A mathematical model of lateral flow bioreactions applied to sandwich assays

Lateral flow (LF) biodetectors facilitate low-cost, rapid identification of various analytes at the point of care. The LF cell consists of a porous membrane containing immobilized ligands at various locations. Through the action of capillary forces, samples and reporter particles are transported to the ligand sites. The LF membrane is then scanned or probed, and the concentration of reporter particles is measured. A mathematical model for sandwich assays is constructed and used to study the performance of the LF device under various operating conditions. The model provides insights into certain experimental observations including the reduction in the level of the detected signal at high target analyte concentrations. Furthermore, the model can be used to test rapidly and inexpensively various operating conditions, assist in the device's design, and optimize the performance of the LF device.     

Effects of blood sample anticoagulants on lateral flow assays using luminescent photon-upconverting and Eu(III) nanoparticle reporters

Many quantitative and semiquantitative lateral flow (LF) assays have been introduced for clinical analytes such as biomarkers for cancer or acute myocardial infarction (AMI). Various detection technologies involving quantitative analyzing devices have been reported to have sufficient analytical sensitivity and quantification capability for clinical point-of-care tests. Fluorescence-based detection technologies such as quantum dots, Eu(III) nanoparticles, and photon-upconverting nanoparticles (UCNPs) have been introduced as promising solutions for point-of-care devices because of their high detectability by optical sensors. Lateral flow assays can be used for various sample types, e.g., urine, saliva, cerebrospinal fluid, and blood. This study focuses on the properties of serum and plasma because of their relevance in cancer and AMI diagnostics. The limit of detection was compared in LF assays having Eu(III) nanoparticles or UCNPs as reporters and the antibody configurations for two different analytes (prostate-specific antigen and cardiac troponin I (cTnI)). The results indicate a significant effect of anticoagulants in venipuncture tubes. The samples in K₃EDTA tubes resulted in significant interference by decreased reporter particle mobility, and thus the limit of detection was up to eightfold less sensitive compared to serum samples. Despite the matrix interference in the cTnI assay with UCNP reporters, limits of detection of 41 ng/L with serum and 66 ng/L with the Li-heparin sample were obtained.     

Combined affinity and rate constant distributions of ligand populations from experimental surface binding kinetics and equilibria

The present article considers the influence of heterogeneity in a mobile analyte or in an immobilized ligand population on the surface binding kinetics and equilibrium isotherms. We describe strategies for solving the inverse problem of calculating two-dimensional distributions of rate and affinity constants from experimental data on surface binding kinetics, such as obtained from optical biosensors. Although the characterization of a heterogeneous population of analytes binding to uniform surface sites may be possible under suitable experimental conditions, computational difficulties currently limit this approach. In contrast, the case of uniform analytes binding to heterogeneous populations of surface sites is computationally feasible, and can be combined with Tikhonov-Phillips and maximum entropy regularization techniques that provide the simplest distribution that is consistent with the data. The properties of this ligand distribution analysis are explored with several experimental and simulated data sets. The resulting two-dimensional rate and affinity constant distributions can describe well experimental kinetic traces measured with optical biosensors. The use of kinetic surface binding data can give significantly higher resolution than affinity distributions from the binding isotherms alone. The shape and the level of detail of the calculated distributions depend on the experimental conditions, such as contact times and the concentration range of the analyte. Despite the flexibility introduced by considering surface site distributions, the impostor application of this model to surface binding data from transport limited binding processes or from analyte distributions can be identified by large residuals, if a sufficient range of analyte concentrations and contact times are used. The distribution analysis can provide a rational interpretation of complex experimental surface binding kinetics, and provides an analytical tool for probing the homogeneity of the populations of immobilized protein.     

