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M Falcke

Publications and source records attributed to M Falcke.

14 recordsLinked to original sources
PubMed2006

Frequency of elemental events of intracellular Ca(2+) dynamics.

The dynamics of intracellular Ca(2+) is driven by random events called Ca(2+) puffs, in which Ca(2+) is liberated from intracellular stores. We show that the emergence of Ca(2+) puffs can be mapped to an escape process. The mean first passage times that correspond to the stochastic fraction of puff periods are computed from a novel master equation and two Fokker-Planck equations. Our results demonstrate that the mathematical modeling of Ca(2+) puffs has to account for the discrete character of the Ca(2+) release sites and does not permit a continuous description of the number of open channels.

Calcium↗
PubMed2005

Reactive clusters on a membrane.

We investigate the reaction dynamics of diffusive molecules with immobile binding partners. The fixed reactants build clusters that are comprised of just a few tens of molecules, which leads to small cluster sizes. These molecules participate in the reaction only if they are activated. The dynamics of activation is mapped to a time-dependent size of an active region within the cluster. We focus on the deterministic description of the dynamics of a single cluster. The spatial setup accounts for one of the most important determinants of the dynamics of a cluster, i.e. diffusional transport of reaction partners towards or away from the active region of the cluster. We provide numerical and analytical evidence that diffusion influences decisively the dynamic regimes of the reactions. The application of our methods to intracellular Ca2+ dynamics shows that large local concentrations saturate the Ca2+ feedback to the channel state control. It eliminates oscillations depending on this feedback.

Animals↗
PubMed2004

Models of the inositol trisphosphate receptor.

The inositol (1,4,5)-trisphosphate receptor (IPR) plays a crucial role in calcium dynamics in a wide range of cell types, and is often a central feature in quantitative models of calcium oscillations and waves. We review deterministic and stochastic mathematical models of the IPR, from the earliest ones of the 1970s and 1980s, to the most recent. The effects of IPR stochasticity on Ca2+ dynamics are briefly discussed.

Allosteric Site↗
PubMed2004

Stability of membrane bound reactions.

We present a novel approach to the dynamics of reactions of diffusing chemical species with species fixed in space, e.g., by binding to a membrane. The nondiffusing reaction partners are clustered in areas with a diameter smaller than the diffusion length of the diffusing partner. The activated fraction of the fixed species determines the size of an active subregion of the cluster. Linear stability analysis reveals that diffusion is one of the major determinants of the stability of the dynamics. We illustrate the model concept with Ca2+ dynamics in living cells, which has release channels as fixed reaction partners. Our results suggest that spatial and temporal structures in intracellular Ca2+ dynamics are caused by fluctuations due to the small number of channels per cluster.

Calcium↗
PubMed2004

Release currents of IP(3) receptor channel clusters and concentration profiles.

We simulate currents and concentration profiles generated by Ca(2+) release from the endoplasmic reticulum (ER) to the cytosol through IP(3) receptor channel clusters. Clusters are described as conducting pores in the lumenal membrane with a diameter from 6 nm to 36 nm. The endoplasmic reticulum is modeled as a disc with a radius of 1-12 microm and an inner height of 28 nm. We adapt the dependence of the currents on the trans Ca(2+) concentration (intralumenal) measured in lipid bilayer experiments to the cellular geometry. Simulated currents are compared with signal mass measurements in Xenopus oocytes. We find that release currents depend linearly on the concentration of free Ca(2+) in the lumen. The release current is approximately proportional to the square root of the number of open channels in a cluster. Cytosolic concentrations at the location of the cluster range from 25 microM to 170 microM. Concentration increase due to puffs in a distance of a few micrometers from the puff site is found to be in the nanomolar range. Release currents decay biexponentially with timescales of <1 s and a few seconds. Concentration profiles decay with timescales of 0.125-0.250 s upon termination of release.

Animals↗
PubMed2000

Discrete stochastic modeling of calcium channel dynamics.

We propose a discrete stochastic model for calcium dynamics in living cells. A set of probabilities for the opening/closing of calcium channels is assumed to depend on the calcium concentration. We study this model in one dimension, analytically in the limit of a large number of channels per site N, and numerically for small N. As the number of channels per site is increased, the transition from a nonpropagating region of activity to a propagating one changes from one described by directed percolation to that of deterministic depinning in a spatially discrete system. Also, for a small number of channels a propagating calcium wave can leave behind a novel fluctuation-driven state.

