Resolution of small molecules by passage through an open capillary

Thermodynamic characterization of amyloid polymorphism by microfluidic transient incomplete separation

Amyloid fibrils of proteins such as α-synuclein are a hallmark of neurodegenerative diseases and much research has focused on their kinetics and mechanisms of formation. The question as to the thermodynamic stability of such structures has received much less attention. Here, we newly utilize the principle of transient incomplete separation of species in laminar flow in combination with chemical depolymerization for the quantification of amyloid fibril stability. The relative concentrations of fibrils and monomer at equilibrium are determined through an in situ separation of these species based on their different diffusivity inside a microfluidic capillary. The method is highly sample economical, using much less than a microliter of sample per data point and its only requirement is the presence of aromatic residues (W, Y) because of its label-free nature, which makes it widely applicable. Using this method, we investigate the differences in thermodynamic stability between different fibril polymorphs of α-synuclein and quantify these differences for the first time. Importantly, we show that fibril formation can be under kinetic or thermodynamic control and that a change in solution conditions can both stabilise and destabilise amyloid fibrils. Taken together, our results establish the thermodynamic stability as a well-defined and key parameter that can contribute towards a better understanding of the physiological roles of amyloid fibril polymorphism.

Template Instrumentation for "Accurate Constant via Transient Incomplete Separation"

Accurate Constant via Transient Incomplete Separation (ACTIS) is a new method for finding the equilibrium dissociation constant K_d of a protein-small molecule complex based on transient incomplete separation of the complex from the unbound small molecule in a capillary. This separation is caused by differential transverse diffusion of the complex and the small molecule in a pressure-driven flow. The advection-diffusion processes underlying ACTIS can be described by a system of partial differential equations allowing for a virtual ACTIS instrument to be built and ACTIS to be studied in silico. The previous in silico studies show that large variations in the fluidic system geometry do not affect the accuracy of K_d determination, thus, proving that ACTIS is conceptually accurate. The conceptual accuracy does not preclude, however, instrumental inaccuracy caused by run-to-run signal drifts. Here we report on assembling a physical ACTIS instrument with a fluidic system that mimics the virtual one and proving the absence of signal drifts. Furthermore, we confirmed method ruggedness by assembling a second ACTIS instrument and comparing the results of experiments performed with both instruments in parallel. Despite some unintentional differences between the instruments (caused by tolerances in sizes, positions, etc.) and noticeable differences in their respective separagrams, we found that the K_d values determined for identical samples with these instruments were equal. Conclusively, the fluidic system presented here can serve as a template for reliable ACTIS instrumentation.

Direct Measurement of Near-Wall Molecular Transport Rate in a Microchannel and Its Dependence on Diffusivity

Solute transport in a narrow space is the most elemental process in chromatography and biological pattern formation. However, the observation of such transport has been quite difficult, and theoretical investigations have therefore preponderated. Here, using a space- and time-resolved surface plasmon resonance (SPR) method, we measured the nanoscale near-wall (next to the wall) transport rate in a narrow channel after a solution and its solvent had come into contact. By combining the SPR method with a capillary injection method, which enables two solution plugs to flow immediately after they have made contact, we were able to measure the solute concentration evolution at the channel wall. We tested three combinations of two plugs of solution-water-glucose, sodium chloride-water, and glucose-sodium chloride-and succeeded in measuring diffusion-coefficient-dependent changes in the concentration of solute flowing through a rectangular microchannel in less than 0.4 s. A numerical analysis of this system revealed the acceleration of the solute/solution boundary moving on the wall and its deceleration at the center of the channel cross section. The observed experimental transport rate agreed with the numerical result quantitatively. These results show that the solute transport followed a laminar flow with a no-slip model and that the molecules were transported in the order of their diffusivity. In the third combination, when the two solutions made contact and started flowing, the interdiffusion of the solutes resulted in temporal concentrations lower than either of the solutions before contact, which indicated that the contact between the two solutions quickly led to separation by the advection-diffusion processes. We found that such a concentration profile could actually be measured. Our techniques are simple and applicable to a wide range of molecules; the method opens the way to direct observation of the space-time near-wall solute transport process and can be used for the rapid determination of diffusivity.

