Mesoscopic dynamics of diffusion-influenced enzyme kinetics

Separation of nanoparticles via surfing on chemical wavefronts

The separation of micro and nanoscale colloids is a necessary step in most biological microassay techniques, and is a common practice in microchemical processing. Chemical waves are frequently encountered in biochemical systems driven far from equilibrium. Here, we put forward a strategy for separating small suspending colloids by means of their surfing on substrate chemical wavefronts. The colloids with catalytic activities sensitive to the substrates are activated to show self-propulsion and consequently exhibit a chemotactic response to the traveling wavefronts, which results in their spontaneous separation from the multicomponent complex mixture via self-diffusiophoresis. The dynamics of the process is analyzed through a particle-based simulation. In addition, it is found that separation can be carried out according to particle size. The mechanisms underpinning the chemical and physical separation processes are discussed, and the dependencies on the reaction rate constant and particle size are presented. The results may prove relevant for further experimental and theoretical studies of separation in complex active environments.

Scale-consistent approach to the derivation of coarse-grained force fields for simulating structure, dynamics, and thermodynamics of biopolymers

In this chapter the scale-consistent approach to the derivation of coarse-grained force fields developed in our laboratory is presented, in which the effective energy function originates from the potential of mean force of the system under consideration and embeds atomistically detailed interactions in the resulting energy terms through use of Kubo's cluster-cumulant expansion, appropriate selection of the major degrees of freedom to be averaged out in the derivation of analytical approximations to the energy terms, and appropriate expression of the interaction energies at the all-atom level in these degrees of freedom. Our approach enables the developers to find correct functional forms of the effective coarse-grained energy terms, without having to import them from all-atom force fields or deriving them on a heuristic basis. In particular, the energy terms derived in such a way exhibit correct dependence on coarse-grained geometry, in particular on site orientation. Moreover, analytical formulas for the multibody (correlation) terms, which appear to be crucial for coarse-grained modeling of many of the regular structures such as, e.g., protein α-helices and β-sheets, can be derived in a systematic way. Implementation of the developed theory to the UNIfied COarse-gRaiNed (UNICORN) model of biological macromolecules, which consists of the UNRES (for proteins), NARES-2P (for nucleic acids), and SUGRES-1P (for polysaccharides) components, and is being developed in our laboratory is described. Successful applications of UNICORN to the prediction of protein structure, simulating the folding and stability of proteins and nucleic acids, and solving biological problems are discussed.

Particle-based modeling of heterogeneous chemical kinetics including mass transfer

Connecting the macroscopic world of continuous fields to the microscopic world of discrete molecular events is important for understanding several phenomena occurring at physical boundaries of systems. An important example is heterogeneous catalysis, where reactions take place at active surfaces, but the effective reaction rates are determined by transport limitations in the bulk fluid and reaction limitations on the catalyst surface. In this work we study the macro-micro connection in a model heterogeneous catalytic reactor by means of stochastic rotation dynamics. The model is able to resolve the convective and diffusive interplay between participating species, while including adsorption, desorption, and reaction processes on the catalytic surface. Here we apply the simulation methodology to a simple straight microchannel with a catalytic strip. Dimensionless Damkohler numbers are used to comment on the spatial concentration profiles of reactants and products near the catalyst strip and in the bulk. We end the discussion with an outlook on more complicated geometries and increasingly complex reactions.

Diffusional correlations among multiple active sites in a single enzyme

Simulations of the enzymatic dynamics of a model enzyme containing multiple substrate binding sites indicate the existence of diffusional correlations in the chemical reactivity of the active sites. A coarse-grain, particle-based, mesoscopic description of the system, comprising the enzyme, the substrate, the product and solvent, is constructed to study these effects. The reactive and non-reactive dynamics is followed using a hybrid scheme that combines molecular dynamics for the enzyme, substrate and product molecules with multiparticle collision dynamics for the solvent. It is found that the reactivity of an individual active site in the multiple-active-site enzyme is reduced substantially, and this effect is analyzed and attributed to diffusive competition for the substrate among the different active sites in the enzyme.

