Contribution of dead-space microdomains to tortuosity of brain extracellular space

Toward Precise Modeling of Dopamine Release Kinetics: Comparison and Validation of Kinetic Models Using Voltammetry

Dopamine (DA) is a neurotransmitter present within the animal brain that is responsible for a wide range of physiologic functions, including motivation, reward, and movement control. Changes or dysfunction in the dynamics of DA release are thought to play a pivotal role in regulating various physiological and behavioral processes, as well as leading to neuropsychiatric diseases. Therefore, it is of fundamental interest to neuroscientists to understand and accurately model the kinetics that govern dopaminergic neurotransmission. In the past several decades, many mathematical models have been proposed to attempt to capture the biologic parameters that govern dopaminergic kinetics, with each model seeking to improve upon a previous model. In this review, each of these models are derived, and the ability of each model to properly fit two fast-scan cyclic voltammetry (FSCV) data sets will be demonstrated and discussed. The dopamine oxidation current in both FSCV data sets exhibits hang-up and overshoot behaviors, which have traditionally been difficult for mathematical models to capture. We show that more recent models are better able to model DA release that exhibits these behaviors but that no single model is clearly the best. Rather, models should be selected based on their mathematical properties to best fit the FSCV data one is trying to model. Developing such differential equation models to describe the kinetics of DA release from the synapse confers significant applications both for advancing scientific understanding of DA neurotransmission and for advancing clinical ability to treat neuropsychiatric diseases.

Mechanisms of Activation of Brain's Drainage during Sleep: The Nightlife of Astrocytes

The study of functions, mechanisms of generation, and pathways of movement of cerebral fluids has a long history, but the last decade has been especially productive. The proposed glymphatic hypothesis, which suggests a mechanism of the brain waste removal system (BWRS), caused an active discussion on both the criticism of some of the perspectives and our intensive study of new experimental facts. It was especially found that the intensity of the metabolite clearance changes significantly during the transition between sleep and wakefulness. Interestingly, at the cellular level, a number of aspects of this problem have been focused on, such as astrocytes-glial cells, which, over the past two decades, have been recognized as equal partners of neurons and perform many important functions. In particular, an important role was assigned to astrocytes within the framework of the glymphatic hypothesis. In this review, we return to the "astrocytocentric" view of the BWRS function and the explanation of its activation during sleep from the viewpoint of new findings over the last decade. Our main conclusion is that the BWRS's action may be analyzed both at the systemic (whole-brain) and at the local (cellular) level. The local level means here that the neuro-glial-vascular unit can also be regarded as the smallest functional unit of sleep, and therefore, the smallest functional unit of the BWRS.

Sheet and void porous media models for brain interstitial space

The interstitial space (ISS) component of brain extracellular space resembles an unconsolidated porous medium. Previous analysis of the diffusion of small molecules in this domain shows that the typical porosity is 0.2 and typical tortuosity 1.6. An ensemble of cubic cells separated by uniform sheets of ISS cannot generate the measured tortuosity, even if some of the tortuosity value is attributed to interstitial viscosity, so more complex models are needed. Here two models are analysed: the corner cubic void (CCV) and the edge tunnel void (ETV). Both models incorporate dead spaces formed from local expansions of the ISS to increase geometrical tortuosity. Using Monte Carlo simulation of diffusion it is found that in the range of normal porosities, the square of the tortuosity is a linear function of the ratio of void to sheet volumes for the CCV model and this model can generate the experimentally observed tortuosities. For abnormally high porosities, however, the linear relation fails. The ETV model shows a quartic functional relation and can only generate the observed tortuosity if interstitial viscosity is present. The CCV model is used to analyse the recently described changes in porosity between asleep and awake brain states.

Characterization of optical clearing mechanisms in muscle during treatment with glycerol and gadobutrol solutions

The recent increasing interest in the application of radiology contrasting agents to create transparency in biological tissues implies that the diffusion properties of those agents need evaluation. The comparison of those properties with the ones obtained for other optical clearing agents allows to perform an optimized agent selection to create optimized transparency in clinical applications. In this study, the evaluation and comparison of the diffusion properties of gadobutrol and glycerol in skeletal muscle was made, showing that although gadobutrol has a higher molar mass than glycerol, its low viscosity allows for a faster diffusion in the muscle. The characterization of the tissue dehydration and refractive index matching mechanisms of optical clearing was made in skeletal muscle, namely by the estimation of the diffusion coefficients for water, glycerol and gadobutrol. The estimated tortuosity values of glycerol (2.2) and of gadobutrol (1.7) showed a longer path-length for glycerol in the muscle.

New insight into brain disease therapy: nanomedicines-crossing blood-brain barrier and extracellular space for drug delivery

INTRODUCTION

Brain diseases including brain tumor, Alzheimer's disease, Parkinson's disease, etc. are difficult to treat. The blood-brain barrier (BBB) is a major obstacle for drug delivery into the brain. Although nano-package and receptor-mediated delivery of nanomedicine markedly increases BBB penetration, it yet did not extensively improve clinical cure rate. Recently, brain extracellular space (ECS) and interstitial fluid (ISF) drainage in ECS have been found to determine whether a drug dissolved in ISF can reach its target cells. Notably, an increase in tortuosity of ECS associated with slower ISF drainage induced by the accumulated harmful substances, such as: amyloid-beta (Aβ), α-synuclein, and metabolic wastes, causes drug delivery failure.

AREAS COVERED

The methods of nano-package and receptor-mediated drug delivery and the penetration efficacy of nanomedicines across BBB and ECS are assessed.

EXPERT OPINION

Invasive delivering drug via ECS and noninvasive near-infrared photo-sensitive nanomedicines may provide a promising benefit to patients with brain disease.

Transport in the Brain Extracellular Space: Diffusion, but Which Kind?

The mechanisms of transport of substances in the brain parenchyma have been a hot topic in scientific discussion in the past decade. This discussion was triggered by the proposed glymphatic hypothesis, which assumes a directed flow of cerebral fluid within the parenchyma, in contrast to the previous notion that diffusion is the main mechanism. However, when discussing the issue of “diffusion or non-diffusion”, much less attention was given to the question that diffusion itself can have a different character. In our opinion, some of the recently published results do not fit into the traditional understanding of diffusion. In this regard, we outline the relevant new theoretical approaches on transport processes in complex random media such as concepts of diffusive diffusivity and time-dependent homogenization, which expands the understanding of the forms of transport of substances based on diffusion.

Auriculocondylar syndrome 2 results from the dominant-negative action of PLCB4 variants

Auriculocondylar syndrome 2 (ARCND2) is a rare autosomal dominant craniofacial malformation syndrome linked to multiple genetic variants in the coding sequence of phospholipase C β4 (PLCB4). PLCB4 is a direct signaling effector of the endothelin receptor type A (EDNRA)-Gq/11 pathway, which establishes the identity of neural crest cells (NCCs) that form lower jaw and middle ear structures. However, the functional consequences of PLCB4 variants on EDNRA signaling is not known. Here, we show, using multiple signaling reporter assays, that known PLCB4 variants resulting from missense mutations exert a dominant-negative interference over EDNRA signaling. In addition, using CRISPR/Cas9, we find that F0 mouse embryos modeling one PLCB4 variant have facial defects recapitulating those observed in hypomorphic Ednra mouse models, including a bone that we identify as an atavistic change in the posterior palate/oral cavity. Remarkably, we have identified a similar osseous phenotype in a child with ARCND2. Our results identify the disease mechanism of ARCND2, demonstrate that the PLCB4 variants cause craniofacial differences and illustrate how minor changes in signaling within NCCs may have driven evolutionary changes in jaw structure and function. This article has an associated First Person interview with the first author of the paper.

