Krasimira Tsaneva-Atanasova

A model of calcium waves in pancreatic and parotid acinar cells

We construct a mathematical model of Ca(2+) wave propagation in pancreatic and parotid acinar cells. Ca(2+) release is via inositol trisphosphate receptors and ryanodine receptors that are distributed heterogeneously through the cell. The apical and basal regions are separated by a region containing the mitochondria. In response to a whole-cell, homogeneous application of inositol trisphosphate (IP(3)), the model predicts that 1), at lower concentrations of IP(3), the intracellular waves in pancreatic cells begin in the apical region and are actively propagated across the basal region by Ca(2+) release through ryanodine receptors; 2), at higher [IP(3)], the waves in pancreatic and parotid cells are not true waves but rather apparent waves, formed as the result of sequential activation of inositol trisphosphate receptors in the apical and basal regions; 3), the differences in wave propagation in pancreatic and parotid cells can be explained in part by differences in inositol trisphosphate receptor density; 4), in pancreatic cells, increased Ca(2+) uptake by the mitochondria is capable of restricting Ca(2+) responses to the apical region, but that this happens only for a relatively narrow range of [IP(3)]; and 5), at higher [IP(3)], the apical and basal regions of the cell act as coupled Ca(2+) oscillators, with the basal region partially entrained to the apical region.

Relocalization of STIM1 for Activation of Store-operated Ca2+ Entry Is Determined by the Depletion of Subplasma Membrane Endoplasmic Reticulum Ca2+ Store

STIM1 (stromal interacting molecule 1), an endoplasmic reticulum (ER) protein that controls store-operated Ca2+ entry (SOCE), redistributes into punctae at the cell periphery after store depletion. This redistribution is suggested to have a causal role in activation of SOCE. However, whether peripheral STIM1 punctae that are involved in regulation of SOCE are determined by depletion of peripheral or more internal ER has not yet been demonstrated. Here we show that Ca2+ depletion in subplasma membrane ER is sufficient for peripheral redistribution of STIM1 and activation of SOCE. 1 μm thapsigargin (Tg) induced substantial depletion of intracellular Ca2+ stores and rapidly activated SOCE. In comparison, 1 nm Tg induced slower, about 60-70% less Ca2+ depletion but similar SOCE. SOCE was confirmed by measuring ISOC in addition to Ca2+, Mn2+, and Ba2+ entry. Importantly, 1 nm Tg caused redistribution of STIM1 only in the ER-plasma membrane junction, whereas 1 μm Tg caused a relatively global relocalization of STIM1 in the cell. During the time taken for STIM1 relocalization and SOCE activation, 1 nm Bodipy-fluorescein Tg primarily labeled the subplasma membrane region, whereas 1 μm Tg labeled the entire cell. The localization of Tg in the subplasma membrane region was associated with depletion of ER in this region and activation of SOCE. Together, these data suggest that peripheral STIM1 relocalization that is causal in regulation of SOCE is determined by the status of [Ca2+] in the ER in close proximity to the plasma membrane. Thus, the mechanism involved in regulation of SOCE is contained within the ER-plasma membrane junctional region.

Full system bifurcation analysis of endocrine bursting models

Plateau bursting is typical of many electrically excitable cells, such as endocrine cells that secrete hormones and some types of neurons that secrete neurotransmitters. Although in many of these cell types the bursting patterns are regulated by the interplay between voltage-gated calcium channels and calcium-sensitive potassium channels, they can be very different. We investigate so-called square-wave and pseudo-plateau bursting patterns found in endocrine cell models that are characterized by a super- or subcritical Hopf bifurcation in the fast subsystem, respectively. By using the polynomial model of Hindmarsh and Rose (Proceedings of the Royal Society of London B 221 (1222) 87-102), which preserves the main properties of the biophysical class of models that we consider, we perform a detailed bifurcation analysis of the full fast-slow system for both bursting patterns. We find that both cases lead to the same possibility of two routes to bursting, that is, the criticality of the Hopf bifurcation is not relevant for characterizing the route to bursting. The actual route depends on the relative location of the full-systems fixed point with respect to a homoclinic bifurcation of the fast subsystem. Our full-system bifurcation analysis reveals properties of endocrine bursting that are not captured by the standard fast-slow analysis.

