Bifurcation and resonance in a model for bursting nerve cells

In this paper we consider a model for the phenomenon of bursting in nerve cells. Experimental evidence indicates that this phenomenon is due to the interaction of multiple conductances with very different kinetics, and the model incorporates this evidence. As a parameter is varied the model undergoes a transition between two oscillatory waveforms; a corresponding transition is observed experimentally. After establishing the periodicity of the subcritical oscillatory solution, the nature of the transition is studied. It is found to be a resonance bifurcation, with the solution branching at the critical point to another periodic solution of the same period. Using this result a comparison is made between the model and experimental observations. The model is found to predict and allow an interpretation of these observations.     

Full system bifurcation analysis of endocrine bursting models

Plateau bursting is typical of many electrically excitable cells, such as endocrine cells that secrete hormones and some types of neurons that secrete neurotransmitters. Although in many of these cell types the bursting patterns are regulated by the interplay between voltage-gated calcium channels and calcium-sensitive potassium channels, they can be very different. We investigate so-called square-wave and pseudo-plateau bursting patterns found in endocrine cell models that are characterized by a super- or subcritical Hopf bifurcation in the fast subsystem, respectively. By using the polynomial model of Hindmarsh and Rose (Proceedings of the Royal Society of London B 221 (1222) 87-102), which preserves the main properties of the biophysical class of models that we consider, we perform a detailed bifurcation analysis of the full fast-slow system for both bursting patterns. We find that both cases lead to the same possibility of two routes to bursting, that is, the criticality of the Hopf bifurcation is not relevant for characterizing the route to bursting. The actual route depends on the relative location of the full-system's fixed point with respect to a homoclinic bifurcation of the fast subsystem. Our full-system bifurcation analysis reveals properties of endocrine bursting that are not captured by the standard fast-slow analysis.     

Analysis of an autonomous phase model for neuronal parabolic bursting

An understanding of the nonlinear dynamics of bursting is fundamental in unraveling structure-function relations in nerve and secretory tissue. Bursting is characterized by alternations between phases of rapid spiking and slowly varying potential. A simple phase model is developed to study endogenous parabolic bursting, a class of burst activity observed experimentally in excitable membrane. The phase model is motivated by Rinzel and Lee's dissection of a model for neuronal parabolic bursting (J. Math. Biol. 25, 653–675 (1987)). Rapid spiking is represented canonically by a one-variable phase equation that is coupled bi-directionally to a two-variable slow system. The model is analyzed in the slow-variable phase plane, using quasi steady-state assumptions and formal averaging. We derive a reduced system to explore where the full model exhibits bursting, steady-states, continuous and modulated spiking. The relative speed of activation and inactivation of the slow variables strongly influences the burst pattern as well as other dynamics. We find conditions of the bistability of solutions between continuous spiking and bursting. Although the phase model is simple, we demonstrate that it captures many dynamical features of more complex biophysical models.This research was partially supported by NSF-JOINT RESEARCH grant 8803573, grant from CONCYT and DGAPA(UNAM) Mexico for H. Carrillo, and for the S. M. Baer NSF DMS-9107538     

Frequency-domain order parameters for the burst and spike synchronization transitions of bursting neurons

We are interested in characterization of synchronization transitions of bursting neurons in the frequency domain. Instantaneous population firing rate (IPFR) R(t), which is directly obtained from the raster plot of neural spikes, is often used as a realistic collective quantity describing population activities in both the computational and the experimental neuroscience. For the case of spiking neurons, a realistic time-domain order parameter, based on R(t), was introduced in our recent work to characterize the spike synchronization transition. Unlike the case of spiking neurons, the IPFR R(t) of bursting neurons exhibits population behaviors with both the slow bursting and the fast spiking timescales. For our aim, we decompose the IPFR R(t) into the instantaneous population bursting rate R_b(t) (describing the bursting behavior) and the instantaneous population spike rate R_s(t) (describing the spiking behavior) via frequency filtering, and extend the realistic order parameter to the case of bursting neurons. Thus, we develop the frequency-domain bursting and spiking order parameters which are just the bursting and spiking “coherence factors” β_b and β_s of the bursting and spiking peaks in the power spectral densities of R_b and R_s (i.e., “signal to noise” ratio of the spectral peak height and its relative width). Through calculation of β_b and β_s, we obtain the bursting and spiking thresholds beyond which the burst and spike synchronizations break up, respectively. Consequently, it is shown in explicit examples that the frequency-domain bursting and spiking order parameters may be usefully used for characterization of the bursting and the spiking transitions, respectively.     

