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Introduction• Patterned networks interfaced with planar multi electrode arrays (MEAs) [1] provide a living model system to study the effect a network’s structure on its function [2],[3].• We varied the convergence of structural connections (i.e. number of nearest connecting neighbor nodes) to study the influence of convergence on functional connectivity and fidelity of information transmission.• We used Conditional Granger Causality (CGC) [4],[5] as a measure of functional connectivity and Victor – Purpura’s (VP) spike train similarity metric [6] as a measure of fidelity of information propagation.

Results

Methods

Acknowledgement

1. Wheeler, B., Corey, J., Brewer, G. & Branch, D. (1999). Microcontact printing for precise control of nerve cell growth in culture. Journal of biomechanical engineering.

2. Boehler, M. D., Leondopulos, S. S., Wheeler, B. C. & Brewer, G. J. (2011). Hippocampal networks on reliable patterned substrates. Journal of Neuroscience Methods. Elsevier.

3. Marconi, E., Nieus, T., Maccione, A., Valente, P., Simi, A., Messa, M., Dante, S., et al. (2012). Emergent Functional Properties of Neuronal Networks with Controlled Topology. PloS one. Public Library of Science

4. Ding, M., Chen, Y. & Bressler, S. L. (2006). Granger causality: basic theory and application to neuroscience. Handbook of time series analysis. Wiley Online Library.

5. Seth, A. K. (2010). A MATLAB toolbox for Granger causal connectivity analysis. Journal of neuroscience methods. Elsevier.

6. Victor, J. D. & Purpura, K. P. (1996). Nature and precision of temporal coding in visual cortex: a metric-space analysis. Journal of Neurophysiology. Am Physiological Soc.

ResultsConclusion

References

This work was partly supported by NIH grant NS052233

SPATIAL DISTRIBUTION OF FUNCTIONAL CONNECTION STRENGTHS IN PATTERNED NETWORKS OF VARYING CONVERGENCESankar Alagapan1, Eric W. Franca1, Liangbin Pan1, Thomas B. DeMarse1, Gregory J. Brewer2 and Bruce C. Wheeler1 1 J. Crayton Pruitt Family Department of Biomedical Engineering, University of Florida, Gainesville, FL2 Department of Biomedical Engineering, University of California, Irvine, CA

• Poly-d-lysine (PDL) was patterned onto each microelectrode array’s (MEA) surface (60 electrodes in 6 x 10 arrangement, 30µm diameter and 500 µm inter electrode distance) and treated with 3-glycidoxypropyl-trimethoxysilane (3-GPS) by microcontact printing.• E18 rat cortical neurons were dissociated and plated at a density of 700 cells/mm2

• Patterns consisted of circular nodes (50µm diameter) connected to neighboring nodes by straight lines (20µm width). Convergence was varied by varying number of nearest neighboring nodes each node was connected to and the patterns are referred according to this number as shown in Fig 1 (2 Connect – 2 nearest neighbors along horizontal axis, 4 Connect – 4 nearest neighbors in both horizontal and vertical axis and 8 Connect – 8 nearest neighbors as in 4 connect but including diagonal). • CGC was calculated from smoothed spike trains of the spontaneous activity recorded from these networks and VP dissimilarity metric (Dv) was calculated from the spike trains of spontaneous activity and the cost parameter varied to account for multiple lengths of time segments.

Slope = -0.0449 Slope = -0.0207

Slope = -0.0205 Slope = -0.0064

Distance in µm

Mea

n N

orm

aliz

ed C

GC

Val

ues

2 Connect 4 Connect

8 Connect Random

Fig 3. CGC strengths vs. distance. •The strength of any functional connectivity decreased with distance from each node. •2 Connect Networks showed a steeper decline in mean CGC strengths compared to 4 and 8 Connect Networks which in turn were steeper than Random Networks.

Fig 2. Overall Distribution of CGC Strengths. •We hypothesized that higher convergence may lead to higher functional connection strengths between nodes in the network. •However, the distribution of CGC strengths among patterned networks were not significantly different. (Random networks were significantly different than patterned)

Effect of Convergence on Functional Connection Strengths

Effect of Convergence on Fidelity of Information Propagation

• Fidelity of information was high at longer time windows suggesting rate based code during propagation.

• Convergence did affect the fidelity of information propagation but depended more upon path length (number of intermediate connections) than physical distance.

• Convergence does not affect the functional connection strengths between nodes in a network.

• Functional connectivity is affected by physical distance. This effect depends on the levels of convergence. Higher the convergence, lesser the effect distance had on connection strength.

Fig 4 A. Fidelity of Information Propagation vs. Convergence

•Higher convergence should lead to better fidelity of information propagation between nodes in the network. Spike trains increased in similarity (decreased dissimilarity) increasing convergence but were most similar in random cultures. •Dissimilarity decreased with longer time windows supporting a strong role for a rate modulation as neural code during transmission. •Random networks had the least dissimilarity (highest fidelity) in transmission and 2 Connect networks had high dissimilarity (low fidelity)

Fig 4 B. Fidelity of Information propagation vs. Distance

•No significant trend was observed in the fidelity of information propagation with respect to distance between nodes

Fig 5. Fidelity of information propagation vs. Path Length

•Fidelity of propagating spike trains was affected by the number of mediating nodes (path length)•The effect of convergence is pronounced at shorter path lengths (path lengths of 1 and 2).•At longer path lengths effect was not significant

A B

Fig 1.Three different convergence patterns based on a serial chain (2 connection), city-block (4 connection), and 8 connection network topologies.

Dissimilarity

Electrode

Neurons (Cell Body Cluster)

4 Connect

2 Connect

8 Connect

Axonal Bundles