Effects of excluded surface area and adsorbate clustering on surface adsorption of proteins. II. Kinetic models

Models for equilibrium surface adsorption of proteins have been recently proposed (Minton, A. P., 2000. Biophys. Chem. 86:239-247) in which negative cooperativity due to area exclusion by adsorbate molecules is compensated to a variable extent by the formation of a heterogeneous population of monolayer surface clusters of adsorbed protein molecules. In the present work this concept is extended to treat the kinetics of protein adsorption. It is postulated that clusters may grow via two distinct kinetic pathways. The first pathway is the diffusion of adsorbed monomer to the edge of a preexisting cluster and subsequent accretion. The second pathway consists of direct deposition of a monomer in solution onto the upper (solution-facing) surface of a preexisting cluster ("piggyback" deposition) and subsequent incorporation into the cluster. Results of calculations of the time course of adsorption, carried out for two different limiting models of cluster structure and energetics, show that in the absence of piggyback deposition, enhancement of the tendency of adsorbate to cluster can reduce, but not eliminate, the negative kinetic cooperativity due to surface area exclusion by adsorbate. Apparently noncooperative (Langmuir-like) and positively cooperative adsorption progress curves, qualitatively similar to those reported in several published experimental studies, require a significant fraction of total adsorption flux through the piggyback deposition pathway. According to the model developed here and in the above-mentioned reference, the formation of surface clusters should be a common concomitant of non-site-specific surface adsorption of proteins, and may provide an important mechanism for assembly of organized "protein machines" in vivo.     

Surface-induced aggregation of ferritin. Kinetics of adsorption to a hydrophobic surface

The adsorption of ferritin from a water solution to a hydrophobic methylised quartz surface was studied by transmission electron microscopy, allowing direct examination of the iron core of the molecule without further preparation. The initial adsorption was seen to result in small clusters of molecules, the number of sites/cm(2) being concentration dependent. The adsorption process continued via cluster growth. The rate of adsorption increased and the process became mass transport limited. The clusters formed initially had low fractal dimensions (D approximately 1.0) and a coordination number, cn of 2.6-2.8, which increased with time. These clusters were abruptly restructured at a coordination number of 3.5, and the apparent rate of adsorption decreased during the reorganisation of the adsorbed layer. Finally, an equilibrium level was reached which was stable for at least 24 h. The distribution of ferritin molecules at equilibrium was in clusters with a fractal dimension of D = 1.14 +/- 0.16 and D= 1.33 +/- 0.08, respectively, for ferritin concentrations in the bulk of 10 and 100 microg/ml. Rinsing of adsorbed ferritin layers with buffered salt solution resulted in a rapid transient condensation of the clusters, but the net dissociation of protein was slow with the rate of dissociation being proportional to the logarithm of time. The condensed clusters were slowly restructured to linear polymers of ferritin molecules with a coordination number of 1.9 after 24 h of rinsing. The dissociation of protein molecules continued slowly for more than 3 days of rinsing. The results of the present study indicate that the rate of protein adsorption and desorption is strongly related to the supramolecular structure of the adsorbed protein film. Dense clusters of protein are not stable and this phenomenon may explain the formation of a dynamic equilibrium in spite of the fact that protein adsorption to a solid phase may appear to be practically irreversible.     

Surface-induced aggregation of ferritin. Concentration dependence of adsorption onto a hydrophobic surface

The isotherm of ferritin adsorption onto a hydrophobic surface was studied by transmission electron microscopy. Adsorbed ferritin was found to be distributed in molecular clusters. The adsorption process was diffusion-rate-limited after 20 h adsorption time at bulk concentrations below 1 mg/1. The clusters formed during the diffusion-rate-limited adsorption had a fractal dimension D approximately 1.0 when averaged over all clusters. The pair distribution function g(r) showed an increased probability of finding nearest neighbours at distances less than 30 nm. The surface concentration of adsorbed ferritin was weakly dependent on the bulk concentration of ferritin in the range 10 mg/1-10 g/1 and the average number of nearest neighbour molecules was constant in this concentration range. The mass distribution of adsorbed ferritin c(r) had a fractal dimension D = 1.8 at a bulk concentration of 10 g/l and a surface concentration corresponding to theta = 0.45 +/- 0.05. The pair correlation function g(r) showed decreasing probability of finding nearest neighbour molecules over long distances as in percolating clusters. The results indicate that ferritin adsorbs strongly to the surface at low surface concentrations and weakly at high surface concentrations. The stability of ferritin adsorption was correlated to the average number of nearest neighbour molecules, indicating a possibility that desorption is a critical supramolecular phenomenon.     