On the dynamics of bursting systems

The dynamics of three-variable models of bursting are studied. It is shown that under certain conditions, the dynamics on the attractor can be essentially reduced to two dimensions. The salient dynamics on the attractor can thus be completely described by the return map of a section which is a logistic interval map. Two specific bursting models from the literature are shown to fit in the general framework which is developed. Bifurcation of the full system for one case in investigated and the dynamical behavior on the attractor is shown to depend on the position of a certain nullcline.Supported in part by N.S.F.On leave at University of Maryland     

Blood plasma resonance Raman spectroscopy combined with multivariate analysis for esophageal cancer detection

We herein report a novel, reliable and inexpensive method for detecting esophageal cancer using blood plasma resonance Raman spectroscopy combined with multivariate analysis methods. The blood plasma samples were divided into late stage cancer group (n = 164), early stage cancer group (n = 35) and normal group (n = 135) based on clinical pathological diagnosis. Using a specially designed quartz capillary tube as sample holder, we obtained higher quality resonance Raman spectra of blood plasma than existing method. The study demonstrated that the carotenoids levels in blood plasma were reduced in esophageal cancer patients. The area under the receiver operating characteristic curve (and 95% confidence interval) calculated by wavenumber selection and principal component analysis combined with linear discriminant analysis (PC-LDA) algorithm were 0.894 (0.858-0.929), 0.901 (0.841-0.960) and 0.871 (0.799-0.942) for differentiating late cancer from normal, late cancer from early cancer, and early cancer from normal respectively. The contribution from the two carotenoids wavenumber regions of 1155 and 1515 cm⁻¹ were more than 84.2%. The results show that the plasma carotenoids could be a potential biomarker for screening esophageal cancer using resonance Raman spectroscopy combined with wavenumber selection and PC-LDA algorithms.      

Comparison of a carboxylated terthiophene surface with carboxymethylated dextran layer for surface plasmon resonance detection of progesterone

Functionalization of a gold surface is usually accomplished by covalent binding via self-assembled monolayers (SAMs) on the gold surface, followed by attachment of flexible polymeric linker layers such as dextran hydrogels. However, these techniques require multiple steps and also have nonspecific interactions and steric problems. In this study, a self-assembled carboxylated terthiophene monolayer was formed onto a gold surface to create a sensitive and stable surface plasmon resonance (SPR) biosensing system. Compared with a commercial carboxymethyl dextran chip (CM5), the terthiophene SAM surface provided more than six times more antibody-binding signals and nearly three times the SPR assay sensitivity for progesterone (P₄).     

Surface plasmon resonance for monitoring the interaction of Potato virus Y with monoclonal antibodies

Surface plasmon resonance (SPR)-based biosensors have been widely utilized for measuring interactions of a variety of molecules. Fewer examples include higher biological entities such as bacteria and viruses, and even fewer deal with plant viruses. Here, we describe the optimization of an SPR sensor chip for evaluation of the interaction of the economically relevant filamentous Potato virus Y (PVY) with monoclonal antibodies. Different virus isolates were efficiently and stably bound to a previously immobilized polyclonal antibody surface, which remained stable over subsequent injection regeneration steps. The ability of the biosensor to detect and quantify PVY particles was compared with ELISA and RT-qPCR. Stably captured virus surfaces were successfully used to explore kinetic parameters of the interaction of a panel of monoclonal antibodies with two PVY isolates representing the main viral serotypes N and O. In addition, the optimized biosensor proved to be suitable for evaluating whether two given monoclonal antibodies compete for the same epitope within the viral particle surface. The strategy proposed in this work can help to improve existing serologic diagnostic tools that target PVY and will allow investigation of the inherent serological variability of the virus and exploration for new interactions of PVY particles with other proteins.     

