Quantal Properties of Voltage-Dependent Ca2+ Release in Frog Skeletal Muscle Persist After Reduction of [Ca2+] in the Sarcoplasmic Reticulum.

In skeletal muscle, the Ca2+ release flux elicited by a voltage clamp pulse rises to an early peak that inactivates rapidly to a much lower steady level. Using a double pulse protocol the fast inactivation follows an arithmetic rule: if the conditioning depolarization is less than or equal to the test depolarization, then decay (peak minus steady level) in the conditioning release is approximately equal to suppression (unconditioned minus conditioned peak) of the test release. This is due to quantal activation by voltage, analogous to the quantal activation of IP3 receptor channels. Two mechanisms are possible. One is the existence of subsets of channels with different sensitivities to voltage. The other is that the clusters of Ca2+-gated Ryanodine Receptor (RyR) ß in the parajunctional terminal cisternae might constitute the quantal units. These Ca2+-gated channels are activated by the release of Ca2+ through the voltage-gated RyR α channels. If the RyR ß were at the basis of quantal release, it should be modified by strong inhibition of the primary voltage-gated release. This was attained in two ways, by sarcoplasmic reticulum (SR) Ca2+ depletion and by voltage-dependent inactivation. Both procedures reduced global Ca2+ release flux, but SR Ca2+ depletion reduced the single RyR current as well. The effect of both interventions on the quantal properties of Ca2+ release in frog skeletal muscle fibers were studied under voltage clamp. The quantal properties of release were preserved regardless of the inhibitory maneuver applied. These findings put a limit on the role of the Ca2+-activated component of release in generating quantal activation.

Assessing wildfire exposure in the Wildland-Urban Interface area of the mountains of central Argentina.

Wildfires are a major threat to people and property in Wildland Urban Interface (WUI) communities worldwide, but while the patterns of the WUI in North America, Europe and Oceania have been studied before, this is not the case in Latin America. Our goals were to a) map WUI areas in central Argentina, and b) assess wildfire exposure for WUI communities in relation to historic fires, with special emphasis on large fires and estimated burn probability based on an empirical model. We mapped the WUI in the mountains of central Argentina (810,000 ha), after digitizing the location of 276,700 buildings and deriving vegetation maps from satellite imagery. The areas where houses and wildland vegetation intermingle were classified as Intermix WUI (housing density > 6.17 hu/km2 and wildland vegetation cover > 50%), and the areas where wildland vegetation abuts settlements were classified as Interface WUI (housing density > 6.17 hu/km2, wildland vegetation cover < 50%, but within 600 m of a vegetated patch larger than 5 km2). We generated burn probability maps based on historical fire data from 1999 to 2011; as well as from an empirical model of fire frequency. WUI areas occupied 15% of our study area and contained 144,000 buildings (52%). Most WUI area was Intermix WUI, but most WUI buildings were in the Interface WUI. Our findings suggest that central Argentina has a WUI fire problem. WUI areas included most of the buildings exposed to wildfires and most of the buildings located in areas of higher burn probability. Our findings can help focus fire management activities in areas of higher risk, and ultimately provide support for landscape management and planning aimed at reducing wildfire risk in WUI communities.

Energy-efficient wastewater treatment via the air-based, hybrid membrane biofilm reactor (hybrid MfBR).

We used modeling to predict the energy and cost savings associated with the air-based, hybrid membrane-biofilm reactor (hybrid MfBR). This process is obtained by replacing fine-bubble diffusers in conventional activated sludge with air-supplying, hollow-fiber membrane modules. Evaluated processes included removal of chemical oxygen demand (COD), combined COD and total nitrogen (TN) removal, and hybrid growth (biofilm and suspended). Target concentrations of COD and TN were based on high-stringency water reuse scenarios. Results showed reductions in power requirements as high as 86%. The decrease mainly resulted from the dramatically lower air flows for the MBfR, resulting from its higher oxygen-transfer efficiencies. When the MBfR was used for COD and TN removal, savings up to US$200/1,000 m(3) of treated water were predicted. Cost savings were highly sensitive to the costs of the membrane modules and electrical power. The costs were also very sensitive to membrane oxidation flux for ammonia, and the membrane life. These results suggest the hybrid MBfR may provide significant savings in energy and costs. Further research on the identified key parameters can help confirm these modeling predictions and facilitate scale-up.

