1
|
A homeostasis criterion for limit cycle systems based on infinitesimal shape response curves. J Math Biol 2022; 84:24. [PMID: 35217884 DOI: 10.1007/s00285-022-01724-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/12/2021] [Revised: 01/25/2022] [Accepted: 01/31/2022] [Indexed: 10/19/2022]
Abstract
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 74(1-2):387-407, 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 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 Syst 82(7):1-43, 2021) to study infinitesimal homeostasis for limit-cycle systems in terms of the mean value of a quantity of interest, averaged around the limit cycle. Using the iSRC, which captures the linearized 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.
Collapse
|
2
|
Sharples SA, Parker J, Vargas A, Milla-Cruz JJ, Lognon AP, Cheng N, Young L, Shonak A, Cymbalyuk GS, Whelan PJ. Contributions of h- and Na+/K+ Pump Currents to the Generation of Episodic and Continuous Rhythmic Activities. Front Cell Neurosci 2022; 15:715427. [PMID: 35185470 PMCID: PMC8855656 DOI: 10.3389/fncel.2021.715427] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/26/2021] [Accepted: 12/29/2021] [Indexed: 12/31/2022] Open
Abstract
Developing spinal motor networks produce a diverse array of outputs, including episodic and continuous patterns of rhythmic activity. Variation in excitability state and neuromodulatory tone can facilitate transitions between episodic and continuous rhythms; however, the intrinsic mechanisms that govern these rhythms and their transitions are poorly understood. Here, we tested the capacity of a single central pattern generator (CPG) circuit with tunable properties to generate multiple outputs. To address this, we deployed a computational model composed of an inhibitory half-center oscillator (HCO). Following predictions of our computational model, we tested the contributions of key properties to the generation of an episodic rhythm produced by isolated spinal cords of the newborn mouse. The model recapitulates the diverse state-dependent rhythms evoked by dopamine. In the model, episodic bursting depended predominantly on the endogenous oscillatory properties of neurons, with Na+/K+ ATPase pump (IPump) and hyperpolarization-activated currents (Ih) playing key roles. Modulation of either IPump or Ih produced transitions between episodic and continuous rhythms and silence. As maximal activity of IPump decreased, the interepisode interval and period increased along with a reduction in episode duration. Decreasing maximal conductance of Ih decreased episode duration and increased interepisode interval. Pharmacological manipulations of Ih with ivabradine, and IPump with ouabain or monensin in isolated spinal cords produced findings consistent with the model. Our modeling and experimental results highlight key roles of Ih and IPump in producing episodic rhythms and provide insight into mechanisms that permit a single CPG to produce multiple patterns of rhythmicity.
Collapse
Affiliation(s)
- Simon A. Sharples
- School of Psychology and Neuroscience, University of St Andrews, St Andrews, United Kingdom
- Hotchkiss Brain Institute, University of Calgary, Calgary, AB, Canada
- Department of Neuroscience, University of Calgary, Calgary, AB, Canada
| | - Jessica Parker
- Neuroscience Institute, Georgia State University, Atlanta, GA, United States
| | - Alex Vargas
- Neuroscience Institute, Georgia State University, Atlanta, GA, United States
| | - Jonathan J. Milla-Cruz
- Hotchkiss Brain Institute, University of Calgary, Calgary, AB, Canada
- Department of Comparative Biology and Experimental Medicine, University of Calgary, Calgary, AB, Canada
| | - Adam P. Lognon
- Hotchkiss Brain Institute, University of Calgary, Calgary, AB, Canada
- Department of Neuroscience, University of Calgary, Calgary, AB, Canada
| | - Ning Cheng
- Hotchkiss Brain Institute, University of Calgary, Calgary, AB, Canada
- Department of Comparative Biology and Experimental Medicine, University of Calgary, Calgary, AB, Canada
| | - Leanne Young
- Department of Comparative Biology and Experimental Medicine, University of Calgary, Calgary, AB, Canada
| | - Anchita Shonak
- Hotchkiss Brain Institute, University of Calgary, Calgary, AB, Canada
- Department of Neuroscience, University of Calgary, Calgary, AB, Canada
| | - Gennady S. Cymbalyuk
