Chemistry and Biology of Proteins - F. Haurowitz 1953

Size and Shape of Protein Molecules
Viscosity of Protein Solutions

It is well known that solutions of certain Proteins, such as gelatin, are exceptionally viscous, whereas solutions of others, such as egg albumin or Serum proteins, exhibit high fluidity even at concentrations significantly higher than that of gelatin. This is evident from Table 3, which presents data on the viscosity of aqueous solutions of egg albumin [39] at 25.2° and gelatin solutions at 37°. At lower temperatures, the viscosity of gelatin cannot be measured because gelatin solutions transform into a gel [40].

Class="center">Table 3 Viscosity of aqueous solutions of egg albumin and gelatin

The high viscosity of gelatin solutions is attributed to the thread-like (filamentous) shape of their molecules, which, owing to Brownian motion, occupy a larger volume of the solvent than spherical molecules of the same molecular weight. Consequently, in solutions containing asymmetric molecules, additional work is required to impart a specified rate of flow.

Viscosity determinations are performed very frequently since they are not associated with any experimental difficulties. The Ostwald viscometer (Fig. 7) is usually employed for this purpose. An aqueous protein solution is allowed to flow out of pipette 3 through capillary 4, and the time required for the meniscus to drop from 1 to 2 is determined. If the viscosity of the protein solution does not differ too greatly from that of Water and if the capillary diameter is chosen correctly, the viscosity η is directly proportional to t — the flow time — and d — the density of the solution:

η = Сdt.

If η₀ is the viscosity of water and η is the viscosity of the protein solution, the relative viscosity will be equal to

η_oтн = η/η₀ = Cd_бt_б/Ct_в = d_бt_б/t_в,

where d_б is the density of the protein solution, and t_б and t_в are the flow times of the protein solution and water, respectively. The relative viscosity η_отн is independent of the constant C, which is a function of the capillary diameter.

For the case of very dilute Suspensions of spherical particles, Einstein derived the following formula:

η = η₀(1+2,5Nv/V),       (4)

where N is the number of suspended particles, v is the volume of each particle, and V is the total volume of the solution. If we know the number of protein molecules N, we can calculate the volume occupied by each particle and thereby determine the extent to which it is hydrated. Conversely, if the Hydration is known, we can use formula (4) to calculate the number of molecules N and the weight of a particle, which is equal to the total weight of the protein divided by N. This method has yielded hydration values for egg albumin, Hemoglobin, and other proteins with spherical molecules that are in good agreement with values obtained by other Methods [41]. However, most proteins do not possess spherical molecules, which severely limits the applicability of this method.

Fig. 7. Ostwald viscometer.

1 and 2 — two positions of the meniscus; 3 — pipette; 4 — capillary.

Since the viscosity η of a protein solution is always higher than η₀, the viscosity of water, the relative viscosity η_отн = η/η₀ will always be greater than unity. The difference between this value and unity (η_отн — 1) is termed the specific viscosity — η_уд. According to Staudinger [42], the specific viscosity of solutions of thread-like macromolecules is directly proportional to the concentration and the Molecular Weight of the dissolved macromolecules. In the equation

η_уд = КсМ

K is a constant for a given Selection/23.html">Homologous Series of molecular chains of the same structural pattern but varying length, c is the concentration, and M is the molecular weight.

When molecular chains are in a dissolved state, they only very rarely adopt the conformation of a fully extended thread. Due to free rotation around valence bonds, the threads will continuously bend and unbend, assuming various spatial configurations at different moments in time (Fig. 8).

Fig. 8. A, B, and C — various configurations of a thread-like macromolecule.

Based on statistical considerations [43], the average length of a thread-like molecule—that is, the distance between the two ends of the thread—should be considered proportional to L, where L is the chain length of the fully extended molecule. Since M is proportional to L, the average length of the thread-like molecule is also proportional to M.

The viscosity of a solution depends not only on the average chain length, but also on the resistance that the thread-like molecule offers to forces acting to alter its spatial configuration. To account for these factors, the quantity M in Staudinger's equation is replaced by its power function M^a, where a takes values from 0.5 to 1.5 [44, 45].

When viscosity measurements of macromolecular solutions are carried out at different concentrations, different values are obtained for η_отн and η_уд. If one plots the specific viscosity as a function of solution concentration and extrapolates the curve to c = 0, the so-called intrinsic viscosity [η] of the molecule can be determined. It is equal to [46–48]

Viscosity measurements make it possible to determine the molecular weight of thread-like macromolecules such as rubber or Cellulose ethers; however, when determining the molecular weights of proteins, the situation is complicated by the electrostatic interaction of anionic and cationic protein side chains and their effect on water molecules. Consequently, the Viscosity of protein solutions depends on the solution pH. The electrostatic effect of ionized groups can be mitigated by adding salts; specifically, the viscosity of polyelectrolytes decreases upon The addition of sodium chloride [49, 50]. It follows that determining the viscosity of protein solutions alone can hardly be used to establish the molecular weight and Shape of Protein molecules; nevertheless, this method can yield highly valuable insights into these properties when combined with other techniques. For instance, by combining viscometry and diffusion measurements, the following molecular weight values were obtained: 40,500 for egg albumin, 41,500 for lactoglobulin, 67,100 for serum albumin, 150,000–200,000 for serum globulin, 330,000 for amandin (from almonds), 676,000 for thyroglobulin, and 2,780,000 for octopus hemocyanin [51, 52]. The molecular weight of tobacco mosaic virus was found to be 63,200,000 and 42,600,000; the particle dimensions, in excellent agreement with diffusion measurements [54], were determined to be 11.5×725 and 12.3×430 mμ [53].

If rod-like particles in a solution are exceptionally long and possess sufficient rigidity, The phenomenon of thixotropy is observed [55]. As is well known, this phenomenon is characterized by The formation of a gel when the solution is left to stand for a prolonged period, which subsequently liquefies again upon agitation. Thixotropy is observed in gels of the contractile Muscle protein Myosin.