Culture dependent and independent analyses of bacterial communities involved in copper plumbing corrosion.

AIMS: This study used culture-dependent and culture-independent approaches to characterize bacterial communities in copper plumbing corrosion and to assess biofilm formation and copper resistance of heterotrophic bacteria isolated from copper pipes. METHODS AND RESULTS: Water and copper pipes were collected from a cold-water household distribution system affected by 'blue water' corrosion and presenting biofilm formation. Corrosion-promoting ageing experiments were performed with conditioned unused copper pipes filled with unfiltered and filtered sampled water as nonsterile and sterile treatments, respectively. During 8 weeks, stagnant water within the pipes was replaced with aerated fresh water every 2 or 3 days. Total copper and pH were determined in sampled water, and copper pipe coupons were cut for microscopic analyses. Biofilms were extracted from field and laboratory pipes, and total DNA was isolated. Bacterial communities' composition was analysed by terminal restriction fragment length polymorphism (T-RFLP) and clonal libraries of 16S rRNA genes. Heterotrophic bacterial isolates were obtained from water and biofilm extracts and characterized in terms of biofilm formation capacity and copper minimum inhibitory concentration. The results indicated that copper concentration in stagnant water from nonsterile treatments was much higher than in sterile treatments and corrosion by-products structure in coupon surfaces was different. Multivariate analysis of T-RFLP profiles and clone sequencing showed significant dissimilarity between field and laboratory biofilm communities, and a low richness and the dominant presence of Gamma- and Betaproteobacteria in both cases. Several bacterial isolates formed biofilm and tolerated high copper concentrations. CONCLUSIONS: The study demonstrates microbially influenced corrosion (MIC) in copper plumbing. Gamma- and Betaproteobacteria dominated the corroded copper piping bacterial community, whose ability to form biofilms may be important for bacterial corrosion promotion and survival in MIC events. SIGNIFICANCE AND IMPACT OF THE STUDY: The characterization of micro-organisms that influence copper plumbing corrosion has significant implications for distribution system management and copper corrosion control.

Integrating fluorescent dye flow-curve testing and acoustic Doppler velocimetry profiling for in situ hydraulic evaluation and improvement of clarifier performance.

Enhancing the performance of clarifiers requires a thorough understanding of their hydraulics. Fluorescence spectroscopy and acoustic doppler velocimeter (ADV) profiling generally have been used separately to evaluate secondary settlers. We propose that simultaneous use of these techniques is needed to obtain a more reliable and useful evaluation. Experiments were performed on laboratory- and full-scale clarifiers. Factors affecting Fluorescein and Rhodamine 6G properties were identified. Underestimations up to 500% in fluorescence intensities may be derived from differential fluorescence quenching by oxygen. A careful control and interpretation of fluorescent dye experiments is needed to minimize artifacts in real settings. While flow-curve tests constructed under controlled conditions provided a more accurate overall quantitative estimation of the hydraulic performance, ADV velocity and turbulence profiling provided a detailed spatial understanding of flow patterns that was used to troubleshoot and fix the causes of hydraulic short-circuits.

Optical measurements of extracellular calcium depletion during a single heartbeat.

The impermeant dye antipyrylazo III was used to measure depletion of extracellular calcium and net influx of calcium through the sarcolemma during the cardiac action potential. It was found that calcium entry occurs continuously during the action potential and is under direct control of the membrane potential. The inotropic action of epinephrine is accompanied by increased influx of calcium, while strophanthidin enhances the twitch without altering calcium influx during the action potential.

