Single particle tracking in systems showing anomalous diffusion: the role of weak ergodicity breaking

Anomalous diffusion has been widely observed by single particle tracking microscopy in complex systems such as biological cells. The resulting time series are usually evaluated in terms of time averages. Often anomalous diffusion is connected with non-ergodic behaviour. In such cases the time averages remain random variables and hence irreproducible. Here we present a detailed analysis of the time averaged mean squared displacement for systems governed by anomalous diffusion, considering both unconfined and restricted (corralled) motion. We discuss the behaviour of the time averaged mean squared displacement for two prominent stochastic processes, namely, continuous time random walks and fractional Brownian motion. We also study the distribution of the time averaged mean squared displacement around its ensemble mean, and show that this distribution preserves typical process characteristics even for short time series. Recently, velocity correlation functions were suggested to distinguish between these processes. We here present analytical expressions for the velocity correlation functions. The knowledge of the results presented here is expected to be relevant for the correct interpretation of single particle trajectory data in complex systems.     

Single particle orientation and rotation tracking discloses distinctive rotational dynamics of drug delivery vectors on live cell membranes

Engineered nanoparticles have emerged as potentially revolutionary drug and gene delivery vectors. Using rod-shaped gold nanoparticles as a model, we studied for the first time the rotational dynamics of nanoparticle vectors on live cell membranes and its impact on the fate of these nanoparticle vectors. The rotational motions of gold nanorods with various surface modifiers were tracked continuously at 200 frames/s under a differential interference contrast microscope. We found that the rotational behaviors of gold nanorod vectors are strongly related to their surface charges. Specific surface functional groups and the availability of receptors on cell membranes also contribute to the rotational dynamics. The study of rotational brownian motion of nanoparticles on cell membranes will lead to a better understanding of the mechanisms of drug delivery and provide guidance in designing surface modification strategies for drug delivery vectors under various circumstances.     

Protonation and diffusion phenomena in poly(4-vinylpyridine)-based weak anion-exchange membranes

Purification and concentration of mineral acids can be carried through dialysis processes with anion-exchange membranes. Weak anion-exchange membranes are active only for sufficient acid concentrations in their structure, however too high concentrations result in significant proton leakage, i.e. reduction in the transport selectivity. The present paper deals with the kinetics of acid diffusion through two commercial poly(4-vinylpyridine)-based weak anion-exchange membranes which comprises protonation of the exchanging groups. The electrical conductivity and the water content of the membranes were shown to be linear function of the protonation degree of poly(4-vinylpyridine) groups. Kinetics of protonation and diffusion of acids have been investigated using dialysis cells. First diffusion kinetics has been studied in a conventional dialysis cell, by observation of the transient acid transport through the membrane (macroscopic studies). Besides, protonation kinetics was investigated using a miniaturised dialysis cell coupled to confocal Raman microspectrometer. Profiles of non-protonated and protonated sites in the membrane were recorded along time, depending on the membrane grade and the nature of the acid transported. Interpretation of the two sources of data yielded permeability coefficient and diffusion coefficient, whose meaning is discussed. A mechanism for protonation/diffusion in this type of weak anion exchangers in acidic media was proposed.     

Coarse‐grained models and collective phenomena in membranes: Computer simulation of membrane fusion

We discuss the role coarse‐grained models play in investigating collective phenomena in bilayer membranes and place them in the context of alternative approaches. By reducing the degrees of freedom and applying simple effective potentials, coarse‐grained models can address the large time scales and length scales of collective phenomena in membranes. Although the mapping from a coarse‐grained model onto chemically realistic models is a challenge, such models provide a direct view on the phenomena that occur on the length scales of a few tens of nanometers. Their relevance is exemplified by the study of fusion of model membranes. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1441–1450, 2003     

Single particle tracking reveals corralling of a transmembrane protein in a double-cushioned lipid bilayer assembly

A predominate question associated with supported bilayer assemblies containing proteins is whether or not the proteins remain active after incorporation. The major cause for concern is that strong interactions with solid supports can render the protein inactive. To address this question, a large transmembrane protein, the serotonin receptor, 5HT(3A), has been incorporated into several supported membrane bilayer assemblies of increasing complexity. The 5HT(3A) receptor has large extracellular domains on both sides of the membrane, which could cause strong interactions. The bilayer assemblies include a simple POPC (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine) supported planar bilayer, a “single-cushion” POPC bilayer with a PEG (poly(ethylene glycol)) layer between membrane and support, and a “double-cushion” POPC bilayer with both a PEG layer and a layer of BSA (bovine serum albumin). Single-cushion systems are designed to lift the bilayer from the surface, and double-cushion systems are designed to both lift the membrane and passivate the solid support. As in previously reported work, protein mobilities measured by ensemble fluorescence recovery after photobleaching (FRAP) are quite low, especially in the double-cushion system. But single-particle tracking of fluorescent 5HT(3A) molecules shows that individual proteins in the double-cushion system have quite high local mobilities but are spatially confined within small corralling domains ( 450 nm). Comparisons with the simple POPC membrane and the single-cushion POPC?PEG membrane reveal that BSA both serves to minimize interactions with the solid support and creates the corrals that reduce the long-range (ensemble averaged) mobility of large transmembrane proteins. These results suggest that in double-cushion assemblies proteins with large extra-membrane domains may remain active and unperturbed despite low bulk diffusion constants.     

