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.

Variants in the human potassium channel gene (KCNN3) are associated with migraine in a high risk genetic isolate

The calcium-activated potassium ion channel gene (KCNN3) is located in the vicinity of the familial hemiplegic migraine type 2 locus on chromosome 1q21.3. This gene is expressed in the central nervous system and plays a role in neural excitability. Previous association studies have provided some, although not conclusive, evidence for involvement of this gene in migraine susceptibility. To elucidate KCNN3 involvement in migraine, we performed gene-wide SNP genotyping in a high-risk genetic isolate from Norfolk Island, a population descended from a small number of eighteenth century Isle of Man ‘Bounty Mutineer’ and Tahitian founders. Phenotype information was available for 377 individuals who are related through the single, well-defined Norfolk pedigree (96 were affected: 64 MA, 32 MO). A total of 85 SNPs spanning the KCNN3 gene were genotyped in a sub-sample of 285 related individuals (76 affected), all core members of the extensive Norfolk Island ‘Bounty Mutineer’ genealogy. All genotyping was performed using the Illumina BeadArray platform. The analysis was performed using the statistical program SOLAR v4.0.6 assuming an additive model of allelic effect adjusted for the effects of age and sex. Haplotype analysis was undertaken using the program HAPLOVIEW v4.0. A total of four intronic SNPs in the KCNN3 gene displayed significant association (P < 0.05) with migraine. Two SNPs, rs73532286 and rs6426929, separated by approximately 0.1 kb, displayed complete LD (r 2 = 1.00, D′ = 1.00, D′ 95% CI = 0.96–1.00). In all cases, the minor allele led to a decrease in migraine risk (beta coefficient = 0.286–0.315), suggesting that common gene variants confer an increased risk of migraine in the Norfolk pedigree. This effect may be explained by founder effect in this genetic isolate. This study provides evidence for association of variants in the KCNN3 ion channel gene with migraine susceptibility in the Norfolk genetic isolate with the rarer allelic variants conferring a possible protective role. This the first comprehensive analysis of this potential candidate gene in migraine and also the first study that has utilised the unique Norfolk Island large pedigree isolate to implicate a specific migraine gene. Studies of additional variants in KCNN3 in the Norfolk pedigree are now required (e.g. polyglutamine variants) and further analyses in other population data sets are required to clarify the association of the KCNN3 gene and migraine risk in the general outbred population.

Association analysis of a highly polymorphic CAG Repeat in the human potassium channel gene KCNN3 and migraine susceptibility

Background Migraine is a polygenic multifactorial disease, possessing environmental and genetic causative factors with multiple involved genes. Mutations in various ion channel genes are responsible for a number of neurological disorders. KCNN3 is a neuronal small conductance calcium-activated potassium channel gene that contains two polyglutamine tracts, encoded by polymorphic CAG repeats in the gene. This gene plays a critical role in determining the firing pattern of neurons and acts to regulate intracellular calcium channels. Methods The present association study tested whether length variations in the second (more 3') polymorphic CAG repeat in exon 1 of the KCNN3 gene, are involved in susceptibility to migraine with and without aura (MA and MO). In total 423 DNA samples from unrelated individuals, of which 202 consisted of migraine patients and 221 non-migraine controls, were genotyped and analysed using a fluorescence labelled primer set on an ABI310 Genetic Analyzer. Allele frequencies were calculated from observed genotype counts for the KCNN3 polymorphism. Analysis was performed using standard contingency table analysis, incorporating the chi-squared test of independence and CLUMP analysis. Results Overall, there was no convincing evidence that KCNN3 CAG lengths differ between Caucasian migraineurs and controls, with no significant difference in the allelic length distribution of CAG repeats between the population groups (P = 0.090). Also the MA and MO subtypes did not differ significantly between control allelic distributions (P > 0.05). The prevalence of the long CAG repeat (>19 repeats) did not reach statistical significance in migraineurs (P = 0.15), nor was there a significant difference between the MA and MO subgroups observed compared to controls (P = 0.46 and P = 0.09, respectively), or between MA vs MO (P = 0.40). Conclusion This association study provides no evidence that length variations of the second polyglutamine array in the N-terminus of the KCNN3 channel exert an effect in the pathogenesis of migraine.