Towards a benchmarking model for winery wastewater treatment and disposal.

We propose a benchmarking model for winery wastewater treatment systems and use it to quantitatively compare the performance of Chilean wine-making operations. The benchmarking model integrates three components: the influent characteristics, the wastewater treatment alternatives, and the location constraints. Four performance levels may be defined when plotting the available data of the wine production versus the ratio of wastewater to wine, for the French, US, and Chilean industries. Knowing where a certain system lies in this diagram helps to quantify the gap between the current and a target performance, and to set performance goals for planned expansions. The analysis of construction and operating costs of treatment systems currently in operation in Chile shows that similar compliance levels can be achieved at remarkably different costs. A steep decrease in the unitary cost is observed as wastewater flow increases; yet, the treatment alternative for achieving that cost may change. Further selection is obtained when location constraints are considered, including stringent discharge standards and proximity to urban settlements. The application of this simple benchmark model to three Chilean winery facilities shows how it produces meaningful quantitative and qualitative results. However, there is still ample room to improve this benchmarking model by considering additional complexity, including technical detail in the treatment options and costs related to technology conversion.

Evaluation of rapid methods for in-situ characterization of organic contaminant load and biodegradation rates in winery wastewater.

Rapid methods for the in-situ evaluation of the organic load have recently been developed and successfully implemented in municipal wastewater treatment systems. Their direct application to winery wastewater treatment is questionable due to substantial differences between municipal and winery wastewater. We critically evaluate the use of UV-VIS spectrometry, buffer capacity testing (BCT), and respirometry as rapid methods to determine organic load and biodegradation rates of winery wastewater. We tested three types of samples: actual and treated winery wastewater, synthetic winery wastewater, and samples from a biological batch reactor. Not surprisingly, respirometry gave a good estimation of biodegradation rates for substrate of different complexities, whereas UV-VIS and BCT did not provide a quantitative measure of the easily degradable sugars and ethanol, typically the main components of the COD in the influent. However, our results strongly suggest that UV-VIS and BCT can be used to identify and estimate the concentration of complex substrates in the influent and soluble microbial products (SMP) in biological reactors and their effluent. Furthermore, the integration of UV-VIS spectrometry, BCT, and mathematical modeling was able to differentiate between the two components of SMPs: substrate utilization associated products (UAP) and biomass associated products (BAP). Since the effluent COD in biologically treated wastewaters is composed primarily by SMPs, the quantitative information given by these techniques may be used for plant control and optimization.

Wetland loss due to land use change in the Lower Paraná River Delta, Argentina.

Wetland loss is a global concern because wetlands are highly diverse ecosystems that provide important goods and services, thus threatening both biodiversity and human well-being. The Paraná River Delta is one of the largest and most important wetland ecosystems of South America, undergoing expanding cattle and forestry activities with widespread water control practices. To understand the patterns and drivers of land cover change in the Lower Paraná River Delta, we quantified land cover changes and modeled associated factors. We developed land cover maps using Landsat images from 1999 and 2013 and identified main land cover changes. We quantified the influence of different socioeconomic (distance to roads, population centers and human activity centers), land management (area within polders, cattle density and years since last fire), biophysical variables (landscape unit, elevation, soil productivity, distance to rivers) and variables related to extreme system dynamics (flooding and fires) on freshwater marsh conversion with Boosted Regression Trees. We found that one third of the freshwater marshes of the Lower Delta (163,000ha) were replaced by pastures (70%) and forestry (18%) in only 14years. Ranching practices (represented by cattle density, area within polders and distance to roads) were the most important factors responsible for freshwater marsh conversion to pasture. These rapid and widespread losses of freshwater marshes have potentially large negative consequences for biodiversity and ecosystem services. A strategy for sustainable wetland management will benefit from careful analysis of dominant land uses and related management practices, to develop an urgently needed land use policy for the Lower Delta.

A damped oscillation in the intramembranous charge movement and calcium release flux of frog skeletal muscle fibers.

