Neuronal calcium wave propagation varies with changes in endoplasmic reticulum parameters: a computer model.

Calcium (Ca²âº) waves provide a complement to neuronal electrical signaling, forming a key part of a neuron's second messenger system. We developed a reaction-diffusion model of an apical dendrite with diffusible inositol triphosphate (IP3), diffusible Ca²âº, IP3 receptors (IP3Rs), endoplasmic reticulum (ER) Ca²âº leak, and ER pump (SERCA) on ER. Ca²âº is released from ER stores via IP3Rs upon binding of IP3 and Ca²âº. This results in Ca²âº-induced-Ca²âº-release (CICR) and increases Ca²âº spread. At least two modes of Ca²âº wave spread have been suggested: a continuous mode based on presumed relative homogeneity of ER within the cell and a pseudo-saltatory model where Ca²âº regeneration occurs at discrete points with diffusion between them. We compared the effects of three patterns of hypothesized IP3R distribution: (1) continuous homogeneous ER, (2) hotspots with increased IP3R density (IP3R hotspots), and (3) areas of increased ER density (ER stacks). All three modes produced Ca²âº waves with velocities similar to those measured in vitro (approximately 50-90 µm /sec). Continuous ER showed high sensitivity to IP3R density increases, with time to onset reduced and speed increased. Increases in SERCA density resulted in opposite effects. The measures were sensitive to changes in density and spacing of IP3R hotspots and stacks. Increasing the apparent diffusion coefficient of Ca²âº substantially increased wave speed. An extended electrochemical model, including voltage-gated calcium channels and AMPA synapses, demonstrated that membrane priming via AMPA stimulation enhances subsequent Ca²âº wave amplitude and duration. Our modeling suggests that pharmacological targeting of IP3Rs and SERCA could allow modulation of Ca²âº wave propagation in diseases where Ca²âº dysregulation has been implicated.

Modeling the neuroprotective role of enhanced astrocyte mitochondrial metabolism during stroke.

A mathematical model that integrates the dynamics of cell membrane potential, ion homeostasis, cell volume, mitochondrial ATP production, mitochondrial and endoplasmic reticulum Ca(2+) handling, IP3 production, and GTP-binding protein-coupled receptor signaling was developed. Simulations with this model support recent experimental data showing a protective effect of stimulating an astrocytic GTP-binding protein-coupled receptor (P2Y1Rs) following cerebral ischemic stroke. The model was analyzed to better understand the mathematical behavior of the equations and to provide insights into the underlying biological data. This approach yielded explicit formulas determining how changes in IP3-mediated Ca(2+) release, under varying conditions of oxygen and the energy substrate pyruvate, affected mitochondrial ATP production, and was utilized to predict rate-limiting variables in P2Y1R-enhanced astrocyte protection after cerebral ischemic stroke.

The low conductance mitochondrial permeability transition pore confers excitability and CICR wave propagation in a computational model.

Mitochondria have long been known to sequester cytosolic Ca(2+) and even to shape intracellular patterns of endoplasmic reticulum-based Ca(2+) signaling. Evidence suggests that the mitochondrial network is an excitable medium which can demonstrate independent Ca(2+) induced Ca(2+) release via the mitochondrial permeability transition. The role of this excitability remains unclear, but mitochondrial Ca(2+) handling appears to be a crucial element in diverse diseases as diabetes, neurodegeneration and cardiac dysfunction that also have bioenergetic components. In this paper, we extend the modular Magnus-Keizer computational model for respiration-driven Ca(2+) handling to include a permeability transition based on a channel-like pore mechanism. We demonstrate both excitability and Ca(2+) wave propagation accompanied by depolarizations qualitatively similar to those reported in cell and isolated mitochondria preparations. These waves depend on the energy state of the mitochondria, as well as other elements of mitochondrial physiology. Our results support the concept that mitochondria can transmit state dependent signals about their function across the mitochondrial network. Our model provides the tools for predictions about the internal physiology that leads to this qualitatively different Ca(2+) excitability seen in mitochondria.

