Composite control of non-linear singularly perturbed systems: a geometric approach

Using a geometric approach, a composite control—the sum of a slow control and a fast control—is derived for a general class of non-linear singularly perturbed systems. A new and simpler method of composite control design is proposed whereby the fast control is completely designed at the outset. The slow control is then free to be chosen such that the slow integral manifold of the original system approximates a desired design manifold to within any specified order of ε accuracy.

Analytic Benchmark Solutions for Open-Channel Flows

An important test of the quality of a computational model is its ability to reproduce standard test cases or benchmarks. For steady open–channel flow based on the Saint Venant equations some benchmarks exist for simple geometries from the work of Bresse, Bakhmeteff and Chow but these are tabulated in the form of standard integrals. This paper provides benchmark solutions for a wider range of cases, which may have a nonprismatic cross section, nonuniform bed slope, and transitions between subcritical and supercritical flow. This makes it possible to assess the underlying quality of computational algorithms in more difficult cases, including those with hydraulic jumps. Several new test cases are given in detail and the performance of a commercial steady flow package is evaluated against two of them. The test cases may also be used as benchmarks for both steady flow models and unsteady flow models in the steady limit.

Statins and selective inhibition of Rho kinase protect small conductance calcium-activated potassium channel function (KCa2.3) in cerebral arteries

Background: In rat middle cerebral and mesenteric arteries the KCa2.3 component of endothelium-dependent hyperpolarization (EDH) is lost following stimulation of thromboxane (TP) receptors, an effect that may contribute to the endothelial dysfunction associated with cardiovascular disease. In cerebral arteries, KCa2.3 loss is associated with NO synthase inhibition, but is restored if TP receptors are blocked. The Rho/Rho kinase pathway is central for TP signalling and statins indirectly inhibit this pathway. The possibility that Rho kinase inhibition and statins sustain KCa2.3 hyperpolarization was investigated in rat middle cerebral arteries (MCA). Methods: MCAs were mounted in a wire myograph. The PAR2 agonist, SLIGRL was used to stimulate EDH responses, assessed by simultaneous measurement of smooth muscle membrane potential and tension. TP expression was assessed with rt-PCR and immunofluorescence. Results: Immunofluorescence detected TP in the endothelial cell layer of MCA. Vasoconstriction to the TP agonist, U46619 was reduced by Rho kinase inhibition. TP receptor stimulation lead to loss of KCa2.3 mediated hyperpolarization, an effect that was reversed by Rho kinase inhibitors or simvastatin. KCa2.3 activity was lost in L-NAME-treated arteries, but was restored by Rho kinase inhibition or statin treatment. The restorative effect of simvastatin was blocked after incubation with geranylgeranyl-pyrophosphate to circumvent loss of isoprenylation. Conclusions: Rho/Rho kinase signalling following TP stimulation and L-NAME regulates endothelial cell KCa2.3 function. The ability of statins to prevent isoprenylation and perhaps inhibit of Rho restores/protects the input of KCa2.3 to EDH in the MCA, and represents a beneficial pleiotropic effect of statin treatment.

Protease-activated receptor 2 sensitizes the transient receptor potential vanilloid 4 ion channel to cause mechanical hyperalgesia in mice

