1
|
Armstrong E. Predicting the Behavior of Sparsely-Sampled Systems Across Neurobiology and Epidemiology. Bull Math Biol 2023; 85:91. [PMID: 37653124 DOI: 10.1007/s11538-023-01176-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2022] [Accepted: 05/30/2023] [Indexed: 09/02/2023]
Abstract
Inference is a term that encompasses many techniques including statistical data assimilation (SDA). Unlike machine learning, which is designed to harness predictive power from extremely large data sets, SDA is designed for sparsely-sampled systems. This is the realm of study of nonlinear dynamical systems in nature. Formulated as an optimization procedure, SDA can be considered a path-integral approach to state and parameter estimation. Within this formulation, we can use the physical principle of least action to identify optimal solutions: solutions that are consistent with both measurements and a dynamical model assumed to give rise to those measurements. I review examples from neurobiology and an epidemiological model tailored to the coronavirus SARS-CoV-2, to demonstrate the versatility of SDA across the sciences, and how these distinct applications possess commonalities that can inform one another.
Collapse
Affiliation(s)
- Eve Armstrong
- Department of Physics, New York Institute of Technology, New York, NY, 10023, USA.
- Department of Astrophysics, American Museum of Natural History, New York, NY, 10024, USA.
| |
Collapse
|
2
|
Armstrong E. Statistical data assimilation for estimating electrophysiology simultaneously with connectivity within a biological neuronal network. Phys Rev E 2020; 101:012415. [PMID: 32069603 DOI: 10.1103/physreve.101.012415] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2019] [Indexed: 06/10/2023]
Abstract
A method of data assimilation (DA) is employed to estimate electrophysiological parameters of neurons simultaneously with their synaptic connectivity in a small model biological network. The DA procedure is cast as an optimization, with a cost function consisting of both a measurement error and a model error term. An iterative reweighting of these terms permits a systematic method to identify the lowest minimum, within a local region of state space, on the surface of a nonconvex cost function. In the model, two sets of parameter values are associated with two particular functional modes of network activity: simultaneous firing of all neurons and a pattern-generating mode wherein the neurons burst in sequence. The DA procedure is able to recover these modes if: (i) the stimulating electrical currents have chaotic waveforms and (ii) the measurements consist of the membrane voltages of all neurons in the circuit. Further, this method is able to prune a model of unnecessarily high dimensionality to a representation that contains the maximum dimensionality required to reproduce the provided measurements. This paper offers a proof-of-concept that DA has the potential to inform laboratory designs for estimating properties in small and isolatable functional circuits.
Collapse
Affiliation(s)
- Eve Armstrong
- Department of Physics, New York Institute of Technology, New York, New York 10023, USA and Department of Astrophysics, American Museum of Natural History, New York, New York 10024, USA
| |
Collapse
|
3
|
Schneider AC, Seichter HA, Neupert S, Hochhaus AM, Smarandache-Wellmann CR. Profiling neurotransmitters in a crustacean neural circuit for locomotion. PLoS One 2018; 13:e0197781. [PMID: 29787606 PMCID: PMC5963771 DOI: 10.1371/journal.pone.0197781] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/25/2018] [Accepted: 05/08/2018] [Indexed: 11/25/2022] Open
Abstract
Locomotor systems are widely used to study rhythmically active neural networks. These networks have to be coordinated in order to produce meaningful behavior. The crayfish swimmeret system is well suited to investigate such coordination of distributed neural oscillators because the neurons and their connectivity for generating and especially for coordinating the motor output are identified. The system maintains a fixed phase lag between the segmental oscillators, independent of cycle period. To further the understanding of the system’s plasticity for keeping the phase lag fixed, we profiled the neurotransmitters used by the Coordinating Neurons, which are necessary and sufficient for coordination of the segmental oscillators. We used a combination of electrophysiological, immunohistochemical, and mass spectrometric methods. This arrangement of methods ensured that we could screen for several specific neurotransmitters, since a single method is often not suitable for all neurotransmitters of interest. In a first step, to preselect neurotransmitter candidates, we investigated the effect of substances known to be present in some swimmeret system neurons on the motor output and coordination. Subsequently, we demonstrated electrophysiologically that the identified synapse between the Coordinating Neurons and their target is mainly chemical, but neither glutamate antagonist nor γ-aminobutyric acid antagonist application affected this synapse. With immunohistochemical experiments, we provide strong evidence that the Coordinating Neurons are not serotonergic. Single-cell MALDI-TOF mass spectrometry with subsequent principal component analysis identified acetylcholine as the putative neurotransmitter for both types of Coordinating Neurons.
