Low Concentration Regime Research Articles

Doped, Two-Dimensional, Semiconducting Transition Metal Dichalcogenides in Low-Concentration Regime

Doped, Two-Dimensional, Semiconducting Transition Metal Dichalcogenides in Low-Concentration Regime

NaCl, MgCl2, and AlCl3 Surface Coverages on Fused Silica and Adsorption Free Energies at pH 4 from Nonlinear Optics.

We employ amplitude- and phase-resolved second harmonic generation experiments to probe interactions of fused silica:aqueous interfaces with Al3+, Mg2+, and Na+ cations at pH 4 and as a function of metal cation concentration. We quantify the second-order nonlinear susceptibility and the total interfacial potential in the presence and absence of a 10 mM screening electrolyte to understand the influence of charge screening on cation adsorption. Strong cation:surface interactions are observed in the absence of the screening electrolyte. The total potential is then employed to estimate the total number of absorbed cations cm-2. The contributions to the total potential from the bound and mobile charges were separated using Gouy-Chapman-Stern model estimates. All three cations bind fully reversibly, indicating physisorption as the mode of interaction. Of the isotherm models tested, the Kd adsorption model fits the data with binding constants of 3-30 and ∼300 mol-1 for the low (<0.1 mM) and high (0.1-3 mM) concentration regimes, corresponding to adsorption free energies of -13 to -18 and -24 kJ mol-1 at room temperature, respectively. The maximum surface coverages are around 1013 cations cm-2, matching the number of deprotonated silanol groups on silica at pH 4. Clear signs of decoupled Stern and diffuse layer nonlinear optical responses are observed and found to be cation-specific.

Visible-Light Driven Control Over Triply and Quadruply Hydrogen-Bonded Supramolecular Assemblies.

Supramolecular polymers offer tremendous potential to produce new "smart" materials, however, there remains a need to develop systems that are responsive to external stimuli. In this work, visible-light responsive hydrogen-bonded supramolecular polymers comprising photoresponsive supramolecular synthons (I-III) consisting of two hydrogen bonding motifs (HBMs) connected by a central ortho-tetrafluorinated azobenzene have been characterized by DOSY NMR and viscometry. Comparison of different hydrogen-bonding motifs reveals that assembly in the low and high concentration regimes is strongly influenced by the strength of association between the HBMs. I, Incorporating a triply hydrogen-bonded heterodimer, was found to exhibit concentration dependent switching between a monomeric pseudo-cycle and supramolecular oligomer through intermolecular hydrogen bonding interactions between the HBMs. II, Based on the same photoresponsive scaffold, and incorporating a quadruply hydrogen-bonded homodimer was found to form a supramolecular polymer which was dependent upon the ring-chain equilibrium and thus dependent upon both concentration and photochemical stimulus. Finally, III, incorporating a quadruply hydrogen-bonded heterodimer represents the first photoswitchable AB type hydrogen-bonded supramolecular polymer. Depending on the concentration and photostationary state, four different assemblies dominate for both monomers II and III, demonstrating the ability to control supramolecular assembly and physical properties triggered by light.

Insights into water extraction and aggregation mechanisms of malonamide-alkane mixtures.

Structure at the nanoscale in the organic phase of liquid-liquid extraction systems is often tied to separation performance. However, the weak interactions that drive extractant assembly lead to poorly defined structures that are challenging to identify. Here, we investigate the mechanism of water extraction for a malonamide extractant commonly applied to f-element separations. We measure extractant concentration fluctuations in the organic phase with small angle X-ray scattering (SAXS) before and after contact with water at fine increments of extractant concentration, finding no qualitative changes upon water uptake that might suggest significant nanoscopic reorganization of the solution. The critical composition for maximum fluctuation intensity is consistent with small water-extractant adducts. The extractant concentration dependence of water extraction is consistent with a power law close to unity in the low concentration regime, suggesting the formation of 1 : 1 water-extractant adducts as the primary extraction mechanism at low concentration. At higher extractant concentrations, the power law slope increases slightly, which we find is consistent with activity effects modeled using Flory-Huggins theory without introduction of additional extractant-water species. Molecular dynamics simulations are consistent with these findings. The decrease in interfacial tension with increasing extractant concentration shows a narrow plateau region, but it is not correlated with any change in fluctuation or water extraction trends, further suggesting no supramolecular organization such as reverse micellization. This study suggests that water extraction in this system is particularly simple: it relies on a single mechanism at all extractant concentrations, and only slightly enhances the concentration fluctuations characteristic of the dry binary extractant/diluent mixture.

