Michał Cieśla

Mechanisms of Fibrinogen Adsorption at Solid Substrates

Adsorption of fibrinogen, modeled as a linear chain of touching beads of various sizes, was theoretically studied using the random sequential adsorption (RSA) model. The adsorption process was assumed to consist of two steps: (i) formation of an irreversibly bound fibrinogen monolayer under the side-on orientation, which is independent of the bulk protein concentration and (ii) formation of the reversibly bound, end-on monolayer, whose coverage was dependent on the bulk concentration. Calculation based on the RSA model showed that the maximum surface concentration of the end-on (reversible) monolayer equals N(⊥∞) = 6.13 × 10(3) μm(-2) which is much larger than the previously found value for the side-on (irreversible) monolayer, equal to N(∞) = 2.27 × 10(3) μm(-2). Hence, the maximum surface concentration of fibrinogen in both orientations is determined to be 8.40 × 10(3) μm(-2) corresponding to the protein coverage of 5.70 mg m(-2) assuming 20% hydration. Additionally, the surface blocking function (ASF) was determined for the end-on fibrinogen adsorption, approximated for the entire range of coverage by the interpolating polynomial. For the coverage approaching the jamming limit, the surface blocking function (ASF) was shown to vanish proportionally to (θ(⊥∞) - θ(⊥))(2). These calculation allowed one to theoretically predict adsorption isotherms for the end-on regime of fibrinogen and adsorption kinetics under various transport conditions (diffusion and convection). Using these theoretical results, a quantitative interpretation of experimental data obtained by TIRF and ellipsometry was successfully performed. The equilibrium adsorption constant for the end-on adsorption regime was found to be 8.04 × 10(-3) m. On the basis of this value, the depth of the adsorption energy minimum, equal to -17.4 kT, was predicted, which corresponds to ΔG = -41.8 kJ mol(-1). This is in accordance with adsorption energy derived as the sum of the van der Waals and electrostatic interactions. Besides having significance for predicting fibrinogen adsorption, theoretical results derived in this work also have implications for basic science providing information on mechanisms of anisotropic protein molecule adsorption on heterogeneous surfaces.

Kinetics of Fibrinogen Adsorption on Hydrophilic Substrates

Irreversible side-on adsorption of fibrinogen, modeled as a linear chain of touching beads of various size, was studied theoretically using the random sequential adsorption (RSA) model. Numerical simulation of the Monte Carlo type enabled one to determine the dependence of the surface blocking function (available surface function) on the protein coverage. These numerical results were interpolated using analytical functions based on a polynomial expansion. The dependence of the jamming coverage on the size of the simulation area was also determined. By an extrapolation of these results to the infinite area size, the maximum surface concentration of fibrinogen for the side-on adsorption was determined to be 2.26 x 10(3) microm(-2). This corresponds to a jamming coverage theta(infinity) of 0.29. It was shown that the blocking function can well be approximated in the limit of high coverage by the dependence C(theta(infinity) - theta)(4). Using this interpolating expression, the kinetics of fibrinogen adsorption under convection and diffusion transport conditions were evaluated for various bulk concentrations of the protein. These kinetic curves were derived by numerically solving the mass transport equation in the bulk with the blocking function used as a nonlinear boundary condition at the interface. It was shown that our theoretical results are in agreement with experimental kinetic data obtained by AFM, ellipsometry, and other techniques for hydrophilic surfaces in the limit of low bulk fibrinogen concentration.

Human fibrinogen monolayers on latex particles: role of ionic strength.

