Large-conductance Ca-dependent K (BK) channels are important regulators of electrical activity. These channels colocalize and form ion channel complexes with voltage-dependent Ca (CaV) channels. Recent stochastic simulations of the BK-CaV complex with 1:1 stoichiometry have given important insight into the local control of BK channels by fluctuating nanodomains of Ca. However, such Monte Carlo simulations are computationally expensive, and are therefore not suitable for large-scale simulations of cellular electrical activity. In this work we extend the stochastic model to more realistic BK-CaV complexes with 1:n stoichiometry, and analyze the single-complex model with Markov chain theory. From the description of a single BK-CaV complex, using arguments based on timescale analysis, we derive a concise model of whole-cell BK currents, which can readily be analyzed and inserted into models of cellular electrical activity. We illustrate the usefulness of our results by inserting our BK description into previously published whole-cell models, and perform simulations of electrical activity in various cell types, which show that BK-CaV stoichiometry can affect whole-cell behavior substantially. Our work provides a simple formulation for the whole-cell BK current that respects local interactions in BK-CaV complexes, and indicates how local-global coupling of ion channels may affect cell behavior.
Key pointsr The control of glucagon secretion from pancreatic alpha-cells is still unclear and, when defective, is involved in the development of diabetes.r We propose a mathematical model of Ca 2+ dynamics and exocytosis to understand better the intracellular mechanisms downstream of electrical activity that control glucagon secretion. r Our results highlight that the number of open Ca 2+ channels is a dominant factor in glucagon release, and clarify why cytosolic Ca 2+ is a poor read-out of alpha-cell secretion.Abstract Glucagon secretion from pancreatic alpha-cells is dysregulated in diabetes. Despite decades of investigations of the control of glucagon release by glucose and hormones, the underlying mechanisms are still debated. Recently, mathematical models have been applied to investigate the modification of electrical activity in alpha-cells as a result of glucose application. However, recent studies have shown that paracrine effects such as inhibition of glucagon secretion by glucagon-like peptide 1 (GLP-1) or stimulation of release by adrenaline involve cAMP-mediated effects downstream of electrical activity. In particular, depending of the intracellular cAMP concentration, specific types of Ca 2+ channels are inhibited or activated, which interacts with mobilization of secretory granules. To investigate these aspects of alpha-cell function theoretically, we carefully developed a mathematical model of Ca 2+ levels near open or closed Ca 2+ channels of various types, which was linked to a description of Ca 2+ below the plasma membrane, in the bulk cytosol and in the endoplasmic reticulum. We investigated how the various subcellular Ca 2+ compartments contribute to control of glucagon-exocytosis in response to glucose, GLP-1 or adrenaline. Our studies refine previous modelling studies of alpha-cell function, and provide deeper insight into the control of glucagon secretion. Abbreviations CFTR, cystic fibrosis transmembrane conductance regulator; Epac2, exchange protein directly activated by cAMP isoform 2; ER, endoplasmic reticulum; FFA, free fatty acid; GLP-1, glucagon-like peptide 1; GS, glucagon secretion; GSR, glucagon secretion rate; HVA, high voltage-activated; KATP channels, ATP-sensitive K + channels; PKA, protein kinase A; SOC, store-operated Ca 2+ current.
Many of the most important potential applications of Synthetic Biology will require the ability to design and implement high performance feedback control systems that can accurately regulate the dynamics of multiple molecular species within the cell. Here, we argue that the use of design strategies based on combining ultrasensitive response dynamics with negative feedback represents a natural approach to this problem that fully exploits the strongly nonlinear nature of cellular information processing. We propose that such feedback mechanisms can explain the adaptive responses observed in one of the most widely studied biomolecular feedback systems—the yeast osmoregulatory response network. Based on our analysis of such system, we identify strong links with a well-known branch of mathematical systems theory from the field of Control Engineering, known as Sliding Mode Control. These insights allow us to develop design guidelines that can inform the construction of feedback controllers for synthetic biological systems.
The problem of reverse engineering in the topology of functional interaction networks from time-course experimental data has received considerable attention in literature, due to the potential applications in the most diverse fields, comprising engineering, biology, economics and social sciences. The present work introduces a novel technique, CORE-Net, which addresses this problem focusing on the case of biological interaction networks. The method is based on the representation of the network in the form of a dynamical system and on an iterative convex optimisation procedure. A first advantage of the proposed approach is that it allows to exploit qualitative prior knowledge about the network interactions, of the same kind as typically available from biological literature and databases. A second novel contribution consists of exploiting the growth and preferential attachment mechanisms to improve the inference performances when dealing with networks which exhibit a scale-free topology. The technique is first assessed through numerical tests on in silico random networks, subsequently it is applied to reverse engineering a cell cycle regulatory subnetwork in Saccharomyces cerevisiae from experimental microarray data. These tests show that the combined exploitation of prior knowledge and preferential attachment significantly improves the predictions with respect to other approaches.
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