Organic-Inorganic hybrid membrane for simultaneous heavy metal removal at drinking water pollution concentration levels

This study proposes a novel approach for simultaneous removal of potentially toxic metals from contaminated drinking water. The strategy is based on multi-layer graphene oxide hybrid membranes made up of Fe3O4@amyloid fibrils nanoclusters intercalated into the graphene oxide sheets via flow through approach. The hybrid membrane outperforms the previously known graphene-based membranes with adsorption capacity in the range of 128–570 mg g−1 of material. The membrane's removal efficacy exceeds 99.9% in both low (150 µg/L) and high (10,000 µg/L) metal concentration regimes, representative of ground water and wastewater contamination and complies with WHO drinking water requirements. Following NSF/ANSI 42,53–2007a American Standard Regulations, samples with metal concentrations of 150 µg/L and 20 mg L−1 calcium coexisted at pH 6.5 ± 0.25, complete removal of heavy metals (100%) in the effluent was observed. Benchmark testing on real municipal and ground water samples in continuous operation mode shows that ∼ 7500 and 5000 L water/g of membrane were treated well while maintaining WHO drinking water standards. The saturated membrane regenerated and successfully reused several times without losing purification performance. The present technique shows a great deal for addressing the worldwide problem of contaminated drinking water due to good selectivity, low fabrication cost, and excellent performance on real water.

Low-frequency noise in AlTiO/AlGaN/GaN metal-insulator-semiconductor field-effect transistors with non-gate-recessed or partially-gate-recessed structures

We have systematically investigated low-frequency noise (LFN) in AlTiO/AlGaN/GaN metal-insulator-semiconductor field-effect transistors (FETs) with non-gate-recessed or partially-gate-recessed structures, where gate insulators using AlTiO, an alloy of Al2O3 and TiO2, are obtained by atomic layer deposition. For drain current LFN, we find pure spectra for the well-above-threshold regime, and superposition of and Lorentzian spectra near the threshold voltage. The Hooge parameters are evaluated from the contribution and found to be independent of the AlTiO thickness. However, the remaining AlGaN thickness strongly affects the Hooge parameter near the threshold voltage; in the low channel electron concentration regime of the partially-gate-recessed FETs, a smaller remaining AlGaN thickness gives a larger Hooge parameter proportional to the inverse of the electron concentration, indicating that channel electron number fluctuation dominates the Hooge parameter. We consider that the channel electron number fluctuation is caused by electron traps introduced by the recess etching process in the remaining AlGaN. On the other hand, the Lorentzian spectra give specific time constants almost independent of the AlTiO thickness and the remaining AlGaN thickness, corresponding to trap depths of 0.6–0.8 eV. This can be attributed to traps in AlTiO near the AlTiO/AlGaN interface.

Metal organic framework derived nanostructured ferropericlase for waterborne Pb(II) ion sensing and organic dye removal

Highly crystalline and chemically stable bimetallic MgFe mixed oxide of ferro-periclase crystal structure has been derived for the first time from thermal decomposition of Prussian Blue metal organic framework. Scanning electron microscopy images confirmed formation of nanoflake like morphology. N2 adsorption-desorption isotherms indicated mesoporous nature with high specific surface area, suitable for sensing applications. Mott-Schottky studies suggested that the material is a p-type semiconductor and optical characterisation revealed a band gap (of ∼1.9 eV), well within the visible light absorption range suggesting its potential as a photocatalyst. When the as-synthesized MgFe oxide was tested against some common organic contaminants like Methylene blue and Rhodamine B dissolved in water (generally found in water bodies carrying textiles wastes), it was able to remove almost 90% of the cationic dyes within 3 h under low power UV–visible lamps. Moreover, Differential Pulse Voltammetry studies using the MgFe oxide film as working electrode revealed its potential as an electrochemical sensor for detection of heavy metal ions such as Pb(II) as it detected the presence of Pb(II) even at a very low concentration regime of 4–24 ppb. Therefore, this metal oxide composed of earth abundant elements is proposed as a low cost photocatalyst for organic pollutant removal and voltametric sensor for Pb(II) ions.

