Inverse solutions for localization of single cell currents based on extracellular measurements

Zoltán Somogyvári1, István Ulbert2, Péter Érdi1,3

1 KFKI Research Institute for Particle and Nuclear Physics of the Hungarian Academy of Sciences, Dept. Biophysics

2 Institute for Psychology of the Hungarian Academy of Sciences3 Center for Complex System Studies, Kalamazoo, Michigan, USA

The aim: To determine the membrane currents

on a single cell, based on extracellular data!

The experimental setup: A 16 channel, extracellular (EC) electrode system is chronically implanted into cats primary auditory cortex: A1.

The high-pass filtered raw data

The data we will work on: Mean spatio-temporal patterns of EC potential is obtained

for each putative single neuron.

StSpike clustering with Spike-o-matic.

Cluster averages of 13 putative single cells.

The EC potential is obtained from the transmembrane current source density via Poisson-equation, but the solution of the Poisson-inverse problem is generally non-unique. Infinitely many source distribution can generate the same measured EC potential distribution.

The EC potential Ф=TJ, where J is

the CSD and T is the lead-field matrix.The affine subspace of the possible

solutions: J(x)=T+Ф+ker(T)x

The problem

The solution in theoryFrom the multitude J(x) the proper solution can be chosen by applying a priory assumptions. In case of a single spike the proper assumptions are:

1, Each cell is a linesource, parallel to the electrode.

2, The spatial CSD distribution has a sharp negative peak (sink) at the soma, superposed onto a smooth positive (source) background. This assumption is shown to be valid during the first negative deflections of the EC spike. (Somogyvári et al. 2005)

Requirement 1 can be incorporated into T. To comply the second requirement, the source with the sharpest peak should be chosen by founding the maximal projection of the theoretically sharpest distributions E

i and the

hyperplane T+Ф⨯ker(T):

maxi (S)=

max

i(E

i*

(T+Ф⨯ker(T)))

The solution in theory II.

The solution in work:The new spike-CSD method

A mathematical “autofocus” algorithm results in not only the sharpest CSD picture, but an estimation for the distance of the cell.

Tests on simulated data I.

The sCSD outperforms the traditional CSD for these sources.

Tests on simulated data II.

The sCSD method reconstructs the original source with significantly smaller error than the traditional CSD, while provides an estimation about the cell-electrode distance also.

Results I.

Spatio-temporal dynamics of action potentials

Results II.

The sCSD method is able to uncover fine details and cell-type specific differences in initiation and spreading of action potentials, and even possible signs of Ranvier-nodes.

Results III.

Initiation of the action potential and the Ranvier-spikelets.

Results IV.

The speed of apical and basal backpropagation

differs and signs of forward propagation also observed

Two dimensional localization of

neurons, results in realistic distances

Results V.

Henze et al. J. Neurphysiology 84 390-400 2000

Reconstruction of membrane potential, based on EC data with current-based compartmental model.

The hope

Identification of cortical synaptic input during paired-pulse experiments, could make possible to distinguish between changes in the network/connections and in single cell response for the same input.

Somewhere here,should be the input current,which cause the cell fire

Thank You!