Clarification and application of an ion parametric resonance model for magnetic field interactions with biological systems

Theoretical models proposed to date have been unable to clearly predict biological results from exposure to low-intensity electric and magnetic fields (EMF). Recently a predictive ionic resonance model was proposed by Lednev, based on an earlier atomic spectroscopy theory described by Podgoretskii and Podgoretskii and Khrustalev. The ion parametric resonance (IPR) model developed in this paper corrects mathematical errors in the earlier Lednev model and extends that model to give explicit predictions of biological responses to parallel AC and DC magnetic fields caused by field-induced changes in combinations of ions within the biological system. Distinct response forms predicted by the IPR model depend explicitly on the experimentally controlled variables: magnetic flux densities of the AC and DC magnetic fields (B_ac and B_dc, respectively); AC frequency (f_ac); and, implicitly, charge to mass ratio of target ions. After clarifying the IPR model and extending it to combinations of different resonant ions, this paper proposes a basic set of experiments to test the IPR model directly which do not rely on the choice of a particular specimen or endpoint. While the fundamental bases of the model are supported by a variety of other studies, the IPR model is necessarily heuristic when applied to biological systems, because it is based on the premise that the magnitude and form of magnetic field interactions with unhydrated resonant ions in critical biological structures alter ion-associated biological activities that may in turn be correlated with observable effects in living systems. © 1994 Wiley-Liss, Inc.     

Surface plasmon resonance imaging for real-time, label-free analysis of protein interactions with carbohydrate microarrays

Plant lectin recognition of glycans was evaluated by SPR imaging using a model array of N-biotinylated aminoethyl glycosides of β-d-glucose (negative control), α-d-mannose (conA-responsive), β-d-galactose (RCA₁₂₀-responsive) and N-acetyl-β-d-glucosamine (WGA-responsive) printed onto neutravidin-coated gold chips. Selective recognition of the cognate ligand was observed when RCA₁₂₀ was passed over the array surface. Limited or no binding was observed for the non-cognate ligands. SPR imaging of an array of 40 sialylated and unsialylated glycans established the binding preference of hSiglec7 for α2-8-linked disialic acid structures over α2-6-sialyl-LacNAcs, which in turn were recognized and bound with greater affinity than α2-3-sialyl-LacNAcs. Affinity binding data could be obtained with as little as 10–20 μg of lectin per experiment. The SPR imaging technique was also able to establish selective binding to the preferred glycan ligand when analyzing crude culture supernatant containing 10–20 μg of recombinant hSiglec7-Fc. Our results show that SPR imaging provides results that are in agreement with those obtained from fluorescence based carbohydrate arrays but with the added advantage of label-free analysis.     

Surface plasmon resonance sensor for femtomolar detection of testosterone with water-compatible macroporous molecularly imprinted film

A novel water-compatible macroporous molecularly imprinted film (MIF) has been developed for rapid, sensitive, and label-free detection of small molecule testosterone in urine. The MIF was synthesized by photo copolymerization of monomers (methacrylic acid [MAA] and 2-hydroxyethyl methacrylate [HEMA]), cross-linker (ethylene glycol dimethacrylate, EGDMA), and polystyrene nanoparticles (PS NPs) in combination with template testosterone molecules. The PS NPs and template molecules were subsequently removed to form an MIF with macroporous structures and the specific recognition sites of testosterone. Incubation of artificial urine and human urine on the MIF and the non-imprinted film (NIF), respectively, indicated undetectable nonspecific adsorption. Accordingly, the MIF was applied on a surface plasmon resonance (SPR) sensor for the detection of testosterone in phosphate-buffered saline (PBS) and artificial urine with a limit of detection (LOD) down to 10⁻¹⁵ g/ml. To the best of our knowledge, the LOD is considered as one of the lowest among the SPR sensors for the detection of small molecules. The control experiments performed with analogue molecules such as progesterone and estradiol demonstrated the good selectivity of this MIF for sensing testosterone. Furthermore, this MIF-based SPR sensor shows high stability and reproducibility over 8 months of storage at room temperature, which is more robust than protein-based biosensors.     