Structural insights into electric field induced polarization and strain responses inK0.5Na0.5NbO3modified morphotropic phase boundary compositions ofNa0.5Bi0.5TiO3-based lead-free piezoelectrics

${\mathrm{K}}_{0.5}{\mathrm{Na}}_{0.5}\mathrm{Nb}{\mathrm{O}}_{3}$ (KNN)-modified morphotropic phase boundary (MPB) compositions of the two ${\mathrm{Na}}_{0.5}{\mathrm{Bi}}_{0.5}\mathrm{Ti}{\mathrm{O}}_{3}$-based lead-free piezoelectrics, namely, $0.94{\mathrm{Na}}_{0.5}{\mathrm{Bi}}_{0.5}\mathrm{Ti}{\mathrm{O}}_{3}\text{\ensuremath{-}}0.06\mathrm{BaTi}{\mathrm{O}}_{3}$ (NBT-6BT) and $0.80{\mathrm{Na}}_{0.5}{\mathrm{Bi}}_{0.5}\mathrm{Ti}{\mathrm{O}}_{3}\text{\ensuremath{-}}0.20{\mathrm{K}}_{0.5}{\mathrm{Bi}}_{0.5}\mathrm{Ti}{\mathrm{O}}_{3}$ (NBT-20KBT) are model systems exhibiting large $(&gt;0.4%)$ electric-field-driven strain. There is a general perception that (i) increasing KNN concentration monotonically weakens the direct piezoelectric response $({d}_{33})$, and (ii) maximum electrostrain occurs when KNN pushes the system in the fully ergodic relaxor state. We have examined these issues using various complementary techniques involving electrostrain, piezoelectric coefficient $({d}_{33})$, ferroelectric switching-current measurements, and field-driven structural studies on the global and local scales using laboratory and synchrotron x-ray diffraction, neutron powder diffraction, and ${\mathrm{Eu}}^{+3}$ photoluminescence techniques. Our investigations revealed the following important features: (i) In the low-concentration regime, KNN induces a tetragonal ferroelectric distortion, which improves the weak signal piezoresponse. (ii) Beyond a threshold concentration, in-phase octahedral tilt sets in and weakens the long-range ferroelectric order to partially stabilize an ergodic state. (iii) The maximum electrostrain (\ensuremath{\sim}0.6%) is achieved in the mixed (nonergodic + ergodic) state. (iv) The mixed state invariably exhibits a less-known phenomenon of field-driven ferroelectric-to-relaxor transformation during bipolar field cycling. (v) The enhanced electrostrain in the mixed state is associated with the electric field increasing the correlation lengths of the short-ranged tetragonal and rhombohedral ferroelectric regions without overall transformation of one phase to the other. We summarize the findings of this work in a comprehensive electric field composition (E-x) phase diagram. The findings reported here are likely to be true for other NBT-based MPB systems.

Biphasic concentration patterns in ionic transport under nanoconfinement revealed in steady-state and time-dependent properties.

Ion permeation across nanoscopic structures differs considerably from microfluidics because of strong steric constraints, transformed solvent properties, and charge-regulation effects revealed mostly in diluted solutions. However, little is known about nanofluidics in moderately concentrated solutions, which are critically important for industrial applications and living systems. Here, we show that nanoconfinement triggers general biphasic concentration patterns in a myriad of ion transport properties by using two contrasting systems: a biological ion channel and a much larger synthetic nanopore. Our findings show a low-concentration regime ruled by classical Debye screening and another one where ion-ion correlations and enhanced ion-surface interactions contribute differently to each electrophysiological property. Thus, different quantities (e.g., conductance vs noise) measured under the same conditions may appear contradictory because they belong to different concentration regimes. In addition, non-linear effects that are barely visible in bulk conductivity only in extremely concentrated solutions become apparent in nanochannels around physiological conditions.