Compromised Astrocyte Swelling/Volume Regulation in the Hippocampus of the Triple Transgenic Mouse Model of Alzheimer’s Disease

In this study, we aimed to disclose the impact of amyloid-β toxicity and tau pathology on astrocyte swelling, their volume recovery and extracellular space (ECS) diffusion parameters, namely volume fraction (α) and tortuosity (λ), in a triple transgenic mouse model of Alzheimer’s disease (3xTg-AD). Astrocyte volume changes, which reflect astrocyte ability to take up ions/neurotransmitters, were quantified during and after exposure to hypo-osmotic stress, or hyperkalemia in acute hippocampal slices, and were correlated with alterations in ECS diffusion parameters. Astrocyte volume and ECS diffusion parameters were monitored during physiological aging (controls) and during AD progression in 3-, 9-, 12- and 18-month-old mice. In the hippocampus of controls α gradually declined with age, while it remained unaffected in 3xTg-AD mice during the entire time course. Moreover, age-related increases in λ occurred much earlier in 3xTg-AD animals than in controls. In 3xTg-AD mice changes in α induced by hypo-osmotic stress or hyperkalemia were comparable to those observed in controls, however, AD progression affected α recovery following exposure to both. Compared to controls, a smaller astrocyte swelling was detected in 3xTg-AD mice only during hyperkalemia. Since we observed a large variance in astrocyte swelling/volume regulation, we divided them into high- (HRA) and low-responding astrocytes (LRA). In response to hyperkalemia, the incidence of LRA was higher in 3xTg-AD mice than in controls, which may also reflect compromised K+ and neurotransmitter uptake. Furthermore, we performed single-cell RT-qPCR to identify possible age-related alterations in astrocytic gene expression profiles. Already in 3-month-old 3xTg-AD mice, we detected a downregulation of genes affecting the ion/neurotransmitter uptake and cell volume regulation, namely genes of glutamate transporters, α2β2 subunit of Na+/K+-ATPase, connexin 30 or Kir4.1 channel. In conclusion, the aged hippocampus of 3xTg-AD mice displays an enlarged ECS volume fraction and an increased number of obstacles, which emerge earlier than in physiological aging. Both these changes may strongly affect intercellular communication and influence astrocyte ionic/neurotransmitter uptake, which becomes impaired during aging and this phenomenon is manifested earlier in 3xTg-AD mice. The increased incidence of astrocytes with limited ability to take up ions/neurotransmitters may further add to a cytotoxic environment.

TUBE Project: Transport-Derived Ultrafines and the Brain Effects

The adverse effects of air pollutants on the respiratory and cardiovascular systems are unquestionable. However, in recent years, indications of effects beyond these organ systems have become more evident. Traffic-related air pollution has been linked with neurological diseases, exacerbated cognitive dysfunction, and Alzheimer's disease. However, the exact air pollutant compositions and exposure scenarios leading to these adverse health effects are not known. Although several components of air pollution may be at play, recent experimental studies point to a key role of ultrafine particles (UFPs). While the importance of UFPs has been recognized, almost nothing is known about the smallest fraction of UFPs, and only >23 nm emissions are regulated in the EU. Moreover, the role of the semivolatile fraction of the emissions has been neglected. The Transport-Derived Ultrafines and the Brain Effects (TUBE) project will increase knowledge on harmful ultrafine air pollutants, as well as semivolatile compounds related to adverse health effects. By including all the major current combustion and emission control technologies, the TUBE project aims to provide new information on the adverse health effects of current traffic, as well as information for decision makers to develop more effective emission legislation. Most importantly, the TUBE project will include adverse health effects beyond the respiratory system; TUBE will assess how air pollution affects the brain and how air pollution particles might be removed from the brain. The purpose of this report is to describe the TUBE project, its background, and its goals.

Interactions of brain, blood, and CSF: a novel mathematical model of cerebral edema

Background

Previous models of intracranial pressure (ICP) dynamics have not included flow of cerebral interstitial fluid (ISF) and changes in resistance to its flow when brain swelling occurs. We sought to develop a mathematical model that incorporates resistance to the bulk flow of cerebral ISF to better simulate the physiological changes that occur in pathologies in which brain swelling predominates and to assess the model’s ability to depict changes in cerebral physiology associated with cerebral edema.

Methods

We developed a lumped parameter model which includes a representation of cerebral ISF flow within brain tissue and its interactions with CSF flow and cerebral blood flow (CBF). The model is based on an electrical analog circuit with four intracranial compartments: the (1) subarachnoid space, (2) brain, (3) ventricles, (4) cerebral vasculature and the extracranial spinal thecal sac. We determined changes in pressure and volume within cerebral compartments at steady-state and simulated physiological perturbations including rapid injection of fluid into the intracranial space, hyperventilation, and hypoventilation. We simulated changes in resistance to flow or absorption of CSF and cerebral ISF to model hydrocephalus, cerebral edema, and to simulate disruption of the blood–brain barrier (BBB).

Results

The model accurately replicates well-accepted features of intracranial physiology including the exponential-like pressure–volume curve with rapid fluid injection, increased ICP pulse pressure with rising ICP, hydrocephalus resulting from increased resistance to CSF outflow, and changes associated with hyperventilation and hypoventilation. Importantly, modeling cerebral edema with increased resistance to cerebral ISF flow mimics key features of brain swelling including elevated ICP, increased brain volume, markedly reduced ventricular volume, and a contracted subarachnoid space. Similarly, a decreased resistance to flow of fluid across the BBB leads to an exponential-like rise in ICP and ventricular collapse.

Conclusions

The model accurately depicts the complex interactions that occur between pressure, volume, and resistances to flow in the different intracranial compartments under specific pathophysiological conditions. In modelling resistance to bulk flow of cerebral ISF, it may serve as a platform for improved modelling of cerebral edema and blood–brain barrier disruption that occur following brain injury.

Improved Pressure Equalization Ratio Following Mannitol Administration in Patients With Severe TBI: A Preliminary Study of a Potential Bedside Marker for Response to Therapy

BACKGROUND

Performing a cerebrospinal fluid (CSF) drainage challenge can be used to measure the pressure equalization (PE) ratio, which describes the extent to which CSF drainage can equalize pressure to the height of the external ventricular drain and may serve as a correlate of cerebral edema. We sought to assess whether treatment with mannitol improves PE ratio in patients with severe traumatic brain injury (TBI) with elevated intracranial pressure (ICP).

METHODS

We studied consecutive patients with TBI and brain edema on computed tomography scan and an external ventricular drain (EVD), admitted to the neurointensive care unit. PE ratio, defined as ICP prior to CSF drainage minus ICP after CSF drainage divided by ICP prior to CSF drainage minus EVD height, was measured as previously described. Patients were treated with mannitol for raised ICP based on clinical indication and PE ratio measured before and after mannitol administration.

RESULTS

We studied 20 patients with severe TBI with raised ICP. Mean ICP prior to mannitol treatment was 29 ± 7 mm Hg. PE ratio rose substantially after mannitol treatment (0.62 ± 0.24 vs. 0.29 ± 0.20, p < 0.0001), indicating an improved ability to drain CSF and equalize ICP with the preset height of the EVD. The combination of mannitol and CSF drainage led to an improved reduction in ICP compared with that seen before mannitol therapy (11 ± 2 mm Hg vs. 6 ± 2 mm Hg, p < 0.01), and led to a decrease in ICP below the 20 mm Hg threshold in 77% of cases.