Collapse
Affiliation(s)
- Anna C. Schneider
- Zoological Institute, Animal Physiology, Emmy Noether Group, University of Cologne, Cologne, Germany
| | - Henriette A. Seichter
- Zoological Institute, Animal Physiology, Emmy Noether Group, University of Cologne, Cologne, Germany
| | - Susanne Neupert
- Zoological Institute, Animal Physiology, University of Cologne, Cologne, Germany
| | - A. Maren Hochhaus
- Zoological Institute, Animal Physiology, Emmy Noether Group, University of Cologne, Cologne, Germany
| | | |
Collapse
|
4
|
Yoshida M, Nagayama T, Newland P. Nitric oxide-mediated intersegmental modulation of cycle frequency in the crayfish swimmeret system. Biol Open 2018; 7:bio.032789. [PMID: 29716944 PMCID: PMC5992521 DOI: 10.1242/bio.032789] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022] Open
Abstract
Crayfish swimmerets are paired appendages located on the ventral side of each abdominal segment that show rhythmic beating during forward swimming produced by central pattern generators in most abdominal segments. For animals with multiple body segments and limbs, intersegmental coordination of central pattern generators in each segment is crucial for the production of effective movements. Here we develop a novel pharmacological approach to analyse intersegmental modulation of swimmeret rhythm by selectively elevating nitric oxide levels and reducing them with pharmacological agents, in specific ganglia. Bath application of L-arginine, the substrate NO synthesis, increased the cyclical spike responses of the power-stroke motor neurons. By contrast the NOS inhibitor, L-NAME decreased them. To determine the role of the different local centres in producing and controlling the swimmeret rhythm, these two drugs were applied locally to two separate ganglia following bath application of carbachol. Results revealed that there was both ascending and descending intersegmental modulation of cycle frequency of the swimmeret rhythm in the abdominal ganglia and that synchrony of cyclical activity between segments of segments was maintained. We also found that there were gradients in the strength effectiveness in modulation, that ascending modulation of the swimmeret rhythm was stronger than descending modulation. Summary: We develop a novel pharmacological approach using a nitric oxide donor and a nitric oxide synthase inhibitor to analyse modulation and segmental synchrony in the swimmeret rhythm of the crayfish.
Collapse
Affiliation(s)
- Misaki Yoshida
- Division of Biology, Graduate School of Science and Engineering, Yamagata University, 990-8560, Yamagata, Japan
| | - Toshiki Nagayama
- Department of Biology, Faculty of Science, Yamagata University, 990-8560, Yamagata, Japan
| | - Philip Newland
- Center of Biological Sciences, University of Southampton, Highfield Campus, Southampton SO17 1BJ, UK
| |
Collapse
|
5
|
Mita A, Yoshida M, Nagayama T. Nitric oxide modulates a swimmeret beating rhythm in the crayfish. ACTA ACUST UNITED AC 2014; 217:4423-31. [PMID: 25452502 DOI: 10.1242/jeb.110551] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022]
Abstract
The modulatory effects of nitric oxide (NO) and cAMP on the rhythmic beating activity of the swimmeret motor neurones in the crayfish were examined. Swimmerets are paired appendages located on the ventral side of each abdominal segment that show rhythmic beating activity during forward swimming, postural righting behaviour and egg ventilation in gravid females. In isolated abdominal nerve cord preparations, swimmeret motor neurones are usually silent or show a continuous low-frequency spiking activity. Application of carbachol, a cholinergic agonist, elicited rhythmic bursts of motor neurone spikes. The co-application of L-arginine, the substrate for NO synthesis with carbachol increased the burst frequency of the motor neurones. The co-application of the NO donor SNAP with carbachol also increased the burst frequency of the motor neurones. By contrast, co-application of a NOS inhibitor, L-NAME, with carbachol decreased beating frequency of the motor neurones. These results indicate that NO may act as a neuromodulator to facilitate swimmeret beating activity. The facilitatory effect of L-arginine was cancelled by co-application of the soluble guanylate cyclase (sGC) inhibitor ODQ suggesting that NO acts by activating sGC to promote the production of cGMP. Application of L-arginine alone or membrane-permeable cGMP analogue 8-Br-cGMP alone did not elicit rhythmic activity of motor neurones, but co-application of 8-Br-cGMP with carbachol increased bursting frequency of the motor neurones. Furthermore, application of the membrane-permeable cAMP analogue CPT-cAMP alone produced rhythmic bursting of swimmeret motor neurones, and the bursting frequency elicited by CPT-cAMP was increased by co-application with L-arginine. Co-application of the adenylate cyclase inhibitor SQ22536 ceased rhythmic bursts of motor neurone spikes elicited by carbachol. These results suggest that a cAMP system enables the rhythmic bursts of motor neurone spikes and that a NO-cGMP signaling pathway increases cAMP activity to facilitate swimmeret beating.
