Synchronization of metabolic oscillations:two cells and ensembles of adsorbed cells

We treat synchronization of metabolic oscillations in two cellsand in ensembles of cells adsorbed at the liquid-solid interface.(i) Synchronization of oscillations in two cells is assumedto occur via perturbation of the metabolite concentration nearone cell due to the metabolite diffusion flux from another cell.This direct channel of synchronization may be important ifthe distance between two cells is comparable with the cell diameter.The corresponding coupling coefficient is found to be proportionalto the metabolite diffusion coefficient and inversely proportionalto the cell radius and the distance between the cells.(ii) In the case of ensembles of adsorbed cells, synchronizationof oscillations is considered to be indirect, i.e., to occur viathe metabolite concentration formed outside the cells nearthe interface due to metabolite diffusion from the cells. We havederived a general integral equation relating the metaboliteconcentration near the interface with concentrations inside the cells.PACS: 82.37.-j, 82.40.Bj.

Interaction of virions with membrane glycolipids

Cellular membranes contain various lipids including glycolipids (GLs). The hydrophilic head groups of GLs extend from the membrane into the aqueous environment outside the cell where they act as recognition sites for specific interactions. The first steps of interaction of virions with cells often include contacts with GLs. To clarify the details of such contacts, we have used the total internal reflection fluorescence microscopy to explore the interaction of individual unlabelled virus-like particles (or, more specifically, norovirus protein capsids), which are firmly bound to a lipid bilayer, and fluorescent vesicles containing glycosphingolipids (these lipids form a subclass of GLs). The corresponding binding kinetics were earlier found to be kinetically limited, while the detachment kinetics were logarithmic over a wide range of time. Here, the detachment rate is observed to dramatically decrease with increasing concentration of glycosphingolipids from 1% to 8%. This effect has been analytically explained by using a generic model describing the statistics of bonds in the contact area between a virion and a lipid membrane. Among other factors, the model takes the formation of GL domains into account. Our analysis indicates that in the system under consideration, such domains, if present, have a characteristic size smaller than the contact area between the vesicle and the virus-like particle.

Interaction of single viruslike particles with vesicles containing glycosphingolipids

Glycosphingolipids are involved in the first steps of virus-cell interaction, where they mediate specific recognition of the host cell membrane. We have employed total-internal-reflection fluorescence microscopy to explore the interaction kinetics between individual unlabeled noroviruslike particles, which are attached to a glycosphingolipid-containing lipid bilayer, and fluorescent vesicles containing different types and concentrations of glycosphingolipids. Under association equilibrium, the vesicle-binding rate is found to be kinetically limited, yielding information on the corresponding activation energy. The dissociation kinetics are logarithmic over a wide range of time. The latter is explained by the vesicle-size-related distribution of the dissociation activation energy. The biological, pharmaceutical, and diagnostic relevance of the study is briefly discussed.

Diffusion-limited kinetics of adsorption of biomolecules on supported nanoparticles

We derive general equations describing the diffusion-limited kinetics of irreversible adsorption of biomolecules on nanoparticles, fabricated on a flat surface, in the case of no hydrodynamic flow in the solution. Under such conditions, the gradients in the concentration of biomolecules occur near the surface, while in more remote regions the gradients may or may not be significant depending on the surface concentration and size of nanoparticles and the bulk concentration of biomolecules. The equations obtained make it possible to understand the conditions of realization of various regimes of adsorption.

Simulation of methane oxidation on Pt

The authors present a generic model of CH4 oxidation on Pt with the emphasis on the role of surface-oxide formation. The latter process is treated in terms of the theory of first-order phase transitions. The corresponding Monte Carlo simulations indicate that the surface-oxide formation may result in stepwise features in the reaction kinetics. Specifically, with increasing CH4 pressure and/or decreasing O2 pressure, the model predicts a sharp transition from a low-reactive state with the surface completely covered by oxide to a high-reactive state with the surface covered by chemisorbed oxygen. In the former case, the reaction is first order in CH4 and zero order in O2. In the latter case, both reaction orders are positive. All these findings help in interpreting available experiments.

