Perrin factor

From Eqs. (5.1.6) and (5.1.7) the mean translation coefficient for a prolate or oblate spheroid is simply 2/5, whereas for a sphere it is just the sphere radius. A quantity of interest, sometimes termed the Perrin factor, is the ratio of the mean translation coefficient (or mean friction coefficient) of a prolate or oblate... 

In Fig. 5.1.2 the Perrin factor is plotted as a function of the axial ratio, defined as the ratio of the long semiaxis to short semiaxis, equal to p for the prolate spheroid and p for the oblate spheroid. As seen, the Perrin factor is always greater than unity, which may have been anticipated, since for equal volumes the surface area of the spheroid will be greater than that of a sphere of the same volume, so the friction coefficients will be greater. Because rhe volume of a molecule is proportional to its molar mass, then, for a constant mass, the more a molecule deviates from a spherical shape, the larger will be its mean friction coefficient. 

Figure 5.1.2 Perrin factor for prolate and oblate spheroids.

Table 3.1.2. Estimation of Perrin factor for various proteins...

If the solute shape is nonspherical, a relation other than Stokes law will apply. For the determination of the resistance of nonspherical macromolecules, the reader may consult pp. 356-364 of Tanford (1961). We will provide a very brief perspective on this effect here. Some cells, and especially many proteins, are ellipsoids of revolution. The drag force encountered by such an ellipsoid of revolution of species i is described in terms of the drag encountered by a sphere of equal volume whose radius is ro via an appropriate correction factor (ff/ffo) which is always greater than 1. This factor is called the Perrin factor. The magnitude of is enhanced by this factor, i.e. 

For a brief introduction, see Probstein (1989) for references to the work by Perrin for greater details, see Happel and Brenner (1983). In Table 3.1.2, we list estimates of the Perrin factor for several proteins (inlbrmation from Basak and Ladisch (1995)). 

The spherical geometry assumed in the Stokes and Einstein derivations gives the highly symmetrical boundary conditions favored by theoreticians. For ellipsoids of revolution having an axial ratio a/b, friction factors have been derived by F. Perrin, and the coefficient of the first-order term in Eq. (9.9) has been derived by Simha. In both cases the calculated quantities increase as the axial ratio increases above unity. For spheres, a/b = 1. 

R/Ro)soiv(f/fo)ellip = n + (mib/m2)(P2/Pi)] (f/fo)eiiip-Briefly justify this expansion of the (f/fo oiv factor. Assuming these particles were solvated to the extent of 0.26 g water (g protein)", calculate (f/fo)eiHp-For prolate ellipsoids of revolution (b/a < 1), Perrin has derived the following expression ... 

Most biological polymers, such as proteins and nucleic acids and some synthetic polymers, have relatively inflexible chains. For rigid particles, the size is no longer of predominant importance, because the polymer chain is no longer in the form of a flexible random coil instead, shape becomes an important parameter. Following are some theoretical proposals for the estimation of the shape factor p from the viscosity measurement (table 4). The term f/fo is sometimes denoted as p, Perrin constant. 

Here, is the distance between atoms i andj, C(/ is a dispersion coefficient for atoms i andj, which can be calculated directly from tabulated properties of the individual atoms, and /dampF y) is a damping function to avoid unphysical behavior of the dispersion term for small distances. The only empirical parameter in this expression is S, a scaling factor that is applied uniformly to all pairs of atoms. In applications of DFT-D, this scaling factor has been estimated separately for each functional of interest by optimizing its value with respect to collections of molecular complexes in which dispersion interactions are important. There are no fundamental barriers to applying the ideas of DFT-D within plane-wave DFT calculations. In the work by Neumann and Perrin mentioned above, they showed that adding dispersion corrections to forces... 

Lewis K, Li C, Perrin MH, Blount A, Kunitake K, Donaldson C, Vaughan J, Reyes TM, Gulyas J, Fischer W, Bilezikjian L, Rivier J, Sawchenko PE, Vale WW (2001) Identification of urocortin III, an additional member of the corticotropin-releasing factor (CRF) family with high affinity for the CRF2 receptor. Proc Natl Acad Sci USA 98 7570-7575... 

Vaughan J, Donaldson C, Bittencourt J, Perrin MH, Lewis K, Sutton S, Chan R, Turnbull AV, Lovejoy D, Rivier C, Rivier J, Sawchenko PE, Vale W (1995) Urocortin, a mammalian neuropeptide related to fish motensin 1 and to corticotropin-releasing factor. Nature 378 287-292... 

Chen F, Bilezikjian LM, Perrin MH, Rivier J, Vale W (1986) Corticotropin releasing factor receptor-mediated stimulation of adenylate cyclase activity in the rat brain. Brain Res 381 49-57... 

Reyes TM, Lewis K, Perrin MH, Kunitake KS, Vaughan J, Arias CA, Hogenesch JB, Gulyas J, Rivier J, Vale WW, Sawchenko PE (2001) Urocortin 11 a member of the corticotropinreleasing factor (CRF) neuropeptide family that is selectively bound by type 2 CRF receptors. Proc Natl Acad Sci USA 98 2843-2848 Richard P, Moos F, Freund-Mercier MJ (1991) Central effects of oxytocin. Physiol Rev 71 331-370... 

Perrin [223] extended Debye s theory of rotational relaxation to consider spheroids and ellipsoids. Using Edwards analysis [224] of the torque on such bodies, Perrin found two or three rotational relaxation times, respectively. However, except for bodies very far from spherical, these times are within a factor of two of the Debye rotational times [eqn. (108)] for stick boundary conditions. 

The constants were computed using a value of 0.80 for factor F (Equation 9). b The pK a values for serine and threonine at 37° in 0.15M KN03 were taken from Perrin ct al. (32) and Sharma (19), respectively. 

Andres E, Kurtz JE, Perrin AE, Dufour P, Schlienger JL, Maloisel F. Haematopoietic growth factor in antithyroid-drug-induced agranulocytosis. QJM 2001 94(8) 423-8. 

Perrin MH, Haas Y, Rivier JE, Vale WW (1986) Corticotropinreleasing factor binding to the anterior pituitary receptor is modulated by divalent cations and guanyl nucleotides. Endocrinology 118 1171-9... 

Seifert H, Perrin M, Rivier J, Vale W (1985) Binding sites for growth hormone releasing factor on rat anterior pituitary cells. Nature 313(6002) 487-9... 

Perrin eqc Prolate Ellipsoid Solvation Factor Circular Dichroism f Fe+3 a Binding9... 

Perrelet D, Perrin FE, Liston P, Korneluk RG, MacKenzie A, Ferrer-Alcon M, Kato AC (2004) Motoneuron resistance to apoptotic cell death in vivo correlates with the ratio between X-linked inhibitor of apoptosis proteins (XIAPs) and its inhibitor, XlAP-assodated factor 1. J Neurosci 24 3777-3785... 

De Souza EB, Insel TR, Perrin MH, Rivier C, Vale WW, Kuhar MJ (1985) Corticotropinreleasing factor receptors are widely distributed within the rat central nervous system tm autoradiographic study. J Neurosci 5 3189-3203... 

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