The Wilson–Cowan model has been widely applied for the simulation of electroencephalography (EEG) waves associated with neural activities in the brain. The Runge–Kutta (RK) method is commonly used to numerically solve the Wilson–Cowan equations. In this paper, we focus on enhancing the accuracy of the numerical method by proposing a strategy to construct a class of fourth-order RK methods using a generalized iterated Crank–Nicolson procedure, where the RK coefficients depend on a free parameter c2. When c2 is set to 0.5, our method becomes a special case of the classical fourth-order RK method. We apply the proposed methods to solve the Wilson–Cowan equations with two and three neuron populations, modeling EEG epileptic dynamics. Our simulations demonstrate that when c2 is set to 0.4, the proposed RK4-04 method yields smaller errors compared to those obtained using the classical fourth-order RK method. This is particularly visible when the spectral radius of the connection matrix or the excitation-inhibition coupling coefficient is relatively large.

We applied laser-induced breakdown spectroscopy (LIBS) and Raman spectroscopy to assess the structural content of alginate solutions and gels prepared at various concentrations (1.0 to 40 mg/mL). Alginate is a natural biopolymer typically extracted from brown seaweed and has been applied in diverse biomedical applications. LIBS measurements in Alginate solutions show spectral lines that can be attributed to calcium (422.6, 393.3, and 396.8 nm), magnesium (279.5 nm), strontium (460.7 nm), and C-N bond (~388.3 nm). Crosslinking the alginate solutions into hydrogels tends to reduce emission intensity, and many LIBS lines are not discerned. Measured Raman spectra show several peaks in addition to those of water and dissolved oxygen and nitrogen. The higher the alginate concentration, the higher the intensity of the alginate peaks. We combined the intensity correlation analysis (ICA), principal component analysis, and first-order derivative method to assess changes of the Raman peaks. Altogether, the results demonstrate how both techniques can provide complementary insight for chemical analysis of alginate solutions and gels.

In this study, we used GROMACS, a versatile package for performing molecular dynamics to simulate the interactions between different nanoparticles and Dipalmitoyl PhosPhatidyl Choline (DPPC) to understand the physical mechanisms that govern the interactions between nanoparticles and lipid membrane. Our simulations show the responses of the lipid bilayer to the nanoparticles, including the formation of an adsorbent layer on the nanoparticle surface, transmembrane ectopic movements and inconspicuous endocytosis of the nanoparticle by the membrane. Effects of the size of the nanoparticles, structural shape and charge state on the interaction and transport processes will be examined and summarized.

Alzheimer’s disease (AD) is the most common form of dementia and is associated with the accumulation of amyloid-β (Aβ), a peptide whose aggregation has been associated with neurotoxicity. Drugs targeting Aβ have shown great promise in 2D in vitro models and mouse models, yet preclinical and clinical trials for AD have been highly disappointing. We propose that current in vitro culture systems for discovering and developing AD drugs have significant limitations; specifically, that Aβ aggregation is vastly different in these 2D cultures carried out on flat plastic or glass substrates vs. in a 3D environment, such as brain tissue, where Aβ confinement very likely alters aggregation kinetics and thermodynamics. In this work, we identified attenuation of Aβ cytotoxicity in 3D hydrogel culture compared to 2D cell culture. We investigated Aβ structure and aggregation in solution vs. hydrogel using Transmission Electron Microscopy (TEM), Fluorescence Correlation Spectroscopy (FCS), and Thioflavin T (ThT) assays. Our results reveal that the equilibrium is shifted to stable β-sheet aggregates in hydrogels and away from the relatively unstable/unstructured presumed toxic oligomeric Aβ species in solution. Volume exclusion imparted by hydrogel confinement stabilizes unfolded, presumably toxic species, promoting stable extended β-sheet fibrils. These results, taken together with the many recent reports that 3D hydrogel cell cultures enable cell morphologies and epigenetic changes that are more similar to cells in vivo compared to 2D cultures, strongly suggest that AD drugs should be tested in 3D culture systems as a step along the development pathway towards new, more effective therapeutics.

