Translating intracellular calcium signaling into models

Kappa opioids inhibit spinal output neurons to suppress itch

Itch is a protective sensation that drives scratching. Although specific cell types have been proposed to underlie itch, the neural basis for itch remains unclear. Here, we used two-photon Ca2+ imaging of the dorsal horn to visualize neuronal populations that are activated by itch-inducing agents. We identify a convergent population of spinal interneurons recruited by diverse itch-causing stimuli that represents a subset of neurons that express the gastrin-releasing peptide receptor (GRPR). Moreover, we find that itch is conveyed to the brain via GRPR-expressing spinal output neurons that target the lateral parabrachial nuclei. We then show that the kappa opioid receptor agonist nalfurafine relieves itch by selectively inhibiting GRPR spinoparabrachial neurons. These experiments provide a population-level view of the spinal neurons that respond to pruritic stimuli, pinpoint the output neurons that convey itch to the brain, and identify the cellular target of kappa opioid receptor agonists for the inhibition of itch.

Identification of a convergent spinal neuron population that encodes itch

Itch is a protective sensation that drives scratching. Although specific cell types have been proposed to underlie itch, the neural circuit basis for itch remains unclear. Here, we used two-photon Ca2+ imaging of the dorsal horn to visualize the neuronal populations that are activated by itch-inducing agents. We identify a convergent population of spinal neurons that is defined by the expression of GRPR. Moreover, we discover that itch is conveyed to the brain via GRPR-expressing spinal output neurons that target the lateral parabrachial nucleus. Further, we show that nalfurafine, a clinically effective kappa opioid receptor agonist, relieves itch by inhibiting GRPR spinoparabrachial neurons. Finally, we demonstrate that a subset of GRPR spinal neurons show persistent, cell-intrinsic Ca2+ oscillations. These experiments provide the first population-level view of the spinal neurons that respond to pruritic stimuli, pinpoint the output neurons that convey itch to the brain, and identify the cellular target of kappa opioid receptor agonists for the inhibition of itch.

The Oscillation Amplitude, Not the Frequency of Cytosolic Calcium, Regulates Apoptosis Induction

Although a rising concentration of cytosolic Ca²⁺ has long been recognized as an essential signal for apoptosis, the dynamical mechanisms by which Ca²⁺ regulates apoptosis are not clear yet. To address this, we constructed a computational model that integrates known biochemical reactions and can reproduce the dynamical behaviors of Ca²⁺-induced apoptosis as observed in experiments. Model analysis shows that oscillating Ca²⁺ signals first convert into gradual signals and eventually transform into a switch-like apoptotic response. Via the two processes, the apoptotic signaling pathway filters the frequency of Ca²⁺ oscillations effectively but instead responds acutely to their amplitude. Collectively, our results suggest that Ca²⁺ regulates apoptosis mainly via oscillation amplitude, rather than frequency, modulation. This study not only provides a comprehensive understanding of how oscillatory Ca²⁺ dynamically regulates the complex apoptotic signaling network but also presents a typical example of how Ca²⁺ controls cellular responses through amplitude modulation.

GPCR mediated control of calcium dynamics: A systems perspective

G-protein coupled receptor (GPCR) mediated calcium (Ca²⁺)-signaling transduction remains crucial in designing drugs for various complex diseases including neurodegeneration, chronic heart failure as well as respiratory diseases. Although there are several reviews detailing various aspects of Ca²⁺-signaling such as the role of IP₃ receptors and Ca²⁺-induced-Ca²⁺-release, none of them provide an integrated view of the mathematical descriptions of GPCR signal transduction and investigations on dose-response curves. This article is the first study in reviewing the network structures underlying GPCR signal transduction that control downstream [Ca_c²⁺]-oscillations. The central theme of this paper is to present the biochemical pathways, as well as molecular mechanisms underlying the GPCR-mediated Ca²⁺-dynamics in order to facilitate a better understanding of how agonist concentration is encoded in Ca²⁺-signals for G_αq, G_αs, and G_αi/o signaling pathways. Moreover, we present the GPCR targeting drugs that are relevant for treating cardiac, respiratory, and neuro-diseases. The current paper presents the ODE formulation for various models along with the detailed schematics of signaling networks. To provide a systems perspective, we present the network motifs that can provide readers an insight into the complex and intriguing science of agonist-mediated Ca²⁺-dynamics. One of the features of this review is to pinpoint the interplay between positive and negative feedback loops that are involved in controlling intracellular [Ca_c²⁺]-oscillations. Furthermore, we review several examples of dose-response curves obtained from [Ca_c²⁺]-spiking for various GPCR pathways. This paper is expected to be useful for pharmacologists and computational biologists for designing clinical applications of GPCR targeting drugs through modulation of Ca²⁺-dynamics.

