Biomedical subjects

Wouter-Jan Rappel

Publications and source records attributed to Wouter-Jan Rappel.

14 recordsLinked to original sources

PubMed2006

Directional sensing in eukaryotic chemotaxis: a balanced inactivation model.

Many eukaryotic cells, including Dictyostelium discoideum amoebae, fibroblasts, and neutrophils, are able to respond to chemoattractant gradients with high sensitivity. Recent studies have demonstrated that, after the introduction of a chemoattractant gradient, several chemotaxis pathway components exhibit a subcellular reorganization that cannot be described as a simple amplification of the external gradient. Instead, this reorganization has the characteristics of a switch, leading to a well defined front and back. Here, we propose a directional sensing mechanism in which two second messengers are produced at equal rates. The diffusion of one of them, coupled with an inactivation scheme, ensures a switch-like response to external gradients for a large range of gradient steepness and average concentration. Furthermore, our model is able to reverse the subcellular organization rapidly, and its response to multiple simultaneous chemoattractant sources is in good agreement with recent experimental results. Finally, we propose that the dynamics of a heterotrimeric G protein might allow for a specific biochemical realization of our model.

Animals↗

PubMed2006

Embryonic pattern scaling achieved by oppositely directed morphogen gradients.

Morphogens are proteins, often produced in a localized region, whose concentrations spatially demarcate regions of differing gene expression in developing embryos. The boundaries of gene expression are typically sharp and the genes can be viewed as abruptly switching from on to off or vice versa upon crossing the boundary. To ensure the viability of the organism these boundaries must be set at certain fractional positions within the corresponding developing field. Remarkably this can be done with high precision despite the fact that the size of the developing field itself can vary widely from embryo to embryo. How this scaling is accomplished is unknown but it is clear that a single morphogen gradient is insufficient. Here we show how a pair of morphogens A and B, produced at opposite ends of a one-dimensional developing field, can solve the pattern-scaling problem. In the most promising scenario the morphogens interact via an effective annihilation reaction A + B --> slashed circle and the switch occurs according to the absolute concentration of A or B. We define a scaling criterion and show that morphogens coupled in this way can set embryonic markers across the entire developing field in proportion to the field size. This scaling occurs at developing-field sizes of a few times the morphogen decay length. The scaling criterion is not met if instead the gradients couple combinatorially such that downstream genes are regulated by the ratio A/B of the morphogen concentrations.

Animals↗

PubMed2006

Dictyostelium discoideum chemotaxis: threshold for directed motion.

The chemotactic response of Dictyostelium discoideum cells to stationary, linear gradients of cyclic adenosine 3',5'-monophosphate (cAMP) was studied using microfluidic devices. In shallow gradients of less than 10(-3) nM/microm, the cells showed no directional response and exhibited a constant basal motility. In steeper gradients, cells moved up the gradient on average. The chemotactic speed and the motility increased with increasing steepness up to a plateau at around 10(-1) nM/microm. In very steep gradients, above 10 nM/microm, the cells lost directionality and the motility returned to the sub-threshold level. In the regime of optimal response the difference in receptor occupancy at the front and back of the cell is estimated to be only about 100 molecules.

Animals↗

PubMed2005

Division accuracy in a stochastic model of Min oscillations in Escherichia coli.

Accurate cell division in Escherichia coli requires the Min proteins MinC, MinD, and MinE as well as the presence of nucleoids. MinD and MinE exhibit spatial oscillations, moving from pole to pole of the bacterium, resulting in an average MinD concentration that is low at the center of the cell and high at the poles. This concentration minimum is thought to signal the site of cell division. Deterministic models of the Min oscillations reproduce many observed features of the system, including the concentration minimum of MinD. However, there are only a few thousand Min proteins in a bacterium, so stochastic effects are likely to play an important role. Here, we show that Monte Carlo simulations with a large number of proteins agree well with the results from a deterministic treatment of the equations. The location of minimum local MinD concentration is too variable to account for cell division accuracy in wild-type, but is consistent with the accuracy of cell division in cells without nucleoids. This finding confirms the need to include additional mechanisms, such as reciprocal interactions with the cell division ring or positioning of the nucleoids, to explain wild-type accuracy.

Adenosine Triphosphatases↗

PubMed2005

Membrane-bound Turing patterns.

