SCIeNTIfIC REPORTS | (2018) 8:4559 | DOI:10.1038/s41598-018-22506-3
Computational Methods for
Estimating Molecular System from
Membrane Potential Recordings in
Nerve Growth Cone
, Makoto Nishiyama
, Shigeyuki Oba
, Henri Claver Jimbo
, Kazushi Ikeda
, Kyonsoo Hong
& Yuichi Sakumura
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
dierent 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.
Estimation or determination of unknown functions or targets by indirect measurements, e.g. the estimation of the
DNA double helix from its X-ray diraction pattern
, the functional connectivity of neurons from the activation
, the identication of cell type from the gene expression pattern
, and cancer diagnosis from breath gas
have been demonstrated. We present a computational derivation for the estimation of bimolecular
interactions from an observed time series of electrophysiological activities recorded from nerve growth cones.
Axon guidance is essential for establishing a neuronal network during nervous system development
biomolecular signaling pathways that instruct the direction of a navigating growth cone have been intensively
. Many studies
, including our’s
, have shown that the second messenger, cGMP, is a down-
stream eecter of the guidance cue, Sema3A. A growth cone normally exhibits a repulsive response to a Sema3A
. However, this repulsion converts to attraction if the intracellular cGMP level is elevated
studies revealed that the growth cone turning direction depends on the state of the growth cone membrane poten-
tial (MP); a hyperpolarized or depolarized state induces, respectively, either repulsion or attraction in response
to many diusible guidance molecules
. Furthermore, it has been shown that a low level of cGMP causes growth
cone hyperpolarization, whereas a high level of cGMP causes depolarization
, demonstrating that a cGMP signal
regulates the MP shis, which determine the growth cone turning direction. e signaling cascade that converts
the guidance cue-induced biomolecular system to electrical signals, however, remains largely unknown.
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
, which aects the observed MP; 3. multiple
unknown factors that potentially cooperate to regulate the molecular network. e current computational study
Graduate School of Information Science, Nara Institute of Science and Technology, Nara, Japan.
Biochemistry, New York University School of Medicine, New York, USA.
Graduate School of Informatics, Kyoto
University, Kyoto, Japan.
Graduate School of Biological Sciences, Nara Institute of Science and Technology, Nara,
KASAH Technology, Inc, New York, USA.
School of Information Science and Technology, Aichi Prefectural
University, Aichi, Japan. Correspondence and requests for materials should be addressed to K.H. (email: kyonsoo.
email@example.com) or Y.S. (email: firstname.lastname@example.org)
Received: 17 November 2017
Accepted: 22 February 2018
Published: xx xx xxxx