinase chymotrypsin, are arranged in two domains that are required to form a functional unit (see Chapter 11). Many of the proteins that are involved in blood coagulation and fibrinolysis, such as urokinase, factor IX, and plasminogen, have long polypeptide chains that comprise different combinations of domains homologous to EGF and serine proteinases and, in addition, calcium-binding domains and Kringle domains.

The Pauli form factor also generates a small contribution to the Lamb shift. This form factor does not produce any contribution if one neglects the lower components of the unperturbed wave functions, since the respective matrix element is identically zero between the upper components in the standard representation for the Dirac matrices which we use everywhere. Taking into account lower components in the nonrelativistic approximation we easily obtain an explicit expression for the respective perturbation... 

This last result is known as the Guinier function and is the basis for determining the radius of gyration from small-angle scattering experiments for objects with unknown form factor. 

Vitamins are growth factors which fulfill specific catalytic needs in biosynthesis and are required in only small amounts. They are organic compounds that function as coenzymes or parts of coenzymes to catalyze many reactions. Table 11 itemizes the vitamins together with their active forms, catalytic function, molecular precursors, and rawmaterial sources.f ... 

At ambient temperature, the values for are typically of the order of 0.01 to O.IOA. For the carbon atoms in diamond, U0.002 is particularly small. For Na and Cl in the structure of NaCl, we find 0.02 A. Figure 3.14 shows that the thermal motion reduces the form factor and hence the intensities diffracted at high 6 angles. It can be shown that, at a suflSciently high temperature, is a linear function of the temperature if the vibrations are harmonic. 

In the simplest approximation, functions Gx(fx) and Gh (z) determine the structure factor. The form-factor contributes to diffraction pattern negligibly for small rod-like molecules comprising typical thermotropic nematics but may be important for biological materials. 

Form Factors The plot of Si(k) as a function of k at small k gives the radius of gyration for any conformation, but, beyond that range, Si(k) depends on the conformation. For a Gaussian chain, SiCk) follows the Debye function. Equations 2.59 and 2.76 allow us to calculate SiCk) for other conformations. Let us first define a form factor P(k) by... 

The pair distance distribution function p r) obtained in small-angle scattering from the form factor P q) is analogous to the distance distribution P r) obtained in... 

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