Enhancement of protein adsorption induced by surface roughness

Using quartz crystal microbalance with dissipation and ellipsometry, we show that during adsorption of fibrinogen on evaporated tantalum films the saturation uptake increases with increasing root-mean-square roughness (from 2.0 to 32.9 nm) beyond the accompanying increase in surface area. This increase is attributed to a change in the geometrical arrangement of the fibrinogen molecules on the surface. For comparison, the adsorption of a nearly globular protein, bovine serum albumin, was studied as well. In this case, the adsorption was less influenced by the roughness. Simple Monte Carlo simulations taking into account surface roughness and the anisotropic shape of fibrinogen reproduce the experimentally observed trend.

Imaging and manipulation of adsorbed lipid vesicles by an AFM tip: Experiment and Monte Carlo simulations

Single lipid vesicles adsorbed on SiO(2) were manipulated using an atomic force microscope (AFM) operated in contact mode. For large force setpoints, single vesicles were either pushed sideways or ruptured by the tip, depending on the tip type (sharp or blunt) used, while for small force setpoints the vesicles were imaged by the tip. To extend the interpretation of and to guide the experiment, we have developed a generic model of the vesicle-tip-substrate system and performed Monte Carlo simulations, addressing the influence of force setpoint and tip speed and shape on the type of imaging or manipulation observed. Specifically, we have explored AFM-image height and width variations versus force setpoint, typical AFM images for small and large force setpoints, tip-induced vesicle strain versus force setpoint, typical vesicle shapes during pushing for different tip speeds, and the details of vesicle rupture induced by the tip.

Simulations of temperature dependence of the formation of a supported lipid bilayer via vesicle adsorption

Recent experimental investigations of the kinetics of vesicle adsorption in solution on SiO2 demonstrate a thermally activated transition from adsorbed intact vesicles to a supported lipid bilayer. Our Monte Carlo simulations clarify the mechanism of this process. The model employed is an extension of the model used earlier to describe vesicle adsorption at room temperature. Specifically, it includes limitations of the adsorption rate by vesicle diffusion in the solution, and adsorption- and lipid-membrane-induced rupture of arriving and already adsorbed vesicles. Vesicles and lipid molecules, formed after rupture of vesicles, are considered immobile. With these ingredients, the model is able to quantitatively reproduce the temperature-dependent adsorption kinetics, including a higher critical surface concentration of intact vesicles for lower temperatures, and the apparent activation energy for the vesicle-to-bilayer transition E(a) approximately 5 kcal/mol.

Kinetics of protein aggregation with formation of unreactive intermediates

Irreversible protein aggregation resulting in formation and deposition of insoluble fibrils or amorphous precipitates is usually assumed to occur via sequential attachment of monomers to soluble intermediates. We complement this scheme by slow conversion of the intermediates to a relatively stable form so that they do not react with monomers but can be trapped by precipitates. For reasonable values of parameters, our model predicts that the aggregation kinetics order may be between 2.0 and 2.5. In particular, the model can be used to explain the reaction order, 2.17 +/- 0.09, observed for aggregation of recombinant human granulocyte colony stimulating factor.

Comment on "Hysteresis phenomena in CO catalytic oxidation system in the presence of inhomogeneities of the catalyst surface"

Scrutinizing the Monte Carlo algorithm, used by D.-Y. Hua and Y.-Q. Ma [Phys. Rev. E 66, 066103 (2002)] in order to simulate the effect of defect sites on bistable kinetics of CO oxidation on single-crystal surfaces, we show that in their study (i) the rules for describing CO adsorption, desorption, and surface diffusion contradict the detailed balance principle and (ii) the ratio of the rates of CO diffusion and reaction between adsorbed CO and O species is opposite compared to that observed in reality.

