Mathematical Modelling of Electrical-Optical Effects in Semiconductor Laser Operation

Smith, Warren R.; King, John R.; Tuck, B.

doi:10.1137/s0036139900366924

Cited by 17 publications

(5 citation statements)

References 13 publications

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“…5,6 In such a microdomain the shape and extent of the Ca 2+ signal are determined by the combined action of mobile and stationary calcium buffers. 5,[7][8][9][10] An analytical approach for the description of signaling gradients arising from multiple compartments inside a cell is given in Ref. 11.…”

Section: Introductionmentioning

confidence: 99%

Investigating the effects of molecular crowding on Ca2+ diffusion using a particle-based simulation model

Straube

Ridgway

2009

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Calcium ions (Ca(2+)) are an important second messenger in eucaryotic cells. They are involved in numerous physiological processes which are triggered by calcium signals in the form of local release events, temporal oscillations, or reaction-diffusion waves. The diffusive spread of calcium signals in the cytosol is strongly affected by calcium-binding proteins (buffers). In addition, the cytosol contains a large number of inert molecules and molecular structures which make it a crowded environment. Here, we investigate the effects of such excluded volumes on calcium diffusion in the presence of different kinds of buffers. We find that the contributions in slowing down Ca(2+) diffusion coming from buffering and molecular crowding are not additive, i.e., the reduction in Ca(2+) diffusivity due to crowding and buffering together is not the sum of each single contribution. In the presence of Ca(2+) gradients and high affinity mobile buffers the effective diffusion coefficient of Ca(2+) can be reduced by up to 60% in highly crowded environments. This suggests that molecular crowding may significantly affect the shape of Ca(2+) microdomains and wave propagation in cell types with high excluded volume fractions.

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Section: Introductionmentioning

confidence: 99%

Investigating the effects of molecular crowding on Ca2+ diffusion using a particle-based simulation model

Straube

Ridgway

2009

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…Clustered IP 3 Rs and RyRs participate in forming a dynamic Ca 2+ microdomain that influences the local [Ca 2+ ] experienced by each channel [33,34]. Assuming that the dwell times of channel states are long compared to the time scale of local [Ca 2+ ] changes, the microdomain [Ca 2+ ] profile can be calculated from the position and source amplitude of open channels using well-known equations for the buffered diffusion of Ca 2+ [35,36]. The coupling of Ca 2+ -regulated channels that are distinguishable due to their spatial location can lead to release site models with large state spaces.…”

Section: Compositional Ca 2+ Release Site Modelsmentioning

confidence: 99%

Reduction of calcium release site models via moment fitting of phase-type distributions

2011

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Models of calcium (Ca(2 +)) release sites derived from continuous-time Markov chain (CTMC) models of intracellular Ca(2 +) channels exhibit collective gating reminiscent of the experimentally observed phenomenon of Ca(2 +) puffs and sparks. In order to overcome the state-space explosion that occurs in compositionally defined Ca(2 +) release site models, we have implemented an automated procedure for model reduction that replaces aggregated states of the full release site model with much simpler CTMCs that have similar within-group phase-type sojourn times and inter-group transitions. Error analysis based on comparison of full and reduced models validates the method when applied to release site models composed of 20 three-state channels that are both activated and inactivated by Ca(2 +). Although inspired by existing techniques for fitting moments of phase-type distributions, the automated reduction method for compositional Ca(2 +) release site models is unique in several respects and novel in this biophysical context.

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“…To specify the values of the N-by-N coupling matrix C, we assume channels are localized on a planar ER membrane (z = 0). If we write r i = x ix + y iŷ as the position of the pore of channel i, then assuming one high-concentration Ca 2+ buffer, the local [Ca 2+ ] at position r = xx + yŷ + zẑ given by the 'steady-state excess buffer approximation' is [53,36]…”

Section: Appendix a Buffered Diffusion Of Ca 2+ And The Coupling Matrixmentioning

confidence: 99%

“…This assumption allows specification of the Ca 2+ concentration experienced by the Ca 2+ -regulatory site of each channel as an instantaneous function of the state of the release site (see appendix A). For simplicity, we use the 'excess buffer approximation' to determine these local Ca 2+ concentrations, but other representations of Ca 2+ buffering could be employed (for review, see [36]). The SAN descriptor for N coupled Ca 2+ -regulated Ca 2+ channels given by equations (7) and (8) assumes that Ca 2+mediated interactions between channels can be superposed, that is, the local [Ca 2+ ] experienced by channel j can be written as c ∞ + i γ i c ij , where c ∞ is the background [Ca 2+ ], c ij is the increase in [Ca 2+ ] experienced by channel j when channel i is open (e.g., equations (A.2) and (A.3)) and γ i = 0 or 1 when channel i is closed or open, respectively.…”

Section: Appendix a Buffered Diffusion Of Ca 2+ And The Coupling Matrixmentioning

confidence: 99%

“…The SAN descriptor for N coupled Ca 2+ -regulated Ca 2+ channels given by equations (7) and (8) assumes that Ca 2+mediated interactions between channels can be superposed, that is, the local [Ca 2+ ] experienced by channel j can be written as c ∞ + i γ i c ij , where c ∞ is the background [Ca 2+ ], c ij is the increase in [Ca 2+ ] experienced by channel j when channel i is open (e.g., equations (A.2) and (A.3)) and γ i = 0 or 1 when channel i is closed or open, respectively. This superposition of Ca 2+ -mediated interactions occurs when the partial differential equations representing the buffered diffusion of intracellular Ca 2+ are linear, as is the case for the excess buffer approximation [35,54,36].…”

Section: Appendix a Buffered Diffusion Of Ca 2+ And The Coupling Matrixmentioning

confidence: 99%

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Markov chain models of coupled calcium channels: Kronecker representations and iterative solution methods

et al. 2008

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Mathematical models of calcium release sites derived from Markov chain models of intracellular calcium channels exhibit collective gating reminiscent of the experimentally observed phenomenon of stochastic calcium excitability (i.e., calcium puffs and sparks). Calcium release site models are stochastic automata networks that involve many functional transitions, that is, the transition probabilities of each channel depend on the local calcium concentration and thus the state of the other channels. We present a Kronecker-structured representation for calcium release site models and perform benchmark stationary distribution calculations using both exact and approximate iterative numerical solution techniques that leverage this structure. When it is possible to obtain an exact solution, response measures such as the number of channels in a particular state converge more quickly using the iterative numerical methods than occupation measures calculated via Monte Carlo simulation. In particular, multi-level methods provide excellent convergence with modest additional memory requirements for the Kronecker representation of calcium release site models. When an exact solution is not feasible, iterative approximate methods based on the power method may be used, with performance similar to Monte Carlo estimates. This suggests approximate methods with multi-level iterative engines as a promising avenue of future research for large-scale calcium release site models.

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Mathematical Modelling of Electrical-Optical Effects in Semiconductor Laser Operation

Cited by 17 publications

References 13 publications

Investigating the effects of molecular crowding on Ca2+ diffusion using a particle-based simulation model

Investigating the effects of molecular crowding on Ca2+ diffusion using a particle-based simulation model

Reduction of calcium release site models via moment fitting of phase-type distributions

Markov chain models of coupled calcium channels: Kronecker representations and iterative solution methods

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