Asymmetric membrane currents and calcium transients were recorded simultaneously from cut segments of frog skeletal muscle fibers voltage clamped in a double Vaseline-gap chamber in the presence of high concentration of EGTA intracellularly. An inward phase of asymmetric currents following the hump component was observed in all fibers during the depolarization pulse to selected voltages (congruent to -45 mV). The average value of the peak inward current was 0.1 A/F (SEM = 0.01, n = 18), and the time at which it occurred was 34 ms (SEM = 1.8, n = 18). A second delayed outward phase of asymmetric current was observed after the inward phase, in those experiments in which hump component and inward phase were large. It peaked at more variable time (between 60 and 130 ms) with amplitude 0.02 A/F (SEM = 0.003, n = 11). The transmembrane voltage during a pulse, measured with a glass microelectrode, reached its steady value in less than 10 ms and showed no oscillations. The potential was steady at the time when the delayed component of asymmetric current occurred. ON and OFF charge transfers were equal for all pulse durations. The inward phase moved 1.4 nC/microF charge (SEM = 0.8, n = 6), or about one third of the final value of charge mobilized by these small pulses, and the second outward phase moved 0.7 nC/microF (SEM = 0.8, n = 6), bringing back about half of the charge moved during the inward phase. When repolarization intersected the peak of the inward phase, the OFF charge transfer was independent of the repolarization voltage in the range -60 to -90 mV. When both pre- and post-pulse voltages were changed between -120 mV and -60 mV, the equality of ON and OFF transfers of charge persisted, although they changed from 113 to 81% of their value at -90 mV. The three delayed phases in asymmetric current were also observed in experiments in which the extracellular solution contained Cd2+, La3+ and no Ca2+. Large increases in intracellular [Cl-] were imposed, and had no major effect on the delayed components of the asymmetric current. The Ca2+ transients measured optically and the calculated Ca2+ release fluxes had three phases whenever a visible outward phase followed the inward phase in the asymmetric current. Several interventions intended to interfere with Ca release, reduced or eliminated the three delayed phases of the asymmetric current.(ABSTRACT TRUNCATED AT 400 WORDS)

Effect of the calcium buffer EGTA on the "hump" component of charge movement in skeletal muscle.

Three manifestations of excitation-contraction (E-C) coupling were measured in cut skeletal muscle fibers of the frog, voltage clamped in a double Vaseline gap: intramembrane charge movements, myoplasmic Ca2+ transients, and changes in optical transparency. Pulsing patterns in the presence of high [EGTA] intracellularly, shown by García et al. (1989. J. Gen. Physiol. 94:973-986) to deplete Ca2+ in the sarcoplasmic reticulum, were found to change the above manifestations. With an intracellular solution containing 15 mM EGTA and 0 Ca, 10-15 pulses (100 ms) to -20 mV at a frequency of 2 min-1 reduced the "hump" component of charge movement current. This effect was reversible by 5 min of rest. The same effect was obtained in 62.5 mM EGTA and 0 Ca by pulsing at 0.2 min-1. This effect was reversible by adding calcium to the EGTA solution, for a nominal [Ca2+]i of 200 nM, and was prevented by adding calcium to the EGTA solution before pulsing. The suppression of the hump was accompanied by elimination of the optical manifestations of E-C coupling. The current suppressed was found by subtraction and had the following properties: delayed onset, a peak at a variable interval (10-20 ms) into the pulse, a negative phase (inward current) after the peak, and a variable OFF transient that could be multi-phasic and carried less charge than the ON transient. In the previous paper (Csernoch et al., 1991. J. Gen. Physiol. 97:845-884) it was shown that several interventions suppress a similar component of charge movement current, identified with the "hump" or Q gamma current (I gamma). Based on the similarity to that component, the charge movement suppressed by the depletion protocols can also be identified with I gamma. The fact that I gamma is suppressed by Ca2+ depletion and the kinetic properties of the charge suppressed is inconsistent with the existence of separate sets of voltage sensors underlying the two components of charge movement, Q beta and Q gamma. This is explicable if Q gamma is a consequence of calcium release from the sarcoplasmic reticulum.