Multiphysics simulation of a microfluidic perfusion chamber for brain slice physiology.

Understanding and optimizing fluid flows through in vitro microfluidic perfusion systems is essential in mimicking in vivo conditions for biological research. In a previous study a microfluidic brain slice device (microBSD) was developed for microscale electrophysiology investigations. The device consisted of a standard perfusion chamber bonded to a polydimethylsiloxane (PDMS) microchannel substrate. Our objective in this study is to characterize the flows through the microBSD by using multiphysics simulations of injections into a pourous matrix to identify optimal spacing of ports. Three-dimensional computational fluid dynamic (CFD) simulations are performed with CFD-ACE + software to model, simulate, and assess the transport of soluble factors through the perfusion bath, the microchannels, and a material that mimics the porosity, permeability and tortuosity of brain tissue. Additionally, experimental soluble factor transport through a brain slice is predicted by and compared to simulated fluid flow in a volume that represents a porous matrix material. The computational results are validated with fluorescent dye experiments.

Microfluidic add-on for standard electrophysiology chambers.

We have developed a microfluidic brain slice device (microBSD) that marries an off-the shelf brain slice perfusion chamber with an array of microfluidic channels set into the bottom surface of the chamber substrate. As this device is created through rapid prototyping, once optimized, it is trivial to replicate and share the devices with other investigators. The device integrates seamlessly into standard physiology and imaging chambers and it is immediately available to the whole slice physiology community. With this technology we can address the flow of neurochemicals and any other soluble factors to precise locations in the brain slice with the temporal profile we choose. Dopamine (DA) was chosen as a model neurotransmitter and we have quantified delivery in brain tissue using cyclic voltammetry (CV) and fluorescence imaging.

Rapid prototyping for neuroscience and neural engineering.

Rapid prototyping (RP) is a useful method for designing and fabricating a wide variety of devices used for neuroscience research. The present study confirms the utility of using fused deposition modeling, a specific form of RP, to produce three devices commonly used for basic science experimentation. The accuracy and precision of the RP method varies according to the type and quality of the printer as well as the thermoplastic substrate. The printer was capable of creating device channels with a minimum diameter of 0.4 or 0.6mm depending on the orientation of fabrication. RP enabled the computer-aided design and fabrication of three custom devices including a cortical recording/stroke induction platform capable of monitoring electrophysiological function during ischemic challenge. In addition to the recording platform, two perfusion chambers and a cranial window device were replicated with sub-millimeter precision. The ability to repeatedly modify the design of each device with minimal effort and low turn-around time is helpful for oft-unpredictable experimental conditions. Results obtained from validation studies using both the cortical recording platform and perfusion chamber did not vary from previous results using traditional hand-fabricated or commercially available devices. Combined with computer-aided design, rapid prototyping is an excellent alternative for developing and fabricating custom devices for neuroscience research.

Thalamocortical bursts trigger recurrent activity in neocortical networks: layer 4 as a frequency-dependent gate.

Sensory information reaches the cortex via thalamocortical (TC) synapses in layer 4. Thalamic relay neurons that mediate information flow to cortex operate in two distinct modes, tonic and burst firing. Burst firing has been implicated in enhancing reliability of information flow between individual neurons. However, little is known about how local networks of neocortical neurons respond to different temporal patterns of TC activity. We studied cortical activity patterns evoked by stimulating TC afferents at different frequencies, using a combination of electrophysiology and calcium imaging in TC slices that allowed for the reconstruction of spatiotemporal activity with single-cell resolution. Stimulation of TC axons at low frequencies triggered action potentials in only a small number of layer 4 neurons. In contrast, brief high-frequency stimulus trains triggered widespread recurrent activity in populations of neurons in layer 4 and then spread into adjacent layers 2/3 and 5. Recurrent activity had a clear threshold, typically lasted 300 msec, and could be evoked repetitively at frequencies up to 0.5 Hz. Moreover, the spatial extent of recurrent activity was controlled by the TC pattern of activity. Recurrent activity triggered within the highly interconnected networks of layer 4 might act to selectively amplify and redistribute transient high-frequency TC inputs, filter out low-frequency inputs, and temporarily preserve a record of past sensory activity.

