Physics 380, 2011: Lecture 19

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Back to Physics 380, 2011: Information Processing in Biology. 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

1. Why are there cascades of enzymatic amplifiers? The total time delay is $\max \tau _{i}$, and the gain is $\prod g_{i}$, while for each specific amplifier $\tau _{i}g_{i}\leq {\rm {const}}$ (aka, the gain-bandwidth tradeoff). So one can have faster, stronger amplifiers with cascades.
2. 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 $\int {\frac {d\omega }{2\pi }}{\frac {k_{XE}S_{\delta E_{a}}(\omega )}{k_{XX}^{2}+\omega ^{2}}}>\int {\frac {d\omega }{2\pi }}{\frac {\Omega }{k_{XX}^{2}+\omega ^{2}}}$
   • This sets the minimum value of $k_{XE}$.
   • Plugging in the numbers, this sets the limit on the minimum $X_{\rm {tot}}$ and hence on the minimum gain $X_{\rm {tot}}>{\frac {1}{\tau k_{a}}}{\frac {1}{\tau k_{d}{\bar {E}}_{d}}}{\frac {{\bar {E}}_{a}}{<\delta E_{a}^{2}>}}$.
3. Why are the enzymatic amplifiers so great? They are tunable. Let's look at one simple version of the tunability: linear negative feedback.