We present here a maximal likelihood algorithm for estimating single-channel kinetic parameters from idealized patch-clamp data. The algorithm takes into account missed events caused by limited time resolution of the recording system. Assuming a fixed dead time, we derive an explicit expression for the corrected transition rate matrix by generalizing the theory of Roux and Sauve (1985, Biophys. J. 48:149-158) to the case of multiple conductance levels. We use a variable metric optimizer with analytical derivatives for rapidly maximizing the likelihood. The algorithm is applicable to data containing substates and multiple identical or nonidentical channels. It allows multiple data sets obtained under different experimental conditions, e.g., concentration, voltage, and force, to be fit simultaneously. It also permits a variety of constraints on rate constants and provides standard errors for all estimates of model parameters. The algorithm has been tested extensively on a variety of kinetic models with both simulated and experimental data. It is very efficient and robust; rate constants for a multistate model can often be extracted in a processing time of approximately 1 min, largely independent of the starting values.

SUMMARYWe present a maximum likelihood method for the modelling of aggregated Markov processes. The method utilizes the joint probability density of the observed dwell time sequence as likelihood. A forward-backward recursive procedure is developed for efficient computation of the likelihood function and its derivatives with respect to the model parameters. Based on the calculated forward and backward vectors, analytical formulae for the derivatives of the likelihood function are derived. The method exploits the variable metric optimizer for search of the likelihood space. It converges rapidly and is numerically stable. Numerical examples are given to show the effectiveness of the method.

Summary The capsaicin receptor, TRPV1, is regulated by phosphatidylinositol-4,5-bisphosphate (PIP2), although the precise nature of this effect (i.e., positive or negative) remains controversial. Here, we reconstitute purified TRPV1 into artificial liposomes, where it is gated robustly by capsaicin, protons, spider toxins and, notably, heat, demonstrating intrinsic sensitivity of the channel to both chemical and thermal stimuli. TRPV1 is fully functional in the absence of phosphoinositides, arguing against their proposed obligatory role in channel activation. Rather, introduction of various phosphoinositides, including PIP2, PI4P and PI, inhibits TRPV1, supporting a model whereby phosphoinositide turnover contributes to thermal hyperalgesia by disinhibiting the channel. Using an orthogonal chemical strategy, we show that association of the TRPV1 C-terminus with the bilayer modulates channel gating, consistent with phylogenetic data implicating this domain as a key regulatory site for tuning stimulus sensitivity. Beyond TRPV1, these findings are relevant to understanding how membrane lipids modulate other “receptor-operated” TRP channels.

Cold is detected by a small subpopulation of peripheral thermoreceptors. TRPM8, a cloned menthol-and cold-sensitive ion channel, has been suggested to mediate cold transduction in the innocuous range. The channel shows a robust response in whole-cell recordings but exhibits markedly reduced activity in excised membrane patches. Here we report that phosphatidylinositol 4,5-bisphosphate (PIP 2 ) is an essential regulator of the channel function. The rundown of the channel is prevented by lipid phosphatase inhibitors. Application of exogenous PIP 2 both activates the channel directly and restores rundown activity. Whole-cell experiments involving intracellular dialysis with polyvalent cations, inhibition of PIP 2 synthesis kinases, and receptor-mediated hydrolysis of PIP 2 show that PIP 2 also modulates the channel activity in the intact cells. The crucial role of PIP 2 on the function of TRPM8 suggests that the membrane PIP 2 level may be an important regulator of cold transduction in vivo. The opposite effects of PIP 2 on the vanilloid receptor TRPV1 and TRPM8 also implies that the membrane lipid may have dual actions as a bimodal switch to selectively control the heat-and cold-induced responses in nociceptors expressing both channels.

Patch-clamp recording provides an unprecedented means for study of detailed kinetics of ion channels at the single molecule level. Analysis of the recordings often begins with idealization of noisy recordings into continuous dwell-time sequences. Success of an analysis is contingent on accuracy of the idealization. I present here a statistical procedure based on hidden Markov modeling and k-means segmentation. The approach assumes a Markov scheme involving discrete conformational transitions for the kinetics of the channel and a white background noise for contamination of the observations. The idealization is sought to maximize a posteriori probability of the state sequence corresponding to the samples. The approach constitutes two fundamental steps. First, given a model, the Viterbi algorithm is applied to determine the most likely state sequence. With the resultant idealization, the model parameters are then empirically refined. The transition probabilities are calculated from the state sequences, and the current amplitudes and noise variances are determined from the ensemble means and variances of those samples belonging to the same conductance classes. The two steps are iterated until the likelihood is maximized. In practice, the algorithm converges rapidly, taking only a few iterations. Because the noise is taken into explicit account, it allows for a low signal/noise ratio, and consequently a relatively high bandwidth. The approach is applicable to data containing subconductance levels or multiple channels and permits state-dependent noises. Examples are given to elucidate its performance and practical applicability.