- Neuroscience Institute, Georgia State University, Atlanta, GA, United States
- Department of Physics and Astronomy, Georgia State University, Atlanta, GA, United States
- Gennady S. Cymbalyuk,
| | - Patrick J. Whelan
- Hotchkiss Brain Institute, University of Calgary, Calgary, AB, Canada
- Department of Neuroscience, University of Calgary, Calgary, AB, Canada
- Department of Comparative Biology and Experimental Medicine, University of Calgary, Calgary, AB, Canada
- *Correspondence: Patrick J. Whelan,
| |
Collapse
|
3
|
Parker JR, Klishko AN, Prilutsky BI, Cymbalyuk GS. Asymmetric and transient properties of reciprocal activity of antagonists during the paw-shake response in the cat. PLoS Comput Biol 2021; 17:e1009677. [PMID: 34962927 PMCID: PMC8759665 DOI: 10.1371/journal.pcbi.1009677] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/03/2021] [Revised: 01/14/2022] [Accepted: 11/22/2021] [Indexed: 12/24/2022] Open
Abstract
Mutually inhibitory populations of neurons, half-center oscillators (HCOs), are commonly involved in the dynamics of the central pattern generators (CPGs) driving various rhythmic movements. Previously, we developed a multifunctional, multistable symmetric HCO model which produced slow locomotor-like and fast paw-shake-like activity patterns. Here, we describe asymmetric features of paw-shake responses in a symmetric HCO model and test these predictions experimentally. We considered bursting properties of the two model half-centers during transient paw-shake-like responses to short perturbations during locomotor-like activity. We found that when a current pulse was applied during the spiking phase of one half-center, let’s call it #1, the consecutive burst durations (BDs) of that half-center increased throughout the paw-shake response, while BDs of the other half-center, let’s call it #2, only changed slightly. In contrast, the consecutive interburst intervals (IBIs) of half-center #1 changed little, while IBIs of half-center #2 increased. We demonstrated that this asymmetry between the half-centers depends on the phase of the locomotor-like rhythm at which the perturbation was applied. We suggest that the fast transient response reflects functional asymmetries of slow processes that underly the locomotor-like pattern; e.g., asymmetric levels of inactivation across the two half-centers for a slowly inactivating inward current. We compared model results with those of in-vivo paw-shake responses evoked in locomoting cats and found similar asymmetries. Electromyographic (EMG) BDs of anterior hindlimb muscles with flexor-related activity increased in consecutive paw-shake cycles, while BD of posterior muscles with extensor-related activity did not change, and vice versa for IBIs of anterior flexors and posterior extensors. We conclude that EMG activity patterns during paw-shaking are consistent with the proposed mechanism producing transient paw-shake-like bursting patterns found in our multistable HCO model. We suggest that the described asymmetry of paw-shaking responses could implicate a multifunctional CPG controlling both locomotion and paw-shaking. The existence of multifunctional central pattern generators (CPGs), circuits which control more than one rhythmic motor behavior, is an intriguing hypothesis. We suggest that the cat paw-shaking response could be a transient response of the locomotor CPG. Our general prediction is that this CPG is multifunctional, and in addition to the locomotor rhythm, it can generate a transient, ten-times faster, paw-shake-like response to a stimulus. In our multistable half-center oscillator (HCO) CPG model, we applied perturbations to the locomotor pattern which resulted in a transient paw-shake-like pattern that eventually returned back to the locomotor pattern. We showed that the inactivation of the slow inward current that drives the locomotor rhythm produced asymmetry of the transient flexor and extensor activity in a symmetric HCO model. To test predictions from our model about the transient nature of the paw-shake response, we compared burst durations (BDs) and interburst intervals (IBIs) of the model half-centers in consecutive cycles of paw-shake-like responses with the BD and IBI of electromyographic (EMG) activity bursts of cat hindlimb flexors and extensors recorded during a paw-shake response. In both cases, we found similar asymmetric trends in the BD and IBI throughout a paw-shake response.
