Influence of Connectivity on Activity Levels

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Influence of Connectivity on Activity Levels

  1. 1. Influence of Connectivity on ActivityLevels in Patterned Neuronal Networks Sankaraleengam Alagapan Wheeler Lab J Crayton Pruitt Family Department of Biomedical Engineering
  2. 2. Brain on a Chip• Confluence of Technologies – In vitro neural culture, Microelectrode Arrays (MEAs), Substrate MEA Dissociated Neuronal Culture Modification, Microfluidic Devices• Simplified small scale model of brain PDL –PLL Pattern Microtunnel Device• Useful in drug screening, in vitro models of pathologies, basic neuroscience Extracellular recordings from MEAIntroduction 2
  3. 3. Brain on a Chip• Patterning Patterned Network – 4 Connect Control the structure of the network – amount of Patterned Network – 8 Connect convergence and divergence• Microtunnel devices Control the direction of information flow- create sub- networks where one drives the other• Understand the influence of structure on network function Microtunnel device Pictures by Eric and KuckuIntroduction 3
  4. 4. Connectivity in Neuronal Networks• Structural Connectivity – Anatomical Connections - Studied using staining, tracing etc• Functional Connectivity – Statistical measure of temporal correlations in activity – “Things that are wired together fire together” – E.g. – Correlation, Coherence, Mutual Information• Effective Connectivity – Gives an idea of which region of the network drives and which region is being driven – Combination of both structure and function – E.g. Transfer Entropy, Granger CausalityBackground 4
  5. 5. Connectivity and Function• Structure plays an important role in enabling a particular function in vivo. E.g., Cerebellum• Small world architecture develops naturally in dissociated cultures and this architecture plays a role in the self-sustained activity patterns observed in such cultures (Srinivas et al. 2007)Background 5
  6. 6. Connectivity and Activity Level• Which network is more active? i.e., which network will have higher average firing rate? Homeostatic Plasticity = More interconnections – Degree of Fewer interconnections – Degree of Connectivity is high Connectivity is low IntuitionHypothesis 6
  7. 7. Previous ResultHypothesis 7
  8. 8. Hypothesis Activity level in neuronal networks is governed by the overall strength of connectivity in the networkHypothesis 8
  9. 9. Specific Aims• Obtain an optimal measure of strength connectivity by comparing different measures on data from living networks• Study the relation between connectivity strength and the degree of convergence in the network.• Study the effect of stimulation on connectivity strengths and influence of degree of convergence on this effectAims 9
  10. 10. Specific Aims• Obtain an optimal measure of strength connectivity by comparing different measures on data from living networks• Study the relation between connectivity strength and the degree of convergence in the network.• Study the effect of stimulation on connectivity strengths and influence of degree of convergence on this effectAims 10
  11. 11. Measures of ConnectivityRequirements for an Optimal Measure:• Reveal the underlying structure as clearly as possible – Should measure the strength of connection between two neurons/nodes in both directions – Should eliminate the effects of other neurons/nodes as much as possibleCross CorrelogramJoint EntropyGranger CausalityBackground 11
  12. 12. Measures of ConnectivityCross Correlogram:• Measures/shows how the spikes of one neuron is distributed in time with respect to another.• Peaks  measure of the strength of connection• Delay corresponding to peaks  Idea of direction of information flowBackground 12
  13. 13. Measures of ConnectivityJoint Entropy:Entropy measure of the cross inter-spike intervals (cISI)between two spike trains X,Y n JE ( X , Y ) = −∑ p (cISI k ).log 2 ( p (cISI k )) k =1 p(cISIk) is the estimated probability of cISIkBackground 13
  14. 14. Measures of ConnectivityGranger Causality:• Suppose X and Y are 2 time series modeled as autoregressive processes, Y G-causes X if the including past of Y in modeling X decreases the variability of residuals in the model and vice versa.• The amount by which the variability is reduced gives a measure of strength and direction is revealed in the relative strengths• Conditional Granger Causality: Same idea as Granger, with both X and Y conditioned on another variable Z which might influence the two time seriesBackground 14
  15. 15. Measures of Connectivity• Garofalo et al (2009) compared the performance of Crosscorrelogram(CC), Mutual Information (MI), Joint Entropy(JE) and Transfer Entropy(TE) in simulated networks – Showed TE performed better than the other measures – MI had the worst performance• Barnett et al (2009) proved mathematically that TE and Granger Causality are the same measure for Gaussian ProcessesBackground 15
  16. 16. Aim 1 Experiment 1Line Pattern A B CWhy line patterns?• A unique structure which can constrain neurons in such a way that strength of AB > strength of AC more oftenResearch Design 16
  17. 17. Aim 1 Experiment 1• Construct line patterned networks• Record spontaneous activity at ~DIV 21• Measure connectivity strengths• Check consistency among measuresValidation• Stimulate spontaneously active nodes and observe evoked responses from other active nodes• If response is evoked consistently from other nodes, the stimulated node is connected with these nodesResearch Design 17
