Multi-disciplinary approaches
quantify and model calcium signaling
in nervous systems and beyond

Online Workshop, CNS*2020 Meeting
July 21, 2020; 9.30am -- 5pm (Berlin Time, CET)
July 22, 2020; 10am -- 5.30pm (Berlin Time, CET)


Watch the recorded talks:

Day 1/Morning Session. Ragajopal, Tilunaite, Semyanov, Brazhe, Savtchenko.

Day 1/Afternoon Session. Friedrich, Schultz, Aljadeff, Graupner.

Day 2/Morning Session. Sneyd, Means, Skupin, Thul, Falcke, Siekmann, Cao.

Day 2/Afternoon Session. Ullah, Giovannucci, Ponce Dawson, Cresswell-Clay, Agarwal.

Talk Abstracts (by speaker's name in alphabetical order)

Amit Agarwal, Heidelberg University, Germany
Decoding cytosolic and mitochondrial calcium dynamics in astrocytes

We discovered that the transient opening of the mitochondrial permeability transition pore induces spatially restricted Ca2+ transients in astrocytes processes, providing a means to link astrocyte respiration rates and Ca2+ dependent effector pathways. However, the cross talk between cytosolic and mitochondrial Ca2+ signals in astrocytes still remains elusive. To simultaneously record and characterize cytosolic and mitochondrial Ca2+ dynamics, we have developed novel transgenic mouse lines and AAV based viral approach to express various fluorescent proteins as well as genetically encoded Ca2+ indicator in various astrocytic compartments. Additionally, to automatically segment mitochondria and study the structural and Ca2+dynamics, we developed a machine-learning based algorithm called mito-CaSCaDe. Using 2-photon microscopy based Ca2+ imaging, we found that mitochondria exhibit spontaneous fluctuations in matrix Ca2+ and the bath application of neuromodulators induced long-lasting Ca2+ transients in mitochondria. In this workshop, I will discuss our new results that are helping us to decipher the role of astrocyte Ca2+ signals in the cytosol and mitochondria in shaping astrocyte functions in the brain.

Johnatan Aljadeff, University of California at San Diego, USA
Synaptic plasticity rules with physiological calcium levels

Like many forms of long-term synaptic plasticity, spike-timing-dependent plasticity (STDP) depends on intracellular Ca2+ signaling for its induction. Yet, all in vitro studies devoted to STDP used abnormally high external Ca2+ concentration. Using a combination of experimental (patch-clamp recording and Ca2+ imaging at CA3-CA1 synapses) and theoretical (Ca2+ based plasticity model) approaches, we show here that the classic STDP rules in which pairs of single pre- and post-synaptic action potentials induce synaptic modifications is not valid in the physiological Ca2+ range. Rather, we found that these pairs of single stimuli are unable to induce any synaptic modification in physiological conditions. Plasticity can only be triggered when bursts of post-synaptic spikes are used, or when neurons fire at sufficiently high frequency. In conclusion, the STDP rule is profoundly altered in physiological Ca2+ but specific activity regimes restore a classical STDP profile.

Alexey Brazhe, Lomonosov Moscow State University, Russia
Patterns of astrocytic Ca2+ activity: from imaging to modeling and back

Intracellular calcium is a convenient measurable indicator of astroglial signaling and active involvement in information processing and regulatory pathways in the CNS. Many laboratories are rapidly accumulating astrocyte calcium imaging data in different modalities, with a global trend towards behaving animal experiments. This creates a demand for astrocyte-oriented data processing and analysis frameworks. Current best performing algorithms for analysis of calcium imaging data are neuron-oriented and rely on stationary, stable, separable spatial sources prior. Astrocytes are less predictable with regards to spatial or temporal characteristics of their calcium activity, displaying patterns from spatially confined microdomains to spreading events to large-scale waves. I will present our in-the-making approach to denoising and description of astrocytic calcium imaging data, addressing event-oriented, continuous, and network-level features in ex vivo and in vivo settings. Further insights into physical principles and molecular mechanisms underlying astroglial calcium dynamics may come from mathematical modeling. I will describe our spatially extended modeling framework, which can be employed to this end, and will present patterns of calcium dynamics simulated with this model set.