Collapse
Affiliation(s)
- Jessica R. Parker
- Neuroscience Institute, Georgia State University, Atlanta, Georgia, United States of America
| | - Alexander N. Klishko
- School of Biological Sciences, Georgia Institute of Technology, Atlanta, Georgia, United States of America
| | - Boris I. Prilutsky
- School of Biological Sciences, Georgia Institute of Technology, Atlanta, Georgia, United States of America
- * E-mail: (BIP); (GSC)
| | - Gennady S. Cymbalyuk
- Neuroscience Institute, Georgia State University, Atlanta, Georgia, United States of America
- * E-mail: (BIP); (GSC)
| |
Collapse
|
4
|
Asymmetric Control of Coexisting Slow and Fast Rhythms in a Multifunctional Central Pattern Generator: A Model Study. NEUROPHYSIOLOGY+ 2020. [DOI: 10.1007/s11062-020-09834-9] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023]
|
5
|
Nguyen KH, Scheurich TE, Gu T, Berkowitz A. Spinal Interneurons With Dual Axon Projections to Knee-Extensor and Hip-Extensor Motor Pools. Front Neural Circuits 2020; 14:7. [PMID: 32226362 PMCID: PMC7080864 DOI: 10.3389/fncir.2020.00007] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/16/2019] [Accepted: 02/21/2020] [Indexed: 11/13/2022] Open
Abstract
The central nervous system (CNS) may simplify control of limb movements by activating certain combinations of muscles together, i.e., muscle synergies. Little is known, however, about the spinal cord interneurons that activate muscle synergies by exciting sets of motoneurons for different muscles. The turtle spinal cord, even without brain inputs and movement-related sensory feedback, can generate the patterns of motoneuron activity underlying forward swimming, three forms of scratching, and limb withdrawal. Spinal interneurons activated during scratching are typically activated during all three forms of scratching, to different degrees, even though each form of scratching has its own knee-hip synergy. Such spinal interneurons are also typically activated rhythmically during scratching motor patterns, with hip-related timing. We proposed a hypothesis that such interneurons that are most active during rostral scratch stimulation project their axons to both knee-extensor and hip-flexor motoneurons, thus generating the rostral scratch knee-hip synergy, while those interneurons most active during pocket scratch stimulation project their axons to both knee-extensor and hip-extensor motoneurons, thus generating the pocket scratch knee-hip synergy. The activity of the entire population would then generate the appropriate synergy, depending on the location of sensory stimulation. Mathematical modeling has demonstrated that this hypothesis is feasible. Here, we provide one test of this hypothesis by injecting two fluorescent retrograde tracers into the regions of knee-extensor motoneurons (more rostrally) and hip-extensor motoneurons (more caudally). We found that there were double-labeled interneurons, which projected their axons to both locations. The dual-projecting interneurons were widely distributed rostrocaudally, dorsoventrally, and mediolaterally within the hindlimb enlargement and pre-enlargement spinal segments examined. The existence of such dual-projecting interneurons is consistent with the hypothesis that they contribute to generating the knee-hip synergy for pocket scratching. The dual-projecting interneurons, however, were only about 1% of the total interneurons projecting to each location, which suggests that they might be one of several contributors to the appropriate knee-hip synergy. Indirect projections to both motor pools and/or knee extensor-dedicated interneurons might also contribute. There is evidence for dual-projecting spinal interneurons in frogs and mice as well, suggesting that they may contribute to limb motor control in a variety of vertebrates.
Collapse
Affiliation(s)
- Khuong H Nguyen
- Department of Biology, University of Oklahoma, Norman, OK, United States
| | - Thomas E Scheurich
- Department of Biology, University of Oklahoma, Norman, OK, United States
| | - Tingting Gu
- Department of Biology, University of Oklahoma, Norman, OK, United States
| | - Ari Berkowitz
- Department of Biology, University of Oklahoma, Norman, OK, United States.,Cellular and Behavioral Neurobiology Graduate Program, University of Oklahoma, Norman, OK, United States
| |
Collapse
|
6
|
Stein PSG. Central pattern generators in the turtle spinal cord: selection among the forms of motor behaviors. J Neurophysiol 2018; 119:422-440. [PMID: 29070633 PMCID: PMC5867383 DOI: 10.1152/jn.00602.2017] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/14/2017] [Revised: 10/16/2017] [Accepted: 10/17/2017] [Indexed: 12/29/2022] Open
Abstract
Neuronal networks in the turtle spinal cord have considerable computational complexity even in the absence of connections with supraspinal structures. These networks contain central pattern generators (CPGs) for each of several behaviors, including three forms of scratch, two forms of swim, and one form of flexion reflex. Each behavior is activated by a specific set of cutaneous or electrical stimuli. The process of selection among behaviors within the spinal cord has multisecond memories of specific motor patterns. Some spinal cord interneurons are partially shared among several CPGs, whereas other interneurons are active during only one type of behavior. Partial sharing is a proposed mechanism that contributes to the ability of the spinal cord to generate motor pattern blends with characteristics of multiple behaviors. Variations of motor patterns, termed deletions, assist in characterization of the organization of the pattern-generating components of CPGs. Single-neuron recordings during both normal and deletion motor patterns provide support for a CPG organizational structure with unit burst generators (UBGs) whose members serve a direction of a specific degree of freedom of the hindlimb, e.g., the hip-flexor UBG, the hip-extensor UBG, the knee-flexor UBG, the knee-extensor UBG, etc. The classic half-center hypothesis that includes all the hindlimb flexors in a single flexor half-center and all the hindlimb extensors in a single extensor half-center lacks the organizational complexity to account for the motor patterns produced by turtle spinal CPGs. Thus the turtle spinal cord is a valuable model system for studies of mechanisms responsible for selection and generation of motor behaviors. NEW & NOTEWORTHY The concept of the central pattern generator (CPG) is a major tenet in motor neuroethology that has influenced the design and interpretations of experiments for over a half century. This review concentrates on the turtle spinal cord and describes studies from the 1970s to the present responsible for key developments in understanding the CPG mechanisms responsible for the selection and production of coordinated motor patterns during turtle hindlimb motor behaviors.
