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

2. competition degeneracy modularity feedback Elements of robustness:

3. Feedback

4. Controller ~100 ms retinal inputs Goal Feedforward Controller Eyeball + eye movement Sensed Variable feedback A classic example of feedback in neural circuits: error correction during smooth pursuit

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. 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

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 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 → UGG Trp

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

11. 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

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 Swensen & Bean, J. Neurosci. 2005 An acute decrease in Na + conductance produces a compensatory increase in voltage-dependent and Ca 2+ –dependent K + conductances.

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 Swensen & Bean, J. Neurosci. 2005 A chronic decrease in Na + conductance produces a compensatory increase in Ca 2+ conductance.

16. Degeneracy and feedback input output system variables set point homeostat In this example, membrane potential is the robust system output a fast feedback loop is created by voltage-dependent and Ca 2+ -dependent K + channels a slow feedback loop regulates Ca 2+ conductances many combinations of conductances (i.e., “system variables”) can produce similar output

17. 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

18. 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

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. 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

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

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 Song & Abbott, Nat. Neurosci. 1999 Abbott, Zoology 2003 pre leads postpre lags post This mechanism creates a competition between independent presynaptic neurons for control of the postsynaptic neuron’s spiking.

26. A mechanism for competitive synaptic interactions: spike-timing dependent plasticity Song & Abbott, Nat. Neurosci. 1999 Abbott, 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 Hzpresynaptic rate = 13 Hz 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. Bell, Han, & Sawtell, Annu. Rev. Neurosci. 2008 Oertel & Young, Trends Neurosci. 2004 Roberts & Portfors, Biol. Cybern. 2008 Modularity in neural circuits mammalian cerebellummammalian dorsal cochlear nucleusteleost cerebellum teleost medial octavolateral nucleusmormyrid electrosensory lobegymnotid electrosensory lobe “cerebellar-like” circuits in vertebrates

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

36. 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 Modularity in neural circuits re-routing experiments show that auditory cortex can process visual inputs

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