Approximate analytical time-dependent solutions to describe large-amplitude local calcium transients in the presence of buffers

Bound Ca2+ moves faster and farther from single open channels than free Ca2

A concept of Ca2+ nanodomains established in the cytoplasm after opening single-calcium channels helps mechanistically understand the physiological mechanisms of Ca2+ signaling. It predicts standing gradients of cytoplasmic free Ca2+ around single channels in the plasma membrane. The fate of bound Ca2+ attracted much less attention. This study aimed to examine the profiles of Ca2+ bound to low-mobility buffers such as bulky Ca2+-binding proteins. The solution of non-linear PDEs for an immobile buffer predicts fast decay of free [Ca2+] from the channel lumen and the traveling wave for bound Ca2+. For low-mobility buffers like calmodulin, the calculated profiles of free and bound Ca2+ are similar. Theoretical predictions are tested by imaging 1D profiles of Ca2+ bound to low-mobility fluo-4-dextran. The traveling waves of bound Ca2+ are observed that develop during the opening of single channels. The findings tempt to propose that Ca2+ signaling may not be solely related by the absolute free [Ca2+] at the sensor location, which is extremely localized, but determined by the time when a wave of bound Ca2+ reaches a threshold needed for sensor activation.

Rethinking calcium profiles around single channels: the exponential and periodic calcium nanodomains

Many fundamental calcium-dependent physiological processes are triggered by high local calcium levels that are established around the sites of calcium entry into the cell (channels). They are dubbed as calcium nanodomains but their exact profiles are still elusive. The concept of calcium nanodomains stems from a linear model of calcium diffusion and is only valid when calcium increases are smaller than the concentration of cytoplasmic buffers. Recent data indicates that much higher calcium levels cause buffer saturation. Therefore, I sought explicit solutions of a nonlinear reaction-diffusion model and found a dichotomous solution. For small fluxes, the steady state calcium profile is quasi-exponential, and when calcium exceeds buffer concentration a spatial periodicity appears. Analytical results are supported by Monte-Carlo simulations. I also imaged 1D- and radial calcium distributions around single α-synuclein channels in cell-free conditions. Measured Ca profiles are consistent with theoretical predictions. I propose that the periodic calcium patterns may well arise under certain conditions and their specific functional role has to be established.

In situ Ca2+ titration in the fluorometric study of intracellular Ca2+ binding

Imaging with Ca(2+)-sensitive fluorescent dye has provided a wealth of insight into the dynamics of cellular Ca(2+) signaling. The spatiotemporal evolution of intracellular free Ca(2+) observed in imaging experiments is shaped by binding and unbinding to cytoplasmic Ca(2+) buffers, as well as the fluorescent indicator used for imaging. These factors must be taken into account in the interpretation of Ca(2+) imaging data, and can be exploited to investigate endogenous Ca(2+) buffer properties. Here we extended the use of Ca(2+) fluorometry in the characterization of Ca(2+) binding molecules within cells, building on a method of titration of intracellular Ca(2+) binding sites in situ with measured amounts of Ca(2+) entering through voltage-gated Ca(2+) channels. We developed a systematic procedure for fitting fluorescence data acquired during a series of voltage steps to models with multiple Ca(2+) binding sites. The method was tested on simulated data, and then applied to 2-photon fluorescence imaging data from rat posterior pituitary nerve terminals patch clamp-loaded with the Ca(2+) indicator fluo-8. Focusing on data sets well described by a single endogenous Ca(2+) buffer and dye, this method yielded estimates of the endogenous buffer concentration and Kd, the dye Kd, and the fraction of Ca(2+) inaccessible cellular volume. The in situ Kd of fluo-8 thus obtained was indistinguishable from that measured in vitro. This method of calibrating Ca(2+)-sensitive fluorescent dyes in situ has significant advantages over previous methods. Our analysis of Ca(2+) titration fluorometric data makes more effective use of the experimental data, and provides a rigorous treatment of multivariate errors and multiple Ca(2+) binding species. This method offers a versatile approach to the study of endogenous Ca(2+) binding molecules in their physiological milieu.

