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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

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slide1

Robustness

the ability of a system to perform consistently under a variety of conditions

slide2

Elements of robustness:

feedback

degeneracy

competition

modularity

a classic example of feedback in neural circuits error correction during smooth pursuit
A classic example of feedback in neural circuits: error correction during smooth pursuit

feedback

retinal

inputs

Feedback

Controller

~100 ms

Sensed

Variable

Feedforward

Controller

eye

movement

Goal

Eyeball

+

slide5

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
slide7

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.

slide8

this is distinct from

redundancy – the condition of having multiple copies of the same mechanism

degeneracy – the condition of having multiple distinct mechanisms for reaching the same outcome

slide9

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 ←

CGU ↔ AGG

→ UGG

Arg

Arg

His

Trp

Evolvability

is the capacity to adapt by natural selection

Degeneracy can increase evolvability by distributing system outcomes near phenotypic transition boundaries.

slide10

Neuron-level degeneracy:

robustness of bursting in cerebellar Purkinje cells

cell 1

cell 2

acutely dissociated Purkinje somata

Swensen & Bean, J. Neurosci. 2005

slide11

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

slide12

Neuron-level degeneracy:

robustness of bursting in cerebellar Purkinje cells

Swensen & Bean, J. Neurosci. 2005

slide13

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

slide14

Neuron-level degeneracy:

robustness of bursting in cerebellar Purkinje cells

Swensen & Bean, J. Neurosci. 2005

slide15

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

slide16

Degeneracy and feedback

system

variables

output

input

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
slide17

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

slide18

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

slide19

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).

slide20

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

slide21

Circuit-level degeneracy:

similar network activity from disparate cellular and synaptic parameters

model neurons of pyloric network

Prinz et al. Nature Neuroscience 2004

slide22

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.

slide24

Another classic example of competition in neural circuits:

developing ocular dominance columns

Luo & O’Leary, Ann. Rev. Neurosci. 2005

slide25

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

slide26

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.

Song & Abbott, Nat. Neurosci. 1999

Abbott, Zoology 2003

model

slide27

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.
slide29

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.

slide30

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

slide31

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

slide32

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

slide33

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 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. 2008

Oertel & Young, Trends Neurosci. 2004

Roberts & Portfors, Biol. Cybern. 2008

slide34

Modularity in neural circuits

a putative example: a visual cortical hypercolumn

Horton & Adams, Philos Trans R Soc Lond B Biol Sci. 2005

slide35

Modularity in evolution

Radial unit lineage model of cortical neurogenesis

Rakic Nature Neuroscience 2009

slide36

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

slide37

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