# Rotation 1, Week 0: Understanding the problem

Its not much one can do in a 6 week rotation in lab, but when Madan Rao asked me to read some literature and if possible do something, I suggested that I will rather work on a problem and read if need arise. Reading without working is pretty stupid thing to do at my age. It might have some use for an undergraduate, at least for his/her exam. In nutshell, just reading  is another way of time-passing without feeling guilty about it. Knowledge is overrated when one wants to work with fundamental ideas.

Fortunately Madan saw it clearly that I don’t want to become Mr. Know-It-All or some sort of Pundit or Mahant with eye on a grand problem but rather a journeyman who solves problem at hand with whatever best tools available at his disposal and build his expertise by practicing his craft.

He politely suggested me to read a paper over coffee. Not a month ago, I was talking to Somya Mani about my bird-eye view of networks in biology and what I lack to deal with them: how to inject probabilistic variation into well-defined and well-behaved system. And to these ends, I want to take course offered by Mukund Thattai this semester at NCBS Bangalore, “Randomness in Biology”. After going through the paper which Madan suggested to read before further discussion what can be done during my rotation, I am happy about the problem I encountered by chance: how cells control a variable when input is mixed with random noise!

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Cells are always trying to control certain processes. Some variables such as cell-size is kept constant in a very variable environment. One can formulate this as a control-system problem and ask what a cell can and can’t do to suppress noise or variability in a parameter under control. Bounds on the performance of a control system under noisy conditions are well-studies by many early pioneers in system science; but this is somewhat a different problem. Since molecules inside cells go through random birth and deaths (I am still not quite clear about the difference).

This paper [1] establishes bounds on networks with negative feedback. This is interesting because negative feedback is often used to minimize the influence of noise on variable under control.

In this paper, authors consider a class of system, which is generic enough to describe many biological networks, and build a mathematical framework which can tell us what a cell (or a network) can not do when a given amount of noise is present in their environment. General structure of system is captured by following three equations: $x_1 \xrightarrow{u(x_2(-\infty,t))} x_1 + 1$, $x_1 \xrightarrow{x_1/\tau_1} x_1 - 1$, $x_2 \xrightarrow{f(x_1)} x_2 + 1$

Variable $x_1$ is under control whose production is controlled by a control daemon $u$ who knows past and present of $x_1$. Variable $x_1$, in turns, contol the production of $x_2$ since rate of its production is controlled by a function $f$ of $x_1$. $\tau$ is mean death rate of $x_1$. System under investigation is a system with negative feedback and signaling. Authors describe part of system using continuous differential equations but keep the controller and singaling discrete. They claim that It is extremely hard for a network to reduce noise where signal $x_2$ is made less frequently than the controlled component i.e. $x_1$. Reducing the standard deviation of $x_1$ tenfold can be achieved by increasing the birth rate of $x_2$ by a factor of 10,000.

In short, authors have developed a framework under which one can say something about what cell can not do under a noisy condition.

I am still trying to understand the theory they have used to established these bounds (see the supplementary material available in reference 1). I am also writing a simulator using SystemC/C++ to play with this idea.

REFERENCES

[1] Lestas, Ioannis, Glenn Vinnicombe, and Johan Paulsson. 2010. “Fundamental Limits on the Suppression of Molecular Fluctuations.” Nature 467 (7312) (Sep 09):Lestas, Ioannis, Glenn Vinnicombe, and Johan Paulsson. 2010. “Fundamental
Limits on the Suppression of Molecular Fluctuations.” Nature 467 (7312) (Sep 09): 174–178. doi:10.1038/nature09333. http://dx.doi.org/10.1038/nature09333.