Diffusion-limited attachment of large spherical particles to flexible membrane-immobilized receptors

Relatively large (~100 nm) spherical particles, e.g., virions, vesicles, or metal nanoparticles, often interact with short (<10 nm) flexible receptors immobilized in a lipid membrane or on other biologically relevant surfaces. The attachment kinetics of such particles may be limited globally by their diffusion toward a membrane or locally by diffusion around receptors. The detachment kinetics, also, can be limited by diffusion. Focusing on local diffusion limitations and using suitable approximations, we present expressions for the corresponding rate constants and identify their dependence on particle size and receptor length. We also illustrate features likely to be observed in such kinetics for particles (e.g., vesicles) with a substantial size distribution. The results obtained are generic and can be used to interpret a variety of situations. For example, we estimate upper values of virion attachment rate constants and clarify the likely effect of vesicle size distribution on previously observed non-exponential kinetics of vesicle detachment.

Kinetics of enzymatic reactions in lipid membranes containing domains

An appreciable part of enzymes operating in vivo is associated with lipid membranes. The function of such enzymes can be influenced by the presence of domains containing proteins and/or composed of different lipids. The corresponding experimental model-system studies can be performed under well controlled conditions, e.g., on a planar supported lipid bilayer or surface-immobilized vesicles. To clarify what may happen in such systems, we propose general kinetic equations describing the enzyme-catalyzed substrate conversion occurring via the Michaelis-Menten (MM) mechanism on a membrane with domains which do not directly participate in reaction. For two generic situations when a relatively slow reaction takes place primarily in or outside domains, we take substrate saturation and lateral substrate-substrate interactions at domains into account and scrutinize the dependence of the reaction rate on the average substrate coverage. With increasing coverage, depending on the details, the reaction rate reaches saturation via an inflection point or monotonously as in the conventional MM case. In addition, we show analytically the types of reaction kinetics occurring primarily at domain boundaries. In the physically interesting situation when the domain growth is fast on the reaction time scale, the latter kinetics are far from conventional. The opposite situation when the reaction is fast and controlled by diffusion has been studied by using the Monte Carlo technique. The corresponding results indicate that the dependence of the reaction kinetics on the domain size may be weak.

Enzyme kinetics and transport in a system crowded by mobile macromolecules

The dynamics of an elastic network model for the enzyme 4-oxalocrotonate tautomerase is studied in a system crowded by mobile macromolecules, also modeled by elastic networks.

Dynamics of solutes with hydrodynamic interactions: comparison between Brownian dynamics and stochastic rotation dynamics simulations

The dynamics of particles in solution or suspension is influenced by thermal fluctuations and hydrodynamic interactions. Several mesoscale methods exist to account for these solvent-induced effects such as Brownian dynamics with hydrodynamic interactions and hybrid molecular dynamics-stochastic rotation dynamics methods. Here we compare two ways of coupling solutes to the solvent with stochastic rotation dynamics (SRD) to Brownian dynamics with and without explicit hydrodynamic interactions. In the first SRD scheme [SRD with collisional coupling (CC)] the solutes participate in the collisional step with the solvent and in the second scheme [SRD with central force coupling (CFC)] the solutes interact through direct forces with the solvent, generating slip boundary conditions. We compare the transport coefficients of neutral and charged solutes in a model system obtained by these simulation schemes. Brownian dynamics without hydrodynamic interactions is used as a reference to quantify the influence of hydrodynamics on the transport coefficients as modeled by the different methods. We show that, in the dilute range, the SRD CFC method provides results similar to those of Brownian dynamics with hydrodynamic interactions for the diffusion coefficients and for the electrical conductivity. The SRD CC scheme predicts diffusion coefficients close to those obtained by Brownian dynamic simulations without hydrodynamic interactions, but accounts for part of the influence of hydrodynamics on the electrical conductivity.

