Effect of anisotropic reactivity on the rate of diffusion-controlled reactions: comparative analysis of the models of patches and hemispheres

Impact of Confinement within a Hydrogel Mesh on Protein Thermodynamic Stability and Aggregation Kinetics

Though protein stability and aggregation have been well characterized in dilute solutions, the influence of a confining environment that exists (e.g., in intercellular and tissue spaces and therapeutic formulations) on the protein structure is largely unknown. Herein, the effects of confinement on stability and aggregation were explored for proteins of different sizes, stability, and hydrophobicity when encapsulated in hydrophilic poly(ethylene glycol) hydrogels. Denaturation curves show linear correlations between confinement size (mesh size) and thermodynamic stability, i.e., unfolding free energy and surface area accessible for solvation (represented by m-value). Two clusters of protein types are identifiable from these correlations; the clusters are defined by differences in protein stability, surface area, and aggregation propensity. Proteins with higher stability, larger surface area, and lower aggregation propensity (e.g., lysozyme and myoglobin) are less affected by the confinement imposed by mesh size than proteins with lower stability, smaller surface area, and higher aggregation propensity (e.g., growth hormone and aldehyde dehydrogenase). According to aggregation kinetics measured by thioflavin T fluorescence, confinement in smaller mesh sizes resulted in slower aggregation rates than that in larger mesh sizes. Compared to that in buffer solution, the confinement of a hydrophobic protein (e.g., human insulin) in the hydrogels accelerates protein aggregation. Conversely, the confinement of a hydrophilic protein (e.g., human amylin) in the hydrogels decelerates or prevents aggregation, with the rates of aggregation inversely proportional to mesh size. These findings provide new insights into protein conformational stability in confined microenvironments relevant to various cellular, tissue, and therapeutics scenarios.

Quantification of protein aggregation rates and quenching effects of amylin–inhibitor complexes

Comparative inhibition capabilities of graphene quantum dots, resveratrol, and curcumin decipher the dose-dependent competitive role of protein aggregation rate and quenching effect in amylin fibrillation.

Dynamics theory for molecular liquids based on an interaction site model

Dynamics theories for molecular liquids based on an interaction site model have been developed over the past few decades and proved to be powerful tools to investigate various dynamical phenomena.

Boundary homogenization for a sphere with an absorbing cap of arbitrary size

This paper focuses on trapping of diffusing particles by a sphere with an absorbing cap of arbitrary size on the otherwise reflecting surface. We approach the problem using boundary homogenization which is an approximate replacement of non-uniform boundary conditions on the surface of the sphere by an effective uniform boundary condition with appropriately chosen effective trapping rate. One of the main results of our analysis is an expression for the effective trapping rate as a function of the surface fraction occupied by the absorbing cap. As the cap surface fraction increases from zero to unity, the effective trapping rate increases from that for a small absorbing disk on the otherwise reflecting sphere to infinity which corresponds to a perfectly absorbing sphere. The obtained expression for the effective trapping rate is applied to find the rate constant describing trapping of diffusing particles by an absorbing cap on the surface of the sphere. Finally, we find the capacitance of a metal cap of arbitrary size on a dielectric sphere using the relation between the capacitance and the rate constant of the corresponding diffusion-limited reaction. The relative error of our approximate expressions for the rate constant and the capacitance is less than 5% over the entire range of the cap surface fraction from zero to unity.

Theory of bimolecular reactions in a solution with linear traps: Application to the problem of target search on DNA

One-dimensional sliding along DNA as a means to accelerate protein target search is a well-known phenomenon occurring in various biological systems. Using a biomimetic approach, we have recently demonstrated the practical use of DNA-sliding peptides to speed up bimolecular reactions more than an order of magnitude by allowing the reactants to associate not only in the solution by three-dimensional (3D) diffusion, but also on DNA via one-dimensional (1D) diffusion [A. Turkin et al., Chem. Sci. (2015)]. Here we present a mean-field kinetic model of a bimolecular reaction in a solution with linear extended sinks (e.g., DNA) that can intermittently trap molecules present in a solution. The model consists of chemical rate equations for mean concentrations of reacting species. Our model demonstrates that addition of linear traps to the solution can significantly accelerate reactant association. We show that at optimum concentrations of linear traps the 1D reaction pathway dominates in the kinetics of the bimolecular reaction; i.e., these 1D traps function as an assembly line of the reaction product. Moreover, we show that the association reaction on linear sinks between trapped reactants exhibits a nonclassical third-order behavior. Predictions of the model agree well with our experimental observations. Our model provides a general description of bimolecular reactions that are controlled by a combined 3D+1D mechanism and can be used to quantitatively describe both naturally occurring as well as biomimetic biochemical systems that reduce the dimensionality of search.