Rapidly characterizing the fast dynamics of RNA genetic circuitry with cell-free transcription-translation (TX-TL) systems.

RNA regulators are emerging as powerful tools to engineer synthetic genetic networks or rewire existing ones. A potential strength of RNA networks is that they may be able to propagate signals on time scales that are set by the fast degradation rates of RNAs. However, a current bottleneck to verifying this potential is the slow design-build-test cycle of evaluating these networks in vivo. Here, we adapt an Escherichia coli-based cell-free transcription-translation (TX-TL) system for rapidly prototyping RNA networks. We used this system to measure the response time of an RNA transcription cascade to be approximately five minutes per step of the cascade. We also show that this response time can be adjusted with temperature and regulator threshold tuning. Finally, we use TX-TL to prototype a new RNA network, an RNA single input module, and show that this network temporally stages the expression of two genes in vivo.

A wave of IP3 production accompanies the fertilization Ca2+ wave in the egg of the frog, Xenopus laevis: theoretical and experimental support.

The fertilization Ca2+ wave in Xenopus laevis is a single, large wave of elevated free Ca2+ that is initiated at the point of sperm-egg fusion and traverses the entire width of the egg. This Ca2+ wave involves an increase in inositol-1,4,5-trisphosphate (IP3) resulting from the interaction of the sperm and egg, which then results in the activation of the endoplasmic reticulum Ca2+ release machinery. The extraordinarily large size of this cell (1.2 mm diameter) together with the small surface region of sperm-receptor activation makes special demands on the IP3-dependent Ca2+ mobilizing machinery. We propose a detailed model of the fertilization Ca2+ wave in Xenopus eggs that requires an accompanying wave of IP3 production. While the Ca2+ wave is initiated by a localized increase of IP3 near the site of sperm-egg fusion, the Ca2+ wave propagates via IP3 production correlated with the Ca2+ wave-possibly via Ca(2+)-mediated PLC activation. Such a Ca(2+)-mediated IP(3) production wave has not been required previously to explain the fertilization Ca2+ wave in eggs; we argue this is necessary to explain the observed IP3 dynamics in Xenopus eggs. To test our hypothesis, we have measured the IP3 levels from 20 nl "sips" of the egg cortex during wave propagation. We were unable to detect the low IP3 levels in unfertilized eggs, but after fertilization, [IP3] ranged from 175 to 430 nM at the sperm entry point and from 120 to 700 nM 90 degrees away once the Ca2+ wave passed that region about 2 min after fertilization. Prior to the Ca2+ wave reaching that region the IP3 levels were undetectable. Since significant IP3 could not diffuse to this region from the sperm entry point within 2 min, this observation is consistent with a regenerative wave of IP3 production.

Enhanced loading of Fura-2/AM calcium indicator dye in adult rodent brain slices via a microfluidic oxygenator.

A microfluidic oxygenator is used to deliver constant oxygen to rodent brain slices, enabling the loading of the cell-permeant calcium indicator Fura-2/AM into cells of adult brain slices. When compared to traditional methods, our microfluidic oxygenator improves loading efficiency, measured by the number of loaded cells per unit area, for all tested age groups. Loading in slices from 1-year-old mice was achieved, which has not been possible with current bulk loading methods. This technique significantly expands the age range for which calcium studies are possible without cellular injection. This technique will facilitate opportunities for the study of calcium signaling of aging and long term stress related diseases. Moreover, it should be applicable to other membrane-permeant physiological indicator varieties.

Precise spatial and temporal control of oxygen within in vitro brain slices via microfluidic gas channels.