Local control model of excitation-contraction coupling in skeletal muscle.

This is a quantitative model of control of Ca release from the sarcoplasmic reticulum in skeletal muscle, based on dual control of release channels (ryanodine receptors), primarily by voltage, secondarily by Ca (Ríos, E., and G. Pizarro. 1988. 3:223-227). Channels are positioned in a double row array of between 10 and 60 channels, where exactly half face voltage sensors (dihydropyridine receptors) in the transverse (t) tubule membrane (Block, B.A., T. Imagawa, K.P. Campbell, and C. Franzini-Armstrong. 1988. 107:2587-2600). We calculate the flux of Ca release upon different patterns of pulsed t-tubule depolarization by explicit stochastic simulation of the states of all channels in the array. Channels are initially opened by voltage sensors, according to an allosteric prescription (Ríos, E., M. Karhanek, J. Ma, A. González. 1993. 102:449-482). Ca permeating the open channels, diffusing in the junctional gap space, and interacting with fixed and mobile buffers produces defined and changing distributions of Ca concentration. These concentrations interact with activating and inactivating channel sites to determine the propagation of activation and inactivation within the array. The model satisfactorily simulates several whole-cell observations, including kinetics and voltage dependence of release flux, the "paradox of control," whereby Ca-activated release remains under voltage control, and, most surprisingly, the "quantal" aspects of activation and inactivation (Pizarro, G., N. Shirokova, A. Tsugorka, and E. Ríos. 1997. 501:289-303). Additionally, the model produces discrete events of activation that resemble Ca sparks (Cheng, H., M.B. Cannell, and W.J. Lederer. 1993. 262:740-744). All these properties result from the intersection of stochastic channel properties, control by local Ca, and, most importantly, the one dimensional geometry of the array and its mesoscopic scale. Our calculations support the concept that the release channels associated with one face of one junctional t-tubule segment, with its voltage sensor, constitute a functional unit, termed the "couplon." This unit is fundamental: the whole cell behavior can be synthesized as that of a set of couplons, rather than a set of independent channels.

The voltage sensor of excitation-contraction coupling in skeletal muscle. Ion dependence and selectivity.

Manifestations of excitation-contraction (EC) coupling of skeletal muscle were studied in the presence of metal ions of the alkaline and alkaline-earth groups in the extracellular medium. Single cut fibers of frog skeletal muscle were voltage clamped in a double Vaseline gap apparatus, and intramembrane charge movement and myoplasmic Ca2+ transients were simultaneously measured. In metal-free extracellular media both charge movement of the charge 1 type and Ca transients were suppressed. Under metal-free conditions the nonlinear charge distribution was the same in depolarized (holding potential of 0 mV) and normally polarized fibers (holding potentials between -80 and -90 mV). The manifestations of EC coupling recovered when ions of groups Ia and IIa of the periodic table were included in the extracellular solution; the extent of recovery depended on the ion species. These results are consistent with the idea that the voltage sensor of EC coupling has a binding site for metal cations--the "priming" site--that is essential for function. A state model of the voltage sensor in which metal ligands bind preferentially to the priming site when the sensor is in noninactivated states accounts for the results. This theory was used to derive the relative affinities of the various ions for the priming site from the magnitude of the EC coupling response. The selectivity sequence thus constructed is: Ca greater than Sr greater than Mg greater than Ba for group IIa cations and Li greater than Na greater than K greater than Rb greater than Cs for group Ia. Ca2+, the most effective of all ions tested, was 1,500-fold more effective than Na+. This selectivity sequence is qualitatively and quantitatively similar to that of the intrapore binding sites of the L-type cardiac Ca channel. This provides further evidence of molecular similarity between the voltage sensor and Ca channels.

Ca2+ release from the sarcoplasmic reticulum compared in amphibian and mammalian skeletal muscle.