The molecular basis of the thermal sensitivity of temperature-sensitive channels appears to arise from a specific protein domain rather than integration of global thermal effects. Using systematic chimeric analysis, we show that the N-terminal region that connects ankyrin repeats to the first transmembrane segment is crucial for temperature sensing in heat-activated vanilloid receptor channels. Changing this region both transformed temperature-insensitive isoforms into temperature-sensitive channels and significantly perturbed temperature sensing in temperature-sensitive wild-type channels. Swapping other domains such as the transmembrane core, the C terminus, and the rest of the N terminus had little effect on the steepness of temperature dependence. Our results support that thermal transient receptor potential channels contain modular thermal sensors that confer the unprecedentedly strong temperature dependence to these channels. chimera | temperature gating | temperature jump | thermosensation | pain T he ability to sense temperature is vital to living organisms. In mammals, the neural input on ambient temperature results from specialized groups of neurons that project to the skin. The transducers involve ion channels known as transient receptor potential (TRP) channels (1, 2), which constitute an array of biological thermometers responsive over a broad temperature gradient from noxious cold to noxious hot (3).The molecular mechanism by which temperature changes induce channel opening is not yet known, but the phenomenological tools to analyze the system are known from classical thermodynamic theory. The probability of channel opening follows a Boltzmann relationship to temperature. The enthalpy change (ΔH) between closed and open determines the slope sensitivity of the curve, whereas the entropy change (ΔS) affects its midpoint (T 1∕2 ). The term "threshold" is also commonly used in studies of temperature-sensitive channels to represent the change in temperature required for the response to be larger than the noise level of the recording. Changes in threshold could occur by changes in ∆H or T 1∕2 or the recording noise level.Thermodynamic analyses reveal that thermal TRP channels undergo large enthalpy changes, which accounts for their high temperature sensitivity (4-8). The opening of TRPV1, for example, involves an activation enthalpy of approximately 100 kcal/mol (7), five times the enthalpy change for ligand-or voltage-dependent gating [Q 10 ∼ 2-3 (ref. 9), equivalent to an enthalpy of approximately 20 kcal/mol]. If the free energy change were determined by enthalpy alone, the rate of gating would be very slow because the barrier would be too high. However, thermal TRP channels have evolved to have tightly coupled enthalpy and entropy changes so that the free energy change is relatively small (7). The threshold of activation summarizes the influence of all the temperature-insensitive processes that can regulate gating including the membrane potential (5, 6, 10) and any other allosteric sources such as li...

Hidden Markov modeling (HMM) provides an effective approach for modeling single channel kinetics. Standard HMM is based on Baum's reestimation. As applied to single channel currents, the algorithm has the inability to optimize the rate constants directly. We present here an alternative approach by considering the problem as a general optimization problem. The quasi-Newton method is used for searching the likelihood surface. The analytical derivatives of the likelihood function are derived, thereby maximizing the efficiency of the optimization. Because the rate constants are optimized directly, the approach has advantages such as the allowance for model constraints and the ability to simultaneously fit multiple data sets obtained at different experimental conditions. Numerical examples are presented to illustrate the performance of the algorithm. Comparisons with Baum's reestimation suggest that the approach has a superior convergence speed when the likelihood surface is poorly defined due to, for example, a low signal-to-noise ratio or the aggregation of multiple states having identical conductances.

Capsaicin and other naturally occurring pungent molecules have long been used as topical analgesics to treat a variety of chronic pain conditions. The analgesic effects of these compounds involve long-term desensitization of nociceptors after strong stimulation. To elucidate the underlying mechanisms, we studied the recovery from desensitization of the vanilloid receptor TRPV1. We showed that prolonged applications of capsaicin led to nearly complete desensitization of the channel and that its functional recovery from desensitization required a high concentration of intracellular ATP. Nonhydrolyzable ATP analogs did not substitute for ATP to promote recovery. Neither inhibition nor activation of protein kinases prevented recovery of the channel from desensitization. In contrast, blockade of lipid kinases, in particular phosphatidylinositol-4-kinase, abolished recovery, as did activation of membrane receptors that stimulate hydrolysis of phosphatidylinositol 4,5-biphosphate (PIP 2 ). Additional experiments using the PIP 2 -sensitive inward rectifier potassium channel Kir2.1 as a biosensor showed a high degree of temporal correlation between the two channels on both functional suppression after capsaicin stimulation and subsequent recovery. These data suggest that depletion of PIP 2 occurs concomitantly with activation of TRPV1 and its replenishment in the membrane determines recovery of the channel from desensitization. In addition to revealing a new role of phosphoinositide signaling in regulation of nociception, our results provide novel insight into the topical mechanisms of the analgesic effects of capsaicin and the strategies to improve its effectiveness.