8/8/2019 Reliable Brains From Unreliable Neurons (Poster)

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Reliable Brains from Unreliable Neurons:The Search for Synfire Chains in the Brain

DJ Strouse, Peiran Gao, Kwabena BoahenStanford Amgen Scholars Program

Abstract

Synfire Chains Increase Reliability

Globally Connected Network

Conclusions

The transmission and processing of information with strings of single neurons facetwo main obstacles. One, single neuron responses have a random element and may differupon repeated presentation of the same input. Two, neurons die throughout the life of anorganism and are generally not replaced. Thus, we cannot expect the brain to reliablytransmit or process information using strings of single neurons. One possible way for thebrain to increase reliability is to use groups of neurons arranged in fully-connected, feed-forward networks which operate most efficiently when inputs are applied synchronously,hence the nickname “synfire chains” (Abeles 1991). Synfire chains can propagate signalsreliably from one group of neurons to the next due to the highly dense and redundantconnectivity between groups. While these structures seem to be useful in theory, its not yetclear whether they occur in real brains.

We studied the likelihood of occurrence and shape of synfire chains in neuralnetwork models. We considered both globally and locally connected networks, the lattermotivated by data from layers 2/3 of cat visual cortex (Hellwig 2000). Assuming randomconnections and no learning rules, we obtained analytic expressions for the most typicalsynfire chains under various conditions. In globally connected networks, we discovered theexistence of a maximum width (above which chains were highly unlikely to occur) and a

strong preference for nonuniform widths (producing chains of oscillating widths). Inlocally connected networks, we discovered that the most common synfire chains consist of circular groups of a characteristic size and radius centered at the same point. Whereas onecould imagine that, in locally connected networks, consecutive groups in chains might bespatially staggered and eventually span the network, this is not the case and typical chainsare highly confined in space. We conclude that the chains in locally connected networks aremore useful for local processing than long-range signal propagation whereas the chains inglobally connected networks may be useful, but not optimal, for long-range signalpropagation. Future studies with more realistic network connectivities and learning rulesmay discover conditions more conducive to producing chains optimized for long-rangesignal propagation.

• “Naturally occurring” synfire chains inLCN are more useful for local processingthan long-range propagation• “Naturally occurring” chains in GCNmay be useful, but not optimal, for long-range propagation• Chains optimal for long-rangepropagation likely require learning orhighly structured connectivities

Goal : Predict the likelihood and shape of synfire chains i n the brainMethod : Analytically explore various biologically plausible neural

network models and derive the probability of occurrenceof various types of synfire chains

Local connections

ConnectionProbability

x-distance

y-distance

Future Work• More realistic networks

• Multiple layers• Realistic connectivity between layers

• The role of learning• With random inputs• With structured inputs

• Compare to biological data (Ikegaya2004)

AcknowledgementsReferences • Abeles M. (1991) Corticonics: Neural Circuitsof the Cerebral Cortex. Cambridge UniversityPress, New-York.• Hellwig B (2000) A quantitative analysis of thelocal connectivity between pyramidal neurons inlayers 2/3 of the rat visual cortex. Biol Cybern82: 111 – 121• Ikegaya Y, Aaron G, Cossart R, et al. Synfirechains and cortical songs: temporal modules of cortical activity. Science (New York, N.Y.) .2004;304(5670):559-64.

Thanks to:• Kwabena Boahen• Peiran Gao• Matt Goldstein• Tenea Nelson & the SSRP staff • Nick Steinmetz & Samir Menon• The grad students in the Clark Center

Locally Connected Network

Synfire Chains are Robust Against Single Neuron Failures

No-Repeat Chains Have a Most Likely Length

Two sources of neural unreliability :1. Neuron death2. Response variability

Two sources of neural reliability :1. Input strength2. Input synchrony

• N neurons• Connectionprobability p• Arbitrary spatialarrangement

ExpectedNumber of Chains

Chain Length

MostLikelyLength

MaxLength

• 1000 neurons• Connection probability .15• Chain width 3

Model

Model

2D circular sheetof neurons

Choose first group Find connection probabilities Identify likely second group

Iterate equations to find mostlikely shape of a synfire chain(sequence of circular groups of a characteristic size and radiuscentered at the same point)

Expected size & radius of second group

Nonuniform Chains are More Likely Than Uniform Chains

Left plot:• 50,000 neurons total• Connection probability .1• 10 neurons in chain link

Right plot:• 50,000 neurons total• Connection probability .1• 18 neurons in chain link

ExpectedNumber of Length-2Chains

Number of Neurons in First Group Number of Neurons in First Group

Maximum Width for Long Chains

ExpectedNumber of Chains

Chain Length

Left plot:• 10,000 neurons• Connection probability .15• Chain width 4

Right plot:• Same network • Chain width 5

Chain Length

Chain Length