Pengxing Cao, School of Mathematics and Statistics, University of Melbourne, Australia
Modelling inositol trisphosphate receptor-mediated calcium oscillations

Oscillations in cytoplasmic calcium concentration ([Ca2+]), mediated by repetitive openings and closings of inositol trisphosphate receptor (IP3R) channels situated on the membrane of the endo/sarcoplasmic reticulum, have been found to be important for modulating many physiological processes. Decades of effort has been made to elucidate the mechanisms of such calcium oscillations, focusing on understanding (1) the dynamical properties of single IP3R in response to binding of various ligands, such as IP3, Ca2+ and ATP; and (2) how the IP3R dynamics contribute to the formation of calcium oscillations. In this talk, I will present how we used mathematical modelling and simulations to advance our understanding of the problems. The talk will be focused on three aspects: (1) the introduction of a mathematical model of IP3R which we established through fitting to single channel measurements; (2) stochastic simulation of localized calcium puffs using our IP3R model; and (3) deterministic approximation of stochastic modeling in the application of predicting calcium oscillations in airway smooth muscle cells. Finally, I will post some existing challenges for modeling calcium oscillations, which would inspire more constructive discussions at the workshop.

Silvina Ponce Dawson, Department of Physics, FCEN-UBA & IFIBA, CONICET-UBA, University of Buenos Aires, Argentina
Calcium release through IP3 receptors equips cells with a fast way to reprogram intracellular calcium signals

Many intracellular calcium signals involve calcium release into the cytosol through inositol 1,4,5-trisphosphate (IP3) receptors (IP3Rs)/calcium channels. IP3Rs need to bind calcium and IP3 to become open. Thus, IP3R-mediated calcium signals can spread through calcium-induced calcium release (CICR) in which the calcium released through an open channel induces the opening of neighboring ones. IP3Rs, however, are also inhibited by high calcium concentrations. This implies that IP3Rs act as "coincidence" detectors where the timing between the relative increase of IP3 and calcium in their vicinity leads to signals that can propagate or remain spatially localized. The nature of the resulting signal has implications for the subsequent end response. Thus, IP3R-mediated calcium release equips cells with a fast way to reprogram their responses. In this talk I will show modeling results that highlight the role of this mechanism in synaptic plasticity. In particular, I will show how the co-existence of different types of changes in homo- and hetero-synapses induced by different protocols can be explained in terms of the differential way in which the IP3 and calcium concentrations increase and how this impacts on the resulting intracellular calcium signal being propagating or not.

Evan Cresswell-Clay* and Maurizio De Pittà, *National Institute of Health, USA and the Basque Center of Applied Mathematics, Spain
Exploring the origin of spatiotemporal patterns of glial calcium by a compartmental model of astrocytic physiology

The growing recognition of spatial compartmentalization of intracellular calcium signals in glial cells such as astrocytes, is regarded as a potential biophysical correlate for the many functions that those cells could fulfill. Nonetheless, we currently miss any understanding of the biophysical mechanisms underpinning such compartmentalization. We present work in progress on an in silico model of astrocytic calcium signaling that combines diffusion of calcium with reaction-diffusion of inositol 1,4,5-trisphosphate. Consideration of different elemental branching configurations allows identification by analytical and numerical approaches of a variety of constraints of cell’s anatomy for the emergence of spatially-confined calcium dynamics.