Proton reduction at surface of transition metal nanocatalysts

Catalytic activities of neutral and charged palladium (Pd) nanoparticles are compared for hydrogen reduction half-reaction. In this work the sequential H₂ dissociation from the surface of a Pd₁₃H₂₄ cluster is systematically studied by ab initio molecular dynamics (AIMD) at the density functional theory level. AIMD simulation is launched by preparing initial values of momenta of all nuclei in the model corresponding to a temperature range of 0–1700 K. AIMD simulation provides the trajectories of all the atoms in the cluster. A sequential H₂ desorption up to seven molecules is observed from the cluster surface due to thermal motion of nuclei. Modifications of total charge on the neutral Pd₁₃H₂₄ cluster model are found to affect surface H₂ desorption behaviour. A desorption rate of H₂ molecule on both neutral and charged Pd₁₃H₂₄ clusters is compared to the data of Pt₁₃H₂₄ cluster reported previously. The H₂ desorption energy on all the investigated clusters is also determined. The results reveal that Pd₁₃ cluster presents a higher catalytic activity than Pt₁₃ cluster.     

Total internal reflection/fluorescence photobleaching recovery study of serum albumin adsorption dynamics.

The total internal reflection/fluorescence photobleaching recovery (TIR/FPR) technique (Thompson et al. 1981. Biophys. J. 33:435) is used to study adsorbed bovine serum albumin dynamics at a quartz glass/aqueous buffer interface. Adsorbed fluorescent labeled protein is bleached by a brief flash of the evanescent wave of a focused totally internally reflected laser beam. The rates of adsorption/desorption and surface diffusion determine the subsequent fluorescence recovery. The protein surface concentration is low enough to be proportional to the observed fluorescence and high enough to insure that the observed recovery rates arise mainly from adsorbed rather than bulk protein dynamics. The photobleaching recovery curves for rhodamine-labeled bovine serum albumin reveal both an irreversibly bound state and a multiplicity of reversibly bound states. The relative amount of reversible to irreversible adsorption increases with increasing bulk protein concentration. Since the adsorbed protein concentration appears to be too high to pack into a homogeneous surface monolayer, the wide range of desorption rates possibly results from multiple layers of protein on the surface. Comparison of the fluorescence recovery curves obtained with various focused laser beam widths suggests that some of the reversibly bound bovine serum albumin molecules can surface diffuse. Aside from their relevance to the surface chemistry of blood, these results demonstrate the feasibility of the TIR/FPR technique for measuring molecular dynamics on solid surfaces.     

Nonlinear kinetics of ferritin adsorption.

The adsorption of ferritin at a methylized quartz surface was measured with off-null ellipsometry and transmission electron microscopy. An initial lag-phase was seen, followed by an accelerating adsorption leading to mass transport limitation of the reaction. The rate of adsorption then decreased at a surface concentration far below monolayer coverage, and a continuously decreasing rate of binding was seen. The slope of the binding rate was linear with the logarithm of time (fractal kinetics). The adsorbed ferritin molecules were distributed in clusters as seen by transmission electron microscopy. Clusters grown during the mass transport limited adsorption had crystalline structure at short range and low fractal dimensions (df = 0.89) over long range. Clusters grown during adsorption with fractal kinetics showed random structure at short range and a high fractal dimension df = 1.86 over all ranges. These findings indicate some new important mechanisms responsible for the complex kinetics of macromolecular reactions at solid-liquid interfaces. The results are discussed in relation to recently developed theories of self-organized criticality.     