Unexpected Slow Kinetics of Poly(Methacrylic Acid) Phase Separation in the Semi-Dilute Regime.

Poly (methacrylic acid) (PMAA) solutions are known to exhibit a lower critical solution temperature (LCST). A temperature-composition phase diagram of PMAA has been constructed by standard cloud point determination through transmittance measurements, and also by studying the steady states reached under phase separation. This allows us to reconstruct the binodal curve describing the phase behavior of PMAA for both low and high concentration regimes, and to determine accurately the LCST temperature. In a second step, the structures formed following a temperature jump above the cloud point and their evolution in time have been investigated at the nanoscale using small angle neutron scattering (SANS). This approach shows that the formation of phase-separated nanostructures is a slow process, requiring more than 12 h. The formed structures are then shown to depend on the amplitude of the temperature jump above the cloud point. An original mechanism of phase separation is identified in the semi-dilute regime. The growth of micrometric-size droplets with an inner structure displaying the rheological properties of a gel leads to the formation of a percolating network which hinders the influence of gravity. Such a result can explain the slow kinetics of the PMAA LCST transition.

Interaction of surfactants with phospholipid vesicles in the low concentration regime

The interactions between diluted phospholipid vesicles (0.3 μM - 40 μM) and surfactants (around their cmc) have been investigated as model of the phenomena taking place when enveloped viruses are challenged by detergent formulations such as mouthwashes or dishwashing liquids. We have used negatively charged Small Unilamellar Vesicles (SUVs) to simulate the negatively charged viral envelope and surfactants with different charges: the anionic Sodium Dodecyl Sulphate (SDS), the cationic Cetylpyridinium Chloride (CPC) and the non-ionic Octaethylene glycol monodecyl ether (C10E8). Dynamic and Electrophoretic Light Scattering have been used to probe variations in size and surface charge of the vesicles. The surfactants effect on the membrane permeability was investigated by measuring the fluorescence of SUVs secluding the fluorophore calcein. All the surfactants perturb the bilayer inducing graded dye leakage. Irrespective of the chemical nature of the surfactant, the membrane leakage follows the same sigmoidal master curve when it is plotted against the ratio surfactant concentration/cmc. The membrane leakage is negligible below cmc/2 and above such a value increases up to the cmc where all the dye has been fully released. For ionic SDS and CPC the dependence of leakage halftime on such a scaled concentration is the same irrespective of the charge of the surfactant and the vesicles. The nonionic surfactant C10E8 induces the dye release from the SUV two orders-of-magnitude faster than the ionic surfactants. These results show that the rate-determining parameter for the permeabilization of the lipid bilayers is the electrostatic penalty to the flip-flop required to transport the surfactant inside the vesicle.

Formation and development of distinct deposit patterns by drying Polyelectrolyte-stabilized colloidal droplets at different surfactant concentrations

Understanding and controlling the formation of various deposit patterns such as coffee stains, multiple ring-like morphologies, and uniform deposition are essential for developing various applications. The presence of polymer and surfactant in a drying colloidal droplet can alter the droplet evaporation mode and deposit structure. In this work, we study the effect of Marangoni stresses on the evaporative dynamics and the structure and alignment of nanoparticles in the dried deposit patterns when a droplet of electro-sterically stabilized (poly(styrene sulfonate)) gold nanorod dispersion (PSS Au-NR) dries on a hydrophilic silicon substrate at low and high concentration regimes of an added surfactant (CTAB). The evaporative kinetics study shows that the evaporating droplets of PSS Au-NR dispersion exhibit rapid pinning and quick evaporation at zero and high CTAB concentrations, which transforms to three stages of droplet evaporation with an initial droplet depinning stage at low CTAB concentration. Pinning of the PSS Au-NR dispersion droplet in the absence of CTAB results in a coffee stain with densely and loosely packed PSS Au-NRs without any nanorod ordering in the outer and inner coffee stain edges. The formation and systematic evolution of various new deposit structures such as depinned region, depletion region, and fingering pattern are noted both outside and inside the coffee stain at different CTAB concentrations. Our study demonstrates that the kinetics of droplet drying and the deposit pattern of an evaporating polyelectrolyte-colloidal droplet can be tailored systematically by controlling the internal flows in the droplet dispersion medium through the addition of surfactant.

