Robustness

1. Robustness the ability of a system to perform consistently under a variety of conditions

2. Elements of robustness: feedback degeneracy competition modularity

3. Feedback

4. 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 +

5. 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

6. Degeneracy

7. 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.

8. 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

9. 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.

10. Neuron-level degeneracy: robustness of bursting in cerebellar Purkinje cells cell 1 cell 2 acutely dissociated Purkinje somata Swensen & Bean, J. Neurosci. 2005

11. 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

12. Neuron-level degeneracy: robustness of bursting in cerebellar Purkinje cells Swensen & Bean, J. Neurosci. 2005

13. 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

14. Neuron-level degeneracy: robustness of bursting in cerebellar Purkinje cells Swensen & Bean, J. Neurosci. 2005

15. 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

16. 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

17. 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

18. 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

19. 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).

20. 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

21. Circuit-level degeneracy: similar network activity from disparate cellular and synaptic parameters model neurons of pyloric network Prinz et al. Nature Neuroscience 2004

22. 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.

23. Competition

24. Another classic example of competition in neural circuits: developing ocular dominance columns Luo & O’Leary, Ann. Rev. Neurosci. 2005

25. 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

26. 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

27. 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.

28. Modularity

29. 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.

30. 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

31. 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

32. 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

33. 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

34. Modularity in neural circuits a putative example: a visual cortical hypercolumn Horton & Adams, Philos Trans R Soc Lond B Biol Sci. 2005

35. Modularity in evolution Radial unit lineage model of cortical neurogenesis Rakic Nature Neuroscience 2009

36. 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

37. 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