Direct observation of intraparticle equilibration and the rate-limiting step in adsorption of proteins in chromatographic adsorbents with confocal laser scanning microscopy

The adsorption of different proteins in a single biospecific and hydrophobic adsorbent particle for preparative protein chromatography has been observed directly by confocal laser scanning microscopy as a function of time at a constant bulk concentration c(b). The bulk concentration was in the non-linear part of the adsorption isotherm. At all times the concentration of free protein at the particle surface was almost equal to the bulk content indicating that external mass transfer resistance is not rate limiting for the adsorption under these conditions. Inside the particles a distinct maximum in adsorbed and free protein concentration that moved inside to a distance of approximately 0.2 R (R particle radius) from the particle surface, was observed. This is due to a decreasing solid-phase density and adsorptive capacity in the particle between 0.8 R and R indicating that the fraction of macropores (or void space) is larger in the outer than in the inner part of the adsorbent particles. By increasing the bulk concentration by a factor of 10 the equilibration time was reduced by about the same magnitude. This is in agreement with the concentration dependence of the effective pore diffusion coefficient D(p,eff)=D(p)/[epsilon(p)[1+nK/(K +c)(2)]] derived from the mass conservation relations describing the adsorption process. The time dependence protein adsorption up to approximately 90% of the equilibration value q* could be described by a bilinear free driving force model. The rapid equilibration in the outer part of the particle with a half-life time of approximately 100 s in the studied systems accounted for 0.3-0.4 q*. The slower equilibration with a up to ten times longer half-life time, was the adsorption in the inner part of the particle that outside 0.5 R accounts for 0.5-0.6 q*. These data were compared with literature data for batch adsorption of proteins in biospecific, hydrophobic and ion-exchange adsorbents. They could also be described by a bilinear free driving force model, with about the same quantitative results as obtained for similar conditions in the single particle experiments. The static adsorption parameters, maximum binding site concentration n, and dissociation constant for the protein binding to a binding site K, were determined from Scatchard plots. For the same protein-adsorbent system the plots changed from linear to non-linear with increasing n. This change occurred when the average distance between adjacent binding sites become of the same order of magnitude as the size of the binding site or adsorbed protein. This causes a shielding of free binding sites increasing with n and the concentration of adsorbed protein, yielding a concentration dependence in K. These results show that for a high throughput and rapid adsorption in preparative chromatography, the adsorption step should be carried out in the non-linear part of the adsorption isotherm with concentrations up to c(b) where q*/c(b)>/=10 to obtain high protein recoveries. To avoid tailing due to the flow of adsorbed proteins in the inner part of the particles further into the particles at the start of the desorption, and to speed up desorption rates, protein adsorption in the particle within 0.5 R from the particle center should be avoided. This requires the further development of suitable pellicular particles for preparative protein chromatography that meet this requirement.     

Sequential adsorption of F(ab')(2) and BSA on negatively and positively charged polystyrene latexes

The aim of the present work is to study the sequential adsorption of F(ab')(2) and bovine serum albumin (BSA) molecules adsorbed onto positively and negatively charged polystyrene latexes. Cationic and anionic latexes were prepared by emulsifier-free emulsion polymerization. Adsorptions of F(ab')(2) on both latexes at a low ionic strength and different pHs were performed. The cationic latex showed a higher adsorption of F (ab')(2) molecules over a range of pH, which could be due to the formation of multilayers. Sequential adsorption of anti-CRP F(ab')(2) and monomeric BSA were performed at two different pre-adsorbed F(ab')(2) amounts on both types of latex. Displacement of F(ab')(2) occurred only when the preadsorbed amounts were larger than a certain critical value, which depends on the adsorption pH. A greater displacement of larger preadsorbed amounts might be the result of a weaker contact between the protein molecules and the polystyrene surface. The displacement of F(ab')(2) previously adsorbed onto both latexes occurred due to pH changes, an increase of ionic strength and the presence of BSA molecules. The effect caused by these three factors was studied independently. The main factors in the desorption of F(ab')(2) on the anionic latex are the changes in pH and ionic strength, whereas on the cationic latex the desorption is mainly caused by the increase of the ionic strength and the presence of BSA. The colloidal stability of the immunotatex was improved by BSA adsorption, especially on cationic latex. (c) 1995 John Wiley & Sons, Inc.     

Adsorption of viral matrix protein M1 in acidic medium

Adsorption of viral matrix protein M1 on the self-assembled monolayer of carboxyhexadecanthiol molecules simulating the surface of the cell membrane was studied by surface plasmon resonance refractometry technique. It was shown that in the acidic medium (pH 4.0) the fraction of irreversibly adsorbed protein increases with time. The protein formed a monolayer on the surface in concentration range from 50 to 500 nM. It was found that the amount of the adsorbed protein increased more than 3 times in this range. An important observation is that even at the lowest concentrations of the protein its molecules totally occupied the entire surface of the substrate, and a further protein addition did not lead to its further adsorption. To explain this phenomena, it was suggested that the number of M1 bonds with the surface increases during the adsorption, which leads to spreading of the protein molecules. Apparently, this effect is caused by the intrinsic disorder of the C-domain of the protein. It is hypothesized that the disassembly of the protein-lipid envelope of the influenza virus in the acidic medium does not result from desorption of the M1, but it is caused by the weakening of protein-protein bonds.     

