Concise Whole-Cell Modeling of BKCa-CaV Activity Controlled by Local Coupling and Stoichiometry

Biophysical modeling of the whole-cell dynamics of C. elegans motor and interneurons families

The nematode Caenorhabditis elegans is a widely used model organism for neuroscience. Although its nervous system has been fully reconstructed, the physiological bases of single-neuron functioning are still poorly explored. Recently, many efforts have been dedicated to measuring signals from C. elegans neurons, revealing a rich repertoire of dynamics, including bistable responses, graded responses, and action potentials. Still, biophysical models able to reproduce such a broad range of electrical responses lack. Realistic electrophysiological descriptions started to be developed only recently, merging gene expression data with electrophysiological recordings, but with a large variety of cells yet to be modeled. In this work, we contribute to filling this gap by providing biophysically accurate models of six classes of C. elegans neurons, the AIY, RIM, and AVA interneurons, and the VA, VB, and VD motor neurons. We test our models by comparing computational and experimental time series and simulate knockout neurons, to identify the biophysical mechanisms at the basis of inter and motor neuron functioning. Our models represent a step forward toward the modeling of C. elegans neuronal networks and virtual experiments on the nematode nervous system.

Ca2+ release or Ca2+ entry, that is the question: what governs Ca2+ oscillations in pancreatic β cells?

The standard model for Ca2+ oscillations in insulin-secreting pancreatic β cells centers on Ca2+ entry through voltage-activated Ca2+ channels. These work in combination with ATP-dependent K+ channels, which are the bridge between the metabolic state of the cells and plasma membrane potential. This partnership underlies the ability of the β cells to secrete insulin appropriately on a minute-to-minute time scale to control whole body plasma glucose. Though this model, developed over more than 40 years through many cycles of experimentation and mathematical modeling, has been very successful, it has been challenged by a hypothesis that calcium-induced calcium release from the endoplasmic reticulum through ryanodine or inositol trisphosphate (IP3) receptors is instead the key driver of islet oscillations. We show here that the alternative model is in fact incompatible with a large body of established experimental data and that the new observations offered in support of it can be better explained by the standard model.

Machine learning provides insight into models of heterogeneous electrical activity in human beta-cells

Understanding how heterogeneous cellular responses emerge from cell-to-cell variations in expression and function of subcellular components is of general interest. Here, we focus on human insulin-secreting beta-cells, which are believed to constitute a population in which heterogeneity is of physiological importance. We exploit recent single-cell electrophysiological data that allow biologically realistic population modeling of human beta-cells that accounts for cellular heterogeneity and correlation between ion channel parameters. To investigate how ion channels influence the dynamics of our updated mathematical model of human pancreatic beta-cells, we explore several machine learning techniques to determine which model parameters are important for determining the qualitative patterns of electrical activity of the model cells. As expected, K^＋ channels promote absence of activity, but once a cell is active, they increase the likelihood of having action potential firing. HERG channels were of great importance for determining cell behavior in most of the investigated scenarios. Fast bursting is influenced by the time scales of ion channel activation and, interestingly, by the type of Ca^2＋ channels coupled to BK channels in BK-CaV complexes. Slow, metabolically driven oscillations are promoted mostly by K(ATP) channels. In summary, combining population modeling with machine learning analysis provides insight into the model and generates new hypotheses to be investigated both experimentally, via simulations and through mathematical analysis.

Structural and Functional Coupling of Calcium-Activated BK Channels and Calcium-Permeable Channels Within Nanodomain Signaling Complexes