Validated spectrofluorimetric and resonance Rayleigh scattering methods for determining naftidrofuryl in varied pharmaceutical samples based on its interaction with erythrosin B

Naftidrofuryl is a vasodilator medication used for treating cerebral and peripheral vascular diseases. In this study, two spectroscopical techniques, spectrofluorimetric and resonance Rayleigh scattering (RRS), were utilized to quantify naftidrofuryl in its pharmaceutical samples. The developed methodologies in this study rely on a facile process of forming an association complex between erythrosine B reagent and naftidrofuryl under acidic conditions. The fluorimetric assay is based on the ability of naftidrofuryl to quench and decrease the native fluorescence intensity of the reagent when measured at ${\lambda }_{\mathit{\text{emis}}.}$ = 550 nm ( ${\lambda }_{\mathit{\text{excit}}.}$ = 526 nm). Under similar reaction conditions, the RRS method relies on the observed amplification in the RRS spectrum of the reagent at a wavelength of 577 nm following its interaction with naftidrofuryl. The methods exhibited linearity within the ranges 0.2–1.6 μg/ml (r² = 0.999) and 0.1–1.4 μg/ml (r² = 0.9994), with limit of quantitation values of 0.146 and 0.099 μg/ml, and limit of detection values of 0.048 and 0.032 μg/ml, for the fluorometric and the RRS methods, respectively. Moreover, the quenching between the dye and naftidrofuryl was studied using Stern–Volmer analysis, and the methodologies were experimentally optimized and validated. Additionally, acceptable recoveries were achieved when the procedures were applied to determine naftidrofuryl in pharmaceutical samples.     

Application of electron spin resonance for evaluation of the level of free radicals in the myometrium in full-term pregnancy with normal labour and uterine inertia

In order to identify and quantify free radicals in the tissues of patients with normal physiological and pathological states of births, we developed a method to evaluate the amount of free radicals in myometrium of subplacental area and from body of uterus, using electron spin resonance spectroscopy. Analysis of the concentration of free radicals in the myometrium in full-term pregnancy with normal labour and during uterine inertia was studied. The activities of Ca2+-ATPase, cytochrome c oxidase and succinate dehydrogenase in samples of these tissues were tested too. Low free radical concentrations in these tissues were associated with disturbances in contractile activity of myometrium along with reduction of Ca2+-ATPase, cytochrome c oxidase and succinate dehydrogenase activity. There proved to be an association between the level of free radicals in the tissues and alteration in the physiological processes.     

Integration of surface plasmon resonance with mass spectrometry: automated ligand fishing and sample preparation for MALDI MS using a Biacore 3000 biosensor.

Integrating surface plasmon resonance analysis with mass spectrometry allows detection and characterization of molecular interactions to be complemented with identification of interaction partners. We have developed a procedure for Biacore 3000 that automatically performs all steps from ligand fishing and recovery to sample preparation for matrix-assisted laser desorption/ionization (MALDI) mass spectrometry including on-target digestion. In the model system used in this study a signal transduction protein, calmodulin, was selectively captured from brain extract by one of its interaction partners immobilized on a sensor chip. The bound material was eluted, deposited directly onto a MALDI target, and analyzed by mass spectrometry both as an intact protein and after on-target tryptic digestion. The procedure with direct deposition of recovered material on the MALDI target reduces sample losses and, in combination with automatic sample processing, increases the throughput of surface plasmon resonance mass spectrometry analysis.     