Interaction of fibrinogen with magnetite nanoparticles

The interaction between fibrinogen and magnetite nanoparticles in solution has been studied by the methods of spin labeling, ferromagnetic resonance, dynamic and Rayleigh light scattering. It is shown that protein molecules adsorb on the surface of nanoparticles to form multilayer protein covers. The number of molecules adsorbed on one nanoparticle amounts to ∼65 and the thickness of the adsorption layer amounts to ∼27 nm. Separate nanoparticles with fibrinogen covers (clusters) form aggregates due to interactions of the end D domains of fibrinogen. Under the influence of direct magnetic field, nanoparticles with adsorbed proteins form linear aggregates parallel to the force lines. It is shown that the rate of protein coagulation during the formation of fibrin gel under the action of thrombin on fibrinogen decreases ∼2 times in the presence of magnetite nanoparticles, and the magnitude of the average fiber mass/length ratio grows.     

Measuring surface dynamics of biomolecules by total internal reflection fluorescence with photobleaching recovery or correlation spectroscopy.

The theoretical basis of a new technique for measuring equilibrium adsorption/desorption kinetics and surface diffusion of fluorescent-labeled solute molecules at solid surfaces has been developed. The technique combines total internal reflection fluorescence (TIR) with either fluorescence photobleaching recovery (FPR) or fluorescence correlation spectroscopy (FCS). A laser beam totally internally reflects at a solid/liquid interface; the shallow evanescent field in the liquid excites the fluorescence of surface adsorbed molecules. In TIR/FPR, adsorbed molecules are bleaching by a flash of the focused laser beam; subsequent fluorescence recovery is monitored as bleached molecules exchange with unbleached ones from the solution or surrounding nonilluminated regions of the surface. In TIR/FCS, spontaneous fluorescence fluctuations due to individual molecules entering and leaving a well-defined portion of the evanescent field are autocorrelated. Under appropriate experimental conditions, the rate constants and surface diffusion coefficient can be readily obtained from the TIR/FPR and TIR/FCS curves. In general, the shape of the theoretical TIR/FPR and TIR/FCS curves depends in a complex manner upon the bulk and surface diffusion coefficients, the size of the iluminated or observed region, and the adsorption/desorption/kinetic rate constants. The theory can be applied both to specific binding between immobilized receptors and soluble ligands, and to nonspecific adsorption processes. A discussion of experimental considerations and the application of this technique to the adsorption of serum proteins on quartz may be found in the accompanying paper (Burghardt and Axelrod. 1981. Biophys. J. 33:455).     

Adsorption of Five Model Organic Compounds on a Peat at Different Stages of Drying

Acridine orange (AO), dinitrobenzoic acid (DNB), bromocresol green (BCG), bromophenol blue (BPB), and methylene blue (MB) were chosen as model aromatic compounds of different polarity, charge, and solubility in water to examine the effects of solute properties on hydrophobic adsorption. These compounds show strict structural similarities to some herbicides and other potential xenobiotic pollutants and exhibit distinct absorption maxima in the visible region, which allows for their easy determination. A well-decomposed peat (medisaprist) at four different stages of drying was used to determine compound adsorption/desorption influences based on the degree of hydrophobicity and charge density of an organic surface. Adsorption and desorption isotherms were investigated using the batch equilibration method and determining the concentration of free chemicals by UV-Vis spectrophotometry. AO had a high tendency of adsorption and was strongly sorbed on peat samples that had been air-dried for 12 months. The lower Freundlich coefficient values found for MB when compared with AO at all the drying stages of the peat indicated that electrostatic attraction has a secondary contribution to sorption. On the contrary, the higher energy that must be spent to break solute-solvent interactions in the case of charged or polar molecules is one of the main factors in determining the position of the equilibrium. For a given solute, K_f values varied with the degree of hydrophobicity and the charge density of the surface, but again solute-solvent interactions appear to be much more important in the overall energy balance of hydrophobic pollutants than the electrostatic sorbate-sorbent interactions. A change in the solution pH does not improve the adsorption of the relatively polar DNB molecule, but sorption increases strongly for BCG and BPB when these molecules are in non-dissociated forms. The larger increase in BPB sorption observed on H⁺ saturated peat suggests that the degree of interaction increases with the suppression of the negative charge, but charge repulsion has a small effect in preventing adsorption of molecules bearing hydrophobic groups such as BCG. Desorption results differed depending on the chemical structure of the compound examined. For example, with AO there was no desorption from the more hydrophobic peat surfaces. A negative hysteresis was observed for DNB; the magnitude of hysteresis, evaluated using the ratio of Freundlich coefficients for adsorption and desorption, increased with the drying stage of the sorbent and was larger on oven-dried samples.     