Biochemical and functional studies of ion channels have shown that many of these integral membrane proteins form macromolecular signaling complexes by physically associating with many other proteins. These macromolecular signaling complexes ensure specificity and proper rates of signal transduction. The large-conductance, Ca²⁺-activated K⁺ (BK) channel is dually activated by membrane depolarization and increases in intracellular free Ca²⁺ ([Ca²⁺]_i). The activation of BK channels results in a large K⁺ efflux and, consequently, rapid membrane repolarization and closing of the voltage-dependent Ca²⁺-permeable channels to limit further increases in [Ca²⁺]_i. Therefore, BK channel-mediated K⁺ signaling is a negative feedback regulator of both membrane potential and [Ca²⁺]_i and plays important roles in many physiological processes and diseases. However, the BK channel formed by the pore-forming and voltage- and Ca²⁺-sensing α subunit alone requires high [Ca²⁺]_i levels for channel activation under physiological voltage conditions. Thus, most native BK channels are believed to co-localize with Ca²⁺-permeable channels within nanodomains (a few tens of nanometers in distance) to detect high levels of [Ca²⁺]_i around the open pores of Ca²⁺-permeable channels. Over the last two decades, advancement in research on the BK channel’s coupling with Ca²⁺-permeable channels including recent reports involving NMDA receptors demonstrate exemplary models of nanodomain structural and functional coupling among ion channels for efficient signal transduction and negative feedback regulation. We hereby review our current understanding regarding the structural and functional coupling of BK channels with different Ca²⁺-permeable channels.

Chronic stress facilitates bursting electrical activity in pituitary corticotrophs

Coordination of an appropriate stress response is dependent upon anterior pituitary corticotroph excitability in response to hypothalamic secretagogues and glucocorticoid negative feedback. A key determinant of corticotroph excitability is large conductance calcium- and voltage-activated (BK) potassium channels that are critical for promoting corticotrophin-releasing hormone (CRH)-induced bursting that enhances adrenocorticotrophic hormone secretion. Previous studies revealed hypothalamic-pituitary-adrenal axis hyperexcitability following chronic stress (CS) is partly a function of increased corticotroph output. Thus, we hypothesise that chronic stress promotes corticotroph excitability through a BK-dependent mechanism. Corticotrophs from CS mice displayed significant increase in spontaneous bursting, which was suppressed by the BK blocker paxilline. Mathematical modelling reveals that the time constant of BK channel activation, plus properties and proportion of BK channels functionally coupled to L-type Ca²⁺ channels determines bursting activity. Surprisingly, CS corticotrophs (but not unstressed) display CRH-induced bursting even when the majority of BK channels are inhibited by paxilline, which modelling suggests is a consequence of the stochastic behaviour of a small number of BK channels coupled to L-type Ca²⁺ channels. Our data reveal that changes in the stochastic behaviour of a small number of BK channels can finely tune corticotroph excitability through stress-induced changes in BK channel properties. Importantly, regulation of BK channel function is highly context dependent allowing dynamic control of corticotroph excitability over a large range of time domains and physiological challenges in health and disease. This is likely to occur in other BK-expressing endocrine cells, with important implications for the physiological processes they regulate and the potential for therapy. KEY POINTS: Chronic stress (CS) is predicted to modify the electrical excitability of anterior pituitary corticotrophs. Electrophysiological recordings from isolated corticotrophs from CS male mice display spontaneous electrical bursting behaviour compared to the tonic spiking behaviour of unstressed corticotrophs. The increased spontaneous bursting from CS corticotrophs is BK-dependent and mathematical modelling reveals that the time constant of activation, properties and proportion of BK channels functionally coupled to L-type calcium channels determines the promotion of bursting activity. CS (but not unstressed) corticotrophs display corticotrophin-releasing hormone-induced bursting even when the majority of BK channels are pharmacologically inhibited, which can be explained by the stochastic behaviour of a small number of BK channels with distinct properties. Corticotroph excitability can be finely tuned by the stochastic behaviour of a small number of BK channels dependent on their properties and functional co-localisation with L-type calcium channels to control corticotroph excitability over diverse time domains and physiological challenges.

The effects of beta-cell mass and function, intercellular coupling, and islet synchrony on [Formula: see text] dynamics