Puzzled by recent reports of differences in specific ligand binding to muscle Ca2+ channels, we quantitatively compared the flux of Ca2+ release from the sarcoplasmic reticulum (SR) in skeletal muscle fibers of an amphibian (frog) and a mammal (rat), voltage clamped in a double Vaseline gap chamber. The determinations of release flux were carried out by the "removal" method and by measuring the rate of Ca2+ binding to dyes in large excess over other Ca2+ buffers. To have a more meaningful comparison, the effects of stretching the fibers, of rapid changes in temperature, and of changes in the Ca2+ content of the SR were studied in both species. In both frogs and rats, the release flux had an early peak followed by fast relaxation to a lower sustained release. The peak and steady values of release flux, Rp and Rs, were influenced little by stretching. Rp in frogs was 31 mM/s (SEM = 4, n = 24) and in rats 7 +/- 2 mM/s (n = 12). Rs was 9 +/- 1 and 3 +/- 0.7 mM/s in frogs and rats, respectively. Transverse (T) tubule area, estimated from capacitance measurements and normalized to fiber volume, was greater in rats (0.61 +/- 0.04 microns-1) than in frogs (0.48 +/- 0.04 micron-1), as expected from the greater density of T tubuli. Total Ca in the SR was estimated as 3.4 +/- 0.6 and 1.9 +/- 0.3 mmol/liter myoplasmic water in frogs and rats. With the above figures, the steady release flux per unit area of T tubule was found to be fourfold greater in the frog, and the steady permeability of the junctional SR was about threefold greater. The ratio Rp/Rs was approximately 2 in rats at all voltages, whereas it was greater and steeply voltage dependent in frogs, going through a maximum of 6 at -40 mV, then decaying to approximately 3.5 at high voltage. Both Rp and Rs depended strongly on the temperature, but their ratio, and its voltage dependence, did not. Assuming that the peak of Ca2+ release is contributed by release channels not in contact with voltage sensors, or not under their direct control, the greater ratio in frogs may correspond to the relative excess of Ca2+ release channels over voltage sensors apparent in binding measurements. From the marked differences in voltage dependence of the ratio, as well as consideration of Ca(2+)-induced release models, we derive indications of fundamental differences in control mechanisms between mammalian and amphibian muscle.

Interfering with calcium release suppresses I gamma, the "hump" component of intramembranous charge movement in skeletal muscle.

Four manifestations of excitation-contraction (E-C) coupling were derived from measurements in cut skeletal muscle fibers of the frog, voltage clamped in a Vaseline-gap chamber: intramembranous charge movement currents, myoplasmic [Ca2+] transients, flux of calcium release from the sarcoplasmic reticulum (SR), and the intrinsic optical transparency change that accompanies calcium release. In attempts to suppress Ca release by direct effects on the SR, three interventions were applied: (a) a conditioning pulse that causes calcium release and inhibits release in subsequent pulses by Ca-dependent inactivation; (b) a series of brief, large pulses, separated by long intervals (greater than 700 ms), which deplete Ca2+ in the SR; and (c) intracellular application of the release channel blocker ruthenium red. All these reduced calcium release flux. None was expected to affect directly the voltage sensor of the T-tubule; however, all of them reduced or eliminated a component of charge movement current with the following characteristics: (a) delayed onset, peaking 10-20 ms into the pulse; (b) current reversal during the pulse, with an inward phase after the outward peak; and (c) OFF transient of smaller magnitude than the ON, of variable polarity, and sometimes biphasic. When the total charge movement current had a visible hump, the positive phase of the current eliminated by the interventions agreed with the hump in timing and size. The component of charge movement current blocked by the interventions was greater and had a greater inward phase in slack fibers with high [EGTA] inside than in stretched fibers with no EGTA. Its amplitude at -40 mV was on average 0.26 A/F (SEM 0.03) in slack fibers. The waveform of release flux determined from the Ca transients measured simultaneously with the membrane currents had, as described previously (Melzer, W., E. Ríos, and M. F. Schneider. 1984. Biophysical Journal. 45:637-641), an early peak followed by a descent to a steady level during the pulse. The time at which this peak occurred was highly correlated with the time to peak of the current suppressed, occurring on average 6.9 ms later (SEM 0.73 ms). The current suppressed by the above interventions in all cases had a time course similar to the time derivative of the release flux; specifically, the peak of the time derivative of release flux preceded the peak of the current suppressed by 0.7 ms (SEM 0.6 ms). The magnitude of the current blocked was highly correlated with the inhibitory effect of the interventions on Ca2+ release flux.(ABSTRACT TRUNCATED AT 400 WORDS)

