Imaging calcium entering the cytosol through a single opening of plasma membrane ion channels: SCCaFTs—fundamental calcium events

Multiphysics and multiscale modeling of uterine contractions: integrating electrical dynamics and soft tissue deformation with fiber orientation

The development of a comprehensive uterine model that seamlessly integrates the intricate interactions between the electrical and mechanical aspects of uterine activity could potentially facilitate the prediction and management of labor complications. Such a model has the potential to enhance our understanding of the initiation and synchronization mechanisms involved in uterine contractions, providing a more profound comprehension of the factors associated with labor complications, including preterm labor. Consequently, it has the capacity to assist in more effective preparation and intervention strategies for managing such complications. In this study, we present a computational model that effectively integrates the electrical and mechanical components of uterine contractions. By combining a state-of-the-art electrical model with the Hyperelastic Mass-Spring Model (HyperMSM), we adopt a multiphysics and multiscale approach to capture the electrical and mechanical activities within the uterus. The electrical model incorporates the generation and propagation of action potentials, while the HyperMSM simulates the mechanical behavior and deformations of the uterine tissue. Notably, our model takes into account the orientation of muscle fibers, ensuring that the simulated contractions align with their inherent directional characteristics. One noteworthy aspect of our contraction model is its novel approach to scaling the rest state of the mesh elements, as opposed to the conventional method of applying mechanical loads. By doing so, we eliminate artificial strain energy resulting from the resistance of soft tissues' elastic properties during contractions. We validated our proposed model through test simulations, demonstrating its feasibility and its ability to reproduce expected contraction patterns across different mesh resolutions and configurations. Moving forward, future research efforts should prioritize the validation of our model using robust clinical data. Additionally, it is crucial to refine the model by incorporating a more realistic uterus model derived from medical imaging. Furthermore, applying the model to simulate the entire childbirth process holds immense potential for gaining deeper insights into the intricate dynamics of labor.

Multi-scale and multi-physics model of the uterine smooth muscle with mechanotransduction

Preterm labor is an important public health problem. However, the efficiency of the uterine muscle during labor is complex and still poorly understood. This work is a first step towards a model of the uterine muscle, including its electrical and mechanical components, to reach a better understanding of the uterus synchronization. This model is proposed to investigate, by simulation, the possible role of mechanotransduction for the global synchronization of the uterus. The electrical diffusion indeed explains the local propagation of contractile activity, while the tissue stretching may play a role in the synchronization of distant parts of the uterine muscle. This work proposes a multi-physics (electrical, mechanical) and multi-scales (cell, tissue, whole uterus) model, which is applied to a realistic uterus 3D mesh. This model includes electrical components at different scales: generation of action potentials at the cell level, electrical diffusion at the tissue level. It then links these electrical events to the mechanical behavior, at the cellular level (via the intracellular calcium concentration), by simulating the force generated by each active cell. It thus computes an estimation of the intra uterine pressure (IUP) by integrating the forces generated by each active cell at the whole uterine level, as well as the stretching of the tissue (by using a viscoelastic law for the behavior of the tissue). It finally includes at the cellular level stretch activated channels (SACs) that permit to create a loop between the mechanical and the electrical behavior (mechanotransduction). The simulation of different activated regions of the uterus, which in this first "proof of concept" case are electrically isolated, permits the activation of inactive regions through the stretching (induced by the electrically active regions) computed at the whole organ scale. This permits us to evidence the role of the mechanotransduction in the global synchronization of the uterus. The results also permit us to evidence the effect on IUP of this enhanced synchronization induced by the presence of SACs. This proposed simplified model will be further improved in order to permit a better understanding of the global uterine synchronization occurring during efficient labor contractions.

From the stochasticity of molecular processes to the variability of synaptic transmission

The variability of the postsynaptic response following a single action potential arises from two sources: the neurotransmitter release is probabilistic, and the postsynaptic response to neurotransmitter release has variable timing and amplitude. At individual synapses, the number of molecules of a given type that are involved in these processes is small enough that the stochastic (random) properties of molecular events cannot be neglected. How the stochasticity of molecular processes contributes to the variability of synaptic transmission, its sensitivity and its robustness to molecular fluctuations has important implications for our understanding of the mechanistic basis of synaptic transmission and of synaptic plasticity.

Multi-dimensional resolution of elementary Ca2+ signals by simultaneous multi-focal imaging

Elementary events such as puffs and sparks are cytosolic microdomains of Ca2+ from which cellular Ca2+ signals are constructed. Because of the tight localization and fast kinetics of elementary events, imaging studies have been hindered by instrumental limitations of confocal and deconvolution fluorescence microscopy which necessitate compromises between spatial and temporal resolution. Here, we describe a novel, yet simple 'multi-focal' fluorescence microscopy system that employs three high-speed cameras focused at different axial depths to enable 4-dimensional imaging with millisecond resolution. We demonstrate the utility of this system for studies of puffs in Xenopus oocytes by mapping the axial distribution of puff sites, by obtaining measurements of puff amplitudes undistorted by focus error, and by deriving deblurred images that reveal novel sub-micron jumps of Ca2+ release sites.

