Diffusion-influenced ligand binding to buried sites in macromolecules and transmembrane channels

We consider diffusion-influenced binding to a buried binding site that is connected to the surface by a narrow tunnel. Under the single assumption of an equilibrium distribution of ligands over the tunnel cross section, we reduce the calculation of the time-dependent rate coefficient to the solution of a one-dimensional diffusion equation with appropriate boundary conditions. We obtain a simple analytical expression for the steady-state rate that depends on the potential of mean force in the tunnel and the diffusion-controlled rate of binding to the tunnel entrance. Potential applications of our theory include substrate binding to a buried active site of an enzyme and permeant ion binding to an internal site in a transmembrane channel.     

Catalyzing the translocation of polypeptides through attractive interactions

Facilitated translocation of polypeptides through a protein pore is a ubiquitous and fundamental process in biology. Several translocation systems possess various well-defined binding sites within the pore lumen, but a clear mechanistic understanding of how the interaction of the polypeptides with the binding site alters the underlying kinetics is still missing. Here, we employed rational protein design and single-channel electrical recordings to obtain detailed kinetic signatures of polypeptide translocation through the staphylococcal alpha-hemolysin (alphaHL) transmembrane pore, a robust, tractable, and versatile beta-barrel protein. Acidic binding sites composed of rings of negatively charged aspartic acid residues, engineered at strategic positions within the beta barrel, produced dramatic changes in the functional properties of the alphaHL protein, facilitating the transport of cationic polypeptides from one side of the membrane to the other. When two electrostatic binding sites were introduced, at the entry and exit of the beta barrel, both the rate constants of association and dissociation increased substantially, diminishing the free energy barrier for translocation. By contrast, more hydrophobic polypeptides exhibited a considerable decrease in the rate constant of association to the pore lumen, having to overcome a greater energetic barrier because of the hydrophilic nature of the pore interior.     

Grand canonical-like molecular dynamics simulations: application to anisotropic mass diffusion in a nanoporous medium

In this work, we describe two grand canonical-like molecular dynamics approaches to investigate mass diffusion phenomenon of a simple Lennard-Jones fluid confined between solid surfaces and in direct contact with reservoirs. In the first method, the density is used as the control variable in the reservoir whereas it is the pressure in the second method. Both methods provide consistent results, however, the constant density approach is the most efficient with respect to the computational time and implementation. Then, employing the constant density approach, we have studied the transient behavior of the diffusion process associated with the migration of one fluid into another one confined between parallel solid walls. Results have shown that the evolution of molar fraction of the invading fluid follows roughly a 1D diffusion model when the solid phase is weakly or moderately adsorbent with a characteristic time increasing when the pore width decreases. However, when the adsorption is high and the pore width small (i.e., below ten molecular sizes), the apparent mass diffusion in the adsorbed layer is reduced compared to that in the center of the slit pore. Hence, this mass diffusion process becomes a two-dimension phenomenon that must take into account an effective mass diffusion coefficient varying locally.     

One-dimensional description of multidimensional electron transfer reactions in condensed phase

We derive a one-dimensional energy diffusion equation for describing the dynamics of multidimensional electron transfer reactions in condensed phase, which is conceptually simpler and computationally more economic than the conventional approaches. We also obtain an analytical expression for the rate of electron transfer reactions for a general one-dimensional effective potential as well as an energy dependent diffusitivity. As an illustrative example, we consider application to electron transfer in a contact ion pair system modeled through harmonic potentials consisting of two slow classical modes and a high frequency vibrational mode for which the numerical results calculated using the proposed one-dimensional approach are shown to be in good agreement with experimental results. The energy diffusion equation and the rate expression for electron transfer obtained from the present theory, therefore, open up the possibility of describing the dynamics of electron transfer in complex systems, through a simpler approach.     

