Download Insights from models of rhythmic motor systems

Insights from models of rhythmic motor systems
Astrid A Prinz
Computational models of rhythmic motor systems are valuable
tools for the study of motor pattern generation and control.
Recent modeling advances, together with experimental results,
suggest that rhythmic behaviors, such as breathing or walking,
are influenced by complex interactions among motor system
components. Such interactions occur at all levels of
organization, from the subcellular through to the cellular,
synaptic, and network levels to the level of neuromuscular
interactions and that of the whole organism. Simultaneously,
safety mechanisms at all levels contribute to network stability
and the generation of robust motor patterns.
Addresses
Emory University Department of Biology, Rollins Research Center,
1510 Clifton Road, Atlanta, GA 30322 USA
Corresponding author: Prinz, Astrid A ([email protected])
Current Opinion in Neurobiology 2006, 16:615–620
This review comes from a themed issue on
Motor systems
Edited by Eve Marder and Peter L Strick
Available online 23rd October 2006
0959-4388/$ – see front matter
# 2006 Elsevier Ltd. All rights reserved.
DOI 10.1016/j.conb.2006.10.001
systems function as tools for the integration of experimental results into a coherent picture of motor systems.
Modeling generates predictions that inspire further
experimentation to validate and refine the models and
to derive new insights into rhythmic motor function.
Furthermore, modeling of motor systems enables the
computational manipulation of system parameters that
might not be experimentally accessible and thus helps to
elucidate the role of parameters such as neuronal or
synaptic properties in motor control.
Recent advances in modeling support two insights into
rhythmic motor systems. First, that rhythmic behaviors
are shaped by the interplay of complex mechanisms
ranging from the subcellular through the neuromechanic
to the organismal level, rather than arising from a one-way
flow of information from the CPG through motor neurons
to the muscles. And second, that rhythmic motor systems
show robustness because of the multiple safety mechanisms at the cellular, synaptic and network levels.
Here, I review motor system modeling efforts in invertebrate and vertebrate model systems, and focus on results
that illustrate the two points described above. Because of
this selection and its limited scope, this review is by no
means a comprehensive account of recent advances in
motor system modeling, but instead attempts to highlight
trends in the field.
Introduction
The periphery is not so peripheral
Many forms of animal behavior are rhythmic, including
different types of locomotion such as walking, swimming,
crawling and flying, and vital behaviors such as breathing
and chewing. The rhythmic movements involved in these
behaviors are governed by central pattern generators
(CPGs), that is, neuronal circuits that generate rhythmic
electrical activity patterns and that, directly or through
intermediate motor neurons, cause the coordinated contraction of muscles that underlies rhythmic behavior.
Rhythmic motor systems in various model organisms have
been the subject of numerous experimental and theoretical studies, partly because they underlie basic and
important behaviors but also because their function is
clearly defined and often easily measurable. Our understanding of the mechanism of pattern generation and the
control of rhythmic motor behaviors in the ‘simple’ motor
systems of invertebrates is, therefore, fairly advanced [1],
but significant progress has also been made in vertebrate
motor systems [2].
One factor that makes a rhythmic motor system a good
model system is that its motor pattern continues to be
expressed when the neural circuitry is removed from the
body and placed in vitro for experimental investigation.
Much of our understanding of motor control comes from
the study of such disembodied preparations, and accompanying computational models have, therefore, long
focused on the CPG circuits that generate fictive movements without including the ‘periphery’, that is, the
musculo-skeletal system that performs the movements
in vivo. Although CPG models have provided many
insights into the mechanisms of motor control, several
recent studies are acknowledging that ‘‘the brain has a
body’’ [3], and that interactions between the neuronal
circuitry and the motor periphery can have significant
influence on the motor pattern [4] (Figure 1).
Computational modeling is an integral part of the effort to
understand rhythmic motor control. Models of motor
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One pathway through which a body part can influence the
CPG that governs it is through proprioceptive information. A recent model of stick insect walking [5,6] integrates a biomechanical model of the insect body with a
model of the neural control system for walking, with the
Current Opinion in Neurobiology 2006, 16:615–620
616 Motor systems
Glossary
Anterior burster neuron: Identified interneuron in the crustacean
pyloric circuit that drives the pyloric rhythm with its periodic burst
activity.
Cable models: A model of a biological neuron in which the spatially
extended axon and dendrites of the neuron are represented by leaky
electrical cables. Cable models reproduce the signal decay and
conduction delays along axons and dendrites of biological neurons.