The physiochemical properties of hydrogels utilized in 3D culture can be used to modulate cell phenotype and morphology with a striking resemblance to cellular processes that occur in vivo. Indeed, research areas including regenerative medicine, tissue engineering, in vitro cancer models, and stem cell differentiation have readily utilized 3D biomaterials to investigate cell biological questions. However, cells are only one component of this biomimetic milieu. In many models of disease such as Alzheimer's disease (AD) that could benefit from the in vivo-like cell morphology associated with 3D culture, other aspects of the disease such as protein aggregation have yet to be methodically considered in this 3D context. A hallmark of AD is the accumulation of the peptide amyloid-β (Aβ), whose aggregation is associated with neurotoxicity. We have previously demonstrated the attenuation of Aβ cytotoxicity when cells were cultured within type I collagen hydrogels versus on 2D substrates. In this work, we investigated the extent to which this phenomenon is conserved when Aβ is confined within hydrogels of varying physiochemical properties, notably mesh size and bioactivity. We investigated the Aβ structure and aggregation kinetics in solution and hydrogels composed of type I collagen, agarose, hyaluronic acid, and polyethylene glycol using fluorescence correlation spectroscopy and thioflavin T assays. Our results reveal that all hydrogels tested were associated with enhanced Aβ aggregation and Aβ cytotoxicity attenuation. We suggest that confinement itself imparts a profound effect, possibly by stabilizing Aβ structures and shifting the aggregate equilibrium toward larger species. If this phenomenon of altered protein aggregation in 3D hydrogels can be generalized to other contexts including the in vivo environment, it may be necessary to reevaluate aspects of protein aggregation disease models used for drug discovery.

We applied fluorescence spectroscopy, fluorescence correlation spectroscopy (FCS), and fluorescence anisotropy (FA) techniques to measure changes of the translational diffusion times and the rotational diffusion times of two nanoprobes, Alexa488 and FITC-Ficoll, dispersed in aqueous Ficoll solutions at room temperature. Analysis of the data indicated that the lifetimes of the nanoprobes appeared to be unaltered by the Ficoll solutions. In contrast, the FCS functions of each nanoprobe, which demonstrated slowing down of diffusion due to Ficoll, were adequately fitted with the expression of a freely diffusing nanoparticle. Similarly, the FA data indicated that the rotational diffusion of both nanoprobes was slowed down. The changes of the diffusion times and the rotational times of both nanoprobes could not be accounted for, however, by the corresponding changes of the viscosity of the solutions. Instead, we applied the entropic model proposed by de-Gennes and his collaborators, and fitted each set of diffusion data with a stretched exponential [exp(-alpha c(n))] with n being related to the quality of the solvent. We determined n-values close to the value one for both nanoprobes and for both diffusions, suggesting a theta-like behavior of the solutions. However, the alpha-values for the translation of both nanoprobes were larger than the corresponding ones derived for their rotation, indicating dissimilar local entropic effects. Together with calculations, the present results confirmed the slowing down of the diffusion processes of the nanoprobes due to crowding and, more significantly, provided through the nanoprobes insight into entangled but flexible polymeric structures of the concentrated solutions.

Noble metallic nanoparticles (NPs) such as gold and silver nanoparticles (AuNPs and AgNPs) have been shown to exhibit anti-tumor effect in anti-angiogenesis, photothermal and radio therapeutics. On the other hand, cell membranes are critical locales for specific targeting of cancerous cells. Therefore, NP-membrane interactions need be studied at molecular level to help better understand the underlying physicochemical mechanisms for future applications in cancer nanotechnology. Herein, we report our study on the interactions between citrate stabilized colloidal AuNPs/AgNPs (10 nm in size) and giant unilamellar vesicles (GUVs) using hyperspectral dark-field microscopy. GUVs are large model vesicle systems well established for the study of membrane dynamics. GUVs used in this study were prepared with dimyristoyl phosphatidylcholine (DMPC) and doped with cholesterol at various molar concentrations. Both imaging and spectral results support that AuNPs and AgNPs interact very differently with GUVs, i.e., AuNPs tend to integrate in between the lipid bilayer and form a uniform golden-brown crust on vesicles, whereas AgNPs are bejeweled on the vesicle surface as isolated particles or clusters with much varied configurations. The more disruptive capability of AuNPs is hypothesized to be responsible for the formation of golden brown crusts in AuNP-GUV interaction. GUVs of 20 mol% CHOL:DMPC were found to be a most economical concentration for GUVs to achieve the best integrity and the least permeability, consistent with the finding from other phase studies of lipid mixture that the liquid-ordered domains have the largest area fraction of the entire membrane at around 20 mol% of cholesterol.