Brownian Sieving Effect for Boosting the Performance of Microcapillary Hydrodynamic Chromatography. Proof of Concept

Microcapillary hydrodynamic chromatography (MHDC) is a well-established technique for the size-based separation of suspensions and colloids, where the characteristic size of the dispersed phase ranges from tens of nanometers to micrometers. It is based on hindrance effects which prevent relatively large particles from experiencing the low velocity region near the walls of a pressure-driven laminar flow through an empty microchannel. An improved device design is here proposed, where the relative extent of the low velocity region is made tunable by exploiting a two-channel annular geometry. The geometry is designed so that the core and the annular channel are characterized by different average flow velocities when subject to one and the same pressure drop. The channels communicate through openings of assigned cut-off length, say A. As they move downstream the channel, particles of size bigger than A are confined to the core region, whereas smaller particles can diffuse through the openings and spread throughout the entire cross section, therein attaining a spatially uniform distribution. By using a classical excluded-volume approach for modeling particle transport, we perform Lagrangian-stochastic simulations of particle dynamics and compare the separation performance of the two-channel and the standard (single-channel) MHDC. Results suggest that a quantitative (up to thirtyfold) performance enhancement can be obtained at operating conditions and values of the transport parameters commonly encountered in practical implementations of MHDC. The separation principle can readily be extended to a multistage geometry when the efficient fractionation of an arbitrary size distribution of the suspension is sought.

Particle Manipulation with External Field; From Recent Advancement to Perspectives

Physical forces, such as dielectric, magnetic, electric, optical, and acoustic force, provide useful principles for the manipulation of particles, which are impossible or difficult with other approaches. Microparticles, including polymer particles, liquid droplets, and biological cells, can be trapped at a particular position and are also transported to arbitrary locations in an appropriate external physical field. Since the force can be externally controlled by the field strength, we can evaluate physicochemical properties of particles from the shift of the particle location. Most of the manipulation studies are conducted for particles of sub-micrometer or larger dimensions, because the force exerted on nanomaterials or molecules is so weak that their direct manipulation is generally difficult. However, the behavior, interactions, and reactions of such small substances can be indirectly evaluated by observing microparticles, on which the targets are tethered, in a physical field. We review the recent advancements in the manipulation of particles using a physical force and discuss its potentials, advantages, and limitations from fundamental and practical perspectives.

Assessing Accuracy of an Analytical Method In Silico: Application to "Accurate Constant via Transient Incomplete Separation" (ACTIS)

Analytical methods may not have reference standards required for testing their accuracy. We postulate that the accuracy of an analytical method can be assessed in the absence of reference standards in silico if the method is built upon deterministic processes. A deterministic process can be precisely computer-simulated, thus allowing virtual experiments with virtual reference standards. Here, we apply this in silico approach to study "Accurate Constant via Transient Incomplete Separation" (ACTIS), a method for finding the equilibrium dissociation constant (K_d) of protein-small-molecule complexes. ACTIS is based on a deterministic process: molecular diffusion of the interacting protein-small-molecule pair in a laminar pipe flow. We used COMSOL software to construct a virtual ACTIS setup with a fluidic system mimicking that of a physical ACTIS instrument. Virtual ACTIS experiments performed with virtual samples-mixtures of a protein and a small molecule with defined rate constants and, thus, K_d of their interaction-allowed us to assess ACTIS accuracy by comparing the determined K_d value to the input K_d value. Further, the influence of multiple system parameters on ACTIS accuracy was investigated. Within multifold ranges of parameter values, the values of K_d did not deviate from the input K_d values by more than a factor of 1.25, strongly suggesting that ACTIS is intrinsically accurate and that its accuracy is robust. Accordingly, further development of ACTIS can focus on achieving high reproducibility and precision. We foresee that in silico accuracy assessment, demonstrated here with ACTIS, will be applicable to other analytical methods built upon deterministic processes.

Size-Tunable Micro-/Nanofluidic Channels Fabricated by Freezing Aqueous Sucrose

Upon freezing aqueous sucrose at temperatures higher than the eutectic point (-14 °C in this case), two phases, that is, ice and freeze concentrated solution (FCS), are spontaneously separated. FCS forms through-pore fluidic channels when thin ice septum is prepared from aqueous sucrose. Total FCS volume depends on temperature but is independent of the initial sucrose concentration. This allows us to control the size of the FCS channels simply by changing the initial sucrose concentration as long as temperature is kept constant. In this paper, we show that the size of the channel, which has a layered structure, can be controlled in a range from 50 nm to 3 μm. Thus, the FCS channel is suitable for size-sorting of micro- and nanoparticles. We discuss the size-sorting efficiency of the channel and demonstrate the separation of particles with different sizes.

