Parallel computation enables precise description of Ca2+ distribution in nerve terminals

Subplasma membrane Ca2+ signals

Ca²⁺ may selectively activate various processes in part by the cell's ability to localize changes in the concentration of the ion to specific subcellular sites. Interestingly, these Ca²⁺ signals begin most often at the plasma membrane space so that understanding subplasma membrane signals is central to an appreciation of local signaling. Several experimental procedures have been developed to study Ca²⁺ signals near the plasma membrane, but probably the most prevalent involve the use of fluorescent Ca²⁺ indicators and fall into two general approaches. In the first, the Ca²⁺ indicators themselves are specifically targeted to the subplasma membrane space to measure Ca²⁺ only there. Alternatively, the indicators are allowed to be dispersed throughout the cytoplasm, but the fluorescence emanating from the Ca²⁺ signals at the subplasma membrane space is selectively measured using high resolution imaging procedures. Although the targeted indicators offer an immediate appeal because of selectivity and ease of use, their limited dynamic range and slow response to changes in Ca²⁺ are a shortcoming. Use of targeted indicators is also largely restricted to cultured cells. High resolution imaging applied with rapidly responding small molecule Ca²⁺ indicators can be used in all cells and offers significant improvements in dynamic range and speed of response of the indicator. The approach is technically difficult, however, and realistic calibration of signals is not possible. In this review, a brief overview of local subplasma membrane Ca²⁺ signals and methods for their measurement is provided. © 2012 IUBMB IUBMB Life, 64(7): 573–585, 2012

Calcium Green FlAsH as a genetically targeted small-molecule calcium indicator

Intracellular Ca(2+) regulates numerous proteins and cellular functions and can vary substantially over submicron and submillisecond scales, so precisely localized fast detection is desirable. We have created a approximately 1-kDa biarsenical Ca(2+) indicator, called Calcium Green FlAsH (CaGF, 1), to probe [Ca(2+)] surrounding genetically targeted proteins. CaGF attached to a tetracysteine motif becomes ten-fold more fluorescent upon binding Ca(2+), with a K(d) of approximately 100 microM, <1-ms kinetics and good Mg(2+) rejection. In HeLa cells expressing tetracysteine-tagged connexin 43, CaGF labels gap junctions and reports Ca(2+) waves after injury. Total internal reflection microscopy of tetracysteine-tagged, CaGF-labeled alpha(1C) L-type calcium channels shows fast-rising depolarization-evoked Ca(2+) transients, whose lateral nonuniformity suggests that the probability of channel opening varies greatly over micron dimensions. With moderate Ca(2+) buffering, these transients decay surprisingly slowly, probably because most of the CaGF signal comes from closed channels feeling Ca(2+) from a tiny minority of clustered open channels. With high Ca(2+) buffering, CaGF signals decay as rapidly as the calcium currents, as expected for submicron Ca(2+) domains immediately surrounding active channels. Thus CaGF can report highly localized, rapid [Ca(2+)] dynamics.

Continuum simulations of acetylcholine diffusion with reaction-determined boundaries in neuromuscular junction models

The reaction-diffusion system of the neuromuscular junction has been modeled in 3D using the finite element package FEtk. The numerical solution of the dynamics of acetylcholine with the detailed reaction processes of acetylcholinesterases and nicotinic acetylcholine receptors has been discussed with the reaction-determined boundary conditions. The simulation results describe the detailed acetylcholine hydrolysis process, and reveal the time-dependent interconversion of the closed and open states of the acetylcholine receptors as well as the percentages of unliganded/monoliganded/diliganded states during the neuro-transmission. The finite element method has demonstrated its flexibility and robustness in modeling large biological systems.

On the Feedback Between Theory and Experiment in Elucidating the Molecular Mechanisms Underlying Neurotransmitter Release

This review describes the development of the molecular level Ca(2+)-voltage hypothesis. Theoretical considerations and feedback between theory and experiments played a key role in its development. The theory, backed by experiments, states that at fast synapses, membrane potential by means of presynaptic inhibitory autoreceptors controls initiation and termination of neurotransmitter release. A molecular kinetic scheme which depicts initiation and termination of evoked release is discussed. This scheme is able to account for both spontaneous release and evoked release. The physiological implications of this scheme are enumerated.

Mathematical Modeling and Optimization of Drug Delivery from Intratumorally Injected Microspheres

Purpose: Paclitaxel is a highly promising phase-sensitive antitumor drug that could conceivably be improved by extended lower dosing as opposed to intermittent higher dosing. Although intratumoral delivery of paclitaxel to the whole tumor at different loads and rates has already been achieved, determining an optimal release mode of paclitaxel for tumor eradication remains difficult. This study set out to rationally design such an optimal microsphere release mode based on mathematical modeling.