Martin Falcke, Max Delbrück Center for Molecular Medicine Berlin, Germany
Modelling concepts for IP3-induced Ca2+ signaling

The task of theory in cell biology is to predict behavior from system parameters. The general features of IP3-induced Ca2+ spiking we find experimentally are: (1) interspike intervals are random; (2) cell-to-cell variability is very large; (3) the agonist concentration-response relation of the average interspike interval is exponential; (4) the moment relation between the average interspike interval and its standard deviation is linear; (5) the moment relation and the agonist sensitivity are cell type and pathway-specific and not subject to cell variability. Identification of the mathematical structure to which a system corresponds is the first and most important step in the development of a theory. The mathematical (some say dynamical) structure corresponding to IP3-induced Ca2+ signaling is an array of noisy excitable (maybe bistable) elements coupled by a diffusion process. There is strong coupling within clusters and weak coupling between clusters. Global feedbacks and processes set long time scales. Starting from there, we can develop a simple theory showing the moment relation and its robustness properties. We find that on a single-cell level in several cases, long time scales may arise from small spike probabilities and not from slow processes, but slow processes are required to obtain a small coefficient of variation for the interspike interval.

Johannes Friedrich, Simons Foundation, USA
Online methods for real-time analysis of calcium imaging data

Calcium imaging methods enable researchers to measure the activity of genetically-targeted large-scale neuronal populations. Whereas earlier methods required the specimen to be stable, e.g. anesthetized or head-fixed, new brain imaging techniques using microendoscopic lenses and miniaturized microscopes have enabled deep brain imaging in freely moving mice. Previously, a constrained matrix factorization approach (CNMF) has been suggested to extract the activity of the imaged neuronal sources. It has been extended further to handle the very large background fluctuations in microendoscopic data (CNMF-E). However, both approaches rely on offline batch processing of the entire video data and are demanding both in terms of computing and memory requirements, in particular CNMF-E. Moreover, in some scenarios we want to perform experiments in real-time and closed-loop -- analyzing data on-the-fly to guide the next experimental steps or to control feedback --, and this calls for new methods for accurate real-time processing. Here we address both issues by introducing an online framework for the analysis of streaming calcium imaging data, including i) motion artifact correction, ii) neuronal source extraction, and iii) activity denoising and deconvolution. Extending previous work on online dictionary learning and calcium imaging data analysis, we first present online adaptations of the CNMF as well as the CNMF-E algorithm, which dramatically reduces memory and computation requirements. Secondly, we propose an algorithm that uses a convolution-based background model for microendoscopic data that enables even faster (real time) processing on GPU hardware. We apply our algorithms on a variety of experimental datasets that employ 2-photon, lightsheet, and microendoscopic imaging techniques, and show that they yield similar high-quality results as the popular offline approaches, but outperform them with regard to computing time and memory requirements. Our algorithms enable faster and scalable analysis, and open the door to new closed-loop experiments.

Andrea Giovannucci, UNC Chapel Hill/North Carolina State University, USA
Enabling real-time brain-machine interfaces via tensor-based computing

While optical methods, genetically encoded fluorescence indicators, and optogenetics already enable fast readout and control of large neuronal populations using light, the lack of corresponding advances in computational algorithms have slowed progress. The fundamental challenge is to reliably extract spikes (neural activity) from fluorescence imaging frames at speeds surpassing the indicator dynamics. To meet these challenges, we devised a set of new algorithms that exploit tensor-based computing on accelerated hardware. We provide optimized motion correction, source extraction and spike detection operations, which for the first time operate at speeds comparable with brain internal communication. We evaluate these algorithms on ground truth data and large datasets, demonstrating reliable and scalable performance. This provides the computational substrates required to interface precisely large neuronal populations and machines in real-time, enabling new applications in neuroprosthetics, brain machine interfaces, and experimental neuroscience.