The adsorption of human serum fibrinogen on polystyrene latex particles was studied using the microelectrophoretic and concentration depletion methods. Measurements were carried out for pH 3.5 and an ionic strength range of 10(-3) to 0.15 M NaCl. The electrophoretic mobility of latex was determined as a function of the amount of adsorbed fibrinogen (surface concentration). A monotonic increase in the electrophoretic mobility (zeta potential) of the latex was observed, indicating a significant adsorption of fibrinogen on latex for all ionic strengths. No changes in the latex mobility were observed for prolonged time periods, suggesting the irreversibility of fibrinogen adsorption. The maximum coverage of fibrinogen on latex particles was precisely determined using the depletion method. The residual protein concentration after making contact with latex particles was determined by electrokinetic measurements and AFM imaging where the surface coverage of fibrinogen on mica was quantitatively determined. The maximum fibrinogen coverage increased monotonically with ionic strength from 1.8 mg m(-2) for 10(-3) M NaCl to 3.6 mg m(-2) for 0.15 M NaCl. The increase in the maximum coverage was interpreted in terms of the reduced electrostatic repulsion among adsorbed fibrinogen molecules. The experimental data agree with theoretical simulations made by assuming a 3D unoriented adsorption of fibrinogen. The stability of fibrinogen monolayers on latex was also determined in ionic strength cycling experiments. It was revealed that cyclic variations in NaCl concentration between 10(-3) and 0.15 M induced no changes in the latex electrophoretic mobility, suggesting that there were no irreversible molecule orientation changes in the monolayers. On the basis of these experimental data, a robust procedure of preparing fibrinogen monolayers on latex particles of well-controlled coverage was proposed.

Human Fibrinogen Adsorption on Positively Charged Latex Particles

Fibrinogen (Fb) adsorption on positively charged latex particles (average diameter of 800 nm) was studied using the microelectrophoretic and the concentration depletion methods based on AFM imaging. Monolayers on latex were adsorbed from diluted bulk solutions at pH 7.4 and an ionic strength in the range of 10(-3) to 0.15 M where fibrinogen molecules exhibited an average negative charge. The electrophoretic mobility of the latex after controlled fibrinogen adsorption was systematically measured. A monotonic decrease in the electrophoretic mobility of fibrinogen-covered latex was observed for all ionic strengths. The results of these experiments were interpreted according to the three-dimensional electrokinetic model. It was also determined using the concentration depletion method that fibrinogen adsorption was irreversible and the maximum coverage was equal to 0.6 mg m(-2) for ionic strength 10(-3) M and 1.3 mg m(-2) for ionic strength 0.15 M. The increase of the maximum coverage was confirmed by theoretical modeling based on the random sequential adsorption approach. Paradoxically, the maximum coverage of fibrinogen on positively charged latex particles was more than two times lower than the maximum coverage obtained for negative latex particles (3.2 mg m(-2)) at pH 7.4 and ionic strength of 0.15 M. This was interpreted as a result of the side-on adsorption of fibrinogen molecules with their negatively charged core attached to the positively charged latex surface. The stability and acid base properties of fibrinogen monolayers on latex were also determined in pH cycling experiments where it was observed that there were no irreversible conformational changes in the fibrinogen monolayers. Additionally, the zeta potential of monolayers was more positive than the zeta potential of fibrinogen in the bulk, which proves a heterogeneous charge distribution. These experimental data reveal a new, side-on adsorption mechanism of fibrinogen on positively charged surfaces and confirmed the decisive role of electrostatic interactions in this process.

Mechanisms of fibrinogen adsorption at solid substrates at lower pH.

Adsorption of fibrinogen was theoretically studied using the three-dimensional random sequential adsorption (RSA) model. Fibrinogen molecule shape was approximated by the bead model considering the presence of flexible side arms. Various cases were considered inter alia, the side-on adsorption mechanisms and the simultaneous side-on/end-on adsorption mechanism. The latter mechanisms is pertinent to fibrinogen adsorption at lower pH (below isoelectric point of 5.8) where the entire molecule is positively charged. Extensive calculations enabled one to determine the jamming surface concentration (coverage) of molecules adsorbed under the side-on and end-on orientations as well as the total coverage. For the simultaneous side-on/end-on model the maximum surface concentration was 7.29 × 10(3) μm(-2) corresponding to the protein coverage of 4.12 mg m(-2) (without considering hydration). Additionally, the surface blocking functions for different adsorption regimes were determined and analytically approximated for the entire range of coverage by the interpolating polynomials. Using these blocking functions, fibrinogen adsorption kinetics for diffusion controlled transport conditions was evaluated. Comparison of these theoretical results with experimental data was made. It was demonstrated that the simultaneous side-on/end-on model properly reflects the maximum coverage of fibrinogen adsorbed on latex particles determined via the electrokinetic (electrophoretic mobility) and AFM measurements. Also, streaming potential measurements of fibrinogen adsorption kinetics on mica were successfully interpreted in terms of this model. The theoretical results derived in this work have implications for basic science providing information on mechanisms of anisotropic protein adsorption.