Motivated by recent observations in biological cells, we study Turing patterns in bounded regions where the nonlinear chemical reactions occur on the boundary and where reagent transport occurs in the bulk. Within a generic model, we formulate the stability problem and discuss the conditions for the occurrence of a Turing instability. By choosing other model parameters to be unequal, we find that Turing patterns exist even in the case of equal diffusion constants. Finally, a recently introduced computation technique is utilized to follow the nascent pattern into the highly nonlinear regime.

Animals↗

PubMed2005

Excitation-contraction coupling gain and cooperativity of the cardiac ryanodine receptor: a modeling approach.

During calcium-induced calcium-release, the ryanodine receptor (RyR) opens and releases large amounts of calcium from the sarcoplasmic reticulum into the cytoplasm of the myocyte. Recent experiments have suggested that cooperativity between the four monomers comprising the RyR plays an important role in the dynamics of the overall receptor. Furthermore, this cooperativity can be affected by the binding of FK506 binding protein, and hence, modulated by adrenergic stimulation through the phosphorylating action of protein kinase A. This has important implications for heart failure, where it has been hypothesized that RyR hyperphosphorylation, resulting in a loss of cooperativity, can lead to a persistent leak and a reduced sarcoplasmic-reticula content. In this study, we construct a theoretical model that examines the cooperativity via the assumption of an allosteric interaction between the four subunits. We find that the level of cooperativity, regulated by the binding of FK506 binding-protein, can have a dramatic effect on the excitation-contraction coupling gain and that this gain exhibits a clear maximum. These findings are compared to currently available data from different species and allows for an evaluation of the aforementioned heart-failure scenario.

Allosteric Site↗

PubMed2005

Dynamics of conduction blocks in a model of paced cardiac tissue.

We study numerically the dynamics of conduction blocks using a detailed electrophysiological model. We find that this dynamics depends critically on the size of the paced region. Small pacing regions lead to stationary conduction blocks while larger pacing regions can lead to conduction blocks that travel periodically towards the pacing region. We show that this size-dependence dynamics can lead to a novel arrhythmogenic mechanism. Furthermore, we show that the essential phenomena can be captured in a much simpler coupled-map model.

Animals↗

PubMed2005

Modeling wave propagation in realistic heart geometries using the phase-field method.

We present a novel algorithm for modeling electrical wave propagation in anatomical models of the heart. The algorithm uses a phase-field approach that represents the boundaries between the heart muscle and the surrounding medium as a spatially diffuse interface of finite thickness. The chief advantage of this method is to automatically handle the boundary conditions of the voltage in complex geometries without the need to track the location of these boundaries explicitly. The algorithm is shown to converge accurately in nontrivial test geometries with no-flux (zero normal current) boundary conditions as the width of the diffuse interface becomes small compared to the width of the cardiac action potential wavefront. Moreover, the method is illustrated for anatomically realistic models of isolated rabbit and canine ventricles as well as human atria.

Action Potentials↗

PubMed2004

Emergent oscillations in unidirectionally coupled overdamped bistable systems.

It is well known that overdamped unforced dynamical systems do not oscillate. However, well-designed coupling schemes, together with the appropriate choice of initial conditions, can induce oscillations when a control parameter exceeds a threshold value. In a recent publication [Phys. Rev. E 68, 045102 (2003)]], we demonstrated this behavior in a specific prototype system, a soft-potential mean-field description of the dynamics in a hysteretic "single-domain" ferromagnetic sample. The previous analysis of this work showed that N (odd) unidirectionally coupled elements with cyclic boundary conditions would, in fact, oscillate when a control parameter-in this case the coupling strength-exceeded a critical value. These oscillations are now finding utility in the detection of very weak "target" signals, via their effect on the oscillation characteristics, e.g., the frequency and asymmetry of the oscillation wave forms. In this paper we explore the underlying dynamics of this system. Scaling laws that govern the oscillation frequency in the vicinity of the critical point, as well as the zero-crossing intervals in the presence of a symmetry-breaking target dc signal, are derived; these quantities are germane to signal detection and analysis.

Journal Article↗

PubMed2004

The role of M cells and the long QT syndrome in cardiac arrhythmias: simulation studies of reentrant excitations using a detailed electrophysiological model.

