Dialysis kinetics measurements have been made to study the effect of ionic strength on the dimerization of lysozyme in acidic solutions that lead to the growth of tetragonal lysozyme crystals. Using glutaraldehyde cross-linked dimers of lysozyme, we have determined that both monomers and dimers can escape from 25,000 molecular weight cutoff dialysis membranes with velocity constants of 5.1 x 10(-7) and 1.0 x 10(-7) s(-1) for the monomer and dimer species, respectively. The flux from 25K MWCO membranes has been measured for lysozyme in pH 4.0 buffered solutions of 1, 3, 4, 5, and 7% NaCl over a wide range of protein concentrations. Assuming that dimerization is the first step in crystallization, a simple monomer to dimer equilibrium was used to model the flux rates. Dimerization constants calculated at low protein concentrations were 265, 750, 1212, and 7879 M(-1) for 3, 4, 5, and 7% NaCl, respectively. These values indicate that dimerization increases with the ionic strength of the solution suggesting that aggregation is moderated by electrostatic interactions. At high protein concentrations and high supersaturation, the dimerization model does not describe the data well. However, the Li model that uses a pathway of monomer <-> dimer <-> tetramer <-> octamer <-> 16-mer fits the measured flux data remarkably well suggesting the presence of higher order aggregates in crystallizing solutions.
Glutaraldehyde cross-linking followed by sodium dodecyl sulfate polyacrylamide gel electrophoresis has been used to detect aggregates of isozyme in solutions which lead to crystals. In solutions of varying NaCl content, the number of aggregates was found to be related to the ionic strength of the solution. Solutions of 1% NaCl, pH 4.0 were monomeric while those containing 7-15% NaCl, pH 4.0 were shown to be as much as 36% aggregated and 64% monomeric. The aggregates detected at the highest salt and protein concentration studied were composed of dimers, trimers and tetramers. The aggregates increased by addition of single units suggesting the aggregation pathway to be that of monomer addition. The kinetics of the cross-linking reaction were slow preventing a study of either the time dependence of aggregation or the effect of temperature on aggregate distributions. Comparison of the total aggregate concentrations for NaCl and Na(2)SO(4) showed that the concentration of aggregates was related to the ionic strength of the solution suggesting that in both crystallization and precipitation, electrostatic shielding of like-charged protein molecules is necessary in order for aggregation to occur.
The authors have adapted a dialysis technique which provides aggregate concentrations of protein molecules in solutions which lead to crystal growth. In dialysis, the flux across a semipermeable membrane is directly proportional to the concentration of the diffusible solute inside the bag provided that the solute concentration in the bulk solution is infinitely dilute. Using membranes of varying porosity, the concentrations of different size solutes can be measured by measuring the flux rate across the membrane. They have used this technique to independently measure the concentrations of monomers, dimers, trimers and higher aggregates of lysozyme in both 1% NaCl and 3% NaCl (0.1 M NaAc, pH4) using 25 K and 50 K molecular weight cut-off membranes. They compare these concentration profiles with (110) face growth rate data under the same conditions.
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