Protein assembly at the air-water interface studied by fluorescence microscopy

Protein assembly at the air-water interface (AWI) occurs naturally in many biological processes and provides a method for creating biomaterials. However, the factors that control protein self-assembly at the AWI and the dynamic processes that occur during adsorption are still underexplored. Using fluorescence microscopy, we investigated assembly at the AWI of a model protein, human serum albumin minimally labeled with Texas Red fluorophore. Static and dynamic information was obtained under low subphase concentrations. By varying the solution protein concentration, ionic strength, and redox state, we changed the microstructure of protein assembly at the AWI accordingly. The addition of pluronic surfactant caused phase segregation to occur at the AWI, with fluid surfactant domains and more rigid protein domains revealed by fluorescence recovery after photobleaching experiments. Protein domains were observed to coalesce during this competitive adsorption process.     

Generalized Langevin dynamics of a nanoparticle using a finite element approach: thermostating with correlated noise

A direct numerical simulation (DNS) procedure is employed to study the thermal motion of a nanoparticle in an incompressible Newtonian stationary fluid medium with the generalized Langevin approach. We consider both the Markovian (white noise) and non-Markovian (Ornstein-Uhlenbeck noise and Mittag-Leffler noise) processes. Initial locations of the particle are at various distances from the bounding wall to delineate wall effects. At thermal equilibrium, the numerical results are validated by comparing the calculated translational and rotational temperatures of the particle with those obtained from the equipartition theorem. The nature of the hydrodynamic interactions is verified by comparing the velocity autocorrelation functions and mean square displacements with analytical results. Numerical predictions of wall interactions with the particle in terms of mean square displacements are compared with analytical results. In the non-Markovian Langevin approach, an appropriate choice of colored noise is required to satisfy the power-law decay in the velocity autocorrelation function at long times. The results obtained by using non-Markovian Mittag-Leffler noise simultaneously satisfy the equipartition theorem and the long-time behavior of the hydrodynamic correlations for a range of memory correlation times. The Ornstein-Uhlenbeck process does not provide the appropriate hydrodynamic correlations. Comparing our DNS results to the solution of an one-dimensional generalized Langevin equation, it is observed that where the thermostat adheres to the equipartition theorem, the characteristic memory time in the noise is consistent with the inherent time scale of the memory kernel. The performance of the thermostat with respect to equilibrium and dynamic properties for various noise schemes is discussed.     

Stetige Lösungen linearer Gleichungssysteme

Ohne Zusammenfassung     

Controlling General Polynomial Networks

We consider networks of massive particles connected by non-linear springs. Some particles interact with heat baths at different temperatures, which are modeled as stochastic driving forces. The structure of the network is arbitrary, but the motion of each particle is 1D. For polynomial interactions, we give sufficient conditions for Hörmander’s “bracket condition” to hold, which implies the uniqueness of the steady state (if it exists), as well as the controllability of the associated system in control theory. These conditions are constructive; they are formulated in terms of inequivalence of the forces (modulo translations) and/or conditions on the topology of the connections. We illustrate our results with examples, including “conducting chains” of variable cross-section. This then extends the results for a simple chain obtained in Eckmann et al. in (Commun Math Phys 201:657–697, 1999).