Microfluidic ballistic regime for the generation of linear gradients inside a capillary column: Proof-of-concept and application to the miniaturized acid-base volumetric titration

This work details a simple and original approach for the generation of linear gradients inside straight cylindrical microchannels such as a capillary column. The concept takes advantage of an oft-overlooked regime of dispersion of flowing liquids inside narrow channels: the ballistic regime. The ballistic regime is a pure convective regime and is produced by imposing a high velocity flow in a pre-filled capillary thus limited diffusion takes place. This is obtained by forcing the injection of a plug of solution on a short time scale t, much shorter than t<110×D/r², D is the diffusion coefficient and r the capillary radius. The result is a stretched solution of a given length or depth of penetration, inside the capillary column. This leads to a linear mean concentration field through the mixing zone forming a linear gradient. In miniaturized systems, this transient regime is followed by mainly radial diffusion of the solution inside the capillary due to the short characteristic diffusion time of narrow channels. A convection-diffusion simulation was used to model the gradient formed under this ballistic regime. A specific experimental prototype set-up was designed to investigate this ballistic regime and the formation of a linear gradient of titrant NaOH solution inside a capillary tubing of 500 µm inner diameter and 35-cm total length pre-filled with nitric acid solution. With this prototype, the linear gradient was then pushed in a non-ballistic regime over a confocal fluorescence point detection system in order to measure the fluorescence emission of a fluorescent dye added to the solutions. Considering strong acid-base reaction, fluorescein was used due to its strong fluorescence dependency with pH near its pKa, i.e 6.4. A first set of experiments was realized to demonstrate the validity of such an approach and to determine the optimal condition for the formation of a linear gradient over 300 mm of the 350-mm capillary length. An injection pressure of 1000-mbars over 0.75 s was chosen. The first result was the stability of the system in its ability to produce reproducible linear gradients. As further proofs of feasibility, samples of different nitric acid concentrations were titrated with a 0.25 M NaOH solution. The result was rapid and reproducible titration curves obtained with a fully automated system that consumes less than approximately 70 µL of sample solution.

Transient Incomplete Separation Facilitates Finding Accurate Equilibrium Dissociation Constant of Protein-Small Molecule Complex

Current practical methods for finding the equilibrium dissociation constant, K_d , of protein-small molecule complexes have inherent sources of inaccuracy. Introduced here is "accurate constant via transient incomplete separation" (ACTIS), which appears to be free of inherent sources of inaccuracy. Conceptually, a short plug of the pre-equilibrated protein-small molecule mixture is pressure-propagated in a capillary, causing fast transient incomplete separation of the complex from the unbound small molecule. A superposition of signals from these two components is measured near the capillary exit and used to calculate a fraction of unbound small molecule, which, in turn, is used to calculate K_d . Herein the validity of ACTIS is proven theoretically, its accuracy is verified by computer simulation, and its practical use is demonstrated. ACTIS has the potential to become a reference-standard method for determining K_d  values of protein-small molecule complexes.

Convection-dominated dispersion regime in wide-bore chromatography: a transport-based approach to assess the occurrence of slip flows in microchannels

This article develops the theoretical analysis of transport and dispersion phenomena in wide-bore chromatography at values of the Peclet number Pe beyond the upper bound of validity of the Taylor-Aris theory. It is shown that for Poiseuille flows in cylindrical capillaries the average residence time grows logarithmically with the Peclet number, while the variance of the outlet chromatogram scales as the power 1/3 of Pe. In the presence of slip boundary conditions, both the mean and the variance of the outlet chromatograms saturate at high Pe, and this phenomenon provides an indirect transport-based way to detect slip flow conditions at the solid walls and, more generally, flow distributions in channel flows.

Spectral analysis of the weighted Laplacian in slip and no-slip flows

Slip boundary conditions for the velocity field impact on the spectral properties of the advection-diffusion operator describing transport of passive particles in laminar parallel flows. By considering the Hermitian operator (referred to as the weighted Laplacian), describing the interplay between axial convection and cross-sectional diffusion of a scalar field, we show that the spectral watershed between slip and no-slip boundary conditions is a qualitatively different scaling behavior of the mean of the normalized eigenfunctions of the weighted Laplacian. The occurrence of slip conditions also influences the scaling of the density of states as regards both the leading and the subleading term in the Weyl's expansion.

Characterization of bromide ions in charge-stacked zwitterionic micellar systems

A novel zwitterionic surfactant, N-dodecyl-N,N,N',N'-tetra-methyl-ethylene-di-ammonio-propane-sulfonate bromide (DEPB), has been synthesized, and Br(-) involved in the micellar system has been characterized by potentiometry, NMR, and X-ray absorption fine structure (XAFS). Although the dissociation degree of Br(-) from the micelle evaluated by potentiometry almost agrees with that determined by NMR, the former is significantly smaller than the latter over the entire range of concentrations of DEPB. This is explained by assuming that the bromide ions in the micellar system have several different peripheral structures. XAFS has given significant insight into the hydration structures of Br(-) involved in the system. Some of the bromide ions partitioned into the micelle are dehydrated and are directly bound by the ammonium groups in the DEP molecules. However, some of the bromide ions are still completely hydrated even when they are partitioned into the micelles. The average hydration number of the bromide ions directly bound by the ammonium groups was determined to be approximately 3.3. The partial dehydration of Br(-) is possibly facilitated by the characteristic hydration circumstances provided by the charge-stacked structure of the surfactant and by the resulting thick palisade layer of the DEP micelle.