Collapse
Affiliation(s)
- Atsuki Mita
- Division of Biology, Graduate School of Science and Engineering, Yamagata University, 990-8560 Yamagata, Japan
| | - Misaki Yoshida
- Division of Biology, Graduate School of Science and Engineering, Yamagata University, 990-8560 Yamagata, Japan
| | - Toshiki Nagayama
- Department of Biology, Faculty of Science, Yamagata University, 990-8560 Yamagata, Japan.
| |
Collapse
|
6
|
Mulloney B, Smarandache-Wellmann C, Weller C, Hall WM, DiCaprio RA. Proprioceptive feedback modulates coordinating information in a system of segmentally distributed microcircuits. J Neurophysiol 2014; 112:2799-809. [PMID: 25185816 PMCID: PMC4254881 DOI: 10.1152/jn.00321.2014] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022] Open
Abstract
The system of modular neural circuits that controls crustacean swimmerets drives a metachronal sequence of power-stroke (PS, retraction) and return-stroke (RS, protraction) movements that propels the animal forward efficiently. These neural modules are synchronized by an intersegmental coordinating circuit that imposes characteristic phase differences between these modules. Using a semi-intact preparation that left one swimmeret attached to an otherwise isolated central nervous system (CNS) of the crayfish, Pacifastacus leniusculus, we investigated how the rhythmic activity of this system responded to imposed movements. We recorded extracellularly from the PS and RS nerves that innervated the attached limb and from coordinating axons that encode efference copies of the periodic bursts in PS and RS axons. Simultaneously, we recorded from homologous nerves in more anterior and posterior segments. Maintained retractions did not affect cycle period but promptly weakened PS bursts, strengthened RS bursts, and caused corresponding changes in the strength and timing of efference copies in the module's coordinating axons. Changes in these efference copies then caused changes in the phase and duration, but not the strength, of PS bursts in modules controlling neighboring swimmerets. These changes were promptly reversed when the limb was released. Each swimmeret is innervated by two nonspiking stretch receptors (NSSRs) that depolarize when the limb is retracted. Voltage clamp of an NSSR changed the durations and strengths of bursts in PS and RS axons innervating the same limb and caused corresponding changes in the efference copies of this motor output.
Collapse
Affiliation(s)
- Brian Mulloney
- Department of Neurobiology, Physiology, and Behavior, University of California, Davis, California;
| | | | - Cynthia Weller
- Department of Neurobiology, Physiology, and Behavior, University of California, Davis, California
| | - Wendy M Hall
- Department of Neurobiology, Physiology, and Behavior, University of California, Davis, California
| | - Ralph A DiCaprio
- Department of Biological Sciences, Ohio University, Athens, Ohio
| |
Collapse
|
7
|
Abstract
We describe synaptic connections through which information essential for encoding efference copies reaches two coordinating neurons in each of the microcircuits that controls limbs on abdominal segments of the crayfish, Pacifastacus leniusculus. In each microcircuit, these coordinating neurons fire bursts of spikes simultaneously with motor neurons. These bursts encode timing, duration, and strength of each motor burst. Using paired microelectrode recordings, we demonstrate that one class of nonspiking neurons in each microcircuit's pattern-generating kernel--IPS--directly inhibits the ASCE coordinating neuron that copies each burst in power-stroke (PS) motor neurons. This inhibitory synapse parallels IPS's inhibition of the same PS motor neurons. Using a disynaptic pathway to control its membrane potential, we demonstrate that a second type of nonspiking interneuron in the pattern-generating kernel--IRSh--inhibits the DSC coordinating neuron that copies each burst in return-stroke (RS) motor neurons. This inhibitory synapse parallels IRS's inhibition of the microcircuit's RS motor neurons. Experimental changes in the membrane potential of one IPS or one IRSh neuron simultaneously changed the strengths of motor bursts, durations, numbers of spikes, and spike frequency in the simultaneous ASCE and DSC bursts. ASCE and DSC coordinating neurons link the segmentally distributed microcircuits into a coordinated system that oscillates with the same period and with stable phase differences. The inhibitory synapses from different pattern-generating neurons that parallel their inhibition of different sets of motor neurons enable ASCE and DSC to encode details of each oscillation that are necessary for stable, adaptive synchronization of the system.