Performance of fluorescent europium(III) nanoparticles and colloidal gold reporters in lateral flow bioaffinity assay

Lateral flow (LF) immunoassays (i.e., immunochromatographic assays) have traditionally been applied to analytes that do not require very high analytical sensitivity or quantitative results. The selection of potential analytes is often limited by the performance characteristics of the assay technology. Analytes with more demanding sensitivity requirements call for reporter systems enabling high analytical sensitivity. In this study, we systematically compared the performance of fluorescent europium(III) [Eu(III)] chelate dyed polystyrene nanoparticles and colloidal gold particles in lateral flow assays. The effect of time-resolved measurement mode was also studied. Because binder molecules used in immunoassays might not behave similarly when conjugated to different reporter particles, two model assays were constructed to provide reliable technical comparison of the two reporter systems. The comparative experiment demonstrated that the fluorescent nanoparticles yielded 7- and 300-fold better sensitivity compared with colloidal gold in the two test systems, respectively. Although the two reporter particles may induce variable effects using individual binders, overall the high specific activity of Eu(III) nanoparticles has superior potential over colloidal gold particles for the development of robust high-sensitivity bioaffinity assays.     

Modeling of immunosensors under nonequilibrium conditions. I. Mathematic modeling of performance characteristics.

Immunosensors for the detection of small analytes that use analyte-enzyme conjugates as signal generators require special attention if operated under nonequilibrium conditions. If the size of the analyte and the analyte-enzyme conjugate differ substantially, the two antigens do not diffuse at the same rate. This can cause time-dependent shifts in the sensitivity of competitive immunoassays. Therefore, immunosensors operating at short incubation times require precise timing that meets closely the specifications for which the sensors were calibrated. As an example, we have analyzed kinetic binding curves for the quantitative determination of progesterone with an immobilized monoclonal antibody and a conjugate between horseradish peroxidase and progesterone as signal generator. Mathematical paradigms have been developed to simulate the diffusion, antigen-antibody complex formation, and competitive binding processes in this analytical system. Dose-response curves obtained under nonequilibrium conditions can vary substantially from those obtained at equilibrium of antigen-antibody interaction. The degree of this variation depends on the performance characteristics of the major components of the immunosensor. The developed mathematical solutions reflect experimental results and can be used to model optimal conditions for immunosensors operating under nonequilibrium conditions. In this paper (Part I), we report on the mathematical modeling of the interaction between analyte, analyte-enzyme conjugate, and an immobilized antibody. In Part II (W. Schramm and S.-H. Paek (1991) Anal. Biochem. 196), we present experimental results and compare them with the theoretical models.     

A novel mathematical model of activation and sensitization of platelets subjected to dynamic stress histories

Blood recirculating devices, such as ventricular assist devices and prosthetic heart valves, are burdened by thromboembolic complications requiring complex and lifelong anticoagulant therapy with its inherent hemorrhagic risks. Pathologic flow patterns occurring in such devices chronically activate platelets, and the optimization of their thrombogenic performance requires the development of flow-induced platelet activation models. However, existing models are based on empirical correlations using the well-established power law paradigm of constant levels of shear stress during certain exposure times as factors for mechanical platelet activation. These models are limited by their range of application and do not account for other relevant phenomena, such as loading rate dependence and platelet sensitization to high stress conditions, which characterize the dynamic flow conditions in devices. These limitations were addressed by developing a new class of phenomenological stress-induced platelet activation models that specifies the rate of platelet activation as a function of the entire stress history and results in a differential equation that can be directly integrated to calculate the cumulative levels of activation. The proposed model reverts to the power law under constant shear stress conditions and is able to describe experimental results in response to a diverse range of highly dynamic stress conditions found in blood recirculating devices. The model was tested in vitro under emulated device flow conditions and correlates well with experimental results. This new model provides a reliable and robust mathematical tool that can be incorporated into computational fluid dynamic studies in order to optimize design, with the goal of improving the thrombogenic performance of blood recirculating devices.     

