Particle-Based Multiscale Modeling of Calcium Puff Dynamics

Dobramysl, Ulrich; Rüdiger, Stephan; Erban, Radek

doi:10.1137/15m1015030

Cited by 27 publications

(63 citation statements)

References 57 publications

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“…Such particle systems are versatile tools that can be used to model the dynamics of various complicated phenomena using relatively simple interactions, e.g., pedestrian dynamics (Helbing and Molnar 1995;Haji-Ali 2012), collective animal behavior Erban and Haskovec 2012), interactions between cells (Dobramysl et al 2016) and in some numerical methods such as ensemble Kalman filters (Pierre Del Moral and Tugaut 2016). One common goal of the simulation of these particle systems is to average some quantity of interest computed on all particles, e.g., the average velocity, average exit time or average number of particles in a specific region.…”

Section: Introductionmentioning

confidence: 99%

Multilevel and Multi-index Monte Carlo methods for the McKean–Vlasov equation

Haji-Ali

Tempone

2017

Stat Comput

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We address the approximation of functionals depending on a system of particles, described by stochastic differential equations (SDEs), in the mean-field limit when the number of particles approaches infinity. This problem is equivalent to estimating the weak solution of the limiting McKean-Vlasov SDE. To that end, our approach uses systems with finite numbers of particles and a timestepping scheme. In this case, there are two discretization parameters: the number of time steps and the number of particles. Based on these two parameters, we consider different variants of the Monte Carlo and Multilevel Monte Carlo (MLMC) methods and show that, in the best case, the optimal work complexity of MLMC, to estimate the functional in one typical setting with an error tolerance of TOL, is O TOL −3 when using the partitioning estimator and the Milstein time-stepping scheme. We also consider a method that uses the recent Multi-index Monte Carlo method and show an improved work complexity in the same typical setting of O TOL −2 log(TOL −1 ) 2 . Our numerical experiments are carried out on the so-called Kuramoto model, a system of coupled oscillators.

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Section: Introductionmentioning

confidence: 99%

Multilevel and Multi-index Monte Carlo methods for the McKean–Vlasov equation

Haji-Ali

Tempone

2017

Stat Comput

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“…We therefore conclude that in this application, the accuracy of our hybrid method is largely limited by the fact that particles are approximated as points. Note also that the handling of strong depletion of continuous variables in the vicinity of discrete particles might be improved by employing multiscale approaches proposed for cases with spatial separation of subsystems with disparate levels of stochasticity [43–46]. Overall, the test shows that even at the limits of applicability, the method produces qualitatively, and in some respects quantitatively, reasonable results.…”

Section: Resultsmentioning

confidence: 94%

“…The current implementation of the method appropriately combines capabilities of one of the Virtual Cell (VCell) [35–39] spatial deterministic solvers and an efficient particle-based simulator called Smoldyn [40, 41]. (Note that Smoldyn has been recently adapted to accommodate a different type of hybrid stochastic models [42], in which the subsystems with disparate levels of stochasticity are segregated in space but can interact in a ‘handshaking’ region [43–46]. ) The development of the VCell hybrid solver benefited from recent integration of Smoldyn into VCell as a method of solving spatial stochastic models [47].…”

Section: Introductionmentioning

confidence: 99%

Numerical Approach to Spatial Deterministic-Stochastic Models Arising in Cell Biology

Schaff¹,

Gao²,

Li³

et al. 2016

PLoS Comput Biol

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Hybrid deterministic-stochastic methods provide an efficient alternative to a fully stochastic treatment of models which include components with disparate levels of stochasticity. However, general-purpose hybrid solvers for spatially resolved simulations of reaction-diffusion systems are not widely available. Here we describe fundamentals of a general-purpose spatial hybrid method. The method generates realizations of a spatially inhomogeneous hybrid system by appropriately integrating capabilities of a deterministic partial differential equation solver with a popular particle-based stochastic simulator, Smoldyn. Rigorous validation of the algorithm is detailed, using a simple model of calcium ‘sparks’ as a testbed. The solver is then applied to a deterministic-stochastic model of spontaneous emergence of cell polarity. The approach is general enough to be implemented within biologist-friendly software frameworks such as Virtual Cell.