Continuum random sequential adsorption of polymer on a flat and homogeneous surface.

Random sequential adsorption (RSA) of polymer, modeled as a chain of identical spheres, is systematically studied. In order to control precisely anisotropy and number of degrees of freedom, two different kinds of polymers are used. In the first one, monomers are placed along a straight line, whereas in the second, relative orientations of particles are random. Such polymers fill a flat homogeneous surface randomly. The paper focuses on maximal random coverage ratio and adsorption kinetics dependence on polymer size, shape anisotropy, and numbers of degrees of freedom. Obtained results were discussed and compared with other numerical experiments and theoretical predictions.

Synchronization in the presence of memory

We study the effect of memory on synchronization of identical chaotic systems driven by common external noises. Our examples show that while in general the synchronization transition becomes more difficult to meet when the memory range increases, for intermediate ranges the synchronization tendency of systems can be enhanced. Generally the synchronization transition is found to depend on the memory profile and range and the ratio of noise strength to memory amplitude, which indicates a possibility of optimizing synchronization by memory. We also point out a close link between dynamics with memory and noise, and recently discovered synchronizing properties of networks with delayed interactions.

Modelling of interacting dimer adsorption

Adsorption of dimers is modelled using random sequential adsorption algorithm. The interaction between molecules is given by screened electrostatic potential. The paper focuses on the properties of adsorbed monolayers as well as the dependence of adsorption kinetics on interaction range. We designate random maximal coverage ratios, density autocorrelations and orientational ordering inside layers. Moreover the detailed analysis of adsorption kinetics is presented including a discussion of Feders law validity and new numerical method for modelling diffusion driven adsorption. Results of numerical simulations are compared with experimental data obtained previously for insulin dimers.

Random packing of spheres in Menger sponge.

Random packing of spheres inside fractal collectors of dimension 2 < d < 3 is studied numerically using Random Sequential Adsorption (RSA) algorithm. The paper focuses mainly on the measurement of random packing saturation limit. Additionally, scaling properties of density autocorrelations in the obtained packing are analyzed. The RSA kinetics coefficients are also measured. Obtained results allow to test phenomenological relation between random packing saturation density and collector dimension. Additionally, performed simulations together with previously obtained results confirm that, in general, the known dimensional relations are obeyed by systems having non-integer dimension, at least for d < 3.

Fibrinogen adsorption mechanisms at the gold substrate revealed by QCM-D measurements and RSA modeling

Adsorption kinetics of fibrinogen at a gold substrate at various pHs was thoroughly studied using the QCM-D method. The experimental were interpreted in terms of theoretical calculations performed according to the random sequential adsorption model (RSA). In this way, the hydration functions and water factors of fibrinogen monolayers were quantitatively evaluated at various pHs. It was revealed that for the lower range of fibrinogen coverage the hydration function were considerably lower than previously obtained for the silica sensor [33]. The lower hydration of fibrinogen monolayers on the gold sensor was attributed to its higher roughness. However, for higher fibrinogen coverage the hydration functions for both sensors became identical exhibiting an universal behavior. By using the hydration functions, the fibrinogen adsorption/desorption runs derived from QCM-D measurements were converted to the Γd vs. the time relationships. This allowed to precisely determine the maximum coverage that varied between 1.6mgm(-2) at pH 3.5 and 4.5mgm(-2) at pH 7.4 (for ionic strength of 0.15M). These results agree with theoretical eRSA modeling and previous experimental data derived by using ellipsometry, OWLS and TIRF. Various fibrinogen adsorption mechanisms were revealed by exploiting the maximum coverage data. These results allow one to develop a method for preparing fibrinogen monolayers of well-controlled coverage and molecule orientation.