Lateral-flow and up-converting phosphor reporters to detect single-stranded nucleic acids in a sandwich-hybridization assay

Up-converting Phosphor Technology (UPT) particles were used as reporters in lateral-flow (LF) assays to detect single-stranded nucleic acids. The 400-nm phosphor particles exhibit strong visible luminescence upon excitation with infrared (IR) light resulting in the total absence of background autofluorescence from other biological compounds. A sandwich-type hybridization assay was applied using two sequence-specific oligonucleotides. One of the oligonucleotides probes was covalently bound to the UPT particle (reporter) for direct labeling and detection, whereas the second oligonucleotide probe contained biotin for capture by avidin during LF. The whole procedure of hybridization, UPT-LF detection, and analysis required a minimum time of 20 min. Moreover, aiming at minimal equipment demands, the hybridization conditions were chosen such that the entire assay could be performed at ambient temperature. During lateral flow, only targets hybridized to both capture and detection oligonucleotide were trapped and detected at an avidin capture line on the LF strip. Analysis (IR scanning) of the strips was performed in an adapted microtiter plate reader provided with a 980-nm IR laser for excitation of the phosphor particles (a portable reader was also available). Visible luminescence was measured and presented as relative fluorescence units (RFU) allowing convenient quantitation of the phosphor signal. With the assay described here as little as 0.1 fmol of a specific single-stranded nucleic acid target was detected in a background of 10 microg fish sperm DNA.     

Reporter genes lucFF, luxCDABE, gfp, and dsred have different characteristics in whole-cell bacterial sensors

The selection of a genetic reporter can be difficult because of the wide range of genes available. In order to reduce the selection, we compared the performance of different reporter genes: firefly luciferase (Photinus pyralis lucFF), bacterial luciferase operon (Photorhabdus luminescens luxCDABE), green fluorescent protein (Aequorea victoria gfp), and red fluorescent protein (Discosoma sp. dsred) in whole-cell bacterial sensors. Escherichia coli sensor bacteria were engineered to contain a reporter plasmid that carries the reporter gene under the control of mercury- (mer from Tn21) or arsenite- (ars from R773) responsive regulatory units. Characteristics of the strains were studied by using different arsenite or mercury concentrations and incubation times. The lowest detectable concentration of analytes and the fastest responses were achieved with lucFF or luxCDABE as reporter genes. The fluorescent proteins, GFP and DsRed, gave responses at higher analyte concentrations and after significantly longer incubation times. The results indicate that luciferases are better reporters in whole-cell sensor bacteria.     

Stability of nicotinamide adenine dinucleotide immobilized to cyanogen bromide activated agarose

The stability of NAD(H) immobilized to a crosslinked agarose support (Sepharose(R)-4B) was examined in buffer solutions at a pH of 7.0 and 8.5. Specifically, this study investigated particle attrition and ligand leakage rates from a cyanogen bromide activated agarose support. Particle attrition did not occur under the experimental conditions. Ligand leakage rates were found to be first order in immobilized ligand concentration with two labile populations of ligand. The two-population model is consistent with the cyanogen bromide coupling chemistry, which results in both an isourea and imidocarbonate ligand linkage. The rate of ligand leakage was found to occur over a time scale of days, with first order rate constants ranging from 0.007 to 0.15 d(-1), depending on solution pH. (c) 1997 John Wiley & Sons, Inc.     

Kinetic study of immobilized chloroplast membranes operating in a continuous flow system

We have focused our interest on the study of the operational stability of immobilized chloroplast membranes. Due to the physical insoluble form of immobilized material this study can be done in a continuous flow system. The activity of immobilized chloroplast membranes is monitored continuously during the inactivation treatment and modelled under operating conditions by taking into account concomitant inactivation with time. Theoretical and experimental results are compared. The effect of light conditions on the operational stability is also reported.     

Effect of biocatalyst swelling on the operation of packed-bed immobilized enzyme bioreactor

A general mathematical model was developed for predicting the performance and simulation of a packed-bed immobilized enzyme reactor performing a reaction that follows Michaelis–Menten kinetics with competitive product inhibition. The performance of a packed-bed immobilized enzyme reactor was analyzed taking into account the effect of bed swelling on various diffusional phenomena such as axial dispersion, internal and external mass transfer limitations. The numerical solutions were compared with experimental data obtained for a packed-bed reactor operating with β-galactosidase entrapped in Ca-alginate-K-κ-carrageenan gels for lactose hydrolysis.     