The acute brain slice preparation is an excellent model for studying the details of how neurons and neuronal tissue respond to a variety of different physiological conditions. But open slice chambers ideal for electrophysiological and imaging access have not allowed the precise spatiotemporal control of oxygen in a way that might realistically model stroke conditions. To address this problem, we have developed a microfluidic add-on to a commercially available perfusion chamber that diffuses oxygen throughout a thin membrane and directly to the brain slice. A microchannel enables rapid and efficient control of oxygen and can be modified to allow different regions of the slice to experience different oxygen conditions. Using this novel device, we show that we can obtain a stable and homogeneous oxygen environment throughout the brain slice and rapidly alter the oxygen tension in a hippocampal slice. We also show that we can impose different oxygen tensions on different regions of the slice preparation and measure two independent responses, which is not easily obtainable with current techniques.

Blunted neuronal calcium response to hypoxia in naked mole-rat hippocampus.

Naked mole-rats are highly social and strictly subterranean rodents that live in large communal colonies in sealed and chronically oxygen-depleted burrows. Brain slices from naked mole-rats show extreme tolerance to hypoxia compared to slices from other mammals, as indicated by maintenance of synaptic transmission under more hypoxic conditions and three fold longer latency to anoxic depolarization. A key factor in determining whether or not the cellular response to hypoxia is reversible or leads to cell death may be the elevation of intracellular calcium concentration. In the present study, we used fluorescent imaging techniques to measure relative intracellular calcium changes in CA1 pyramidal cells of hippocampal slices during hypoxia. We found that calcium accumulation during hypoxia was significantly and substantially attenuated in slices from naked mole-rats compared to slices from laboratory mice. This was the case for both neonatal (postnatal day 6) and older (postnatal day 20) age groups. Furthermore, while both species demonstrated more calcium accumulation at older ages, the older naked mole-rats showed a smaller calcium accumulation response than even the younger mice. A blunted intracellular calcium response to hypoxia may contribute to the extreme hypoxia tolerance of naked mole-rat neurons. The results are discussed in terms of a general hypothesis that a very prolonged or arrested developmental process may allow adult naked mole-rat brain to retain the hypoxia tolerance normally only seen in neonatal mammals.

Near-real-time connectivity estimation for multivariate neural data.

Optical imaging in vivo is an important tool for allowing researchers to understand neural ensemble interactions during awake behavior, sleep, anesthesia and during seizure activity. A major bottleneck in the overall efficiency of neural imaging experiments is the need for post-hoc analysis of imaging data. Computational capabilities are now at the point where real- or near-real-time multivariate analysis of imaging data is possible as data is acquired. In this paper we address the feasibility of performing real-time data analysis with a desktop computer, MATLAB, and a graphics processing unit (GPU). Important components of any real-time functional imaging analysis system are 1) dimensional reduction of the data, 2) visualization of the reduced vector space and 3) rapid calculation of functional connectivities. The ability to assess sources of variability in the data, and connectivity estimates on the fly, are potentially transformative for the way imaging laboratories perform their work. Here, we present benchmarks for analysis of functional imaging data using dimensional reduction methods and estimation of functional connectivities using least-squares and ridge regression methods.

Brain slice stimulation using a microfluidic network and standard perfusion chamber.

We have demonstrated the fabrication of a two-level microfluidic device that can be easily integrated with existing electrophysiology setups. The two-level microfluidic device is fabricated using a two-step standard negative resist lithography process. The first level contains microchannels with inlet and outlet ports at each end. The second level contains microscale circular holes located midway of the channel length and centered along with channel width. Passive pumping method is used to pump fluids from the inlet port to the outlet port. The microfluidic device is integrated with off-the-shelf perfusion chambers and allows seamless integration with the electrophysiology setup. The fluids introduced at the inlet ports flow through the microchannels towards the outlet ports and also escape through the circular openings located on top of the microchannels into the bath of the perfusion. Thus the bottom surface of the brain slice placed in the perfusion chamber bath and above the microfluidic device can be exposed with different neurotransmitters. The microscale thickness of the microfluidic device and the transparent nature of the materials [glass coverslip and PDMS (polydimethylsiloxane)] used to make the microfluidic device allow microscopy of the brain slice. The microfluidic device allows modulation (both spatial and temporal) of the chemical stimuli introduced to the brain slice microenvironments.

