Diffusion on membrane tubes: a highly discriminatory test of the Saffman-Delbruck theory

The efficient transport of membrane proteins is vital in maintaining life. In this work, we investigate the transport of such membrane proteins along long thin membrane tubes or tethers. We calculate the diffusion constant to leading order in the low Reynolds number regime to be D = (4 pi eta)-1 log(r/a), with r and a being the tube and protein radii, respectively, and eta being the membrane viscosity. Thus we propose an exact limiting form for the controversial logarithmic correction, such as originally introduced by Saffman and Delbruck, that involves the tube radius rather than some "frame size". Our work suggests a test of this logarithmic correction could be achieved by measuring diffusion on membrane tubes, exploiting the fact that the equilibrium tube radius can be controlled by the membrane tension and varied over several orders of magnitude. We analyze the time taken for a protein to transit a membrane tube between cells and find that this can vary by an order of magnitude over physiological tensions. This is a strong effect in biological terms and suggests a possible regulatory coupling between membrane tension and signaling.     

Flow-Induced Precipitation in Thin Capillaries Creates Helices,Lamellae, and Tubes

Precipitation reactions under flow in confined media are relevant to the control of pathological biomineralization, processes affecting aquifers, and challenges in the petroleum industry. Here we show that for a simple geometry, such conditions create macroscopic structures including helices, tubes, lamellae, slugs, and disordered patterns. All structures emerge when salt solution is slowly injected into thin capillaries filled with hydroxide solution. For the helices, the pitch is proportional to the pump rate revealing a constant period of 0.63 s. Different morphologies of the insoluble metal hydroxide can co-exist causing random transitions along the capillary. On average, 15 % of the final system contains residual hydroxide solution. While mechanically stable for flow speeds above 25 mm min⁻¹, structures collapse and sediment for slower injection speeds. Some of the observed features share similarities with precipitate tubes in chemical gardens and the dynamics of liquid–liquid pipe flow.     

Characterization of iron-phosphate-silicate chemical garden structures

Chemical gardens form when ferrous chloride hydrate seed crystals are added or concentrated solutions are injected into solutions of sodium silicate and potassium phosphate. Various precipitation morphologies are observed depending on silicate and phosphate concentrations, including hollow plumes, bulbs, and tubes. The growth of precipitates is controlled by the internal osmotic pressure, fluid buoyancy, and membrane strength. Additionally, rapid bubble-led growth is observed when silicate concentrations are high. ESEM/EDX analysis confirms compositional gradients within the membranes, and voltage measurements across the membranes during growth show a final potential of around 150-200 mV, indicating that electrochemical gradients are maintained across the membranes as growth proceeds. The characterization of chemical gardens formed with iron, silicate, and phosphate, three important components of an early earth prebiotic hydrothermal system, can help us understand the properties of analogous structures that likely formed at submarine alkaline hydrothermal vents in the Hadean-structures offering themselves as the hatchery of life.     

Electrophoretic transport of latex particles in lipid nanotubes

Lipid vesicles can be connected by membrane nanotubes to build networks with promising bioanalytical properties. Here we characterize electrophoretic transport in such membrane tubes, with a particular eye to how their soft-material nature influences the intratube migration. In the absence of field, the tube radius is 110 +/- 26 nm, and it remains in this range during electrophoresis even though the applied electric field causes a slight decrease in the tube radius (approximately 6-11%). The electrophoretic velocity of the membrane wall (labeled with quantum dots) varies linearly with the field strength. Intratube migration is studied with latex spheres of radii 15, 50, 100, and 250 nm. The largest particle size does not enter the tube at fields strengths lower than 1250 V/m because the energy cost for expanding the tube around the particles is too high. The smaller particles migrate with essentially the same velocity as the membrane at low fields. Above 250 V/cm, the 15 nm particles exhibit an upward deviation from linear behavior and in fact migrate faster than in free solution whereas the 100 nm particles deviate downward. We propose that these nonlinear effects arise because of lipid adsorption to the particles (dominating for 15 nm particles) and a pistonlike compression of the solvent in front of the particles (dominating for 100 nm). As expected from such complexities, existing theories for a sphere migrating in a rigid-wall cylinder cannot explain our velocity results in lipid nanotubes.     

Compositional analysis of copper-silica precipitation tubes

Silica gardens consist of hollow tubular structures that form from salt crystals seeded into silicate solution. We investigate the structure and elemental composition of these tubes in the context of a recently developed experimental model that allows quantitative analyses based on predetermined reactant concentrations and flow rates. In these experiments, cupric sulfate solution is injected into large volumes of waterglass. The walls of the resulting tubular structures have a typical width of 10 microm and are gradient materials. Micro-Raman spectroscopy along with energy dispersive X-ray fluorescence data identify amorphous silica and copper(ii) hydroxide as the main compounds within the inner and outer tube surfaces, respectively. Upon heating the blueish precipitates to approximately 150 degrees C, the material turns black as copper(ii) hydroxide decomposes to copper(ii) oxide. Moreover, we present high resolution transmission electron micrographs that reveal polycrystalline morphologies.     

