Kir4.1-mediated spatial buffering of K+: Experimental challenges in determination of its temporal and quantitative contribution to K+ clearance in the brain

Neuronal activity results in release of K⁺ into the extracellular space of the central nervous system. If the excess K⁺ is allowed to accumulate, neuronal firing will be compromised by the ensuing neuronal membrane depolarization. The surrounding glial cells are involved in clearing K⁺ from the extracellular space by molecular mechanism(s), the identity of which have been a matter of controversy for over half a century. Kir4.1-mediated spatial buffering of K⁺ has been promoted as a major contributor to K⁺ removal although its quantitative and temporal contribution has remained undefined. We discuss the biophysical and experimental challenges regarding determination of the contribution of Kir4.1 to extracellular K⁺ management during neuronal activity. It is concluded that 1) the geometry of the experimental preparation is crucial for detection of Kir4.1-mediated spatial buffering and 2) Kir4.1 enacts spatial buffering of K⁺ during but not after neuronal activity.     

Kir4.1-mediated spatial buffering of K+: Experimental challenges in determination of its temporal and quantitative contribution to K+ clearance in the brain

Neuronal activity results in release of K⁺ into the extracellular space of the central nervous system. If the excess K⁺ is allowed to accumulate, neuronal firing will be compromised by the ensuing neuronal membrane depolarization. The surrounding glial cells are involved in clearing K⁺ from the extracellular space by molecular mechanism(s), the identity of which have been a matter of controversy for over half a century. Kir4.1-mediated spatial buffering of K⁺ has been promoted as a major contributor to K⁺ removal although its quantitative and temporal contribution has remained undefined. We discuss the biophysical and experimental challenges regarding determination of the contribution of Kir4.1 to extracellular K⁺ management during neuronal activity. It is concluded that 1) the geometry of the experimental preparation is crucial for detection of Kir4.1-mediated spatial buffering and 2) Kir4.1 enacts spatial buffering of K⁺ during but not after neuronal activity.     

A reduced-dimensional model for near-wall transport in cardiovascular flows

Near-wall mass transport plays an important role in many cardiovascular processes, including the initiation of atherosclerosis, endothelial cell vasoregulation, and thrombogenesis. These problems are characterized by large Péclet and Schmidt numbers as well as a wide range of spatial and temporal scales, all of which impose computational difficulties. In this work, we develop an analytical relationship between the flow field and near-wall mass transport for high-Schmidt-number flows. This allows for the development of a wall-shear-stress-driven transport equation that lies on a codimension-one vessel-wall surface, significantly reducing computational cost in solving the transport problem. Separate versions of this equation are developed for the reaction-rate-limited and transport-limited cases, and numerical results in an idealized abdominal aortic aneurysm are compared to those obtained by solving the full transport equations over the entire domain. The reaction-rate-limited model matches the expected results well. The transport-limited model is accurate in the developed flow regions, but overpredicts wall flux at entry regions and reattachment points in the flow.     

A Bidomain Model for Lens Microcirculation

There exists a large body of research on the lens of the mammalian eye over the past several decades. The objective of this work is to provide a link between the most recent computational models and some of the pioneering work in the 1970s and 80s. We introduce a general nonelectroneutral model to study the microcirculation in the lens of the eye. It describes the steady-state relationships among ion fluxes, between water flow and electric field inside cells, and in the narrow extracellular spaces between cells in the lens. Using asymptotic analysis, we derive a simplified model based on physiological data and compare our results with those in the literature. We show that our simplified model can be reduced further to the first-generation models, whereas our full model is consistent with the most recent computational models. In addition, our simplified model captures in its equations the main features of the full computational models. Our results serve as a useful link intermediate between the computational models and the first-generation analytical models. Simplified models of this sort may be particularly helpful as the roles of similar osmotic pumps of microcirculation are examined in other tissues with narrow extracellular spaces, such as cardiac and skeletal muscle, liver, kidney, epithelia in general, and the narrow extracellular spaces of the central nervous system, the “brain.” Simplified models may reveal the general functional plan of these systems before full computational models become feasible and specific.     