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“…Yet, none of those models take into account the 67 stochastic effects associated with the small volumes and the low copy number of 68 molecules involved in fine processes. Recently, individual-based modeling has been 69 introduced to evaluate the impact of diffusive noise on IP3R opening dynamics [56], but 70 this simplified model disregarded IP3 dynamics and restricted stochasticity to the 71 vicinity of the IP3Rs.…”

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confidence: 99%

Simulation of calcium signaling in fine astrocytic processes: effect of spatial properties on spontaneous activity

Denizot

Arizono

Valentin

et al. 2019

Preprint

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Astrocytes, a glial cell type of the central nervous system, have emerged as detectors and regulators of neuronal information processing. Astrocyte excitability resides in transient variations of free cytosolic calcium concentration over a range of temporal and spatial scales, from sub-microdomains to waves propagating throughout the cell. Despite extensive experimental approaches, it is not clear how these signals are transmitted to and integrated within an astrocyte. The localization of the main molecular actors and the geometry of the system, including calcium channels IP3R spatial organization, are deemed essential. However, as most calcium signals occur in astrocytic ramifications that are too fine to be resolved by conventional light microscopy, most of those spatial data are unknown and computational modeling remains the only methodology to study this issue. Here, we propose an IP3R-mediated calcium signaling model for dynamics in such small sub-cellular volumes. To account for the expected stochasticity and low copy numbers, our model is both spatially explicit and particle-based. Extensive simulations show that spontaneous calcium signals arise in the model via the interplay between excitability and stochasticity. The model reproduces the main forms of calcium signals and indicates that their frequency crucially depends on the spatial organization of the IP3R channels. Importantly, we show that two processes expressing exactly the same calcium channels can display different types of calcium signals depending on channels spatial organization. Our model with realistic process volume and calcium concentrations successfully reproduces spontaneous calcium signals that we measured in calcium micro-domains with confocal microscopy. To our knowledge, this model is the first model suited to investigate calcium dynamics in fine astrocytic processes and to propose plausible mechanisms responsible for their variability. Introduction 1 Astrocytes were first characterized as non-excitable cells of the central nervous 2 system since, although they express voltage-gated channels [1], they do not exhibit 3 electrical excitability [2]. Astrocytes excitability instead results from variations of 4 cytosolic calcium concentration [3]. At the cellular level, those calcium signals emerge in 5 astrocytes in response to synaptic activity and may cause the release of molecules called 6 1 gliotransmitters such as glutamate, ATP, tumor necrosis factor-α, or D-serine, which 7can modulate synaptic transmission [4][5][6][7] and vasoconstriction/vasodilatation [8][9][10][11]. 8 This close association of astrocytes to pre-and post-synaptic elements, both 9 structurally and functionally, is referred to as tripartite synapse (see e.g. [12][13][14][15] for 10 reviews on tripartite synapses and the associated controversies). On a larger scale, 11 astrocytic calcium signals can modulate neuronal synchronization and firing 12 pattern [16][17][18] and have been observed in vivo in response to external stimuli [19,20]. 13 Altogether, those obse...

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Particle-Based Multiscale Modeling of Calcium Puff Dynamics

Cited by 27 publications

References 57 publications

Multilevel and Multi-index Monte Carlo methods for the McKean–Vlasov equation

Multilevel and Multi-index Monte Carlo methods for the McKean–Vlasov equation

Numerical Approach to Spatial Deterministic-Stochastic Models Arising in Cell Biology

Simulation of calcium signaling in fine astrocytic processes: effect of spatial properties on spontaneous activity

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