Three-dimensional morphological chirality induction using high magnetic fields in membrane tubes prepared by a silicate garden reaction

Using a vertical superconducting magnet (max. 15 T), we studied magnetic field effects on membrane tube morphology prepared by a silicate garden reaction. At zero field, semipermeable membrane tubes grew upward when metal salts were added to a sodium silicate aqueous solution. In the presence of a magnetic field (15 T, downward) right-handed helical membrane tubes grew along a glass vessel's inner surface when magnesium chloride and copper sulfate were added. Referring to membrane tubes by the names of metal cations used in their preparation, in the case of Mg(II) and Zn(II) membrane tubes, the left-handed helical tubes grew when the field direction was reversed upward. The left-handed helical Mg(II) membrane tubes grew in the magnetic field when a glass rod was placed in a vessel. Mg(II) and Zn(II) tubes, separate from a vessel wall, grew in a twisted shape in the magnetic field. In situ observation of the solution's motion during the reaction revealed that the Lorentz force on the outflow from the opened top of the hollow membrane tube induced convection of the solution near the tube exit, engendering chiral growth of the membrane tubes. Relative orientation of the outflow and a boundary (a vessel wall or glass rod surface) helped to determine the convection's direction.     

Precipitative growth templated by a fluid jet

Tubular growth by chemical precipitation at the interface between two fluids, a jet and its surroundings, underlies the development of such important structures as chimneys at hydrothermal vents. This growth is associated with strong thermal and/or solute gradients localized at those interfaces, and these gradients, in turn, often produce radial compositional stratification of the resulting tube wall. A fundamental question underlying these processes is how the interplay between diffusion, advection, and precipitation determines the elongation rate of the tubes. Here we report experimental and theoretical results that reveal a regime in which there exists a new scaling law for tube growth. The model system studied consists of a jet of aqueous ammonia injected into a ferrous sulfate solution, precipitating iron hydroxides with varying oxidation states at the jet boundary. Despite the complex chemistry and dynamics underlying the precipitation, the tube growth exhibits a strikingly simple scaling form, with characteristic lengths and times increasing linearly with the mean velocity of the jet. These observations follow from a kinetic model of advection-dominated flows.     

Formation of tubes during self-assembly of bacterial surface layers

Based on experimental studies on tube formation during self-assembly of bacterial surface (S)-layers, a mechanistic model for describing the underlying basic mechanisms is proposed and the effect of process parameters on growth velocity and tube radius is investigated. The S-layer is modeled as a curved sheet with discrete binding sites for the association of monomers distributed along the S-layer edges. Reported changes of the tube radius owing to genetic protein modifications are explained within the framework of continuum mechanics. S-layer growth velocity and shape development are analyzed by Monte Carlo simulation in their dependence on the attachment and detachment frequencies of monomers at the S-layer. For curved S-layer patches, a criterion for the formation of S-layer tubes is derived. Accordingly, tubes can form only within a certain range of the initial monomer concentration. Furthermore, the effect of calcium ion concentration on tube formation is discussed, including recent experimental findings on the calcium effect.     

Electrophoresis of concentrically and eccentrically positioned cylindrical particles in a long tube

We study analytically and numerically the electrophoretic motion of cylindrical particles translating slowly in long tubes filled with an electrolyte solution and subjected to axial electric fields. Both thin and thick double layers are considered. Of particular interest is the case when the particle's and tube's radii are of the same order of magnitude. The model accounts for the flow induced by the particle's motion (the particle acts as a leaky piston) and the electroosmotic flow in the tube. The electrophoretic velocity of the particle and the forces and torques acting on it are determined as functions of the particle's radius, length, and position, the particle's and tube's zeta potentials, the tube's length, and the externally imposed pressures. When the particle is positioned off center, it rotates and its trajectory traces an oscillatory path.     

Pressure-driven fluidic delivery through carbon tube bundles

The aim of this work is to demonstrate controlled flow through macroscopically long (approximately 1 cm) carbon tubes (0.5-1.8 microm in radius). A model, high-throughput, pressure-driven fluidic setup, which features a large number of parallel carbon tubes forming a bundle, is fabricated and tested. The carbon tubes are synthesized and self-assembled via co-electrospinning and subsequent carbonization. The setup accommodates pressure-driven flows with flow discharge rates of the order of 1 nL s(-1) (73 x 10(-11) kg s(-1)) for low-viscosity liquids and 30 nL s(-1) (36.3 x 10(-12) kg s(-1)) for gases into a water pool under imposed pressure drops below 4 bar. The measurements demonstrate the ability to sustain well-controlled laminar flows through these long carbon tube bundles and elucidate the main transport features. A novel procedure is also formulated to recover the flow-carrying tube inner-diameter distribution from the measured dependence of the fluid volumetric or mass flow rate on the imposed pressure drop.     