Collapse
|
8
|
Tupal S, Huang WH, Picardo MCD, Ling GY, Del Negro CA, Zoghbi HY, Gray PA. Atoh1-dependent rhombic lip neurons are required for temporal delay between independent respiratory oscillators in embryonic mice. eLife 2014; 3:e02265. [PMID: 24842997 PMCID: PMC4060005 DOI: 10.7554/elife.02265] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022] Open
Abstract
All motor behaviors require precise temporal coordination of different muscle groups. Breathing, for example, involves the sequential activation of numerous muscles hypothesized to be driven by a primary respiratory oscillator, the preBötzinger Complex, and at least one other as-yet unidentified rhythmogenic population. We tested the roles of Atoh1-, Phox2b-, and Dbx1-derived neurons (three groups that have known roles in respiration) in the generation and coordination of respiratory output. We found that Dbx1-derived neurons are necessary for all respiratory behaviors, whereas independent but coupled respiratory rhythms persist from at least three different motor pools after eliminating or silencing Phox2b- or Atoh1-expressing hindbrain neurons. Without Atoh1 neurons, however, the motor pools become temporally disorganized and coupling between independent respiratory oscillators decreases. We propose Atoh1 neurons tune the sequential activation of independent oscillators essential for the fine control of different muscles during breathing.DOI: http://dx.doi.org/10.7554/eLife.02265.001.
Collapse
Affiliation(s)
- Srinivasan Tupal
- Department of Anatomy and Neurobiology, Washington University School of Medicine, St Louis, United States
| | - Wei-Hsiang Huang
- Program in Developmental Biology, Baylor College of Medicine, Houston, United States Jan and Dan Duncan Neurological Research Institute at Texas Children's Hospital, Baylor College of Medicine, Houston, United States
| | | | - Guang-Yi Ling
- Department of Anatomy and Neurobiology, Washington University School of Medicine, St Louis, United States
| | | | - Huda Y Zoghbi
- Program in Developmental Biology, Baylor College of Medicine, Houston, United States Jan and Dan Duncan Neurological Research Institute at Texas Children's Hospital, Baylor College of Medicine, Houston, United States Department of Molecular and Human Genetics, Howard Hughes Medical Institute, Baylor College of Medicine, Houston, United States
| | - Paul A Gray
- Department of Anatomy and Neurobiology, Washington University School of Medicine, St Louis, United States
| |
Collapse
|
9
|
Calabrese RL. Motor coordination: a local hub for coordination. Curr Biol 2014; 24:R274-5. [PMID: 24698375 DOI: 10.1016/j.cub.2014.02.035] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
Abstract
A local interneuron of a crayfish central pattern generator serves as a hub that integrates ascending and descending coordinating information and passes it on to a local oscillatory microcircuit to coordinate a series of segmental appendages known as swimmerets.
Collapse
Affiliation(s)
- Ronald L Calabrese
- Department of Biology, Emory University, 1510 Clifton Road, Atlanta, GA 30322, USA.
| |
Collapse
|
10
|
Mechanisms of coordination in distributed neural circuits: decoding and integration of coordinating information. J Neurosci 2014; 34:793-803. [PMID: 24431438 DOI: 10.1523/jneurosci.2642-13.2014] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022] Open
Abstract
We describe the synaptic connections through which information required to coordinate limb movements reaches the modular microcircuits that control individual limbs on different abdominal segments of the crayfish, Pacifastacus leniusculus. In each segmental ganglion, a local commissural interneuron, ComInt 1, integrates information about other limbs and transmits it to one microcircuit. Five types of nonspiking local interneurons are components of each microcircuit's pattern-generating kernel (Smarandache-Wellmann et al., 2013). We demonstrate here, using paired microelectrode recordings, that the pathway through which information reaches this kernel is an electrical synapse between ComInt 1 and one of these five types, an IRSh interneuron. Using single-electrode voltage clamp, we show that brief changes of ComInt 1's membrane potential affect the timing of its microcircuit's motor output. Changing ComInt 1's membrane potential also changes the phase, duration, and strengths of bursts of spikes in its microcircuit's motor neurons and corresponding changes in its efferent coordinating neurons that project to other ganglia. These effects on coordinating neurons cause changes in the phases of motor output from other microcircuits in those distant ganglia. ComInt 1s function as hub neurons in the intersegmental circuit that synchronizes distributed microcircuits. The synapse between each ComInt 1 and its microcircuit's IRSh neuron completes a five synapse pathway in which analog information is encoded as a digital signal by efference-copy neurons and decoded from digital to analog form by ComInt 1. The synaptic organization of this pathway provides a cellular explanation of this nervous system's key dynamic properties.
