Homework 6 - Problem 1

1. In this problem we'll explore the role of noise in enhancing information transmission for weak signals via a stochastic resonance mechanism. Use you integrate-and-fire neuron model from Homework #2 with the following parameters: R = 10 MOhm, C = 1 nF, Vrest = 0 mV, Vthr = 5 mV, Vspk = 70 mV. Drive the model with the following weak input current: I(t) = 0.3*sin(2*pi*f*t), with f = 1 Hz. (NOTE: Be careful with units; if time is in msec, what are the corresponding units of frequency?) Add random gaussian noise (randn) to the input current at each of the following noise levels (standard deviation): 0.0, 0.1, 0.2, 0.5, 1.0, 2.0, 5.0 and 10.0 nA Generate plots of membrane potential versus time for each noise level. Arrange the outputs vertically with an offset of 100 mV between traces, as in the following plot. Simulate 5 seconds of the response at each noise level (DT = 1 msec). Based on visual inspection of your plot, at what noise level(s) does the spike output appear to convey the most information about the frequency and phase of the sinusoidal input signal?

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