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Objectives and Significance
Objectives and Significance
The broad aim for this project is to enhance the understanding of biological information processing mechanisms. The immediate goals are to uncover the fundamental roles of sensory feedback mechanisms in the neuronal control of animal locomotion and to establish mathematical models that predict the dynamical behavior of and supply missing information about the biological system. More specifically, the aims are to I) perform biophysical and physiological experiments on leech preparations to collect neuronal and mechanical input/output data needed for quantitative models, II) develop a mathematical model of the neuronal control system for leech swimming that includes sensory feedback, III) predict the effects of sensory feedback through numerical simulations of the model, and IV) test these predictions through physiological experiments on leech preparations.
Design principles embedded in biological systems are often difficult to decipher due to the extreme complexity. The leech swimming system provides an ideal research platform. Much is known about the individual neurons that comprise the leech CPG and about their interactions, unlike sensory-motor systems in humans and most other vertebrates. Yet, behaviors of leeches, including their undulatory pattern formation, are more diverse and complex than those of more primitive animals. Our research exploits this unique opportunity, in combination with systems approaches, to gain a new perspective on neuronal computation mechanisms. Systems-level integration of component models (CPG, muscle, body, fluid) allows for understanding of feedback principles that cannot be explained by sequential cause-result logic alone. General control principles will be revealed to explain how the CPG maintains or modifies its oscillation pattern through sensory feedback when environmental changes or neuro-mechanical failures occur. Potential applications of the knowledge to be generated include insights into the cause of walking disability and development of rehabilitation methodologies, in addition to immediate applications to feedback control design for rhythmic pattern generation.
Results
Results
Animals can adapt the frequency and shape of their oscillatory body movements during locomotion in response to changes in the environment. Although central pattern generators (CPGs) are known to be the basic neuronal circuits responsible for generation of rhythmic movements, no conclusive evidence has so far been found to attribute adaptive behaviors solely to the function of CPGs. We have found a blueprint of a design by nature in terms of mathematical equations. Our experimental and computational studies confirm the capability of the leech CPG for adaptive pattern formation without detailed guidance from the brain; the CPG detects the change in the environment through sensory feedback of the local muscle tensions, and adjust the oscillation pattern via distributed control mechanisms.
The leech is an elongated annelid that swims by vertically undulating its flattened, segmented body. The undulation results from anti-phasic local contractions of dorsal and ventral longitudinal muscles, which propagate along the flexible body, interacting with fluid for thrust generation. The muscle contractions are controlled, not directly by brains, but by neuronal CPG circuits distributed over a chain of ganglia connected by the nerve cord running through the body. The CPG exhibits various robust and adaptive control performances that appear attractive for engineering applications.
The leech CPG is modeled as a chain of 17 segmental oscillators (two segments are shown on left). We assumed that the intrasegmental details were not important, and the CPG neurons within each segment were separated into three phase groups and connected in a simple recurrent cyclic inhibition loop. Dynamics for neurons and their synaptic interactions were modeled by a threshold nonlinearity and time lag/delay using experimentally-derived input-output membrane potential data.
The mechanics of the leech body with hydroskeleton are modeled as a chain of 18 rigid links that are connected in series through rotational joints. The equations of motion have been derived to capture the nonlinear dynamics of the body shape, orientation, and position in response to the muscle bending moment under the influence of the fluid forces. The essential effects of the fluid forces were captured by resistive and reactive (or added-mass) terms, with drag coefficients estimated by kinematic data of leech swimming. For the neuro-mechanical interface, dynamical models were developed for the MN impulse adaptation, passive muscle stiffness, and muscle activation by MNs, through physiological experiments on semi-intact preparations. The models describe the muscle bending moment as the sum of passive and active torques, which are dynamic functions of the body curvature (or joint angles) and CPG membrane potentials, respectively.
The integrated model reproduces undulatory movements of leech swimming in water (left), high viscosity fluid (middle), and air (right); live leech data (black) and simulated model (blue). In water, the body expresses a full spatial period of a quasisinusoid wave traveling to the right (swim progression is to left). In high viscosity fluid (400 cp), the body wavelength is shorter and the swim speed is low. When the body is hung in air, traveling waves are lost and the undulation becomes standing waves.
Neuronal cell membrane potential during undulation. Transition from water to high viscosity fluid at t=4 s.
Neuronal cell membrane potential during undulation. Transition from water to air at t=3 s.
References
References
Systems-level modeling of neuronal circuits for leech swimming
J. Chen, W.O. Friesen, T. Iwasaki, Journal of Computational Neuroscience, vol.22, no.1, pp.21-38, 2007.
Muscle function in animal movement: passive mechanical properties of leech muscle
J. Tian, T. Iwasaki, W.O. Friesen, Journal of Comparative Physiology, vol.193, no.12, pp.1205-1219, 2007.
Analysis of impulse adaptation in motoneurons
J. Tian, T. Iwasaki, W.O. Friesen, Journal of Comparative Physiology, vol.196, no.2, pp.123-136, 2010
Mechanisms underlying rhythmic locomotion: body–fluid interaction in undulatory swimming
J. Chen, W.O. Friesen, T. Iwasaki, Journal of Experimental Biology, vol.214, pp.561-574, 2011.
Mechanisms underlying rhythmic locomotion: dynamics of muscle activation
J. Chen, J. Tian, T. Iwasaki, W.O. Friesen, Journal of Experimental Biology, vol.214, pp.1955-1964, 2011.
J. Chen, W.O. Friesen, T. Iwasaki, Journal of Experimental Biology, vol.215, pp.211-219, 2012.
Biological clockwork underlying adaptive rhythmic movements
T. Iwasaki, J. Chen, W.O. Friesen, Proceedings of the National Academy of Sciences, vol.111, no.3, pp.978-983, 2014.
Mechanisms underlying undulatory swimming: From neuromuscular activation to body-fluid interactions
Jun Chen, Ph.D Dissertation, University of Virginia, May 2011
Muscle function and neuromuscular transformation in leech swimming
Jianghong Tian, Ph.D Dissertation, University of Virginia, August 2008
Modeling of CPG-based control mechanisms for leech swimming
Min Zheng, Ph.D Dissertation, University of Virginia, August 2007
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