Bayesian dictionary learning estimation of cell membrane permeability from surface pH data

TL;DR

This study addresses estimating gas membrane permeability from surface pH data by combining a forward reaction-diffusion model for CO2 transport with a Bayesian dictionary learning estimator. The approach precomputes a dictionary of model outputs across a grid of parameters, factors subdictionaries with nonnegative matrix factorization, and uses a sparsity promoting IAS-based inference to identify a best subdictionary and map sparse coefficients to a parameter vector $\xi$; in particular it targets $(\xi_\lambda, \xi_A, \xi_\gamma)$ corresponding to the physical parameters $\lambda$, $A^0$, and $\gamma$. The main contributions are the three phase dictionary workflow, the treatment of dictionary compression error via Gaussian approximations, and the demonstration of substantial speedups over particle filtering while maintaining accuracy on synthetic data. This work enables faster, parallelizable inference for low dimensional parameter spaces in biophysical membrane transport with practical implications for testing the gas channel hypothesis.

Abstract

Gas transport across cell membrane is a very important process in biochemistry which is essential for many crucial tasks, including cell respiration pH regulation in the cell. In the late 1990's, the suggestion that gasses are transported via preferred gas channels embedded into the cell membrane challenged the century old Overton's theory that gases pass through the lipid cell membrane by diffusing across the concentration gradient. Since experimental evidence alone does not provide enough evidence to favor one of the proposed mechanisms, mathematical models have been introduced to provide a context for the interpretation of laboratory measurement. Following up on previous work where the membrane permeability was estimated using particle filter, in this article we propose an algorithm based on dictionary learning for estimating cell membrane permeability. Computed examples illustrate that the novel approach, which can be applied when the properties of the membrane do not change in the course of the data collection process, is computationally much more efficient than particle filter.

Figures (4)

• Figure 1: A schematic illustration of the ${\rm CO}_2$ based pH regulation across the cell membrane. A passage of a ${\rm CO}_2$ molecule, together with the reversible association/dissociation of the carbonic acid leads to a virtual transport of a proton across the membrane. The carbonic anhydrase (CA) enzyme acting on the membrane and inside the cell promote the dissociation or the association process of ${\rm H}_2{\rm CO}_3$.
• Figure 2: A schematic explanation of the hypothesized microenvironment created by the measurement device pushed against the membrane (left and center). The simplified geometry simulating the phenomenon is shown on the right. The free diffusion between the outside domain and the micro-compartment under the electrode is limited under the electrode edge.
• Figure 3: Visualization of the parameter space: Parameter triples $(\xi_1,\xi_2,\xi_3) = (\xi_\lambda,\xi_A,\xi_\gamma)$ corresponding to dictionary entries in each of the seven subdictionaries are indicated with a different color. The two cubes represent two different view angles, and to facilitate the interpretation, a green fiducial dot is added on the top of the cube.
• Figure 4: The pH curves of the three computed experiments. The solid green curve, labeled as "true', represents the computed output with parameter values that were used to generate the synthetic data, and the dashed black curve, labeled as "estimated", is the pH response computed with the parameter values estimated by the dictionary learning algorithm.