Stochastic models and simulation of ion channel dynamics

The behaviour of ion channels within cardiac and neuronal cells is intrinsically stochastic in nature. When the number of channels is small this stochastic noise is large and can have an impact on the dynamics of the system which is potentially an issue when modelling small neurons and drug block in cardiac cells. While exact methods correctly capture the stochastic dynamics of a system they are computationally expensive, restricting their inclusion into tissue level models and so approximations to exact methods are often used instead. The other issue in modelling ion channel dynamics is that the transition rates are voltage dependent, adding a level of complexity as the channel dynamics are coupled to the membrane potential. By assuming that such transition rates are constant over each time step, it is possible to derive a stochastic differential equation (SDE), in the same manner as for biochemical reaction networks, that describes the stochastic dynamics of ion channels. While such a model is more computationally efficient than exact methods we show that there are analytical problems with the resulting SDE as well as issues in using current numerical schemes to solve such an equation. We therefore make two contributions: develop a different model to describe the stochastic ion channel dynamics that analytically behaves in the correct manner and also discuss numerical methods that preserve the analytical properties of the model.

Modeling ion channel dynamics through reflected stochastic differential equations

Ion channels are membrane proteins that open and close at random and play a vital role in the electrical dynamics of excitable cells. The stochastic nature of the conformational changes these proteins undergo can be significant, however current stochastic modeling methodologies limit the ability to study such systems. Discrete-state Markov chain models are seen as the "gold standard," but are computationally intensive, restricting investigation of stochastic effects to the single-cell level. Continuous stochastic methods that use stochastic differential equations (SDEs) to model the system are more efficient but can lead to simulations that have no biological meaning. In this paper we show that modeling the behavior of ion channel dynamics by a reflected SDE ensures biologically realistic simulations, and we argue that this model follows from the continuous approximation of the discrete-state Markov chain model. Open channel and action potential statistics from simulations of ion channel dynamics using the reflected SDE are compared with those of a discrete-state Markov chain method. Results show that the reflected SDE simulations are in good agreement with the discrete-state approach. The reflected SDE model therefore provides a computationally efficient method to simulate ion channel dynamics while preserving the distributional properties of the discrete-state Markov chain model and also ensuring biologically realistic solutions. This framework could easily be extended to other biochemical reaction networks. © 2012 American Physical Society.

Nedd4-2(NEDD4L) controls intracellular Na(+)-mediated activity of voltage-gated sodium channels in primary cortical neurons.

Nedd4-2, a HECT (homologous with E6-associated protein C-terminus)-type ubiquitin protein ligase, has been implicated in regulating several ion channels, including Navs (voltage-gated sodium channels). In Xenopus oocytes Nedd4-2 strongly inhibits the activity of multiple Navs. However, the conditions under which Nedd4-2 mediates native Nav regulation remain uncharacterized. Using Nedd4-2-deficient mice, we demonstrate in the present study that in foetal cortical neurons Nedd4-2 regulates Navs specifically in response to elevated intracellular Na(+), but does not affect steady-state Nav activity. In dorsal root ganglia neurons from the same mice, however, Nedd4-2 does not control Nav activities. The results of the present study provide the first physiological evidence for an essential function of Nedd4-2 in regulating Navs in the central nervous system.

Molecular architecture of the human sinus node: insights into the function of the cardiac pacemaker.

BACKGROUND: Although we know much about the molecular makeup of the sinus node (SN) in small mammals, little is known about it in humans. The aims of the present study were to investigate the expression of ion channels in the human SN and to use the data to predict electrical activity. METHODS AND RESULTS: Quantitative polymerase chain reaction, in situ hybridization, and immunofluorescence were used to analyze 6 human tissue samples. Messenger RNA (mRNA) for 120 ion channels (and some related proteins) was measured in the SN, a novel paranodal area, and the right atrium (RA). The results showed, for example, that in the SN compared with the RA, there was a lower expression of Na(v)1.5, K(v)4.3, K(v)1.5, ERG, K(ir)2.1, K(ir)6.2, RyR2, SERCA2a, Cx40, and Cx43 mRNAs but a higher expression of Ca(v)1.3, Ca(v)3.1, HCN1, and HCN4 mRNAs. The expression pattern of many ion channels in the paranodal area was intermediate between that of the SN and RA; however, compared with the SN and RA, the paranodal area showed greater expression of K(v)4.2, K(ir)6.1, TASK1, SK2, and MiRP2. Expression of ion channel proteins was in agreement with expression of the corresponding mRNAs. The levels of mRNA in the SN, as a percentage of those in the RA, were used to estimate conductances of key ionic currents as a percentage of those in a mathematical model of human atrial action potential. The resulting SN model successfully produced pacemaking. CONCLUSIONS: Ion channels show a complex and heterogeneous pattern of expression in the SN, paranodal area, and RA in humans, and the expression pattern is appropriate to explain pacemaking.