Type 2 diabetes (T2D) is a challenging metabolic disorder characterized by a substantial loss of [Formula: see text]-cell mass and alteration of [Formula: see text]-cell function in the islets of Langerhans, disrupting insulin secretion and glucose homeostasis. The mechanisms for deficiency in [Formula: see text]-cell mass and function during the hyperglycemia development and T2D pathogenesis are complex. To study the relative contribution of [Formula: see text]-cell mass to [Formula: see text]-cell function in T2D, we make use of a comprehensive electrophysiological model of human [Formula: see text]-cell clusters. We find that defect in [Formula: see text]-cell mass causes a functional decline in single [Formula: see text]-cell, impairment in intra-islet synchrony, and changes in the form of oscillatory patterns of membrane potential and intracellular [Formula: see text] concentration, which can lead to changes in insulin secretion dynamics and in insulin levels. The model demonstrates a good correspondence between suppression of synchronizing electrical activity and published experimental measurements. We then compare the role of gap junction-mediated electrical coupling with both [Formula: see text]-cell synchronization and metabolic coupling in the behavior of [Formula: see text] concentration dynamics within human islets. Our results indicate that inter-[Formula: see text]-cellular electrical coupling depicts a more important factor in shaping the physiological regulation of islet function and in human T2D. We further predict that varying the whole-cell conductance of delayed rectifier [Formula: see text] channels modifies oscillatory activity patterns of [Formula: see text]-cell population lacking intercellular coupling, which significantly affect [Formula: see text] concentration and insulin secretion.

Deciphering the Role of Wnt and Rho Signaling Pathway in iPSC-Derived ARVC Cardiomyocytes by In Silico Mathematical Modeling

Arrhythmogenic Right Ventricular cardiomyopathy (ARVC) is an inherited cardiac muscle disease linked to genetic deficiency in components of the desmosomes. The disease is characterized by progressive fibro-fatty replacement of the right ventricle, which acts as a substrate for arrhythmias and sudden cardiac death. The molecular mechanisms underpinning ARVC are largely unknown. Here we propose a mathematical model for investigating the molecular dynamics underlying heart remodeling and the loss of cardiac myocytes identity during ARVC. Our methodology is based on three computational models: firstly, in the context of the Wnt pathway, we examined two different competition mechanisms between β-catenin and Plakoglobin (PG) and their role in the expression of adipogenic program. Secondly, we investigated the role of RhoA-ROCK pathway in ARVC pathogenesis, and thirdly we analyzed the interplay between Wnt and RhoA-ROCK pathways in the context of the ARVC phenotype. We conclude with the following remark: both Wnt/β-catenin and RhoA-ROCK pathways must be inactive for a significant increase of PPARγ expression, suggesting that a crosstalk mechanism might be responsible for mediating ARVC pathogenesis.

Ion channel noise shapes the electrical activity of endocrine cells

Endocrine cells in the pituitary gland typically display either spiking or bursting electrical activity, which is related to the level of hormone secretion. Recent work, which combines mathematical modelling with dynamic clamp experiments, suggests the difference is due to the presence or absence of a few large-conductance potassium channels. Since endocrine cells only contain a handful of these channels, it is likely that stochastic effects play an important role in the pattern of electrical activity. Here, for the first time, we explicitly determine the effect of such noise by studying a mathematical model that includes the realistic noisy opening and closing of ion channels. This allows us to investigate how noise affects the electrical activity, examine the origin of spiking and bursting, and determine which channel types are responsible for the greatest noise. Further, for the first time, we address the role of cell size in endocrine cell electrical activity, finding that larger cells typically display more bursting, while the smallest cells almost always only exhibit spiking behaviour.

From Local to Global Modeling for Characterizing Calcium Dynamics and Their Effects on Electrical Activity and Exocytosis in Excitable Cells

Electrical activity in neurons and other excitable cells is a result of complex interactions between the system of ion channels, involving both global coupling (e.g., via voltage or bulk cytosolic Ca²⁺ concentration) of the channels, and local coupling in ion channel complexes (e.g., via local Ca²⁺ concentration surrounding Ca²⁺ channels (CaVs), the so-called Ca²⁺ nanodomains). We recently devised a model of large-conductance BK_Ca potassium currents, and hence BK_Ca–CaV complexes controlled locally by CaVs via Ca²⁺ nanodomains. We showed how different CaV types and BK_Ca–CaV stoichiometries affect whole-cell electrical behavior. Ca²⁺ nanodomains are also important for triggering exocytosis of hormone-containing granules, and in this regard, we implemented a strategy to characterize the local interactions between granules and CaVs. In this study, we coupled electrical and exocytosis models respecting the local effects via Ca²⁺ nanodomains. By simulating scenarios with BK_Ca–CaV complexes with different stoichiometries in pituitary cells, we achieved two main electrophysiological responses (continuous spiking or bursting) and investigated their effects on the downstream exocytosis process. By varying the number and distance of CaVs coupled with the granules, we found that bursting promotes exocytosis with faster rates than spiking. However, by normalizing to Ca²⁺ influx, we found that bursting is only slightly more efficient than spiking when CaVs are far away from granules, whereas no difference in efficiency between bursting and spiking is observed with close granule-CaV coupling.