We labeled poly(vinyl) alcohol (PVA, M-w approximate to 85 kDa) linear chains with 5-([4,6-Dichlorotriazin-2-yl]amino) fluorescein hydrochloride and measured their translational diffusion within similar non-fluorescent PVA solutions using fluorescence correlation spectroscopy (FCS). We found that the measured correlation functions could be readily fit with an expression derived for a freely diffusive nanoprobe, allowing us to determine changes of apparent diffusion coefficients with changes of PVA concentration. The data indicate slowing down of the diffusion of the fluorescent PVA as the surrounding PVA concentration is increased. However, the changes of the diffusion of the labeled chains cannot be accounted for by corresponding changes of solution viscosity. Instead, we use an entropic-based model suggested by de Gennes and his collaborators, and fit the data with a stretched exponential [exp(-alpha c(n))] with c denoting the PVA concentration, n being related to the solvent quality, and alpha being a prefactor that is predicted to depend on probe size. We determined n = 0.75, suggesting that the host solvent, water, is a good solvent for the PVA as this value is close to the theoretical value n = 3/4. This result is similar to other measurements for different nanoprobes such as rhodamine 6G (n = 0.77) and phycoerythrin (n = 0.84), as previously reported (Michelman-Ribeiro, A., et al., Biomacromolecules 8, 1595-1600 (2007)). Further, we tested the alpha-dependence on probe size by collecting FCS data for various other nanoprobes, and found a systematic linear increase with size for globular nanoprobes which, however, differs from that of the PVA chains That is, the hydrodynamic diameter of the non-globular, linear PVA chains appears not to be the determinant size for their diffusion within the polymeric PVA solution, indicating possible structural reconfiguration of the flexible, moving chains These results are consistent with the proposed entropic-based model devised by de Gennes et al., and demonstrate how diffusing nanoprobes -globular or linear- can probe the quality of a host polymeric system.

A novel method of determining the total uncertainty in the integrated intensity of fitted emission lines in multipeaked emission spectra is presented. The proposed method does not require an assumption of the type of line profile to be specified. The absolute difference between a fit and measured spectrum defines the uncertainty of the integrated signal intensity and is subsequently decomposed to determine the uncertainty of each peak in multiline fits. Decomposition relies on tabulating a weighting factor, which describes how each peak contributes to the total integral uncertainty. Applications of this method to quantitative approaches in laser-induced breakdown spectroscopy analysis are described.

We describe a systematic approach to image, track, and quantify the movements of HIV viruses embedded in human cervical mucus. The underlying motivation for this study is that, in HIV-infected adults, women account for more than half of all new cases and most of these women acquire the infection through heterosexual contact. The endocervix is believed to be a susceptible site for HIV entry. Cervical mucus, which coats the endocervix, should play a protective role against the viruses. Thus, we developed a methodology to apply time-resolved confocal microscopy to examine the motion of HIV viruses that were added to samples of untreated cervical mucus. From the images, we identified the viruses, tracked them over time, and calculated changes of the statistical mean-squared displacement (MSD) of each virus. Approximately half of tracked viruses appear constrained while the others show mobility with MSDs that are proportional to tau(alpha) + upsilon(2) tau(2), over time range tau, depicting a combination of anomalous diffusion (0 < alpha < 0.4) and flow-like behavior. The MSD data also reveal plateaus attributable to possible stalling of the viruses. Although a more extensive study is warranted, these results support the assumption of mucus being a barrier against the motion of these viruses. (C) 2016 Society of Photo-Optical Instrumentation Engineers (SPIE)

Biological systems routinely produce nanoscopic molecular structures with considerably less dispersion in size and shape than encountered in most manufactured materials. Indeed, Biological structures are frequently and essentially monodisperse. An example of this uniformity, combined with an intriguing geometry, is the nanometer-scale protein nanorings produced by interaction of the protein tubulin with certain hydrophobic tri-, tetra- and pentapeptides originally extracted as natural products from marine biosystems. Different peptides produce different sized nanorings, but we focus on those produced by binding to tubulin of the cyclic depsipeptide cryptophycin. The nanorings that form upon binding of this ligand show a sharp mass distribution indicating that the nanorings are made of 8 tubulin dimers of 100 kDa. In this submission, we demonstrate how a combination of fluorescence correlation spectroscopy, dynamic light scattering, electron microscopy, analytical ultracentrifugation, small-angle neutron scattering, and modeling is applied to reveal interactions of tubulin and cryptophycin in solution and to characterize their structures. We find that the cryptophycin-tubulin nanorings (~25 nm diameter) are single-walled, appear rigid, are composed of 8 tubulin dimers in a single closed ring, and are stable upon dilution to nanomolar concentrations. Similar studies with a different peptide, the linear pentapeptide dolastatin 10, demonstrated that binding of this peptide to tubulin produces larger nanorings (14 tubulin dimers, ~45 nm diameter rings), with slightly different properties. The ability to adjust the ring size with different peptides, and produce uniform nanorings with properties that differ slightly between size classes, makes the tubulin-peptide ring structures an appealing structural system.