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].

Stromal upregulation of lateral epithelial adhesions : gene expression analysis of signalling pathways in prostate epithelium

BACKGROUND: Stromal signalling increases the lateral cell adhesions of prostate epithelial cells grown in 3D culture. The aim of this study was to use microarray analysis to identify significant epithelial signalling pathways and genes in this process. METHODS: Microarray analysis was used to identify genes that were differentially expressed when epithelial cells were grown in 3D Matrigel culture with stromal co-culture compared to without stroma. Two culture models were employed: primary epithelial cells (ten samples) and an epithelial cell line (three experiments). A separate microarray analysis was performed on each model system and then compared to identify tissue-relevant genes in a cell line model. RESULTS: TGF beta signalling was significantly ranked for both model systems and in both models the TGF beta signalling gene SOX4 was significantly down regulated. Analysis of all differentially expressed genes to identify genes that were common to both models found several morphology related gene clusters; actin binding (DIAPH2, FHOD3, ABLIM1, TMOD4, MYH10), GTPase activator activity (BCR, MYH10), cytoskeleton (MAP2, MYH10, TMOD4, FHOD3), protein binding (ITGA6, CD44), proteinaceous extracellular matrix (NID2, CILP2), ion channel/ ion transporter activity (CACNA1C, CACNB2, KCNH2, SLC8A1, SLC39A9) and genes associated with developmental pathways (POFUT1, FZD2, HOXA5, IRX2, FGF11, SOX4, SMARCC1). CONCLUSIONS: In 3D prostate cultures, stromal cells increase lateral epithelial cell adhesions. We show that this morphological effect is associated with gene expression changes to TGF beta signalling, cytoskeleton and anion activity.

The search for migraine genes : an overview of current knowledge

Migraine is a complex familial condition that imparts a significant burden on society. There is evidence for a role of genetic factors in migraine, and elucidating the genetic basis of this disabling condition remains the focus of much research. In this review we discuss results of genetic studies to date, from the discovery of the role of neural ion channel gene mutations in familial hemiplegic migraine (FHM) to linkage analyses and candidate gene studies in the more common forms of migraine. The success of FHM regarding discovery of genetic defects associated with the disorder remains elusive in common migraine, and causative genes have not yet been identified. Thus we suggest additional approaches for analysing the genetic basis of this disorder. The continuing search for migraine genes may aid in a greater understanding of the mechanisms that underlie the disorder and potentially lead to significant diagnostic and therapeutic applications.

Experimental evidence for competitive N–O and O–C bond homolysis in gasphase alkoxyamines

The extensive use of alkoxyamines in controlled radical polymerisation and polymer stabilisation is based on rapid cycling between the alkoxyamine (R1R2NO–R3) and a stable nitroxyl radical (R1R2NO•) via homolysis of the labile O–C bond. Competing homolysis of the alkoxyamine N–O bond has been predicted to occur for some substituents leading to production of aminyl and alkoxyl radicals. This intrinsic competition between the O–C and N–O bond homolysis processes has to this point been difficult to probe experimentally. Herein we examine the effect of local molecular structure on the competition between N–O and O–C bond cleavage in the gas phase by variable energy tandem mass spectrometry in a triple quadrupole mass spectrometer. A suite of cyclic alkoxyamines with remote carboxylic acid moieties (HOOC–R1R2NO–R3) were synthesised and subjected to negative ion electrospray ionisation to yield [M – H]− anions where the charge is remote from the alkoxyamine moiety. Collision-induced dissociation of these anions yield product ions resulting, almost exclusively, from homolysis of O–C and/or N–O bonds. The relative efficacy of N–O and O–C bond homolysis was examined for alkoxyamines incorporating different R3 substituents by varying the potential difference applied to the collision cell, and comparing dissociation thresholds of each product ion channel. For most R3 substituents, product ions from homolysis of the O–C bond are observed and product ions resulting from cleavage of the N–O bond are minor or absent. A limited number of examples were encountered however, where N–O homolysis is a competitive dissociation pathway because the O–C bond is stabilised by adjacent heteroatom(s) (e.g., R3 = CH2F). The dissociation threshold energies were compared for different alkoxyamine substituents (R3) and the relative ordering of these experimentally determined energies is shown to correlate with the bond dissociation free energies, calculated by ab initio methods. Understanding the structure-dependent relationship between these rival processes will assist in the design and selection of alkoxyamine motifs that selectively promote the desirable O–C homolysis pathway.