Biophysical modeling of C. elegans neurons: Single ion currents and whole-cell dynamics of AWCon and RMD

C. elegans neuronal system constitutes the ideal framework for studying simple, yet realistic, neuronal activity, since the whole nervous system is fully characterized with respect to the exact number of neurons and the neuronal connections. Most recent efforts are devoted to investigate and clarify the signal processing and functional connectivity, which are at the basis of sensing mechanisms, signal transmission, and motor control. In this framework, a refined modelof whole neuron dynamics constitutes a key ingredient to describe the electrophysiological processes, both at thecellular and at the network scale. In this work, we present Hodgkin-Huxley-based models of ion channels dynamics black, built on data available both from C. elegans and from other organisms, expressing homologous channels. We combine these channel models to simulate the electrical activity oftwo among the most studied neurons in C. elegans, which display prototypical dynamics of neuronal activation, the chemosensory AWCON and the motor neuron RMD. Our model properly describes the regenerative responses of the two cells. We analyze in detail the role of ion currents, both in wild type and in in silico knockout neurons. Moreover, we specifically investigate the behavior of RMD, identifying a heterogeneous dynamical response which includes bistable regimes and sustained oscillations. We are able to assess the critical role of T-type calcium currents, carried by CCA-1 channels, and leakage currents in the regulation of RMD response. Overall, our results provide new insights in the activity of key C. elegans neurons. The developed mathematical framework constitute a basis for single-cell and neuronal networks analyses, opening new scenarios in the in silico modeling of C. elegans neuronal system.

Explicit Theoretical Analysis of How the Rate of Exocytosis Depends on Local Control by Ca2+ Channels

Hormones and neurotransmitters are released from cells by calcium-regulated exocytosis, and local coupling between Ca²⁺ channels (CaVs) and secretory granules is a key factor determining the exocytosis rate. Here, we devise a methodology based on Markov chain models that allows us to obtain analytic results for the expected rate. First, we analyze the property of the secretory complex obtained by coupling a single granule with one CaV. Then, we extend our results to a more general case where the granule is coupled with n CaVs. We investigate how the exocytosis rate is affected by varying the location of granules and CaVs. Moreover, we assume that the single granule can form complexes with inactivating or non-inactivating CaVs. We find that increasing the number of CaVs coupled with the granule determines a much higher rise of the exocytosis rate that, in case of inactivating CaVs, is more pronounced when the granule is close to CaVs, while, surprisingly, in case of non-inactivating CaVs, the highest relative increase in rate is obtained when the granule is far from the CaVs. Finally, we exploit the devised model to investigate the relation between exocytosis and calcium influx. We find that the quantities are typically linearly related, as observed experimentally. For the case of inactivating CaVs, our simulations show a change of the linear relation due to near-complete inactivation of CaVs.

Proximal clustering between BK and CaV1.3 channels promotes functional coupling and BK channel activation at low voltage

Ca_V-channel dependent activation of BK channels is critical for feedback control of both calcium influx and cell excitability. Here we addressed the functional and spatial interaction between BK and Ca_V1.3 channels, unique Ca_V1 channels that activate at low voltages. We found that when BK and Ca_V1.3 channels were co-expressed in the same cell, BK channels started activating near −50 mV, ~30 mV more negative than for activation of co-expressed BK and high-voltage activated Ca_V2.2 channels. In addition, single-molecule localization microscopy revealed striking clusters of Ca_V1.3 channels surrounding clusters of BK channels and forming a multi-channel complex both in a heterologous system and in rat hippocampal and sympathetic neurons. We propose that this spatial arrangement allows tight tracking between local BK channel activation and the gating of Ca_V1.3 channels at quite negative membrane potentials, facilitating the regulation of neuronal excitability at voltages close to the threshold to fire action potentials.

DOI:http://dx.doi.org/10.7554/eLife.28029.001