Exacerbated sensitivity to mechanical stimuli that are normally innocuous or mildly painful (mechanical allodynia and hyperalgesia) occurs during inflammation and underlies painful diseases. Proteases that are generated during inflammation and disease cleave protease-activated receptor 2 (PAR2) on afferent nerves to cause mechanical hyperalgesia in the skin and intestine by unknown mechanisms. We hypothesized that PAR2-mediated mechanical hyperalgesia requires sensitization of the ion channel transient receptor potential vanilloid 4 (TRPV4). Immunoreactive TRPV4 was coexpressed by rat dorsal root ganglia (DRG) neurons with PAR2, substance P (SP) and calcitonin gene-related peptide (CGRP), mediators of pain transmission. In PAR2-expressing cell lines that either naturally expressed TRPV4 (bronchial epithelial cells) or that were transfected to express TRPV4 (HEK cells), pretreatment with a PAR2 agonist enhanced Ca2+ and current responses to the TRPV4 agonists phorbol ester 4alpha-phorbol 12,13-didecanoate (4alphaPDD) and hypotonic solutions. PAR2-agonist similarly sensitized TRPV4 Ca2+ signals and currents in DRG neurons. Antagonists of phospholipase Cbeta and protein kinases A, C and D inhibited PAR2-induced sensitization of TRPV4 Ca2+ signals and currents. 4alphaPDD and hypotonic solutions stimulated SP and CGRP release from dorsal horn of rat spinal cord, and pretreatment with PAR2 agonist sensitized TRPV4-dependent peptide release. Intraplantar injection of PAR2 agonist caused mechanical hyperalgesia in mice and sensitized pain responses to the TRPV4 agonists 4alphaPDD and hypotonic solutions. Deletion of TRPV4 prevented PAR2 agonist-induced mechanical hyperalgesia and sensitization. This novel mechanism, by which PAR2 activates a second messenger to sensitize TRPV4-dependent release of nociceptive peptides and induce mechanical hyperalgesia, may underlie inflammatory hyperalgesia in diseases where proteases are activated and released.

Carbon monoxide mediates the anti-apoptotic effects of heme oxygenase-1 in medulloblastoma DAOY cells via K+ channel inhibition

Tumor cell survival and proliferation is attributable in part to suppression of apoptotic pathways, yet the mechanisms by which cancer cells resist apoptosis are not fully understood. Many cancer cells constitutively express heme oxygenase-1 (HO-1), which catabolizes heme to generate biliverdin, Fe(2+), and carbon monoxide (CO). These breakdown products may play a role in the ability of cancer cells to suppress apoptotic signals. K(+) channels also play a crucial role in apoptosis, permitting K(+) efflux which is required to initiate caspase activation. Here, we demonstrate that HO-1 is constitutively expressed in human medulloblastoma tissue, and can be induced in the medulloblastoma cell line DAOY either chemically or by hypoxia. Induction of HO-1 markedly increases the resistance of DAOY cells to oxidant-induced apoptosis. This effect was mimicked by exogenous application of the heme degradation product CO. Furthermore we demonstrate the presence of the pro-apoptotic K(+) channel, Kv2.1, in both human medulloblastoma tissue and DAOY cells. CO inhibited the voltage-gated K(+) currents in DAOY cells, and largely reversed the oxidant-induced increase in K(+) channel activity. p38 MAPK inhibition prevented the oxidant-induced increase of K(+) channel activity in DAOY cells, and enhanced their resistance to apoptosis. Our findings suggest that CO-mediated inhibition of K(+) channels represents an important mechanism by which HO-1 can increase the resistance to apoptosis of medulloblastoma cells, and support the idea that HO-1 inhibition may enhance the effectiveness of current chemo- and radiotherapies.

Immunopharmacology: utilizing antibodies as ion channel modulators

Development of the patch clamp technique by the Nobel Prize winners Bert Sakmann and Erwin Neher led to huge advances in ion channel research. Their work laid the foundations and revolutionized electrophysiological studies of cells and ion channels. These ion channels underlie many basic cellular physiological processes and, therefore, are key therapeutic targets for pharmaceutical companies. However, current pharmacological strategies are hampered by the lack of specific ion channel blockers. Intense research and development programs are now actively employing antibodies to target ion channels in various formats. This review discusses the use of ion channel antibodies and their associated small molecules as pharmacological tools, termed immunopharmacology. In addition, we will review some recent studies looking into clinical applications of immunopharmacology and intrabodies.

Suppression of a pro-apoptotic K+ channel as a mechanism for hepatitis C virus persistence

An estimated 3% of the global population are infected with hepatitis C virus (HCV), and the majority of these individuals will develop chronic liver disease. As with other chronic viruses, establishment of persistent infection requires that HCV-infected cells must be refractory to a range of pro-apoptotic stimuli. In response to oxidative stress, amplification of an outward K(+) current mediated by the Kv2.1 channel, precedes the onset of apoptosis. We show here that in human hepatoma cells either infected with HCV or harboring an HCV subgenomic replicon, oxidative stress failed to initiate apoptosis via Kv2.1. The HCV NS5A protein mediated this effect by inhibiting oxidative stress-induced p38 MAPK phosphorylation of Kv2.1. The inhibition of a host cell K(+) channel by a viral protein is a hitherto undescribed viral anti-apoptotic mechanism and represents a potential target for antiviral therapy.