Computational modeling of combined cell population dynamics and oxygen transport in engineered tissue subject to interstitial perfusion

This work presents a computational model of tissue growth under interstitial perfusion inside a tissue engineering bioreactor. The model accounts both for the cell population dynamics, using a model based on cellular automata, and for the hydrodynamic microenvironment imposed by the bioreactor, using a model based on the Lattice-Boltzmann equation and the convection-diffusion equation. The conditions of static culture versus perfused culture were compared, by including the population dynamics along with oxygen diffusion, convective transport and consumption. The model is able to deal with arbitrary complex geometries of the spatial domain; in the present work, the domain modeled was the void space of a porous scaffold for tissue-engineered cartilage. The cell population dynamics algorithm provided results which qualitatively resembled population dynamics patterns observed in experimental studies, and these results were in good quantitative agreement with previous computational studies. Simulation of oxygen transport and consumption showed the fundamental contribution of convective transport in maintaining a high level of oxygen concentration in the whole spatial domain of the scaffold. The model was designed with the aim to be computationally efficient and easily expandable, i.e. to allow straightforward implementability of further models of complex biological phenomena of increasing scientific interest in tissue engineering, such as chemotaxis, extracellular matrix deposition and effect of mechanical stimulation.     

LDL receptor-related proteins in neurodevelopment

Low-density lipoprotein receptor-related proteins (LRPs) are evolutionarily ancient cell-surface receptors with diverse biological functions. All are expressed in the central nervous system and, for most receptors, animal models have shown that they are indispensable for successful neurodevelopment. The mechanisms by which they regulate the formation of the nervous system are varied and include the transduction of extracellular signals and the modulation of intracellular signal propagation, as well as cargo transport, the function most commonly attributed to this gene family. Here, we will summarize recent advances in our understanding of the molecular basis on which these receptors function during development .     

Zn(2+) inhibits the anion conductance of the glutamate transporter EEAT4

Glutamate transport by the excitatory amino acid transporters (EAATs) is coupled to the co-transport of 3 Na(+) ions and 1 H(+) and the counter-transport of 1 K(+) ion, which ensures that extracellular glutamate concentrations are maintained in the submicromolar range. In addition to the coupled ion fluxes, glutamate transport activates an uncoupled anion conductance that does not influence the rate or direction of transport but may have the capacity to influence the excitability of the cell. Free Zn(2+) ions are often co-localized with glutamate in the central nervous system and have the capacity to modulate the dynamics of excitatory neurotransmission. In this study we demonstrate that Zn(2+) ions inhibit the uncoupled anion conductance and also reduce the affinity of L-aspartate for EAAT4. The molecular basis for this effect was investigated using site-directed mutagenesis. Two histidine residues in the extracellular loop between transmembrane domains three and four of EAAT4 appear to confer Zn(2+) inhibition of the anion conductance.     

Structural Basis of Activation of Cys-Loop Receptors: the Extracellular–Transmembrane Interface as a Coupling Region

Cys-loop receptors mediate rapid transmission throughout the nervous system by converting a chemical signal into an electric one. They are pentameric proteins with an extracellular domain that carries the transmitter binding sites and a transmembrane region that forms the ion pore. Their essential function is to couple the binding of the agonist at the extracellular domain to the opening of the ion pore. How the structural changes elicited by agonist binding are propagated through a distance of 50?Å to the gate is therefore central for the understanding of the receptor function. A step forward toward the identification of the structures involved in gating has been given by the recently elucidated high-resolution structures of Cys-loop receptors and related proteins. The extracellular–transmembrane interface has attracted attention because it is a structural transition zone where β-sheets from the extracellular domain merge with α-helices from the transmembrane domain. Within this zone, several regions form a network that relays structural changes from the binding site toward the pore, and therefore, this interface controls the beginning and duration of a synaptic response. In this review, the most recent findings on residues and pairwise interactions underlying channel gating are discussed, the main focus being on the extracellular–transmembrane interface.     

Validity of the rapid buffering approximation near a point source of calcium ions.

In the presence of rapid buffers the full reaction-diffusion equations describing Ca2+ transport can be reduced using the rapid buffering approximation to a single transport equation for [Ca2+]. Here we simulate the full and reduced equations, exploring the conditions necessary for the validity of the rapid buffering approximation for an isolated Ca2+ channel or a cluster of channels. Using a point source and performing numerical simulations of different durations, we quantify the error of the rapid buffering approximation as a function of buffer and source parameters as well as the time and spatial scale set by the resolution of confocal microscopic measurements. We carry out simulations of Ca2+ "sparks" and "puffs," both with and without the indicator dye Ca2+ Green-1, and find that the rapid buffering approximation is excellent. These calculations also show that the traditional calculation of [Ca2+] from a fluorescence signal may grossly underestimate the true value of [Ca2+] near a source. Finally, we use the full model to simulate the transient Ca2+ domain near the pore of an open Ca2+ channel in a cell dialyzed with millimolar concentrations of 1,2-bis(2-aminophenoxy)ethane-N,N,N,N-tetraacetic acid or EGTA. In this regime, where the rapid buffering approximation is poor. Neher's equation for the steady-state Ca2+ profile is shown to be a reliable approximation adjacent to the pore.     