Structural Mechanisms of Store-Operated and Mitochondrial Calcium Regulation: Initiation Points for Drug Discovery

Calcium (Ca2+) is a universal signaling ion that is essential for the life and death processes of all eukaryotes. In humans, numerous cell stimulation pathways lead to the mobilization of sarco/endoplasmic reticulum (S/ER) stored Ca2+, resulting in the propagation of Ca2+ signals through the activation of processes, such as store-operated Ca2+ entry (SOCE). SOCE provides a sustained Ca2+ entry into the cytosol; moreover, the uptake of SOCE-mediated Ca2+ by mitochondria can shape cytosolic Ca2+ signals, function as a feedback signal for the SOCE molecular machinery, and drive numerous mitochondrial processes, including adenosine triphosphate (ATP) production and distinct cell death pathways. In recent years, tremendous progress has been made in identifying the proteins mediating these signaling pathways and elucidating molecular structures, invaluable for understanding the underlying mechanisms of function. Nevertheless, there remains a disconnect between using this accumulating protein structural knowledge and the design of new research tools and therapies. In this review, we provide an overview of the Ca2+ signaling pathways that are involved in mediating S/ER stored Ca2+ release, SOCE, and mitochondrial Ca2+ uptake, as well as pinpoint multiple levels of crosstalk between these pathways. Further, we highlight the significant protein structures elucidated in recent years controlling these Ca2+ signaling pathways. Finally, we describe a simple strategy that aimed at applying the protein structural data to initiating drug design.

A simple mechanochemical model for calcium signalling in embryonic epithelial cells

Calcium signalling is one of the most important mechanisms of information propagation in the body. In embryogenesis the interplay between calcium signalling and mechanical forces is critical to the healthy development of an embryo but poorly understood. Several types of embryonic cells exhibit calcium-induced contractions and many experiments indicate that calcium signals and contractions are coupled via a two-way mechanochemical feedback mechanism. We present a new analysis of experimental data that supports the existence of this coupling during apical constriction. We then propose a simple mechanochemical model, building on early models that couple calcium dynamics to the cell mechanics and we replace the hypothetical bistable calcium release with modern, experimentally validated calcium dynamics. We assume that the cell is a linear, viscoelastic material and we model the calcium-induced contraction stress with a Hill function, i.e. saturating at high calcium levels. We also express, for the first time, the "stretch-activation" calcium flux in the early mechanochemical models as a bottom-up contribution from stretch-sensitive calcium channels on the cell membrane. We reduce the model to three ordinary differential equations and analyse its bifurcation structure semi-analytically as two bifurcation parameters vary-the [Formula: see text] concentration, and the "strength" of stretch activation, [Formula: see text]. The calcium system ([Formula: see text], no mechanics) exhibits relaxation oscillations for a certain range of [Formula: see text] values. As [Formula: see text] is increased the range of [Formula: see text] values decreases and oscillations eventually vanish at a sufficiently high value of [Formula: see text]. This result agrees with experimental evidence in embryonic cells which also links the loss of calcium oscillations to embryo abnormalities. Furthermore, as [Formula: see text] is increased the oscillation amplitude decreases but the frequency increases. Finally, we also identify the parameter range for oscillations as the mechanical responsiveness factor of the cytosol increases. This work addresses a very important and not well studied question regarding the coupling between chemical and mechanical signalling in embryogenesis.

Composite mathematical modeling of calcium signaling behind neuronal cell death in Alzheimer's disease

Background

Alzheimer’s disease (AD) is a progressive neurological disorder, recognized as the most common cause of dementia affecting people aged 65 and above. AD is characterized by an increase in amyloid metabolism, and by the misfolding and deposition of β-amyloid oligomers in and around neurons in the brain. These processes remodel the calcium signaling mechanism in neurons, leading to cell death via apoptosis. Despite accumulating knowledge about the biological processes underlying AD, mathematical models to date are restricted to depicting only a small portion of the pathology.

Results

Here, we integrated multiple mathematical models to analyze and understand the relationship among amyloid depositions, calcium signaling and mitochondrial permeability transition pore (PTP) related cell apoptosis in AD. The model was used to simulate calcium dynamics in the absence and presence of AD. In the absence of AD, i.e. without β-amyloid deposition, mitochondrial and cytosolic calcium level remains in the low resting concentration. However, our in silico simulation of the presence of AD with the β-amyloid deposition, shows an increase in the entry of calcium ions into the cell and dysregulation of Ca ²⁺ channel receptors on the Endoplasmic Reticulum. This composite model enabled us to make simulation that is not possible to measure experimentally.