Entropy of electrolytes with off-centre charge cations. Monte Carlo studies

Monte Carlo techniques including Inverse Grand Canonical Monte Carlo simulations are utilized to calculate the entropy of a restricted primitive model electrolyte with the caveat that the cation charge centre is displaced from the geographical centre of the cation sphere towards the surface of the sphere. Calculations have been performed for symmetric valency (1:1) and asymmetric valency (2:1) electrolytes at 298.15 K for a range of electrolyte concentrations. The cation charge centre displacement accompanied by an increase of temperature leads to an increase of entropy. For the 2:1 valency system the entropy as a function of the square root of concentration reveals a broad inflexion region that separates the domains of deformation due to the electrostatic and steric interactions. When the central ion is an anion, and the charge centres of the surrounding cations are oriented towards the anion then the electrostatic interactions are stronger than in the standard restricted primitive model and the entropy decreases, while a central cation deforms the ionic atmosphere surrounding it and the entropy increases. In the low concentration regime good agreement is seen between the results from the Debye-Hückel limiting law and the corresponding simulations.

Binding and stability properties of PEG2000 to globular proteins: The case of lysozyme

• Lysozyme-PEG interaction was studied using calorimetry and spectroscopic techniques. • A PEG/lysozyme interaction in the low polymer concentration regime occurs. • The interaction process is weak, and it is entropically driven. • At low concentration, PEG induces an increase of the denaturation temperature. Poly(ethylene glycol) is a linear polymer widely used in many biotechnological and industrial applications. It is thought that PEG is an inert polymer and its effect on protein stability and dynamics is essentially due to the excluded volume effect which depends on its concentration. However, increasing evidence suggests that direct interactions can be established between PEG and proteins. With the aim to shed more light on PEG-protein interactions, this work evaluated the enthalpy pair interaction coefficient and the enthalpy cross-interaction coefficient for the system PEG2000-lysozyme. In addition, using calorimetry and spectroscopy, the binding, the stability and the conformational behaviour of lysozyme were evaluated in the low polymer concentration regime. We found that a weak interaction between lysozyme and PEG occurs with a binding constant of 1600 ± 230 M −1 . The interaction process is mainly entropically driven: the release of water molecules associated to protein surface and polymer chains may account for this phenomenon. In addition, we found that the general lysozyme structure was only marginally affected by PEG interaction. A small but significant increase in the denaturation temperature was observed most likely due to weak interactions with the polymer and to the dehydration of protein surface.

Mapping odorant sensitivities reveals a sparse but structured representation of olfactory chemical space by sensory input to the mouse olfactory bulb.

In olfactory systems, convergence of sensory neurons onto glomeruli generates a map of odorant receptor identity. How glomerular maps relate to sensory space remains unclear. We sought to better characterize this relationship in the mouse olfactory system by defining glomeruli in terms of the odorants to which they are most sensitive. Using high-throughput odorant delivery and ultrasensitive imaging of sensory inputs, we imaged responses to 185 odorants presented at concentrations determined to activate only one or a few glomeruli across the dorsal olfactory bulb. The resulting datasets defined the tuning properties of glomeruli - and, by inference, their cognate odorant receptors - in a low-concentration regime, and yielded consensus maps of glomerular sensitivity across a wide range of chemical space. Glomeruli were extremely narrowly tuned, with ~25% responding to only one odorant, and extremely sensitive, responding to their effective odorants at sub-picomolar to nanomolar concentrations. Such narrow tuning in this concentration regime allowed for reliable functional identification of many glomeruli based on a single diagnostic odorant. At the same time, the response spectra of glomeruli responding to multiple odorants was best predicted by straightforward odorant structural features, and glomeruli sensitive to distinct odorants with common structural features were spatially clustered. These results define an underlying structure to the primary representation of sensory space by the mouse olfactory system.

