A computational model integrating brain electrophysiology and metabolism highlights the key role of extracellular potassium and oxygen

Nanoscale potassium sensing based on valinomycin-anchored fluorescent gold nanoclusters

Gold nanoclusters are a smart platform for sensing potassium ions (K+). They have been synthesized using bovine serum albumin (BSA) and valinomycin (Val) to protect and cap the nanoclusters. The nanoclusters (Val-AuNCs) produced have a red emission at 616 nm under excitation with 470 nm. In the presence of K+, the valinomycin polar groups switch to the molecule's interior by complexing with K+, forming a bracelet structure, and being surrounded by the hydrophobic exterior conformation. This structure allows a proposed fluorometric method for detecting K+ by switching between the Val-AuNCs' hydrophilicity and hydrophobicity, which induces the aggregation of gold nanoclusters. As a result, significant quenching is seen in fluorescence after adding K+. The quenching in fluorescence in the presence of K+ is attributed to the aggregation mechanism. This sensing technique provides a highly precise and selective sensing method for K+ in the range 0.78 to 8 µM with LOD equal to 233 nM. The selectivity of Val-AuNCs toward K+ ions was investigated compared to other ions. Furthermore, the Val-AuNCs have novel possibilities as favorable sensor candidates for various imaging applications. Our detection technique was validated by determining K+ ions in postmortem vitreous humor samples, which yielded promising results.

Fluorescence 'turn-off-on' assays for neomycin sulphate and K+ ions with orange-red fluorescent molybdenum nanoclusters

Fluorescent metal nanoclusters (MNCs) have found extensive application in recognizing molecular species. Here, orange-red fluorescent Arg-A. paniculata-MoNCs were synthesized using Andrographis paniculata leaf extract, arginine as a ligand, and MoCl5 as a metal precursor. The Arg-A. paniculata-MoNCs complex exhibited a quantum yield (QY) of 16.91% and excitation/emission wavelengths of 400/665 nm. The synthesized Arg-A. paniculata-MoNCs successfully acted as a probe for assaying neomycin sulphate (NS) via fluorescence turn-off and K+ ions via fluorescence turn-on mechanisms, respectively. Moreover, the developed probe was effectively used to develop a cellulose paper strip-based sensor for detection of NS and K+ ions. Arg-A. paniculata-MoNCs demonstrated great potential for sensing NS and K+ ions, with concentration ranges of 0.1-80 and 0.25-110 μM for NS and K+ ions, respectively. The as-synthesized Arg-A. paniculata-MoNCs efficiently detected NS and K+ ions in food and biofluid samples, respectively.

A spatially distributed model of brain metabolism highlights the role of diffusion in brain energy metabolism

The different active roles of neurons and astrocytes during neuronal activation are associated with the metabolic processes necessary to supply the energy needed for their respective tasks at rest and during neuronal activation. Metabolism, in turn, relies on the delivery of metabolites and removal of toxic byproducts through diffusion processes and the cerebral blood flow. A comprehensive mathematical model of brain metabolism should account not only for the biochemical processes and the interaction of neurons and astrocytes, but also the diffusion of metabolites. In the present article, we present a computational methodology based on a multidomain model of the brain tissue and a homogenization argument for the diffusion processes. In our spatially distributed compartment model, communication between compartments occur both through local transport fluxes, as is the case within local astrocyte-neuron complexes, and through diffusion of some substances in some of the compartments. The model assumes that diffusion takes place in the extracellular space (ECS) and in the astrocyte compartment. In the astrocyte compartment, the diffusion across the syncytium network is implemented as a function of gap junction strength. The diffusion process is implemented numerically by means of a finite element method (FEM) based spatial discretization, and robust stiff solvers are used to time integrate the resulting large system. Computed experiments show the effects of ECS tortuosity, gap junction strength and spatial anisotropy in the astrocyte network on the brain energy metabolism.

