Abstract
Biological cells express intracellular biomolecular information to the extracellular environment as various physical responses. We show a novel computational approach to estimate intracellular biomolecular pathways from growth cone electrophysiological responses. Previously, it was shown that cGMP signaling regulates membrane potential (MP) shifts that control the growth cone turning direction during neuronal development. We present here an integrated deterministic mathematical model and Bayesian reversed-engineering framework that enables estimation of the molecular signaling pathway from electrical recordings and considers both the system uncertainty and cell-to-cell variability. Our computational method selects the most plausible molecular pathway from multiple candidates while satisfying model simplicity and considering all possible parameter ranges. The model quantitatively reproduces MP shifts depending on cGMP levels and MP variability potential in different experimental conditions. Lastly, our model predicts that chloride channel inhibition by cGMP-dependent protein kinase (PKG) is essential in the core system for regulation of the MP shifts.
Highlights
To computationally estimate the biomolecular network responsible for axon guidance from growth cone membrane potential (MP) recordings, three major hurdles must be overcome: 1. the limited availability of the recording data due to the amount of labor required; 2. the large cell-to-cell variability[17,18,19], which affects the observed MP; 3. multiple unknown factors that potentially cooperate to regulate the molecular network
The sampled MP time series (MPTS) provides a sufficient number of data points to allow us to develop a quantitative and deterministic mathematical model to dissect the cGMP signaling responsible for inducing growth cone MP shifts
Our model incorporates the mesoscopic molecular signal flows within a core system of the model with parameter set, θ, that regulate chloride and sodium channels (ClC and NaC), respectively, hyperpolarizing and depolarizing channels that regulate MP shifts (Fig. 1d)
Summary
To computationally estimate the biomolecular network responsible for axon guidance from growth cone MP recordings, three major hurdles must be overcome: 1. the limited availability of the recording data due to the amount of labor required; 2. the large cell-to-cell variability[17,18,19], which affects the observed MP; 3. multiple unknown factors that potentially cooperate to regulate the molecular network. Considers the limited availability of data by utilizing each MP time series (MPTS) that contain over 10,000 data points within one recording sample, thereby providing sufficient data points to perform quantitative computational analysis and to fit a deterministic model to a cell-dependent characteristic. By the Bayesian reverse-engineering framework of the system comprised of different physical quantities, we computed the posterior distributions of the parameters that are derived from a fitness of the deterministic biochemical reaction model developed using the experimental MP data sets and prior constraints. The study considers the involvement of multiple unknown factors in the signaling pathway by developing a signaling cascade-based model that simplifies the multiple bio-molecular cascades, and introduced MPTSs data sets into the model. We provide a novel computational methodology to estimate the essential molecular signaling components in transducing the electrical responses elicited during growth cone turning
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