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Modeling of bursting mechanisms and coordination in a spinal central pattern generator
KTH, Superseded Departments, Numerical Analysis and Computer Science, NADA.ORCID iD: 0000-0002-0550-0739
1998 (English)Doctoral thesis, comprehensive summary (Other scientific)
Abstract [en]

Mechanisms underlying lotal bursting as well as coordinationbetween different levels of a spinal CPG generating locomotionhave been investigated using computer simulations. A"primitive" jawless vertebrate, the lamprey, is used a.s aprototype model. Most simulations have been conducted using abiophysical neu ron model built on the Hodgkin-Huxley formalismand equipped with Nu+, K+,Ca²+, Kca, LVACa²+ and NMDA activated channels. Inhibitory andexcitatory AMPA/kainate and NMDA synapses are modeled as timedependent conductances with appropriate reversal potentials.For tomparison, Morris-Letar oscillators as well as adaptingleaky integrator-like units are also used.

The basic identified building blocks of the CPG, generatingalternating left right burst activity, tonsist of ipsilaterallyprojecting excitatory neurons (E) and contralaterallyprojecting inhibitory neurons (C). The model neurons are connected in the same way ss has been established experimentally.Sinte several complementary mechanisms may play a role, thepotential of two different neural mechanisms have been exploredwhich can provide burst activity at the segmen tal level, andintersegmental coordination. When alternating left-rightactivity is produced through an escape-like mechanism the quietside is able to become ac tive despite ongoing inhibition fromthe contralateral side. Reciprocal inhibition is then a crucialburst terminating factor. Burst frequency is strongly affectedby the effective inhibition and the drive to escape fromongoing inhibition. Several factors influence this process. Kcacurrents control spike frequency on the active sideand also a post-burst hyperpolarization on the inactive side.Postin hibitory rebound properties, carried by e.g. low voltageactivatedCa²+ currents further can promote escape. Phasicipsilateral excitation and NMDA membrane properties stabilizethe rhythm, especially in the lower frequency range. Severalexperimental observations can be explained based on the effectthese different factors have on effective inhibition andtendency for escape.

Bursting can, however, also be produced by a networkdeprived of inhibition, showing that powerful burst terminatingmechanisms not requiring inhibition exist. In the model withbiophysically detailed neurons such a mechanism could beactivation ofKcacurrents due to accumulation ofCa²+ during the active phase. As shown innon-spiking, as well as biophysically detailed models, aconstant burst proportion over a wide frequency range can beachieved by modulation of the rel ative strength of adaptationin such networks. The left-right inhibition causes left-rightalternation but may not affect the frequency of bursting.

When both types of lotal oscillatory networks are extendedlongitudinally, a rostral to caudal phase delay is producedwhen caudal projections are extended further than the rostralenes. However, the excitatory versus inhibitory projec tionsmay have different roles in the two alternative models. Thisrelative phase delay expressed as % of cycle duration,increases in general with frequency. The simulations suggestthat the conditions at the ends of the simulated chain arecritical for the resulting phase lag. The capability ofbuffering against frequency variations and rapid adjustmentsfollowing perturbations is discussed and com pared with chainsof relaxation oscillators and phase-coupled oscillators.

Place, publisher, year, edition, pages
Stockholm: KTH , 1998. , 82 p.
Series
Trita-NA, ISSN 0348-2952 ; 98:10
Keyword [en]
adaptation, central pattern generator, computer simulation, inter segmental coordination, lamprey, locomotion, neural network, rhythmogenesis
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:kth:diva-2673ISBN: 91-7170-255-5 (print)OAI: oai:DiVA.org:kth-2673DiVA: diva2:8354
Public defence
1998-06-16, 00:00
Note
QC 20100616Available from: 2000-01-01 Created: 2000-01-01 Last updated: 2010-06-16Bibliographically approved
List of papers
1. Computer simulation of the segmental neural network generation locomotion in laprey by using populations of network inteneurons
Open this publication in new window or tab >>Computer simulation of the segmental neural network generation locomotion in laprey by using populations of network inteneurons
1992 (English)In: Biological Cybernetics, ISSN 0340-1200, E-ISSN 1432-0770, Vol. 68, 1-13 p.Article in journal (Other academic) Published
National Category
Engineering and Technology
Identifiers
urn:nbn:se:kth:diva-13356 (URN)
Note
QC 20100614Available from: 2010-06-14 Created: 2010-06-14 Last updated: 2017-12-12Bibliographically approved
2. Low-voltage-activated calcium channels in the lamprey locomotor network: Simulation and experiment
Open this publication in new window or tab >>Low-voltage-activated calcium channels in the lamprey locomotor network: Simulation and experiment
1997 (English)In: Journal of Neurophysiology, ISSN 0022-3077, E-ISSN 1522-1598, Vol. 77, no 4, 1795-1812 p.Article in journal (Refereed) Published
Abstract [en]