Synthesis of multicolor silver nanostructures for colorimetric sensing of metal ions (Cr3+, Hg2+ and K+) in industrial water and urine samples with different spectral characteristics

In this work, we have synthesized four different color (yellow, orange, green, and blue (multicolor)) silver nanostructures (AgNSs) by chemical reduction method where silver nitrate, sodium borohydride and hydrogen peroxide were used as reagents. The as-synthesized multicolor AgNSs were successfully functionalized with bovine serum albumin (BSA) and applied as a colorimetric sensor for the assaying of metal cations (Cr³⁺, Hg²⁺, and K⁺). The addition of metal ions (Cr³⁺, Hg²⁺, and K⁺) into BSA functionalized AgNSs (BSA-AgNSs) causes the aggregation of BSA-AgNSs, and are accompanied by visual color changes with red or blue shift in the surface plasmon resonance (SPR) band of BSA-AgNSs. The BSA-AgNSs show different SPR characteristic for each metal ions (Cr³⁺, Hg²⁺, and K⁺) with exhibiting different spectral shift and color change. The yellow color BSA-AgNSs (Y-BSA-AgNSs) act as a probe for sensing Cr³⁺, orange color BSA-AgNSs (O-BSA-AgNSs) act as probe for Hg²⁺ ion assay, green color BSA-AgNSs (G-BSA-AgNSs) act as a probe for the assaying of both K⁺ and Hg²⁺, and blue color BSA-AgNSs (B-BSA-AgNSs) act as a sensor for colorimetric detection of K⁺ ion. The detection limits were found to be 0.26 μM for Cr³⁺ (Y-BSA-AgNSs), 0.14 μM for Hg²⁺ (O-BSA-AgNSs), 0.05 μM for K⁺ (G-BSA-AgNSs), 0.17 μM for Hg²⁺ (G-BSA-AgNSs), and 0.08 μM for K⁺ (B-BSA-AgNSs), respectively. Furthermore, multicolor BSA-AgNSs were also applied for assaying of Cr³⁺, and Hg²⁺ in industrial water samples and K⁺ in urine sample.

A Standardized Brain Molecular Atlas: A Resource for Systems Modeling and Simulation

Accurate molecular concentrations are essential for reliable analyses of biochemical networks and the creation of predictive models for molecular and systems biology, yet protein and metabolite concentrations used in such models are often poorly constrained or irreproducible. Challenges of using data from different sources include conflicts in nomenclature and units, as well as discrepancies in experimental procedures, data processing and implementation of the model. To obtain a consistent estimate of protein and metabolite levels, we integrated and normalized data from a large variety of sources to calculate Adjusted Molecular Concentrations. We found a high degree of reproducibility and consistency of many molecular species across brain regions and cell types, consistent with tight homeostatic regulation. We demonstrated the value of this normalization with differential protein expression analyses related to neurodegenerative diseases, brain regions and cell types. We also used the results in proof-of-concept simulations of brain energy metabolism. The standardized Brain Molecular Atlas overcomes the obstacles of missing or inconsistent data to support systems biology research and is provided as a resource for biomolecular modeling.

Metabolism plays a central role in the cortical spreading depression: Evidence from a mathematical model