Collapse
Affiliation(s)
- Paul S G Stein
- Department of Biology, Washington University , St. Louis, Missouri
| |
Collapse
|
7
|
Nalborczyk ZR, McFadyen AK, Jovanovik J, Tauro A, Driver CJ, Fitzpatrick N, Knower SP, Rusbridge C. MRI characteristics for "phantom" scratching in canine syringomyelia. BMC Vet Res 2017; 13:340. [PMID: 29145838 PMCID: PMC5691609 DOI: 10.1186/s12917-017-1258-2] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/23/2017] [Accepted: 11/07/2017] [Indexed: 01/07/2023] Open
Abstract
BACKGROUND A classic sign of canine syringomyelia (SM) is scratching towards one shoulder. Using magnetic resonance imaging (MRI) we investigate the spinal cord lesion relating to this phenomenon which has characteristics similar to fictive scratch secondary to spinal cord transection. Medical records were searched for Cavalier King Charles spaniels with a clinical and MRI diagnosis of symptomatic SM associated with Chiari-like malformation (CM). The cohort was divided into SM with phantom scratching (19 dogs) and SM but no phantom scratching (18 dogs). MRI files were anonymised, randomised and viewed in EFILM ™. For each transverse image, the maximum perpendicular dimensions of the syrinx in the dorsal spinal cord quadrants were determined. Visual assessment was made as to whether the syrinx extended to the superficial dorsal horn (SDH). RESULTS We showed that phantom scratching appears associated with a large dorsolateral syrinx that extends to the SDH in the C3-C6 spinal cord segments (corresponding to C2-C5 vertebrae). Estimated dorsal quadrant syrinx sizes based on the perpendicular diameters were between 2.5 and 9.5 times larger in dogs with phantom scratching, with the largest mean difference p-value being 0.009. CONCLUSION SM associated phantom scratching appears associated with MRI findings of a large syrinx extending into the mid cervical SDH. We hypothesise that damage in this region might influence the lumbosacral scratching central pattern generator (CPG). If a scratching SM affected dog does not have a large dorsolateral cervical syrinx with SDH involvement then alternative explanations for scratching should be investigated.
Collapse
Affiliation(s)
- Zoe R Nalborczyk
- School of Veterinary Medicine, Faculty of Health & Medical Sciences, Daphne Jackson Road, Guildford, Surrey, GU2 7AL, UK
| | | | - Jelena Jovanovik
- Fitzpatrick Referrals Orthopaedics and Neurology, Halfway Lane, Eashing, Godalming, Surrey, UK
| | - Anna Tauro
- Fitzpatrick Referrals Orthopaedics and Neurology, Halfway Lane, Eashing, Godalming, Surrey, UK
| | - Colin J Driver
- Fitzpatrick Referrals Orthopaedics and Neurology, Halfway Lane, Eashing, Godalming, Surrey, UK
| | - Noel Fitzpatrick
- School of Veterinary Medicine, Faculty of Health & Medical Sciences, Daphne Jackson Road, Guildford, Surrey, GU2 7AL, UK.,Fitzpatrick Referrals Orthopaedics and Neurology, Halfway Lane, Eashing, Godalming, Surrey, UK
| | - Susan P Knower
- School of Veterinary Medicine, Faculty of Health & Medical Sciences, Daphne Jackson Road, Guildford, Surrey, GU2 7AL, UK
| | - Clare Rusbridge
- School of Veterinary Medicine, Faculty of Health & Medical Sciences, Daphne Jackson Road, Guildford, Surrey, GU2 7AL, UK. .,Fitzpatrick Referrals Orthopaedics and Neurology, Halfway Lane, Eashing, Godalming, Surrey, UK.