Coordinating interneurons: Neurons that connect and coordinate
different pattern-generating circuits, for example the rhythmic circuits
in different segments of a leech or the rhythmic circuits in both halves
of the body in bilateral animals.
Eupneic rhythm: The rhythmic respiratory activity associated with
normal, unlabored breathing.
Follower neurons: Neurons that are rhythmically active as part of a
pattern-generating circuit in response to rhythmic synaptic inputs, but
that do not generate rhythmic activity themselves when isolated from
the circuit.
Not intrinsically bursting neurons: Neurons that do not generate
bursts of action potentials when isolated from synaptic inputs.
Open-loop system: In an open-loop system, the flow of information
is unidirectional, that is, from component A to component B without
feedback from B to A. In an open-loop motor system, for example, the
muscles would be controlled by neuronal commands from the brain,
but would provide no sensory feedback about their actual movements
to the brain.
Pacemaker kernel: The subset of neurons in a pattern-generating
circuit that drive the rhythmic activity, and that remain rhythmically
active even when isolated from the rest of the circuit.
Solution space: The region in the parameter space of a neuron or
network model that generates a desired electrical activity pattern.
Swimmeret: One of the paired abdominal appendages of certain
aquatic crustaceans that function primarily for carrying the eggs in
females and are usually adapted for swimming.
biomechanical component providing proprioceptive
information to the neural component of the model.
The mutual entrainment of the oscillations of neural
and mechanical components in such coupled locomotion
models can have significant influence on the frequency of
the motor pattern, which tends to deviate from the
intrinsic oscillation frequency of the isolated neural circuit and to approach the natural frequency of the body
part [7]. Furthermore, a closed loop between a neuronal
oscillator and a mechanical system can lead to the emergence of modes of oscillation not present in open-loop
systems (see glossary) [8]. An important parameter that
influences the motor patterns generated by closed-loop
locomotion models is the time delay incurred by signal
transmission in the sensorimotor loop, which, therefore, is
a sensitive parameter in such integrated models [9].
Including the periphery in models of motor control also
enables the validation of CPG models, and was used with
that intent in an integrated model of larval zebrafish
swimming and escape [10]. This model confirms that
the neural component of the model generates the
expected behavior when used to control a hydrodynamic
model of the animal. Similarly, respiratory CPG models
have been integrated with a neurochemical feedback
model of ventilation to demonstrate that they can reproduce various forms of periodic breathing [11].
Current Opinion in Neurobiology 2006, 16:615–620
Figure 1
Motor behavior arises from interactions between neural motor circuits
and the body they control. (a) A more linear notion of information flow in
the generation of motor behavior focuses on the role of the nervous
system in processing incoming sensory information and responding with
motor outputs that are then executed by the body. (b) Recent models of
motor systems reviewed here have adopted a more integrated view of
motor behaviour, in which the nervous system (NS) is perceived to be
embedded within a body, which is in turn embedded in an environment,
with interactions among these levels shaping motor behavior. Modified
from [3] with permission.
Modeling studies that examine the biomechanics of
Aplysia californica feeding [12,13] demonstrate that passive mechanical forces can impose constraints on the
movements possible in a motor system, and that neural
control must take into account that the effect of activation
of a muscle depends on its current biomechanical environment. How an Aplysia feeding muscle responds to
neuronal commands is also influenced by neuromodulation (i.e. the modification of muscular properties by
modulatory substances released onto the muscles), which
enables the feeding apparatus to express a wide range of
movements and effectively renders it ‘semi-autonomous’
[14].
Interactions among motor systems
Pattern generation by a motor system can be affected not
only through feedback from the periphery but also
through interactions with other motor systems in the
same animal. This is most obvious in the entrainment
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Insights from models of rhythmic motor systems Prinz 617
of respiration and locomotion that we experience when
running. Locomotion can entrain respiration indirectly
through somatic afferents, as demonstrated experimentally and in a model of the rat respiratory system [15], or
directly through inhibitory connections from the locomotor to the respiratory CPG, as in a model of coordination
between locomotion and respiration in the snail Lymnaea
stagnalis [16]. Interactions between neuronal circuits
involved in motor control — the pons and the medulla
— have also recently been included in a model of
respiratory pattern generation. This model suggests that
the rhythmic activity produced by the reduced medullary
preparations used in many studies of respiration might
differ from the in vivo eupneic rhythm (see glossary) [17].
Influence of cellular properties on motor
patterns
In addition to neuromechanical influences, motor pattern
generation can be influenced by the morphology and
biophysical properties of the CPG interneurons and
motor neurons. The often relatively simple neuron models used in models of rhythmic motor systems might,
therefore, have to be replaced with more detailed and
biophysically realistic model neurons to reproduce certain
features of motor pattern generation accurately [18].