A boundary preserving numerical algorithm for the Wright-Fisher model with mutation

The Wright-Fisher model is an Itô stochastic differential equation that was originally introduced to model genetic drift within finite populations and has recently been used as an approximation to ion channel dynamics within cardiac and neuronal cells. While analytic solutions to this equation remain within the interval [0,1], current numerical methods are unable to preserve such boundaries in the approximation. We present a new numerical method that guarantees approximations to a form of Wright-Fisher model, which includes mutation, remain within [0,1] for all time with probability one. Strong convergence of the method is proved and numerical experiments suggest that this new scheme converges with strong order 1/2. Extending this method to a multidimensional case, numerical tests suggest that the algorithm still converges strongly with order 1/2. Finally, numerical solutions obtained using this new method are compared to those obtained using the Euler-Maruyama method where the Wiener increment is resampled to ensure solutions remain within [0,1].

Neuronal nicotinic acetylcholine receptors : neuroplastic changes underlying alcohol and nicotine addictions

Addictive drugs can activate systems involved in normal reward-related learning, creating long-lasting memories of the drug's reinforcing effects and the environmental cues surrounding the experience. These memories significantly contribute to the maintenance of compulsive drug use as well as cue-induced relapse which can occur even after long periods of abstinence. Synaptic plasticity is thought to be a prominent molecular mechanism underlying drug-induced learning and memories. Ethanol and nicotine are both widely abused drugs that share a common molecular target in the brain, the neuronal nicotinic acetylcholine receptors (nAChRs). The nAChRs are ligand-gated ion channels that are vastly distributed throughout the brain and play a key role in synaptic neurotransmission. In this review, we will delineate the role of nAChRs in the development of ethanol and nicotine addiction. We will characterize both ethanol and nicotine's effects on nAChR-mediated synaptic transmission and plasticity in several key brain areas that are important for addiction. Finally, we will discuss some of the behavioral outcomes of drug-induced synaptic plasticity in animal models. An understanding of the molecular and cellular changes that occur following administration of ethanol and nicotine will lead to better therapeutic strategies.

Functional analysis of missense variants in the TRESK (KCNK18) K+ channel

A loss of function mutation in the TRESK K2P potassium channel (KCNK18), has recently been linked with typical familial migraine with aura. We now report the functional characterisation of additional TRESK channel missense variants identified in unrelated patients. Several variants either had no apparent functional effect, or they caused a reduction in channel activity. However, the C110R variant was found to cause a complete loss of TRESK function, yet is present in both sporadic migraine and control cohorts, and no variation in KCNK18 copy number was found. Thus despite the previously identified association between loss of TRESK channel activity and migraine in a large multigenerational pedigree, this finding indicates that a single non-functional TRESK variant is not alone sufficient to cause typical migraine and highlights the genetic complexity of this disorder. Migraine is a common, disabling neurological disorder with a genetic, environmental and in some cases hormonal component. It is characterized by attacks of severe, usually unilateral and throbbing headache, can be accompanied by nausea, vomiting and photophobia and is clinically divided into two main subtypes, migraine with aura (MA) when a migraine is accompanied by transient and reversible focal neurological symptoms and migraine without aura (MO)1. The multifactorial and clinical heterogeneity of the disorder have considerably hindered the identification of common migraine susceptibility genes and most of our current understanding comes from the studies of familial hemiplegic migraine (FHM), a rare monogenic autosomal dominant form of MA2. So far, the three susceptibility genes that have been convincingly identified in FHM families all encode ion channels or transporters: CACNA1A encoding the α1 subunit of the Cav2.1 calcium channel3, SCN1A encoding the Nav1.1 sodium channel4 and ATP1A2 encoding the α2 subunit of the Na+/K+ pump5. It is believed that mutations in these genes may lead to increased efflux of glutamate and potassium in the synapse and thereby cause migraine by rendering the brain more susceptible to cortical spreading depression (CSD)6 which is thought to play a role in initiating a migraine attack7,8. However, these genes have not to date been implicated in common forms of migraine9. Nevertheless, current opinion suggests that typical migraine, like FHM, is also disorder of neuronal excitability, ion homeostasis and neurotransmitter release10,11,12. Mutations in the SLC4A4 gene encoding the sodium-bicarbonate cotransporter NBCe1, have recently been implicated in several different forms of migraine13, and a variety of genes involved in glutamate homeostasis (PGCP, MTDH14 and LRP115) and a cation channel (TRPM8)15 have also recently been implicated in migraine via genome-wide association studies. Ion channels are therefore highly likely to play an important role in the pathogenesis of typical migraine. TRESK (KCNK18), is a member of the two-pore domain (K2P) family of potassium channels involved in the control of cellular electrical excitability16. Regulation of TRESK activity by the calcium-dependent phosphatase calcineurin17, as well as its expression in dorsal root ganglia (DRG)18 and trigeminal ganglia (TG)19,20 has led to a proposed role for this channel in a variety of pain pathways. In a recent study, a frameshift mutation (F139Wfsx24) in TRESK was identified in a large multigenerational pedigree where it co-segregated perfectly with typical MA and a significant genome-wide linkage LOD score of 3.0. Furthermore, functional analysis revealed that this mutation caused a complete loss of TRESK function and that the truncated subunit was also capable of down regulating wild-type channel function. This therefore highlighted KCNK18 as potentially important candidate gene and suggested that TRESK dysfunction might play a possible role in the pathogenesis of familial migraine with visual aura20. Additional screening for KCNK18 mutations in unrelated sporadic migraine and control cohorts also identified a number of other missense variants; R10G, A34V, C110R, S231P and A233V20. The A233V variant was found only in the control cohort, whilst A34V was identified in a single Australian migraine proband for which family samples were not available, but it was not detected in controls. By contrast, the R10G, C110R, and S231P variants were found in both migraineurs and controls in both cohorts. In this study, we have investigated the functional effect of these variants to further probe the potential association of TRESK dysfunction with typical migraine.

