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nemenman>Ilya at 13:55, 3 November 2011

2011-11-03T13:55:44Z

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{{PHYS380-2011}}
This is the last lecture following the article by Detwiler et al., 2000.

==Student Presentation==
Zhenya Botezat will present the paper Vergassola et al., 2007.

'''unfinished'''
==Main lecture==
#Why are there cascades of enzymatic amplifiers? The total time delay is <math>\max \tau_i</math>, and the gain is <math>\prod g_i</math>, while for each specific amplifier <math>\tau_ig_i\le {\rm const}</math> (aka, the gain-bandwidth tradeoff). So one can have faster, stronger amplifiers with cascades.
#But one should be careful since each new step introduces extra noise.
#*We should have the amplified fluctuations of the input be larger than the intrinsic fluctuations of the amplifier.
#*Since, at minimum, we have input fluctuations (but no input signal), we should, at minimum, have <math>\int \frac{d\omega}{2\pi} \frac{k_{XE}S_{\delta E_a}(\omega)}{k_{XX}^2+\omega^2} > \int \frac{d\omega}{2\pi} \frac{\Omega}{k_{XX}^2+\omega^2}</math>
#*This sets the minimum value of <math>k_{XE}</math>.
#*Plugging in the numbers, this sets the limit on the minimum <math>X_{\rm tot}</math> and hence on the minimum gain <math>X_{\rm tot}>\frac{1}{\tau k_a}\frac{1}{\tau k_d \bar{E}_d}\frac{\bar{E}_a}{<\delta E_a^2>}</math>.
#Why are the enzymatic amplifiers so great? They are tunable. Let's look at one simple version of the tunability: linear negative feedback.

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Physics 380, 2011: Lecture 19 - Revision history

Ilya: 1 revision imported

nemenman>Ilya at 13:55, 3 November 2011