Graphene-MoS2 with TiO2SiO2 layers based surface plasmon resonance biosensor: Numerical development for formalin detection

In this article, numerically a surface plasmon resonance (SPR) biosensor is developed based on Graphene-M_OS₂ with TiO₂SiO₂ hybrid structure for the detection of formalin. Based on attenuated total reflection (ATR) method, we used angular interrogation technique to sense the presence the formalin by observing the change of “minimum reflectance with respect to SPR angle” and “maximum transmittance with respect to surface plasmon resonance frequency (SPRF)”. Here, we used Chitosan as probe analyte to perform chemical reaction with formalin (formaldehyde) which is consider as target analyte. Simulation results show a negligible variation of SPRF and SPR angle for improper sensing of formalin that confirms absence of formalin whereas for proper sensing is considerably countable that confirms the presence of formalin. Thereafter, a comparison of sensitivity for different sensor structure is made. It is observed that the sensitivity without TiO₂, SiO₂, MoS₂ and Graphene (conventional structure) is very poor and 73.67% whereas the sensitivity with graphene but without TiO₂, SiO₂ and MoS₂ layers is 74.67% consistently better than the conventional structure. This is due to the electron loss of graphene, which is accompanying with the imaginary dielectric constant. Furthermore, the sensitivity without TiO₂, SiO₂ and graphene but with MoS₂ layer is 79.167%. After more if both graphene and MoS2 are used and TiO₂ and SiO₂ layers are not used then sensitivity improves to 80.5%. This greater than before performance is due to the absorption ability and optical characteristics of graphene biomolecules and high fluorescence quenching ability of MoS₂. Further again, if TiO₂SiO₂ composite layer is used with the Graphene-MoS2 then the sensitivity enhances from 80.5% to 82.5%. Finally, the sensitivity for the proposed structure has been carried out, and result is 82.83%, the highest value among all the previous structures to integrate the advantages of graphene, MoS₂, TiO₂ and SiO₂.     

Determination of intermolecular distance for a model peptide of Bombyx mori silk fibroin, GAGAG, with rotational echo double resonance

Rotational echo double resonance NMR spectroscopy is applied for the determination of the distance of intermolecular chains of pentapeptide, GAGAG (G: Gly, A: Ala), a model typical of the crystalline domain in Bombyx mori silk fibroin. 1:4 mixture of G[1-(13)C]AGAG and GAG[(15)N]AG with antiparallel beta-sheet structure was used to determine the distance of intermolecular hydrogen bonding between adjacent molecules within pleated sheet and the (13)C-(15)N interatomic distance was determined to be 4.3 A. On the other hand, 1:4 mixture of GAG[1-(13)C]AG and GAG[(15)N]AG gave information on the interpleated sheet arrangement. When we assumed the same distances between two interpleated sheets, the distance was calculated to be 5.3 A and the angle (15)N-(13)C-(15)N was 180 degrees.     

Gd(III) complexes as contrast agents for magnetic resonance imaging: a proton relaxation enhancement study of the interaction with human serum albumin

 The non-covalent interaction between human serum albumin (HSA) and DOTA-like Gd(III) complexes containing hydrophobic benzyloxymethyl (BOM) substituents has been thoroughly investigated by measuring the solvent proton relaxation rates of their aqueous solutions. The binding association constants (K _A) to HSA are directly related to the number of hydrophobic substituents present on the surface of the complexes. Furthermore, an estimation of ΔH° and ΔS° has been obtained by the temperature dependence of K _A. Assays performed with the competitor probes warfarin and ibuprofen established that the complexes interact with HSA through two nearly equivalent binding sites located in the subdomains IIA and IIIA of the protein. Strong relaxation enhancements, promoted by the formation of slowly tumbling paramagnetic adducts, have been measured at 20 MHz for complexes containing two and three hydrophobic substituents. The macromolecular adduct with the latter species has a relaxivity of 53.2±0.7 mM^–1 s^–1, which represents the highest value so far reported for a Gd(III) complex. The temperature dependence of the relaxivity for the paramagnetic adducts with HSA indicates long exchange lifetimes for the water molecules dipolarly interacting with the paramagnetic centre. This is likely to be related to the formation, upon hydrophobic interaction of the complexes with HSA, of a clathrate-like, second-coordination-sphere arrangement of water molecules. Besides affecting the dissociative pathway of the coordinated water molecule, this water arrangement may itself significantly contribute to enhancement of the bulk solvent relaxation rate. Received: 6 November 1995 / Accepted: 17 April 1996     