Encoding and Decoding Mechanisms of Pulsatile Hormone Secretion

Ultradian pulsatile hormone secretion underlies the activity of most neuroendocrine systems, including the hypothalamic‐pituitary adrenal (HPA) and gonadal (HPG) axes, and this pulsatile mode of signalling permits the encoding of information through both amplitude and frequency modulation. In the HPA axis, glucocorticoid pulse amplitude increases in anticipation of waking, and, in the HPG axis, changing gonadotrophin‐releasing hormone pulse frequency is the primary means by which the body alters its reproductive status during development (i.e. puberty). The prevalence of hormone pulsatility raises two crucial questions: how are ultradian pulses encoded (or generated) by these systems, and how are these pulses decoded (or interpreted) at their target sites? We have looked at mechanisms within the HPA axis responsible for encoding the pulsatile mode of glucocorticoid signalling that we observe in vivo. We review evidence regarding the ‘hypothalamic pulse generator’ hypothesis, and describe an alternative model for pulse generation, which involves steroid feedback‐dependent endogenous rhythmic activity throughout the HPA axis. We consider the decoding of hormone pulsatility by taking the HPG axis as a model system and focussing on molecular mechanisms of frequency decoding by pituitary gonadotrophs.

Pulsatile and sustained gonadotropin-releasing hormone (GnRH) receptor signaling: Does the Ca2+/NFAT signaling pathway decode GnRH pulse frequency?

Gonadotropin-releasing hormone (GnRH) acts via 7 transmembrane region receptors on gonadotrophs to stimulate synthesis and secretion of the luteinizing hormone and follicle-stimulating hormone. It is secreted in pulses, and its effects depend on pulse frequency, but decoding mechanisms are unknown. Here we have used (nuclear factor of activated T-cells 2 (NFAT2)-emerald fluorescent protein) to monitor GnRH signaling. Increasing [Ca2+]i causes calmodulin/calcineurin-dependent nuclear NFAT translocation, a response involving proteins (calmodulins and NFATs) that decode frequency in other systems. Using live cell imaging, pulsatile GnRH caused dose- and frequency-dependent increases in nuclear NFAT2-emerald fluorescent protein, and at low frequency, translocation simply tracked GnRH exposure (albeit with slower kinetics). At high frequency (30-min intervals), failure to return to basal conditions before repeat stimulation caused integrative tracking, illustrating how the relative dynamics of up- and downstream signals can increase efficiency of GnRH action. Mathematical modeling predicted desensitization of GnRH effects on [Ca2+]i and that desensitization would increase with dose, frequency, and receptor number, but no such desensitization was seen in HeLa and/or LβT2 cells possibly because pulsatile GnRH did not reduce receptor expression (measured by immunofluorescence). GnRH also caused dose- and frequency-dependent activation of αGSU, luteinizing hormone β, and follicle-stimulating hormone β luciferase reporters, effects that were blocked by calcineurin inhibition. Pulsatile GnRH also activated an NFAT-responsive luciferase reporter, but this response was directly related to cumulative pulse duration. This together with the lack of desensitization of translocation responses suggests that NFAT may mediate GnRH action but is not a genuine decoder of GnRH pulse frequency.

FKBP12 Activates the Cardiac Ryanodine Receptor Ca2+-Release Channel and Is Antagonised by FKBP12.6

Changes in FKBP12.6 binding to cardiac ryanodine receptors (RyR2) are implicated in mediating disturbances in Ca2+-homeostasis in heart failure but there is controversy over the functional effects of FKBP12.6 on RyR2 channel gating. We have therefore investigated the effects of FKBP12.6 and another structurally similar molecule, FKBP12, which is far more abundant in heart, on the gating of single sheep RyR2 channels incorporated into planar phospholipid bilayers and on spontaneous waves of Ca2+-induced Ca2+-release in rat isolated permeabilised cardiac cells. We demonstrate that FKBP12 is a high affinity activator of RyR2, sensitising the channel to cytosolic Ca2+, whereas FKBP12.6 has very low efficacy, but can antagonise the effects of FKBP12. Mathematical modelling of the data shows the importance of the relative concentrations of FKBP12 and FKBP12.6 in determining RyR2 activity. Consistent with the single-channel results, physiological concentrations of FKBP12 (3 µM) increased Ca2+-wave frequency and decreased the SR Ca2+-content in cardiac cells. FKBP12.6, itself, had no effect on wave frequency but antagonised the effects of FKBP12. We provide a biophysical analysis of the mechanisms by which FK-binding proteins can regulate RyR2 single-channel gating. Our data indicate that FKBP12, in addition to FKBP12.6, may be important in regulating RyR2 function in the heart. In heart failure, it is possible that an alteration in the dual regulation of RyR2 by FKBP12 and FKBP12.6 may occur. This could contribute towards a higher RyR2 open probability, ‘leaky’ RyR2 channels and Ca2+-dependent arrhythmias.