Calmodulin and calmodulin kinase II mediate emergent bursting activity in the brainstem respiratory network (preBötzinger complex)

Emergence of persistent activity in networks can be controlled by intracellular signalling pathways but the mechanisms involved and their role are not yet fully explored. Using calcium imaging and patch-clamp we examined the rhythmic activity in the preBötzinger complex (preBötC) in the lower brainstem that generates the respiratory motor output. In functionally intact acute slices brief hypoxia, electrical stimulation and activation of AMPA receptors transiently depressed bursting activity which then recovered with augmentation. The effects were abrogated after chelation of intracellular calcium, blockade of L-type calcium channels and inhibition of calmodulin (CaM) and CaM kinase (CaMKII). Rhythmic calcium transients and synaptic drive currents in preBötC neurons in the organotypic slices showed similar CaM- and CaMKII-dependent responses. The stimuli increased the amplitude of spontaneous and miniature excitatory synaptic currents indicating postsynaptic changes at glutamatergic synapses. In the acute and organotypic slices, CaM stimulated and ADP inhibited calcium-dependent TRPM4 channels and CaMKII augmented synaptic drive currents. Experimental data and simulations show the role of ADP and CaMKII in the control of bursting activity and its relation to intracellular signalling. I propose that CaMKII-mediated facilitation of glutamatergic transmission strengthens emergent synchronous activity within preBötC that is then maintained by periodic surges of calcium during the bursts. This may find implications in restoration and consolidation of autonomous activity in the respiratory disorders.

Combined computational and experimental approaches to understanding the Ca(2+) regulatory network in neurons

Ca(2+) is a ubiquitous signaling ion that regulates a variety of neuronal functions by binding to and altering the state of effector proteins. Spatial relationships and temporal dynamics of Ca(2+) elevations determine many cellular responses of neurons to chemical and electrical stimulation. There is a wealth of information regarding the properties and distribution of Ca(2+) channels, pumps, exchangers, and buffers that participate in Ca(2+) regulation. At the same time, new imaging techniques permit characterization of evoked Ca(2+) signals with increasing spatial and temporal resolution. However, understanding the mechanistic link between functional properties of Ca(2+) handling proteins and the stimulus-evoked Ca(2+) signals they orchestrate requires consideration of the way Ca(2+) handling mechanisms operate together as a system in native cells. A wide array of biophysical modeling approaches is available for studying this problem and can be used in a variety of ways. Models can be useful to explain the behavior of complex systems, to evaluate the role of individual Ca(2+) handling mechanisms, to extract valuable parameters, and to generate predictions that can be validated experimentally. In this review, we discuss recent advances in understanding the underlying mechanisms of Ca(2+) signaling in neurons via mathematical modeling. We emphasize the value of developing realistic models based on experimentally validated descriptions of Ca(2+) transport and buffering that can be tested and refined through new experiments to develop increasingly accurate biophysical descriptions of Ca(2+) signaling in neurons.

Intracellular signaling by diffusion: can waves of hydrogen peroxide transmit intracellular information in plant cells?

Amplitude- and frequency-modulated waves of Ca(2+) ions transmit information inside cells. Reactive Oxygen Species (ROS), specifically hydrogen peroxide, have been proposed to have a similar role in plant cells. We consider the feasibility of such an intracellular communication system in view of the physical and biochemical conditions in plant cells. As model system, we use a H(2)O(2) signal originating at the plasma membrane (PM) and spreading through the cytosol. We consider two maximally simple types of signals, isolated pulses and harmonic oscillations. First we consider the basic limits on such signals as regards signal origin, frequency, amplitude, and distance. Then we establish the impact of ROS-removing enzymes on the ability of H(2)O(2) to transmit signals. Finally, we consider to what extent cytoplasmic streaming distorts signals. This modeling allows us to predict the conditions under which diffusion-mediated signaling is possible. We show that purely diffusive transmission of intracellular information by H(2)O(2) over a distance of 1 μm (typical distance between organelles, which may function as relay stations) is possible at frequencies well above 1 Hz, which is the highest frequency observed experimentally. This allows both frequency and amplitude modulation of the signal. Signaling over a distance of 10 μm (typical distance between the PM and the nucleus) may be possible, but requires high signal amplitudes or, equivalently, a very low detection threshold. Furthermore, at this longer distance a high rate of enzymatic degradation is required to make signaling at frequencies above 0.1 Hz possible. In either case, cytoplasmic streaming does not seriously disturb signals. We conclude that although purely diffusion-mediated signaling without relaying stations is theoretically possible, it is unlikely to work in practice, since it requires a much faster enzymatic degradation and a much lower cellular background concentration of H(2)O(2) than observed experimentally.

