Biological Rhythms and Motor Control

Thursday, June 17 at 09:30am (PDT)
Thursday, June 17 at 05:30pm (BST)
Friday, June 18 01:30am (KST)

SMB2021 SMB2021 Follow Thursday (Friday) during the "MS19" time block.
Note: this minisymposia has multiple sessions. The second session is MS20-NEUR (click here).

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Yangyang Wang (University of Iowa, USA), Peter Thomas (Case Western Reserve University, USA)


The brain is strongly coupled to the body. Within the mathematical neuroscience community, there is growing appreciation that the analysis of neural circuits involved in motor control is inseparable from the analysis of the motor system that coevolved with, and is the raison d'etre for the brain. This double minisymposium will showcase efforts by applied mathematicians, typically in collaboration with experimental biologists, to understand the dynamics of rhythmic motor systems including respiration, swallowing, and locomotion, and to describe how phenomena such as robustness and homeostasis arise from rhythmic brain-body interactions. The first of two sessions will address control of respiratory rhythms in vertebrates and ingestive/digestive rhythms in invertebrates. The second session will address modeling of locomotory control systems, as well as the notion of homeostasis for general limit cycle systems.

Yangyang Wang

(University of Iowa, USA)
"Shape and timing: using variational analysis to dissect motor robustness"
To survive and reproduce, an animal must adjust to changes in its internal state and the external environment. We refer to the ability of a motor system to maintain performance despite perturbations as “robustness”. Although it is well known that sensory feedback supports robust adaptive motor behaviors, specific mechanisms of robustness are not well understood either experimentally or theoretically. In this work, we explore how sensory feedback could alter a neuromechanical trajectory to enhance robustness for motor control. As a concrete example, we focus on a piecewise smooth neuromechanical model of triphasic motor patterns in the feeding apparatus of the marine mollusk, Aplysia californica. We investigate the mechanisms by which sensory feedback generates robust adaptive behavior, quantify the robustness of the Aplysia model to the applied perturbation (increased mechanical load), and compare them to experimental observations.

Zhuojun Yu

(Case Western Reserve University, USA)
"A homeostasis criterion for Limit cycle systems based on infinitesimal shape response curves"
Homeostasis occurs in a control system when a quantity remains approximately constant as a parameter, representing an external perturbation, varies over some range. Golubitsky and Stewart (J.~Math.~Biol., 2017) developed a notion of infinitesimal homeostasis for equilibrium systems using singularity theory. Rhythmic physiological systems (breathing, locomotion, feeding) maintain homeostasis through control of large-amplitude limit cycles rather than equilibrium points. Here we take an initial step to study (infinitesimal) homeostasis for limit-cycle systems in terms of the emph{average} of a quantity taken around the limit cycle. We apply the infinitesimal shape response curve (iSRC) introduced by Wang et al.~(SIAM J.~Appl.~Dyn.~Sys, to appear) to study infinitesimal homeostasis for limit-cycle systems in terms of the emph{mean} value of a quantity of interest, averaged around the limit cycle. Using the iSRC, which captures the linearized emph{shape} displacement of an oscillator upon a static perturbation, we provide a formula for the derivative of the averaged quantity with respect to the control parameter. Our expression allows one to identify homeostasis points for limit cycle systems in the averaging sense. We demonstrate in the Hodgkin-Huxley model and in a metabolic regulatory network model that the iSRC-based method provides an accurate representation of the sensitivity of averaged quantities.

Silvia Daun

(University of Cologne, Germany)
"Stimulus transformation into motor action: Dynamic graph analysis on neural oscillations reveals aging effects on brain network communication"
Cognitive performance slows down with increasing age. This includes cognitive processes that are essential for the performance of a motor act, such as the slowing down in response to an external stimulus. The objective of this study was to identify aging-associated functional changes in the brain networks that are involved in the transformation of external stimuli into motor action. To investigate this topic, we employed dynamic graphs based on phase-locking of Electroencephalography signals recorded from healthy younger and older subjects while performing a simple visually-cued finger-tapping task. The network analysis yielded specific age-related network structures varying in time in the low frequencies (2-7 Hz), which are closely connected to stimulus processing, movement initiation and execution in both age groups. The networks in older subjects, however, contained several additional, particularly interhemispheric, connections and showed an overall increased coupling density. Cluster analyses revealed reduced variability of the subnetworks in older subjects, particularly during movement preparation. In younger subjects, occipital, parietal, sensorimotor and central regions were-temporally arranged in this order-heavily involved in hub nodes. Whereas in older subjects, a hub in frontal regions preceded the noticeably delayed occurrence of sensorimotor hubs, indicating different neural information processing in older subjects. All observed changes in brain network organization, which are based on neural synchronization in the low frequencies, provide a possible neural mechanism underlying previous fMRI data, which report an overactivation, especially in the prefrontal and pre-motor areas, associated with a loss of hemispheric lateralization in older subjects.

Ansgar Bueschges

(University of Cologne, Germany)
"Task-specificity in the control of insect walking"
When terrestrial animals locomote through their environment they need to control the rhythmic stepping movements of each leg as well as the coordination between all stepping legs, being it two, four, six or eight legs to continuously assure stability as well as to optimally serve the actual behavioral task. The presentation will report recent advances in unravelling the neural organization and operation of the walking system in six legged insects by focusing on walking direction and speed in the fruit fly. Individual descending interneurons from the brain were identified, which are in charge of controlling walking direction. Fruit flies generate a continuum of interleg coordination patterns spanning from wave gait to tetrapod to tripod coordination with increasing walking speed from less than one bodylength/s to more than 15 bodylengths/s assuring optimal stability. Removal of single legs indicates that the leg muscle control system of the fruit fly is organized in a modular fashion with segmental rhythm generating networks.

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Virtual conference of the Society for Mathematical Biology, 2021.