robustness
DESCRIPTION
Robustness. the ability of a system to perform consistently under a variety of conditions. Elements of robustness:. feedback. degeneracy. competition. modularity. Feedback. A classic example of feedback in neural circuits: error correction during smooth pursuit. feedback. retinal - PowerPoint PPT PresentationTRANSCRIPT
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Robustness
the ability of a system to perform consistently under a variety of conditions
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competition
degeneracy
modularity
feedback
Elements of robustness:
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Feedback
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FeedbackController
~100 msretinalinputs
GoalFeedforward
Controller Eyeball+ eyemovement
SensedVariable
feedback
A classic example of feedback in neural circuits: error correction during smooth pursuit
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The big idea:
Feedback• permits feedforward programs to be corrected according to the success of feedforward control• can correct for both fluctuations in the target and fluctuations in the feedforward program
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Degeneracy
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A classic example of degeneracy in biology: the genetic code
Because multiple codes can specify the same amino acid, the genetic code is said to be degenerate.
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degeneracy – the condition of having multiple distinct mechanisms for reaching the same outcome
redundancy – the condition of having multiple copies of the same mechanism
this is distinct from
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Degeneracy in the genetic code confers
• tolerance to synonymous mutations• thus greater genetic diversity within a species• and thus more simultaneously possible avenues for evolution
Evolvability is the capacity to adapt by natural selection
Degeneracy can increase evolvability by distributing system outcomes near phenotypic transition boundaries.
CGU ↔ AGGCAU ←
His Arg Arg
→ UGG
Trp
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Swensen & Bean, J. Neurosci. 2005
cell 1 cell 2
Neuron-level degeneracy:robustness of bursting in cerebellar Purkinje cells
acutely dissociated Purkinje somata
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Swensen & Bean, J. Neurosci. 2005
cell 1
cell 2
cell 3
cell 4
cell 5
cell 6
Neuron-level degeneracy:robustness of bursting in cerebellar Purkinje cells
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Neuron-level degeneracy:robustness of bursting in cerebellar Purkinje cells
Swensen & Bean, J. Neurosci. 2005
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Neuron-level degeneracy:robustness of bursting in cerebellar Purkinje cells
Swensen & Bean, J. Neurosci. 2005
An acute decrease in Na+ conductance produces a compensatory increase in voltage-dependent and Ca2+–dependent K+ conductances.
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Neuron-level degeneracy:robustness of bursting in cerebellar Purkinje cells
Swensen & Bean, J. Neurosci. 2005
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Neuron-level degeneracy:robustness of bursting in cerebellar Purkinje cells
Swensen & Bean, J. Neurosci. 2005
A chronic decrease in Na+ conductance produces a compensatory increase in Ca2+ conductance.
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Degeneracy and feedback
input outputsystemvariables
set point
homeostat
In this example, • membrane potential is the robust system output• a fast feedback loop is created by voltage-dependent and Ca2+-dependent K+ channels• a slow feedback loop regulates Ca2+ conductances• many combinations of conductances (i.e., “system variables”) can produce similar output
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Goldman, Golowasch, Marder, & Abbott, J. Neurosci. 2001
Mapping the state space of neuron-level degeneracy:robustness of bursting in stomatogastric ganglion neurons
model stomatogastric ganglion neuron
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Goldman, Golowasch, Marder, & Abbott, J. Neurosci. 2001
Mapping the state space of neuron-level degeneracy:robustness of bursting in stomatogastric ganglion neurons
model stomatogastric ganglion neuron
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Degeneracy can increase the capacity for modulation by allowing the neuron to reside near firing state transition boundaries.
To maximally change the firing behavior of the neuron, a neuromodulator would modify conductances along an axis of high sensitivity (green arrow).
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Prinz et al. Nature 2004
Circuit-level degeneracy:robustness of patterns in the stomastogastric ganglion
lobster stomatogastric ganglion recording with sharp microelectrodes
the pyloric network the pyloric rhythm
note: all synapses are inhibitory
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Prinz et al. Nature Neuroscience 2004
Circuit-level degeneracy:similar network activity from disparate cellular and synaptic parameters
model neurons of pyloric network
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The big idea:
Degeneracy• permits tolerance to many kinds of perturbations• while also maintaining sensitivity to other sorts of perturbations
Degeneracy also allows a population to harbor latent diversity, potentially creating diverse avenues for evolution or modulation.
