A phenomenological cluster-based model of Ca2+ waves and oscillations for Inositol 1,4,5-trisphosphate receptor (IP3R) channels

Clusters of IP3 receptor channels in the membranes of the endoplasmic reticulum (ER) of many non-excitable cells release calcium ions in a cooperative manner giving rise to dynamical patterns such as Ca2+ puffs, waves, and oscillations that occur on multiple spatial and temporal scales. We introduce a minimal yet descriptive reaction-diffusion model of IP3 receptors for a saturating concentration of IP3 using a principled reduction of a detailed Markov chain description of individual channels. A dynamical systems analysis reveals the possibility of excitable, bistable and oscillatory dynamics of this model that correspond to three types of observed patterns of calcium release -- puffs, waves, and oscillations respectively. We explain the emergence of these patterns via a bifurcation analysis of a coupled two-cluster model, compute the phase diagram and quantify the speed of the waves and period of oscillations in terms of system parameters. We connect the termination of large-scale Ca2+ release events to IP3 unbinding or stochasticity.Comment: 18 pages, 10 figure

Distinguishing between models of mammalian gene expression:Telegraph-like models versus mechanistic models

Two-state models (telegraph-like models) have a successful history of predicting distributions of cellular and nascent mRNA numbers that can well fit experimental data. These models exclude key rate limiting steps, and hence it is unclear why they are able to accurately predict the number distributions. To answer this question, here we compare these models to a novel stochastic mechanistic model of transcription in mammalian cells that presents a unified description of transcriptional factor, polymerase and mature mRNA dynamics. We show that there is a large region of parameter space where the first, second and third moments of the distributions of the waiting times between two consecutively produced transcripts (nascent or mature) of two-state and mechanistic models exactly match. In this region: (i) one can uniquely express the two-state model parameters in terms of those of the mechanistic model, (ii) the models are practically indistinguishable by comparison of their transcript numbers distributions, and (iii) they are distinguishable from the shape of their waiting time distributions. Our results clarify the relationship between different gene expression models and identify a means to select between them from experimental data. </p

Distinguishing between models of mammalian gene expression : telegraph-like models versus mechanistic models

Funding Information: S.B. and R.G. were supported by a Leverhulme Trust grant no. (RPG-2018-423). J.H. was supported by a BBSRC EASTBIO PhD studentship.Two-state models (telegraph-like models) have a successful history of predicting distributions of cellular and nascent mRNA numbers that can well fit experimental data. These models exclude key rate limiting steps, and hence it is unclear why they are able to accurately predict the number distributions. To answer this question, here we compare these models to a novel stochastic mechanistic model of transcription in mammalian cells that presents a unified description of transcriptional factor, polymerase and mature mRNA dynamics. We show that there is a large region of parameter space where the first, second and third moments of the distributions of the waiting times between two consecutively produced transcripts (nascent or mature) of two-state and mechanistic models exactly match. In this region: (i) one can uniquely express the two-state model parameters in terms of those of the mechanistic model, (ii) the models are practically indistinguishable by comparison of their transcript numbers distributions, and (iii) they are distinguishable from the shape of their waiting time distributions. Our results clarify the relationship between different gene expression models and identify a means to select between them from experimental data.Publisher PDFPeer reviewe

The spatial arrangements of stochastic Ca 2+ signals triggered by IP3 release

Clusters of IP3 receptor channels in the membranes of the endoplasmic reticulum (ER) of many non-excitable cells release calcium ions in a cooperative manner giving rise to dynamical patterns such as Ca2+ puffs, waves and oscillations that occur on various spatial and temporal scales. We introduce a stochastic reaction-diffusion model of randomly distributed IP3 receptors using a principled reduction of a detailed Markov chain description of individual channels. Our model reveals how the crucial characteristic of cell regulation such as inter-wave intervals (IWI) depends on the IP3 loads. Furthermore, by performing a correlation analysis of the [Ca2+] at the neighbouring clusters, we obtain the principal characteristics of the membrane which define the possibility of Ca2+ wave initiation and propagation. Using given approach, we aim to link the local properties of IP3R channels and clusters, such as channel type or coupling between channels, with the global patterns which may emerge from these channels, e. g. spikes, waves or oscillations