Antibiotic-Loaded Smart Platelet: A Highly Effective Invisible Mode of Killing Both Antibiotic-Sensitive and -Resistant Bacteria.

Microbial pathogenesis is considered one of the most critical health challenges worldwide. Although several antibiotics have been procured and used, the microbes often manage to escape and become resistant to antibiotics. Thus, the discovery of new antibiotics and designing smart approaches toward their delivery are of great importance. In many cases, the delivery agents using foreign chemicals like lipids or polymers induce immunogenic responses of varying degrees and are limited to a shorter circulatory time and burst release. In the current work, we have designed a novel antibiotic delivery system where the antibiotic is encapsulated into a blood component—platelet. Platelets have been previously reported as efficient drug delivery vehicles for targeting cancer cells. On the other hand, during platelet–bacterial interaction, platelets can act as covercytes. Keeping this in mind, smart antibiotic-loaded platelets have been used for killing bacterial cells. The loading of the antibiotic was done using its typical nature of engulfing surrounding small molecules. The water-soluble antibiotics were loaded directly into the platelet, whereas the hydrophobic antibiotics were preloaded in polycaprolactone (FDA-approved polymer)-based nanovesicles to make them solubilized prior to loading inside the platelets. The antibiotic-loaded platelets (containing hydrophilic antibiotics or hydrophobic antibiotic -encapsulated polymer nanoparticles) were found to be stable when studied through platelet aggregometry. The carrier showed bactericidal effects at a significantly lower concentration at which the free antibiotic has negligible efficacy. This could be attributed to the molecular confinement of the antibiotics inside the platelets, therefore causing localization of the drug and leading to efficient activity against bacteria. Interestingly, the smart antibiotic-loaded platelets were capable of killing the resistant strains too at the same lower concentration regime. Therefore, the antibiotic-loaded platelet could emerge as a potential strategy for efficient delivery of antibiotics with a significant reduction of the dose required to achieve the intended antibacterial efficacy. Moreover, this antibiotic delivery method can be very useful to minimize immunogenic responses due to antibiotic administration and to avoid the development of drug resistance due to the invisible mode of delivery.

Quantification of Rare Earth Elements in the Parts Per Million Range: A Novel Approach in the Application of Laser-Induced Breakdown Spectroscopy.

This work extends a previous percentage level concentration study of the optical emission spectra for six rare earth elements, europium (Eu), gadolinium (Gd), lanthanum (La), praseodymium (Pr), neodymium (Nd), and samarium (Sm), along with the transition metal, yttrium (Y) using laser-induced breakdown spectroscopy (LIBS). The concentration of these six rare earth elements and yttrium has been attempted for the first time systematically down to parts per million (ppm) concentration levels ranging from 30 to 300 ppm. The authors have developed multivariate models for each element capable of predicting concentration with acceptable to excellent levels of accuracy. Additionally, partial least squares regression coefficients were used to identify key spectral features able to be used in this lower concentration regime. This study has demonstrated that it is conceivable to quantify the six rare earth elements along with yttrium at low concentrations in the parts per million levels.

Simultaneous thermoosmotic and thermoelectric responses in nanoconfined electrolyte solutions: Effects of nanopore structures and membrane properties