Experimental Design: A computational reaction-diffusion framework was used to model drug release from intratumorally injected microspheres, drug transport and binding in tumor interstitum, and drug clearance by microvasculature and intracellular uptake and binding.

Results: Numerical simulations suggest that interstitial drug concentration is characterized by a fast spatially inhomogeneous rise phase, during which interstitial and intracellular binding sites are saturated, followed by a slow spatially homogeneous phase that is governed by the rate of drug release from microspheres. For zero-order drug release, the slow phase corresponds to a plateau drug concentration that is proportional to the ratio of the rate of blood clearance of drug to the rate of drug release from microspheres. Consequently, increasing the duration of intratumoral drug release extends the duration of cell exposure to the drug but lowers the plateau drug concentration. This tradeoff implies that intratumoral drug release can be designed to optimize tumor cell kill. Synthesizing our modeling predictions with published dose-response data, we propose an optimal protocol for the delivery of paclitaxel-loaded microspheres to small solid tumors.

Reaction diffusion model of the enzymatic erosion of insoluble fibrillar matrices

Predicting the time course of in vivo biodegradation is a key issue in the design of an increasing number of biomedical applications such as sutures, tissue analogs and drug-delivery devices. The design of such biodegradable devices is hampered by the absence of quantitative models for the enzymatic erosion of solid protein matrices. In this work, we derive and simulate a reaction diffusion model for the enzymatic erosion of fibrillar gels that successfully reproduces the main qualitative features of this process. A key aspect of the proposed model is the incorporation of steric hindrance into the standard Michaelis-Menten scheme for enzyme kinetics. In the limit of instantaneous diffusion, the model equations are analogous to the standard equations for enzymatic degradation in solution. Invoking this analogy, the total quasi-steady-state approximation is used to derive approximate analytical solutions that are valid for a wide range of in vitro conditions. Using these analytical approximations, an experimental-theoretical method is derived to unambiguously estimate all the kinetic model parameters. Moreover, the analytical approximations correctly describe the characteristic hyperbolic dependence of the erosion rate on enzyme concentration and the zero-order erosion of thin fibers. For definiteness, the analysis of published experimental results of enzymatic degradation of fibrillar collagen is demonstrated, and the role of diffusion in these experiments is elucidated.

Autoreceptors, membrane potential and the regulation of transmitter release

It has been suggested that depolarization per se can control neurotransmitter release, in addition to its role in promoting Ca2+ influx. The 'Ca2+ hypothesis' has provided an essential framework for understanding how Ca2+ entry and accumulation in nerve terminals controls transmitter release. Yet, increases in intracellular Ca2+ levels alone cannot account for the initiation and termination of release; some additional mechanism is needed. Several experiments from various laboratories indicate that membrane potential has a decisive role in controlling this release. For example, depolarization causes release when Ca2+ entry is blocked and intracellular Ca2+ levels are held at an elevated level. The key molecules that link membrane potential with release control have not yet been identified: likely candidates are presynaptic autoreceptors and perhaps the Ca2+ channel itself.

Geometry of dendritic spines affects calcium dynamics in hippocampal neurons: theory and experiments

The role of dendritic spine morphology in the regulation of the spatiotemporal distribution of free intracellular calcium concentration ([Ca2+]i) was examined in a unique axial-symmetrical model that focuses on spine-dendrite interactions, and the simulations of the model were compared with the behavior of real dendritic spines in cultured hippocampal neurons. A set of nonlinear differential equations describes the behavior of a spherical dendritic spine head, linked to a dendrite via a cylindrical spine neck. Mechanisms for handling of calcium (including internal stores, buffers, and efflux pathways) are placed in both the dendrites and spines. In response to a calcium surge, the magnitude and time course of the response in both the spine and the parent dendrite vary as a function of the length of the spine neck such that a short neck increases the magnitude of the response in the dendrite and speeds up the recovery in the spine head. The generality of the model, originally constructed for a case of release of calcium from stores, was tested in simulations of fast calcium influx through membrane channels and verified the impact of spine neck on calcium dynamics. Spatiotemporal distributions of [Ca2+]i, measured in individual dendritic spines of cultured hippocampal neurons injected with Calcium Green-1, were monitored with a confocal laser scanning microscope. Line scans of spines and dendrites at a <1-ms time resolution reveal simultaneous transient rises in [Ca2+]i in spines and their parent dendrites after application of caffeine or during spontaneous calcium transients associated with synaptic or action potential discharges. The magnitude of responses in the individual compartments, spine-dendrite disparity, and the temporal distribution of [Ca2+]i were different for spines with short and long necks, with the latter being more independent of the dendrite, in agreement with prediction of the model.

