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Human ether-a-go-go-related gene (HERG, Kv11.1, KCNH2) voltage-gated [K.sup.+] channels dominate cardiac action potential repolarization. In addition, HERG channels play a role in neuronal and smooth cell excitability as well as cancer pathology. Extracellular pH ([pH.sub.o]) is modified during myocardial ischemia, inflammation, and respiratory alkalosis, so understanding the response of HERG channels to changes in pH is of clinical significance. The relationship between [pH.sub.o] and HERG channel gating appears complex. Acidification has previously been reported to speed, slow, or have no effect on activation. We therefore undertook comprehensive analysis of the effect of [pH.sub.o] on HERG channel activation. HERG channels have unique and complex activation gating characteristics with both voltage-sensitive and voltage-insensitive steps in the activation pathway. Acidosis decreased the activation rate, suppressed peak current, and altered the sigmoidicity of gating near threshold potentials. At positive voltages, where the voltage-insensitive transition is rate limiting, [pH.sub.o] modified the voltage-insensitive step with a pKa similar to that of histidine. Hill coefficient analysis was incompatible with a coefficient of 1 but was well described by a Hill coefficient of 4. We derived a [pH.sub.o]-sensitive term for a five-state Markov model of HERG channel gating. This model demonstrates the mechanism of [pH.sub.o] sensitivity in HERG channel activation. Our experimental data and mathematical model demonstrate that the [pH.sub.o] sensitivity of HERG channel activation is dominated by the [pH.sub.o] sensitivity of the voltage-insensitive step, in a fashion that is compatible with the presence of at least one proton-binding site on each subunit of the channel tetramer. voltage-gated channels; potassium channels; gating kinetics; Kv11.1; human ether-a-go-go gene doi: 10.1152/ajpheart.01246.2009.

Electrophysiological studies often seek to relate changes in ion current properties caused by a chemical modifier to changes in cellular properties. Therefore, quantifying concentration-dependent effects of modifiers on ion currents is a topic of importance. In this paper, we sought a mathematical method for using ion current data to predict the effect of several theoretical ion current modifiers on cellular and tissue properties that is computationally efficient without compromising predictive power. We focused on the [K.sup.+] current [I.sub.K,r] as an example case due to its link to long QT syndrome and arrhythmias, but these methods should be generally applicable to other electrophysiological studies. We compared predictions using a Markov model with mass action binding of the modifiers to specific conformational states of the channel to predictions generated by two simplified models. We investigated scaling [I.sub.K,r] conductance, and found that although this method produced predictions that agreed qualitatively with the more complicated model, it did not generate quantitatively consistent predictions for all modifiers tested. Our simulations showed that a more computationally efficient Hodgkin-Huxley model that incorporates the effect of modifiers through functional changes in the current produced quantitatively consistent predictions of concentration-dependent changes in cell and tissue properties for all modifiers tested. Index Terms--Computer simulation, electropharmacology, electrophysiology, mathematical modeling.

Introduction: We used a computer simulation of HIV progression and transmission to evaluate the cost-effectiveness of a scale-up of 3 strategies to seek out and test individuals with undiagnosed HIV in New York City (NYC)., Setting: Hypothetical NYC population., Methods: We incorporated the observed effects and costs of the 3 "seek and test" strategies in a computer simulation of HIV in NYC, comparing a scenario in which the strategies were scaled up with a 1-year implementation or a long-term implementation with a counterfactual scenario with no scale-up. The simulation combined a deterministic compartmental model of HIV transmission with a stochastic microsimulation of HIV progression, calibrated to NYC epidemiological data from 2003 to 2015. The 3 approaches were respondent-driven sampling (RDS) with anonymous HIV testing ("RDS-A"), RDS with a 2-session confidential HIV testing approach ("RDS-C"), and venue-based sampling ("VBS")., Results: RDS-A was the most cost-effective strategy tested. When implemented for only 1 year and then stopped thereafter, using a societal perspective, the cost per quality-adjusted life-year (QALY) gained versus no intervention was $812/QALY, $18,110/QALY, and $20,362/QALY for RDS-A, RDS-C, and VBS, respectively. When interventions were implemented long term, the cost per QALY gained versus no intervention was cost-saving, $31,773/QALY, and $35,148/QALY for RDS-A, RDS-C, and VBS, respectively. When compared with RDS-A, the incremental cost-effectiveness ratios for both VBS and RDS-C were dominated., Conclusions: The expansion of the RDS-A strategy would substantially reduce HIV-related deaths and new HIV infections in NYC, and would be either cost-saving or have favorable cost-effectiveness.

A continuum model was introduced to analyze the pressure-flow relationship for steady flow in human pulmonary circulation. The continuum approach was based on the principles of continuum mechanics in conjunction with detailed measurement of vascular geometry, vascular elasticity and blood rheology. The pulmonary arteries and veins were considered as elastic tubes and the "fifth-power law" was used to describe the pressure-flow relationship. For pulmonary capillaries, the "sheet-flow" theory was employed and the pressure-flow relationship was represented by the "fourth-power law". In this paper, the pressure-flow relationship for the whole pulmonary circulation and the longitudinal pressure distribution along the streamlines were studied. Our computed data showed general agreement with the experimental data for the normal subjects and the patients with mitral stenosis and chronic bronchitis in the literature. In conclusion, our continuum model can be used to predict the changes of steady flow in human pulmonary circulation.

Vascular impedance is determined by morphometry and mechanical properties of the vascular system, as well as the rheology of the blood. The interactions between all these factors are complicated and difficult to investigate solely by experiments. A mathematical model representing the entire system of human pulmonary circulation was constructed based on experimentally measured morphometric and elasticity data of the vessels. The model consisted of 16 orders of arteries and 15 orders of veins. The pulmonary arteries and veins were considered as elastic tubes and their impedance was calculated based on Womersley's theory. The flow in capillaries was described by the "sheet-flow" theory. The model yielded an impedance modulus spectrum that fell steeply from a high value at 0 Hz to a minimum around 1.5 Hz. At about 4 Hz, it reached a second high and then oscillated around a relatively small value at higher frequencies. Characteristic impedance was 27.9 dyn-sec/cm5. Influence of variations in vessel geometry and elasticity on impedance spectra was analyzed. Simulation results showed good agreement with experimental measurements.