Crowding effects on the formation and maintenance of nuclear bodies: insights from molecular-dynamics simulations of simple spherical model particles

The physics of structure formation and maintenance of nuclear bodies (NBs), such as nucleoli, Cajal bodies, promyelocytic leukemia bodies, and speckles, in a crowded nuclear environment remains largely unknown. We investigate the role of macromolecular crowding in the formation and maintenance of NBs using computer simulations of a simple spherical model, called Lennard-Jones (LJ) particles. LJ particles form a one-phase, dilute fluid when the intermolecular interaction is weaker than a critical value, above which they phase separate and form a condensed domain. We find that when volume-exclusive crowders exist in significant concentrations, domain formation is induced even for weaker intermolecular interactions, and the effect is more pronounced with increasing crowder concentration. Simulation results show that a previous experimental finding that promyelocytic leukemia bodies disappear in the less-crowded condition and reassemble in the normal crowded condition can be interpreted as a consequence of the increased intermolecular interactions between NB proteins due to crowding. Based on further analysis of the simulation results, we discuss the acceleration of macromolecular associations that occur within NBs, and the delay of diffusive transport of macromolecules within and out of NBs when the crowder concentration increases. This study suggests that in a polydisperse nuclear environment that is enriched with a variety of macromolecules, macromolecular crowding not only plays an important role in the formation and maintenance of NBs, but also may perform some regulatory functions in response to alterations in the crowding conditions.

Diffusion-influenced reactions involving a reactant with two active sites

We consider the kinetics of diffusion-influenced reactions which involve a reactant species that can be modeled as a sphere with two reactive patches located on its surface at an arbitrary angular distance. An approximate analytic expression for the rate coefficient is derived based on the Wilemski-Fixman-Weiss decoupling approximation and a multivariable Padé approximation. The accuracy of the rate expression is evaluated against computer simulations as well as an exact analytic expression available for a special case. The present theory provides accurate estimates for the magnitude of diffusive interference effects between the two reactive patches. We also present an efficient Brownian dynamics method for calculating the time-dependent rate coefficient, which is applicable when the reactants involve multiple active sites.

Lumry-Eyring nucleated-polymerization model of protein aggregation kinetics. 2. Competing growth via condensation and chain polymerization

The Lumry-Eyring with nucleated polymerization (LENP) model from part 1 (Andrews, J. M.; Roberts, C. J. J. Phys. Chem. B 2007, 111, 7897-7913) is expanded to explicitly account for kinetic contributions from aggregate-aggregate condensation polymerization. Experimentally accessible quantities described by the resulting model include monomer mass fraction (m), weight-average molecular weight (Mw), and ratio of Mw to number-average molecular weight (Mn) as a function of time (t). Analysis of global model behavior illustrates ways to identify which steps in the overall aggregation process are kinetically important on the basis of the qualitative behavior of m, Mw, and Mw/Mn vs t, and on whether bulk phase separation or precipitation occurs. For cases in which all aggregates remain soluble, moment equations are provided that permit straightforward numerical regression of experimental data to give separate time scales or inverse rate coefficients for nucleation and for growth by chain and condensation polymerization. Analysis of simulated data indicates that it may be possible to neglect condensation reactions if only early time data are considered and also highlights difficulties in conclusively distinguishing between alternative mechanisms of condensation, even when kinetics are monitored with both m and Mw.

Effect of macromolecular crowding on reaction rates: a computational and theoretical study

The effect of macromolecular crowding on the rates of association reactions are investigated using theory and computer simulations. Reactants and crowding agents are both hard spheres, and when two reactants collide they form product with a reaction probability, p(rxn). A value of p(rxn) < 1 crudely mimics the fact that proteins must be oriented properly for an association reaction to occur. The simulations show that the dependence of the reaction rate on the volume fraction of crowding agents varies with the reaction probability. For reaction probabilities close to unity where most of encounters between reactants lead to a reaction, the reaction rate always decreases as the volume fraction of crowding agents is increased due to the reduced diffusion coefficient of reactants. On the other hand, for very small reaction probabilities where, in most of encounters, the reaction does not occur, the reaction rate increases with the volume fraction of crowding agents--in this case, due to the increase probability of a recollision. The Smoluchowski theory refined with the radiation boundary condition and the radial distribution function at contact is in quantitative agreement with simulations for the reaction rate constant and allows the quantitative analysis of both effects separately.

