Full Hill-type muscle model of the I1/I3 retractor muscle complex in Aplysia californica

Biological Cybernetics https://doi.org/10.1007/s00422-024-00990-3 ORIGINAL ARTICLE Full Hill-type muscle model of the I1/I3 retractor muscle complex in Aplysia californica Ravesh Sukhnandan1 · Qianxue Chen2 · Jiayi Shen3 · Samantha Pao2 · Yu Huan2 · Gregory P. Sutton8 · Jeffrey P. Gill2 · Hillel J. Chiel2,4,5 · Victoria A. Webster-Wood1,6,7 Received: 29 November 2023 / Accepted: 22 April 2024 © The Author(s) 2024 Abstract The coordination of complex behavior requires knowledge of both neural dynamics and the mechanics of the periphery. The feeding system of Aplysia californica is an excellent model for investigating questions in soft body systems’ neuromechanics because of its experimental tractability. Prior work has attempted to elucidate the mechanical properties of the periphery by using a Hill-type muscle model to characterize the force generation capabilities of the key protractor muscle responsible for moving Aplysia’s grasper anteriorly, the I2 muscle. However, the I1/I3 muscle, which is the main driver of retractions of Aplysia’s grasper, has not been characterized. Because of the importance of the musculature’s properties in generating functional behavior, understanding the properties of muscles like the I1/I3 complex may help to create more realistic simulations of the feeding behavior of Aplysia, which can aid in greater understanding of the neuromechanics of soft-bodied systems. To bridge this gap, in this work, the I1/I3 muscle complex was characterized using force-frequency, length-tension, and forcevelocity experiments and showed that a Hill-type model can accurately predict its force-generation properties. Furthermore, the muscle’s peak isometric force and stiffness were found to exceed those of the I2 muscle, and these results were analyzed in the context of prior studies on the I1/I3 complex’s kinematics in vivo. Keywords Aplysia californica · Hill-type model · muscle · dynamics 1 Introduction Communicated by Benjamin Lindner. B Victoria A. Webster-Wood Hillel J. Chiel Understanding how neuromuscular systems coordinate complex multifunctional behavior requires a detailed understanding of both neural dynamics and the mechanics of the peripheral musculature. The periphery shapes the dynamics of each behavior differently due to changing mechanical advantages, contact interactions, and variations in the stiffness and damping of various muscle elements. For example, changing limb positions throughout walking changes the apparent stiffness at given joints (Silder et al. 2008). Similarly, variations in the shape of peripheral components can change the mechanical advantage of individual muscles to change overall forces in different behaviors (Olberding et al. 2019). Integral to such dynamic changes is the behavior and 1 Department of Mechanical Engineering, Carnegie Mellon University, 5000 Forbes Ave., Pittsburgh, PA 15213, USA 2 Department of Biology, Case Western Reserve University, 2080 Adelbert Road, Cleveland, OH 44106-7080, USA 3 Department of Nutrition, Case Western Reserve University, 2080 Adelbert Road, Cleveland, OH 44106-7080, USA 4 Department of Neurosciences, Case Western Reserve University, 2080 Adelbert Road, Cleveland, OH 44106-7080, USA 5 Department of Biomedical Engineering, Case Western Reserve University, 2080 Adelbert Road, Cleveland, OH 44106-7080, USA 7 McGowan Institute for Regenerative Medicine, Carnegie Mellon University, 5000 Forbes Ave., Pittsburgh, PA 15213, USA 6 Department of Biomedical Engineering, Carnegie Mellon University, 5000 Forbes Ave., Pittsburgh, PA 15213, USA 8 School of Life and Environmental Sciences, University of Lincoln, Green Lane, Lincoln LN67DL, UK 123 Biological Cybernetics mechanics of individual muscles. These mechanics may vary as a function of species (McMahon 1984), muscle type (Srinivasan et al. 2007), fiber orientation (Kuthe and Uddanwadiker 2016) and degradation of the biomaterials that compose muscle tissue (Zhang et al. 2020). A detailed understanding of these properties is critical to understanding and modeling multifunctional behavior in neuromuscular systems. Studying the neuromuscular control of soft-bodied animals and muscular hydrostatic systems, systems in which muscle plays both a structural and force-generating role such as tongues, trunks or tentacles (Longren et al. 2023), is particularly challenging due to the complex interactions of muscles throughout behavior. One model system for studying the neural control of a soft-bodied system is the sea slug, Aplysia californica (Webster-Wood et al. 2020). Aplysia generates multifunctional feeding behavior using a soft-bodied feeding structure made of muscle and cartilage. Feeding in Aplysia is typically classified into three primary behavioral types (Webster-Wood et al. 2020; Neustadter et al. 2007): (1) biting, which is an attempt to grasp food, (2) swallowing, which is an ingestive behavior in which seaweed is pulled into the esophagus by the feeding apparatus, and (3) rejection, which allows non-edible food to be pushed out of the feeding apparatus. Throughout each of these behaviors, the timing and degree of muscle activity vary, allowing all three behaviors to be generated with a limited number of neurons and a single periphery. To understand how the nervous system coordinates the complex musculature of the Aplysia feeding apparatus to generate multifunctional behavior, researchers have used neuromechanical modeling (Sutton et al. 2004; Webster-Wood et al. 2020). Neuromechanical models allow hypotheses about functions of muscles and neurons to be generated and tested in simulations (Prilutsky et al. 2016; Valero-Cuevas and Santello 2017). However, for such models to be used to guide experimental research, they must be as biomimetic as possible while still enabling high throughput simulation (Webster-Wood et al. 2020). Models with varying bioplausibility have been developed for Aplysia feeding, which has greatly enhanced our understanding of multifunctional softbodied control in this system. These models range from conductance-based models without periphery or sensory feedback (Costa et al. 2020), to highly abstracted biomechanical models of key muscle forces and elastic elements (Sutton et al. 2004; Webster-Wood et al. 2020; Shaw et al. 2015) to complex kinematic models (Neustadter et al. 2007). Each of these models has provided insight into the neuromuscular system. However, detailed biomechanical models of the system are limited due to the dearth of muscle property data available in the literature. To date, few Aplysia muscles have been characterized in detail to facilitate modeling the force-frequency, length-tension, and force-velocity properties of each muscle. In fact, only the I2 protractor muscle 123 has a detailed Hill-type model available as of the writing of this paper (Yu et al. 1999, 1997). The I2 muscle is a critical muscle for protracting Aplysia’s soft grasper called the odontophore during fe (...truncated)