To evaluate the role of low-voltage-activated (LVA) calcium channels in the lamprey spinal locomotor network, a previous computer simulation model has been extended to include LVA calcium channels. It is also of interest to explore the consequences of a LVA conductance for the electrical behavior of the single neuron. The LVA calcium channel was modeled with voltage-dependent activation and inactivation using the m(3)h form, following a Hodgkin-Huxley paradigm. Experimental data from lamprey neurons was used to provide parameter values of the single cell model. The presence of a LVA calcium conductance in the model could account for the occurrence of a rebound depolarization in the simulation model. The influence of holding potential on the occurrence of a rebound as well the latency at which it is elicited was investigated and compared with previous experiments. The probability of a rebound increased at a more depolarized holding potential and the latency was also reduced under these conditions. Furthermore, the effect of changing the holding potential and the reversal potential of the calcium dependent potassium conductance were tested to determine under which conditions several rebound spikes could be elicited after a single inhibitory pulse in the simulation model. A reduction of the slow afterhyperpolarization (sAHP) after the action potential reduced the tendency for a train of rebound spikes. The experimental effects of gamma-aminobutyric acid-B (GABA(B)) receptor activation were simulated by reducing the maximal LVA calcium conductance. A reduced tendency for rebound firing and a slower rising phase with sinusoidal current stimulation was observed, in accordance with earlier experiments. The effect of reducing the slow afterhyperpolarization and reducing the LVA calcium current was tested experimentally in the lamprey spinal cord, during N-methyl-D-aspartate (NMDA)-induced fictive locomotion. The reduction of burst frequency was more pronounced with GABA(B) agonists than with apamin (inhibitor of K-(Ca) current) when using high NMDA concentration (high burst frequency). The burst frequency increased after the addition of a LVA calcium current to the simulated segmental network, due to a faster recovery during the inhibitory phase as the activity switches between the sides. This result is consistent with earlier experimental findings because GABA(B) receptor agonists reduce the locomotor frequency. These results taken together suggest that the LVA calcium chancels contribute to a larger degree with respect to the burst frequency regulation than the sAHP mechanism at higher burst frequencies. The range in which a regular burst pattern can be simulated is extended in the lower range by the addition of LVA calcium channels, which leads to more stable activity at low locomotor frequencies. We conclude that the present model can account for rebound firing and trains of rebound spikes in lamprey neurons. The effects of GABA(B) receptor activation on the network level is consistent with a reduction of the calcium current through LVA calcium channels even though GABA(B) receptor activation will affect the sAHP indirectly and also presynaptic inhibition.

Keyword
THALAMOCORTICAL RELAY NEURONS, ELICITS FICTIVE LOCOMOTION, COMPUTER-BASED MODEL, SPINAL-CORD INVITRO, MEMBRANE-PROPERTIES, NEURAL NETWORKS, THALAMIC RELAY, INTERSEGMENTAL COORDINATION, REALISTIC SIMULATIONS, SYNAPTIC-INTERACTIONS
National Category
Engineering and Technology
Identifiers
urn:nbn:se:kth:diva-13357 (URN)A1997WU25200010 ()
Note
QC 20100614Available from: 2010-06-14 Created: 2010-06-14 Last updated: 2017-12-12Bibliographically approved
3. Intersegmental coordination in the lamprey: Simulations using a network model without segmental boundaries
Open this publication in new window or tab >>Intersegmental coordination in the lamprey: Simulations using a network model without segmental boundaries
1997 (English)In: Biological Cybernetics, ISSN 0340-1200, E-ISSN 1432-0770, Vol. 76, no 1, 1-9 p.Article in journal (Refereed) Published
Abstract [en]