Theoretical analysis of time-dependent diffusion, reaction and electromigration in membranes

 The transport of material through a membrane of finite thickness via the process of diffusion is examined theoretically. The membrane is assumed to be sandwiched between a donor and a receptor compartment and it is assumed that infinite source and sink conditions pertain. The effect of an externally applied electric field and concurrent first-order chemical reaction of the diffusant species with sites in the membrane on the diffusion rate is examined via the formulation of a time-dependent differential equation and its subsequent solution via the technique of Laplace transformation. Closed form expressions for the diffusant lag time and permeability are derived and compared with expressions previously presented in the literature. Received: 9 February 1999 / Accepted: 8 October 1999     

Electrokinetic phenomena in porous membranes: Determination of phenomenological coefficients and transport numbers

Electrokinetic phenomena in porous membranes were studied in the framework of the linear thermodynamics of irreversible processes. Phenomenological coefficients of two commercial porous membranes were determined. The variation of these coefficients with the different concentrations of NaCl used was also studied. Onsager's reciprocal relationship between cross-coefficients holds within the limits of experimental error.Membrane potentials were measured at concentrations ranging from 10^?3M to 75 X 10^?3M. The apparent transport number of the cation,

, was calculated from the diffusion potential expression. An electrometric method was used to obtain the true cation transport number,

, and the water transport number,

, for different solution concentrations, ranging from 15 x 10^?3M to 75 x 10^?3M. The true transport number of the cation,

, was also determined, taking into account water transport across the membrane. A good agreement was found between

and

values.     

Effect of molecular association on solubility,diffusion, and permeability in polymeric membranes

The filling‐type membrane is composed of grafted polymer and solvent‐resistant substrate; the calculation of solubility, diffusivity and swelling‐suppression effect by the substrate permits the prediction of solvent permeability. As noted in our previous article, the use of this approach, called membrane design, resulted in accurate prediction of the permeability of aromatic compounds. In this study, the influence of hydrogen bonding on solubility and diffusivity is investigated both theoretically and experimentally. The solubility of chloroform and dichloromethane in poly(acrylate)s increases, and their diffusivity decreases, compared with that estimated without considering the hydrogen‐bonding effect. Solubilities predicted by the lattice‐fluid hydrogen‐bonding (LFHB) model show good agreement with the results of vapor sorption. Comparison of diffusion coefficients measured by vapor permeation with those predicted from free volume theory reveals that the decrease of solvent diffusion coefficient is approximately proportional to the fraction of associated molecules. Fluxes of chloroform and dichloromethane were measured by vapor permeation experiments through filling‐type acrylate membranes, and predictions agree well with experiments. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 171–181, 2000     

MD simulation of the Na+-phenylalanine complex in water: competition between cation-pi interaction and aqueous solvation

The competition between cation-pi interaction and aqueous solvation for the Na+ ion has been investigated by molecular dynamics simulations, using the phenylalanine amino acid as the test pi system. Starting from one of the best standard force fields, we have developed new parameters that significantly improve the agreement with experimental and high quality quantum mechanical results for the complexes of Na+ with phenylalanine, benzene, and water. The modified force field performs very well in forecasting energy and geometry of cation coordination for the complexes. Next, analysis of MD trajectories and steered MD simulations indicate that the Na+-phenylalanine complex survives for a significant time in aqueous solution and that the free energy barrier opposing dissociation of the complex is sizable. Finally, we analyze the role of different intermolecular interactions in determining the preference for cation-pi bonding with respect to aqueous solvation. We thus confirm that the Na+-phenylalanine stabilization energy may overcome the interactions with water.     

Molecular simulation of binary colloidal mixtures: Gelation and aging phenomena

We investigate the aging dynamics of colloidal depletion gel by computer simulation. In this study, we employ an alternative approach using the effective pair potential to avoid the slow convergence in binary mixtures due to cage effect, and the structural formation of colloidal depletion gels is then clarified. We study the mean square displacement (MSD) of each segment in depletion gels by stochastic molecular dynamic simulations. It is shown that the MSD obeys a power-law, indicating sub-diffusive behavior of depletion gels. We also observe aging phenomena of the colloidal depletion gels from intermediate scattering functions. Power-law behavior of a characteristic time in this system, as a function of a waiting time, is also clarified.     

