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.

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.

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.

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.