Enzymatic activity under tangential flow conditions of photochemically grafted membranes containing immobilized catalase

Catalase has been immobilized within sandwich membranes prepared by the photoinduced grafting of an epoxy-diacrylate prepolymer onto commercial asymmetric cellulose membranes. The enzymatic activity of the membrane composite of hydrogen peroxide decomposition has been studied in a recirculation apparatus under tangential flow conditions without ultrafiltration. The enzymatic membranes were exposed to very low mechanical stresses and showed a very good catalytic performance and durability. Initial reaction rates, measured at 25 degrees C as a function of both substrate concentration and enzyme amount immobilized per unit membrane surface, indicate that the mechanism of action of catalase is not altered after immobilization, although substrate diffusion through the original thin layer of membranes may become rate controlling. (c) 1993 John Wiley & Sons, Inc.     

Comparison of sexual compatibility between laboratory and wild Mexican fruit flies under laboratory and field conditions

The sexual compatibility between laboratory (LF) and wild (WF) strains of the Mexican fruit fly, Anastrepha ludens (Loew), was analyzed using analogous methodologies and experimental arenas under both laboratory and field conditions. Sexual compatibility was quantified with the following indices: the isolation index (ISI), male relative performance index (MRP), female relative performance index (FRPI), and the relative sterility index (RSI). ISI detected a certain level of incompatibility between strains under both laboratory and field conditions, because LF females tended to mate with LF males. LF mating performance was higher under laboratory than under field conditions. The relative performance indices for LF and the relative sterility index were higher in the laboratory than in the field. Differences between LF and WF in the times that males started calling and mating were observed in both environments. Importantly, WF males reduced their sexual activity under laboratory environments, whereas LF maintained similar activity levels in both conditions. The possible applications of the above-mentioned methods, not only to assess fly quality but also to determine the suitability of conditions in mass-rearing facilities, are discussed. Correlating laboratory quality to sexual behavior may contribute in the development of environmental parameters for mass-rearing facilities.     

Comparison of label-free biosensing in microplate, microfluidic, and spot-based affinity capture assays

Using both experimental assays and fluid-dynamic finite element simulation models, we directly compared the achievable performance limits of four distinct assay configurations for label-free detection of an analyte from a test sample on a biosensor surface. The assay configurations studied in this work included a biosensor incorporated into the bottom surface of a microplate well and a microfluidic channel. For each configuration, we compared assay performance for the scenario in which the entire bottom surface of the fluid-handling vessel is coated with capture ligands with assay performance for the scenario in which the capture ligands are applied in the form of localized spots. As a model system, we used detection of the protein biomarker tumor necrosis factor-alpha (TNF-α) using immobilized TNF-α capture antibody. Results show that the microfluidic assay format dramatically reduces the time required to establish a stable equilibrium. Spot-based assays are advantageous for microplate-based detection for reducing the time required for equilibrium sensor response. The results derived are generally applicable to any label-free biosensor technology and any ligand-analyte system with adjustable variables that include sensor mass density sensitivity, analyte-ligand adsorption/desorption rate constants, immobilized ligand density, flow channel geometry, flow rate, and spot size.     

Coupled reactions for the determination of analytes and enzymes based on the use of luminescence

Immobilized enzymes are widely used in the clinical laboratory in the assay of several analytes and enzymes. The use of immobilized enzymes makes these reagents recoverable and re-usable, and in most cases increases their stability and catalytic activity. In conjunction with bioluminescent enzymes (firefly and bacterial luciferases) and chemiluminescent catalyst (peroxidase) we set up high-sensitive flow methods based on the use of nylon tube coil or epoxy methacrylate column as solid support. All the NAD(P)/NAD(P)H-dependent dehydrogenases (bacterial luciferase), ATP-dependent enzymes (firefly luciferase) and oxidases producing H₂O₂ (peroxidase) can be immobilized and a large variety of analytes have been sensitively measured. As an alternative format we also reported a dry chemistry method in which all the enzymes, substrates and cofactors are ready to use, supported on dry cellulose disks. Methodological problems such as flow conditions, stability, pH, ionic strength and analytical performances are also reported.     