Michael Graupner, Université de Paris, CNRS, SPPIN, France
Calcium as trigger of synaptic plasticity

Multiple stimulation protocols have been found to be effective in changing synaptic efficacy by inducing long-term potentiation or depression. In many of those protocols, increases in postsynaptic calcium concentration have been shown to play a crucial role. Here, we discuss a calcium-based model of a synapse in which potentiation and depression are activated whenever calcium crosses distinct thresholds. We show that this model gives rise to a large diversity of spike timing-dependent plasticity curves, most of which have been observed experimentally in different systems. Moreover, we use the model to investigate synaptic changes elicited by in vivo-like firing, where cells fire irregularly and the timing between pre- and postsynaptic spikes varies. We show that the influence of spike-timing on plasticity is weaker than expected from regular stimulation protocols. The model provides a mechanistic understanding of how various stimulation protocols provoke specific synaptic changes through the dynamics of calcium concentration and thresholds implementing in simplified fashion protein signaling cascades, leading to long-term potentiation and long-term depression.

Shawn Means, School of Natural and Computer Sciences, Massey University, New Zealand
Calcium signaling in cellular space

Space – the not-so-final frontier. Cellular systems, ranging from atrial tissue, to gastro-intestinal cellular walls, and salivary glands, all exploit spatial distributions of signaling mechanisms. I will present investigations of arrangements for calcium (Ca2+) transporters within varied geometric configurations for several cell types, illustrating the importance for the cellular spatial frontier. For instance, arrangements of Ca2+ release sites (ryanodine receptor in the cardiac tissue, inositol trisphosphate in other tissues) lead to either waves of Ca2+ disrupting coupled electrical control, essential depletions of endoplasmic reticulum Ca2+ reservoirs triggering pacemaking contractions, or cell-wide spatially organised induction of ion and fluid transport. These studies were all performed computationally, exploiting the precision available to mathematical and computing methods complementing experimental techniques for teasing out the subtle and important influence of space.

Vijai Rajagopal, University of Melbourne, AUS
Elucidating the role of cell architecture and its remodeling in maintain a healthy heartbeat using high-resolution 3D computational models

When an aspiring athlete builds cardiac endurance, when a mom-to-be is pregnant and as we all grow and age from tiny embryos into adults, the heart has to generate enough force to pump the blood that the body needs to supply oxygen and nutrients to sustain life. The heart’s ability to pump blood to the rest of the body is determined by the coordinated contraction of millions of its constituent cardiac cells. Soon after completion of embryonic development and formation of the heart, cardiac cells lose their ability to divide and multiply. Therefore, the only way that the heart can increase its force of contraction and capacity to meet long-term increases in demand for blood supply through most of life is by increasing the size and re-arranging the internal components of each cardiac cell to accommodate more force generating proteins within them. These architectural changes at the cellular level are referred to as cell remodeling and little is known about the biophysical mechanisms that drive this important process of life and how changes to cell architecture impact on cardiac cell signaling and the heartbeat. In this talk I will present our recent findings on the role that spatial organization of cardiac cell signaling proteins and organelles have on in maintaining a healthy heartbeat. I will demonstrate how we can gain quantitative insights on the contribution of sub-cellular organization to cell function using 3D computational models of the cell’s subcellular architecture and the signaling processes that are derived from microscopy data. I will also briefly outline our vision for making spatially detailed models useful for drug-discovery applications.

Leonid Savtchenko & Dimitri Rusakov, Queen Square Institute of Neurology, University College London, UK
Cloud-based parallel computing of cellular dynamics in a realistic model of astroglia

Modelling the dynamics of cellular processes in astrocytes with their realistic, highly complex geometry has been a challenge. We have developed a NEURON-Python-based modelling platform ASTRO that enables parallel processing of cellular signalling within a recreated astrocyte shape using the Amazon Web Service. ASTRO offers versatile exploration of cell membrane physiology and spatiotemporal calcium dynamics, including multicomponent diffusion-reaction, against multi-disciplinary experimental data. The platform enables users to parallelise the process of calculating intracellular calcium dynamics depending on the availability of computing nodes, virtual machine memory and cloud service elasticity. Our preliminary results indicate that having built-in tuning options is likely to be the most efficient way to tackle the configuration of virtual machines aiming at the fastest and budget-efficient computations.