This is supported by a recent model of the leech heartbeat CPG [19], which showed that representing coordinating interneurons by complex multi-compartment
cable models (see glossary) with realistic synaptic inputs,
spike adaptation, and multiple spike initiation sites was
necessary to capture the behavior of the system under
different experimental conditions. In the same system,
the detailed dynamical properties of the motor neurons
driven by the CPG have been implicated in switching the
motor pattern between two different states, peristaltic
and synchronous heartbeat [20]. Similarly, comparison of
different versions of a multi-compartment model of the
leech heartbeat interneuron shows that the detailed morphological properties of the neuron can affect burst activity and lead to different mechanisms for burst generation
[21,22].
In Xenopus laevis tadpoles, changes of the swimming
motor pattern during development can be reproduced
by a model of the swim CPG that incorporates the
lengthening of motor neuron axons and the increasing
complexity of the motor neuron dendritic trees that
occurs during development. This model suggests that
the changes in the motor pattern are partly due to changes
in the morphological details of motor neurons [23].
Some motor patterns might even rely on subcellular
phenomena. In the developing chick spinal cord, episodes of rhythmic discharges occur on a time-scale of
minutes. A model of the underlying network with excitatory connections reproduces the episodic activity if
slow, activity-dependent variations of the intracellular
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chloride concentration are incorporated [24], showing
that network-level rhythmic behavior can arise from
the dynamics of ion concentrations in the circuit neurons.
Adding biophysical details to models of rhythmic motor
systems thus can improve model performance. However,
in some cases the opposite is true, such as in a recent
study of crayfish swimming, in which simplifications of
the model of a swimmeret (see glossary) circuit did not
result in any decrease in model performance [25].
Furthermore, morphologically complex multi-compartment model neurons can often be reduced to simpler
models with fewer compartments by grouping functionally similar compartments without dramatic effects on
model behavior, as was recently demonstrated in a leech
heart interneuron model [21].
Cellular and synaptic contributions to
network robustness
Rhythmic motor systems are robust, and function reliably
throughout an animal’s life [26]. Several recent experimental and modeling studies have highlighted cellular
and synaptic mechanisms that could potentially contribute to this robustness.
Brute-force computational exploration of the parameter
space of bursting neurons in the pyloric CPG of crustaceans has shown that bursting with physiologically meaningful characteristics can occur in pacemaker neurons
with widely differing cellular properties [27]. This infers
that pacemaker neurons need not be narrowly tuned to a
unique ‘solution’ to function, but instead have an entire
‘solution space’ (see glossary) available to them, making
pacemaker activity robust to parameter variations. A
combination of experimental and modeling work [28]
furthermore shows that pyloric CPG neurons use activityindependent homeostatic regulation to ensure a constant
ratio of two antagonistic membrane currents, the transient
potassium current IA and the hyperpolarization-activated
cation current Ih. This regulation thus ensures that the
effects of the two currents on CPG activity compensate
each other, which again promotes robust pacemaking.
IA also interacts with depressing pyloric synapses to
ensure another robust property of pyloric circuits, phase
constancy, meaning that the pyloric circuit is able to
maintain constant phase relationships between the bursts
of its component neurons over wide ranges of rhythm
frequency [29,30].
In addition to these cellular contributions to CPG robustness, the dynamic properties of pyloric synapses also
seem suited to ensure robust network performance.
The only feedback synapse from the follower neurons
in the pyloric circuit onto the pacemaker kernel (see
glossary) shows dynamic properties that enable it to
influence the pacemaker in a negative feedback loop to
Current Opinion in Neurobiology 2006, 16:615–620
618 Motor systems
counteract changes in pyloric frequency, thus stabilizing
the rhythm period [31]. Furthermore, the synapses from
one neuron in the circuit, the lateral pyloric neuron, onto
different targets in the pyloric CPG have target-specific
short-term dynamics that are tailored to the specific
function of each synapse in ensuring proper circuit function [32].
Beyond the pyloric circuit, the effect of changes in the
maximal conductance and activation time constant of Ih in
leech heartbeat interneurons is independent of cycle
period, suggesting that neuromodulation of Ih has robust
effects in animals with different heart frequencies, such
as juvenile leeches (fast heartbeat) versus adult leeches
(slower heartbeat) [33].
