Intercellular calcium waves in the fire-diffuse-fire framework: Green’s function for gap-junctional coupling

Harris, Jamie; Timofeeva, Yulia

doi:10.1103/physreve.82.051910

Cited by 9 publications

(6 citation statements)

References 45 publications

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“…These solutions generalise earlier results of Harris and Timofeeva [ 23 ] applicable to a neural network, but with gap-junctional coupling at tip-to-tip contacts of two branches.…”

Section: Appendix A: Two Simplified Identical Cells With Passive Membsupporting

confidence: 87%

Gap Junctions, Dendrites and Resonances: A Recipe for Tuning Network Dynamics

Timofeeva

Coombes

Michieletto

2013

The Journal of Mathematical Neuroscience

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Gap junctions, also referred to as electrical synapses, are expressed along the entire central nervous system and are important in mediating various brain rhythms in both normal and pathological states. These connections can form between the dendritic trees of individual cells. Many dendrites express membrane channels that confer on them a form of sub-threshold resonant dynamics. To obtain insight into the modulatory role of gap junctions in tuning networks of resonant dendritic trees, we generalise the “sum-over-trips” formalism for calculating the response function of a single branching dendrite to a gap junctionally coupled network. Each cell in the network is modelled by a soma connected to an arbitrary structure of dendrites with resonant membrane. The network is treated as a single extended tree structure with dendro-dendritic gap junction coupling. We present the generalised “sum-over-trips” rules for constructing the network response function in terms of a set of coefficients defined at special branching, somatic and gap-junctional nodes. Applying this framework to a two-cell network, we construct compact closed form solutions for the network response function in the Laplace (frequency) domain and study how a preferred frequency in each soma depends on the location and strength of the gap junction.

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“…These solutions generalise earlier results of Harris and Timofeeva [ 23 ] applicable to a neural network, but with gap-junctional coupling at tip-to-tip contacts of two branches.…”

Section: Appendix A: Two Simplified Identical Cells With Passive Membsupporting

confidence: 87%

Gap Junctions, Dendrites and Resonances: A Recipe for Tuning Network Dynamics

Timofeeva

Coombes

Michieletto

2013

The Journal of Mathematical Neuroscience

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“…The sum-over-trips formalism can then be generalised to support a presence of new boundary conditions. Recent results of Harris and Timofeeva [37] can be applied to the case of tip-to-tip coupling of the dendritic branches. The proposed algorithms can then be modified by including additional sum-over-trips rules.…”

Section: Discussionmentioning

confidence: 99%

Computational Convergence of the Path Integral for Real Dendritic Morphologies

Caudron

Donnelly

Brand

et al. 2012

The Journal of Mathematical Neuroscience

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Neurons are characterised by a morphological structure unique amongst biological cells, the core of which is the dendritic tree. The vast number of dendritic geometries, combined with heterogeneous properties of the cell membrane, continue to challenge scientists in predicting neuronal input-output relationships, even in the case of sub-threshold dendritic currents. The Green’s function obtained for a given dendritic geometry provides this functional relationship for passive or quasi-active dendrites and can be constructed by a sum-over-trips approach based on a path integral formalism. In this paper, we introduce a number of efficient algorithms for realisation of the sum-over-trips framework and investigate the convergence of these algorithms on different dendritic geometries. We demonstrate that the convergence of the trip sampling methods strongly depends on dendritic morphology as well as the biophysical properties of the cell membrane. For real morphologies, the number of trips to guarantee a small convergence error might become very large and strongly affect computational efficiency. As an alternative, we introduce a highly-efficient matrix method which can be applied to arbitrary branching structures.

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“…The parameter d denotes the strength of gap junctional coupling; the stronger the gap junctional coupling, the faster the diffusion of Ca 2+ ions between linked cells. For simplicity, only the diffusion of Ca 2+ ions is considered in the models reported in the Main Text, in line with the study of Hofer [27] or Harris and Timofeeva [28]. In the supplemental S1 Text, we extend these models by also considering InsP 3 diffusion through gap junction and show that InsP 3 can also function as the molecule involved in synchronization of Ca 2+ oscillation in cell types, where Ca 2+ spikes are connected to InsP 3 fluctuations [29].…”

Section: Methodsmentioning

confidence: 99%

The Effect of Gap Junctional Coupling on the Spatiotemporal Patterns of Ca2+ Signals and the Harmonization of Ca2+-Related Cellular Responses

et al. 2016

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Calcium ions (Ca2+) are important mediators of a great variety of cellular activities e.g. in response to an agonist activation of a receptor. The magnitude of a cellular response is often encoded by frequency modulation of Ca2+ oscillations and correlated with the stimulation intensity. The stimulation intensity highly depends on the sensitivity of a cell to a certain agonist. In some cases, it is essential that neighboring cells produce a similar and synchronized response to an agonist despite their different sensitivity. In order to decipher the presumed function of Ca2+ waves spreading among connecting cells, a mathematical model was developed. This model allows to numerically modifying the connectivity probability between neighboring cells, the permeability of gap junctions and the individual sensitivity of cells to an agonist. Here, we show numerically that strong gap junctional coupling between neighbors ensures an equilibrated response to agonist stimulation via formation of Ca2+ phase waves, i.e. a less sensitive neighbor will produce the same or similar Ca2+ signal as its highly sensitive neighbor. The most sensitive cells within an ensemble are the wave initiator cells. The Ca2+ wave in the cytoplasm is driven by a sensitization wave front in the endoplasmic reticulum. The wave velocity is proportional to the cellular sensitivity and to the strength of the coupling. The waves can form different patterns including circular rings and spirals. The observed pattern depends on the strength of noise, gap junctional permeability and the connectivity probability between neighboring cells. Our simulations reveal that one highly sensitive region gradually takes the lead within the entire noisy system by generating directed circular phase waves originating from this region.

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Intercellular calcium waves in the fire-diffuse-fire framework: Green’s function for gap-junctional coupling

Cited by 9 publications

References 45 publications

Gap Junctions, Dendrites and Resonances: A Recipe for Tuning Network Dynamics

Gap Junctions, Dendrites and Resonances: A Recipe for Tuning Network Dynamics

Computational Convergence of the Path Integral for Real Dendritic Morphologies

The Effect of Gap Junctional Coupling on the Spatiotemporal Patterns of Ca2+ Signals and the Harmonization of Ca2+-Related Cellular Responses

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