Hydrodynamic measurements, shape

This experiment shows that folding of the non-helix or poor helix-forming sequence is encouraged in the triple helix too, even if this part of the helix contributes to a decrease of the folding strength. Sedimentation and hydrodynamic measurements clearly show the formation of a trimer aggregation and of an extended shape. 

Interpretation of the hydrodynamic data of a macromolecule requires that the shape of the molecule in a given solvent be known in advance from other sources and that there exist adequate expressions to relate the hydrodynamic quantities under consideration to a few parameters characterizing the dimensions of the molecule. Thus, in general, hydrodynamic measurements are informative as a supplementary means for the characterization of macromolecules. 

Proteins with chemical functions such as, for example, enzymes, adopt their native macroconformations under physiological conditions. In general, their shapes are very rigid and compact on account of the many inter- and intramolecular bonds these proteins mostly occur in spheres or ellipsoids. The external shape can often be determined by hydrodynamic measurements or electron microscopy. Information on the internal structure can often be obtained by X-ray measurements on protein crystals doped with heavy metals (see also Section 5.3.1). 

Proteins adopt their native conformation under physiological conditions. This conformation is usually very rigid and compact due to the many intra- and intercatenary, intra- and intermolecular bonds (secondary, tertiary, and quaternary structures). Therefore the detailed conformation of native proteins can be evaluated by X-ray diffraction measurements on protein crystals. Hydrodynamic measurements, on the other hand, only yield information about the external shape (sphere, rod, ellipsoid) of these compact structures. 

In dilute solutions the problem may be attacked by light scattering. X-ray scattering, or hydrodynamic measurements. In solution, the acquisition of experimental data is relatively easy, but the interpretation presents formidable problems which have not yet been solved completely satisfactorily. The main trouble arises from the fact that models are required to interpret data on dilute solutions, and it is difficult to assess how applicable the models are to molecularly dispersed species. Very often dubious assumptions are introduced which tend to render the results meaningless. Our first task, therefore, shall be to examine a variety of hydrodynamic experiments and see to what extent the data from such experiments can be interpreted in terms of size and shape. We shall not discuss scattering measurements here, except to mention that they too involve difficulties of the same kind in the interpretation of the data. 

In the hydrodynamic theories for any of the quantities in the last column of Table I, each quantity depends on two parameters, the size and the shape. For example, for an ellipsoid of revolution these two parameters could be the volume and axial ratio, F and p, respectively, of the effective hydrodynamic ellipsoid. Therefore, we may draw a first very important conclusion, viz., that a determination of only one quantity, e.g., /, cannot provide us with a value of Ve or p. It is clear that two quantities are required, e.g., f and [r ] if two such quantities are available, then both F, and p may be computed. Of course, if one has information in advance as to the value of F or p (e.g., if the particle behaves as a sphere, with p = 1), then a single hydrodynamic quantity suffices to give the value of the other parameter. Unfortunately, one never has this advance information and, therefore, must carry out two different kinds of hydrodynamic measurements in order to obtain a pair of hydrodynamic quantities. 

We have seen that a pair of hydrodynamic measurements is required to determine the size and shape of the hydrodynamic ellipsoid. It is then of interest to raise the following question Are the equivalent ellipsoids computed from /3, 5, and m the same This is a very important question and, in the absence of hydrodynamic theories for nonellipsoidal particles, can be settled only by experiment. Tobacco mosaic virus might be a good model substance with which to carry out the required hydrodynamic measurements with sufficient precision. However, thus far such tests of the theory have not been carried out for a homogeneous preparation. 

Theoretical models of the film viscosity lead to values about 10 times smaller than those often observed [113, 114]. It may be that the experimental phenomenology is not that supposed in derivations such as those of Eqs. rV-20 and IV-22. Alternatively, it may be that virtually all of the measured surface viscosity is developed in the substrate through its interactions with the film (note Fig. IV-3). Recent hydrodynamic calculations of shape transitions in lipid domains by Stone and McConnell indicate that the transition rate depends only on the subphase viscosity [115]. Brownian motion of lipid monolayer domains also follow a fluid mechanical model wherein the mobility is independent of film viscosity but depends on the viscosity of the subphase [116]. This contrasts with the supposition that there is little coupling between the monolayer and the subphase [117] complete explanation of the film viscosity remains unresolved. 

Hydrodynamic volume refers to the combined physical properties of size and shape. Molecules of larger volume have a limited ability to enter the pores and elute the fastest. A molecule larger than the stationary phase pore volume elutes first and defines the column s void volume (Vo). In contrast, intermediate and smaller volume molecules may enter the pores and therefore elute later. As a measure of hydrodynamic volume (size and shape), SE-HPLC provides an approximation of a molecule s apparent molecular weight. For further descriptions of theoretical models and mathematical equations relating to SE-HPLC, the reader is referred to Refs. 2-5. 

DIVER METHOD- This is a modification of the hydrometer method. Variation in effective density i and hence concn, is measured by totally immersed divers. These are small glass vessels of approximately streamline shape, ballasted to be in stable equilibrium, with the axis vertical, and to have a known density slightly greater than that of the sedimentation liq. As the particles settle, the diver moves downwards in hydrodynamic equilibrium at the appropriate density level. The diver indicates the position of a weight concn equal to the density difference between the diver and the sedimentation liq. Several divers of various densities are required, since each gives only one point on the size distribution curve... 

Scheraga-Mandelkern equations (1953), for effective hydrodynamic ellipsoid factor p (Sun 2004), suggested that [rj] is the function of two independent variables p, the axial ratio, which is a measure of shape, and Ve, the effective volume. To relate [r ] to p and Ve, introduced f, the frictional coefficient, which is known to be a direct function of p and Ve. Thus, for a sphere we have... 

To measure the strength of the forces exerted on particles, various analytical techniques have been developed [6, 7]. Unfortunately, since most of these techniques are based on hydrodynamics, assumption of the potential profiles is required and the viscosities of the fiuid and the particle sizes must be precisely determined in separate experiments, for example, using the viscous flow technique [8,9] and power spectrum analysis of position fluctuation [10]. Furthermore, these methods provide information on ensemble averages for a mass of many particles. The sizes, shapes, and physical and chemical properties of individual particles may be different from each other, which will result in a variety of force strengths. Thus, single-particle... 

In the narrow tubes used by Beek and van Heuven, the bubbles assumed the shape of Dumitrescu (or Taylor) bubbles. Using the hydrodynamics of bubble rise and the penetration theory of absorption, an expression was developed for the total absorption rate from one bubble. The liquid surface velocity was assumed to be that of free fall, and the bubble surface area was approximated by a spherical section and a hyperbola of revolution. Values calculated from this model were 30% above the measured absorption rates. Further experiments indicated that velocities are reduced at the rear of the bubble, and are certainly much less than free fall velocities. A reduction in surface tension was also indicated by extreme curvature at the rear of the bubble. 

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