In this numerical study, we investigate the role of intrinsic heterogeneities of cardiac tissue due to M cells in the generation and maintenance of reentrant excitations using the detailed Luo-Rudy dynamic model. This model has been extended to include a description of the long QT 3 syndrome, and is studied in both one dimension, corresponding to a cable traversing the ventricular wall, and two dimensions, representing a transmural slice. We focus on two possible mechanisms for the generation of reentrant events. We first investigate if early-after-depolarizations occurring in M cells can initiate reentry. We find that, even for large values of the long QT strength, the electrotonic coupling between neighboring cells prevents early-after-depolarizations from creating a reentry. We then study whether M cell domains, with their slow repolarization, can function as wave blocks for premature stimuli. We find that the inclusion of an M cell domain can result in some cases in reentrant excitations and we determine the lifetime of the reentry as a function of the size and geometry of the domain and of the strength of the long QT syndrome.

Action Potentials↗

PubMed2004

Cooperativity can reduce stochasticity in intracellular calcium dynamics.

The opening of inositol (1,4,5)-triphosphate (IP(3)) receptors, clustered at discrete sites on the endoplasmic reticulum, can lead to large-scale intracellular calcium waves. Recent experiments in Xenopus oocytes have shown that the inter-wave intervals for these waves have a standard deviation that is much smaller than their mean and that the background calcium concentration exhibits a slow rise during the interwave interval. Using a simple mathematical model, we examine the possibility that this slow rise increases the cooperativity between the openings of the clusters. We find that our model, coupled to the usual assumption that the pumps on the endoplasmic reticulum are activated instantaneously, is unable to explain the observed data: the clusters are found to fire independently and the inter-wave interval distribution is a Poisson distribution with a standard deviation that is approximately equal to its mean. On the other hand, we find that incorporating pumps that slowly activate leads to a slow increase in the background calcium concentration which makes global events progressively more likely to occur. We show that this cooperativity results in much smaller standard deviations and inter-wave interval distributions that are clearly not Poisson distributions.

Animals↗

PubMed2003

Computational approach for modeling intra- and extracellular dynamics.

We introduce a phase-field approach for diffusion inside and outside a closed cell with damping and with source terms at the stationary interface. The method is compared to exact solutions (where possible) and the more traditional finite element method. It is shown to be very accurate, easy to implement, and computationally inexpensive. We apply our method to a recently introduced model for chemotaxis by Rappel et al. [Biophys. J. 83, 1361 (2002)].

Journal Article↗

PubMed2002

Establishing direction during chemotaxis in eukaryotic cells.

Several recent studies have demonstrated that eukaryotic cells, including amoeboid cells of Dictyostelium discoideum and neutrophils, respond to chemoattractants by translocation of PH-domain proteins to the cell membrane, where these proteins participate in the modulation of the cytoskeleton and relay of the signal. When the chemoattractant is released from a pipette, the localization is found predominantly on the proximal side of the cell. The recruitment of PH-domain proteins, particularly for Dictyostelium cells, occurs very rapidly (<2 s). Thus, the mechanism responsible for the first step in the directional sensing process of a cell must be able to establish an asymmetry on the same time scale. Here, we propose a simple mechanism in which a second messenger, generated by local activation of the membrane, diffuses through the interior of the cell, suppresses the activation of the back of the cell, and converts the temporal gradient into an initial cellular asymmetry. Numerical simulations show that such a mechanism is plausible. Available evidence suggests that the internal inhibitor may be cGMP, which accumulates within less than a second following treatment of cells with external cAMP.

Animals↗

PubMed2001

Filament instability and rotational tissue anisotropy: A numerical study using detailed cardiac models.

The role of cardiac tissue anisotropy in the breakup of vortex filaments is studied using two detailed cardiac models. In the Beeler-Reuter model, modified to produce stable spiral waves in two dimensions, we find that anisotropy can destabilize a vortex filament in a parallelepipedal slab of tissue. The mechanisms of the instability are similar to the ones reported in previous work on a simplified cardiac model by Fenton and Karma [Chaos 8, 20 (1998)]. In the Luo-Rudy model, also modified to produce stable spiral waves in two dimensions, we find that anisotropy does not destabilize filaments. A possible explanation for this model-dependent behavior based on spiral tip trajectories is offered. (c) 2001 American Institute of Physics.

Journal Article↗