### Analog synthetic and systems biology

9 May 2014

Rahul Sarpeshkar

Research Laboratory of Electronics, MIT

#### Abstract

The fundamental laws of noise in gene and protein expression set limits on the energy, time, space, molecular count, and part-count resources needed to compute at a given level of precision in the cell. Based on these laws, we conclude that analog computation is significantly more efficient in its use of resources than deterministic digital computation in the cell. Hence, synthetic and natural circuits in cells must use analog, collective analog, probabilistic, and hybrid analog-digital computational approaches to function; otherwise, even relatively simple computations in cells like addition will exceed energy and molecular-count budgets. We present schematics for efficiently representing analog DNA-protein computation in cells. A deep connection between analog circuits and cell biology enables us to also engineer synthetic analog computation in cells efficiently.

Analog electronic flow in subthreshold transistors and analog molecular flux in chemical reactions obey Boltzmann exponential laws of thermodynamics and are described by astoundingly similar logarithmic electrochemical potentials. Therefore, cytomorphic circuits can help to map circuit designs between electronic and biochemical domains. We describe recent work that uses positive-feedback linearization circuits to architect wide-dynamic-range logarithmic analog computation in *Escherichia coli* using three transcription factors, nearly two orders of magnitude more efficient in parts than prior digital implementations.

- R Sarpeshkar,
*"Analog synthetic biology"*, Phil Trans R Soc A 372:20130110 2014. Full text

current theory lunch schedule