Determining calcium concentration in heterogeneous model systems using multiple indicators

Intracellular free calcium concentrations ([Ca2+]i) are assessed by measuring indicator fluorescence in entire cells or subcellular regions using fluorescence microscopy. [Ca2+]i is calculated using equations which link fluorescence intensities (or intensity ratios) to calcium concentrations [G. Grynkiewicz, M. Poenie, R.Y. Tsien, A new generation of Ca2+ indicators with greatly improved fluorescence properties, J. Biol. Chem. 260 (1985) 3440-3450]. However, if calcium ions are heterogeneously distributed within a region of interest, then the observed average fluorescence intensity may not reflect average [Ca2+]i. We assessed potential calcium determination errors in mathematical and experimental models consisting of 'low' and 'high' calcium compartments, using indicators with different affinity for calcium. [Ca2+] calculated using average fluorescence intensity was lower than the actual mean concentrations. Low affinity indicators reported higher (more accurate) values than their high affinity counterparts. To estimate compartment dimensions and respective [Ca2+], we extended the standard approach by using different indicator responses to the same [Ca2+]. While two indicators were sufficient to provide a partial characterization of two-compartment model systems, the use of three or more indicators offered full description of the model provided compartmental [Ca2+] were within the indicator sensitivity ranges. These results show that uneven calcium distribution causes underestimation of actual [Ca2+], and offers novel approaches to estimating calcium heterogeneity.

Imaging single-channel calcium microdomains

The Ca(2+) microdomains generated around the mouth of open ion channels represent the basic building blocks from which cytosolic Ca(2+) signals are constructed. Recent improvements in optical imaging techniques now allow these microdomains to be visualized as single channel calcium fluorescence transients (SCCaFTs), providing information about channel properties that was previously accessible only by electrophysiological patch-clamp recordings. We review recent advances in single channel Ca(2+) imaging methodologies, with emphasis on total internal reflection fluorescence microscopy (TIRFM) as the technique of choice for recording SCCaFTs from voltage- and ligand-gated plasmalemmal ion channels. This technique of 'optical patch-clamp recording' is massively parallel, permitting simultaneous imaging of hundreds of channels; provides millisecond resolution of gating kinetics together with sub-micron spatial resolution of channel locations; and is applicable to diverse families of membrane channels that display partial permeability to Ca(2+) ions.

"Optical patch-clamping": single-channel recording by imaging Ca2+ flux through individual muscle acetylcholine receptor channels

We describe an optical technique using total internal reflection fluorescence (TIRF) microscopy to obtain simultaneous and independent recordings from numerous ion channels via imaging of single-channel Ca²⁺ flux. Muscle nicotinic acetylcholine (ACh) receptors made up of αβγδ subunits were expressed in Xenopus oocytes, and single channel Ca²⁺ fluorescence transients (SCCaFTs) were imaged using a fast (500 fps) electron-multiplied c.c.d. camera with fluo-4 as the indicator. Consistent with their arising through openings of individual nicotinic channels, SCCaFTs were seen only when a nicotinic agonist was present in the bathing solution, were blocked by curare, and increased in frequency as roughly the second power of [ACh]. Their fluorescence amplitudes varied linearly with membrane potential and extrapolated to zero at about +60 mV. The rise and fall times of fluorescence were as fast as 2 ms, providing a kinetic resolution adequate to characterize channel gating kinetics; which showed mean open times of 7.9 and 15.8 ms when activated, respectively, by ACh or suberyldicholine. Simultaneous records were obtained from >400 channels in the imaging field, and we devised a novel “channel chip” representation to depict the resultant large dataset as a single image. The positions of SCCaFTs remained fixed (<100 nm displacement) over tens of seconds, indicating that the nicotinic receptor/channels are anchored in the oocyte membrane; and the spatial distribution of channels appeared random without evidence of clustering. Our results extend single-channel TIRFM imaging to ligand-gated channels that display only partial permeability to Ca²⁺, and demonstrate an order-of-magnitude improvement in kinetic resolution. We believe that functional single-channel imaging opens a new approach to ion channel study, having particular advantages over patch-clamp recording in that it is massively parallel, and provides high-resolution spatial information that is inaccessible by electrophysiological techniques.