A mathematical model for dynamics of CD40 clustering

Ligand bound-receptors in a signalosome complex trigger signals to determine cellular functions. Upon ligand binding, the ligand–receptor complexes form clusters on cell membrane. Guided by the previous experimental reports on the cluster formation of CD40, a trans membrane receptor for CD40-ligand, we built a minimal model of the receptor cluster formation. In this model, we studied co-operative and non-co-operative clustering of a maximum of four CD40 molecules assuming a positive mediator of clustering such as cholesterol to be present in both cases. We observed that co-operative interactions between CD40 molecules resulted in more of the largest CD40 clusters than that observed with the non-co-operatively interacting CD40 molecules. We performed global sensitivity analysis on the model parameters and the analyses suggested that cholesterol influenced only the initial stage of the co-operatively clustering CD40 molecules but it affects both the initial and the final stages in case of the non-co-operatively clustering CD40 molecules. Robustness analyses revealed that in both co-operative and non-co-operative interactions, the higher order clusters beyond a critical size are more robust with respect to alterations in the environmental parameters including the cholesterol. Thus, the role of co-operative and non-co-operative interactions in environment-influenced receptor clustering is reported for the first time.     

Acetylene hydrogenation on anatase TiO2(101) supported Pd4 cluster: oxygen deficiency effect

Acetylene hydrogenation on both the perfect and oxygen defective anatase TiO(2)(101) surfaces supported Pd(4) cluster has been studied using density functional theory calculations with a Hubbard U correction (DFT + U). The adsorbed Pd(4) cluster on the perfect surface prefers to form a tetrahedral structure, while it likely moves to the oxygen defective site to form a distorted tetrahedral structure by removing a bridging oxygen atom. For the defective surface, it exhibits a stronger ability to capture Pd(4) cluster as charge transfer is significantly performed due to the oxygen deficiency. Moreover, it is found that the oxygen defective surface shows higher activity for acetylene hydrogenation, and the possible reason may lie in the weaker adsorption strength between the Pd cluster and the adsorbed molecules on the defective surface as compared to the case on the perfect surface.     

The adsorption of DNA in the mercury electrolyte interface. 3. Reaction of DNA in the mercury-electrolyte interface

The adsorption of deoxyribonucleic acid in the mercury-electrolyte interface was investigated. The effect of this adsorption on the differential capacity of the electrical double layer at the interface between a stationary mercury drop electrode (HMDE) and a buffered aqueous sodium chloride solution was measured. The dependences of this differential capacity on potential, time, and pH was studied in the presence of native and also of denatured DNA. These results were compared with the adsorption of model compounds and with the general theory of the adsorption of polymers. The structure of the adsorbed DNA molecules corresponds to an alternating arrangement of two-dimensional, totally adsorbed sequences and three-dimensional loops extending into the solution. The adsorbed sequences and loops consist of several segments with a specific free-energy change of adsorption. Essentially this energy determines the distribution of the segments between adsorbed sequences and loops. The absolute value of this energy change per segment is fairly large in the case of negatively charged poly-electrolyte DNA at the weakly positively charged interface near the electrocapillary maximum (ECM). The fraction of totally adsorbed segments is relatively large in this potential region. The more negative the potential the lower is the absolute value of free energy change of adsorption per segment. Under the conditions unfavorable for the adsorption, only a few segments can be adsorbed. Most of the segments of the adsorbed DNA molecules extend into the solution and therefore fairly high interface concentrations can be reached. Thus, the arrangement of DNA molecules in the electrode surface is changed when the potential is altered from values near the ECM to more negative ones. This change should produce the wave on the differential capacity curves at a little more negative potential than that of ECM. At a more negative potential, intermolecular interactions between the loops extending into the solution may occur. The adsorption tendency of the resulting associates is higher than that of the isolated molecules. Therefore the isolated molecules desorb at sufficient negatively charged interface producing a round wave while the associates stay adsorbed. At this potential it is impossible for native DNA to generate associates because they are formed from the isolated molecules. This explains the hysteresis loop of the curves of differential capacity vs. potential by using the HMDE. The desorption of the associates is indicated by a sharp wave at much more negative potential. For denatured DNA the associates arise from the very few isolated adsorbed molecules at this potential; therefore, no hysteresis loop occurs. The association constant of denatured DNA must be much higher than that of the native DNA. The reasons for this are discussed.     