Electrochemical reactions on catalyst particles with three-phase boundaries

In fuel cells, electrochemical reactions are often assumed to occur on metal catalyst particles contacting simultaneously the ion-conducting electrolyte and gas phase. Our kinetic Monte Carlo simulations demonstrate that in this case the deviations from the Tafel law in the dependence of the reaction rate on the electrode potential may be related to diffusion of one of the adsorbed reactants along catalyst particles.

Dependence of the efficiency of a multicapillary column on the liquid phase loading method

One of the main approaches employed to reach fast chromatographic separation is based on using columns containing up to 1000 capillaries with the diameter size down to 10-100 microm. The efficiency of such columns depends on the dispersion of the capillary radius and on the way of the liquid-film loading. We present general equations describing these effects. Specifically, we show theoretically and experimentally that the separation efficiency can be improved by using the loading methods specially designed in order to take into account correlation between the film thickness and capillary radius.

Coupled catalytic oscillators: Beyond the mass-action law

We present Monte Carlo simulations of the reaction kinetics corresponding to two coupled catalytic oscillators in the case when oscillations result from the interplay between the reaction steps and adsorbate-induced surface restructuring. The model used is aimed to mimic oscillations on a single nm catalyst particle with two kinds of facets or on two catalyst particles on a support. Specifically, we treat the NO reduction by H(2) on a composite catalyst containing two catalytically active Pt(100) parts connected by an inactive link. The catalyst is represented by a rectangular fragment of a square lattice. The left- and right-hand parts of the lattice mimic Pt(100). With an appropriate choice of the model parameters, these sublattices play a role of catalytic oscillators. The central catalytically inactive sublattice is considered to be able only to adsorb NO reversibly and can be viewed as a Pt(111) facet or a support. The interplay of the reactions running on the catalytically active areas occurs via NO diffusion over the boundaries between the sublattices. Using this model, we show that the coupling of the catalytically active sublattices may synchronize nearly harmonic oscillations observed on these sublattices and also may result in the appearance of aperiodic partly synchronized oscillations. The spatio-temporal patterns corresponding to these regimes are nontrivial. In particular, the model predicts that, due to phase separation, the reaction may be accompanied by the formation of narrow NO-covered zones on the left and right sublattices near the boundaries between these sublattices and the central sublattice. Such patterns cannot be obtained by using the conventional mean-field reaction-diffusion equations based on the mass-action law. The experimental opportunities to observe the predicted phenomena are briefly discussed. (c) 2001 American Institute of Physics.

Simulation of two-dimensional streptavidin crystallization

We present lattice Monte Carlo simulations of the growth of streptavidin islands at a biotinylated lipid layer. The model employed takes into account attractive anisotropic lateral interactions between streptavidin tetramers. With a minimal set of interactions, we reproduce the formation of rectangular islands experimentally observed at pH > or = 9.0. Specifically, we analyze two scenarios of the island growth. First, if streptavidin is rapidly adsorbed at t = 0 (stepwise coverage change without ongoing adsorption), the average linear island size is found to grow according to the Lifshitz-Slyozov law, R proportional to t(1/3). Second, if the island growth occurs in parallel with streptavidin adsorption limited by diffusion in the solution, the Lifshitz-Slyozov law is also applicable, but only at the late stage, when the streptavidin coverage is appreciable.

Folding of bundles of alpha-helices in solution, membranes, and adsorbed overlayers

We propose a coarse-grained lattice model for Monte Carlo simulations of folding of proteins consisting of several alpha-helices. A chain representing a protein is considered to contain A and B monomers forming relatively stiff A subchains, mimicking helices, and flexible B links between these subchains, respectively. Using this model, we simulate (1) folding of four-helix proteins in solution; (2) folding of membrane proteins containing one, two, or four helices; and (3) refolding of four-helix proteins adsorbed at the liquid-solid interface. For these cases, we show typical scenarios of protein folding and refolding and study the dependence of the folding time on the chain length. Combining the latter results with those already available in the literature, we discuss the relative rates of folding of proteins belonging to different classes.