Non-equilibrium molecular dynamics simulation study on permeation phenomena of LJ particles in slit-shaped membranes with periodic belt-like heterogeneous surfaces

In order to make clear the relationship between the pore structure and the diffusivity, we have carried out permeation simulations of pure gases through simple model membranes by using the external-field non-equilibrium molecular dynamics method. As the membrane, we model slit-shaped pores with periodic belt-like heterogeneous pore surfaces which are caused by the upheaval of surface atoms. Applying simulation results for membranes with several upheaval interval distances to Maxwell–Stefan (MS) theory, we calculate the effects of the molecular loading of permeating molecules in the pores on MS diffusivity (D_MS). In addition, the permeation potential barrier is estimated as the difference between the maximum and minimum permeation potential energies. The effect of the molecular loading on the permeation potential barrier and the D_MS are in inverse proportion. It is noted that, when the width of the adsorption area in the permeation direction is not common multiples of the molecular diameter, the permeation potential barrier decreases with the increase in the molecular loading. This is because the positive force against the permeation direction is caused to the permeating molecules by interactions with permeating molecules in the adsorpton area between adjacent upheavals. Therefore, we could suggest that the key factor for controlling diffusion property is the structural relationship between the adsorption area and the permeating molecules.     

A dual-electrode approach for highly selective detection of glucose based on diffusion layer theory: experiments and simulation

A dual-electrode configuration for the highly selective detection of glucose in the diffusion layer of the substrate electrode is presented. In this approach, a glassy carbon electrode (GCE, substrate) modified with a conductive layer of glucose oxidase/Nafion/graphite (GNG) was used to create an interference-free region in its diffusion layer by electrochemical depletion of interfering electroactive species. A Pt microelectrode (tip, 5 microm in radius) was located in the diffusion layer of the GNG-modified GCE (GNG-G) with the help of scanning electrochemical microscopy. Consequently, the tip of the electrode could sense glucose selectively by detecting the amount of hydrogen peroxide (H2O2) formed from the oxidization of glucose on the glucose oxidase layer. The influences of parameters, including tip-substrate distance, substrate potential, and electrolyzing time, on the interference-removing efficiency of this dual-electrode approach have been investigated systematically. When the electrolyzing time was 30 s, the tip-substrate distance was 1.8 a (9.0 microm) (where a is the radius of the tip electrode), the potentials of the tip and substrate electrodes were 0.7 V and 0.4 V, respectively, and a mixture of ascorbic acid (0.3 mM), uric acid (0.3 mM), and 4-acetaminophen (0.3 mM) had no influence on the glucose detection. In addition, the current-time responses of the tip electrode at different tip-substrate distances in a solution containing interfering species were numerically simulated. The results from the simulation are in good agreement with the experimental data. This research provides a concept of detection in the diffusion layer of a substrate electrode, as an interference-free region, for developing novel microelectrochemical devices.     

Structure,thermodynamics and diffusion in asymmetric binary mixtures: a molecular dynamics simulation study

Structural and thermodynamic properties as well as diffusion coefficients of binary fluid mixtures with asymmetry in mass, size, charge and their combinations have been studied using classical molecular dynamics simulations. The fluid mixture is modelled as spherical particles interacting via the Weeks–Chandler–Andersen and Coulomb potential. The diameter, charge and mass of the fluid particles are in the range 6–60 Å, 1–10e and 1—500 amu, respectively. Systematic variations in pair-correlation functions, thermodynamic properties as well as the self-diffusion coefficient are found with the size, charge and mass ratio of the particles. The self-diffusion coefficient for systems having more than one type of asymmetry is calculated and expressed in terms of diffusion coefficients of systems with only one type of asymmetry.     

Statistical mechanics of diffusion in polymers: Conductivity and electroosmosis in ion exchange membranes

The dependency of swelling of an ion exchange membrane and its ion-exchange capacity on the conductivity and electroosmosis are investigated. The analysis is based on a rigorous statistical mechanics theory employing the formalism of the generalized Nernst–Planck equation in the dusty gas membrane model. The simulation uses binary diffusivities computed from experimental data. Some unexpected conclusions can be drawn from the computed transport characteristics: at constant swelling of the polymeric membrane the equivalent conductivity decreases with the exchange capacity; the enhancement of conductivity by electroosmosis is rather poor, in all cases smaller than 15 %; conductivity of the material is more dependent on its exchange capacity than on swelling.