CONCLUSIONS

Treatment with mannitol leads to a substantial improvement in PE ratio that reflects the ability to achieve a greater decrease in ICP when CSF drainage is performed after mannitol administration. This preliminary study raises the possibility that PE ratio may be useful to follow response to therapy in patients with cerebral edema and raised ICP. Further studies to determine whether PE ratio may serve as an easily obtained and clinically useful surrogate marker for the extent of brain edema are warranted.

Characterizing extracellular diffusion properties using diffusion-weighted MRS of sucrose injected in mouse brain

Brain water and some critically important energy metabolites, such as lactate or glucose, are present in both intracellular and extracellular spaces (ICS/ECS) at significant levels. This ubiquitous nature makes diffusion MRI/MRS data sometimes difficult to interpret and model. While it is possible to glean information on the diffusion properties in ICS by measuring the diffusion of purely intracellular endogenous metabolites (such as NAA), the absence of endogenous markers specific to ECS hampers similar analyses in this compartment. In past experiments, exogenous probes have therefore been injected into the brain to assess their apparent diffusion coefficient (ADC) and thus estimate tortuosity in ECS. Here, we use a similar approach in mice by injecting sucrose, a well-known ECS marker, in either the lateral ventricles or directly in the prefrontal cortex. For the first time, we propose a thorough characterization of ECS diffusion properties encompassing (1) short-range restriction by looking at signal attenuation at high b values, (2) tortuosity and long-range restriction by measuring ADC time-dependence at long diffusion times and (3) microscopic anisotropy by performing double diffusion encoding (DDE) measurements. Overall, sucrose diffusion behavior is strikingly different from that of intracellular metabolites. Acquisitions at high b values not only reveal faster sucrose diffusion but also some sensitivity to restriction, suggesting that the diffusion in ECS is not fully Gaussian at high b. The time evolution of the ADC at long diffusion times shows that the tortuosity regime is not reached yet in the case of sucrose, while DDE experiments suggest that it is not trapped in elongated structures. No major difference in sucrose diffusion properties is reported between the two investigated routes of injection and brain regions. These original experimental insights should be useful to better interpret and model the diffusion signal of molecules that are distributed between ICS and ECS compartments.

Governing Transport Principles for Nanotherapeutic Application in the Brain

Neurological diseases account for a significant portion of the global disease burden. While research efforts have identified potential drugs or drug targets for neurological diseases, most therapeutic platforms are still ineffective at reaching the target location selectively and with high yield. Restricted transport, including passage across the blood-brain barrier, through the brain parenchyma, and into specific cells, is a major cause of ineffective therapeutic delivery. However, nanotechnology is a promising, tailorable platform for overcoming these transport barriers and improving therapeutic delivery to the brain. We provide a transport-oriented analysis of nanotechnology's ability to navigate these transport barriers in the brain. We also provide an opinion on the need for technology development for increasing our capacity to characterize and quantify nanoparticle passage through each transport barrier. Finally, we highlight the importance of incorporating the effect of disease, metabolic state, and regional dependencies to better understand transport of nanotherapeutics in the brain.

Characterizing the Response to Cerebrospinal Fluid Drainage in Patients with an External Ventricular Drain: The Pressure Equalization Ratio

BACKGROUND

An external ventricular drain (EVD) is the gold standard for measurement of intracranial pressure (ICP) and allows for drainage of cerebrospinal fluid (CSF). Different causes of elevated ICP, such as CSF outflow obstruction or cerebral swelling, respond differently to CSF drainage. This is a widely recognized but seldom quantified distinction. We sought to define an index to characterize the response to CSF drainage in neurocritical care patients.

METHODS

We studied consecutive patients admitted to the neurointensive care unit who had an EVD. The EVD was closed for 30 min prior to assessment. We documented pre-drainage ICP, opened EVD to drainage allowing CSF to drain until it ceased, and recorded post-drainage ICP at EVD closure. We calculated the pressure equalization (PE) ratio as the difference between pre-drainage ICP and post-drainage ICP divided by the difference between pre-drainage ICP and EVD height.

RESULTS

We studied 60 patients (36 traumatic brain injury [TBI], 24 non-TBI). As expected, TBI patients had more signs of cerebral swelling on CT and smaller ventricles. Although TBI patients had significantly higher pre-drainage ICP (26 ± 10 mm Hg) than non-TBI patients (19 ± 5 mm Hg, p < 0.001) they drained less CSF (7 cc vs. 4 cc, p < 0.01). PE ratio was substantially higher in non-TBI than in TBI patients (0.86 ± 0.36 vs. 0.43 ± 0.31, p < 0.0001), indicating that non-TBI patients were better able to equalize pressure with EVD height than TBI patients.

CONCLUSIONS

PE ratio reflects the ability to equalize pressure with the preset height of the EVD and differs substantially between TBI and non-TBI patients. A high PE ratio likely indicates CSF outflow obstruction effectively treated by CSF diversion, while a lower PE ratio occurs when cerebral swelling predominates. Further studies could assess whether the PE ratio would be useful as a surrogate marker for cerebral edema or the state of intracranial compliance.

Realistic spiking neural network: Non-synaptic mechanisms improve convergence in cell assembly

Learning in neural networks inspired by brain tissue has been studied for machine learning applications. However, existing works primarily focused on the concept of synaptic weight modulation, and other aspects of neuronal interactions, such as non-synaptic mechanisms, have been neglected. Non-synaptic interaction mechanisms have been shown to play significant roles in the brain, and four classes of these mechanisms can be highlighted: (i) electrotonic coupling; (ii) ephaptic interactions; (iii) electric field effects; and iv) extracellular ionic fluctuations. In this work, we proposed simple rules for learning inspired by recent findings in machine learning adapted to a realistic spiking neural network. We show that the inclusion of non-synaptic interaction mechanisms improves cell assembly convergence. By including extracellular ionic fluctuation represented by the extracellular electrodiffusion in the network, we showed the importance of these mechanisms to improve cell assembly convergence. Additionally, we observed a variety of electrophysiological patterns of neuronal activity, particularly bursting and synchronism when the convergence is improved.

Effective Diffusion and Tortuosity in Brain White Matter

Patients affected by glioblastomas have a very low survival rate. Emerging techniques, such as convection enhanced delivery (CED), need complex numerical models to be effective; furthermore, the estimation of the main parameters to be used to instruct constitutive laws in simulations represents a major challenge. This work proposes a new method to compute tortuosity, a key parameter for drug diffusion in fibrous tissue, starting from a model which incorporates the main white matter geometrical features. It is shown that tortuosity increases from 1.35 to 1.85 as the extracellular space width decreases. The results are in good agreement with experimental data reported in the literature.

Unveiling the Extracellular Space of the Brain: From Super-resolved Microstructure to In Vivo Function

The extracellular space occupies approximately one-fifth of brain volume, molding a spider web of gaps filled with interstitial fluid and extracellular matrix where neurons and glial cells perform in concert. Yet, very little is known about the spatial organization and dynamics of the extracellular space, let alone its influence on brain function, owing to a lack of appropriate techniques (and a traditional bias toward the inside of cells, not the spaces in between). At the same time, it is clear that understanding fundamental brain functions, such as synaptic transmission, memory, sleep, and recovery from disease, calls for more focused research on the extracellular space of the brain. This review article highlights several key research areas, covering recent methodological and conceptual progress that illuminates this understudied, yet critically important, brain compartment, providing insights into the opportunities and challenges of this nascent field.