Swimming in vertebrates such as eel and lamprey involves the coordination of alternating left and right activity in each segment. Forward swimming is achieved by a lag between the onset of activity in consecutive segments rostrocaudally along the spinal cord. The intersegmental phase lag is approximately 1% of the cycle duration per segment and is independent of the swimming frequency. Since the lamprey has approximately 100 spinal segments, at any given time one wave of activity is propagated along the body. Most previous simulations of intersegmental coordination in the lamprey have treated the cord as a chain of coupled oscillators or well-defined segments. Here a network model without segmental boundaries is described which can produce coordinated activity with a phase lag. This 'continuous' pattern-generating network is composed of a column of 420 excitatory interneurons (E1 to E420) and 300 inhibitory interneurons (C1 to C300) on each half of the simulated spinal cord. The interneurons are distributed evenly along the simulated spinal cord, and their connectivity is chosen to reflect the behavior of the intact animal and what is known about the length and strength of the synaptic connections. For example, E100 connects to all interneurons between E51 and E149, but at varying synaptic strengths, while E101 connects to all interneurons between E52 and E150. This unsegmented E-C network generates a motor pattern that is sampled by output elements similar to motoneurons (M cells), which are arranged along the cell column so that they receive input from seven E and five C interneurons. The M cells thus represent the summed excitatory and inhibitory input at different points along the simulated spinal cord and can be regarded as representing the ventral root output to the myotomes along the spinal cord. E and C interneurons have five simulated compartments and Hodgkin-Huxley based dynamics. The simulated network produces rhythmic output over a wide range of frequencies (1-11 Hz) with a phase lag constant over most of the length, with the exception of the 'cut' ends due to reduced synaptic input. As the inhibitory C interneurons in the simulation have more extensive caudal than rostral projections, the output of the simulation has positive phase lags, as occurs in forward swimming. However, unlike the biological network, phase lags in the simulation increase significantly with burst frequency, from 0.5% to 2.3% over the range of frequencies of the simulation. Local rostral or caudal increases in excitatory drive in the simulated network are sufficient to produce motor patterns with increased or decreased phase lags, respectively.

Keyword
CENTRAL PATTERN GENERATOR, COUPLED NONLINEAR OSCILLATORS, AMINO-ACID RECEPTORS, COMPUTER-BASED MODEL, SPINAL-CORD, FICTIVE LOCOMOTION, NEURAL NETWORKS, REALISTIC SIMULATIONS, MATHEMATICAL-MODELS, MEMBRANE-PROPERTIES
National Category
Engineering and Technology
Identifiers
urn:nbn:se:kth:diva-13365 (URN)10.1007/s004220050316 (DOI)A1997WJ06100001 ()
Note
QC 20100615Available from: 2010-06-15 Created: 2010-06-15 Last updated: 2017-12-12Bibliographically approved
4. Production of phase lag in chains of neural networks oscillating through an escape mechanism
Open this publication in new window or tab >>Production of phase lag in chains of neural networks oscillating through an escape mechanism
1998 (English)In: Proceedings of the sixth annual conference on Computational neuroscience: trends in research, 1998, 65-70 p.Conference paper, Published paper (Other academic)
National Category
Engineering and Technology
Identifiers
urn:nbn:se:kth:diva-13366 (URN)0-306-45919-1 (ISBN)
Conference
sixth annual conference on Computational neuroscience : trends in research
Note
QC 20100615Available from: 2010-06-15 Created: 2010-06-15 Last updated: 2010-06-16Bibliographically approved
5. Neural mechanisms potentially contributing to the intersegmental phase lag in lamprey I.: Segmental oscillations dependent on reciprocal inhibition
Open this publication in new window or tab >>Neural mechanisms potentially contributing to the intersegmental phase lag in lamprey I.: Segmental oscillations dependent on reciprocal inhibition
1999 (English)In: Biological Cybernetics, ISSN 0340-1200, E-ISSN 1432-0770, Vol. 81, no 4, 317-330 p.Article in journal (Refereed) Published
Abstract [en]