Non-Markovian stochastic Liouville equation and its Markovian representation: Extensions of the continuous-time random-walk approach

Some specific features and extensions of the continuous-time random-walk (CTRW) approach are analyzed in detail within the Markovian representation (MR) and CTRW-based non-Markovian stochastic Liouville equation (SLE). In the MR, CTRW processes are represented by multidimensional Markovian ones. In this representation the probability density function (PDF) W(t) of fluctuation renewals is associated with that of reoccurrences in a certain jump state of some Markovian controlling process. Within the MR the non-Markovian SLE, which describes the effect of CTRW-like noise on the relaxation of dynamic and stochastic systems, is generalized to take into account the influence of relaxing systems on the statistical properties of noise. Some applications of the generalized non-Markovian SLE are discussed. In particular, it is applied to study two modifications of the CTRW approach. One of them considers cascaded CTRWs in which the controlling process is actually a CTRW-like one controlled by another CTRW process, controlled in turn by a third one, etc. Within the MR a simple expression for the PDF W(t) of the total controlling process is obtained in terms of Markovian variants of controlling PDFs in the cascade. The expression is shown to be especially simple and instructive in the case of anomalous processes determined by the long-time tailed W(t) . The cascaded CTRWs can model the effect of the complexity of a system on the relaxation kinetics (in glasses, fractals, branching media, ultrametric structures, etc.). Another CTRW modification describes the kinetics of processes governed by fluctuating W(t) . Within the MR the problem is analyzed in a general form without restrictive assumptions on the correlations of PDFs of consecutive renewals. The analysis shows that fluctuations of W(t) can strongly affect the kinetics of the process. Possible manifestations of this effect are discussed.

Exact solution for anisotropic diffusion-controlled reactions with partially reflecting conditions

We investigate a generalization of the model of Solc and Stockmayer to describe the diffusion-controlled reactions between chemically anisotropic reactants taking into account the partially reflecting conditions on two parts of the reaction surface. The exact solution of the relevant mixed boundary-value problem was found for different ratios of the intrinsic rate constants. The results obtained may be used to test numerical programs that describe diffusion-controlled reactions in real systems of particles with anisotropic reactivity.

A dynamical study of antibody-antigen encounter reactions

The effects of internal dynamics in diffusion-driven encounters between macro-molecules represent a problem of broad relevance in molecular biology. In this view, we investigate a typical antigen-antibody reaction chain, based on a coarse-grained mechanical model parameterized directly upon results from single-molecule experiments. We demonstrate that the internal dynamics is a crucial factor in the encounter process. To describe our numerical results, we formulate a simple, intuitive theoretical framework, and we develop it analytically. This enables us to show that the inner dynamics of antibody molecules results in a cooperative behavior of their individual sub-units. Along the same lines, we also investigate the case of double binding to multi-valent antigens. Our results quantify the enhancement of avidity afforded by the double binding in excellent agreement with the available experimental data.

Electrostatic potential of aminoacyl-tRNA synthetase navigates tRNA on its pathway to the binding site

In the first stage of a diffusion-controlled enzymatic reaction, aminoacyl-tRNA synthetases (aaRSs) interact with cognate tRNAs forming non-specific encounters. The aaRSs catalyzing the same overall aminoacylation reaction vary greatly in subunit organization, structural domain composition and amino acid sequence. The diffusional association of aaRS and tRNA was found to be governed by long-range electrostatic interactions when the homogeneous negative potential of tRNA fits to the patches of positive potential produced by aaRS; one patch for each tRNA substrate molecule. Considering aaRS as a molecule with anisotropic reactivity and on the basis of continuum electrostatics and Smoluchowski's theory, the reaction conditions for tRNA-aaRS diffusional encounters were formulated. The domains, categorized as enzymatically relevant, appeared to be non-essential for field sculpturing at long distances. On the other hand, a set of complementary domains exerts primary control on the aaRS isopotential surface formation. Subdividing the aaRS charged residues into native, conservative and non-conservative subsets, we evaluated the contribution of each group to long-range electrostatic potential. Surprisingly, the electrostatic potential landscapes generated by native and non-conservative subsets are fairly similar, thus suggesting the non-conservative subset is developed specifically for efficient tRNA attraction.

Kinetic studies on the sulfate radical-initiated polymerization of vinyl acetate and 4-vinyl pyridine in the presence of silica nanoparticles

The photolysis of silica suspensions of pH approximately 8 containing peroxodisulfate ions leads to the generation of two "surface transients" with a distinct spectrum and reactivity. Time-resolved and continuous irradiation experiments of similar dispersions also containing variable concentrations of vinyl acetate (VA) or 4-vinyl pyridine (4-VP) allowed the evaluation of the contribution of silica/water interfacial reactions to the kinetics and structural pattern of polymers synthesized using sulfate radicals as initiators. The rate constants measured for the reactions of the surface transients with 4-VP are 1 order of magnitude higher than those of VA, despite the fact that both species show similar reactivity in homogeneous solution toward sulfate radicals. It is suggested that both the sorption capacity and the different specific interactions with the silica surface of 4-VP and VA contribute to the observed reaction rates. Micrometer-sized latex particles of 4-VP and VP showed higher stability and more homogeneous size distributions when obtained in the presence of silica nanoparticles. Under the experimental conditions required for obtaining polymer particles, both the contribution of the described interfacial reactions and the effect of silica adsorbed monomer on the initiation steps of the polymerization may be neglected. The importance of in situ adsorption of the oligomer/polymer chains to silica NP during the polymerization propagation steps in determining the particle morphology is discussed.