Simon Schultz, Centre for Neurotechnology and Department of Bioengineering, Imperial College London, UK
Multiphoton imaging of calcium signals in populations of hippocampal neurons during behaviour in mouse models of neurodegenerative disorders

The hippocampus plays an important role in learning, memory and spatial navigation, impairments of which are typically among the first symptoms of Alzheimer’s Disease. Structural abnormalities, amyloid plaques, and aberrant neuronal excitability appear in disease-affected hippocampi, resulting in abnormal activity visible through multiphoton calcium imaging of the hippocampus. We imaged calcium signals in populations of CA1 hippocampal neurons in 5xFAD transgenic mice and wildtype littermates following viral transduction of the hippocampus with hSyn1-GCaMP6s-mRuby. Mice were head-fixed and trained to run along a circular linear track lined with visuotactile cues, floating on an air table (Neurotar Ltd). The three-dimensional distribution of amyloid plaques was mapped following i.p. injection of Methoxy-X04 by acquiring depth stacks at 720 nm excitation. On each imaging session on subsequent days, calcium signals were monitored in several hundred CA1 neurons within 500 x 500 µm field of view. We took advantage of the activity-independent red channel (mRuby) information for motion-correction using a non-rigid deformation algorithm. Imaging files were collected in 4 min sections, for ~20 min periods in which the mouse ran in a single environment; several environments were imaged per session. Regions of interest corresponding to individual neurons were cross-registered across files, environments, sessions and days, with in some cases cells being tracked through imaging sessions for up to 14 days. We were able to observe features of CA1 activity reminiscent of electrophysiological recordings in freely moving animals, including well-defined place fields, phase-precession of place fields, and place field remapping. In contrast, place fields in a two-dimensional version of the task were impoverished, presumably due to the lack of vestibular input in the head-fixed preparation. In ongoing work, we are using this preparation to study the circuit basis of impairments in learning and memory in the 5xFAD model, as well as to test therapeutic strategies.

Alexey Semyanov, Shemyakin and Ovchinnikov Institute of Bioorganic Chemistry, Russian Academy of Sciences, Moscow, Russia
Spatiotemporal properties of Ca2+ activity in single astrocytes and astrocytic networks

Ivo Siekmann, Department of Applied Mathematics, Liverpool John Moores University, UK
Statistical analysis and data-driven modeling of type 1 and type 2 IP3 receptors

Patch clamp recordings enable us to watch a single inositol-trisphosphate receptor (IP3R) in action. At first glance we only see that the IP3R opens and closes stochastically but a closer look reveals that the channel alternates between two different levels of activity – a highly active mode where the IP3R opens and closes frequently and a nearly inactive mode in which the channel is mostly closed. Applying statistical change point analysis to the most comprehensive single channel data set currently available highlights the importance of this observation: We find that the dynamics of the IP3R is entirely regulated by switching between these two modes. In order to build a mathematical model based on this underlying principle the hierarchical Markov model is developed and then fitted to type 1 and type 2 IP3R data for a wide range of concentrations of IP3R, Ca2+ and ATP. I will present this model and will especially emphasize the insights in the biophysics of the IP3R that were gained along the way.

Alexander Skupin, University of Luxembourg, Luxembourg
Calcium: a mediator between metabolism and cell fate


James Sneyd, The University of Auckland, New Zealand
Modeling calcium signaling in live animals

The vast majority of previous experimental and theoretical work on calcium signalling has been in cell lines, cultured cells, or, more recently, in whole organs. The underlying assumption of these studies is that the mechanisms that control calcium signalling in a live animal are essentially similar, and one can extrapolate from one to the other. Although this assumption is, to a large extent, valid and useful, recent measurements of cytosolic calcium oscillations in salivary acinar cells from a live mouse have necessitated a major rethink of the mechanisms underlying whole-cell calcium responses and water transport in salivary cells. We shall present these new experimental data, and show how previous models have needed to be significantly modified in order to understand and explain these new results.