Modeling study of the effects of overlapping Ca2+ microdomains on neurotransmitter release

Although single-channel Ca2+ microdomains are capable of gating neurotransmitter release in some instances, it is likely that in many cases the microdomains from several open channels overlap to activate vesicle fusion. We describe a mathematical model in which transmitter release is gated by single or overlapping Ca2+ microdomains produced by the opening of nearby Ca2+ channels. This model accounts for the presence of a mobile Ca2+ buffer, provided either that the buffer is unsaturable or that it is saturated near an open channel with Ca2+ binding kinetics that are rapid relative to Ca2+ diffusion. We show that the release time course is unaffected by the location of the channels (at least for distances up to 50 nm), but paired-pulse facilitation is greater when the channels are farther from the release sites. We then develop formulas relating the fractional release following selective or random channel blockage to the cooperative relationship between release and the presynaptic Ca2+ current. These formulas are used with the transmitter release model to study the dependence of this form of cooperativity, which we call Ca2+ current cooperativity, on mobile buffers and on the local geometry of Ca2+ channels. We find that Ca2+ current cooperativity increases with the number of channels per release site, but is considerably less than the number of channels, the theoretical upper bound. In the presence of a saturating mobile buffer the Ca2+ current cooperativity is greater, and it increases more rapidly with the number of channels. Finally, Ca2+ current cooperativity is an increasing function of channel distance, particularly in the presence of saturating mobile buffer.

Enhanced pulmonary and active skeletal muscle gas exchange during intense exercise after sprint training in men

1. This study investigated the effects of 7 weeks of sprint training on gas exchange across the lungs and active skeletal muscle during and following maximal cycling exercise in eight healthy males. 2. Pulmonary oxygen uptake (VO2) and carbon dioxide output (VCO2) were measured before and after training during incremental exercise (n = 8) and during and in recovery from a maximal 30 s sprint exercise bout by breath-by-breath analysis (n = 6). To determine gas exchange by the exercising leg muscles, brachial arterial and femoral venous blood O2 and CO2 contents and lactate concentration were measured at rest, during the final 10 s of exercise and during 10 min of recovery. 3. Training increased (P < 0.05) the maximal incremental exercise values of ventilation (VE, by 15.7 +/- 7.1%), VCO2 (by 9.3 +/- 2.1%) and VO2 (by 15.0 +/- 4.2%). Sprint exercise peak power (3.9 +/- 1.0% increase) and cumulative 30 s work (11.7 +/- 2.8% increase) were increased and fatigue index was reduced (by -9.2 +/- 1.5%) after training (P < 0.05). The highest VE, VCO2 and VO2 values attained during sprint exercise were not significantly changed after training, but a significant (P < 0.05) training effect indicated increased VE (by 19.2 +/- 7.9%), VCO2 (by 9.3 +/- 2.1%) and VO2 (by 12.7 +/- 6.5%), primarily reflecting elevated post-exercise values after training. 4. Arterial O2 and CO2 contents were lower after training, by respective mean differences of 3.4 and 21.9 ml l-1 (P < 0.05), whereas the arteriovenous O2 and CO2 content differences and the respiratory exchange ratio across the leg were unchanged by training. 5. Arterial whole blood lactate concentration and the net lactate release by exercising muscle were unchanged by training. 6. The greater peak pulmonary VO2 and VCO2 with sprint exercise, the increased maximal incremental values, unchanged arterial blood lactate concentration and greater sprint performance all point strongly towards enhanced gas exchange across the lungs and in active muscles after sprint training. Enhanced aerobic metabolism after sprint training may contribute to reduced fatigability during maximal exercise, whilst greater pulmonary CO2 output may improve acid-base control after training.

Simultaneous measurement of intracellular Ca2+ and asynchronous transmitter release from the same crayfish bouton

1. A technique has been developed to monitor neurotransmitter release simultaneously with intracellular Ca2+ concentration ([Ca2+]i) in single release boutons whose diameters range from 3 to 5 microns. 2. Using this technique, we have found a highly non-linear relationship between the rate of asynchronous release and [Ca2+]i. The Hill coefficient lies between 3 and 4. 3. The affinity (Kd) of the putative release-related Ca2+ receptor for asynchronous release was calculated to be in the range of 2-4 microM. 4. The same range of values of Hill coefficient and Kd were obtained when [Ca2+]i was elevated both by bath application of ionomycin and by repetitive stimulation at high frequency. 5. Our results show that the Ca2+ receptor(s) associated with asynchronous release exhibits high affinity for Ca2+.