Optical single-channel recording by imaging Ca2+ flux through individual ion channels: theoretical considerations and limits to resolution

Recent developments in microscopy and fluorescent indicators now make it possible to monitor the activity and localization of membrane ion channels by imaging Ca(2+) flux through individual channels. Such optical approaches have advantages over electrophysiological single-channel techniques in that they are less invasive, provide spatial information and can simultaneously and independently monitor hundreds of channels. However, their kinetic resolution does not yet approach that of patch-clamp recordings. To help understand the processes that determine the temporal resolution and noise level of single-channel Ca(2+) fluorescence signals (SCCaFTs), we simulated the microdomains of Ca(2+) ions and Ca(2+)-bound indicator dye that exist around the mouth of an open channel. Further, as an aid to development of improved optical techniques, we modeled the dependence of the amplitude and kinetics of SCCaFTs on parameters such as the imaging volume, the indicator concentration, affinity and mobility, and the presence of endogenous and exogenous Ca(2+) buffers. The results indicate that under optimal conditions, including the use of confocal or total-internal reflection microscopy to image from sub-femtolitre volumes, SCCaFTs should resolve channel openings as brief as 1ms with a signal-to-noise ratio >10.

A model-independent algorithm to derive Ca2+ fluxes underlying local cytosolic Ca2+ transients

Local intracellular Ca(2+) signals result from Ca(2+) flux into the cytosol through individual channels or clusters of channels. To gain a mechanistic understanding of these events we need to know the magnitude and spatial distribution of the underlying Ca(2+) flux. However, this is difficult to infer from fluorescence Ca(2+) images because the distribution of Ca(2+)-bound dye is affected by poorly characterized processes including diffusion of Ca(2+) ions, their binding to mobile and immobile buffers, and sequestration by Ca(2+) pumps. Several methods have previously been proposed to derive Ca(2+) flux from fluorescence images, but all require explicit knowledge or assumptions regarding these processes. We now present a novel algorithm that requires few assumptions and is largely model-independent. By testing the algorithm with both numerically generated image data and experimental images of sparklets resulting from Ca(2+) flux through individual voltage-gated channels, we show that it satisfactorily reconstructs the magnitude and time course of the underlying Ca(2+) currents.

Optical single-channel recording: imaging Ca2+ flux through individual ion channels with high temporal and spatial resolution

Developments in imaging technology now enable visualization of the functioning of individual ion channels in living cells: something previously possible only by the electrophysiological patch-clamp technique. We review techniques that track channel gating via changes in intracellular [Ca2+] resulting from openings of Ca(2+)-permeable channels. Spatial and temporal resolution are optimized by monitoring Ca2+ close to the channel mouth, and we describe the use of two imaging modalities: confocal laser scan microscopy (linescan CLSM) and total internal reflection fluorescence microscopy (TIRFM). Both currently achieve a kinetic resolution of <10 ms, provide a simultaneous and independent readout from many channels, and enable their locations to be mapped with submicrometer resolution. TIRFM provides 2-D images from a very thin (approximately 100 nm) optical section, but it is restricted to channels in the plasma membrane of cells adhering close to a cover glass. In contrast, CLSM can image channels in intracellular membranes but, to achieve good temporal resolution, has been utilized only in a linescan mode with limited spatial information. We anticipate that imaging techniques will develop as a useful adjunct to patch-clamping for single-channel studies, with capabilities including simultaneous readout from multiple channels, high-resolution mapping of channel location, and mobility that is inaccessible by electrophysiological means. Optical single-channel recording is applicable to diverse voltage- and ligand-gated Ca(2+)-permeable channels and has potential for high-throughput functional analysis.

Using total fluorescence increase (signal mass) to determine the Ca2+ current underlying localized Ca2+ events

The feasibility of determining localized Ca(2+) influx using only wide-field fluorescence images was explored by imaging (using fluo-3) single channel Ca(2+) fluorescence transients (SCCaFTs), due to Ca(2+) entry through single openings of Ca(2+)-permeable ion channels, while recording unitary channel currents. Since the image obtained with wide-field optics is an integration of both in-focus and out-of-focus light, the total fluorescence increase (DeltaF(total) or "signal mass") associated with a SCCaFT can be measured directly from the image by adding together the fluorescence increase due to Ca(2+) influx in all of the pixels. The assumptions necessary for obtaining the signal mass from confocal linescan images are not required. Two- and three-dimensional imaging was used to show that DeltaF(total) is essentially independent of the position of the channel with respect to the focal plane of the microscope. The relationship between Ca(2+) influx and DeltaF(total) was obtained using SCCaFTs from plasma membrane caffeine-activated cation channels when Ca(2+) was the only charge carrier of the inward current. This relationship was found to be linear, with the value of the slope (or converting factor) affected by the particular imaging system set-up, the experimental conditions, and the properties of the fluorescent indicator, including its binding capacity with respect to other cellular buffers. The converting factor was used to estimate the Ca(2+) current passing through caffeine-activated channels in near physiological saline and to estimate the endogenous buffer binding capacity. In addition, it allowed a more accurate estimate of the Ca(2+) current underlying Ca(2+) sparks resulting from Ca(2+) release from intracellular stores via ryanodine receptors in the same preparation.