Adsorption and desorption of pentachlorophenol on cells of Mycobacterium chlorophenolicum PCP-1

The sorption behavior of pentachlorophenol (PCP) by the Gram-positive bacterium Mycobacterium chlorophenolicum PCP-1 was quantitatively characterized in this work, with emphasis on the effects of biomass and pH and on the reversibility of PCP adsorption. Both the adsorption and desorption of PCP showed a fast kinetic, reaching an equilibrium in less than 1.5-min mixing under the experimental conditions. For PCP concentrations up to 600 mumol/L no saturation of the adsorption was observed and the adsorption isotherms can be adequately described by the Freundlich equation. The adsorption capacity (q(ads)) of M. chlorophenolicum PCP-1 increased significantly with decreasing biomass in the low concentration range (below 0.5 g/L). The biomass concentration merely affected the capacity constant K of the Freundlich model while the intensity parameter n remained constant. The q(ads) also increased with decreasing pH, particularly at acidic pH values. Again, the pH effect was mainly reflected by the change of K. Based on these results a correlation for q(ads), in which K is a function of both biomass concentration and pH, was obtained to describe the adsorption isotherms at different biomass concentrations and pH values. The desorption of PCP was also found to be strongly affected by pH. At pH 5.4 the adsorption was almost completely irreversible, while a nearly complete desorption was obtained at pH 7. The effect of pH on the sorption behavior was found to be related to the ionization of PCP. The irreversibly adsorbed PCP is a strict function of concentration of undissociated PCP, while the reversibly adsorbed PCP correlates well with the concentration of ionic PCP. The irreversible adsorption has a much higher adsorption capacity than the reversible adsorption. These findings led to the derivation of a semimechanistic model that satisfactorily describes the sorption of PCP by M. chlorophenolicum. The results obtained also give clues to the patterns and mechanism(s) of PCP adsorption by microbial cells. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 55: 480-489, 1997.     

Computer simulation of surface-induced aggregation of ferritin.

Models are presented describing the transient mass-transport limited adsorption and cluster growth of ferritin at a solid surface. Computer simulations are carried out on a hexagonal lattice using a computer model that can be characterized as a two-dimensional stochastic cellular automaton allowing different rules regarding association, lateral interaction and dissociation to be incorporated in the model. The fractal dimensions of individual clusters were extracted from simulated aggregates and for similar rules found to be consistent with literature values on reversible diffusion-limited aggregation in two dimensions. The distribution of clusters versus free surface were shown to be affected by neighbor-dependent association probability. Low fractal dimension clusters were generated by a combination of strong lateral cohesion and neighbor-dependent dissociation to the bulk. By comparing computer simulated aggregation to experimental electron micrographs of adsorbed ferritin layers it is suggested that neighbor-dependent association, neighbor-dependent dissociation and lateral interactions are important factors in the complex dynamics of adsorbed protein layers.     