Functional dynamics of ion channels: modulation of proton movement by conformational switches

Detailed comparative studies of proton relay in native and chemically modified gramicidin channels provide a unique opportunity to uncover the structural basis of biological proton transport. The function of ion channels hinges on their ability to provide surrogate solvation in narrow pore filters so as to overcome the dielectric barrier presented by biological membranes. In the potassium channel KcsA and in the cation channel gramicidin, permeant selectivity and mobility are determined by the proteinaceous matrix via hydrogen bonding, charge-dipole, and dipole-dipole interactions. In particular, main-chain carbonyl groups in these pore interiors play an essential role in the solvation of alkali ions and of protons. In this study, molecular dynamics simulations reveal how the translocation of H(+) is controlled by nanosecond conformational transitions exchanging distorted states of the peptidic backbone in the single-file region of a dioxolane-linked analogue of the gramicidin dimer. These results underline the functional role of channel dynamics and provide a mechanism for the modulation of proton currents by fluctuating dipoles.     

Radial dependence of DNA translocation velocity in a solid-state nanopore

The physical features (such as size and charge) of a molecule transiting a nanopore whose cross-section area is only slightly larger than that of the molecule can be inferred from the measured ion-current through the pore. The transport of DNA molecules through nanopores has been extensively studied in the hope to enable low-cost and high-throughput DNA sequencing. However, the experimentally measured velocities of DNA translocation have a wide distribution, and this compromises the sequencing. In order to better understand the origin of the wide distribution, I have carried out molecular dynamics simulations to study the radial dependence of the translocation velocity. The results suggest a stick-slip type of motion of the dsDNA near the pore surface and a smooth translocation of the dsDNA near the pore center. The smooth dsDNA translocation (with a constant velocity) is governed by the zeta-potential of the pore surface which can be modified by adjusting the pH value and/or the ion concentration of the bulk electrolyte. This enables the mean translocation velocity of the dsDNA to be tuned and reduced. In addition, simulation results suggest that the smooth transport of dsDNA can be achieved by minimizing the dsDNA’s interaction with the pore, for example by chemical modification of its surface.     

Diffusive flux of nanoparticles through chemically modified alumina membranes

Surface chemistry plays an important role in determining flux through porous media such as in the environment. In this paper diffusive flux of nanoparticles through alkylsilane modified porous alumina is measured as a model for understanding transport in porous media of differing surface chemistries. Experiments are performed as a function of particle size, pore diameter, attached hydrocarbon chain length and chain terminus, and solvent. Particle fluxes are monitored by the change in absorbance of the solution in the receiving side of a diffusion cell. In general, flux increases when the membranes are modified with alkylsilanes compared to untreated membranes, which is attributed to the hydrophobic nature of the porous membranes and differences in wettability. We find that flux decreases, in both hexane and aqueous solutions, when the hydrocarbon chain lining the interior pore wall increases in length. The rate and selectivity of transport across these membranes is related to the partition coefficient (K(p)) and the diffusion coefficient (D) of the permeating species. By conducting experiments as a function of initial particle concentration, we find that K(p)D increases with increasing particle size, is greater in alkylsilane-modified pores, and larger in hexane solution than water. The impact of the alkylsilane terminus (-CH(3), -Br, -NH(2), -COOH) on permeation in water is also examined. In water, the highest K(p)D is observed when the membranes are modified with carboxylic acid terminated silanes and lowest with amine terminated silanes as a result of electrostatic effects during translocation.     

Transport of ionic species through functionalized poly(vinylbenzyl chloride) membranes

Solid polymeric membranes of poly(vinylbenzyl chloride) (VBC), lightly crosslinked with divinyl benzene, were incompletely reacted such that a fraction of the benzyl chlorines in different membranes was replaced with either dimethyl phosphonate esters (MPE) or triethyl ammonium chloride groups (QA). This work was conducted in an effort to investigate ionic transport through charged and uncharged membranes and to develop fixed site carrier membranes to facilitate the transport of selected metal ions from an aqueous feed stream to a concentrated acid receiving stream. Bulk solution flow does not occur through these membranes. Instead, solute diffusion occurs through the membrane matrix. The effects of hydrogen ion gradient, metal ion identity and charge, reactive site type, acid type, and ionic strength on metal ion transport were investigated. Results are also presented on the effect of membrane orientation and pretreatment (swelling) on metal ion transport. Facilitated transport was investigated through the testing of membranes with varying MPE percent functionalization. The results presented compare the metal ion transport rate to the functionalization of the membranes.     