Factors contributing to the production of a phase lag along chains of oscillatory networks consisting of Hodgkin-Huxley type neurons are analyzed by means of simulations. Simplified network configurations are explored consisting of the basic building blocks of the spinal central pattern generator (CPG) generating swimming in the lamprey. It consists of reciprocally coupled crossed inhibitory C interneurons and ipsilateral excitatory E interneurons that activate C neurons and other E neurons. Oscillatory activity in the model network can, in the simplest case, be produced by a pair of reciprocally coupled C interneurons oscillating through an escape mechanism. Different levels of tonic excitation drive the network over a wide burst frequency range. In this type of network, powerful frequency-regulating factors are the effective inhibition produced by the active side, in combination with the tendency of the inactive side to escape from the inhibition. These two mechanisms can be affected by several factors, e.g. spike frequency adaptation (calcium-dependent K+ channels): N-methyl-D-aspartate membrane properties as well as presence of low-voltage activated calcium channels. A rostrocaudal phase lag can be produced either by extending the contralateral inhibitory projections or the ipsilateral excitatory projections relatively more in the caudal than the rostral direction, since both an increased inhibition and a phasic excitation slow down the receiving network. The phase lag becomes decreased if the length of the intersegmental projections is increased or if the projections are extended symmetrically in both the rostral and the caudal directions. The simulations indicate that the conditions in the ends of an oscillator chain may significantly affect sign, magnitude and constancy of the phase lag. Also, with short and relatively weak intersegmental connections, the network remains robust against perturbations as well as intrinsic frequency differences along the chain. The phase lag (percentage of cycle duration) increases, however, with burst frequency also when the coupling strength is comparatively weak. The results are discussed and compared with previous "phase pulling" models as well as relaxation oscillators.

Keyword
COMPUTER-BASED MODEL, SPINAL-CORD, FICTIVE LOCOMOTION, REALISTIC SIMULATIONS, COUPLED OSCILLATORS, MEMBRANE-PROPERTIES, PATTERN GENERATOR, NETWORK MODEL, LOW-VOLTAGE, NEURONS
National Category
Engineering and Technology
Identifiers
urn:nbn:se:kth:diva-13367 (URN)10.1007/s004220050565 (DOI)000083208800004 ()
Note
QC 20100616Available from: 2010-06-16 Created: 2010-06-16 Last updated: 2017-12-12Bibliographically approved
6. Activity-dependent modulation of adaptation produces a constant burst proportion in a model of the lamprey spinal locomotor generator.
Open this publication in new window or tab >>Activity-dependent modulation of adaptation produces a constant burst proportion in a model of the lamprey spinal locomotor generator.
Show others...
1998 (English)In: Biological Cybernetics, ISSN 0340-1200, E-ISSN 1432-0770, Vol. 79, no 1, 1-14 p.Article in journal (Refereed) Published
Abstract [en]

The neuronal network underlying lamprey swimming has stimulated extensive modelling on different levels of abstraction. The lamprey swims with a burst frequency ranging from 0.3 to 8-10 Hz with a rostrocaudal lag between bursts in each segment along the spinal cord. The swimming motor pattern is characterized by a burst proportion that is independent of burst frequency and lasts around 30%-40% of the cycle duration. This also applies in preparations in which the reciprocal inhibition in the spinal cord between the left and right side is blocked. A network of coupled excitatory neurons producing hemisegmental oscillations may form the basis of the lamprey central pattern generator (CPG). Here we explored how such networks, in principle, could produce a large frequency range with a constant burst proportion. The computer simulations of the lamprey CPG use simplified, graded output units that could represent populations of neurons and that exhibit adaptation. We investigated the effect of an active modulation of the degree of adaptation of the CPG units to accomplish a constant burst proportion over the whole frequency range when, in addition, each hemisegment is assumed to be self-oscillatory. The degree of adaptation is increased with the degree of stimulation of the network. This will make the bursts terminate earlier at higher burst rates, allowing for a constant burst proportion. Without modulated adaptation the network operates in a limited range of swimming frequencies due to a progressive increase of burst duration with increasing background stimulation. By introducing a modulation of the adaptation, a broad burst frequency range can be produced. The reciprocal inhibition is thus not the primary burst terminating factor, as in many CPG models, and it is mainly responsible for producing alternation between the left and right sides. The results are compared with the Morris-Lecar oscillator model with parameters set to produce a type A and type B oscillator, in which the burst durations stay constant or increase, respectively, when the background stimulation is increased. Here as well, burst duration can be controlled by modulation of the slow variable in a similar way as above. When oscillatory hemisegmental networks are coupled together in a chain a phase lag is produced. The production of a phase lag in chains of such oscillators is compared with chains of Morris-Lecar relaxation oscillators. Models relating to the intact versus isolated spinal cord preparation are discussed, as well as the role of descending inhibition.