Kinetics of protein adsorption and desorption on surfaces with grafted polymers

The kinetics of protein adsorption are studied using a generalized diffusion approach which shows that the time-determining step in the adsorption is the crossing of the kinetic barrier presented by the polymers and already adsorbed proteins. The potential of mean-force between the adsorbing protein and the polymer-protein surface changes as a function of time due to the deformation of the polymer layers as the proteins adsorb. Furthermore, the range and strength of the repulsive interaction felt by the approaching proteins increases with grafted polymer molecular weight and surface coverage. The effect of molecular weight on the kinetics is very complex and different than its role on the equilibrium adsorption isotherms. The very large kinetic barriers make the timescale for the adsorption process very long and the computational effort increases with time, thus, an approximate kinetic approach is developed. The kinetic theory is based on the knowledge that the time-determining step is crossing the potential-of-mean-force barrier. Kinetic equations for two states (adsorbed and bulk) are written where the kinetic coefficients are the product of the Boltzmann factor for the free energy of adsorption (desorption) multiplied by a preexponential factor determined from a Kramers-like theory. The predictions from the kinetic approach are in excellent quantitative agreement with the full diffusion equation solutions demonstrating that the two most important physical processes are the crossing of the barrier and the changes in the barrier with time due to the deformation of the polymer layer as the proteins adsorb/desorb. The kinetic coefficients can be calculated a priori allowing for systematic calculations over very long timescales. It is found that, in many cases where the equilibrium adsorption shows a finite value, the kinetics of the process is so slow that the experimental system will show no adsorption. This effect is particularly important at high grafted polymer surface coverage. The construction of guidelines for molecular weight/surface coverage necessary for kinetic prevention of protein adsorption in a desired timescale is shown. The time-dependent desorption is also studied by modeling how adsorbed proteins leave the surface when in contact with a pure water solution. It is found that the kinetics of desorption are very slow and depend in a nonmonotonic way in the polymer chain length. When the polymer layer thickness is shorter than the size of the protein, increasing polymer chain length, at fixed surface coverage, makes the desorption process faster. For polymer layers with thickness larger than the protein size, increases in molecular weight results in a longer time for desorption. This is due to the grafted polymers trapping the adsorbed proteins and slowing down the desorption process. These results offer a possible explanation to some experimental data on adsorption. Limitations and extension of the developed approaches for practical applications are discussed.     

Staphylococcus aureus-Fibronectin Interactions with and without Fibronectin-Binding Proteins and Their Role in Adhesion and Desorption

Adhesion and residence-time-dependent desorption of two Staphylococcus aureus strains with and without fibronectin (Fn) binding proteins (FnBPs) on Fn-coated glass were compared under flow conditions. To obtain a better understanding of the role of Fn-FnBP binding, the adsorption enthalpies of Fn with staphylococcal cell surfaces were determined using isothermal titration calorimetry (ITC). Interaction forces between staphylococci and Fn coatings were measured using atomic force microscopy (AFM). The strain with FnBPs adhered faster and initially stronger to an Fn coating than the strain without FnBPs, and its Fn adsorption enthalpies were higher. The initial desorption was high for both strains but decreased substantially within 2 s. These time scales of staphylococcal bond ageing were confirmed by AFM adhesion force measurement. After exposure of either Fn coating or staphylococcal cell surfaces to bovine serum albumin (BSA), the adhesion of both strains to Fn coatings was reduced, suggesting that BSA suppresses not only nonspecific but also specific Fn-FnBP interactions. Adhesion forces and adsorption enthalpies were only slightly affected by BSA adsorption. This implies that under the mild contact conditions of convective diffusion in a flow chamber, adsorbed BSA prevents specific interactions but does allow forced Fn-FnBP binding during AFM or stirring in ITC. The bond strength energies calculated from retraction force-distance curves from AFM were orders of magnitude higher than those calculated from desorption data, confirming that a penetrating Fn-coated AFM tip probes multiple adhesins in the outermost cell surface that remain hidden during mild landing of an organism on an Fn-coated substratum, like that during convective diffusional flow.     

Thermodynamic model of the formation of bridges between nucleic acid molecules in a liquid crystal]

A thermodynamic model of the formation of bridges consisting of alternating daunomycin molecules and copper ions and connecting neighboring nucleic acid molecules in a particle of a liquid crystalline dispersion was constructed. The model is based on the conception that ligands are adsorbed on lattices of reaction centers which are formed in a liquid crystal at a particular spatial arrangement of adjacent nucleic acid molecules (phasing). Equations were derived that describe typical experimentally obtained S-shaped dependences of bridge concentration on the concentration of copper ions and daunomycin molecules in an initial solution. It was shown that dependences of this kind take place in two variants of the adsorption model: when the binding of daunomycin with adjacent nucleic acid molecules is considered to be independent on the formation of bridges and when bridges compete with single daunomycin molecules for the sites on adjacent nucleic acid molecules.