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
inputs
Sensed
Variable
Goal
~100 ms
Feedback
Controller
Feedforward
Controller
+
Eyeball
eye
movement
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
Degeneracy
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.
degeneracy – the condition of having multiple distinct mechanisms
for reaching the same outcome
this is distinct from
redundancy – the condition of having multiple copies of the same
mechanism
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
CAU ←
His
CGU ↔ AGG
Arg
Arg
→ UGG
Trp
Evolvability is the capacity to adapt by natural selection
Degeneracy can increase evolvability by distributing system
outcomes near phenotypic transition boundaries.
Neuron-level degeneracy:
robustness of bursting in cerebellar Purkinje cells
cell 1
acutely dissociated Purkinje somata
cell 2
Swensen & Bean, J. Neurosci. 2005
Neuron-level degeneracy:
robustness of bursting in cerebellar Purkinje cells
cell 1
cell 2
cell 3
cell 4
cell 5
cell 6
Swensen & Bean, J. Neurosci. 2005
Neuron-level degeneracy:
robustness of bursting in cerebellar Purkinje cells
Swensen & Bean, J. Neurosci. 2005
Neuron-level degeneracy:
robustness of bursting in cerebellar Purkinje cells
An acute decrease in Na+ conductance produces a compensatory increase in
voltage-dependent and Ca2+–dependent K+ conductances.
Swensen & Bean, J. Neurosci. 2005
Neuron-level degeneracy:
robustness of bursting in cerebellar Purkinje cells
Swensen & Bean, J. Neurosci. 2005
Neuron-level degeneracy:
robustness of bursting in cerebellar Purkinje cells
A chronic decrease in Na+ conductance produces a compensatory increase in Ca2+
conductance.
Swensen & Bean, J. Neurosci. 2005
Degeneracy and feedback
input
system
variables
output
homeostat
set point
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
Mapping the state space of neuron-level degeneracy:
robustness of bursting in stomatogastric ganglion neurons
model stomatogastric ganglion neuron
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
Goldman, Golowasch, Marder, & Abbott, J. Neurosci. 2001
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).
Circuit-level degeneracy:
robustness of patterns in the stomastogastric ganglion
the pyloric network
the pyloric rhythm
note: all synapses are inhibitory
lobster stomatogastric ganglion recording with sharp microelectrodes
Prinz et al. Nature 2004
Circuit-level degeneracy:
similar network activity from disparate cellular and synaptic parameters
model neurons of pyloric network
Prinz et al. Nature Neuroscience 2004
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.
Competition
Another classic example of competition in neural circuits:
developing ocular dominance columns
Luo & O’Leary, Ann. Rev. Neurosci. 2005
A mechanism for competitive synaptic interactions:
spike-timing dependent plasticity
pre leads post
pre lags post
This mechanism creates a competition between independent
presynaptic neurons for control of the postsynaptic neuron’s spiking.
Song & Abbott, Nat. Neurosci. 1999
Abbott, Zoology 2003
A mechanism for competitive synaptic interactions:
spike-timing dependent plasticity
presynaptic rate = 10 Hz
presynaptic rate = 13 Hz
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.
model
Song & Abbott, Nat. Neurosci. 1999
Abbott, Zoology 2003
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.
Modularity
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.
Modularity in neural circuits
a putative example: “cerebellar-like” circuits
Bell, Han, & Sawtell, Annu. Rev. Neurosci. 2008
Oertel & Young, Trends Neurosci. 2004
Roberts & Portfors, Biol. Cybern. 2008
Modularity in neural circuits
“cerebellar-like” circuits in vertebrates
mammalian cerebellum
teleost cerebellum
mammalian dorsal cochlear nucleus
teleost medial octavolateral nucleus
mormyrid electrosensory lobe
gymnotid electrosensory lobe
Bell, Han, & Sawtell, Annu. Rev. Neurosci. 2008
Oertel & Young, Trends Neurosci. 2004
Roberts & Portfors, Biol. Cybern. 2008
Modularity in neural circuits
a 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. 2008
Oertel & Young, Trends Neurosci. 2004
Roberts & Portfors, Biol. Cybern. 2008
Modularity in neural circuits
a 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 lowerlevel 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. 2008
Oertel & Young, Trends Neurosci. 2004
Roberts & Portfors, Biol. Cybern. 2008
Modularity in neural circuits
a putative example: a visual cortical hypercolumn
Horton & Adams, Philos Trans R Soc Lond B Biol Sci. 2005
Modularity in evolution
Radial unit lineage model of cortical neurogenesis
Rakic Nature Neuroscience 2009
Modularity in neural circuits
re-routing experiments show that auditory cortex can process visual inputs
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 2001
von Melchner, Pallas, & Sur, Nature 2001
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