Link between a high k on for drug binding and a fast clinical action: to be or not to be?

Review articles on binding kinetics essentially focus on drugs that dissociate slowly from their target since this is required for the successful treatment of many pathophysiological conditions. Recently, the therapeutic benefit of a high k on (i.e. the second order association rate constant) has also been linked to fast association and to a fast clinical action. Other studies, however, called this assertion into question since additional factors, like the dosing paradigm and the binding mechanism, are important as well. The still ongoing reticence about integrating binding kinetics in lead optimization programs motivated us to critically review the link between the drug's kinetic rate constants and their in vitro and in vivo target occupancy profile, with special focus on k on. The presented simulations tally with a positive link between a drug's effective/observed association rate (which is quite easy to determine in vitro) and the swiftness of its clinical action. On the other hand, the simulations show that the k on-concept should not be confounded with the effective association process since increasing this parameter only enhances the drug's in vitro and in vivo association under certain conditions: the binding mechanism should be suitable, rebinding (and thus the factors within the target's micro-environment that favour this mechanism) should not be too prominent and the dosage should not be kept in par with the drug's affinity. Otherwise, increasing k on could be ineffective or even be counter-productive.

Ex Vivo Measurement of Electrically Evoked Dopamine Release in Zebrafish Whole Brain

Zebrafish (Danio rerio) have recently emerged as useful model organism for the study of neuronal function. Here, fast-scan cyclic voltammetry (FSCV) at carbon-fiber microelectrodes was used to measure locally evoked dopamine release and uptake in zebrafish whole brain preparations and results were compared with those obtained from brain slices. Evoked dopamine release ([DA]_max) was similar in whole brain and sagittal brain slice preparations (0.49 ± 0.13 μM in whole brain and 0.59 ± 0.28 μM in brain slices). Treatment with α-methyl-p-tyrosine methyl ester (αMPT), an inhibitor of tyrosine hydroxylase, diminished release and the electrochemical signal reappeared after subsequent drug washout. No observed change in stimulated release current occurred after treatment with desipramine or fluoxetine in the whole brain. Treatment with the uptake inhibitors, nomifensine or GBR 12909 increased [DA]_max, while treatment with sulpiride, a D2 dopamine autoreceptor antagonist, resulted in increased stimulated dopamine release in whole brain, but had no effect on release in slices. Dopamine release in whole brains increased progressively up to an electrical stimulation frequency of 25 Hz, while release in slices increased up to a frequency of only 10 Hz and then plateaued, highlighting another key difference between these preparations. We observed a lag in peak dopamine release following stimulation, which we address using diffusion models and pharmacological treatments. Collectively, these results demonstrate the electrochemical determination of dopamine release in the whole, intact brain of a vertebrate species ex vivo and are an important step for carrying out further experiments in zebrafish.

Brain Extracellular Space: The Final Frontier of Neuroscience

Brain extracellular space is the narrow microenvironment that surrounds every cell of the central nervous system. It contains a solution that closely resembles cerebrospinal fluid with the addition of extracellular matrix molecules. The space provides a reservoir for ions essential to the electrical activity of neurons and forms an intercellular chemical communication channel. Attempts to reveal the size and structure of the extracellular space using electron microscopy have had limited success; however, a biophysical approach based on diffusion of selected probe molecules has proved useful. A point-source paradigm, realized in the real-time iontophoresis method using tetramethylammonium, as well as earlier radiotracer methods, have shown that the extracellular space occupies ∼20% of brain tissue and small molecules have an effective diffusion coefficient that is two-fifths that in a free solution. Monte Carlo modeling indicates that geometrical constraints, including dead-space microdomains, contribute to the hindrance to diffusion. Imaging the spread of macromolecules shows them increasingly hindered as a function of size and suggests that the gaps between cells are predominantly ∼40 nm with wider local expansions that may represent dead-spaces. Diffusion measurements also characterize interactions of ions and proteins with the chondroitin and heparan sulfate components of the extracellular matrix; however, the many roles of the matrix are only starting to become apparent. The existence and magnitude of bulk flow and the so-called glymphatic system are topics of current interest and controversy. The extracellular space is an exciting area for research that will be propelled by emerging technologies.

Cell membranes… and how long drugs may exert beneficial pharmacological activity in vivo

The time course of the beneficial pharmacological effect of a drug has long been considered to depend merely on the temporal fluctuation of its free concentration. Only in the last decade has it become widely accepted that target-binding kinetics can also affect in vivo pharmacological activity. Although current reviews still essentially focus on genuine dissociation rates, evidence is accumulating that additional micro-pharmacokinetic (PK) and -pharmacodynamic (PD) mechanisms, in which the cell membrane plays a central role, may also increase the residence time of a drug on its target. The present review provides a compilation of otherwise widely dispersed information on this topic. The cell membrane can intervene in drug binding via the following three major mechanisms: (i) by acting as a sink/repository for the drug; (ii) by modulating the conformation of the drug and even by participating in the binding process; and (iii) by facilitating the approach (and rebinding) of the drug to the target. To highlight these mechanisms, we focus on drugs that are currently used in clinical therapy, such as the antihypertensive angiotensin II type 1 receptor antagonist candesartan, the atypical antipsychotic agent clozapine and the bronchodilator salmeterol. Although the role of cell membranes in PK-PD modelling is gaining increasing interest, many issues remain unresolved. It is likely that novel biophysical and computational approaches will provide improved insights in the near future.

Enhanced Dopamine Release by Dopamine Transport Inhibitors Described by a Restricted Diffusion Model and Fast-Scan Cyclic Voltammetry

Fast-scan cyclic voltammetry (FSCV) using carbon fiber electrodes is widely used to rapidly monitor changes in dopamine (DA) levels in vitro and in vivo. Current analytical approaches utilize parameters such as peak oxidation current amplitude and decay times to estimate release and uptake processes, respectively. However, peak amplitude changes are often observed with uptake inhibitors, thereby confounding the interpretation of these parameters. To overcome this limitation, we demonstrate that a simple five-parameter, two-compartment model mathematically describes DA signals as a balance of release (r/ke) and uptake (ku), summed with adsorption (kads and kdes) of DA to the carbon electrode surface. Using nonlinear regression, we demonstrate that our model precisely describes measured DA signals obtained in brain slice recordings. The parameters extracted from these curves were then validated using pharmacological manipulations that selectively alter vesicular release or DA transporter (DAT)-mediated uptake. Manipulation of DA release through altering the Ca(2+)/Mg(2+) ratio or adding tetrodotoxin reduced the release parameter with no effect on the uptake parameter. DAT inhibitors methylenedioxypyrovalerone, cocaine, and nomifensine significantly reduced uptake and increased vesicular DA release. In contrast, a low concentration of amphetamine reduced uptake but had no effect on DA release. Finally, the kappa opioid receptor agonist U50,488 significantly reduced vesicular DA release but had no effect on uptake. Together, these data demonstrate a novel analytical approach to distinguish the effects of manipulations on DA release or uptake that can be used to interpret FSCV data.

