Abstract
The neural dynamics of the nematode Caenorhabditis elegans are experimentally low-dimensional and may be understood as long-timescale transitions between multiple low-dimensional attractors. Previous modeling work has found that dynamic models of the worm's full neuronal network are capable of generating reasonable dynamic responses to certain inputs, even when all neurons are treated as identical save for their connectivity. This study investigates such a model of C. elegans neuronal dynamics, finding that a wide variety of multistable responses are generated in response to varied inputs. Specifically, we generate bifurcation diagrams for all possible single-neuron inputs, showing the existence of fixed points and limit cycles for different input regimes. The nature of the dynamical response is seen to vary according to the type of neuron receiving input; for example, input into sensory neurons is more likely to drive a bifurcation in the system than input into motor neurons. As a specific example we consider compound input into the neuron pairs PLM and ASK, discovering bistability of a limit cycle and a fixed point. The transient timescales in approaching each of these states are much longer than any intrinsic timescales of the system. This suggests consistency of our model with the characterization of dynamics in neural systems as long-timescale transitions between discrete, low-dimensional attractors corresponding to behavioral states.
Highlights
The complex structure of neuronal networks must be designed to balance a variety of competing factors
We explore the input space of model for the neuronal network dynamics of C. elegans developed in Kunert et al (2014), and find that various multistabilities can arise in response to inputs
Since we wish to understand the neural dynamics as consisting of long-timescale transients in the presence of multiple discrete attractors, we develop a method for (1) identifying the existence and nature of attractors in response to arbitrary inputs, (2) characterizing transient timescales, and (3) providing interpretable biophysical meaning to calculated trajectories via projection onto a meaningful low-dimensional space
Summary
The complex structure of neuronal networks must be designed to balance a variety of competing factors. Such networks must robustly respond to a wide range of inputs with a broad variety of output behaviors, while approximately minimizing constraints, such as their overall wiring cost (Chen et al, 2006; Bullmore and Sporns, 2012). It is no surprise, that the connectivities of such networks are typically far from random (Sporns, 2011). The robust functional responses and behavioral assays are characterized by low-dimensional attractors or transient trajectories between them (Gold and Shadlen, 1999; Laurent et al, 2001; Rabinovich et al, 2001, 2008; Jones et al, 2007; Rabinovich and Varona, 2011; Stephens et al, 2011; Kunert et al, 2014; Shlizerman et al, 2014).
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
