Noise, Power Laws, and the Local Field Potential Joshua Milstein 1, Florian Morman 1,2, Itzhak Fried 2 and Christof Koch 1 1 California Institute of Technology 2 David Geffen School of Medicine and Semel Institute of Neuroscience and Human Behavior, University of California, Los Angeles Sloan-Swartz 2008 Summer Meeting

Physical Motivation Human Intracranial Recordings N = Scaling Exponent (  )

Compartmental Model To generate the membrane currents Hodgkin-Huxley Style Kinetics o Voltage dependent Na +, K +,Ca 2+ currents o 12 different processes NEURON Simulation Environment Used to compare intracellular to extracellular recordings Henze (2000) & Gold (2006) 3-D topological reconstruction Pyramidal hippocampal cell within rat CA1 t (ms) i (nA)

Power Laws Power/Slope Number of Earthquakes/Year Earthquake Magnitude Scale Invariance:

Time Pulse Amplitude Electron Shot Noise

Neuron Shot Noise Spike Timing Pulse Shape Stochastic Variable: t k1 t k2 t k3 t k5 t k6 t k7 t k4 Time

Wiener-Kinchin Theorem: Power SpectrumAutocorrelation Function

Simple Case I: Uncorrelated, Slow Synaptic Pulses

Simple Case II: Sharp Spike Pulse Amplitude Time Contains All Time/Frequency Dependence

White Noise Independent at each timestep Binary Sequence:

Brown(ian) Noise Autocorrelation Function: Power Spectrum:

Timestep Amplitude Random Walk with a Threshold Spike Train White Noise ?!?

Telegraph Process and Let Autocorrelation Function:

 = -2

Summary 1.Experimental Evidence for a Universal 1/f^2 Scaling in the LFP of Humans 2. Developed a Simple Mathematical Treatment for Understanding Power Laws in the LFP 3. Brownian Noise Can Arise From Single Neuron Activity Biophysical Examples: a. Sharp spikes followed by slow decay b. UP-DOWN states of activity ** Funded by the Swartz Foundation **