Robustness

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

competition

degeneracy

modularity

feedback

Elements of robustness:

Feedback

FeedbackController

~100 msretinalinputs

GoalFeedforward

Controller Eyeball+ eyemovement

SensedVariable

feedback

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

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

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

this is distinct from

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

Swensen & Bean, J. Neurosci. 2005

cell 1 cell 2

Neuron-level degeneracy:robustness of bursting in cerebellar Purkinje cells

acutely dissociated Purkinje somata

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

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

Swensen & Bean, J. Neurosci. 2005

An acute decrease in Na+ conductance produces a compensatory increase in voltage-dependent and Ca2+–dependent K+ conductances.

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

Swensen & Bean, J. Neurosci. 2005

A chronic decrease in Na+ conductance produces a compensatory increase in Ca2+ conductance.

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

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

Mapping the state space of neuron-level degeneracy:robustness of bursting in stomatogastric ganglion neurons

model stomatogastric ganglion neuron

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).

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

Prinz et al. Nature Neuroscience 2004

Circuit-level degeneracy:similar network activity from disparate cellular and synaptic parameters

model neurons of pyloric network

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

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.

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

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 circuitsa putative example: “cerebellar-like” circuits

Bell, Han, & Sawtell, Annu. Rev. Neurosci. 2008Oertel & Young, Trends Neurosci. 2004Roberts & Portfors, Biol. Cybern. 2008

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

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

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

Modularity in neural circuitsa putative example: a visual cortical hypercolumn

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

Rakic Nature Neuroscience 2009

Modularity in evolutionRadial unit lineage model of cortical neurogenesis

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

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