HypothesisNanofluidic systems provide an emerging and efficient platform for thermoelectric conversion and fluid pumping with low-grade heat energy. As a basis of their performance enhancement, the effects of the structures and properties of the nanofluidic systems on the thermoelectric response (TER) and the thermoosmotic response (TOR) are yet to be explored. MethodsThe simultaneous TER and TOR of electrolyte solutions in nanofluidic membrane pores on which an axial temperature gradient is exerted are investigated numerically and semi-analytically. A semi-analytical model is developed with the consideration of finite membrane thermal conductivity and the reservoir/entrance effect. FindingsThe increase in the access resistance due to the nanopore-reservoir interfaces accounts for the decrease of short circuit current at the low concentration regime. The decrease in the thermal conductivity ratio can enhance the TER and TOR. The maximum power density occurring at the nanopore radius twice the Debye length ranges from several to dozens of mW K−2 m−2 and is an order of magnitude higher than typical thermo-supercapacitors. The surface charge polarity can heavily affect the sign and magnitude of the short-circuit current, the Seebeck coefficient and the open-circuit thermoosmotic coefficient, but has less effect on the short-circuit thermoosmotic coefficient. Furthermore, the membrane thickness makes different impacts on TER and TOR for zero and finite membrane thermal conductivity.

Concentration-dependent thermodynamic analysis of the partition process of small ligands into proteins

In the category of functional low-affinity interactions, small ligands may interact with multiple protein sites in a highly degenerate manner. Better conceived as a partition phenomenon at the molecular interface of proteins, such low-affinity interactions appear to be hidden to our current experimental resolution making their structural and functional characterization difficult in the low concentration regime of physiological processes. Characterization of the partition phenomenon under higher chemical forces could be a relevant strategy to tackle the problem provided the results can be scaled back to the low concentration range. Far from being trivial, such scaling demands a concentration-dependent understanding of self-interactions of the ligands, structural perturbations of the protein, among other molecular effects. Accordingly, we elaborate a novel and detailed concentration-dependent thermodynamic analysis of the partition process of small ligands aiming at characterizing the stability and structure of the dilute phenomenon from high concentrations. In analogy to an “aggregate” binding constant of a small molecule over multiple sites of a protein receptor, the model defines the stability of the process as a macroscopic equilibrium constant for the partition number of ligands that can be used to analyze biochemical and functional data of two-component systems driven by low-affinity interactions. Acquisition of such modeling-based structural information is expected to be highly welcome by revealing more traceable protein-binding spots for non-specific ligands.

A Revisit to Turnover Kinetics of Individual Escherichia coli β-Galactosidase Molecules.

Single-molecule experiments on β-galactosidase from Escherichia coli that catalyzes the hydrolysis of resorufin-β-d-galactopyranoside revealed important observations like fluctuating catalytic rate, memory effects arising from temporal correlations between the enzymatic turnovers and nonexponential waiting time distributions. The root cause of the observed results is intrinsic fluctuations among the different conformers of the active species, during the course of the reaction, thereby imparting dynamic disorder in the system under investigation. Originally, a multistate stochastic kinetic theory was employed that, despite satisfying the measured waiting time distributions and the mean waiting times at different substrate concentrations, yields a constant estimate of the randomness parameter. Inevitably, this manifests a strong disagreement with the substrate-concentration-dependent time variations of the said distribution, which at the same time misinterprets the measured magnitudes of the randomness parameter at lower concentrations. Here, we suggest a dual approach to the single-enzyme reaction, independently, making important improvements over the parent study and the recently suggested two-state stochastic analyses followed by quantitative rationalization of the experimental data. In the first case, an off-pathway mechanism satisfied the Michaelis-Menten equation under the circumstance of prevailing disorder while tested against the single-molecule data. However, recovery of randomness data in the lower-concentration regime, albeit primarily marks a significant refinement, a qualitative agreement at the growing concentrations seems to be reasoned by an account of switching among the limited numbers of discrete conformers. Consequently, in the second case, we circumvented the conventional way of approaching the enzyme catalysis and mapped the dynamics of structural transitions of the biocatalyst with the temporal fluctuations of the spatial distance between the different locations along a coarse-grained polymer chain. Exploiting a general mechanism for dynamic disorder, a reaction-diffusion formalism yielded an analytical expression for the waiting time distribution of the enzymatic turnovers, from which the mean waiting time and the randomness parameter were readily determined. Application of our results to the findings of the experiment on single β-galactosidase shows a quantitative agreement in each case. This soundly validates the usefulness of accounting for a more rigorous microscopic description pertinent to the conformational multiplicity in rationalizing the real-time data over the routine state-based sketch of the reaction system.