Study of an enzyme membrane reactor with immobilized fumarase for production of L-malic acid

The conversion of fumaric acid into L-malic acid by fumarase immobilized in a membrane reactor was analyzed experimentally. The enzyme was entrapped in asymmetric capillary membranes made of polysulfone. The performance of the reactor was evaluated in terms of conversion degree, reaction rate, and stability. The influence of operating conditions, such as amount of immobilized enzyme, substrate concentration, residence time, and axial flow rate, were investigated. The kinetic parameters K(m), V(max), and k(+2) were also measured. The stability of the immobilized enzyme was very good, showing no activity decay during more than 2 weeks of continuous operation.     

剪切流动法研究表面固定化配基与目标分子的相互作用力

基于剪切流动腔技术,以微球作为受力载体,设计了一套可用于研究表面固定化配基与目标分子特异性相互作用力的实验和分析方法,并以人免疫球蛋白 G (human IgG) 和羊抗人免疫球蛋白 G (goat anti-human IgG) 分别作为模型配基和模型目标分子进行了研究 . 基于平面 Poiseuille 层流模型设计了流场参数,以数值计算结果验证了设计的合理性 . 使用牛血清白蛋白 (BSA) 作为非特异性对照,判断微球与基片表面的结合力来自配基和目标分子的生物特异性相互作用,并由进一步的目标分子灭活对比实验确认了这一结论 . 实验观察到微球与基片表面的结合力受到配基面密度的影响,说明发生结合的是多对而非单对蛋白质分子 . 将 95 ％的微球被剥离时对应的壁面剪切率设定为临界剪切率,由大量实验结果拟合得到了临界剪切率与配基面密度间的定量关系 . 在受力分析模型中,考虑到多分子的结合,以及分子键位置不同造成的力臂长度的差异,最终计算得到单对配基与目标分子的平均结合力约为 342pN.     

Fluid mechanics of a spinner-flask bioreactor

Spinner-flask bioreactors have been used for the production of articular cartilage in vitro. The dynamic environment within bioreactors is known to significantly affect the growth and development of the tissue. The present research focuses on the experimental and numerical characterization of the flow field within a spinner flask operating under conditions used to produce cartilage. Laboratory experiments carried out in a scaled-up model bioreactor employ particle-image velocimetry (PIV) to determine velocity and shear-rate fields in the vicinity of the construct closest to the stir bar, in addition to turbulence properties. Numerical computations calculated using FLUENT, a commercial software package, simulate the flow field in the same model bioreactor under similar operating conditions. In the computations, scaffolds were modeled as both solid and porous media with different permeabilities and flow rates through various faces of the construct nearest the stir bar were examined.     

A reporter cell system to monitor autophagy based on p62/SQSTM1

Macroautophagy (hereafter referred to as autophagy) is a catabolic pathway to isolate and transport cytosolic components to the lysosome for degradation. Recently, autophagy receptors, like p62/SQSTM1 and NBR1, which physically link autophagic cargo to ATG8/MAP1-LC3/GABARAP family members located on the forming autophagic membranes, have been identified. To identify conditions or compounds that affect autophagy cell systems that efficiently report on autophagic flux are required. Here we describe reporter cell systems based on induced expression of GFP-p62, GFP-NBR1 or GFP-LC3B. The degradation of the fusion proteins was followed after promoter shut off by flow cytometry of live cells. All three fusion proteins were degraded at a basal rate by autophagy. Surprisingly, the basal degradation rate varied for the three reporter fusion proteins. GFP-LC3B was the most stable protein. GFP-NBR1 was most efficiently degraded under basal conditions while degradation of GFP-p62 displayed the strongest response to amino acid starvation. GFP-p62 was found to perform best of the tested reporters. Single cell analysis of autophagic flux by flow cytometry allows estimates of heterogeneous cell populations. The feasibility of this approach was demonstrated using transient overexpression of a dominant negative ULK1 kinase and siRNA-mediated knock-down of LC3B to inhibit autophagic degradation of GFP-p62. The inducible GFP-p62 cell system allows quantification by several approaches and will be useful in screening for compounds or conditions that affect the rate of autophagy. Inducers of autophagy can be identified using rich medium whereas inhibitors are identified under starvation conditions.