Collapse
|
11
|
Toth TI, Grabowska M, Schmidt J, Büschges A, Daun-Gruhn S. A neuro-mechanical model explaining the physiological role of fast and slow muscle fibres at stop and start of stepping of an insect leg. PLoS One 2013; 8:e78246. [PMID: 24278108 PMCID: PMC3838373 DOI: 10.1371/journal.pone.0078246] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/29/2013] [Accepted: 09/10/2013] [Indexed: 11/18/2022] Open
Abstract
Stop and start of stepping are two basic actions of the musculo-skeletal system of a leg. Although they are basic phenomena, they require the coordinated activities of the leg muscles. However, little is known of the details of how these activities are generated by the interactions between the local neuronal networks controlling the fast and slow muscle fibres at the individual leg joints. In the present work, we aim at uncovering some of those details using a suitable neuro-mechanical model. It is an extension of the model in the accompanying paper and now includes all three antagonistic muscle pairs of the main joints of an insect leg, together with their dedicated neuronal control, as well as common inhibitory motoneurons and the residual stiffness of the slow muscles. This model enabled us to study putative processes of intra-leg coordination during stop and start of stepping. We also made use of the effects of sensory signals encoding the position and velocity of the leg joints. Where experimental observations are available, the corresponding simulation results are in good agreement with them. Our model makes detailed predictions as to the coordination processes of the individual muscle systems both at stop and start of stepping. In particular, it reveals a possible role of the slow muscle fibres at stop in accelerating the convergence of the leg to its steady-state position. These findings lend our model physiological relevance and can therefore be used to elucidate details of the stop and start of stepping in insects, and perhaps in other animals, too.
Collapse
Affiliation(s)
- Tibor Istvan Toth
- Emmy Noether Research Group of Computational Biology, Department of Animal Physiology, University of Cologne, Cologne, Germany
| | - Martyna Grabowska
- Emmy Noether Research Group of Computational Biology, Department of Animal Physiology, University of Cologne, Cologne, Germany
| | - Joachim Schmidt
- Department of Animal Physiology, University of Cologne, Cologne, Germany
| | - Ansgar Büschges
- Department of Animal Physiology, University of Cologne, Cologne, Germany
| | - Silvia Daun-Gruhn
- Emmy Noether Research Group of Computational Biology, Department of Animal Physiology, University of Cologne, Cologne, Germany
| |
Collapse
|
12
|
Zhang C, Lewis TJ. Phase response properties of half-center oscillators. J Comput Neurosci 2013; 35:55-74. [PMID: 23456595 DOI: 10.1007/s10827-013-0440-1] [Citation(s) in RCA: 30] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/17/2012] [Revised: 12/18/2012] [Accepted: 01/14/2013] [Indexed: 11/30/2022]
Abstract
We examine the phase response properties of half-center oscillators (HCOs) that are modeled by a pair of Morris-Lecar-type neurons connected by strong fast inhibitory synapses. We find that the two basic mechanisms for half-center oscillations, "release" and "escape", give rise to strikingly different phase response curves (PRCs). Release-type HCOs are most sensitive to perturbations delivered to cells at times when they are about to transition from the active to the suppressed state, and PRCs are dominated by a large negative peak (phase delays) at corresponding phases. On the other hand, escape-type HCOs are most sensitive to perturbations delivered to cells at times when they are about to transition from the suppressed to the active state, and PRCs are dominated by a large positive peak (phase advances) at corresponding phases. By analyzing the phase space structure of Morris-Lecar-type HCO models with fast synaptic dynamics, we identify the dynamical mechanisms underlying the shapes of the PRCs. To demonstrate the significance of the different shapes of the PRCs for the release-type and escape-type HCOs, we link the shapes of the PRCs to the different frequency modulation properties of release-type and escape-type HCOs, and we show that the different shapes of the PRCs for the release-type and escape-type HCOs can lead to fundamentally different phase-locking dynamics.
Collapse
Affiliation(s)
- Calvin Zhang
- Department of Mathematics, University of California, Davis, Davis, CA 95616, USA
| | | |
Collapse
|
13
|
Mulloney B, Smarandache-Wellmann C. Neurobiology of the crustacean swimmeret system. Prog Neurobiol 2012; 96:242-67. [PMID: 22270044 PMCID: PMC3297416 DOI: 10.1016/j.pneurobio.2012.01.002] [Citation(s) in RCA: 45] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2011] [Revised: 12/21/2011] [Accepted: 01/05/2012] [Indexed: 10/14/2022]
Abstract
The crustacean swimmeret system includes a distributed set of local circuits that individually control movements of one jointed limb. These modular local circuits occur in pairs in each segmental ganglion, and normally operate synchronously to produce smoothly coordinated cycles of limb movements on different body segments. The system presents exceptional opportunities for computational and experimental investigation of neural mechanisms of coordination because: (a) The system will express in vitro the periodic motor pattern that normally drives cycles of swimmeret movements during forward swimming. (b) The intersegmental neurons which encode information that is necessary and sufficient for normal coordination have been identified, and their activity can be recorded. (c) The local commissural neurons that integrate this coordinating information and tune the phase of each swimmeret are known. (d) The complete set of synaptic connections between coordinating neurons and these commissural neurons have been described. (e). The synaptic connections onto each local pattern-generating circuit through which coordinating information tunes the circuit's phase have been discovered. These factors make possible for the first time a detailed, comprehensive cellular and synaptic explanation of how this neural circuit produces an effective, behaviorally significant output. This paper is the first comprehensive review of the system's neuroanatomy and neurophysiology, its local and intersegmental circuitry, its transmitter pharmacology, its neuromodulatory control mechanisms, and its interactions with other motor systems. Each of these topics is covered in detail in an attempt to provide a complete review of the literature as a foundation for new research. The series of hypotheses that have been proposed to account for the system's properties are reviewed critically in the context of experimental tests of their validity.