  18. 18. Patterned Line Networks 1 2 3 4 5 DIV 3 6 • Patterned Networks with Line 2 Patterns 3 • Activity Recorded DIV 24 4 5 6 27 37 57 7 8 9 310 10Preliminary Results 18
  19. 19. Cross-Correlogram – Line Patterns CrossCorrelogram (Z-Scores) Ref: 57 Ref: 27 Weaker Connections Stronger Connections 17 27 37 47 57 67Preliminary Results 19
  20. 20. CG Causality – Line Patterns 0.5 Illustration 1 2 0.25 17 27 37 47 57 67Preliminary Results 20
  21. 21. Aim 1 Experiment 2• Alternate Approach: Use of two-welled microtunnel devices• Plating cells in wells with few days interval leads to axon growth through tunnels predominantly in one direction• Strength of A B > Strength of B  A i.e., Network A affects network B more than network B affecting network A• Electrodes under microtunnels capture axonal propagation of action potential and these act as a model of two interacting nodes and measures can Microwell B (Output Well) be tested in this model DIV 10 Microtunnels Microwell A (Input Well) DIV 20 Arrow indicates direction 100 µm of growth of axonsResearch Design 21
  22. 22. Microtunnel Data• Conditional Granger Causality and Cross Correlograms• Microtunnel Devices – Tunnel DataPreliminary Results 22
  23. 23. Microwell Data• When bin size = 1ms, interactions in microwell not evident (lesser causal values) Bin size 10 ms Bin size 1 ms TunnelsPreliminary Results 23
  24. 24. Microwell Data• When bin size = 10ms, interactions between wells have causal values higher than those within tunnels Tunnels Causal values from A B greater than BAPreliminary Results 24
  25. 25. Specific Aims• Obtain an optimal measure of strength connectivity by comparing different measures on data from living networks• Study the relation between connectivity strength and the degree of convergence in the network.• Study the effect of stimulation on connectivity strengths and influence of degree of connectivity on this effectAims 25
  26. 26. Convergence and Connectivity strength• Higher convergence  More pathways between nodes  More possibility for correlated activity  Higher connection strength Mean Connection Strength ∝ Convergence• Convergence controlled in patterned networks and connection strengths can be comparedResearch Design 26
  27. 27. Aim 2 Experiment• Construct patterned networks with different convergence 2,4,8 and random• Spontaneous and evoked activity from DIV 21• Compute mean connectivity strengths for each network using the measures• Test for statistically significant difference between connectivity strengths of different patterns• Compute mean firing rate for each network• Test for Connectivity strength = k x ConvergenceResearch Design 27
  28. 28. Specific Aims• Obtain an optimal measure of strength connectivity by comparing different measures on data from living networks• Study the relation between connectivity strength and the degree of convergence in the network.• Study the effect of stimulation on connectivity strengths and influence of degree of connectivity on this effectAims 28
  29. 29. Stimulation of cultured networks• Activity dependent plasticity in neurons: “Things that fire together, wire together” (Hebbian Theory)• Electrical stimulation analogous to external stimuli and has been used to induce LTP (High Frequency) and LTD (Low Frequency) in slices• Induce a change in plasticity (connection strength) in in vitro dissociated networks through stimulationBackground 29
  30. 30. Stimulation induced change in firing rate • Jimbo et al. (1999) stimulated in vitro networks with a tetanus Potentiated pulse and found that there was a pathway specific long term change in the firing rate of neurons Depressed • Change in the post synaptic currents confirming a change in the plasticity of the synapsesBackground 30
  31. 31. Stimulation induced change in connectivity measures - GC• Cadotte et al (2008) repeated Jimbo’s experiment and used Granger Causality/ Conditional Granger Causality to measure the changes in the network• Confirmed Jimbo’s results as well showed change in Granger/Conditional Granger values before and after tetanusBackground 31
  32. 32. Aim 3 Experiment• Measure connectivity strengths in networks of Aim 2• Induce change in connection strength using tetanic stimulation• Measure connectivity strengths again and compare against pre-tetanic connectivity strength• Compare change in connectivity strengths in the different networksResearch Design 32
  33. 33. ReferencesCadotte AJ, Demarse TB, He P, Ding M. Causal Measures of Structure and Plasticity in Simulated and Living Neural Networks. PLOS One. 2008;3(10).Jimbo Y, Tateno T, Robinson HP. Simultaneous induction of pathway-specific potentiation and depression in networks of cortical neurons. Biophysical journal. 1999;76(2):670-8.Srinivas KV, Jain R, Saurav S, Sikdar SK. Small-world network topology of hippocampal neuronal network is lost, in an in vitro glutamate injury model of epilepsy. The European journal of neuroscience. 2007;25(11):3276-86.Garofalo M, Nieus T, Massobrio P, Martinoia S. Evaluation of the performance of information theory-based methods and cross-correlation to estimate the functional connectivity in cortical networks. PloS one. 2009;4(8):e6482.Perkel DH, Gerstein GL, Moore GP. Neuronal spike trains and stochastic point processes. II. Simultaneous spike trains. Biophysical journal. 1967;7(4):419-40.Dworak B, Varghese K, Pan L, Brewer G, Wheeler BC. Creating Unidirectional Neural Networks on a Chip. In: Proceedings of MEA2010. Reutlingen, Germany; 2010:320-21.References 33
  34. 34. Acknowledgement• Dr. Bruce Wheeler• Dr. Thomas DeMarse• Eric, Pan, KuckuAcknowledgement 34

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