Lymphatic Clearance of the Brain: Perivascular, Paravascular and Significance for Neurodegenerative Diseases

The lymphatic clearance pathways of the brain are different compared to the other organs of the body and have been the subject of heated debates. Drainage of brain extracellular fluids, particularly interstitial fluid (ISF) and cerebrospinal fluid (CSF), is not only important for volume regulation, but also for removal of waste products such as amyloid beta (Aβ). CSF plays a special role in clinical medicine, as it is available for analysis of biomarkers for Alzheimer's disease. Despite the lack of a complete anatomical and physiological picture of the communications between the subarachnoid space (SAS) and the brain parenchyma, it is often assumed that Aβ is cleared from the cerebral ISF into the CSF. Recent work suggests that clearance of the brain mainly occurs during sleep, with a specific role for peri- and para-vascular spaces as drainage pathways from the brain parenchyma. However, the direction of flow, the anatomical structures involved and the driving forces remain elusive, with partially conflicting data in literature. The presence of Aβ in the glia limitans in Alzheimer's disease suggests a direct communication of ISF with CSF. Nonetheless, there is also the well-described pathology of cerebral amyloid angiopathy associated with the failure of perivascular drainage of Aβ. Herein, we review the role of the vasculature and the impact of vascular pathology on the peri- and para-vascular clearance pathways of the brain. The different views on the possible routes for ISF drainage of the brain are discussed in the context of pathological significance.

Anomalous extracellular diffusion in rat cerebellum

Extracellular space (ECS) is a major channel transporting biologically active molecules and drugs in the brain. Diffusion-mediated transport of these substances is hindered by the ECS structure but the microscopic basis of this hindrance is not fully understood. One hypothesis proposes that the hindrance originates in large part from the presence of dead-space (DS) microdomains that can transiently retain diffusing molecules. Because previous theoretical and modeling work reported an initial period of anomalous diffusion in similar environments, we expected that brain regions densely populated by DS microdomains would exhibit anomalous extracellular diffusion. Specifically, we targeted granular layers (GL) of rat and turtle cerebella that are populated with large and geometrically complex glomeruli. The integrative optical imaging (IOI) method was employed to evaluate diffusion of fluorophore-labeled dextran (MW 3000) in GL, and the IOI data analysis was adapted to quantify the anomalous diffusion exponent dw from the IOI records. Diffusion was significantly anomalous in rat GL, where dw reached 4.8. In the geometrically simpler turtle GL, dw was elevated but not robustly anomalous (dw = 2.6). The experimental work was complemented by numerical Monte Carlo simulations of anomalous ECS diffusion in several three-dimensional tissue models containing glomeruli-like structures. It demonstrated that both the duration of transiently anomalous diffusion and the anomalous exponent depend on the size of model glomeruli and the degree of their wrapping. In conclusion, we have found anomalous extracellular diffusion in the GL of rat cerebellum. This finding lends support to the DS microdomain hypothesis. Transiently anomalous diffusion also has a profound effect on the spatiotemporal distribution of molecules released into the ECS, especially at diffusion distances on the order of a few cell diameters, speeding up short-range diffusion-mediated signals in less permeable structures.

Penetration and intracellular uptake of poly(glycerol-adipate) nanoparticles into three-dimensional brain tumour cell culture models

Nanoparticle (NP) drug delivery systems may potentially enhance the efficacy of therapeutic agents. It is difficult to characterize many important properties of NPs in vivo and therefore attempts have been made to use realistic in vitro multicellular spheroids instead. In this paper, we have evaluated poly(glycerol-adipate) (PGA) NPs as a potential drug carrier for local brain cancer therapy. Various three-dimensional (3-D) cell culture models have been used to investigate the delivery properties of PGA NPs. Tumour cells in 3-D culture showed a much higher level of endocytic uptake of NPs than a mixed normal neonatal brain cell population. Differences in endocytic uptake of NPs in 2-D and 3-D models strongly suggest that it is very important to use in vitro 3-D cell culture models for evaluating this parameter. Tumour penetration of NPs is another important parameter which could be studied in 3-D cell models. The penetration of PGA NPs through 3-D cell culture varied between models, which will therefore require further study to develop useful and realistic in vitro models. Further use of 3-D cell culture models will be of benefit in the future development of new drug delivery systems, particularly for brain cancers which are more difficult to study in vivo.

Modeling the kinetic diversity of dopamine in the dorsal striatum

Dopamine is an important neurotransmitter that exhibits numerous functions in the healthy, injured, and diseased brain. Fast scan cyclic voltammetry paired with electrical stimulation of dopamine axons is a popular and powerful method for investigating the dynamics of dopamine in the extracellular space. Evidence now suggests that the heterogeneity of electrically evoked dopamine responses reflects the inherent kinetic diversity of dopamine systems, which might contribute to their diversity of physiological function. Dopamine measurements by fast scan cyclic voltammetry are affected by the adsorption of dopamine to carbon fiber electrodes. The temporal distortion caused by dopamine adsorption is correctable by a straightforward mathematical procedure. The corrected responses exhibit excellent agreement with a dopamine kinetic model cast to provide a generic description of restricted diffusion, short-term plasticity of dopamine release, and first-order dopamine clearance. The new DA kinetic model brings to light the rich kinetic information content of electrically evoked dopamine responses recorded via fast scan cyclic voltammetry in the rat dorsal striatum.

Biased diffusion in three-dimensional comb-like structures

In this paper, we study biased diffusion of point Brownian particles in a three-dimensional comb-like structure formed by a main cylindrical tube with identical periodic cylindrical dead ends. It is assumed that the dead ends are thin cylinders whose radius is much smaller than both the radius of the main tube and the distance between neighboring dead ends. It is also assumed that in the main tube, the particle, in addition to its regular diffusion, moves with a uniform constant drift velocity. For such a system, we develop a formalism that allows us to derive analytical expressions for the Laplace transforms of the first two moments of the particle displacement along the main tube axis. Inverting these Laplace transforms numerically, one can find the time dependences of the two moments for arbitrary values of both the drift velocity and the dead-end length, including the limiting case of infinitely long dead ends, where the unbiased diffusion becomes anomalous at sufficiently long times. The expressions for the Laplace transforms are used to find the effective drift velocity and diffusivity of the particle as functions of its drift velocity in the main tube and the tube geometric parameters. As might be expected from common-sense arguments, the effective drift velocity monotonically decreases from the initial drift velocity to zero as the dead-end length increases from zero to infinity. The effective diffusivity is a more complex, non-monotonic function of the dead-end length. As this length increases from zero to infinity, the effective diffusivity first decreases, reaches a minimum, and then increases approaching a plateau value which is proportional to the square of the particle drift velocity in the main tube.

Kinetic diversity of dopamine transmission in the dorsal striatum

Dopamine (DA), a highly significant neurotransmitter in the mammalian central nervous system, operates on multiple time scales to affect a diverse array of physiological functions. The significance of DA in human health is heightened by its role in a variety of pathologies. Voltammetric measurements of electrically evoked DA release have brought to light the existence of a patchwork of DA kinetic domains in the dorsal striatum (DS) of the rat. Thus, it becomes necessary to consider how these domains might be related to specific aspects of DA's functions. Responses evoked in the fast and slow domains are distinct in both amplitude and temporal profile. Herein, we report that responses evoked in fast domains can be further classified into four distinct types, types 1-4. The DS, therefore, exhibits a total of at least five distinct evoked responses (four fast types and one slow type). All five response types conform to kinetic models based entirely on first-order rate expressions, which indicates that the heterogeneity among the response types arises from kinetic diversity within the DS terminal field. We report also that functionally distinct subregions of the DS express DA kinetic diversity in a selective manner. Thus, this study documents five response types, provides a thorough kinetic explanation for each of them, and confirms their differential association with functionally distinct subregions of this key DA terminal field. The dorsal striatum is composed of five significantly different dopamine domains (types 1-4 and slow, average ± SEM responses to medial forebrain bundle (MFB) stimulation are shown in the figure). Responses from each of these five domains exhibit significantly different ascending and descending kinetic profiles and return to a long lasting elevated dopamine state, termed the dopamine hang-up. All features of these responses are modeled with high correlation using first-order modeling as well as our recently published restricted diffusion model of evoked dopamine overflow. We also report that functionally distinct subregions of the dorsal striatum express selective dopamine kinetic diversity.