Keyword
adaptation, animal, article, biological model, cybernetics, in vitro study, lamprey, locomotion, nerve cell network, oscillometry, physiology, spinal cord, swimming
National Category
Engineering and Technology
Identifiers
urn:nbn:se:kth:diva-13369 (URN)10.1007/s004220050453 (DOI)000075594700001 ()9742673 (PubMedID)2-s2.0-0032116815 (Scopus ID)
Note

QC 20100616

Available from: 2010-06-16 Created: 2010-06-16 Last updated: 2017-12-12Bibliographically approved
7. Neural mechanisms potentially contributing to the intersegmental phase lag in lamprey II.: Hemisegmental oscillations produced by mutually coupled excitatory neurons
Open this publication in new window or tab >>Neural mechanisms potentially contributing to the intersegmental phase lag in lamprey II.: Hemisegmental oscillations produced by mutually coupled excitatory neurons
1999 (English)In: Biological Cybernetics, ISSN 0340-1200, E-ISSN 1432-0770, Vol. 81, no 4, 299-315 p.Article in journal (Refereed) Published
Abstract [en]

Most previous models of the spinal central pattern generator (CPG) underlying locomotion in the lamprey have relied on reciprocal inhibition between the left and right side for oscillations to be produced. Here, we have explored the consequences of using self-oscillatory hemisegments. Within a single hemisegment, the oscillations are produced by a network of recurrently coupled excitatory neurons (E neurons) that by themselves are not oscillatory but when coupled together through N-methyl-D-aspartate (NMDA) and x-amino-3-hydroxy-5-methyl-4-isoxazolepropionicacid (AMPA)/kainate transmission can produce oscillations. The bursting mechanism relies on intracellular accumulation of calcium that activates Ca2+-dependent KC The intracellular calcium is modeled by two different intracellular calcium pools, one of which represents the calcium entry following the action potential, Ca-AP pool, and the other represents the calcium inflow through the NMDA channels, Ca-NMDA pool. The Ca2+-dependent K+ activated by these two calcium pools are referred to as K-CaAP and K-CaNMDA respectively, and their relative conductances are modulated and increase with the background activation of the network. When changing the background stimulation, the bursting activity in this network can be made to cover a frequency range of 0.5-5.5 Hz with reasonable burst proportions if the adaptation is modulated with the activity. When a chain of such hemisegments are coupled together, a phase lag along the chain can be produced. The local oscillations as well as the phase lag is dependent on the axonal conduction delay as well as the types of excitatory coupling that are assumed, i.e. AMPA/kainate and/or NMDA. When the caudal excitatory projections are extended further than the rostral ones, and assumed to be of approximately equal strength, this kind of network is capable of reproducing several experimental observations such as those occurring during strychnine blockade of the left-right reciprocal inhibition. Addition of reciprocally coupled inhibitory neurons in such a network gives rise to antiphasic activity between the left and right side, but not necessarily to any change of the frequency if the burst proportion of the hemisegmental bursts is well below 50%. Prolongation of the C neuron projection in the rostrocaudal direction restricts the phase lag produced by only the excitatory hemisegmental network by locking together the interburst intervals at different levels of the spinal cord.

Keyword
DEPENDENT POTASSIUM CHANNELS, SPINAL-CORD, FICTIVE LOCOMOTION, GLYCINERGIC INHIBITION, SYNAPTIC DRIVE, NETWORK, MODEL, INTERNEURONS, SIMULATIONS, MODULATION
National Category
Engineering and Technology
Identifiers
urn:nbn:se:kth:diva-13368 (URN)10.1007/s004220050564 (DOI)000083208800003 ()
Note
QC 20100616Available from: 2010-06-16 Created: 2010-06-16 Last updated: 2017-12-12Bibliographically approved

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