A stochastic exponential Euler scheme for simulation of stiff biochemical reaction systems

In order to simulate stiff biochemical reaction systems, an explicit exponential Euler scheme is derived for multidimensional, non-commutative stochastic differential equations with a semilinear drift term. The scheme is of strong order one half and A-stable in mean square. The combination with this and the projection method shows good performance in numerical experiments dealing with an alternative formulation of the chemical Langevin equation for a human ether a-go-go related gene ion channel mode

Partial epilepsy syndrome in a Gypsy family linked to 5q31.3-q32

PURPOSE The restricted genetic diversity and homogeneous molecular basis of Mendelian disorders in isolated founder populations have rarely been explored in epilepsy research. Our long-term goal is to explore the genetic basis of epilepsies in one such population, the Gypsies. The aim of this report is the clinical and genetic characterization of a Gypsy family with a partial epilepsy syndrome. METHODS Clinical information was collected using semistructured interviews with affected subjects and informants. At least one interictal electroencephalography (EEG) recording was performed for each patient and previous data obtained from records. Neuroimaging included structural magnetic resonance imaging (MRI). Linkage and haplotype analysis was performed using the Illumina IVb Linkage Panel, supplemented with highly informative microsatellites in linked regions and Affymetrix SNP 5.0 array data. RESULTS We observed an early-onset partial epilepsy syndrome with seizure semiology strongly suggestive of temporal lobe epilepsy (TLE), with mild intellectual deficit co-occurring in a large proportion of the patients. Psychiatric morbidity was common in the extended pedigree but did not cosegregate with epilepsy. Linkage analysis definitively excluded previously reported loci, and identified a novel locus on 5q31.3-q32 with an logarithm of the odds (LOD) score of 3 corresponding to the expected maximum in this family. DISCUSSION The syndrome can be classified as familial temporal lobe epilepsy (FTLE) or possibly a new syndrome with mild intellectual deficit. The linked 5q region does not contain any ion channel-encoding genes and is thus likely to contribute new knowledge about epilepsy pathogenesis. Identification of the mutation in this family and in additional patients will define the full phenotypic spectrum.

Structural analysis of the roles of influenza A virus membrane-associated proteins in assembly and morphology

The assembly of influenza A virus at the plasma membrane of infected cells leads to release of enveloped virions that are typically round in tissue culture-adapted strains but filamentous in strains isolated from patients. The viral proteins hemagglutinin (HA), neuraminidase (NA), matrix protein 1 (M1), and M2 ion channel all contribute to virus assembly. When expressed individually or in combination in cells, they can all, under certain conditions, mediate release of membrane-enveloped particles, but their relative roles in virus assembly, release, and morphology remain unclear. To investigate these roles, we produced membrane-enveloped particles by plasmid-derived expression of combinations of HA, NA, and M proteins (M1 and M2) or by infection with influenza A virus. We monitored particle release, particle morphology, and plasma membrane morphology by using biochemical methods, electron microscopy, electron tomography, and cryo-electron tomography. Our data suggest that HA, NA, or HANA (HA plus NA) expression leads to particle release through nonspecific induction of membrane curvature. In contrast, coexpression with the M proteins clusters the glycoproteins into filamentous membrane protrusions, which can be released as particles by formation of a constricted neck at the base. HA and NA are preferentially distributed to differently curved membranes within these particles. Both the budding intermediates and the released particles are morphologically similar to those produced during infection with influenza A virus. Together, our data provide new insights into influenza virus assembly and show that the M segment together with either of the glycoproteins is the minimal requirement to assemble and release membrane-enveloped particles that are truly virus-like.