Binding of ADP in the mitochondrial ADP/ATP carrier is driven by an electrostatic funnel

The ADP/ATP carrier (AAC) is a membrane protein of paramount importance for the energy-fueling function of the mitochondria, transporting ADP from the intermembrane space to the matrix and ATP in the opposite direction. On the basis of the high-resolution, 2.2-A structure of the bovine carrier, a total of 0.53 micros of classical molecular dynamics simulations were conducted in a realistic membrane environment to decipher the early events of ADP (3-) translocation across the inner membrane of the mitochondria. Examination of apo-AAC underscores the impermeable nature of the carrier, impeding passive transport of permeants toward the matrix. The electrostatic funnel illuminated from three-dimensional mapping of the electrostatic potential forms a privileged passageway anticipated to drive the diphosphate nucleotide rapidly toward the bottom of the internal cavity. This conjecture is verified in the light of repeated, independent numerical experiments, whereby the permeant is dropped near the mouth of the mitochondrial carrier. Systematic association of ADP (3-) to the crevice of the AAC, an early event in its transport across the inner membrane, is accompanied by the formation of an intricate network of noncovalent bonds. Simulations relying on the use of an adaptive biasing force reveal for the first time that the proposed binding site corresponds to a minimum of the free energy landscape delineating the translocation of ADP (3-) in the carrier. The present work paves the way to the design of novel nucleotides and new experiments aimed at unveiling key structural features in the chronology of ADP/ATP transport across the mitochondrial membrane.     

Fluorescence recovery after photobleaching reveals the biochemistry of nucleocytoplasmic exchange

Fluorescence recovery after photobleaching (FRAP) can help unveil subtle dynamical and biochemical properties of intracellular components. A peculiar aspect of this method is that it is based on the change of optical properties only, whereas dynamics and biochemistry of the molecules of interest are not perturbed. This makes FRAP particularly suitable for the study of protein translocation, e.g., between nucleus and cytoplasm. Here we present a comprehensive theoretical treatment of FRAP applied to protein nucleocytoplasmic translocation by passive diffusion and/or energy-driven processes across the nuclear envelope. Our mathematical model is validated by experimental FRAP studies with functionalized fluorescent protein chimeras. Using this approach we demonstrate that molecular crowding at the nuclear pore does not hamper passive diffusion and calculate the dimension of the nuclear pore size (5.33 nm). Additionally, our FRAP analysis reveals the biochemical parameters (maximum translocation rate and dissociation constant of the transport complex in cytoplasm) associated with the active import of a prototypical nuclear localization sequence (NLS of SV40) and related mutants. We demonstrate that transportin binding and active import into the nucleus are independent processes that can be separately modulated. The present results are discussed in light of their potential to help in engineering sequences for intracellular targeted delivery of sensors and/or therapeutic compounds. Finally, the limits of validity of our mathematical model are addressed.     

Convection, diffusion and reaction in a surface-based biosensor: modeling of cooperativity and binding site competition on the surface and in the hydrogel

We study theoretically the transport and kinetic processes underlying the operation of a biosensor (particularly the surface plasmon sensor "Biacore") used to study the surface binding kinetics of biomolecules in solution to immobilized receptors. Unlike previous studies, we concentrate mainly on the modeling of system-specific phenomena rather than on the influence of mass transport limitations on the intrinsic kinetic rate constants determined from binding data. In the first problem, the case of two-site binding where each receptor unit on the surface can accommodate two analyte molecules on two different sites is considered. One analyte molecule always binds first to a specific site. Subsequently, the second analyte molecule can bind to the adjacent unoccupied site. In the second problem, two different analytes compete for one binding site on the same surface receptor. Finally, the third problem considers the case of positive cooperativity among bound molecules in the hydrogel using a simple mean-field approach. The transport in both the flow channel and the hydrogel phases of the biosensor is taken into account in this case (with few exceptions, most previous studies assume a simpler model in which the hydrogel is treated as a planar surface with the receptors). We consider simultaneously diffusion and convection through the flow channel together with diffusion and cooperativity binding on the surface and in the hydrogel. In each case, typical results for the concentration contours of the free and bound molecules in the flow channel and hydrogel regions are presented together with the time-dependent association/dissociation curves and reaction rates. For binding site competition, the analysis predicts overshoot phenomena.     