Ghanim Ullah, University of South Florida, USA
Analyzing and modeling the kinetics and evolution of Ca2+-permeable β amyloid pores associated with Alzheimer’s disease

Extensive evidence implicates cation-permeable plasma membrane pores formed by oligomeric forms of β amyloid (Aβ) in cytotoxicity during Alzheimer’s disease (AD) [Ullah et al., PLoS One, 2015, 10(9); Demuro et al., J. Cell. Biol. 2011, 195(2):515-524]. We use total internal reflection fluorescence microscopy (TIRFM) to monitor the Ca2+ flux through these pores, revealing detailed information about their gating kinetics and time evolution. This massively parallel imaging technique provides simultaneous and independent recording from thousands of pores in a patch of membrane of living cells for extended time. Manual analysis of these data consisting of tens of thousands of image frames is very challenging. Thus, we developed a pipeline of computational tools to retrieve, analyze, and predict the behavior of these pores at extended timescales to shed light on their toxicity and better understand disease progression [Shah et al., Biophys. J. 2018, 115(1):9-21; Biophys. J. 2018, 114(3):291a]. Analyzing the imaging data includes detection of pores, generating their location maps, tracking their movement, retrieval of time series data for each pore, separating signal from noisy and drifting background, and extracting the key statistics about their gating kinetics and evolution. The information extracted from tens of thousands of pores is used to develop Markov chain models in order to understand and correlate their kinetics and long-term behavior with cytotoxicity. This talk will give an overview of the tools mentioned above, our current understanding of Aβ pores, and their implications for intracellular Ca2+ signaling.

Agne Tilūnaitė, School of Mathematics and Statistics, University of Melbourne, Australia
Inositol trisphosphate receptors can increase calcium spark activity in cardiomyocyte dyads without altering signal shape

Calcium signals perform integral roles in cardiac cells, coordinating each heartbeat and regulating the biochemical reactions that control growth. Inositol 1,4,5-triphosphate receptors (IP3Rs) are intracellular calcium channels that are known to influence these processes during cellular hypertrophy. Recent protein localisation experiments suggest IP3Rs may exist in close proximity to ryanodine receptors (RyRs), the channels primarily responsible for the flood of calcium from intracellular stores (sparks) during calcium-induced calcium release. In this study, we seek to untangle the contribution of IP3Rs to spark formation. We develop mathematical models incorporating the stochastic behavior of opening receptors that allow for the parametric tuning of the system to reveal the impact of IP3Rs on spark activation. By testing multiple spark initiation mechanisms, we find that consistently opening (“leaky”) IP3Rs can result in spark initiation more reliably than intermittently opening IP3Rs. We also find that while increasing numbers of IP3Rs increase the probability of formation of a spark, they have little impact on its resultant amplitude, duration, or overall shape.

Ruediger Thul, The University of Nottingham, UK
Antipodes of calcium signalling: subcellular microdomains and whole cell calcium spikes

There is now compelling evidence that subcellular signalling microdomains are crucial for encoding and relaying calcium (Ca2+) signals. The STIM-Orai system constitutes a critical illustration of this concept. Upon depletion of the endoplasmic reticulum (ER), both proteins move to so-called ER-PM junctions, where the plasma membrane (PM) closely apposes the ER membrane with a separation of approximately 15nm. I will present the first three-dimensional model of such ER-PM junctions and will show how the spatial organisation of Orai channels in the PM and Ca2+ pumps in the ER membrane shape the local Ca2+ signature in a non-trivial manner, which has direct consequences for downstream Ca2+ signalling. The coordination of Ca2+ increases in such microdomains can lead to whole cell Ca2+ oscillations. Given their intrinsic stochasticity, we have pursued a statistical analysis of Ca2+ spikes using concepts from stochastic point processes and Bayesian inference. I will show how we can quantify Ca2+ spiking at the single cell level in the presence of dynamic stimulation. This will not only move us closer to characterizing the role of cellular heterogeneity in Ca2+ signalling, but will also highlight how we can use whole-cell Ca2+ signals to infer properties of the subcellular Ca2+ signalling toolkit.