Hypoxia-mimicking mesoporous bioactive glass scaffolds with controllable cobalt ion release for bone tissue engineering

Low oxygen pressure (hypoxia) plays an important role in stimulating angiogenesis; there are, however, few studies to prepare hypoxia-mimicking tissue engineering scaffolds. Mesoporous bioactive glass (MBG) has been developed as scaffolds with excellent osteogenic properties for bone regeneration. Ionic cobalt (Co) is established as a chemical inducer of hypoxia-inducible factor (HIF)-1α, which induces hypoxia-like response. The aim of this study was to develop hypoxia-mimicking MBG scaffolds by incorporating ionic Co2+ into MBG scaffolds and investigate if the addition of Co2+ ions would induce a cellular hypoxic response in such a tissue engineering scaffold system. The composition, microstructure and mesopore properties (specific surface area, nano-pore volume and nano-pore distribution) of Co-containing MBG (Co-MBG) scaffolds were characterized and the cellular effects of Co on the proliferation, differentiation, vascular endothelial growth factor (VEGF) secretion, HIF-1α expression and bone-related gene expression of human bone marrow stromal cells (BMSCs) in MBG scaffolds were systematically investigated. The results showed that low amounts of Co (< 5%) incorporated into MBG scaffolds had no significant cytotoxicity and that their incorporation significantly enhanced VEGF protein secretion, HIF-1α expression, and bone-related gene expression in BMSCs, and also that the Co-MBG scaffolds support BMSC attachment and proliferation. The scaffolds maintain a well-ordered mesopore channel structure and high specific surface area and have the capacity to efficiently deliver antibiotics drugs; in fact, the sustained released of ampicillin by Co-MBG scaffolds gives them excellent anti-bacterial properties. Our results indicate that incorporating cobalt ions into MBG scaffolds is a viable option for preparing hypoxia-mimicking tissue engineering scaffolds and significantly enhanced hypoxia function. The hypoxia-mimicking MBG scaffolds have great potential for bone tissue engineering applications by combining enhanced angiogenesis with already existing osteogenic properties.

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.

Mass spectrometric study of the dissociation of Group XI metal complexes with fatty acids and glycerolipids : Ag2H+ and Cu2H+ ion formation in the presence of a double bond

Results of mass spectrometric studies are reported for the collisional dissociation of Group XI (Cu, Ag, Au) metal ion complexes with fatty acids (palmitic, oleic, linoleic and a-linolenic) and glycerolipids. Remarkably, the formation of M2H+ ions (M = Cu, Ag) is observed as a dissociation product of the ion complexes containing more than one metal cation and only if the lipid in the complex contains a double bond. Ag2H+ is formed as the main dissociation channel for all three of the fatty acids containing double bonds that were investigated while Cu2H+ is formed with one of the fatty acids and, although abundant, is not the dominant dissociation channel. Also. Cu(I) and Ag(I) ion complexes were observed with glycerolipids (including triacylglycerols and glycerophospholipids) containing either saturated or unsaturated fatty acid substituents. Interestingly. Ag2H+ ion is formed in a major fragmentation channel with the lipids that are able to form the complex with two metal cations (triacylglycerols and glycerophosphoglycerols), while lipids containing a fixed positive charge (glycerophospocholines) complex only with a single metal cation. The formation of Ag2H+ ion is a significant dissociation channel from the complex ion Ag-2(L-H)(+) where L = Glycerophospholipid (GP) (18:1/18:1). Cu(I) also forms complexes of two metal cations with glycerophospholipids but these do not produce Cu2H+ upon dissociation. Rather organic fragments, not containing Cu(I), are formed, perhaps due to different interactions of these metal cations with lipids resulting from the much smaller ionic radius of Cu(I) compared to Ag(I) (C).