Skewed firing rate distribution and fluctuation-driven regime

Transcription

1 Skewed firing rate distribution and fluctuation-driven regime Rune W. Berg University of Copenhagen MathStatNeuro Université Nice Sophia Antipolis, September 2015

2 Spinal Cord Advantages: Purpose: Function is well-defined Morphology: Primarily a one-dimensional Blueprint: Phylogenetically old structure Complete: Contains an entire functional circuitry

3 Central Pattern Generators Chewing, Swimming, scratching, breathing and walking

4 Central Pattern Generators Chewing, Swimming, scratching, breathing and walking Sensory feedback not necessary, but strongly enhances movement

5 Decerebrate cat: Whelan, Prog. Neurobiol 1996 MacKay-Lyons, Phys. Therap. 2002

6 Fictive locomotion by adding neuro-chemicals a Swimming CPG (lamprey) Intact animal b Walking CPG (mouse, cat) Intact animal L-5 R-Tr R-5 R-25 R-46 L-Tr R-VI L-VI 0.1 s 0.2 s Isolated spinal cord R-6 R-26 Isolated spinal cord R-L2 R-L5 L-L2 L-L5 R-6 R-L2 R-26 R-46 L-L2 1 s R-L5 2 s Goulding, Nat Rev Neurosci 2009

7 Model for motor pattern generation: Turtle scratch reflex Robertson & Stein, J. Physiol Rune W. Berg :: INF University of Copenhagen

8 Sensory-specific spinal scratching Turtle is upside-down performing hindlimb scratching

9

10 Firing rate (Hz) Subthreshold High noise level Intermediate noise level Low noise level Superthreshold Current (I)

11 Firing rate (Hz) Subthreshold High noise level Intermediate noise level Low noise level Superthreshold Current (I) Vm Subtreshold 500 ms 50 ms

12 Firing rate (Hz) Subthreshold High noise level Intermediate noise level Low noise level Superthreshold Vm Subtreshold Current (I) Vm Superthreshold 500 ms 1 sec 50 ms 20 ms

13 Two regimes: Fluctuation-driven Mean-driven Gerstner, Kistler, Naud and Paninski : Neuronal dynamics

14 Two regimes: Fluctuation-driven Mean-driven Definition Hallmarks Hallmarks Causes Gerstner, Kistler, Naud and Paninski Neuronal dynamics

15 Two regimes: Fluctuation-driven Mean-driven Definition Hallmarks Low rates High rates Hallmarks Causes Gerstner, Kistler, Naud and Paninski Neuronal dynamics

16 Two regimes: Fluctuation-driven Mean-driven Definition Hallmarks Low rates High rates Hallmarks Irregular Regular Causes Gerstner, Kistler, Naud and Paninski Neuronal dynamics

17 Two regimes: Fluctuation-driven Mean-driven Definition Hallmarks Low rates High rates Hallmarks Irregular Regular Causes Balanced E/I Anything Softky and Koch, J Neurosci 1993 Gerstner, Kistler, Naud and Paninski Neuronal dynamics

18 Shape of rate distribution in the two regimes?

19 Shape of rate distribution is skewed The Journal of Neuroscience, November 9, (45): Behavioral/Systems/Cognitive On the Distribution of Firing Rates in Networks of Cortical Neurons Alex Roxin, 1,3 Nicolas Brunel, 2 David Hansel, 2,4 Gianluigi Mongillo, 2 and Carl van Vreeswijk 2 1 Center for Theoretical Neuroscience, Columbia University, New York, New York 10032, 2 Centre National de la Recherche Scientifique, Unité Mixte de Recherche 8119, Université Paris Descartes, Paris, France, 3 Insitut d Investigacions Biomèdiques August Pi i Sunyer, Barcelona 08036, Spain, and 4 Interdisciplinary Center for Neural Computation, Hebrew University, Jerusalem, Israel We argue that skewed rate distributions are a signature of the nonlinearity of the in vivo F-I-curve

20 Transformation of input-to-output Distribution Distribution Spike Rate Input Current [na] Roxin et al, J Neurosci 2011

21 Transformation of input-to-output Distribution Distribution Spike Rate Distribution Distribution Spike Rate Input Current [na] Input Current [na] Roxin et al, J Neurosci 2011