A novel restricted diffusion model of evoked dopamine

In vivo fast-scan cyclic voltammetry provides high-fidelity recordings of electrically evoked dopamine release in the rat striatum. The evoked responses are suitable targets for numerical modeling because the frequency and duration of the stimulus are exactly known. Responses recorded in the dorsal and ventral striatum of the rat do not bear out the predictions of a numerical model that assumes the presence of a diffusion gap interposed between the recording electrode and nearby dopamine terminals. Recent findings, however, suggest that dopamine may be subject to restricted diffusion processes in brain extracellular space. A numerical model cast to account for restricted diffusion produces excellent agreement between simulated and observed responses recorded under a broad range of anatomical, stimulus, and pharmacological conditions. The numerical model requires four, and in some cases only three, adjustable parameters and produces meaningful kinetic parameter values.

From normal to anomalous diffusion in comb-like structures in three dimensions

Diffusion in a comb-like structure, formed by a main cylindrical tube with identical periodic dead ends of cylindrical shape, occurs slower than that in the same system without dead ends. The reason is that the particle, entering a dead end, interrupts its propagation along the tube axis. The slowdown becomes stronger and stronger as the dead end length increases, since the particle spends more and more time in the dead ends. In the limiting case of infinitely long dead ends, diffusion becomes anomalous with the exponent equal to 1/2. We develop a formalism which allows us to study the mean square displacement of the particle along the tube axis in such systems. The formalism is applicable for an arbitrary dead end length, including the case of anomalous diffusion in a tube with infinitely long dead ends. In particular, we demonstrate how intermediate anomalous diffusion arises when the dead ends are long enough.

Plasticity of GABA transporters: an unconventional route to shape inhibitory synaptic transmission

The brain relies on GABAergic neurons to control the ongoing activity of neuronal networks. GABAergic neurons control the firing pattern of excitatory cells, the temporal structure of membrane potential oscillations and the time window for integration of synaptic inputs. These actions require a fine control of the timing of GABA receptor activation which, in turn, depends on the precise timing of GABA release from pre-synaptic terminals and GABA clearance from the extracellular space. Extracellular GABA is not subject to enzymatic breakdown, and its clearance relies entirely on diffusion and uptake by specific transporters. In contrast to glutamate transporters, GABA transporters are abundantly expressed in neuronal pre-synaptic terminals. GABA transporters move laterally within the plasma membrane and are continuously trafficked to/from intracellular compartments. It is hypothesized that due to their proximity to GABA release sites, changes in the concentration and lateral mobility of GABA transporters may have a significant effect on the time course of the GABA concentration profile in and out of the synaptic cleft. To date, this hypothesis remains to be tested. Here we use 3D Monte Carlo reaction-diffusion simulations to analyze how changes in the density of expression and lateral mobility of GABA transporters in the cell membrane affect the extracellular GABA concentration profile and the activation of GABA receptors. Our results indicate that these manipulations mainly alter the GABA concentration profile away from the synaptic cleft. These findings provide novel insights into how the ability of GABA transporters to undergo plastic changes may alter the strength of GABAergic signals and the activity of neuronal networks in the brain.

Gliotoxin-induced swelling of astrocytes hinders diffusion in brain extracellular space via formation of dead-space microdomains

One of the hallmarks of numerous life-threatening and debilitating brain diseases is cellular swelling that negatively impacts extracellular space (ECS) structure. The ECS structure is determined by two macroscopic parameters, namely tortuosity (λ) and volume fraction (α). Tortuosity represents hindrance imposed on the diffusing molecules by the tissue in comparison with an obstacle-free medium. Volume fraction is the proportion of tissue volume occupied by the ECS. From a clinical perspective, it is essential to recognize which factors determine the ECS parameters and how these factors change in brain diseases. Previous studies demonstrated that dead-space (DS) microdomains increased λ during ischemia and hypotonic stress, as these pocket-like structures transiently trapped diffusing molecules. We hypothesize that astrocytes play a key role in the formation of DS microdomains because their thin processes have concave shapes that may elongate as astrocytes swell in these pathologies. Here we selectively swelled astrocytes in the somatosensory neocortex of rat brain slices with a gliotoxin DL-α-Aminoadipic Acid (DL-AA), and we quantified the ECS parameters using Integrative Optical Imaging (IOI) and Real-Time Iontophoretic (RTI) diffusion methods. We found that α decreased and λ increased during DL-AA application. During recovery, α was restored whereas λ remained elevated. Increase in λ during astrocytic swelling and recovery is consistent with the formation of DS microdomains. Our data attribute to the astrocytes an important role in determining the ECS parameters, and indicate that extracellular diffusion can be improved not only by reducing the swelling but also by disrupting the DS microdomains.

Extracellular sheets and tunnels modulate glutamate diffusion in hippocampal neuropil

Although the extracellular space in the neuropil of the brain is an important channel for volume communication between cells and has other important functions, its morphology on the micron scale has not been analyzed quantitatively owing to experimental limitations. We used manual and computational techniques to reconstruct the 3D geometry of 180 μm(3) of rat CA1 hippocampal neuropil from serial electron microscopy and corrected for tissue shrinkage to reflect the in vivo state. The reconstruction revealed an interconnected network of 40-80 nm diameter tunnels, formed at the junction of three or more cellular processes, spanned by sheets between pairs of cell surfaces with 10-40 nm width. The tunnels tended to occur around synapses and axons, and the sheets were enriched around astrocytes. Monte Carlo simulations of diffusion within the reconstructed neuropil demonstrate that the rate of diffusion of neurotransmitter and other small molecules was slower in sheets than in tunnels. Thus, the non-uniformity found in the extracellular space may have specialized functions for signaling (sheets) and volume transmission (tunnels).

Restricted diffusion of dopamine in the rat dorsal striatum

Recent evidence has shown that the dorsal striatum of the rat is arranged as a patchwork of domains that exhibit distinct dopamine kinetics and concentrations. This raises the pressing question of how these distinct domains are maintained, especially if dopamine is able to diffuse through the extracellular space. Diffusion between the domains would eliminate the concentration differences and, thereby, the domains themselves. The present study is a closer examination of dopamine's ability to diffuse in the extracellular space. We used voltammetry to record dopamine overflow in dorsal striatum while stimulating the medial forebrain bundle over a range of stimulus currents and frequencies. We also examined the effects of drugs that modulated the dopamine release (raclopride and quinpirole) and uptake (nomifensine). Examining the details of the temporal features of the evoked profiles reveals no clear evidence for long-distance diffusion of dopamine between fast and slow domains, even though uptake inhibition by nomifensine clearly prolongs the time that dopamine resides in the extracellular space. Our observations support the conclusion that striatal tissue has the capacity to retain dopamine molecules, thereby limiting its tendency to diffuse through the extracellular space.

