From Average Transient Transporter Currents to Microscopic Mechanism─A Bayesian Analysis

Abstract

Electrophysiology studies of secondary active transporters have revealed quantitative mechanistic insights over many decades of research. However, the emergence of new experimental and analytical approaches calls for investigation of the capabilities and limitations of the newer methods. We examine the ability of solid-supported membrane electrophysiology (SSME) to characterize discrete-state kinetic models with >10 rate constants. We use a Bayesian framework applied to synthetic data for three tasks: to quantify and check (i) the precision of parameter estimates under different assumptions, (ii) the ability of computation to guide the selection of experimental conditions, and (iii) the ability of our approach to distinguish among mechanisms based on SSME data. When the general mechanism, i.e., event order, is known in advance, we show that a subset of kinetic parameters can be "practically identified" within ∼1 order of magnitude, based on SSME current traces that visually appear to exhibit simple exponential behavior. This remains true even when accounting for systematic measurement bias and realistic uncertainties in experimental inputs (concentrations) are incorporated into the analysis. When experimental conditions are optimized or different experiments are combined, the number of practically identifiable parameters can be increased substantially. Some parameters remain intrinsically difficult to estimate through SSME data alone, suggesting that additional experiments are required to fully characterize parameters. We also demonstrate the ability to perform model selection and determine the order of events when that is not known in advance, comparing Bayesian and maximum-likelihood approaches. Finally, our studies elucidate good practices for the increasingly popular but subtly challenging Bayesian calculations for structural and systems biology.

Bayesian Mechanistic Inference, Statistical Mechanics, and a New Era for Monte Carlo

“…In other words, can you trust the maximum likelihood estimates? In our hands, working with systems that are challengingbut possibleto sample, optimization algorithms do not provide reproducible, truly optimal results . We know this because we can simply compare optimization results to the maximum likelihood observed in MC sampling, which is reproducible when sampling is adequate.…”

“…Metropolis-Hastings with a standard Normal proposal distribution is used, enabling efficient sample generation subject to the accuracy of transformation. We have found this method to be valuable for the Bayesian inference of dynamic models of membrane transporters with 10–20 parameters …”

“…Operationally, BI is performed using the same physical model and priors but different synthetic data sets generated across a range of experimental conditions. Quantitative measures such the Kullback–Leibler (KL) divergence (i.e., relative entropy) may be used to compare separation of the posterior and prior distributions. , These quantities can then be used to determine the optimal experiment or set of experiments that maximizes the information gain. Here the use of synthetic data saves the potentially significant experimental costs needed to generate the data.…”

“…We also note that BI credibility regions can help to reveal bias in experimental measurements. This can be done directly if an explicit “nuisance” parameter is used to represent bias in experimental measurements . Alternatively, bias can be assessed implicitly based on nuisance parameters describing uncertainty for input experimental values: if the posterior marginal for such a nuisance parameter is found to have significant probability at the extremes of the assumed range, that suggests the original experimental range for the parameter was underestimated (assuming the model itself is correct).…”