Effect of fast and slow calcium buffers on induced secretion of neurotransmitter

Loading of mouse motor nerve terminals with EGTA-AM, but not with BAPTA-AM, inhibited the release of the neurotransmitter in response to stimulation of the nerve with rare (0.3 Hz) "single" pulses. During rhythmic stimulation with short (50 EPP) high-frequency (20 Hz) series, BAPTA-AM buffer modified burst pattern in a dose-dependent manner: it replaced the phase of initial facilitation by persistent depression of secretion and decreased its plateau level at the end of the burst. In contrast, loading of the nerve terminals with EGTA-AM buffer produced no effect on the phase of initial facilitation, but decreased the plateau level to the same degree as BAPTA-AM did. Probably, the different effects of both buffers on secretion of neurotransmitter reflect peculiarities of involvement of fast and slow Ca(2+)signals of motor terminals in single and rhythmic release of the neurotransmitter.

Imaging cytoplasmic cAMP in mouse brainstem neurons

BACKGROUND

cAMP is an ubiquitous second messenger mediating various neuronal functions, often as a consequence of increased intracellular Ca2+ levels. While imaging of calcium is commonly used in neuroscience applications, probing for cAMP levels has not yet been performed in living vertebrate neuronal tissue before.

RESULTS

Using a strictly neuron-restricted promoter we virally transduced neurons in the organotypic brainstem slices which contained pre-Bötzinger complex, constituting the rhythm-generating part of the respiratory network. Fluorescent cAMP sensor Epac1-camps was expressed both in neuronal cell bodies and neurites, allowing us to measure intracellular distribution of cAMP, its absolute levels and time-dependent changes in response to physiological stimuli. We recorded [cAMP]i changes in the micromolar range after modulation of adenylate cyclase, inhibition of phosphodiesterase and activation of G-protein-coupled metabotropic receptors. [cAMP]i levels increased after membrane depolarisation and release of Ca2+ from internal stores. The effects developed slowly and reached their maximum after transient [Ca2+]i elevations subsided. Ca2+-dependent [cAMP]i transients were suppressed after blockade of adenylate cyclase with 0.1 mM adenylate cyclase inhibitor 2'5'-dideoxyadenosine and potentiated after inhibiting phosphodiesterase with isobutylmethylxanthine and rolipram. During paired stimulations, the second depolarisation and Ca2+ release evoked bigger cAMP responses. These effects were abolished after inhibition of protein kinase A with H-89 pointing to the important role of phosphorylation of calcium channels in the potentiation of [cAMP]i transients.

CONCLUSION

We constructed and characterized a neuron-specific cAMP probe based on Epac1-camps. Using viral gene transfer we showed its efficient expression in organotypic brainstem preparations. Strong fluorescence, resistance to photobleaching and possibility of direct estimation of [cAMP] levels using dual wavelength measurements make the probe useful in studies of neurons and the mechanisms of their plasticity. Epac1-camps was applied to examine the crosstalk between Ca2+ and cAMP signalling and revealed a synergism of actions of these two second messengers.

Metabotropic glutamate receptors activate dendritic calcium waves and TRPM channels which drive rhythmic respiratory patterns in mice

Respiration in vertebrates is generated by a compact network which is located in the lower brainstem but cellular mechanisms which underlie persistent oscillatory activity of the respiratory network are yet unknown. Using two-photon imaging and patch-clamp recordings in functional brainstem preparations of mice containing pre-Bötzinger complex (preBötC), we examined the actions of metabotropic glutamate receptors (mGluR1/5) on the respiratory patterns. The agonist DHPG potentiated and antagonist LY367385 depressed respiration-related activities. In the inspiratory neurons, we observed rhythmic activation of non-selective channels which had a conductance of 24 pS. Their activity was enhanced with membrane depolarization and after elevation of calcium from the cytoplasmic side of the membrane. They were activated by a non-hydrolysable PIP(2) analogue and blocked by flufenamate, ATP4- and Gd3+. All these properties correspond well to those of TRPM4 channels. Calcium imaging of functional slices revealed rhythmic transients in small clusters of neurons present in a network. Calcium transients in the soma were preceded by the waves in dendrites which were dependent on mGluR activation. Initiation and propagation of waves required calcium influx and calcium release from internal stores. Calcium waves activated TPRM4-like channels in the soma and promoted generation of inspiratory bursts. Simulations of activity of neurons communicated via dendritic calcium waves showed emerging activity within neuronal clusters and its synchronization between the clusters. The experimental and theoretical data provide a subcellular basis for a recently proposed group-pacemaker hypothesis and describe a novel mechanism of rhythm generation in neuronal networks.