scholarly journals An optic ray theory for durotactic axon guidance

2020 ◽  
Author(s):  
Hadrien Oliveri ◽  
Kristian Franze ◽  
Alain Goriely
Keyword(s):  
Nervous System ◽  
Axon Guidance ◽  
Neuronal Network ◽  
Ray Theory ◽  
Directional Information ◽  
Substrate Rigidity ◽  
External Cues ◽  
Snell’S Law ◽  
Snell's Law ◽  
Simple Behavior

During the development of the nervous system, neurons extend bundles of axons that grow and meet other neurons to form the neuronal network. Robust guidance mechanisms are needed for these bundles to migrate and reach their functional target. Directional information depends on external cues such as chemical or mechanical gradients. Unlike chemotaxis that has been extensively studied, the role and mechanism of durotaxis, the directed response to variations in substrate rigidity, remain unclear. We model bundle migration and guidance by rigidity gradients by using the theory of morphoelastic rods. We show that at a rigidity interface, the motion of axon bundles follows a simple behavior analogous to optic ray theory and obeys Snell’s law for refraction and reflection. We use this powerful analogy to demonstrate that axons can be guided by the equivalent of optical lenses and fibers created by regions of different stiffnesses.

scholarly journals Snell's law for spin waves at a 90° magnetic domain wall

2020 ◽  
Vol 116 (11) ◽  
pp. 112402 ◽  
Author(s):  
Tomosato Hioki ◽  
Rei Tsuboi ◽  
Tom H. Johansen ◽  
Yusuke Hashimoto ◽  
Eiji Saitoh
Keyword(s):  
Domain Wall ◽  
Spin Waves ◽  
Magnetic Domain ◽  
Magnetic Domain Wall ◽  
Snell’S Law ◽  
Snell's Law

scholarly journals Functional Connectomics from Data: Probabilistic Graphical Models for Neuronal Network of C. elegans

2017 ◽  
Author(s):  
Hexuan Liu ◽  
Jimin Kim ◽  
Eli Shlizerman
Keyword(s):  
Time Series ◽  
Nervous System ◽  
Neuronal Network ◽  
Graphical Model ◽  
Data Matrix ◽  
Series Data ◽  
Response Dynamics ◽  
Functional Connectome ◽  
Network Response ◽  
Posterior Inference

AbstractWe propose a data-driven approach to represent neuronal network dynamics as a Probabilistic Graphical Model (PGM). Our approach learns the PGM structure by employing dimension reduction to network response dynamics evoked by stimuli applied to each neuron separately. The outcome model captures how stimuli propagate through the network and thus represents functional dependencies between neurons, i.e., functional connectome. The benefit of using a PGM as the functional connectome is that posterior inference can be done efficiently and circumvent the complexities in direct inference of response pathways in dynamic neuronal networks. In particular, posterior inference reveals the relations between known stimuli and downstream neurons or allows to query which stimuli are associated with downstream neurons. For validation and as an example for our approach we apply our methodology to a model of Caenorhabiditis elegans nervous system which structure and dynamics are well-studied. From its dynamical model we collect time series of the network response and use singular value decomposition to obtain a low-dimensional projection of the time series data. We then extract dominant patterns in each data matrix to get pairwise dependency information and create a graphical model for the full somatic nervous system. The PGM enables us to obtain and verify underlying neuronal pathways dominant for known behavioral scenarios and to detect possible pathways for novel scenarios.

scholarly journals Strength in the Periphery: Growth Cone Biomechanics and Substrate Rigidity Response in Peripheral and Central Nervous System Neurons

2012 ◽  
Vol 102 (3) ◽  
pp. 452-460 ◽  
Author(s):  
Daniel Koch ◽  
William J. Rosoff ◽  
Jiji Jiang ◽  
Herbert M. Geller ◽  
Jeffrey S. Urbach
Keyword(s):  
Central Nervous System ◽  
Nervous System ◽  
Growth Cone ◽  
Substrate Rigidity

Snell's law: Optimum pathway analysis

1977 ◽  
Vol 21 (6) ◽  
pp. 464-466 ◽  
Author(s):  
Robert J. Schechter
Keyword(s):  
Pathway Analysis ◽  
Snell’S Law ◽  
Snell's Law

scholarly journals Functional connectomics from neural dynamics: probabilistic graphical models for neuronal network of Caenorhabditis elegans

2018 ◽  
Vol 373 (1758) ◽  
pp. 20170377 ◽  
Author(s):  
Hexuan Liu ◽  
Jimin Kim ◽  
Eli Shlizerman
Keyword(s):  
Time Series ◽  
Nervous System ◽  
Caenorhabditis Elegans ◽  
Graphical Models ◽  
Neuronal Network ◽  
Graphical Model ◽  
Time Series Data ◽  
Series Data ◽  
Neuronal Responses ◽  
C Elegans

We propose an approach to represent neuronal network dynamics as a probabilistic graphical model (PGM). To construct the PGM, we collect time series of neuronal responses produced by the neuronal network and use singular value decomposition to obtain a low-dimensional projection of the time-series data. We then extract dominant patterns from the projections to get pairwise dependency information and create a graphical model for the full network. The outcome model is a functional connectome that captures how stimuli propagate through the network and thus represents causal dependencies between neurons and stimuli. We apply our methodology to a model of the Caenorhabditis elegans somatic nervous system to validate and show an example of our approach. The structure and dynamics of the C. elegans nervous system are well studied and a model that generates neuronal responses is available. The resulting PGM enables us to obtain and verify underlying neuronal pathways for known behavioural scenarios and detect possible pathways for novel scenarios. This article is part of a discussion meeting issue ‘Connectome to behaviour: modelling C. elegans at cellular resolution’.

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