The relationship between Q gamma and Ca release from the sarcoplasmic reticulum in skeletal muscle.

Asymmetric membrane currents and fluxes of Ca2+ release were determined in skeletal muscle fibers voltage clamped in a Vaseline-gap chamber. The conditioning pulse protocol 1 for suppressing Ca2+ release and the "hump" component of charge movement current (I gamma), described in the first paper of this series, was applied at different test pulse voltages. The amplitude of the current suppressed during the ON transient reached a maximum at slightly suprathreshold test voltages (-50 to -40 mV) and decayed at higher voltages. The component of charge movement current suppressed by 20 microM tetracaine also went through a maximum at low pulse voltages. This anomalous voltage dependence is thus a property of I gamma, defined by either the conditioning protocol or the tetracaine effect. A negative (inward-going) phase was often observed in the asymmetric current during the ON of depolarizing pulses. This inward phase was shown to be an intramembranous charge movement based on (a) its presence in the records of total membrane current, (b) its voltage dependence, with a maximum at slightly suprathreshold voltages, (c) its association with a "hump" in the asymmetric current, (d) its inhibition by interventions that reduce the "hump", (e) equality of ON and OFF areas in the records of asymmetric current presenting this inward phase, and (f) its kinetic relationship with the time derivative of Ca release flux. The nonmonotonic voltage dependence of the amplitude of the hump and the possibility of an inward phase of intramembranous charge movement are used as the main criteria in the quantitative testing of a specific model. According to this model, released Ca2+ binds to negatively charged sites on the myoplasmic face of the voltage sensor and increases the local transmembrane potential, thus driving additional charge movement (the hump). This model successfully predicts the anomalous voltage dependence and all the kinetic properties of I gamma described in the previous papers. It also accounts for the inward phase in total asymmetric current and in the current suppressed by protocol 1. According to this model, I gamma accompanies activating transitions at the same set of voltage sensors as I beta. Therefore it should open additional release channels, which in turn should cause more I gamma, providing a positive feedback mechanism in the regulation of calcium release.

Calcium release flux underlying Ca2+ sparks of frog skeletal muscle.

An algorithm for the calculation of Ca2+ release flux underlying Ca2+ sparks (Blatter, L.A., J. Hüser, and E. Ríos. 1997. Proc. Natl. Acad. Sci. USA. 94:4176-4181) was modified and applied to sparks obtained by confocal microscopy in single frog skeletal muscle fibers, which were voltage clamped in a two-Vaseline gap chamber or permeabilized and immersed in fluo-3-containing internal solution. The performance of the algorithm was characterized on sparks obtained by simulation of fluorescence due to release of Ca2+ from a spherical source, in a homogeneous three-dimensional space that contained components representing cytoplasmic molecules and Ca2+ removal processes. Total release current, as well as source diameter and noise level, was varied in the simulations. Derived release flux or current, calculated by volume integration of the derived flux density, estimated quite closely the current used in the simulation, while full width at half magnitude of the derived release flux was a good monitor of source size only at diameters >0. 7 micrometers. On an average of 157 sparks of amplitude >2 U resting fluorescence, located automatically in a representative voltage clamp experiment, the algorithm reported a release current of 16.9 pA, coming from a source of 0.5 micrometer, with an open time of 6.3 ms. Fewer sparks were obtained in permeabilized fibers, so that the algorithm had to be applied to individual sparks or averages of few events, which degraded its performance in comparable tests. The average current reported for 19 large sparks obtained in permeabilized fibers was 14.4 pA. A minimum estimate, derived from the rate of change of dye-bound Ca2+ concentration, was 8 pA. Such a current would require simultaneous opening of between 8 and 60 release channels with unitary Ca2+ currents of the level recorded in bilayer experiments. Real sparks differ from simulated ones mainly in having greater width. Correspondingly, the algorithm reported greater spatial extent of the source for real sparks. This may again indicate a multichannel origin of sparks, or could reflect limitations in spatial resolution.