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Competition
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Another classic example of competition in neural circuits: developing ocular dominance columns
Luo & O’Leary, Ann. Rev. Neurosci. 2005
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A mechanism for competitive synaptic interactions: spike-timing dependent plasticity
Song & Abbott, Nat. Neurosci. 1999Abbott, Zoology 2003
pre leads post pre lags post
This mechanism creates a competition between independent presynaptic neurons for control of the postsynaptic neuron’s spiking.
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A mechanism for competitive synaptic interactions: spike-timing dependent plasticity
Song & Abbott, Nat. Neurosci. 1999Abbott, Zoology 2003
Competitive interactions between neurons are enforced over a large range of presynaptic firing rates. Thus, total input synapse strength onto the postsynaptic cell remains roughly constant despite large changes in presynaptic input.
presynaptic rate = 10 Hz presynaptic rate = 13 Hz
model
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The big idea:
Competition• allows a circuit to self-assemble in a manner appropriate to current conditions• tends to enforce constancy of total synapse strength while allocating strong synapses to the most effective inputs.
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Modularity
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A classic example of modularity in biology:the domain structure of genes and proteins
“Exon shuffling” was recognized early in molecular biology as a potential mechanism to generate diverse novel proteins based on existing functional building-blocks.
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Modularity in neural circuitsa putative example: “cerebellar-like” circuits
Bell, Han, & Sawtell, Annu. Rev. Neurosci. 2008Oertel & Young, Trends Neurosci. 2004Roberts & Portfors, Biol. Cybern. 2008
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Bell, Han, & Sawtell, Annu. Rev. Neurosci. 2008Oertel & Young, Trends Neurosci. 2004Roberts & Portfors, Biol. Cybern. 2008
Modularity in neural circuits
mammalian cerebellum mammalian dorsal cochlear nucleusteleost cerebellum
teleost medial octavolateral nucleus mormyrid electrosensory lobe gymnotid electrosensory lobe
“cerebellar-like” circuits in vertebrates
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Modularity in neural circuitsa putative example: “cerebellar-like” circuits
• principal cells receive excitatory input from a very large population of granule cells forming parallel axon bundles that target the spiny dendrites of principal cells
• principal cells also receive excitatory ascending input from sensory regions targeting the perisomatic/proximal region of principal cells
Bell, Han, & Sawtell, Annu. Rev. Neurosci. 2008Oertel & Young, Trends Neurosci. 2004Roberts & Portfors, Biol. Cybern. 2008
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Modularity in neural circuitsa putative example: “cerebellar-like” circuits
• parallel fibers carry “higher-level” information (corollary discharge, proprioceptive info)
• ascending inputs carry lower-level information (pertaining to the same sensory modality or task)
• parallel fiber signals can in principle “predict” the lower-level signals
• “prediction” is learned by pairing parallel fiber input with ascending input
• pairing produces a depression of parallel fiber inputs (anti-Hebbian plasticity)
Bell, Han, & Sawtell, Annu. Rev. Neurosci. 2008Oertel & Young, Trends Neurosci. 2004Roberts & Portfors, Biol. Cybern. 2008
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Modularity in neural circuitsa putative example: a visual cortical hypercolumn
Horton & Adams, Philos Trans R Soc Lond B Biol Sci. 2005
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Rakic Nature Neuroscience 2009
Modularity in evolutionRadial unit lineage model of cortical neurogenesis
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Modularity can permit an organism to process a new input without evolving an entirely novel circuit from scratch—in effect, building diverse objects using existing building-blocks.
Sharma, Angelucci, & Sur, Nature 2001von Melchner, Pallas, & Sur, Nature 2001
Modularity in neural circuitsre-routing experiments show that auditory cortex can process visual inputs
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The big idea:
Modularity• permits diverse outcomes from recombination of structural/functional units• allows continuous expansion of modular structures by regulation of module number• may permit new inputs to “plug in” to existing structures