Diffusion of D-glucose measured in the cytosol of a single astrocyte

Astrocytes interact with neurons and endothelial cells and may mediate exchange of metabolites between capillaries and nerve terminals. In the present study, we investigated intracellular glucose diffusion in purified astrocytes after local glucose uptake. We used a fluorescence resonance energy transfer (FRET)-based nano sensor to monitor the time dependence of the intracellular glucose concentration at specific positions within the cell. We observed a delay in onset and kinetics in regions away from the glucose uptake compared with the region where we locally super-fused astrocytes with the D-glucose-rich solution. We propose a mathematical model of glucose diffusion in astrocytes. The analysis showed that after gradual uptake of glucose, the locally increased intracellular glucose concentration is rapidly spread throughout the cytosol with an apparent diffusion coefficient (D app) of (2.38 ± 0.41) × 10(-10) m(2) s(-1) (at 22-24 °C). Considering that the diffusion coefficient of D-glucose in water is D = 6.7 × 10(-10) m(2) s(-1) (at 24 °C), D app determined in astrocytes indicates that the cytosolic tortuosity, which hinders glucose molecules, is approximately three times higher than in aqueous solution. We conclude that the value of D app for glucose measured in purified rat astrocytes is consistent with the view that cytosolic diffusion may allow glucose and glucose metabolites to traverse from the endothelial cells at the blood-brain barrier to neurons and neighboring astrocytes.

Exploring avidity: understanding the potential gains in functional affinity and target residence time of bivalent and heterobivalent ligands

Bivalent ligands are increasingly important therapeutic agents. Although the naturally occurring antibodies are predominant, it is becoming more common to combine different antibody fragments or even low molecular weight compounds to generate heterobivalent ligands. Such ligands exhibit markedly increased affinity (i.e. avidity) and target residence time when both pharmacophores can bind simultaneously to their target sites. This is because binding of one pharmacophore forces the second tethered one to stay close to its corresponding site. This 'forced proximity' favours its binding and rebinding (once dissociated) to that site. However, rebinding will also take place when the diffusion of freshly dissociated ligands is merely slowed down. The present differential equation-based simulations explore the way both situations affect ligand binding. Both delay the attainment of binding equilibrium (resulting in steep saturation curves) and also increase the target residence time. Competitive ligands are able to interfere in a concentration-dependent manner, although much higher concentrations are required in the 'forced proximity' situation. Also, it is only in that situation that the ligand shows increased affinity. These simulations shed light on two practical consequences. Depending on the pharmacokinetic half-life of the bivalent ligand in the body, it may not have sufficient time to achieve equilibrium with the target. This will result in lower potency than expected, although it would have significant advantages in terms of residence time. In in vitro experiments, the manifestation of steep saturation curves and of accelerated dissociation in the presence of competitive ligands could mistakenly be interpreted as evidence for non-competitive, allosteric interactions.

Brain Extracellular Space as a Diffusion Barrier

The extracellular space (ECS) consists of the narrow channels between brain cells together with their geometrical configuration and contents. Despite being only 20-60 nm in width, the ECS typically occupies 20% of the brain volume. Numerous experiments over the last 50 years have established that molecules moving through the ECS obey the laws of diffusion but with an effective diffusion coefficient reduced by a factor of about 2.6 compared to free diffusion. This review considers the origins of the diffusion barrier arising from the ECS and its properties. The paper presents a brief overview of software for implementing two point-source paradigms for measurements of localized diffusion properties: the real-time iontophoresis or pressure method for small ions and the integrative optical imaging method for macromolecules. Selected results are presented. This is followed by a discussion of the application of the MCell Monte Carlo simulation program to determining the importance of geometrical constraints, especially dead-space microdomains, and the possible role of interaction with the extracellular matrix. It is concluded that we can predict the impediment to diffusion of many molecules of practical importance and also use studies of the diffusion of selected molecular probes to reveal the barrier properties of the ECS.

Clozapine, atypical antipsychotics, and the benefits of fast-off D2 dopamine receptor antagonism

Drug-receptor interactions are traditionally quantified in terms of affinity and efficacy, but there is increasing awareness that the drug-on-receptor residence time also affects clinical performance. While most interest has hitherto been focused on slow-dissociating drugs, D(2) dopamine receptor antagonists show less extrapyramidal side effects but still have excellent antipsychotic activity when they dissociate swiftly. Fast dissociation of clozapine, the prototype of the "atypical antipsychotics", has been evidenced by distinct radioligand binding approaches both on cell membranes and intact cells. The surmountable nature of clozapine in functional assays with fast-emerging responses like calcium transients is confirmatory. Potential advantages and pitfalls of the hitherto used techniques are discussed, and recommendations are given to obtain more precise dissociation rates for such drugs. Surmountable antagonism is necessary to allow sufficient D(2) receptor stimulation by endogenous dopamine in the striatum. Simulations are presented to find out whether this can be achieved during sub-second bursts in dopamine concentration or rather during much slower, activity-related increases thereof. While the antagonist's dissociation rate is important to distinguish between both mechanisms, this becomes much less so when contemplating time intervals between successive drug intakes, i.e., when pharmacokinetic considerations prevail. Attention is also drawn to the divergent residence times of hydrophobic antagonists like haloperidol when comparing radioligand binding data on cell membranes with those on intact cells and clinical data.

Response to 'comment on recent modeling studies of astrocyte-neuron metabolic interactions': much ado about nothing

For many years, a tenet of cerebral metabolism held that glucose was the obligate energy substrate of the mammalian brain and that neuronal oxidative metabolism represented the majority of this glucose utilization. In 1994, Pellerin and Magistretti formulated the astrocyte-neuron lactate shuttle (ANLS) hypothesis, in which astrocytes, not neurons, metabolized glucose, with subsequent transport of the glycolytically derived lactate to fuel the energy needs of the neuron during neurotransmission. By considering the concentrations and kinetic characteristics of the nutrient transporter proteins, Simpson et al later supported the opposite view, in which lactate flows from neurons to astrocytes, thus leading to the neuron-astrocyte lactate shuttle (NALS). Most recently, a commentary was published in this journal attempting to discredit the NALS. This challenge has stimulated the present response in which we detail the inaccuracies of the commentary and further model several different possibilities. Although our simulations continue to support the predominance of neuronal glucose utilization during activation and neuronal to astrocytic lactate flow, the most important result is that, regardless of the direction of the flow, the overall contribution of lactate to cerebral glucose metabolism is found to be so small as to make this ongoing debate 'much ado about nothing'.

Noninvasive quantification of human brain antioxidant concentrations after an intravenous bolus of vitamin C

Until now, the lack of a means to detect a deficiency or to measure the pharmacologic effect in the human brain in situ has been a hindrance to the development of antioxidant-based prevention and treatment of dementia. In this study, a recently developed (1) H MRS approach was applied to quantify key human brain antioxidant concentrations throughout the course of an aggressive antioxidant-based intervention. The concentrations of the two most abundant central nervous system chemical antioxidants, vitamin C and glutathione, were quantified noninvasively in the human occipital cortex prior to and throughout 24 h after bolus intravenous delivery of 3 g of vitamin C. Although the kinetics of the sodium-dependent vitamin C transporter and physiologic blood vitamin C concentrations predict theoretically that brain vitamin C concentration will not increase above its homeostatically maintained level, this theory has never been tested experimentally in the living human brain. Therefore, human brain vitamin C and glutathione concentrations were quantified noninvasively using MEGA-PRESS double-edited (1) H MRS and LCModel. Healthy subjects (age, 19-63 years) with typical dietary consumption, who did not take vitamin supplements, fasted overnight and then reported for the measurement of baseline antioxidant concentrations. They then began controlled feeding which they adhered to until after vitamin C and glutathione concentrations had been measured at 2, 6, 10 and 24 h after receiving intravenous vitamin C. Two of the twelve studies were sham controls in which no vitamin C was administered. The main finding was that human brain vitamin C and glutathione concentrations remained constant throughout the protocol, even though blood serum vitamin C concentrations spanned from the low end of the normal range to very high.