Role of the microtubule destabilizing proteins SCG10 and stathmin in neuronal growth

The related proteins SCG10 and stathmin are highly expressed in the developing nervous system. Recently it was discovered that they are potent microtubule destabilizing factors. While stathmin is expressed in a variety of cell types and shows a cytosolic distribution, SCG10 is neuron-specific and membrane-associated. It contains an N-terminal targeting sequence that mediates its transport to the growing tips of axons and dendrites. SCG10 accumulates in the central domain of the growth cone, a region that also contains highly dynamic microtubules. These dynamic microtubules are known to be important for growth cone advance and responses to guidance cues. Because overexpression of SCG10 strongly enhances neurite outgrowth, SCG10 appears to be an important factor for the dynamic assembly and disassembly of growth cone microtubules during axonal elongation. Phosphorylation negatively regulates the microtubule destabilizing activity of SCG10 and stathmin, suggesting that these proteins may link extracellular signals to the rearrangement of the neuronal cytoskeleton. A role for these proteins in axonal elongation is also supported by their growth-associated expression pattern in nervous system development as well as during neuronal regeneration.     

Review. The molecular logic of sodium-coupled neurotransmitter transporters

Synaptic transmission at chemical synapses requires the removal of neurotransmitter from extracellular spaces. At synapses in the central nervous system, this is accomplished by sodium-coupled transport proteins, integral membrane proteins that thermodynamically couple the uptake of neurotransmitter to the uptake of sodium and, in some cases, the uptake and export of additional ions. Recent X-ray crystallographic studies have revealed the architecture of the two major families of neurotransmitter transporters and, together with additional biochemical and biophysical studies, have provided insights into mechanisms of ion coupling, substrate uptake, and inhibition of transport.     

Allosteric regulation of pentameric ligand-gated ion channels: An emerging mechanistic perspective

Pentameric ligand-gated ion channels (pLGICs) play a central role in intercellular communications in the nervous system by converting the binding of a chemical messenger—a neurotransmitter—into an ion flux through the postsynaptic membrane. They are oligomeric assemblies that provide prototypical examples of allosterically regulated integral membrane proteins. Here, we present an overview of the most recent advances on the signal transduction mechanism based on the X-ray structures of both prokaryotic and invertebrate eukaryotic pLGICs and on atomistic Molecular Dynamics simulations. The present results suggest that ion gating involves a large structural reorganization of the molecule mediated by two distinct quaternary transitions, a global twisting and the blooming of the extracellular domain, which can be modulated by ligand binding at the topographically distinct orthosteric and allosteric sites. The emerging model of gating is consistent with a wealth of functional studies and will boost the development of novel pharmacological strategies.     

Structural elements necessary for oligomerization, trafficking, and cell sorting function of paraxial protocadherin

Protocadherins have been shown to regulate cell adhesion, cell migration, cell survival, and tissue morphogenesis in the embryo and the central nervous system, but little is known about the mechanism of protocadherin function. We previously showed that Xenopus paraxial protocadherin (PAPC) mediates cell sorting and morphogenesis by down-regulating the adhesion activity of a classical cadherin, C-cadherin. Classical cadherins function by forming lateral dimers that are necessary for their adhesive function. However, it is not known whether oligomerization also plays a role in protocadherin function. We show here that PAPC forms oligomers that are stabilized by disulfide bonds formed between conserved Cys residues in the extracellular domain. Disruption of these disulfide bonds by dithiothreitol or mutation of the conserved cysteines results in defects in oligomerization, post-translational modification, trafficking to the cell surface and cell sorting function of PAPC. Furthermore, none of the residues in the cytoplasmic domain of PAPC is required for its cell sorting activity, whereas both the transmembrane domain and the extracellular domain are necessary. Therefore, protein oligomerization and/or protein interactions via the extracellular and transmembrane domains of PAPC are required for its cell sorting function.     

Model-Based Analysis of Mechanisms Responsible for Sleep-Induced Carbon Dioxide Differences

This work describes a comprehensive mathematical model of the human respiratory control system which incorporates the central mechanisms for predicting sleep-induced changes in chemical regulation of ventilation. The model integrates four individual compartments for gas storage and exchange, namely alveolar air, pulmonary blood, tissue capillary blood, body tissues, and gas transport between them. An essential mechanism in the carbon dioxide transport is its dissociation into bicarbonate and acid, where a buffering mechanism through hemoglobin is used to prevent harmfully low pH levels. In the current model, we assume high oxygen levels and consider intracellular hydrogen ion concentration as the principal respiratory control variable. The resulting system of delayed differential equations is solved numerically. With an appropriate choice of key parameters, such as velocity of blood flow and gain of a non-linear controller function, the model provides steady-state results consistent with our experimental observations measured in subjects across sleep onset. Dynamic predictions from the model give new insights into the behaviour of the system in subjects with different buffering capacities and suggest novel hypotheses for future experimental and clinical studies.     