Calculation of the dynamic temperature characteristics of a heated graphite tube used in electrothermal atomic absorption measurements

A method and computer program were developed for calculating the temperature of any part of a graphite furnace tube at any instant of time after onset of the heating cycle. Results for tubes of the Massman design show large differences in spatial temperature distributions during and at the end of the heating cycle when equilibrium is reached. When constant current is applied to contoured tubes, greater heating rates at the tube centres are obtained than with standard tubes.     

Molybdenum dichalcogenide nanotube arrays for hydrogen-evolution-reaction catalysis: Synergistic effects of sulfur and selenium in a core-shell tube wall

The present work shows the growth and conversion of self-organized anodic Mo-oxide nanotube arrays to core-shell structures consisting of a conducting molybdenum sub-oxide core and a shell of Mo-Se/S – this structure is then investigated for electrochemical hydrogen evolution catalysis. To form the core-shell tubes, we first anneal MoO₃ nanotube arrays under vacuum conditions, to induce reduction to MoO₂. Subsequently these oxide tubes are thermally sulfurized and selenized resulting in dichalcogenide@sub-oxide structures. Under optimized conditions, the mixed dichalcogenide (selenized and sulfurized) tube walls on the conductive oxide core lead to a synergistic beneficial effect for the electrocatalytic H₂ generation from H₂SO₄ solution.     

Distribution of carbon nanotube sizes from adsorption measurements and computer simulation

The method for the evaluation of the distribution of carbon nanotube sizes from the static adsorption measurements and computer simulation of nitrogen at 77 K is developed. We obtain the condensation/evaporation pressure as a function of pore size of a cylindrical carbon tube using Gauge Cell Monte Carlo Simulation (Gauge Cell MC). To obtain the analytical form of the relationships mentioned above we use Derjaguin-Broekhoff-deBoer theory. Finally, the pore size distribution (PSD) of the single-walled carbon nanohorns (SWNHs) is determined from a single nitrogen adsorption isotherm measured at 77 K. We neglect the conical part of an isolated SWNH tube and assume a structureless wall of a carbon nanotube. We find that the distribution of SWNH sizes is broad (internal pore radii varied in the range 1.0-3.6 nm with the maximum at 1.3 nm). Our method can be used for the determination of the pore size distribution of the other tubular carbon materials, like, for example, multiwalled or double-walled carbon nanotubes. Besides the applicable aspect of the current work the deep insight into the problem of capillary condensation/evaporation in confined carbon cylindrical geometry is presented. As a result, the critical pore radius in structureless single-walled carbon tubes is determined as being equal to three nitrogen collision diameters. Below that size the adsorption-desorption isotherm is reversible (i.e., supercritical in nature). We show that the classical static adsorption measurements combined with the proper modeling of the capillary condensation/evaporation phenomena is a powerful method that can be applied for the determination of the distribution of nanotube sizes.     

介绍一种改进内压力盐效应公式的计算方法

式中k_s为盐析常数,c_s为盐的浓度,分别为非电解质和盐在无限稀释溶液中的偏摩尔体积,V_s为盐在液体状态下的摩尔体积,β_o为水的压缩系数,p_e为盐溶于水而产生的有效压力。此式推导过程中所用的极限条件为V_n→0,因此(1)式仅能用在极小的非电解质分子上,对于苯及苯的衍生物讲,K_s计算值约为实验值的2～3倍。当非电解质体积较大时,Mc-     

Delineating the first few seconds of supramolecular self-assembly of mesostructured titanium oxide thin films through time-resolved small angle X-ray scattering

The early stages of evaporation induced self-assembly of titanium oxide mesophases from a precursor solution containing TiCl4 and the Pluronic triblock copolymer F-127 in HCl-water-ethanol solution have been studied using time-resolved SAXS techniques. Two experimental protocols were used to conduct these experiments. In one of these, the precursor solution was pumped around a closed loop as solvent was allowed to evaporate at a constant humidity-controlled rate. In the second protocol, a film of precursor solution was measured periodically as it dried completely to a residue under a stream of dry air. This permitted the detailed monitoring of changes in solution chemistry as a function of the elimination of volatile components followed by the actual drying process itself. The SAXS data were modeled in terms of two Guinier radii for soft nanoparticles while a broad Gaussian feature in the scatter profiles was accounted for by particle-article scattering interference due to close packing. For the initial precursor solution, one Guinier radius was found to be about 17 angstroms while the other ranged from 4 to 11 angstroms. Changing the rate of evaporation affected the two radii differently with a more pronounced effect on the smaller particle size range. Analysis gave an interparticle distance in the range 55-80 angstroms for the initial precursor solution which decreased steadily at both of the humidities investigated as evaporation proceeded and the particle packing increased. These results represent the first attempts to monitor in a precise fashion the growth of nano building blocks during the initial stages of the self-assembly process of a titanium oxide mesophase.     

