New expressions to describe solution nonideal osmotic pressure, freezing point depression, and vapor pressure.

New empirical expressions for osmotic pressure, freezing point depression, and vapor pressure are proposed based on the concepts of volume occupancy and (or) hydration force. These expressions are in general inverse relationships in comparison to the standard ideal expressions for the same properties. The slopes of the new equations are determined by the molecular weight of the solute and known constants. The accuracy and precision of the molecular weights calculated from the slope are identical and approximately 1% for the experiments reported here. The nonideality of all three colligative expressions is described by a dimensionless constant called the solute-solvent interaction parameter I. The results on sucrose have the same I = 0.26 for all three solution properties. The nonideality parameter I increased from 0.26 on sucrose to 1.7 on hemoglobin to successfully describe the well-known nonideal response of macromolecules.     

Observations of rapid freezing of salt solutions.

Crystallization patterns of binary aqueous solutions of sodium chloride, potassium chloride, and calcium chloride have been observed and photographed during rapid freezing of thin films at very low subfreezing temperatures.One to three crystallization waves were observed to come in succession, usually ice first, then solute. Time delays for nucleation, and times for complete crystallization were of the order of seconds or fractions of a second for the first two salts, and minutes for the calcium chloride solutions.     

Early time expansions for sedimentation of weakly nonideal solutions

An expansion valid for short times is presented for the rectangular approximation to the Lamm equation when the sedimentation coefficient can be expressed as s = S₀(1?kc). The expansion allows the study of meniscus perturbations on the Faxén approximation, as well as a determination of when reflections from the base become significant.     

Self-association in highly concentrated solutions of myoglobin: a novel analysis of sedimentation equilibrium of highly nonideal solutions

The sedimentation equilibrium in concentrated solutions of hemoglobin and myoglobin has been measured. The ratio of the apparent molecular weight of hemoglobin to that of myoglobin. R. is found to obey the empirical relation R(c) = 3.8–4.25 × 10^?2c+6.44 × 10^?4c² ? 2.21 × 10^?5c³, where c is the protein concentration in g/dl. for c??40 g/dl. A theoretical relation for the dependence of R upon c in the absence of protein self-association is presented. This relation cannot be fitted to the experimental results, and the discrepancy is attributed to self-association of myoglobin.     

Ultrasonic Cole-Cole diagram for solutions and application to alpha-chymotrypsin.

Deconvolution of ultrasonic data into single relaxations is rarely feasible when only the absorption or the velocity of the waves is measured. Here we use both series of data to construct a Cole-Cole diagram for a solution. When applied to alpha-chymotrypsin, this method shows two relaxations that are well separated on the time scale, a result that will help simplify analyses of the ultrasonic data for this enzyme.     

The concentration of protein solutions by normal freezing

An apparatus is described which is designed for preparative freeze concentration experiments by the technique of normal freezing. It has a capacity of approximately 22 liters distributed over twelve vessels. The influence of various geometrical and chemical parameters such as stirring speed, crystallization rate, and sample composition on the normal freezing of protein solutions are discussed. For dilute protein solutions (<0.1%) the concentration factor generally was 8- to 10-fold with recoveries of 90–100 percent. With higher protein concentrations and at ionic strengths higher than approximately 0.05, the recovery was decreased. No loss of activity was detected when concentrating enzyme solutions.     

Transport across homoporous and heteroporous membranes in nonideal, nondilute solutions. II. Inequality of phenomenological and tracer solute permeabilities.