We have conducted fluorescence anisotropy measurements of fluorescein fluorophores embedded in Ficoll solutions. Ficoll, a highly branched, hydrophilic polysaccharide, is used as a model crowding agent for studies of the effects of crowding on the behavior of nanoparticles. Fluorescein is a bright fluorophore with well-known fluorescence spectrum. We have collected the measurements with an ISS K2 frequency-domain fluorometer (470-nm excitation wavelength and 1-100 MHz modulation frequency), and determined the fluorescence lifetime, the fluorescence anisotropy, and the rotational correlation coefficient of the fluorescein as a function of ficoll concentration (up to 1200 mg/ml.) As the ficoll concentration is increased, the lifetime of the fluorophores show little change from 4.08 in water to 4.23 in 1200 mg/ml ficoll. However, the rotational correlation coefficient measurements show significant changes. At low ficoll concentrations no measureable interactions was observed. As the ficoll concentration is increased, two rotational modes emerge for better fitting of the data, which can be associated with free fluorophores and fluorophore-ficoll interactions. Above 1000 mg/ml ficoll solutions the data can be fit with a single rotational mode due to slowing down of the rotation of fluorophores. We compare the results from the fluorescence anisotropy and lifetime measurements with those from viscosity measurements and fluorescence correlation spectroscopy measurements, the latter being related to the translation diffusion.

We report femtosecond Laser-induced Breakdown Spectroscopy (fs-LIBS) measurements on several amino acids (Serine, Glutamine, and Cysteine) and Albumin protein solutions mixed with Ficoll polysaccharide at different proportions. The goal is to assess the effects of a host matrix on the identification and spectral characterization of amino acids by fs-LIBS. fs-LIBS utilizes an intense short laser pulse to obliterate a sample into basic constituents and to record the emission spectrum of atoms, ions, and molecules in the cooling down of the plasma plume. Several spectral peaks associated primarily with elemental composition of a sample were observed in the fs-LIBS spectra in a range from 200 to 950 nm. In addition, some molecular information associated with diatomic vibrational modes in certain molecules such as C-C and C-N were also obtained. The presence of Ficoll affects the relative intensity and broadening of the CN band, which could be considered as signatures of the amino acids. The fs-LIBS data and their analysis compare favorably with those derived from Fourier Transform Infrared Spectroscopy (FTIR). Interpretation of the spectral information enclosed in the emission of the diatomic molecules during laser ablation may lead to a better understanding of plume chemistry with a direct consequence on chemical analysis of complex samples such as amino acids. Altogether, the results demonstrate the potential of fs-LIBS technique as a detection method of biomolecules and for probing interactions of these biomolecules with a host matrix.

We report fluorescence correlation spectroscopy (FCS) measurements of the translational diffusion of two fluorescent nanoprobes, rhodamine (R6G) and carboxytetramethylrhodamine (TAMRA), embedded in poly(vinyl alcohol) (PVA) solutions and gels. The diffusion coefficient was measured as a function of the PVA concentration and pH. Furthermore, we designed and built an optical chamber to determine the diffusion coefficient of the nanoprobes within the PVA solutions and gels subjected to controlled dehydration. We find that 1) lowering pH causes an apparent slowing down of the diffusion of the nanoprobes, 2) increase of PVA concentration and crosslink density also induce slowing down of both nanoprobes, and 3) dehydration induces systematic decrease of the diffusion of TAMRA in both solutions and gels. Taken together, these results demonstrate that transient physical interactions between the nanoprobes and the PVA linear polymers have a significant effect upon nanoprobe diffusion.

Our kinetic studies have characterized the mechanisms of deoxyhemoglobin S polymer depolymerization when exposed to CO (used as a model for oxygen because rates can be controlled photolytically). Fibers dissolve slowly, losing monomers from their ends at low partial pressure, and very rapidly at higher partial pressures that induce fiber fracture and therefore many new ends. Slow dissolution that is not complete in the time red cells traverse the pulmonary microvasculature will generate residual arterial polymers (RAPs), enhancing pathogenesis by seeding nucleation of new polymers, accelerating repolymerization and increasing its extent. We now demonstrate, to the best of our knowledge for the first time by direct observation, that anaerobically drawn arterial blood of sickle patients shows birefringence in many red cells and therefore RAPs exist, which we confirm by EM observation of aligned polymers. RAPs exist not only under hypoxemic conditions, when they can be explained by limited solubility due to the presence of deoxyHbS, but also when hypoxemia is absent. RAPs without hypoxemia imply that slow depolymerization kinetics are responsible. One minute of voluntary hyperventilation and (separately) brief nasal oxygen greatly decrease RAPs. RAPs increase during sleep. We attribute these results to accelerated depolymerization at increasing levels of oxygen that cooperatively induce polymer fracture (fracture, using CO, exhibits a 4.7 power dependence on pCO). These results and the interdependent progress of oxygen saturation, partial pressure, fracture rate and remaining polymer that we model bear on pathogenesis and particularly on vaso-occlusive crises, which result from red cell rigidification and from cellular adhesion due to polymer-dependent cellular damage. Under these mechanisms, the lungs may play an important role in initiating pathology; and remediation of dysfunction by breathing assists is potentially prophylactic.