Fluid flows and forces in development: functions, features and biophysical principles

Throughout morphogenesis, cells experience intracellular tensile and contractile forces on microscopic scales. Cells also experience extracellular forces, such as static forces mediated by the extracellular matrix and forces resulting from microscopic fluid flow. Although the biological ramifications of static forces have received much attention, little is known about the roles of fluid flows and forces during embryogenesis. Here, we focus on the microfluidic forces generated by cilia-driven fluid flow and heart-driven hemodynamics, as well as on the signaling pathways involved in flow sensing. We discuss recent studies that describe the functions and the biomechanical features of these fluid flows. These insights suggest that biological flow determines many aspects of cell behavior and identity through a specific set of physical stimuli and signaling pathways.     

Structure-function analysis of Nel, a thrombospondin-1-like glycoprotein involved in neural development and functions

Nel (neural epidermal growth factor (EGF)-like molecule) is a multimeric, multimodular extracellular glycoprotein with heparin-binding activity and structural similarities to thrombospondin-1. Nel is predominantly expressed in the nervous system and has been implicated in neuronal proliferation and differentiation, retinal axon guidance, synaptic functions, and spatial learning. The Nel protein contains an N-terminal thrombospondin-1 (TSP-N) domain, five cysteine-rich domains, and six EGF-like domains. However, little is known about the functions of specific domains of the Nel protein. In this study, we have performed structure-function analysis of Nel, by using a series of expression constructs for different regions of the Nel protein. Our studies demonstrate that the TSP-N domain is responsible for homo-multimer formation of Nel and its heparin-binding activity. In vivo, Nel and related Nell1 are expressed in several regions of the mouse central nervous system with partly overlapping patterns. When they are expressed in the same cells in vitro, Nel and Nell1 can form hetero-multimers through the TSP-N domain, but they do not hetero-oligomerize with thrombospondin-1. Whereas both the TSP-N domain and cysteine-rich domains can bind to retinal axons in vivo, only the latter causes growth cone collapse in cultured retinal axons, suggesting that cysteine-rich domains interact with and activate an inhibitory axon guidance receptor. These results suggest that Nel interacts with a range of molecules through its different domains and exerts distinct functions.     

An All-Atom Model of the Structure of Human Copper Transporter 1

Human copper transporter 1 (hCTR1) is the major high affinity copper influx transporter in mammalian cells that also mediates uptake of the cancer chemotherapeutic agent cisplatin. A low resolution structure of hCTR1 determined by cryoelectron microscopy was recently published. Several protein structure simulation techniques were used to create an all-atom model of this important transporter using the low resolution structure as a starting point. The all-atom model provides new insights into the roles of specific residues of the N-terminal extracellular domain, the intracellular loop, and C-terminal region in metal ion transport. In particular, the model demonstrates that the central region of the pore contains four sets of methionine triads in the intramembranous region. The structure confirms that two triads of methionine residues delineate the intramembranous region of the transporter, and further identifies two additional methionine triads that are located in the extracellular N-terminal part of the transporter. Together, the four triads create a structure that promotes stepwise transport of metal ions into and then through the intramembranous channel of the transporter via transient thioether bonds to methionine residues. Putative copper-binding sites in the hCTR1 trimer were identified by a program developed by us for prediction of metal-binding sites. These sites correspond well with the known effects of mutations on the ability of the protein to transport copper and cisplatin.     

Is the potassium channel distribution in glial cells optimal for spatial buffering of potassium?

Glial cells in the nervous system are believed to reduce changes of extracellular potassium concentration ([K+]o), caused by neural activity, by carrying out spatial buffering of potassium. In the case of retinal glial cells (Müller cells), light-evoked increases of [K+]o within the retina are reduced by K ions flowing through the Müller cell to the vitreous fluid of the eye. We have calculated the optimal way to distribute the potassium conductance of the Müller cell to maximize spatial buffering to the vitreous fluid. The best distribution is with half the potassium conductance in the outer part of the cell, where K+ enters, and half the conductance in the vitreal endfoot, where K+ leaves the cell. This calculated distribution is very different from the actual distribution measured by Newman (1984, Nature [Lond.], 309: 155-157), where only 6% of the Müller cell conductance is in the outer cell and 94% is in the endfoot. The experimentally observed distribution gives less than a quarter of the spatial buffering that would be produced by the optimal distribution. The possible advantages of this arrangement are discussed.