Modulation of potassium ion channel proteins utilising antibodies

The application of antibodies to living cells has the potential to modulate the function of specific proteins by virtue of their high specificity. This specificity has proven effective in determining the involvement of many proteins in neuronal function where specific agonists and antagonists do not exist, e.g. ion channel subunits. We discuss a way to utilise subunit specific antibodies to target individual channel subunits in electrophysiological experiments to determine functional roles within native neurones. Utilising this approach, we have investigated the role of the voltage-gated potassium channel Kv3.1b subunit within a region of the brainstem important in the regulation of autonomic function. We provide some useful control experiments in order to help validate this method. We conclude that antibodies can be extremely valuable in determining the functions of specific proteins in living neurones in neuroscience research.

Molecular requirements for L-type Ca2+ channel blockade by testosterone

Despite being generally perceived as detrimental to the cardiovascular system, testosterone has marked beneficial vascular effects; most notably it acutely and directly causes vasodilatation. Indeed, men with hypotestosteronaemia can present with myocardial ischemia and angina which can be rapidly alleviated by infusion of testosterone. To date, however, in vitro studies have failed to provide a convincing mechanism to account for this clinically important effect. Here, using whole-cell patch-clamp recordings to measure current flow through recombinant human L-type Ca2+ channel alpha(1C) subunits (Ca(v)1.2), we demonstrate that testosterone inhibits such currents in a concentration-dependent manner. Importantly, this occurs over the physiological range of testosterone concentrations (IC50 34 nM), and is not mimicked by the metabolite 5alpha-androstan-17beta-ol-3-one (DHT), nor by progesterone or estradiol, even at high (10 microM) concentration. L-type Ca2+ channels in the vasculature are also important clinical targets for vasodilatory dihydropyridines. A single point mutation (T1007Y) almost completely abolishes nifedipine sensitivity in our recombinant expression system. Crucially, the same mutation renders the channels insensitive to testosterone. Our data strongly suggest, for the first time, the molecular requirements for testosterone binding to L-type Ca2+ channels, thereby supporting its beneficial role as an endogenous Ca2+ channel antagonist in the treatment of cardiovascular disease.

Phosphorylation of the voltage-gated potassium channel Kv2.1 by AMP-activated protein kinase regulates membrane excitability

Firing of action potentials in excitable cells accelerates ATP turnover. The voltage-gated potassium channel Kv2.1 regulates action potential frequency in central neurons, whereas the ubiquitous cellular energy sensor AMP-activated protein kinase (AMPK) is activated by ATP depletion and protects cells by switching off energy-consuming processes. We show that treatment of HEK293 cells expressing Kv2.1 with the AMPK activator A-769662 caused hyperpolarizing shifts in the current-voltage relationship for channel activation and inactivation. We identified two sites (S440 and S537) directly phosphorylated on Kv2.1 by AMPK and, using phosphospecific antibodies and quantitative mass spectrometry, show that phosphorylation of both sites increased in A-769662-treated cells. Effects of A-769662 were abolished in cells expressing Kv2.1 with S440A but not with S537A substitutions, suggesting that phosphorylation of S440 was responsible for these effects. Identical shifts in voltage gating were observed after introducing into cells, via the patch pipette, recombinant AMPK rendered active but phosphatase-resistant by thiophosphorylation. Ionomycin caused changes in Kv2.1 gating very similar to those caused by A-769662 but acted via a different mechanism involving Kv2.1 dephosphorylation. In cultured rat hippocampal neurons, A-769662 caused hyperpolarizing shifts in voltage gating similar to those in HEK293 cells, effects that were abolished by intracellular dialysis with Kv2.1 antibodies. When active thiophosphorylated AMPK was introduced into cultured neurons via the patch pipette, a progressive, time-dependent decrease in the frequency of evoked action potentials was observed. Our results suggest that activation of AMPK in neurons during conditions of metabolic stress exerts a protective role by reducing neuronal excitability and thus conserving energy.