The calculations confirm that an optimized membrane with low electroosmosis is a highly charged membrane with low swelling. We show that the simple binary theories lead to wrong predictions of the conductivity even qualitatively. Finally, we propose a simple empirical theory, compatible with the generalized Nernst–Planck equation, where the diffusivities increase exponentially with swelling.     

CHARMM‐GUI Martini Maker for modeling and simulation of complex bacterial membranes with lipopolysaccharides

A complex cell envelope, composed of a mixture of lipid types including lipopolysaccharides, protects bacteria from the external environment. Clearly, the proteins embedded within the various components of the cell envelope have an intricate relationship with their local environment. Therefore, to obtain meaningful results, molecular simulations need to mimic as far as possible this chemically heterogeneous system. However, setting up such systems for computational studies is far from trivial, and consequently the vast majority of simulations of outer membrane proteins still rely on oversimplified phospholipid membrane models. This work presents an update of CHARMM‐GUI Martini Maker for coarse‐grained modeling and simulation of complex bacterial membranes with lipopolysaccharides. The qualities of the outer membrane systems generated by Martini Maker are validated by simulating them in bilayer, vesicle, nanodisc, and micelle environments (with and without outer membrane proteins) using the Martini force field. We expect this new feature in Martini Maker to be a useful tool for modeling large, complicated bacterial outer membrane systems in a user‐friendly manner. © 2017 Wiley Periodicals, Inc.     

Structure, dynamics, and phase transitions of tethered membranes: a Monte Carlo simulation study

A coarse-grained model of a self-avoiding tethered membrane with hexagonal coordination, embedded in three-dimensional space, is studied by means of extensive Monte Carlo computer simulations. The simulations are performed at various temperatures for membranes with linear size 5< or =L< or =50. We find that the membrane undergoes several folding transitions from a high-temperature flat phase to multiple-folded structure as the temperature is steadily decreased. Using a suitable order parameter and finite size scaling analysis, these phase transitions are shown to be of first order. The equilibrium shape of the membranes is analyzed by calculating the eigenvalues lambda(max) (2)> or =lambda(med) (2)> or =lambda(min) (2) of the inertia tensor. We present a systematic finite size scaling analysis of the radius of gyration and the eigenvalues of the inertia tensor at different phases of the observed folding transitions. In the high-temperature flat phase, the radius of gyration R(g) grows with the linear size of the membrane L as R(g) proportional to L(nu), where the exponent nu is approximately equal to 1.0. The eigenvalues of the inertia tensor scale as lambda(max) proportional to lambda(med) proportional to L(nu) and lambda(min) proportional to L(nu(min) ), whereby the roughness exponent nu(min) is approximately equal to 0.7. We also find that the time tau(R) of a self-avoiding membrane to diffuse a distance R(g) scales as tau(R) proportional to L(2nu+2), which is in good agreement with the theoretical predictions.     

Bead-bead interaction parameters in dissipative particle dynamics: relation to bead-size, solubility parameter, and surface tension

Dissipative particle dynamics (DPD) is a mesoscale modeling method for simulating equilibrium and dynamical properties of polymers in solution. The basic idea has been around for several decades in the form of bead-spring models. A few years ago, Groot and Warren established an important link between DPD and the Flory-Huggins chi-parameter theory for polymer solutions. We revisit the Groot-Warren theory and investigate the DPD interaction parameters as a function of bead size. In particular, we show a consistent scheme of computing the interfacial tension in a segregated binary mixture. Results for three systems chosen for illustration are in excellent agreement with experimental results. This opens the door for determining DPD interactions using interfacial tension as a fitting parameter.     

Contribution of convection,diffusion and migration to electrolyte transport through nanofiltration membranes

Transport mechanisms through nanofiltration membranes are investigated in terms of contribution of convection, diffusion and migration to electrolyte transport. A Donnan steric pore model, based on the application of the extended Nernst-Planck equation and the assumption of a Donnan equilibrium at both membrane-solution interfaces, is used. The study is focused on the transport of symmetrical electrolytes (with symmetric or asymmetric diffusion coefficients). The influence of effective membrane charge density, permeate volume flux, pore radius and effective membrane thickness to porosity ratio on the contribution of the different transport mechanisms is investigated. Convection appears to be the dominant mechanism involved in electrolyte transport at low membrane charge and/or high permeate volume flux and effective membrane thickness to porosity ratio. Transport is mainly governed by diffusion when the membrane is strongly charged, particularly at low permeate volume flux and effective membrane thickness to porosity ratio. Electromigration is likely to be the dominant mechanism involved in electrolyte transport only if the diffusion coefficient of coions is greater than that of counterions.