22 Two regimes: Fluctuation-driven Mean-driven Definition Hallmarks Low rates High rates Hallmarks Irregular Regular Hallmarks Skewed Symmetric Causes Balanced E/I Anything Lagzi and Rotter, Front Comp Neurosci 2014 Buzsaki and Mizuseki, Nat Rev Neurosci 2014

23

24 Recording Population activity

25 Peter Petersen Recording Population activity

26 Berg64-Probe by Neuronexus 8 shanks with 8 leads = 64 ch

27 Electrophysiology: Multichannel recording A Silicon probes 64 channels Ventral Dorsal Spinal cord D10 D9 D8 Caudal Rostral B C

28 Experimental Setup

29 Experimental Setup

30 Histology DiD-labeling and Nissle ChAT DiD Nissl Transverse section Sagittal section Petersen and Berg, in preparation

31

32 Spike sorting Different units on same probe

33 Onset Right Pocket scracth Left Hip extensor Right Knee extensor Right Hip extensor Right dd8 Right Hip Flexor Inter-neuron Vm Rastergram of spinal neurons 1 sec Petersen and Berg, in preparation Rune W. Berg :: INF University of Copenhagen

34 Petersen and Berg, in preparation

35 Petersen and Berg, in preparation

36 Population Distribution of Spike Rates Distribution Spike Rate [Hz] Petersen and Berg, in preparation

37 Population Distribution of Spike Rates Distribution Distribution Spike Rate [Hz] LOG (Spike Rate [Hz]) Petersen and Berg, in preparation

38 Single cell rate distribution Distribution Linear Spike frequency [Hz] Distribution Log LOG (Spike frequency [Hz])

39 Single cell rate distribution Distribution Linear Spike frequency [Hz] Distribution Log LOG (Spike frequency [Hz])

40 Single cell rate distribution Distribution Linear Spike frequency [Hz] Distribution Log LOG (Spike frequency [Hz])

41 Time dependence of distribution?

42 Petersen and Berg, in preparation

43 Time-dependent distribution 2 Distribution Log( Spike Rate ) Normal fit Time 2 sec Petersen and Berg, in preparation Rune W. Berg :: INF University of Copenhagen

44 Time-dependent lognormal distribution Skewness Mean Frequency Time Time Petersen and Berg, in preparation

45 Time-dependent lognormal distribution Skewness Mean Frequency Time Standard Deviation Time Mean frequency Petersen and Berg, in preparation

46 Irregularity? Petersen and Berg, in preparation

47 Irregularity measure Holt et al, J Neurophysiol 1996

48 Irregularity measure Holt et al, J Neurophysiol 1996

49 Driving a cell across regimes B Spike Rate A -1.0 na C +1.7 na 0 na Current 20 mv C 0.2 Mean D -1.0 na Irregularity (CV2) Irregularity (CV2) 0.1 Distribution Irregularity CV2 500 ms % R = ** Injected Current [na] Petersen and Berg, in preparation

50 Samples: Fluctuation- and mean-driven neurons Petersen and Berg, in preparation

51 Samples: Fluctuation- and mean-driven neurons Cumulative time spent % FD MD 35 % Distance from threshold [mv] Neurons [%] Neurons % 96 % 84 % Least time below threshold Petersen and Berg, in preparation

52 Irregularity for the population over time Irregular Regular Young et al, J Neurophysiol 1988 Prut and Perlmutter, J Neurosci 2003

53 40 Number of cells Time in irregular regime for each cell (%) Petersen and Berg, in preparation

54 40 Number of cells Percentage of cells Time in irregular regime for each cell (%) TIR50 = 56% Time in irregular regime [%] Petersen and Berg, in preparation

55 40 Number of cells Time in irregular regime for each cell (%) Percentage of cells TIR50 = 56% Time in irregular regime [%] Animals: Petersen and Berg, in preparation

56

57 Conclusions Skewed, log-normal firing rate distribution in some neurons some of the time Two regimes: fluctuation- and mean driven TIR50 ~ 50%, i.e. half of cells are in irregular regime half of the time.

58 Peter Petersen Alex Willumsen Kristian Reveles Jensen Henrik Linden Mikkel Vestergaard Marija Radosevic Jonas Villadsen Andrea Dietz Funding: Danish Research council Novo Nordisk Foundation