Fluorescence correlation spectroscopy (FCS) is increasingly being used to assess the movement of particles diffusing in complex, optically dense surroundings, in which case measurement conditions may complicate data interpretation. It is considered how a single-photon FCS measurement can be affected if the sample properties result in scattering of the incident light. FCS autocorrelation functions of Atto 488 dye molecules diffusing in solutions of polystyrene beads are measured, which acted as scatterers. Data indicated that a scattering-linked increase in the illuminated volume, as much as two fold, resulted in minimal increase in diffusivity. To analyze the illuminated beam profile, Monte-Carlo simulations were employed, which indicated a larger broadening of the beam along the axial than the radial directions, and a reduction of the incident intensity at the focal point. The broadening of the volume in the axial direction has only negligible effect on the measured diffusion time, since intensity fluctuations due to diffusion events in the radial direction are dominant in FCS measurements. Collectively, results indicate that multiple scattering does not result in FCS measurement artifacts and thus, when sufficient signal intensity is attainable, single-photon FCS can be a useful technique for measuring probe diffusivity in optically dense media.

Photothermal lens spectrometry is a highly-sensitive technique used to measure simultaneously absorption and thermal parameters of various scatter free samples. However, recently researchers have extended the use of this technique to for measuring the absorption of light in complex samples, including highly scattering media such as biological samples, . It is commonly applied in either scattering-free samples or without a systematic study of assumed that the effects of scattering on the photothermal signals. measurements are negligible. In this work, we report the results of a pump-probe experiment in which In the present study we measured both the photothermal signal and the scattering intensity at 90o angle from samples of water solutions prepared with a mixture of absorptive gold nanoparticles (concentration 150 ppb and 2-nm diameter) and scattering latex microspheres (0.2-25 microm diameter and concentrations 1.3-50 microg/ml). The data show that the photothermal signal slowly decreases when the concentration of the latex scatterers is increased. At latex concentration 50 microg/ml, the scattered signal increases more than 2 orders of magnitude for 0.2-microm latex microspheres while the photothermal signal reduces by less than 50%. This result suggests that the signal reduction may be caused by the distortion of the excitation beam profile due to multiple scattering, inducing hence reduction of the local temperature gradient necessary for thermal lensing. In the case of Latex, we show that the photothermal lens method can be considered scattering free for turbidity values smaller than ?? (1/cm).

We apply fluorescence correlation spectroscopy (FCS) and dynamic light scattering (DLS) to measure both the translational diffusion coefficient, D, of different fluorescent probes embedded in Ficoll solutions and the density fluctuations of the Ficoll solutions. Ficoll (MW=70 kDa) is a water-soluble, branched polysaccharide usually considered to be a spherical nanoparticle. The probes (R6G, dextran10, R-Erythrin proteins, clathrin, polystyrene beads,..) vary not only in size (1.8 nm to 34 nm) but also in shape (globular, branched polymers, triskelia). We find, using FCS, that the decrease of D as a function of Ficoll concentration (up to 500 mg/ml) can be described by an exponential, exp(-αc), with α being dependent on the probe size. This can interpreted within a model proposed by DeGennes and co-workers, which predicts a stretched exponential, D ∼exp(-αc-ν), with ν being related to the solvent quality and α proportional to the probe size. Thus, ν≈1, indicating a θsolvent like quality for the water-Ficoll system. The DLS measurements were performed as a function of the scattering angle and Ficoll concentration. At low concentrations (< 1mg/ml), we determined the hydrodynamic diameter of the Ficoll to be about 11 nm. As the Ficoll concentration is increased, a second mode appears in the correlation function, indicating possible interactions between the Ficoll polymers. We fitted the correlations with double stretched exponentials and determined the relaxation times of both modes as a function of the concentration. While one mode increases by several orders of magnitude, the other decreases weakly and exponentially, whose prefactor depends on the scattering angle. Estimates based on packing criteria of spherical beads show that the Ficoll polymers must intertwine in order to fit the volumetric space, indicating that Ficoll polymers are not compact nanoparticles and confirming the observations from DLS.