Reply to "Comment on 'Surface restructuring, kinetic oscillations, and chaos in heterogeneous catalytic reactions' "

In my numeration, the criticism of my simulations of kinetic oscillations in NO reduction by H2 on Pt(100) [V. P. Zhdanov, Phys. Rev. E 59, 6292 (1999)] by Kuzovkov, Kortlüke, and von Niessen [preceding paper, Phys. Rev. 63, 023101 (2001)] contains 19 comments. I show that four comments are irrelevant. The other 15 comments are wrong, because they either contradict the basic principles of the theory of phase transitions, Monte Carlo simulations, and catalytic chemistry or ignore numerous experimental data on adsorbate-induced restructuring of the Pt(100) surface.

Simulation of enzymatic cellular reactions complicated by phase separation

We present two-dimensional Monte Carlo simulations of enzymatic cellular reaction occurring via the Michaelis-Menten scheme in the case of attractive interactions between the reaction products. The model employed predicts phase separation in the cell provided that the reaction is relatively fast. The shape of the corresponding patterns varies from a few separate islands to a large patch located in the center of the cell. The fluctuations of the reaction rate during such regimes are found to be much higher than those predicted by the Poissonian distribution.

Ordering of adsorbed proteins

Adapting a hard hexagon model to describing protein adsorption, we show by using Monte Carlo simulations that the ordering of adsorbed proteins may strongly depend on the relative location of the hydrophilic and hydrophobic patches on their surface. Specifically, proteins may form dimers, trimers, small rings, and zig-zag or straight chains or islands consisting of such fragments.

Formation of supported membranes from vesicles

Using a combination of the quartz crystal microbalance and surface plasmon resonance techniques, we have studied the spontaneous formation of supported lipid bilayers from small (approximately 25 nm) unilamellar vesicles. Together these experimental methods measure the amount of lipid adsorbed on the surface and the amount of water trapped by the lipid. With this approach, we have, for the first time, been able to observe in detail the progression from the adsorption of intact vesicles to rupture and bilayer formation. Monte Carlo simulations reproduce the data.

Monte Carlo simulation of diffusion of adsorbed proteins

We present the results of three-dimensional lattice Monte Carlo simulations of protein diffusion on the liquid-solid interface in a wide temperature range including the most interesting temperatures (from slightly below T(f) and up to T(c), where T(f) and T(c) are the folding and collapse temperatures). For the model under consideration (27 monomers of two types), the temperature dependence of the diffusion coefficient is found to obey the Arrhenius law with the normal value (approximately 10(-2)-10(-3) cm(2)/s) of the preexponential factor. Proteins 2000;39:76-81.

Surface restructuring and kinetic oscillations in heterogeneous catalytic reactions

We extend our earlier Monte Carlo simulations of isothermal kinetic oscillations in the NO-H(2)/Pt(100) system [V. P. Zhdanov, Phys. Rev. E 59, 6292 (1999)]. The analysis, based on a lattice-gas model describing surface restructuring in terms of the statistical theory of first-order phase transitions, is primarily focused on adsorbate-diffusion-mediated synchronization of oscillations. The conventional condition for synchronization, (D tau)(1/2)>L (D is the diffusion coefficient, tau the oscillation period, and L the lattice size), is proved to considerably underestimate the role of surface diffusion. Due to the formation of mesoscopic islands, well developed oscillations are found to be possible in the cases when the left part of this condition is much lower than the right part.