The spark and its ember: separately gated local components of Ca(2+) release in skeletal muscle.

Amplitude, spatial width, and rise time of Ca(2+) sparks were compared in frog fast-twitch muscle, in three conditions that alter activation of release channels by [Ca(2+)]. A total of approximately 17,000 sparks from 30 cells were evaluated. In cells under voltage clamp, caffeine (0.5 or 1 mM) increased average spark width by 28%, rise time by 18%, and amplitude by 7%. Increases in width were significant even among events of the same rise time. Spontaneous events recorded in permeabilized fibers with low internal [Mg(2+)] (0.4 mM), had width and rise times greater than in reference, and not significantly different than those in caffeine. The spark average in reference rides on a continuous fluorescence "ridge" and is continued by an "ember," a prolongation of width approximately 1 microm and amplitude <0.2, vanishing in approximately 100 ms. Ridge and ember were absent in caffeine and in permeabilized cells. Exposure of voltage-clamped cells to high internal [Mg(2+)] (7 mM) had effects opposite to caffeine, reducing spark width by 26% and amplitude by 27%. In high [Mg(2+)], the ember was visible in individual sparks as a prolongation of variable duration and amplitude up to 1.2. Based on simulations and calculation of Ca(2+) release flux from averaged sparks, the increase in spark width caused by caffeine was interpreted as evidence of an increase in radius of the release source-presumably by recruitment of additional channels. Conversely, spark narrowing suggests loss of contributing channels in high Mg(2+). Therefore, these changes in spark width at constant rise times are evidence of a multichannel origin of sparks. Because ridge and ember were reduced by promoters of Ca(2+)-dependent activation (caffeine, low [Mg(2+)]) and became more visible in the presence of its inhibitors, they are probably manifestations of Ca(2+) release directly operated by voltage sensors.

Two-dimensional cellular automaton model for mixed-culture biofilm.

Structural and microbial heterogeneity occurs in almost any type of biofilm system. General approaches for the design of biofilm systems consider biofilms as homogeneous and of constant thickness. In order to improve the design of biofilms systems, models need to incorporate structural heterogeneity and the effect of inert microbial mass. We have improved a 2D biofilm model based on cellular automata (CA) and used it to simulate multidimensional biofilms with active and inert biomass including a self-organizing development. Results indicate that the presence of inert biomass within biofilm structures does not change considerably the substrate flux into the biofilm because the active biomass is located at the surface of the biofilm. Long-term simulations revealed that although the biofilm system is highly heterogeneous and the microstructure is continuously changing, the biofilm reaches a dynamic steady-state with prediction of biofilm thickness and substrate flux stabilizing on a delimited range.

Comparing biofilm models for a single species biofilm system.

A benchmark problem was defined to evaluate the performance of different mathematical biofilm models. The biofilm consisted of heterotrophic bacteria degrading organic substrate and oxygen. Mathematical models tested ranged from simple analytical to multidimensional numerical models. For simple and more or less flat biofilms it was shown that analytical biofilm models provide very similar results compared to more complex numerical solutions. When considering a heterogeneous biofilm morphology it was shown that the effect of an increased external mass transfer resistance was much more significant compared to the effect of an increased surface area inside the biofilm.