Connectivity supports stability
Besides cellular and synaptic contributions to network
robustness, the connectivity of rhythmic motor circuits
can also contribute to network stability. In the pyloric
circuit, the anterior burster neuron that drives the rhythm
is electrically coupled to two not intrinsically bursting
neurons (see glossary) in a configuration that increases the
dynamic range of the pacemaker [34]. Similarly, isolated
hemisegments in the lamprey spinal cord can generate
rhythmic swim activity, and reciprocal inhibition between
the hemisegments functions to stabilize and coordinate
that activity [35].
Excitatory connections can enable rhythmic activity to
emerge as a network property in the absence of pacemaker neurons [36], or can lead to the coexistence of a
cellular and a network rhythmogenic mechanism in the
same circuit. This has been suggested to be the case for
the pre-Bötzinger Complex (pBC) in the respiratory
system [37] and for Xenopus tadpole brainstem circuits
involved in swimming [38]. In addition to providing an
extra rhythmogenic mechanism — and thus increasing
the robustness of rhythm generation — excitatory coupling among oscillatory neurons also increases the parameter range over which robust bursting can occur in a
model of the pBC [39]. The dynamic range of respiratory
pattern generation also increases with the number of
oscillatory neurons in a pBC model [11], suggesting that
Figure 2
Similar network activity on the basis of different cellular and synaptic properties in a model of the crustacean pyloric CPG circuit. (a and b)
Simulated voltage traces from two different versions of the pyloric CPG model. Both models generate functional tri-phasic activity. Scale bars
are 0.5 s and 50 mV. (c and d) Cellular (top) and synaptic properties (bottom) of the same two network models. Bars in the top plots indicate the
conductances of different membrane currents (ICaS, transient calcium current; IA, transient potassium current; IKCa, calcium-dependent potassium
current; INa, fast sodium current; IH, hypolarization-activated cation current) in the circuit neurons AB/PD, LP, and PY. Bars in the bottom plots
indicate the strength of different synapses in the circuit (AB-to-LP, AB-to-PY, etc.). Although the models produce similar activity, they do so
on the basis of different network parameters. From [41] with permission. Abbreviations: AB/PD, anterior burster and pyloric dilator pacemaker
kernel; LP, lateral pyloric neuron; PY, pyloric neuron.
Current Opinion in Neurobiology 2006, 16:615–620
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Insights from models of rhythmic motor systems Prinz 619
the large cell numbers in vertebrate CPG circuits also
contribute to robustness.
Connectivity patterns among CPG neurons can also support robustness by including seemingly redundant connections, such that the failure or loss of any given synapse
can be compensated for by other connections [40]. Bruteforce exploration of millions of different combinations of
synaptic conductances in a model of the pyloric circuit
confirms this by showing that functional pyloric network
activity can be generated on the basis of different synaptic
connection patterns and strengths [41] (Figure 2). Similarly, a model of the zebrafish locomotor network generates stable oscillations with realistic frequencies for a
wide range of synaptic connection strengths [42]. Rhythmic network activity in model networks with appropriate
connectivity also appears to be largely independent of the
cell type used in the model, suggesting robustness to
variations in cellular properties [43].
Even irregular motor patterns, such as those governing
feeding in Aplysia, can be adaptive in variable environments and provide a trial-and-error strategy that leads to
overall — albeit not cycle-by-cycle — robust performance
[14].
References and recommended reading
Papers of particular interest, published within the annual period of
review, have been highlighted as:
of special interest
of outstanding interest
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Conclusions
The recent models of rhythmic motor systems reviewed
here support the notion that motor patterns can be shaped
by complex interactions at all levels of circuit operation,
ranging from the subcellular level through interactions
between cellular and synaptic properties to network-level
rhythmogenic mechanisms and interactions with the
motor periphery. Depending on the purpose of the model
in question, it might not be necessary to include biophysical details at all — or any — of these levels to achieve
realistic model performance, but it seems advisable to
keep in mind the possibility of influences on motor
control from all of these levels when constructing models.
This complexity of potential influences on the motor
pattern endows motor networks with enormous flexibility, but can also make their analysis difficult [44].
Many different levels can influence motor pattern generation, but they can also contribute to its robustness.
Modeling work from the past few years has provided
several examples of contributions to network robustness
from cellular, synaptic and network level sources. The
role of rhythmic motor systems in important behaviors,
such as respiration and locomotion, has obviously provided sufficient evolutionary pressure to install a variety
of safety mechanisms in motor systems that ensure their
reliable functioning throughout life.
Acknowledgements
Support from the Burroughs Wellcome Fund in the form of a Career
Award at the Scientific Interface is gratefully acknowledged.
www.sciencedirect.com
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