Anticooperativity in diffusion-controlled reactions with pairs of anisotropic domains: a model for the antigen–antibody encounter

The encounter between anisotropic agents in diffusion-controlled reactions is a topic of very general relevance in chemistry and biology. Here we introduce a simplified model of encounter of an isotropic molecule with a pair of partially reacting agents and apply it to the encounter reaction between an antibody and its antigen. We reduce the problem to the solution of dual series relations, which can be solved iteratively, yielding the exact solution for the encounter rate constant at any desired order of accuracy. We quantify the encounter effectiveness by means of a simple indicator and show that the two binding centers systematically behave in an anti-cooperative fashion. However, we demonstrate that a reduction of the binding active sites allows the composite molecule to recover binding effectiveness, in spite of the overall reduction of the rate constant. In addition, we provide a simple formula that enables one to calculate the anti-cooperativity as a function of the size of the binding site for any values of the separation between the two active lobes and of the antigen size. Finally, some biological implications of our results are discussed.

Water/Silica Nanoparticle Interfacial Kinetics of Sulfate, Hydrogen Phosphate, and Dithiocyanate Radicals

The values of the rate constants for the reactions of the sulfate (2.5 x 10(9) M(-1) s(-1)) and hydrogen phosphate (2.2 x 10(8) M(-1) s(-1)) radicals with silica nanoparticles are obtained by flash photolysis experiments with silica suspensions containing S(2)O(8)(2-) or P(2)O(8)(4-), respectively. The interaction of these radicals with the silica nanoparticles leads to formation of transients, probably adsorbed sulfate and hydrogen phosphate radicals, with absorption maxima at around 320 and 350 nm, respectively. A different mechanism takes place for the interaction of the less oxidizing dithiocyanate radicals with the silica nanoparticles. These radicals selectively react with the dissociated silanol groups of the nanoparticles with a rate constant at 298.2K of 7 x 10(7) M(-1) s(-1) (per mol of SiO(-) groups), and there is no evidence for their adsorption at the surface. All the results are discussed in terms of the Smoluchowski equation and redox potential of the inorganic radicals.

Molecular recognition of oxygen by protein mimics: dynamics on the femtosecond to microsecond time scale

Molecular recognition by biological macromolecules involves many elementary steps, usually convoluted by diffusion processes. Here we report studies of the dynamics, from the femtosecond to the microsecond time scale, of the different elementary processes involved in the bimolecular recognition of a protein mimic, cobalt picket-fence porphyrin, with varying oxygen concentration at controlled temperatures. Electron transfer, bond breakage, and thermal "on" (recombination) and "off" (dissociation) reactions are the different processes involved. The reaction on-rate is 30 to 60 times smaller than that calculated from standard Smoluchowski theory. Introducing a two-step recognition model, with reversibility being part of both steps, removes the discrepancy and provides consistency for the reported thermodynamics, kinetics, and dynamics. The transient intermediates are configurations defined by the contact between oxygen (diatomic) and the picket-fence porphyrin (macromolecule). This intermediate is critical in the description of the potential energy landscape but, as shown here, both enthalpic and entropic contributions to the free energy are important. In the recognition process, the net entropy decrease is -33 cal mol(-1) K(-1); Delta H is -13.4 kcal mol(-1).

Effect of local molecular shape and anisotropic reactivity on the rate of diffusion-controlled reactions

The role of distance-dependent anisotropic reactivity and molecular geometry in the vicinity of localized reaction centers in influencing the rate of bimolecular diffusion-controlled reactions is analyzed in detail, both analytically and numerically. The effect of local molecular shape is considered within the model of reflective hemispheres of small radius l(h) on the surfaces of otherwise spherical molecules of radius R (l(h) << R). The distance-dependent reactivity is modeled by reactive hemispheres of radius l(r) on top of the reflective hemispheres (l(r) << R). It is shown that the presence of the reflective hemispheres leads to a markedly large increase of the reaction rate. The maximum effect is ~R/l(h) >> 1 times, as described by the ratio of local to average molecular curvature. It is observed for l(h) approximately R(l(r)/R)(1/2) >> l(r). The effect of thickness of the reaction regions is described within the model of reactive cylinders of height l(r) and angular radius theta << 1. It is shown that the characteristic parameter in the expansion of the reaction rate as a function of l(r)/R is l(r)/(Rtheta(2)), and therefore, even for small relative thickness d = l(r)/theta, its effect on the rate is very strong, i.e., the conventional model of reactive patches, which assumes zero thickness of the reaction region, may considerably underestimate the reaction rate.