A new meta-ANOVA approach for synthesizing information under signal-heterogeneity setting with application to nuclear magnetic resonance spectroscopic data

A new synthesizing statistical methodology is proposed to resolve issues of signal-heterogeneity in data sets collected through high-resolution ¹H nuclear magnetic resonance (NMR) spectroscopy. This signal-heterogeneity is typically caused by subjective operations for processing spectral profiles and measuring peak areas, non-homogeneous biological phases of experimental subjects, and variations of systems in multi-center. All these causes are likely to simultaneously impact signals of metabolic changes and their precision in a nonlinear fashion. As a combined effect, signal-heterogeneity chiefly manifests through non-homomorphic patterns of standardized treatment mean deviations spanning all experiments, and makes most remedial statistical models with linearity structure invalid. By avoiding a huge and very complex model, we develop a simple meta-ANOVA approach to synthesize many one-way-layout ANOVA analyses from individual experiments. A scale-invariant F-ratio statistic is taken as the summarizing sufficient statistic of a non-centrality parameter that supposedly captures the information about metabolic change from each experiment. Then a joint-likelihood function of a common non-centrality is constructed as the basis for maximum likelihood estimation and Chi-square likelihood ratio testing for statistical inference. We apply the meta-ANOVA to detect metabolic changes of three metabolites identified through pattern recognition on NMR spectral profiles obtained from muscle and liver tissues. We also detect effect differences among different treatments via meta-ANOVA multiple comparison.     

Contrast agents for magnetic resonance angiographic applications: 1H and 17O NMR relaxometric investigations on two gadolinium(III) DTPA-like chelates endowed with high binding affinity to human serum albumin

N,N′,N″,N‴ -pentaacetic acid) bearing different substituents for binding to human serum albumin (HSA) are compared. In spite of the structural differences of the recognition synthon and of the residual electric charge, the two chelates display an analogous binding affinity for the serum protein. Upon formation of the adducts with HSA, the exchange rates of the coordinated water appear slowed down by an amount corresponding to ca. 50% of the rates found for the free complexes. The relaxivity of [Gd(BOM)₃DTPA (H₂O)]^2 − is significantly higher than that of MS-325 either in the free complex or in the macromolecular adduct. Finally, the effect of pH on the stability of the HSA adducts and on the values of their relaxivities has been investigated. Received: 11 June 1999 / Accepted: 15 September 1999     

Flow dynamics within a bioreactor for tissue engineering by residence time distribution analysis combined with fluorescence and magnetic resonance imaging to investigate forced permeability and apparent diffusion coefficient in a perfusion cell culture chamber

This study reveals that residence time distribution (RTD) analysis with pH monitoring after acid bolus injection can be used to globally study the flow dynamics of a perfusion bioreactor, while fluorescence microscopy and magnetic resonance imaging (MRI) were used to locally investigate mass transport within a hydrogel scaffold seeded or not with cells. The bioreactor used in this study is a close‐loop tubular reactor. A dispersion model in one dimension has been used to describe the non‐ideal behavior of the reactor. From open‐loop experiments (single‐cycle analysis), the presence of stagnant zones and back mixing were observed. The impact of the flow rate, the compliance chamber volume and mixing were investigated. Intermediate flows (30, 45, 60, and 90 mL min⁻¹) had no effect over RTD function expressed in reduced time (θ). Lower flow rates (5 and 15 mL min⁻¹) were associated to smaller extent of dispersion. The compliance chamber volume greatly affected the dynamics of the RTD function, while the effects of mixing and flow were small to non‐significant. An empirical equation has been proposed to localize minima of the RTD function and to predict Pe_r. Finally, cells seeded in a gelatin gel at a density of 800,000 cells mL⁻¹ had no effect over the permeability and the apparent diffusion coefficient, as revealed by fluorescent microscopy and MRI experiments. Biotechnol. Bioeng. 2011;108: 2488–2498. © 2011 Wiley Periodicals, Inc.