Chemical-garden formation, morphology, and composition. II. Chemical gardens in microgravity

We studied the growth of metal-ion silicate chemical gardens under Earth gravity (1 g) and microgravity (μg) conditions. Identical sets of reaction chambers from an automated system (the Silicate Garden Habitat or SGHab) were used in both cases. The μg experiment was performed on board the International Space Station (ISS) within a temperature-controlled setup that provided still and video images of the experiment downlinked to the ground. Calcium chloride, manganese chloride, cobalt chloride, and nickel sulfate were used as seed salts in sodium silicate solutions of several concentrations. The formation and growth of osmotic envelopes and microtubes was much slower under μg conditions. In 1 g, buoyancy forces caused tubes to grow upward, whereas a random orientation for tube growth was found under μg conditions.     

Influence of poly-L-lysine on the biomimetic growth of silica tubes in confined media

Pore channels of polycarbonate membranes were recently used as biomimetic models to study the effect of confinement on silicate condensation, leading to the formation of silica tubes exhibiting a core-shell structure. In this work, we preimmobilized poly-L-lysine on the membrane pores, leading to modification of the tube shell formation process and variation in core particle size. These data strengthen previous assumptions on the role of confinement on silica growth, i.e., interfacial interactions and perturbation of the diffusion coefficient. They also suggest that this approach is suitable to investigate in more detail the contribution of confinement effects on silica biomineralization.     

A Hexanuclear Niobium Cluster Compound Crystallizing as Macroscopic Tubes

Compounds with ordered structures in one or two dimensions are exciting materials and investigated intensively in many different areas of science. Many activities have been put into the preparation of low-dimensional nano-scaled structures and many compounds in this size regime are known. Contrary, the number of known compounds that have low-dimensional macroscopic sized structures that form directly in a chemical reaction is very limited. Here, we present the synthesis of the niobium cluster compound [(Et₂O)₂H]₂[Nb₆Cl₁₈], crystals of which grow in form of large hexagonal empty tubes of several centimeter length and diameters in the range of 2 mm. The single-crystal X-ray structure of this compound has been refined. Under warming, the compound readily eliminates diethyl ether molecules and decomposes. From a closer look at the crystallization process a step-by-step scheme of the procedure of the tube growth is proposed. The overall conclusion from this proposal is that a crucial balance between the cluster solution concentration, the crystal growth speed and the ether diffusion speed results in the formation of macroscopic crystal tubes.     

流体力学半径对估算胶体微球聚集速率常数的影响

胶体粒子聚集速率常数实验值远低于理论值一直是被普遍关注的问题.聚集速率常数的理论推导是基于粒子的几何半径来考虑的,但决定粒子扩散速率及聚集速率的应该是粒子的流体力学半径(大于几何半径),因而它是使聚集速率常数实验值低于理论值的因素之一.影响流体力学半径的因素很多,其中,带电粒子在溶液中因表面存在双电层,会明显增大流体力学半径,造成聚集速率减慢.而双电层的厚度又随溶液中离子强度的不同而改变.本工作在聚集速率的公式中引入了修正因子,即几何半径与其流体力学半径之比,以修正由于用几何半径代替流体力学半径带来的误差.其中几何半径和流体力学半径可以分别用扫描电镜(SEM)和动态光散射(DLS)来测定.以两种粒径的聚苯乙烯带电微球为例,考察了在不同离子强度下,该误差的大小.结果发现,对于半径为30 nm的微球,用流体力学半径计算的慢聚集速率常数比理论值偏低约8%.该误差随离子强度增加而减少.对于快聚集情况,流体力学半径对聚集速率基本没有影响.     

Flow-driven Surface Instabilities of Tubular Chitosan Hydrogel

Spatial structures break their symmetry under the influence of shear stress arising from fluid flow. Here, we present surface instabilities appearing on chitosan tubes when an acidic solution of chitosan with various molecular weight is injected into a pool of sodium hydroxide solution. At slow flow rates wrinkle-to-fold transition takes place along the direction of the flow yielding a banded structure. For greater injection rates we observe coexisting modes of wrinkles and folds which are stabilized to periodic wrinkles when the alkaline concentration is increased. The instabilities are characterized by the scaling laws of the pattern wavelength and amplitude with the tube characteristics. Our experimental adaptation of mechanical instabilities provides a new in situ method to create soft biomaterials with the desired surface morphology without the use of any prefabricated templates.