Conclusions

Our mathematical model depicting the mechanisms affecting calcium signaling in neurons can help understand AD at the systems level and has potential for diagnostic and therapeutic applications.

Electronic supplementary material

The online version of this article (10.1186/s12918-018-0529-2) contains supplementary material, which is available to authorized users.

Computational Models for Calcium-Mediated Astrocyte Functions

The computational neuroscience field has heavily concentrated on the modeling of neuronal functions, largely ignoring other brain cells, including one type of glial cell, the astrocytes. Despite the short history of modeling astrocytic functions, we were delighted about the hundreds of models developed so far to study the role of astrocytes, most often in calcium dynamics, synchronization, information transfer, and plasticity in vitro, but also in vascular events, hyperexcitability, and homeostasis. Our goal here is to present the state-of-the-art in computational modeling of astrocytes in order to facilitate better understanding of the functions and dynamics of astrocytes in the brain. Due to the large number of models, we concentrated on a hundred models that include biophysical descriptions for calcium signaling and dynamics in astrocytes. We categorized the models into four groups: single astrocyte models, astrocyte network models, neuron-astrocyte synapse models, and neuron-astrocyte network models to ease their use in future modeling projects. We characterized the models based on which earlier models were used for building the models and which type of biological entities were described in the astrocyte models. Features of the models were compared and contrasted so that similarities and differences were more readily apparent. We discovered that most of the models were basically generated from a small set of previously published models with small variations. However, neither citations to all the previous models with similar core structure nor explanations of what was built on top of the previous models were provided, which made it possible, in some cases, to have the same models published several times without an explicit intention to make new predictions about the roles of astrocytes in brain functions. Furthermore, only a few of the models are available online which makes it difficult to reproduce the simulation results and further develop the models. Thus, we would like to emphasize that only via reproducible research are we able to build better computational models for astrocytes, which truly advance science. Our study is the first to characterize in detail the biophysical and biochemical mechanisms that have been modeled for astrocytes.

Mathematical Techniques for Understanding Platelet Regulation and the Development of New Pharmacological Approaches

Mathematical and computational modeling is currently in the process of becoming an accepted tool in the arsenal of methods utilized for the investigation of complex biological systems. For some problems in the field, like cellular metabolic regulation, neural impulse propagation, or cell cycle, progress is already unthinkable without use of such methods. Mathematical models of platelet signaling, function, and metabolism during the last years have not only been steadily increasing in their number, but have also been providing more in-depth insights, generating hypotheses, and allowing predictions to be made leading to new experimental designs and data. Here we describe the basic approaches to platelet mathematical model development and validation, highlighting the challenges involved. We then review the current theoretical models in the literature and how these are being utilized to increase our understanding of these complex cells.

A Bayesian approach to modelling heterogeneous calcium responses in cell populations

Calcium responses have been observed as spikes of the whole-cell calcium concentration in numerous cell types and are essential for translating extracellular stimuli into cellular responses. While there are several suggestions for how this encoding is achieved, we still lack a comprehensive theory. To achieve this goal it is necessary to reliably predict the temporal evolution of calcium spike sequences for a given stimulus. Here, we propose a modelling framework that allows us to quantitatively describe the timing of calcium spikes. Using a Bayesian approach, we show that Gaussian processes model calcium spike rates with high fidelity and perform better than standard tools such as peri-stimulus time histograms and kernel smoothing. We employ our modelling concept to analyse calcium spike sequences from dynamically-stimulated HEK293T cells. Under these conditions, different cells often experience diverse stimulus time courses, which is a situation likely to occur in vivo. This single cell variability and the concomitant small number of calcium spikes per cell pose a significant modelling challenge, but we demonstrate that Gaussian processes can successfully describe calcium spike rates in these circumstances. Our results therefore pave the way towards a statistical description of heterogeneous calcium oscillations in a dynamic environment.

Upon stimulation a large number of cell types respond with transient increases of the intracellular calcium concentration, which often take the form of repetitive spikes. It is therefore believed that calcium spikes play a central role in cellular signal transduction. A critical feature of these calcium spikes is that they occur randomly, which raises the question of how we can predict the timing of calcium spikes. We here show that by using Bayesian ideas and concepts from stochastic processes, we can quantitatively compute the calcium spike rate for a given stimulus. Our analysis also demonstrates that traditional methods for spike rate estimation perform less favourably compared to a Bayesian approach when small numbers of cells are investigated. To test our methodology under conditions that closely mimic those experienced in vivo we challenged cells with agonist concentrations that vary both in space and time. We find that cells that experience similar stimulus profiles are described by similar calcium spike rates. This suggests that calcium spike rates may constitute a quantitative description of whole-cell calcium spiking that reflects both the randomness and the spatiotemporal organisation of the calcium signalling machinery.