The nature of surface barriers on nanoporous solids explored by microimaging of transient guest distributions

Nanoporous solids are attractive materials for energetically efficient and environmentally friendly catalytic and adsorption separation processes. Although the performance of such materials is largely dependent on their molecular transport properties, our fundamental understanding of these phenomena is far from complete. This is particularly true for the mechanisms that control the penetration rate through the outer surface of these materials (commonly referred to as surface barriers). Recent detailed sorption rate measurements with Zn(tbip) crystals have greatly enhanced our basic understanding of such processes. Surface resistance in this material has been shown to arise from the complete blockage of most of the pore entrances on the outer surface, while the transport resistance of the remaining open pores is negligibly small. More generally, the revealed correlation between intracrystalline diffusion and surface permeation provides a new view of the nature of transport resistances in nanoporous materials acting in addition to the diffusion resistance of the regular pore network, leading to a rational explanation of the discrepancy which is often observed between microscopic and macroscopic diffusion measurements.     

Quantifying barriers to monovalent anion transport in narrow non-polar pores

The transport of anionic drinking water contaminants (fluoride, chloride, nitrate and nitrite) through narrow pores ranging in effective radius from 2.5 to 6.5 ? was systematically evaluated using molecular dynamics simulations to elucidate the magnitude and origin of energetic barriers encountered in nanofiltration. Free energy profiles for ion transport through the pores show that energy barriers depend on pore size and ion properties and that there are three key regimes that affect transport. The first is where the ion can fit in the pore with its full inner hydration shell, the second is where the pore size is between the bare ion and hydrated radius, and the third is where the ion size approaches that of the pore. Energy barriers in the first regime are relatively small and due to rearrangement of the inner hydration shell and/or displacement of further hydration shells. Energy barriers in the second regime are due to partial dehydration and are larger than barriers seen in the first regime. In the third regime, the pore becomes too small for bare ions to fit regardless of hydration and thus energy barriers are very high. In the second regime where partial dehydration controls transport, the trend in the slopes of the change in energy barrier with pore size corresponds to the hydration strength of the anions.     

纳滤膜对电解质溶液分离特性的理论研究(II): 混合电解质溶液

假定纳滤膜具有狭缝状孔, 使用纯水透过系数、膜孔径及膜表面电势来表征纳滤膜的分离特征, 用流体力学半径和无限稀释扩散系数表征了离子特性. 采用扩展Nernst-Planck方程、Donnan平衡模型和Poisson-Boltzmann理论描述了混合电解质溶液中离子在膜孔内的传递现象, 计算了三种商用纳滤膜(ESNA1-LF, ESNA1和LES90)对同阴离子、同阳离子和含四种离子的混合电解质体系中离子的截留率, 并与实验数据进行了比较. 计算结果表明, 电解质溶液中离子在纳滤膜孔内传递的主要机理是离子的扩散和电迁移, 纳滤膜对混合电解质溶液中离子的分离效果主要由空间位阻和静电效应决定. 该模型在低浓度时对含一价离子的混合电解质溶液通过纳滤膜的截留率计算结果比较准确, 但对高浓度或含高价离子的混合电解质溶液则偏差较大.     

Modeling of temperature-programmed desorption thermograms for the determination of adsorption heat considering pore and surface diffusion

In this work, two partial differential equation-based models have been proposed for the quantitative analysis of temperature-programmed desorption (TPD) thermograms when the adsorption cell can be modeled as a well-mixed reactor, using the Langmuir equation as the adsorption isotherm and including the effect of diffusional resistance. One model considers pore diffusion, and the other considers surface diffusion. For both models, the rate of adsorption is proportional to the gas pressure. By nondimensionalizing these models, the range of design parameters for which the accumulation in the gas cell, diffusional resistance, and readsorption have an important effect on the TPD signal is proposed. An important conclusion is that the dimensionless numbers accounting for the diffusional resistance and the corresponding range of parameters are quite different for both mechanisms. The models have been validated with two systems where surface and pore diffusion are the relevant mechanisms: (i) CO2-Na-mordenite and (ii) CO2-Na-mordenite pellets.     