Structural and mechanistic insights into the electron flow through protein for cytochrome c-tethering copper nitrite reductase

Copper-containing nitrite reductases (CuNiRs), which catalyse the reversible one-electron reduction of nitrite to nitric oxide, are members of a large family of multi-copper enzymes that require an interprotein electron transfer (ET) reaction with redox partner proteins. Here, we show that the naturally fused type of CuNiR tethering a cytochrome c (Cyt c) at the C-terminus folds as a unique trimeric domain-swapped structure and has a self-sufficient electron flow system. The C-terminal Cyt c domain is located at the surface of the type 1 copper (T1Cu) site in the N-terminal CuNiR domain from the adjacent subunit, the heme-to-Cu distance (10.6 Å) of which is comparable to the transient ET complex of normal CuNiR with Cyt c. The structural aspects for the domain-domain interface and the ET kinetics indicate that the Cyt c-CuNiR domain interaction should be highly transient. The further electrochemical analysis of the interprotein ET reaction with a cognate redox partner protein suggested that an electron is directly transferred from the partner to the T1Cu. Structural and mechanistic comparisons of Cyt c-CuNiR with another cupredoxin-tethering CuNiR highlight the behaviours of extra domains on the fusion types of CuNiRs required for ET through proteins.

Phoretic self-propulsion: a mesoscopic description of reaction dynamics that powers motion

The fabrication of synthetic self-propelled particles and the experimental investigations of their dynamics have stimulated interest in self-generated phoretic effects that propel nano- and micron-scale objects. Theoretical modeling of these phenomena is often based on a continuum description of the solvent for different phoretic propulsion mechanisms, including, self-electrophoresis, self-diffusiophoresis and self-thermophoresis. The work in this paper considers various types of catalytic chemical reaction at the motor surface and in the bulk fluid that come into play in mesoscopic descriptions of the dynamics. The formulation is illustrated by developing the mesoscopic reaction dynamics for exothermic and dissociation reactions that are used to power motor motion. The results of simulations of the self-propelled dynamics of composite Janus particles by these mechanisms are presented.

Modeling of solvent flow effects in enzyme catalysis under physiological conditions

A stochastic model for the dynamics of enzymatic catalysis in explicit, effective solvents under physiological conditions is presented. Analytically-computed first passage time densities of a diffusing particle in a spherical shell with absorbing boundaries are combined with densities obtained from explicit simulation to obtain the overall probability density for the total reaction cycle time of the enzymatic system. The method is used to investigate the catalytic transfer of a phosphoryl group in a phosphoglycerate kinase-ADP-bis phosphoglycerate system, one of the steps of glycolysis. The direct simulation of the enzyme-substrate binding and reaction is carried out using an elastic network model for the protein, and the solvent motions are described by multiparticle collision dynamics which incorporates hydrodynamic flow effects. Systems where solvent-enzyme coupling occurs through explicit intermolecular interactions, as well as systems where this coupling is taken into account by including the protein and substrate in the multiparticle collision step, are investigated and compared with simulations where hydrodynamic coupling is absent. It is demonstrated that the flow of solvent particles around the enzyme facilitates the large-scale hinge motion of the enzyme with bound substrates, and has a significant impact on the shape of the probability densities and average time scales of substrate binding for substrates near the enzyme, the closure of the enzyme after binding, and the overall time of completion of the cycle.

Dynamic allostery: linkers are not merely flexible

Most proteins consist of multiple domains. How do linkers efficiently transfer information between sites that are on different domains to activate the protein? Mere flexibility only implies that the conformations would be sampled. For fast timescales between triggering events and cellular response, which often involves large conformational change, flexibility on its own may not constitute a good solution. We posit that successive conformational states along major allosteric propagation pathways are pre-encoded in linker sequences where each state is encoded by the previous one. The barriers between these states that are hierarchically populated are lower, achieving faster timescales even for large conformational changes. We further propose that evolution has optimized the linker sequences and lengths for efficiency, which explains why mutations in linkers may affect protein function and review the literature in this light.