Calcium Channels↗
PubMed2000

Dispersion gap and localized spiral waves in a model for intracellular Ca2+ dynamics.

The dispersion relation is the dependence of the velocity of periodic planar wave trains on their wavelength. We study the occurrence of a velocity gap in the dispersion relation in a bistable three component reaction-diffusion system modeling intracellular Ca2+ dynamics. In two spatial dimensions, localized pinned spirals are observed, if their wavelength falls into the dispersion gap. Destruction of free spirals occurs already for conditions where the asymptotic planar wave train exists and the dispersion gap is absent.

Calcium↗
PubMed2000

Modeling observed chaotic oscillations in bursting neurons: the role of calcium dynamics and IP3.

Chaotic bursting has been recorded in synaptically isolated neurons of the pyloric central pattern generating (CPG) circuit in the lobster stomatogastric ganglion. Conductance-based models of pyloric neurons typically fail to reproduce the observed irregular behavior in either voltage time series or state-space trajectories. Recent suggestions of Chay [Biol Cybern 75: 419-431] indicate that chaotic bursting patterns can be generated by model neurons that couple membrane currents to the nonlinear dynamics of intracellular calcium storage and release. Accordingly, we have built a two-compartment model of a pyloric CPG neuron incorporating previously described membrane conductances together with intracellular Ca2+ dynamics involving the endoplasmic reticulum and the inositol 1,4,5-trisphosphate receptor IP3R. As judged by qualitative inspection and quantitative, nonlinear analysis, the irregular voltage oscillations of the model neuron resemble those seen in the biological neurons. Chaotic bursting arises from the interaction of fast membrane voltage dynamics with slower intracellular Ca2+ dynamics and, hence, depends on the concentration of IP3. Despite the presence of 12 independent dynamical variables, the model neuron bursts chaotically in a subspace characterized by 3-4 active degrees of freedom. The critical aspect of this model is that chaotic oscillations arise when membrane voltage processes are coupled to another slow dynamic. Here we suggest this slow dynamic to be intracellular Ca2+ handling.

Action Potentials↗
PubMed2000

Stochastic spreading of intracellular Ca(2+) release.

We study the spreading of calcium-induced calcium release with the stochastic DeYoung-Keizer-model of the inositol 1,4,5-trisphosphate receptor channel. The model shows a transition from isolated release events to steadily propagating waves with increasing IP3 concentration. A state--stochastic backfiring--was found in the regime of steady propagation. The model can be reduced by an adiabatic elimination of the partial differential equation for the Ca(2+) concentration to a lattice of stochastic channel clusters.

Calcium↗
PubMed1999

Impact of mitochondrial Ca2+ cycling on pattern formation and stability.

Energization of mitochondria significantly alters the pattern of Ca2+ wave activity mediated by activation of the inositol (1,4,5) trisphosphate (IP3) receptor (IP3R) in Xenopus oocytes. The number of pulsatile foci is reduced and spiral Ca2+ waves are no longer observed. Rather, target patterns of Ca2+ release predominate, and when fragmented, fail to form spirals. Ca2+ wave velocity, amplitude, decay time, and periodicity are also increased. We have simulated these experimental findings by supplementing an existing mathematical model with a differential equation for mitochondrial Ca2+ uptake and release. Our calculations show that mitochondrial Ca2+ efflux plays a critical role in pattern formation by prolonging the recovery time of IP3Rs from a refractory state. We also show that under conditions of high energization of mitochondria, the Ca2+ dynamics can become bistable with a second stable stationary state of high resting Ca2+ concentration.

Animals↗
PubMedDate not supplied

A comparison of three models of the inositol trisphosphate receptor.

The inositol (1,4,5)-trisphosphate receptor (IPR) plays a crucial role in calcium dynamics in a wide range of cell types, and is often a central feature in quantitative models of calcium oscillations and waves. We compare three mathematical models of the IPR, fitting each of them to the same data set to determine ranges for the parameter values. Each of the fits indicates that fast activation of the receptor, followed by slow inactivation, is an important feature of the model, and also that the speed of inositol trisphosphate IP3 binding cannot necessarily be assumed to be faster than Ca2+ activation. In addition, the model which assumed saturating binding rates of Ca2+ to the IPR demonstrated the best fit. However, lack of convergence in the fitting procedure indicates that responses to step increases of Ca2+ and IP3 provide insufficient data to determine the parameters unambiguously in any of the models.

Animals↗