Surface restructuring, kinetic oscillations, and chaos in heterogeneous catalytic reactions

We present comprehensive Monte Carlo simulations of isothermal kinetic oscillations and chaos in catalytic reactions accompanied by adsorbate-induced surface restructuring. Our analysis is based on the lattice-gas model describing surface restructuring in terms of the statistical theory of first-order phase transitions. As an example, we treat the kinetics of the NO-H2 reaction on the Pt(100) surface. A proposed reduced mechanism of this reaction includes NO adsorption, desorption, and decomposition occurring on the restructured patches of the surface (the decomposition products are rapidly removed from the surface via N2 desorption and H2O formation and desorption). Calculations are performed with a qualitatively realistic ratio between the rates of different elementary steps. In particular, NO diffusion is several orders of magnitude faster compared to the other steps. On the nm scale, the model predicts formation of restructured islands with atomically sharp boundaries. The shape of the islands is found to change dramatically with varying reaction conditions. Despite phase separation on the surface, the transition from almost harmonic oscillations (with relatively small separate islands) to chaos (with merging islands) is demonstrated to occur via the standard Feigenbaum scenario. Near the critical point, the dependence of the amplitude of oscillations on the governing parameter is shown to be close to that predicted for the Hopf supercritical bifurcation.

Monte Carlo simulation of denaturation of adsorbed proteins

Denaturation of model proteinlike molecules at the liquid-solid interface is simulated over a wide temperature range by employing the lattice Monte Carlo technique. Initially, the molecule containing 27 monomers of two types (A and B) is assumed to be adsorbed in the native folded state (a 3 x 3 x 3 cube) so that one of its sides is in contact with the surface. The details of the denaturation kinetics are found to be slightly dependent on the choice of the side, but the main qualitative conclusions hold for all the sides. In particular, the kinetics obey approximately the conventional first-order law at T > Tc (Tc is the collapse temperature for solution). With decreasing temperature, below Tc but above Tf (Tf is the folding temperature for solution), deviations appear from the first-order kinetics. For the most interesting temperatures, that is, below Tf, the denaturation kinetics are shown to be qualitatively different from the conventional ones. In particular, the denaturation process occurs via several intermediate steps due to trapping in metastable states. Mathematically, this means that (i) the transition to the denatured state of a given molecule is nonexponential, and (ii) the denaturation process cannot be described by a single rate constant kappar. One should rather introduce a distribution of values of this rate constant (different values of kappar correspond to the transitions to the altered state via different metastable states).

Monte Carlo simulation of the kinetics of protein adsorption

Adsorption of proteins occurs via diffusion toward the interface, actual adsorption, and subsequent irreversible conformational changes resulting in denaturation of the native protein structure. The conventional kinetic models describing these steps are based on the assumption that the denaturation transitions obey the first-order law with a single value of the denaturation rate constant kappar. Meanwhile, recent Monte Carlo simulations indicate that, in general, the denaturation process cannot be described by a single rate constant kappar. One should rather introduce a distribution of this rate constant (physically, different values of kappar correspond to the transitions to the altered state via different metastable states). We have calculated the kinetics of irreversible adsorption of proteins with and without distribution of the denaturation rate constant kappar in the limits when protein diffusion in the solution is, respectively, rapid or slow. In both cases, the adsorption kinetics with distribution of kappar are found to be close to those with a single-valued rate constant kappar provided that the average value of kappar in the former case is equal to kappar for the latter case. This conclusion holds even for wide distributions of kappar. The consequences of this finding for the fitting of global experimental kinetics on the basis of phenomenological equations are briefly discussed.

Monte Carlo simulation of protein folding with orientation-dependent monomer-monomer interactions

We present the results of lattice Monte Carlo simulations of protein folding in the framework of a model taking into account (i) the dependence of the energy of interaction of amino-acid residues on their orientation and (ii) the rigidity of the polypeptide chain with respect to the formation of kinks. If the chain is flexible, the final protein structures are predicted to be compact. Increasing the energy cost of creation of kinks is found to favor the formation of flat structures mimicking an ideal antiparallel beta sheet. For compact structures, the kinetics of folding exhibit the standard two-phase regime (a rapid collapse to one of the metastable stable, followed by slow reconfiguration of the chain to the native structure). For flat structures, the transition to the native state is often gradual.