MICPA: a client-assisted channel assignment scheme for throughput enhancement in WLANs

The emergence of high-density wireless local area network (WLAN) deployments in recent years is a testament to the insatiable demands for wireless broadband services. The increased density of WLAN deployments brings with it the potential of increased capacity, extended coverage, and exciting new applications. However, the corresponding increase in contention and interference can significantly degrade throughputs, unless new challenges in channel assignment are effectively addressed. In this paper, a client-assisted channel assignment scheme that can provide enhanced throughput is proposed. A study on the impact of interference on throughput with multiple access points (APs)is first undertaken using a novel approach that determines the possibility of parallel transmissions. A metric with a good correlation to the throughput, i.e., the number of conflict pairs, is used in the client-assisted minimum conflict pairs (MICPA) scheme. In this scheme, measurements from clients are used to assist the AP in determining the channel with the minimum number of conflict pairs to maximize its expected throughput. Simulation results show that the client-assisted MICPA scheme can provide meaningful throughput improvements over other schemes that only utilize the AP’s measurements.

Use of synthetic CaV2.2 Ca2+ channel peptides to study presynaptic function

Small, synthetic peptides based on specific regions of voltage-gated Ca2+ channels (VGCCs) have been widely used to study Ca2+ channel function and have been instrumental in confirming the contribution of specific amino acid sequences to interactions with putative binding partners. In particular, peptides based on the Ca2+ channel Alpha Interaction Domain (AID) on the intracellular region connecting domains I and II (the I-II loop) and the SYNaptic PRotein INTerction (synprint) site on the II-III loop have been widely used. Emerging evidence suggests that such peptides may themselves possess inherent functionality, a property that may be exploitable for future drug design. Here, we review our recent work using synthetic Ca2+ channel peptides based on sequences within the CaV2.2 amino terminal and I-II loop, originally identified as molecular determinates for G protein modulation, and their effects on VGCC function. These CaV2.2 peptides act as inhibitory modules to decrease Ca2+ influx with direct effects on VGCC gating, ultimately leading to a reduction of synaptic transmission. CaV2.2 peptides also attenuate G protein modulation of VGCCs. Amino acid substitutions generate CaV2.2 peptides with increased or decreased inhibitory effects suggesting that synthetic peptides can be used to further probe VGCC function and, potentially, form the basis for novel therapeutic development.

A bank lending channel or a credit supply shock?

Shifts in credit supply could have a bearing on house prices e.g. through financial innovations and changes in regulation independently of the existence of a bank lending channel of monetary policy. This paper assesses the responses of US house prices to an exogenous credit supply shock and compares them with the effects from variations in credit supply associated with a bank lending channel. The contribution of the study is twofold. First, innovations in credit supply are identified using a mortgage mix variable, thereby accounting for the market-based financial intermediaries. As a robustness check a survey variable of bank lending standards for mortgage loans is also used. Second, the policy-induced credit supply effect on house prices is disentangled and compared with the effect from an exogenous credit supply shock. It is shown that in the first 3 years credit supply shocks affect house prices exogenously rather than through the bank lending channel. Monetary policy has still a large impact on house prices, even when the bank lending channel is ‘turned off’.

Compliant Multi-electrode Micro-channel Array for Recording Afferent Nerve Activity

We have fabricated a compliant neural interface to record afferent nerve activity. Stretchable gold electrodes were evaporated on a polydimethylsiloxane (PDMS) substrate and were encapsulated using photo-patternable PDMS. The built-in microstructure of the gold film on PDMS allows the electrodes to twist and flex repeatedly, without loss of electrical conductivity. PDMS microchannels (5mm long, 100μm wide, 100μm deep) were then plasma bonded irreversibly on top of the electrode array to define five parallel-conduit implants. The soft gold microelectrodes have a low impedance of ~200kΩ at the 1kHz frequency range. Teased nerves from the L6 dorsal root of an anaesthetized Sprague Dawley rat were threaded through the microchannels. Acute tripolar recordings of cutaneous activity are demonstrated, from multiple nerve rootlets simultaneously. Confinement of the axons within narrow microchannels allows for reliable recordings of low amplitude afferents. This electrode technology promises exciting applications in neuroprosthetic devices including bladder fullness monitors and peripheral nervous system implants.