The slow propagating waves of strong depolarization of neural cells characterizing cortical spreading depression, or depolarization, (SD) are known to break cerebral homeostasis and induce significant hemodynamic and electro-metabolic alterations. Mathematical models of cortical spreading depression found in the literature tend to focus on the changes occurring at the electrophysiological level rather than on the ensuing metabolic changes. In this paper, we propose a novel mathematical model which is able to simulate the coupled electrophysiology and metabolism dynamics of SD events, including the swelling of neurons and astrocytes and the concomitant shrinkage of extracellular space. The simulations show that the metabolic coupling leads to spontaneous repetitions of the SD events, which the electrophysiological model alone is not capable to produce. The model predictions, which corroborate experimental findings from the literature, show a strong disruption in metabolism accompanying each wave of spreading depression in the form of a sharp decrease of glucose and oxygen concentrations, with a simultaneous increase in lactate concentration which, in turn, delays the clearing of excess potassium in extracellular space. Our model suggests that the depletion of glucose and oxygen concentration is more pronounced in astrocyte than neuron, in line with the partitioning of the energetic cost of potassium clearing. The model suggests that the repeated SD events are electro-metabolic oscillations that cannot be explained by the electrophysiology alone. The model highlights the crucial role of astrocytes in cleaning the excess potassium flooding extracellular space during a spreading depression event: further, if the ratio of glial/neuron density increases, the frequency of cortical SD events decreases, and the peak potassium concentration in extracellular space is lower than with equal volume fractions.

Mathematical Modeling of Substrates Fluxes and Tumor Growth in the Brain

The aim of this article is to show how a tumor can modify energy substrates fluxes in the brain to support its own growth. To address this question we use a modeling approach to explain brain nutrient kinetics. In particular we set up a system of 17 equations for oxygen, lactate, glucose concentrations and cells number in the brain. We prove the existence and uniqueness of nonnegative solutions and give bounds on the solutions. We also provide numerical simulations.

Estimating hemodynamic stimulus and blood vessel compliance from cerebral blood flow data

Several key brain imaging modalities that are intended for retrieving information about neuronal activity in brain, the BOLD fMRI as a foremost example, rely on the assumption that elevated neuronal activity elicits spatiotemporally well localized increase of the oxygenated blood volume, which in turn can be monitored non-invasively. The details of the signaling in the neurovascular unit during hyperemia are still not completely understood, and remain a topic of active research, requiring good mathematical models that are able to couple the different aspects of the signaling event. In this work, the question of estimating the hemodynamic stimulus function from cerebral blood flow data is addressed. In the present model, the hemodynamic stimulus is a non-specific signal from the electrophysiological and metabolic complex that controls the compliance of the blood vessels, leading to a vasodilation and thereby to an increase of blood flow. The underlying model is based on earlier literature, and it is further developed in this article for the needs of the inverse problem, which is solved using hierarchical Bayesian methodology, addressing also the poorly known model parameters.

Using NEURON for Reaction-Diffusion Modeling of Extracellular Dynamics

Development of credible clinically-relevant brain simulations has been slowed due to a focus on electrophysiology in computational neuroscience, neglecting the multiscale whole-tissue modeling approach used for simulation in most other organ systems. We have now begun to extend the NEURON simulation platform in this direction by adding extracellular modeling. The extracellular medium of neural tissue is an active medium of neuromodulators, ions, inflammatory cells, oxygen, NO and other gases, with additional physiological, pharmacological and pathological agents. These extracellular agents influence, and are influenced by, cellular electrophysiology, and cellular chemophysiology-the complex internal cellular milieu of second-messenger signaling and cascades. NEURON's extracellular reaction-diffusion is supported by an intuitive Python-based where/who/what command sequence, derived from that used for intracellular reaction diffusion, to support coarse-grained macroscopic extracellular models. This simulation specification separates the expression of the conceptual model and parameters from the underlying numerical methods. In the volume-averaging approach used, the macroscopic model of tissue is characterized by free volume fraction-the proportion of space in which species are able to diffuse, and tortuosity-the average increase in path length due to obstacles. These tissue characteristics can be defined within particular spatial regions, enabling the modeler to account for regional differences, due either to intrinsic organization, particularly gray vs. white matter, or to pathology such as edema. We illustrate simulation development using spreading depression, a pathological phenomenon thought to play roles in migraine, epilepsy and stroke. Simulation results were verified against analytic results and against the extracellular portion of the simulation run under FiPy. The creation of this NEURON interface provides a pathway for interoperability that can be used to automatically export this class of models into complex intracellular/extracellular simulations and future cross-simulator standardization.