Collapse
Affiliation(s)
- Brian Mulloney
- Department of Neurobiology, Physiology, and Behavior, Center for Neuroscience, University of California, Davis, CA 95616-8519, USA.
| | | |
Collapse
|
14
|
Calabrese RL, Norris BJ, Wenning A, Wright TM. Coping with variability in small neuronal networks. Integr Comp Biol 2011; 51:845-55. [PMID: 21724619 DOI: 10.1093/icb/icr074] [Citation(s) in RCA: 33] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Experimental and corresponding modeling studies indicate that there is a 2- to 5-fold variation of intrinsic and synaptic parameters across animals while functional output is maintained. Here, we review experiments, using the heartbeat central pattern generator (CPG) in medicinal leeches, which explore the consequences of animal-to-animal variation in synaptic strength for coordinated motor output. We focus on a set of segmental heart motor neurons that all receive inhibitory synaptic input from the same four premotor interneurons. These four premotor inputs fire in a phase progression and the motor neurons also fire in a phase progression because of differences in synaptic strength profiles of the four inputs among segments. Our work tested the hypothesis that functional output is maintained in the face of animal-to-animal variation in the absolute strength of connections because relative strengths of the four inputs onto particular motor neurons is maintained across animals. Our experiments showed that relative strength is not strictly maintained across animals even as functional output is maintained, and animal-to-animal variations in strength of particular inputs do not correlate strongly with output phase. Further experiments measured the precise temporal pattern of the premotor inputs, the segmental synaptic strength profiles of their connections onto motor neurons, and the temporal pattern (phase progression) of those motor neurons all in the same animal for a series of 12 animals. The analysis of input and output in this sample of 12 individuals suggests that the number (four) of inputs to each motor neuron and the variability of the temporal pattern of input from the CPG across individuals weaken the influence of the strength of individual inputs. Moreover, the temporal pattern of the output varies as much across individuals as that of the input. Essentially, each animal arrives at a unique solution for how the network produces functional output.
Collapse
Affiliation(s)
- Ronald L Calabrese
- Department of Biology, Emory University, 1510 Clifton Road, Atlanta, GA 30322, USA.
| | | | | | | |
Collapse
|
15
|
Wagenaar DA, Gonzalez R, Ries DC, Kristan WB, French KA. Alpha-conotoxin ImI disrupts central control of swimming in the medicinal leech. Neurosci Lett 2010; 485:151-6. [PMID: 20833225 DOI: 10.1016/j.neulet.2010.08.078] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/26/2010] [Revised: 08/05/2010] [Accepted: 08/26/2010] [Indexed: 11/17/2022]
Abstract
Medicinal leeches (Hirudo spp.) swim using a metachronal, front-to-back undulation. The behavior is generated by central pattern generators (CPGs) distributed along the animal's midbody ganglia and is coordinated by both central and peripheral mechanisms. Here we report that a component of the venom of Conus imperialis, α-conotoxin ImI, known to block nicotinic acetyl-choline receptors in other species, disrupts swimming. Leeches injected with the toxin swam in circles with exaggerated dorsoventral bends and reduced forward velocity. Fictive swimming in isolated nerve cords was even more strongly disrupted, indicating that the toxin targets the CPGs and central coordination, while peripheral coordination partially rescues the behavior in intact animals.
Collapse
Affiliation(s)
- Daniel A Wagenaar
- Broad Fellows Program and Division of Biology, California Institute of Technology, 1200 E California Blvd 216-76, Pasadena, CA 91125, USA.