Cluster-based model for calcium excitations from coupled IP3R channels

Clusters of IP3 receptor channels in the membranes of the endoplasmic reticulum (ER) of many non-excitable cells release calcium ions in a cooperative manner giving rise to dynamical patterns such as puffs, waves and oscillations that occur on various spatial and temporal scales. We introduce a minimal yet descriptive reaction-diffusion model of IP3 receptors for a saturating concentration of IP3 using a principled reduction of a detailed Markov chain description of individual channels. A dynamical systems analysis reveals the possibility of excitable, bistable and oscillatory dynamics of this model that correspond to three types of observed patterns of calcium release puffs, waves and spikes respectively. We explain the emergence of these patterns via a bifurcation analysis of a coupled two-cluster model, compute the phase diagram and quantify the speed of the waves and period of oscillations in terms of system parameters. Further, we extend our approach to a stochastic reaction-diffusion model with the IP3 dependent randomly distributed clusters of channels. Our model reveals how the main characteristics of the activity of clusters, namely inter-puff intervals (IPIs), depend on the IP3 loads. Furthermore, by performing a correlation analysis of [Ca2+] traces at the neighbouring clusters, we obtain the principal characteristics of the membrane which define the possibility of Ca2+ wave initiation and propagation. Using given approach, we aim to link the local properties of IP3R channels and clusters, such as channel type or coupling between channels, with the global patterns which may emerge from these channels, e. g. spikes, waves or oscillations. We study the effect of cooperative behaviour of the IP3 clusters found by Tauq-Ur-Rahman et al. [2009] and also introduce insight into the clustering of the channels using the Ising-like approach

The spatial arrangements of stochastic Ca2+ signals triggered by IP3 release

Clusters of IP3 receptor channels in the membranes of the endoplasmic reticulum (ER) of many non-excitable cells release calcium ions in a cooperative manner giving rise to dynamical patterns such as Ca2+ puffs, waves and oscillations that occur on various spatial and temporal scales. We introduce a stochastic reaction-diffusion model of randomly distributed IP3 receptors using a principled reduction of a detailed Markov chain description of individual channels. Our model reveals how the crucial characteristic of cell regulation such as inter-wave intervals (IWI) depends on the IP3 loads. Furthermore, by performing a correlation analysis of the [Ca2+] at the neighbouring clusters, we obtain the principal characteristics of the membrane which define the possibility of Ca2+ wave initiation and propagation

Bayesian learning of effective chemical master equations in crowded intracellular conditions

Biochemical reactions inside living cells often occur in the presence of crowders -- molecules that do not participate in the reactions but influence the reaction rates through excluded volume effects. However the standard approach to modelling stochastic intracellular reaction kinetics is based on the chemical master equation (CME) whose propensities are derived assuming no crowding effects. Here, we propose a machine learning strategy based on Bayesian Optimisation utilising synthetic data obtained from spatial cellular automata (CA) simulations (that explicitly model volume-exclusion effects) to learn effective propensity functions for CMEs. The predictions from a small CA training data set can then be extended to the whole range of parameter space describing physiologically relevant levels of crowding by means of Gaussian Process regression. We demonstrate the method on an enzyme-catalyzed reaction and a genetic feedback loop, showing good agreement between the time-dependent distributions of molecule numbers predicted by the effective CME and CA simulations.Comment: 20 pages, 8 figure

Calcium release dynamics in clusters of IP3 channels

Clusters of IP3 receptor channels in the membranes of the endoplasmic reticulum (ER) of many non-excitable cells release calcium ions in a cooperative manner giving rise to dynamical patterns such as Ca2+ puffs, waves and oscillations that occur on multiple spatial and temporal scales. We introduce a minimal yet descriptive reaction- diffusion model of IP3 receptors for a saturating concentration of IP3 using a principled reduction of a detailed Markov chain description of individual channels. A dynamical systems analysis reveals the possibility of excitable, bistable and oscillatory dynamics of this model that correspond to three types of observed patterns of calcium releases -- puffs, waves and spikes respectively. We explain the emergence of these patterns via a bifurcation analysis of a coupled two-cluster model, compute the phase diagram and quantify the speed of the waves and period of oscillations in terms of system parameters