Lysozyme Mutual Diffusion in Solutions Crowded by Poly(ethylene glycol)

Diffusiophoresis of a Nonionic Micelle in Salt Gradients; Roles of Preferential Hydration and Salt-Induced Surfactant Aggregation

Diffusiophoresis is the migration of a colloidal particle in water driven by concentration gradients of cosolutes such as salts. We have experimentally characterized the diffusiophoresis of tyloxapol micelles in the presence of MgSO4, a strong salting-out agent. Specifically, we determined the multicomponent-diffusion coefficients using Rayleigh interferometry, cloud points, and dynamic-light-scattering diffusion coefficients on the ternary tyloxapol-MgSO4-water system at 25 °C. Our experimental results show that micelle diffusiophoresis occurs from a high to a low salt concentration (positive diffusiophoresis). Moreover, our data were used to characterize the effect of salt concentration on micelle size and salt osmotic diffusion, which occurs from a high to a low surfactant concentration. Although micelle diffusiophoresis can be attributed to the preferential hydration of the polyethylene glycol surface groups, salting-out salts also promote an increase in the size of micellar aggregates, ultimately leading to phase separation at high salt concentration. This complicates diffusiophoresis description, as it is not clear how salt-induced surfactant aggregation contributes to micelle diffusiophoresis. We, therefore, developed a two-state aggregation model that successfully describes the observed effect of salt concentration on the size of tyloxapol micelles, in the case of MgSO4 and the previously reported case of Na2SO4. Our model was then used to theoretically evaluate the contribution of salt-induced aggregation to diffusiophoresis. Our analysis indicates that salt-induced aggregation promotes micelle diffusiophoresis from a low to a high salt concentration (negative diffusiophoresis). However, we also determined that this mechanism marginally contributes to overall diffusiophoresis, implying that preferential hydration is the main mechanism causing micelle diffusiophoresis. Our results suggest that sulfate salts may be exploited to induce the diffusiophoresis of PEG-functionalized particles such as micelles, with potential applications to microfluidics, enhanced oil recovery, and controlled-release technologies.

Exhibiting cross-diffusion-induced patterns for reaction-diffusion systems on evolving domains and surfaces

The aim of this manuscript is to present for the first time the application of the finite element method for solving reaction-diffusion systems with cross-diffusion on continuously evolving domains and surfaces. Furthermore we present pattern formation generated by the reaction-diffusion system with cross-diffusion on evolving domains and surfaces. A two-component reaction-diffusion system with linear cross-diffusion in both u and v is presented. The finite element method is based on the approximation of the domain or surface by a triangulated domain or surface consisting of a union of triangles. For surfaces, the vertices of the triangulation lie on the continuous surface. A finite element space of functions is then defined by taking the continuous functions which are linear affine on each simplex of the triangulated domain or surface. To demonstrate the role of cross-diffusion to the theory of pattern formation, we compute patterns with model kinetic parameter values that belong only to the cross-diffusion parameter space; these do not belong to the standard parameter space for classical reaction-diffusion systems. Numerical results exhibited show the robustness, flexibility, versatility, and generality of our methodology; the methodology can deal with complicated evolution laws of the domain and surface, and these include uniform isotropic and anisotropic growth profiles as well as those profiles driven by chemical concentrations residing in the domain or on the surface.

Cross-diffusion-driven instability for reaction-diffusion systems: analysis and simulations