| | | | | | | | | |
Collapse
|
16
|
Mulloney B, Smarandache C. Fifty Years of CPGs: Two Neuroethological Papers that Shaped the Course of Neuroscience. Front Behav Neurosci 2010; 4. [PMID: 20700502 PMCID: PMC2917247 DOI: 10.3389/fnbeh.2010.00045] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/07/2010] [Accepted: 06/29/2010] [Indexed: 11/13/2022] Open
Abstract
Half a century ago, two independent papers that described unexpected results of experiments on locomotion in insects and crayfish appeared almost simultaneously. Together these papers demonstrated that an animal's central nervous system (CNS) was organized to produce behaviorally important motor output without the need for constant sensory feedback. These results contradicted the established line of thought that was based on interpretations of reflexes and ablation experiments, and established that in these animals the CNS contained neural circuits that could produce complex, periodic, multisegmental patterns of activity. These papers stimulated a flowering of research on central pattern-generating mechanisms that displaced reflex-based thinking everywhere except in medical physiology texts. Here we review these papers and their influence on thinking in the 1960s, 1970s, and today. We follow the development of ideas about central organization and control of expression of motor patterns, the roles of sensory input to central pattern-generating circuits, and integration of continuous sensory signals into a periodic motor system. We also review recent work on limb coordination that provides detailed cellular explanations of observations and speculations contained in those original papers.
Collapse
Affiliation(s)
- Brian Mulloney
- Department of Neurobiology, Physiology, and Behavior, University of California Davis, CA, USA
| | | |
Collapse
|
17
|
Coordination of rhythmic motor activity by gradients of synaptic strength in a neural circuit that couples modular neural oscillators. J Neurosci 2009; 29:9351-60. [PMID: 19625525 DOI: 10.1523/jneurosci.1744-09.2009] [Citation(s) in RCA: 39] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022] Open
Abstract
Synchronization of distributed neural circuits is required for many behavioral tasks, but the mechanisms that coordinate these circuits are largely unknown. The modular local circuits that control crayfish swimmerets are distributed in four segments of the CNS, but when the swimmeret system is active their outputs are synchronized with a stable intersegmental phase difference of 0.25, an example of metachronal synchronization (Izhikevich, 2007). In each module, coordinating neurons encode detailed information about each cycle of the module's motor output as bursts of spikes, and their axons conduct this information to targets in other segments. This information is both necessary and sufficient for normal intersegmental coordination. In a comprehensive set of recordings, we mapped the synaptic connections of two types of coordinating neurons onto their common target neurons in other segments. Both types of coordinating axons caused large, brief EPSPs in their targets. The shape indices of these EPSPs are tuned to transmit the information from each axon precisely. In each target neuron's own module, these bursts of EPSPs modified the phase of the module's motor output. Each axon made its strongest synapse onto the target neuron in the nearest neighboring segment. Its synapses onto homologous targets in more remote segments were progressively weaker. Each target neuron decodes information from several coordinating axons, and the strengths of their synapses differ systematically. These differences in synaptic strength weight information from each segment differently, which might account for features of the system's characteristic metachronal synchronization.
Collapse
|
18
|
Achuthan S, Canavier CC. Phase-resetting curves determine synchronization, phase locking, and clustering in networks of neural oscillators. J Neurosci 2009; 29:5218-33. [PMID: 19386918 PMCID: PMC2765798 DOI: 10.1523/jneurosci.0426-09.2009] [Citation(s) in RCA: 93] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2009] [Revised: 03/17/2009] [Accepted: 03/20/2009] [Indexed: 11/21/2022] Open
Abstract
Networks of model neurons were constructed and their activity was predicted using an iterated map based solely on the phase-resetting curves (PRCs). The predictions were quite accurate provided that the resetting to simultaneous inputs was calculated using the sum of the simultaneously active conductances, obviating the need for weak coupling assumptions. Fully synchronous activity was observed only when the slope of the PRC at a phase of zero, corresponding to spike initiation, was positive. A novel stability criterion was developed and tested for all-to-all networks of identical, identically connected neurons. When the PRC generated using N-1 simultaneously active inputs becomes too steep, the fully synchronous mode loses stability in a network of N model neurons. Therefore, the stability of synchrony can be lost by increasing the slope of this PRC either by increasing the network size or the strength of the individual synapses. Existence and stability criteria were also developed and tested for the splay mode in which neurons fire sequentially. Finally, N/M synchronous subclusters of M neurons were predicted using the intersection of parameters that supported both between-cluster splay and within-cluster synchrony. Surprisingly, the splay mode between clusters could enforce synchrony on subclusters that were incapable of synchronizing themselves. These results can be used to gain insights into the activity of networks of biological neurons whose PRCs can be measured.