BSim: An Agent-Based Tool for Modeling Bacterial Populations in Systems and Synthetic Biology

Large-scale collective behaviors such as synchronization and coordination spontaneously arise in many bacterial populations. With systems biology attempting to understand these phenomena, and synthetic biology opening up the possibility of engineering them for our own benefit, there is growing interest in how bacterial populations are best modeled. Here we introduce BSim, a highly flexible agent-based computational tool for analyzing the relationships between single-cell dynamics and population level features. BSim includes reference implementations of many bacterial traits to enable the quick development of new models partially built from existing ones. Unlike existing modeling tools, BSim fully considers spatial aspects of a model allowing for the description of intricate micro-scale structures, enabling the modeling of bacterial behavior in more realistic three-dimensional, complex environments. The new opportunities that BSim opens are illustrated through several diverse examples covering: spatial multicellular computing, modeling complex environments, population dynamics of the lac operon, and the synchronization of genetic oscillators. BSim is open source software that is freely available from http://bsim-bccs.sf.net and distributed under the Open Source Initiative (OSI) recognized MIT license. Developer documentation and a wide range of example simulations are also available from the website. BSim requires Java version 1.6 or higher.

Quantifying Neurite Growth Mediated by Interactions among Secretory Vesicles, Microtubules, and Actin Networks

Neurite growth is a fundamental process of neuronal development, which requires both membrane expansions by exocytosis and cytoskeletal dynamics. However, the specific contribution of these processes has not been yet assessed quantitatively. To study and quantify the growth process, we construct a biophysical model in which we relate the overall neurite outgrowth rate to the vesicle dynamics. By considering the complex motion of vesicles in the cell soma, we demonstrate from biophysical consideration that the main step of finding the neurite initiation site relies mainly on a two-dimensional diffusion/sequestration/fusion at the cell surface and we obtain a novel formula for the flux of vesicles at the neurite base. In the absence of microtubules, we show that a nascent neurite initiated by vesicular delivery can only reach a small length. By adding the microtubule dynamics to the secretory pathway and using stochastic analysis and simulations, we study the complex dynamics of neurite growth. Within this model, depending on the coupling parameter between the microtubules and the neurite, we find different regimes of growth, which describe dendritic and axonal growth. To validate one aspect of our model, we demonstrate that the experimental flux of TI-VAMP but not Synaptobrevin 2 vesicles contributes to the neurite growth. We conclude that although vesicles can be generated randomly in the cell body, the search for the neurite position using the microtubule network and diffusion is quite fast. Furthermore, when the TI-VAMP vesicular flow is large enough, the interactions between the microtubule bundle and the neurite control the growth process. In addition, all of these processes intimately cooperate to mediate the various modes of neurite growth: the model predicts three different growing modes including, in addition to the stable axonal growth and the stochastic dendritic growth, a fast oscillatory regime. Finally our study demonstrates that cytoskeletal dynamics is necessary to generate long protrusion, while vesicular delivery alone can only generate small neurite.

A phenomenological model of seizure initiation suggests network structure may explain seizure frequency in idiopathic generalised epilepsy

We describe a phenomenological model of seizure initiation, consisting of a bistable switch between stable fixed point and stable limit-cycle attractors. We determine a quasi-analytic formula for the exit time problem for our model in the presence of noise. This formula--which we equate to seizure frequency--is then validated numerically, before we extend our study to explore the combined effects of noise and network structure on escape times. Here, we observe that weakly connected networks of 2, 3 and 4 nodes with equivalent first transitive components all have the same asymptotic escape times. We finally extend this work to larger networks, inferred from electroencephalographic recordings from 35 patients with idiopathic generalised epilepsies and 40 controls. Here, we find that network structure in patients correlates with smaller escape times relative to network structures from controls. These initial findings are suggestive that network structure may play an important role in seizure initiation and seizure frequency.

A unified model of CA1/3 pyramidal cells: an investigation into excitability

After-depolarisation is a hallmark of excitability in hippocampal pyramidal cells of CA1 and CA3 regions, because it constitutes the subthreshold relation between inward and outward ionic currents. This relationship determines the nominal response to stimuli and provides the necessary conditions for firing a spike or a burst of action potentials. Nevertheless, after-depolarisation is an inherently transient phenomenon that is not very well understood. We study after-depolarisation using a single-compartment pyramidal-cell model based on recent voltage- and current-clamp experimental data. We systematically investigate CA1 and CA3 behaviour and show that changes to maximal conductances of T-type Ca(2+)-current and muscarinic-sensitive and delayed rectifier K(+)-currents are sufficient to switch the behaviour of the model from a CA3 to a CA1 neuron. We use model analysis to define after-depolarisation and bursting threshold. We also explain the influence of particular ionic currents on this phenomenon. This study ends with a sensitivity analysis that demonstrates the influence of specific currents on excitability. Counter-intuitively, we find that a decrease of Na(+)-current could cause an increase in excitability. Our analysis suggests that a change of high-voltage activated Ca(2+)-current can have a similar effect.