Statistical methods for understanding complex biophysical neural - - PowerPoint PPT Presentation

Statistical methods for understanding complex biophysical neural data

Liam Paninski

Department of Statistics and Center for Theoretical Neuroscience Columbia University http://www.stat.columbia.edu/∼liam liam@stat.columbia.edu June 27, 2007

Back to detailed models

Can we recover detailed biophysical properties?

• Active: membrane channel densities
• Passive: axial resistances, “leakiness” of membranes
• Dynamic: spatiotemporal synaptic input

Spatiotemporal voltage recordings

Djurisic et al, 2004

Conductance-based models

Key point: if we observe full Vi(t) + cell geometry, channel kinetics known + current noise is log-concave, then loglikelihood of unknown parameters is concave. Gaussian noise = ⇒ standard nonnegative regression (albeit high-d).

Estimating channel densities from V (t)

(Huys et al., 2006)

Estimating channel densities from V (t)

−60 −40 −20 V 20 40 60 80 100 −100 −50 50 dV/dt summed currents Time [ms] NaHH KHH Leak NaM KM NaS KAS 50 100 conductance [mS/cm2] True Inferred

Measuring uncertainty in channel densities

Estimating non-homogeneous channel densities and axial resistances from spatiotemporal voltage recordings

A big cell

A big cell

Estimating synaptic inputs given V (t)

Estimating synaptic inputs given V (t)

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 with regularisation Time [s] 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 23 −57 −52 −47 12 without regularisation Inh spikes | Voltage | Exc spikes [mS/cm2] [mV] [mS/cm2] Time [s]

A B

Estimating synaptic inputs given V (t)

500 1000 1500 2000 1 −70 mV −25 mV 20 mV 1

Synaptic conductances Time [ms] Inh spikes | Voltage [mV] | Exc spikes

A B C

HHNa HHK Leak MNa MK SNa SKA SKDR 20 40 60 80 100 120

max conductance [mS/cm2] Channel conductances

True parameters (spikes and conductances) Data (voltage trace) Inferred (MAP) spikes Inferred (ML) channel densities 1280 1300 1320 1340 1360 1380 1400 1 −70 mV −25 mV 20 mV 1 Time [ms]

Estimating stimulus effects

dV/dt = Ichannel + k · x(t) + σNt

−2 2 s1(t) −60 −40 −20 20 V 20 40 60 80 100 −50 50 100 150 dV/dt summed currents Time [ms]

C

NaHH KHH Leak NaM KM NaS KAS 20 40 60 80 100 120 conductance [mS/cm2] True Inferred 1 2 3 4 5 6 7 8 9 10 1.5 2 2.5 3 3.5 4 filter

A B D E

True Inferred

Dealing with incomplete observations: Kalman filter

−60.5 −60 −59.5 V (mV) −60.6 −60.4 −60.2 −60 −59.8 −59.6 V (mV) 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.1 0.2 t (sec) est std (mV) E[V(t) | Y(0:t)] E[V(t) | Y(1:T)]

Spatiotemporal filtering

compartment 5 10 15 compartment 5 10 15 t (sec) compartment 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 5 10 15

Estimating parameters in the Kalman setting

Simulated data: five-compartment model V (t), noisy observations

−40 −20 20 40 Voltage [mV] 1000 2000 Time [ms]

Estimating parameters in the Kalman setting

10 20 30 5 10 15 20 25 Leak 50 100 150 10 15 intercompartmental conductance 10 20 30 1 1.5 2 EM iteration R 10 20 30 10 20 30 40 50 EM iteration Observation noise

Smoothing given nonlinear dynamics

— via particle filtering (Huys and Paninski, 2006)

Subsampling and noise

EM estimation via particle filter

[mS/cm2] K EM iteration Voltage [mV] R 50 100 [mS/cm2] Na 20 40 60 2 4 EM iteration [mS/cm2] Leak

Particle filter to infer calcium from voltage

• bservations

Inferring spike rates from calcium observations

(play ohki movie here)

Collaborators

Theory and numerical methods — J. Kulkarni, G. Szirtes, G. Fudenberg, K. Rahnama, Columbia — J. Pillow, E. Simoncelli, NYU — S. Shoham, Princeton — A. Haith, C. Williams, Edinburgh — M. Ahrens, Q. Huys, Gatsby — J. Lewi, R. Butera, Georgia Tech Motor cortex physiology — M. Fellows, J. Donoghue, Brown — N. Hatsopoulos, U. Chicago — B. Townsend, R. Lemon, U.C. London Retinal physiology — V. Uzzell, J. Shlens, E.J. Chichilnisky, UCSD Cortical in vitro physiology — B. Lau and A. Reyes, NYU

References

Huys, Q., Ahrens, M., and Paninski, L. (2006). Efficient estimation of detailed single-neuron models. Journal

• f Neurophysiology, 96:872–890.

Huys, Q. and Paninski, L. (2006). Model-based optimal interpolation and filtering for noisy, intermittent biophysical recordings. CNS*06 Meeting, Edinburgh.