Collapse
Affiliation(s)
- Srisairam Achuthan
- Neuroscience Center of Excellence, Louisiana State University Health Sciences Center, New Orleans, Louisiana 70112, USA.
| | | |
Collapse
|
19
|
Chen Z, Zheng M, Friesen WO, Iwasaki T. Multivariable harmonic balance analysis of the neuronal oscillator for leech swimming. J Comput Neurosci 2008; 25:583-606. [PMID: 18663565 DOI: 10.1007/s10827-008-0105-7] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/27/2007] [Revised: 05/30/2008] [Accepted: 06/02/2008] [Indexed: 11/29/2022]
Abstract
Biological systems, and particularly neuronal circuits, embody a very high level of complexity. Mathematical modeling is therefore essential for understanding how large sets of neurons with complex multiple interconnections work as a functional system. With the increase in computing power, it is now possible to numerically integrate a model with many variables to simulate behavior. However, such analysis can be time-consuming and may not reveal the mechanisms underlying the observed phenomena. An alternative, complementary approach is mathematical analysis, which can demonstrate direct and explicit relationships between a property of interest and system parameters. This paper introduces a mathematical tool for analyzing neuronal oscillator circuits based on multivariable harmonic balance (MHB). The tool is applied to a model of the central pattern generator (CPG) for leech swimming, which comprises a chain of weakly coupled segmental oscillators. The results demonstrate the effectiveness of the MHB method and provide analytical explanations for some CPG properties. In particular, the intersegmental phase lag is estimated to be the sum of a nominal value and a perturbation, where the former depends on the structure and span of the neuronal connections and the latter is roughly proportional to the period gradient, communication delay, and the reciprocal of the intersegmental coupling strength.
Collapse
Affiliation(s)
- Zhiyong Chen
- School of Electrical Engineering and Computer Science, The University of Newcastle, Callaghan, New South Wales 2308, Australia.
| | | | | | | |
Collapse
|
20
|
Abstract
Locomotion in segmented animals is thought to be based on the coupling of "unit burst generators," but the biological nature of the unit burst generator has been revealed in only a few animal systems. We determined that dopamine (DA), a universal modulator of motor activity, is sufficient to activate fictive crawling in the medicinal leech, and can exert its actions within the smallest division of the animal's CNS, the segmental ganglion. In the entire isolated nerve cord or in the single ganglion, DA induced slow antiphasic bursting (approximately 15 s period) of motoneurons known to participate in the two-step elongation-contraction cycle underlying crawling behavior. During each cycle, the dorsal (DE-3) and ventral (VE-4) longitudinal excitor motoneurons fired approximately 180 degrees out of phase from the ventrolateral circular excitor motoneuron (CV), which marks the elongation phase. In many isolated whole nerve cords, DE-3 bursting progressed in an anterior to posterior direction with intersegmental phase delays appropriate for crawling. In the single ganglion, the dorsal (DI-1) and ventral (VI-2) inhibitory longitudinal motoneurons fired out of phase with each DE-3 burst, further confirming that the crawl unit burst generator exists in the single ganglion. All isolated ganglia of the CNS were competent to produce DA-induced robust fictive crawling, which typically lasted uninterrupted for 5-15 min. A quantitative analysis indicated that DA-induced crawling was not significantly different from electrically evoked or spontaneous crawling. We conclude that DA is sufficient to activate the full crawl motor program and that the kernel for crawling resides within each segmental ganglion.
Collapse
|
21
|
Norris BJ, Weaver AL, Wenning A, García PS, Calabrese RL. A central pattern generator producing alternative outputs: phase relations of leech heart motor neurons with respect to premotor synaptic input. J Neurophysiol 2007; 98:2983-91. [PMID: 17728387 DOI: 10.1152/jn.00407.2007] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022] Open
Abstract
The central pattern generator (CPG) for heartbeat in leeches consists of seven identified pairs of segmental heart interneurons and one unidentified pair. Four of the identified pairs and the unidentified pair of interneurons make inhibitory synaptic connections with segmental heart motor neurons. The CPG produces a side-to-side asymmetric pattern of intersegmental coordination among ipsilateral premotor interneurons corresponding to a similarly asymmetric fictive motor pattern in heart motor neurons, and asymmetric constriction pattern of the two tubular hearts: synchronous and peristaltic. Using extracellular techniques, we recorded, in 61 isolated nerve cords, the activity of motor neurons in conjunction with the phase reference premotor heart interneuron, HN(4), and another premotor interneuron that allowed us to assess the coordination mode. These data were then coupled with a previous description of the temporal pattern of premotor interneuron activity in the two coordination modes to synthesize a global phase diagram for the known elements of the CPG and the entire motor neuron ensemble. These average data reveal the stereotypical side-to-side asymmetric patterns of intersegmental coordination among the motor neurons and show how this pattern meshes with the activity pattern of premotor interneurons. Analysis of animal-to-animal variability in this coordination indicates that the intersegmental phase progression of motor neuron activity in the midbody in the peristaltic coordination mode is the most stereotypical feature of the fictive motor pattern. Bilateral recordings from motor neurons corroborate the main features of the asymmetric motor pattern.
Collapse
Affiliation(s)
- Brian J Norris
- Department of Biology, Emory University, Atlanta, GA 30322, USA
| | | | | | | | | |
Collapse
|