Aggregation rate

Relaxations in the double layers between two interacting particles can retard aggregation rates and cause them to be independent of particle size [101-103]. Discrepancies between theoretical predictions and experimental observations of heterocoagulation between polymer latices, silica particles, and ceria particles [104] have promptetl Mati-jevic and co-workers to propose that the charge on these particles may not be uniformly distributed over the surface [105, 106]. Similar behavior has been seen in the heterocoagulation of cationic and anionic polymer latices [107]. 

For monodisperse partieles, [V + L"][L + L" ] = 4, the aggregation kernel beeomes independent of partiele volume and the aggregation rate is given by... 

Figure 6.25 Dependence of calcium oxalate aggregation rates on power input (Zauner and Jones, 2000a)...

It was shown in Chapter 6 that if the erystals are suffieiently small, for whieh the aggregation rate is determined by the perikinetie meehanism, then the mean partiele volume inereases linearly with time ... 

Collier, A.P. and Hounslow, M.J., 1999. Growth and aggregation rates for calcite and calcium oxalate monohydrate. American Institute of Chemical Engineers Journal, 45, 2298-2305. 

Hounslow, M.J., 1990b. Nucleation, growth and aggregation rates from steady-state experimental data. American Institution of Chemical Engineers Journal, 36, 1748-1753. 

Barber KL, Mesular MM, Kraft GA, Klein WL, Butyrylcholinesterase alters the aggregation rate of -amyloid, Proc Soc Neurosci 72 1172—1178, 1996. 

Two examples where metal ions confer stability or increased activity in proteins are human deoxyribonuclease (rhDNase, Pulmozyme ), and Factor VIII. In the case of rhDNase, Ca2+ ions (up to 100 mM) increased the stability of the enzyme through a specific binding site (64). In fact, the removal of calcium ions from the solution with EGTA caused an increase in deamidation and aggregation. However, this effect was observed only with Ca+2 ions other divalent cations, Mg2+, Mn2+, and Zn2+, were observed to destabilize rhDNase. Similar effects were observed in Factor VIII. Ca2+ and Sr2+ ions stabilized the protein, whereas others such as Mg2+, Mn2+ and Zn2+, Cu2+, and Fe2+ destabilized the enzyme (65). In a separate study with Factor VIII, a significant increase in the aggregation rate was observed in the presence of Al3+ ions (66). The authors note that other excipients like buffer salts are often contaminated with Al3+ ions and illustrate the need to use excipients of appropriate quality in formulated products. 

The aggregation rate is modeled as second-order because dimerization is often the initial step to the formation of aggregates of aggregation number A, with initial dimerization as the rate-limiting step. 

The application of gold nanoparticles for quantitative immunoassays was a departure from common practice. Previously, gold nanoparticles were only used as additives in aggregation assays that involve larger particles to provide color to the aggregates formed. In our immunoassays the aggregation rate... 

In order to take particle-particle interactions into account, a stability ratio W is included which relates the collision kernel /So to the aggregation kernel /3agg. The stability ratio W depends on the interaction potential with interactions additional to the omnipresent van der Waals forces. For Brownian motion as dominant reason for collisions, the stability ratio W can be calculated according to Eq. (6) taken from Fuchs [ 10]. In case of shear as aggregation mechanism, the force dip/dr relative to the friction force should rather be considered instead of the ratio of interaction energy relative to thermal energy. 

If velocity or shear gradients are present and are sufficiently large, the frequency of collisions depends on the volume fraction of solids and the mean velocity gradient. Assuming that sedimentation is slow compared to other collision mechanisms, the overall aggregation rate, -dN/dt, is ... 

A constant reaction kernel is to be expected in the absence of enzyme reaction if the aggregation rate is determined by the Brownian motion of spherical particles which coalesce to form larger spheres. To a first approximation, the increased collisional cross-section is then compensated for by the decrease in diffusion rate (von Smoluchowski,... 

Keywords aluminium salts, hydrolysis products, size, electrokinetic potential, hydration, aggregation rate, salt dosage, pH, alkalinity, ionic strength, water treatment, disinfection, electric sparks... 

The model solutions discussed above were compared with experimental data collected using a laser diffraction particle size analyzer. Hematite was dispersed in solutions at various pH values and moderate ionic strength (0.02 M) such that aggregation rates varied from slow to fast, and aggregation was allowed to occur in quiescent solution. The aggregating dispersion was sampled over time, and data was represented in three dimensions as the change in particle size distributions over time. Figure 10a shows hematite... 

Even though the ability to aggregate to form amyloid fibrils appears to be generic, the propensity to do so under given circumstances can vary dramatically between different sequences [5]. It has proved possible to correlate the relative aggregation rates of a wide range of peptides and proteins with... 

Fig. 13.6. Calculated vs. observed changes in aggregation rates upon mutation. The experimental data relate to mutations of short peptides or natively unfolded proteins including amylin, the A(3-peptide and a-synuclein. The calculated values are determined from an equation involving the changes in just three variables -hydrophobicity, charge and secondary structure propensities - caused by the mutations. The plot shows, for both experimental and calculated data, In (umut/vwt), he., the natural logarithm of the aggregation rate of the mutant umut divided by that of the wild-type molecule vwt. From [36]...

Fig. 13.8. Correlation between expression levels and the measured aggregation rates for a set of human proteins. The aggregation rates represent all the data obtained from a comprehensive search of the amyloid aggregation literature, for studies carried out at pH values between 4.0 and 8.0. The expression levels are estimated from the cellular mRNA concentration and are taken from published databases. The standard deviations of the aggregation rates are reported only in four cases, as these values are generally not available or difficult to extract from the literature. Data for two proteins not involved in any known medical conditions are included in the plot while the other points correspond to proteins that are associated with amyloid diseases. From [4]...

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