Induction of epithelial-mesenchymal transition (EMT) in breast cancer cells is calcium signal dependent

Signals from the tumor microenvironment trigger cancer cells to adopt an invasive phenotype through epithelial-mesenchymal transition (EMT). Relatively little is known regarding key signal transduction pathways that serve as cytosolic bridges between cell surface receptors and nuclear transcription factors to induce EMT. A better understanding of these early EMT events may identify potential targets for the control of metastasis. One rapid intracellular signaling pathway that has not yet been explored during EMT induction is calcium. Here we show that stimuli used to induce EMT produce a transient increase in cytosolic calcium levels in human breast cancer cells. Attenuation of the calcium signal by intracellular calcium chelation significantly reduced epidermal growth factor (EGF)- and hypoxia-induced EMT. Intracellular calcium chelation also inhibited EGF-induced activation of signal transducer and activator of transcription 3 (STAT3), while preserving other signal transduction pathways such as Akt and extracellular signal-regulated kinase 1/2 (ERK1/2) phosphorylation. To identify calcium-permeable channels that may regulate EMT induction in breast cancer cells, we performed a targeted siRNA-based screen. We found that transient receptor potential-melastatin-like 7 (TRPM7) channel expression regulated EGF-induced STAT3 phosphorylation and expression of the EMT marker vimentin. Although intracellular calcium chelation almost completely blocked the induction of many EMT markers, including vimentin, Twist and N-cadherin, the effect of TRPM7 silencing was specific for vimentin protein expression and STAT3 phosphorylation. These results indicate that TRPM7 is a partial regulator of EMT in breast cancer cells, and that other calcium-permeable ion channels are also involved in calcium-dependent EMT induction. In summary, this work establishes an important role for the intracellular calcium signal in the induction of EMT in human breast cancer cells. Manipulation of calcium-signaling pathways controlling EMT induction in cancer cells may therefore be an important therapeutic strategy for preventing metastases.

UV Photodissociation Action Spectroscopy of Haloanilinium Ions in a Linear Quadrupole Ion Trap Mass Spectrometer

UV-vis photodissociation action spectroscopy is becoming increasingly prevalent because of advances in, and commercial availability of, ion trapping technologies and tunable laser sources. This study outlines in detail an instrumental arrangement, combining a commercial ion-trap mass spectrometer and tunable nanosecond pulsed laser source, for performing fully automated photodissociation action spectroscopy on gas-phase ions. The components of the instrumentation are outlined, including the optical and electronic interfacing, in addition to the control software for automating the experiment and performing online analysis of the spectra. To demonstrate the utility of this ensemble, the photodissociation action spectra of 4-chloroanilinium, 4-bromoanilinium, and 4-iodoanilinium cations are presented and discussed. Multiple photoproducts are detected in each case and the photoproduct yields are followed as a function of laser wavelength. It is shown that the wavelength-dependent partitioning of the halide loss, H loss, and NH3 loss channels can be broadly rationalized in terms of the relative carbon-halide bond dissociation energies and processes of energy redistribution. The photodissociation action spectrum of (phenyl)Ag-2 (+) is compared with a literature spectrum as a further benchmark.

A germanium/single-walled carbon nanotube composite paper as a free-standing anode for lithium-ion batteries

Paper-like free-standing germanium (Ge) and single-walled carbon nanotube (SWCNT) composite anodes were synthesized by the vacuum filtration of Ge/SWCNT composites, which were prepared by a facile aqueous-based method. The samples were characterized by X-ray diffraction, field emission scanning electron microscopy, and transmission electron microscopy. Electrochemical measurements demonstrate that the Ge/SWCNT composite paper anode with the weight percentage of 32% Ge delivered a specific discharge capacity of 417 mA h g-1 after 40 cycles at a current density of 25 mA g-1, 117% higher than the pure SWCNT paper anode. The SWCNTs not only function as a flexible mechanical support for strain release, but also provide excellent electrically conducting channels, while the nanosized Ge particles contribute to improving the discharge capacity of the paper anode.