| |
Collapse
|
8
|
Schwarz O, Bohra AA, Liu X, Reichert H, VijayRaghavan K, Pielage J. Motor control of Drosophila feeding behavior. eLife 2017; 6:e19892. [PMID: 28211791 PMCID: PMC5315463 DOI: 10.7554/elife.19892] [Citation(s) in RCA: 32] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/21/2016] [Accepted: 02/02/2017] [Indexed: 12/01/2022] Open
Abstract
The precise coordination of body parts is essential for survival and behavior of higher organisms. While progress has been made towards the identification of central mechanisms coordinating limb movement, only limited knowledge exists regarding the generation and execution of sequential motor action patterns at the level of individual motoneurons. Here we use Drosophila proboscis extension as a model system for a reaching-like behavior. We first provide a neuroanatomical description of the motoneurons and muscles contributing to proboscis motion. Using genetic targeting in combination with artificial activation and silencing assays we identify the individual motoneurons controlling the five major sequential steps of proboscis extension and retraction. Activity-manipulations during naturally evoked proboscis extension show that orchestration of serial motoneuron activation does not rely on feed-forward mechanisms. Our data support a model in which central command circuits recruit individual motoneurons to generate task-specific proboscis extension sequences.
Collapse
Affiliation(s)
- Olivia Schwarz
- Friedrich Miescher Institute for Biomedical Research, Basel, Switzerland
- Biozentrum University of Basel, Basel, Switzerland
- Division of Zoology and Neurobiology, Technical University Kaiserslautern, Kaiserslautern, Germany
| | - Ali Asgar Bohra
- National Centre for Biological Sciences, Tata Institute for Fundamental Research, Bangalore, India
| | - Xinyu Liu
- Friedrich Miescher Institute for Biomedical Research, Basel, Switzerland
- Biozentrum University of Basel, Basel, Switzerland
| | | | | | - Jan Pielage
- Friedrich Miescher Institute for Biomedical Research, Basel, Switzerland
- Biozentrum University of Basel, Basel, Switzerland
- Division of Zoology and Neurobiology, Technical University Kaiserslautern, Kaiserslautern, Germany
| |
Collapse
|
9
|
Lyttle DN, Gill JP, Shaw KM, Thomas PJ, Chiel HJ. Robustness, flexibility, and sensitivity in a multifunctional motor control model. BIOLOGICAL CYBERNETICS 2017; 111:25-47. [PMID: 28004255 PMCID: PMC5326633 DOI: 10.1007/s00422-016-0704-8] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/18/2015] [Accepted: 10/07/2016] [Indexed: 05/25/2023]
Abstract
Motor systems must adapt to perturbations and changing conditions both within and outside the body. We refer to the ability of a system to maintain performance despite perturbations as "robustness," and the ability of a system to deploy alternative strategies that improve fitness as "flexibility." Different classes of pattern-generating circuits yield dynamics with differential sensitivities to perturbations and parameter variation. Depending on the task and the type of perturbation, high sensitivity can either facilitate or hinder robustness and flexibility. Here we explore the role of multiple coexisting oscillatory modes and sensory feedback in allowing multiphasic motor pattern generation to be both robust and flexible. As a concrete example, we focus on a nominal neuromechanical model of triphasic motor patterns in the feeding apparatus of the marine mollusk Aplysia californica. We find that the model can operate within two distinct oscillatory modes and that the system exhibits bistability between the two. In the "heteroclinic mode," higher sensitivity makes the system more robust to changing mechanical loads, but less robust to internal parameter variations. In the "limit cycle mode," lower sensitivity makes the system more robust to changes in internal parameter values, but less robust to changes in mechanical load. Finally, we show that overall performance on a variable feeding task is improved when the system can flexibly transition between oscillatory modes in response to the changing demands of the task. Thus, our results suggest that the interplay of sensory feedback and multiple oscillatory modes can allow motor systems to be both robust and flexible in a variable environment.
Collapse
Affiliation(s)
- David N Lyttle
- Department of Mathematics and Biology, Case Western Reserve University, 10900 Euclid Ave., Cleveland, OH, 44106, USA.
| | - Jeffrey P Gill
- Department of Biology, Case Western Reserve University, 10900 Euclid Ave., Cleveland, OH, 44106, USA
| | - Kendrick M Shaw
- Department of Anesthesia, Critical Care, and Pain Medicine, Massachusetts General Hospital, Boston, MA, 02114, USA
| | - Peter J Thomas
- Department of Mathematics, Applied Mathematics, and Statistics, Case Western Reserve University, 10900 Euclid Ave., Cleveland, OH, 44106, USA
| | - Hillel J Chiel
- Department of Biology, Neurosciences and Biomedical Engineering, Case Western Reserve University, 10900 Euclid Ave., Cleveland, OH, 44106, USA
| |
Collapse
|