The phenomenological solute permeability (omega p) of a membrane measures the flux of solute across it when the concentrations of the solutions on the two sides of the membrane differ. The relationship between omega p and the the conventionally measured tracer permeability (omega T) is examined for homoporous and heteroporous (parallel path) membranes in nonideal, nondilute solutions and in the presence of boundary layers. In general, omega p and omega T are not equal; therefore, predictions of transmembrane solute flux based on omega T are always subject to error. For a homoporous membrane, the two permeabilities become equal as the solutions become ideal and dilute. For heteroporous membranes, omega p is always greater than omega T. An upper bound on omega p- omega T is derived to provide an estimate of the maximum error in predicted solute flux. This bound is also used to show that the difference between omega P and omega T demonstrated earlier for the sucrose-Cuprophan system can be explained if the membrane is heteroporous. The expressions for omega P developed here support the use of a modified osmotic driving force to describe membrane transport in nonideal, nondilute solutions.     

Changes in apparent pH on freezing aqueous buffer solutions and their relevance to biochemical electron-paramagnetic-resonance spectroscopy.

Changes in apparent pH occurring during fast freezing of aqueous buffer solutions and cooling to -196 degrees C were studied by various semiquantitative methods, including simple visual measurements of colour changes with pH indicators, as well as measurements of pH-dependent changes in the e.p.r. (electron paramagnetic resonance) spectra of solutions of three different metalloenzymes. It is concluded that apparent pH changes of up to about 3pH units may occur under particular conditions. Such changes were independent of the time taken to freeze the samples, when this was varied from about 3ms t0 20s, but were affected by the presence of some proteins in solution. Recommendations on the buffers that should be used to avoid such apparent pH changes in e.p.r. spectroscopy and other low-temperature biochemical work are made. Phosphate and pyrophosphate buffers, which gave large decreases (2-3 pH units), and Tris, which under some conditions gave increases of about the same magnitude, are to be avoided. Certain zwitterionic buffers such as Bicine [NN-bis-(2-hydroxyethyl)glycine] are satisfactory. Apparent pH effects were found to depend on buffer and protein concentration. It is therefore recommended that as a prelude to future detailed low-temperature biochemical work, appropriate tests with an indicator system should be performed.     

Fluctuation analysis of nonideal shot noise. Application to the neuromuscular junction

Procedures are described for analyzing shot noise and determining the waveform, w(t), mean amplitude, (h), and mean rate of occurrence, (r), of the shots under a variety of nonideal conditions that include: (a) slow, spurious changes in the mean, (b) nonstationary shot rates, (c) nonuniform distribution of shot amplitudes, and (d) nonlinear summation of the shots. The procedures are based upon Rice's (1944. Bell Telephone System Journal. 23: 282-332) extension of Campbell's theorem to the second (variance), lambda 2, third (skew), lambda 3, and fourth, lambda 4, semi-invariants (cumulants) of the noise. It is shown that the spectra of lambda 2 and lambda 3 of nonstationary shot noise contain a set of components that are proportional to (r) and arise from w(t), and a set of components that are independent of (r) and arise from the temporal variations in r(t). Since the latter components are additive and are limited by the bandwidth of r(t), they can be removed by appropriate filters; then (r) and (h) can be determined from the lambda 2 and lambda 3 of the filtered noise. We also show that a factor related to the ratio (lambda 3)2/(lambda 2)(lambda 4) monitors the spread in the distribution of shot amplitudes and can be used to correct the estimates of (r) and (h) for the effects of that spread, if the shape of the distribution is known and if r(t) is stationary. The accuracy of the measurements of lambda 4 is assessed and corrections for the effects of nonlinear summation of lambda 2, lambda 3, and lambda 4 are derived. The procedures give valid results when they are used to analyze shot noise produced by the (linear) summation of simulated miniature endplate potentials, which are generated either at nonstationary rates or with a distribution of amplitudes.     

Fluctuation approach to description of nonideal plasma. I: Equilibrium plasma

A model capable of describing the kinetics of collisional recombination in nonideal plasmas by the methods of molecular dynamics is developed. The dependence of the collisional recombination rate on the coupling parameter is found to differ substantially from the extrapolation of the three-body recombination rate in nonideal plasmas. A sharp decrease in the recombination rate in strongly nonideal plasmas is revealed. As the coupling parameter decreases, collisional recombination transforms into three-body recombination.