An intracellular Ca2+ subsystem as a biologically plausible source of intrinsic conditional bistability in a network model of working memory.

We have developed a firing rate network model for working memory that combines Mexican-hat-like synaptic coupling with intrinsic or cellular dynamics that are conditionally bistable. While our approach is in the spirit of Camperi and Wang (1998) we include a specific and plausible mechanism for the cellular bistability. Modulatory neurotransmitters are known to activate second messenger signaling systems, and our model includes an intracellular Ca(2+) handling subsystem whose dynamics depend upon the level of the second messenger inositol 1,4,5 trisphosphate (IP3). This Ca(2+) subsystem endows individual units with conditional intrinsic bistability for a range of IP3. The full "hybrid" network sustains IP3-dependent persistent ("bump") activity in response to a brief transient stimulus. The bump response in our hybrid model, like that of Camperi-Wang, is resistant to noise-- its position does not drift with time.

Background-activity-dependent properties of a network model for working memory that incorporates cellular bistability.

In models of working memory, transient stimuli are encoded by feature-selective persistent neural activity. Network models of working memory are also implicitly bistable. In the absence of a brief stimulus, only spontaneous, low-level, and presumably nonpatterned neural activity is seen. In many working-memory models, local recurrent excitation combined with long-range inhibition (Mexican hat coupling) can result in a network-induced, spatially localized persistent activity or "bump state" that coexists with a stable uniform state. There is now renewed interest in the concept that individual neurons might have some intrinsic ability to sustain persistent activity without recurrent network interactions. A recent visuospatial working-memory model (Camperi and Wang 1998) incorporates both intrinsic bistability of individual neurons within a firing rate network model and a single population of neurons on a ring with lateral inhibitory coupling. We have explored this model in more detail and have characterized the response properties with changes in background synaptic input I(o) and stimulus width. We find that only a small range of I(o) yields a working-memory-like coexistence of bump and uniform solutions that are both stable. There is a rather larger range where only the bump solution is stable that might correspond instead to a feature-selective long-term memory. Such a network therefore requires careful tuning to exhibit working-memory-like function. Interestingly, where bumps and uniform stable states coexist, we find a continuous family of stable bumps representing stimulus width. Thus, in the range of parameters corresponding to working memory, the model is capable of capturing a two-parameter family of stimulus features including both orientation and width.

Cortically restricted production of IP3 leads to propagation of the fertilization Ca2+ wave along the cell surface in a model of the Xenopus egg.

The fertilization Ca2+ wave in Xenopus laevis is a single, large wave of elevated free cytosolic Ca2+ concentration that emanates from the point of sperm-egg fusion and traverses the entire diameter of the egg. This phenomenon appears to involve an increase in inositol-1,4,5-trisphosphate (IP3) resulting from interaction of the sperm and egg, which then results in the activation of the endoplasmic reticulum Ca2+ release machinery. We have proposed models based on a static elevated distribution of IP3, and dynamic [IP3], however, these models have suggested that the fertilization wave passes through the center of the egg. Complementing these earlier models, we propose a more detailed model of the fertilization Ca2+ wave in Xenopus eggs to explore the hypothesis that IP3 is produced only at or near the plasma membrane. In this case, we find that the wave propagates primarily through the cortex of the egg, and that Ca2+ -induced production of IP3 at the plasma membrane allows IP3 to propagate in advance of the wave. Our model includes Ca2+ -dependent production of IP3 at the plasma membrane and IP3 degradation. Simulations in 1 dimension and axi-symmetric 3 dimensions illustrate the basic features of the wave.