By introducing linear cross-diffusion for a two-component reaction-diffusion system with activator-depleted reaction kinetics (Gierer and Meinhardt, Kybernetik 12:30-39, 1972; Prigogine and Lefever, J Chem Phys 48:1695-1700, 1968; Schnakenberg, J Theor Biol 81:389-400, 1979), we derive cross-diffusion-driven instability conditions and show that they are a generalisation of the classical diffusion-driven instability conditions in the absence of cross-diffusion. Our most revealing result is that, in contrast to the classical reaction-diffusion systems without cross-diffusion, it is no longer necessary to enforce that one of the species diffuse much faster than the other. Furthermore, it is no longer necessary to have an activator-inhibitor mechanism as premises for pattern formation, activator-activator, inhibitor-inhibitor reaction kinetics as well as short-range inhibition and long-range activation all have the potential of giving rise to cross-diffusion-driven instability. To support our theoretical findings, we compute cross-diffusion induced parameter spaces and demonstrate similarities and differences to those obtained using standard reaction-diffusion theory. Finite element numerical simulations on planary square domains are presented to back-up theoretical predictions. For the numerical simulations presented, we choose parameter values from and outside the classical Turing diffusively-driven instability space; outside, these are chosen to belong to cross-diffusively-driven instability parameter spaces. Our numerical experiments validate our theoretical predictions that parameter spaces induced by cross-diffusion in both the [Formula: see text] and [Formula: see text] components of the reaction-diffusion system are substantially larger and different from those without cross-diffusion. Furthermore, the parameter spaces without cross-diffusion are sub-spaces of the cross-diffusion induced parameter spaces. Our results allow experimentalists to have a wider range of parameter spaces from which to select reaction kinetic parameter values that will give rise to spatial patterning in the presence of cross-diffusion.

Analysis of main- and cross-term diffusion coefficients in bile salt mixtures

Mutual diffusion coefficients have been measured for several average compositions of the system sodium cholate-sodium deoxycholate-water at 25 °C. The experiments have been grouped in different sets having constant concentration of one component and variable concentration of the other one. Following this approach, it has been found that the trends of the main- and cross-term diffusion coefficients can be interpreted on the basis of the diffusion and equilibrium results of similar experiments performed on the two binary systems sodium cholate-water and sodium deoxycholate-water. Implications of the presented results in the transport of lipids operated by bile salt aggregates are mentioned. The method proposed in this work, able to connect the diffusivities of an n-component system to those of the related n-1 subsystems, can be extended to obtain qualitative prediction on the diffusion coefficient trends for mixtures of other surfactants, of both industrial and biological interest.

Modulation of enzyme-substrate selectivity using tetraethylene glycol functionalized gold nanoparticles

Tetraethylene glycol (TEG) functionalized gold nanoparticles with 2 nm core diameters (AuTEG) enhance alpha-chymotrypsin (ChT) enzyme activity in a substrate-selective fashion. We explored the hydrolysis of four different substrates and observed a marked increase in activity with the most hydrophobic substrate N-succinyl-alanine-alanine-proline-phenylalanine- p-nitroanilide (TP), while the other substrates remain virtually unaffected by the AuTEG 'crowding effect' in solution. The enhancement in catalysis is indicated by an increase in K(cat)/K(m) as obtained from Lineweaver-Burk analysis and we hypothesize it to arise from a macromolecular crowding effect analogous to that observed with high molecular weight poly(ethylene glycol) (PEG) polymers.

Comparison between Protein−Polyethylene Glycol (PEG) Interactions and the Effect of PEG on Protein−Protein Interactions Using the Liquid−Liquid Phase Transition

Phase transitions of protein aqueous solutions are important for protein crystallization and biomaterials science in general. One source of thermodynamic complexity in protein solutions and their phase transitions is the required presence of additives such as polyethylene glycol (PEG). To investigate the effects of PEG on the thermodynamic behavior of protein solutions, we report measurements on the liquid-liquid phase separation (LLPS) of aqueous bovine serum albumin (BSA) in the presence of relatively small amounts of PEG with an average molecular weight of 1450 g/mol (PEG1450) as a model system. We experimentally characterize two thermodynamically independent properties of the phase boundary: (1) the effect of PEG1450 concentration on the LLPS temperature, (2) BSA/PEG1450 partitioning in the two liquid coexisting phases. We then use a thermodynamic perturbation theory to relate the first property to the effect of PEG concentration on protein-protein interactions and the second property to protein-PEG interactions. As criteria to determine the accuracy of a microscopic model, we examine the model's ability to describe both experimental thermodynamic properties. We believe that the parallel examination of these two properties is a valuable tool for verifying the validity of existing models and for developing more accurate ones. For our system, we have found that a depletion-interaction model satisfactorily explains both protein-PEG interactions and the effect of PEG concentration on protein-protein interactions. Finally, due to the general importance of LLPS, we will experimentally show that protein-PEG-buffer mixtures can exhibit two distinct types of liquid-liquid phase transitions.