Analytical treatment of biased diffusion in tubes with periodic dead ends

Effective mobility and diffusion coefficient of a particle in a tube with identical periodic dead ends characterize the motion on large time scale, when the particle displacement significantly exceeds the tube period. We derive formulas that show how these transport coefficients depend on the driving force and the geometric parameters of the system. Numerical tests show that values of the transport coefficients obtained from Brownian dynamics simulations are in excellent agreement with our theoretical predictions.

Astrocytes as gatekeepers of GABAB receptor function

The long-lasting actions of the inhibitory neurotransmitter GABA result from the activation of metabotropic GABA(B) receptors. Enhanced GABA(B)-mediated IPSCs are critical for the generation of generalized thalamocortical seizures. Here, we demonstrate that GABA(B)-mediated IPSCs recorded in the thalamus are primarily defined by GABA diffusion and activation of distal extrasynaptic receptors potentially up to tens of micrometers from synapses. We also show that this diffusion is differentially regulated by two astrocytic GABA transporters, GAT1 and GAT3, which are localized near and far from synapses, respectively. A biologically constrained model of GABA diffusion and uptake shows how the two GATs differentially modulate amplitude and duration of GABA(B) IPSCs. Specifically, the perisynaptic expression of GAT1 enables it to regulate GABA levels near synapses and selectively modulate peak IPSC amplitude, which is primarily dependent on perisynaptic receptor occupancy. GAT3 expression, however, is broader and includes distal extrasynaptic regions. As such, GAT3 acts as a gatekeeper to prevent diffusion of GABA away from synapses toward extrasynaptic regions that contain a potentially enormous pool of GABA(B) receptors. Targeting this gatekeeper function may provide new pharmacotherapeutic opportunities to prevent the excessive GABA(B) receptor activation that appears necessary for thalamic seizure generation.

Long-lasting target binding and rebinding as mechanisms to prolong in vivo drug action

An increasing number of examples in the literature suggest that the in vivo duration of drug action not only depends on macroscopic pharmacokinetic properties like plasma half-life and the time needed to equilibrate between the plasma and the effect compartments, but is also influenced by long-lasting target binding and rebinding. The present review combines information from different research areas and simulations to explore the nature of these mechanisms and the conditions in which they are most prevalent. Simulations reveal that these latter phenomena become especially influential when there is no longer sufficient free drug around to maintain high levels of receptor occupancy. There is not always a direct link between slow dissociation and long-lasting in vivo target protection, as the rate of free drug elimination from the effect compartment is also a key influencing factor. Local phenomena that hinder the diffusion of free drug molecules away from their target may allow them to consecutively bind to the same target and/or targets nearby (denoted as 'rebinding') even when their concentration in the bulk phase has already dropped to insignificant levels. The micro-anatomic properties of many effect compartments are likely to intensify this phenomenon. By mimicking the complexity of tissues, intact cells offer the opportunity to investigate both mechanisms under the same, physiologically relevant conditions.

Rebinding: or why drugs may act longer in vivo than expected from their in vitro target residence time

IMPORTANCE OF THE FIELD

It is well established that the in vivo duration of drug action not only depends on macroscopic pharmacokinetic properties like its plasma half-life, but also on the residence time of the drug-target complexes. However, drug 'rebinding' (i.e., the consecutive binding of dissociated drug molecules to the original target and/or targets nearby) can be influential in vivo as well.

AREAS COVERED IN THIS REVIEW

Information about rebinding is available since the 1980s but it is dispersed in the life sciences literature. This review compiles this information. In this respect, neurochemists and biopohysicians advance the same equations to describe drug rebinding.

WHAT THE READER WILL GAIN

The rebinding mechanism is explained according to the prevailing viewpoint in different life science disciplines. There is a general consensus that high target densities, high association rates and local phenomena that hinder the diffusion of free drug molecules away from their target all promote rebinding.

TAKE HOME MESSAGE

Simulations presented here for the first time suggest that rebinding may increase the duration and even the constancy of the drug's clinical action. Intact cell radioligand dissociation and related ex vivo experiments offer useful indications about a drug's aptitude to experience target rebinding.

Ligands, their receptors and ... plasma membranes

Ligand-receptor interactions are customarily described by equations that apply to solutes. Yet, most receptors are present in cell membranes so that sufficiently lipophilic ligands could reach the receptor by a two-dimensional approach within the membrane. As summarized in this review, this may affect the ligand-receptor interaction in many ways. Biophysicians calculated that, compared to a three-dimensional approach from the liquid phase, such approach could alter the time the ligands need to find a receptor. Biochemists found that ligand incorporation in lipid bilayers modifies their conformation. This, along with the depth at which the ligands reside in the bilayer, will affect the probability of successful receptor interaction. Novel mechanisms were also introduced, including "exosite" binding and ligand translocation between the receptor's alpha-helical transmembrane domains. Pharmacologists focused attention at ligand concentrations in membrane, their adsorption and release rates and the effects thereof on ligand potency and residence time at the receptor.

Determining the neurotransmitter concentration profile at active synapses

Establishing the temporal and concentration profiles of neurotransmitters during synaptic release is an essential step towards understanding the basic properties of inter-neuronal communication in the central nervous system. A variety of ingenious attempts has been made to gain insights into this process, but the general inaccessibility of central synapses, intrinsic limitations of the techniques used, and natural variety of different synaptic environments have hindered a comprehensive description of this fundamental phenomenon. Here, we describe a number of experimental and theoretical findings that has been instrumental for advancing our knowledge of various features of neurotransmitter release, as well as newly developed tools that could overcome some limits of traditional pharmacological approaches and bring new impetus to the description of the complex mechanisms of synaptic transmission.

Steady-state brain glucose transport kinetics re-evaluated with a four-state conformational model

Glucose supply from blood to brain occurs through facilitative transporter proteins. A near linear relation between brain and plasma glucose has been experimentally determined and described by a reversible model of enzyme kinetics. A conformational four-state exchange model accounting for trans-acceleration and asymmetry of the carrier was included in a recently developed multi-compartmental model of glucose transport. Based on this model, we demonstrate that brain glucose (G(brain)) as function of plasma glucose (G(plasma)) can be described by a single analytical equation namely comprising three kinetic compartments: blood, endothelial cells and brain. Transport was described by four parameters: apparent half saturation constant K(t), apparent maximum rate constant T(max), glucose consumption rate CMR(glc), and the iso-inhibition constant K(ii) that suggests G(brain) as inhibitor of the isomerisation of the unloaded carrier. Previous published data, where G(brain) was quantified as a function of plasma glucose by either biochemical methods or NMR spectroscopy, were used to determine the aforementioned kinetic parameters. Glucose transport was characterized by K(t) ranging from 1.5 to 3.5 mM, T(max)/CMR(glc) from 4.6 to 5.6, and K(ii) from 51 to 149 mM. It was noteworthy that K(t) was on the order of a few mM, as previously determined from the reversible model. The conformational four-state exchange model of glucose transport into the brain includes both efflux and transport inhibition by G(brain), predicting that G(brain) eventually approaches a maximum concentration. However, since K(ii) largely exceeds G(plasma), iso-inhibition is unlikely to be of substantial importance for plasma glucose below 25 mM. As a consequence, the reversible model can account for most experimental observations under euglycaemia and moderate cases of hypo- and hyperglycaemia.