Ion-transfer voltammetry at silicon membrane-based arrays of micro-liquid-liquid interfaces

Microporous silicon membranes, fabricated by lithographic patterning and wet and dry silicon etching processes, were used to create arrays of micro-scale interfaces between two immiscible electrolyte solutions (muITIES) for ion-transfer voltammetry. These membranes served the dual functions of interface stabilization and enhancement of the rate of mass-transport to the interface. The pore radii were 6.5 microm, 12.8 microm and 26.6 microm; the pore-pore separations were ca. 20- to 40-times the pore radii and the membrane thickness was 100 microm. Deep reactive ion etching (DRIE) was used for pore drilling through the silicon, which had been previously selectively thinned by potassium hydroxide etching. DRIE produces hydrophobic fluorocarbon-coated internal pore walls. The small pore sizes and large pore-pore separations used resulted in steady-state voltammograms for the transfer of tetramethylammonium cation (TMA(+)) from the aqueous to the organic phase, whereas the reverse voltammetric sweeps were peak-shaped. These asymmetric voltammograms are consistent with the location of the ITIES at the aqueous side of the silicon membrane such that the organic phase fills the micropores. Comparison of the experimental currents to calculated currents for an inlaid disc micro-interface revealed that the interfaces were slightly recessed, up to 10 microm (or 10% of the pore length) in one case. Facilitated ion transfer, with an organic-phase ionophore, confirmed the location of the organic phase within the pores. These microporous silicon membranes offer opportunities for various analytical operations, including enhancing the rate of mass transport to ITIES-based sensing devices and stabilization of the ITIES for hydrodynamic applications.     

Estimation of diffusion parameters in functionalized silicas with modulated porosity. Part II: pore network modeling

In this work, the pore structure of those five (5) silicas SiO2-X (see Part I) which have suffered gradual functionalization with functional groups X of increasing length (X = psi, [triple bond]Si-H, [triple bond]Si-CH2OH, [triple bond]Si-(CH2)3OH, [triple bond]Si-(CH2)11CH3), is modeled as a three-dimensional cubic network of cylindrical pores. Those hybrids organic-inorganic SiO2-X samples are characterized by different extent of pore blocking effects. The pores of samples are represented in a 9 x 9 x 9 lattice by the nodes as well the bonds that are interconnected in a so-called dual site-bond model, DSBM, network. The pore network is developed using a Monte Carlo statistical method where the cylindrical pores (nodes and bonds) are randomly assigned into the lattice, until matching of the theoretical results to the experimental data of N2 adsorption-desorption measurements. Thus, a visual picture of the porous solid is possible. This realistic network is used next in order to study the steady-state gas transport (Knudsen gas-phase and viscous diffusion) properties for the examined materials and how flow processes depend on the morphology of the pore structure. The pore diffusivity Dp and total permeability P of each porous medium is determined based on theoretical calculations and the structural statistical parameters, such as porosity epsilonp, tortuosity factor tau and connectivity c of pores is discussed with the corresponding experimental data described in Part I of this work. The results indicate clearly that the diffusion model made it possible to predict pore effective diffusivity in these porous media in very good agreement with the corresponding experimental results for all the examined solids (Part I). The pore diffusivity increases significantly as the value of the pore connectivity increases but the transport properties of the network are influenced strongly at lowest connectivity. Also the predicted tortuosity factor is related inversely to the extent of interconnection of pores in these solids, which indicates that the influence of pore branching to the tortuosity factor of the pore network decreases, as connectivity increases.     

Theoretical modeling of water vapor transport in cellulose-based materials

The theory of mass transport in porous media is of fundamental importance for different applications such as food, paper packaging, textiles, and wood for building materials. In this study, a theoretical water vapor transport model has been developed for cellulose-based materials, such as paper and regenerated cellulose film. Pore diffusivities were determined from the dynamic moisture breakthrough experiments comprising a stack of paper sheets and regenerated cellulose films in a configuration similar to a packed adsorption column. Other mass transfer parameters were determined from transient moisture uptake rate measurements. The model incorporates pore and surface diffusion as a lump parameter into a variable effective diffusion coefficient. The mass transport, involving both pore and surface diffusions, is evaluated independently. The theoretical water vapor transmission rates (WVTRs) obtained from the model were compared with experimentally determined WVTRs measured under steady-state conditions. The theoretical model, based on intrinsic diffusion, stipulates higher WVTR values compared to the experimental results. However, the theoretical water vapor transfer rates agree well with the experimental results when external mass transfer resistance is incorporated in the model.