Any system, be it a human, bacterium, or robot, must predict the future based on information from the past. That first of all requires this information to be stored. Whereas we do that in our brain, bacteria do it with the help of proteins and energy in the cell, a so-called biochemical network. Ultimately, how much information any system can possibly have about the future, the so-called predictive information, is always limited by the amount and quality of information that it extracts from the past signal. Our work showed that living cells like bacteria can, in principle, reach the fundamental limit on the predictive information as set by the past information: they can extract those bits of past information that are most informative about the future. Yet, our work also shows that reaching this fundamental bound is prohibitively costly, in terms of protein copies and energy. Optimal systems that maximize the predictive information for a given resource cost, as set by protein copies and energy, are indeed not at the information bound. They extract the bits of past information with the best price-to-quality ratio of cost versus predictive power.
We applied our theory to the chemotaxis system of the bacterium E. coli. Using experimental data, we showed that E. coli is indeed not at the information bound, as predicted by our theory. Moreover, our work revealed that for shallow ligand-concentration gradients where sensing becomes particularly challenging, the bacterium is very close to being optimal in terms of predictive information per resource cost. This analysis thus not only suggests that E. coli has been optimized for chemotaxis in challenging environments, but also provides firm support for our newly uncovered design principle that biological systems extract information with the best price-quality ratio.
In parallel, we have also developed a new algorithm, called PWS, that, for the first time, enables the exact computation of the information transmission rate for any stochastic system.
