LIVING ON THE EDGE?
Physical & Mathematical laws dictate limits and trade-offs that constrain the design and performance of man-made systems. Living systems are bound by similar constraints, which gives rise to the hypothesis that the latter played a role in shaping life as we know it. To study this hypothesis, we look for situations where evolution pushed living cells, or components within them, to the edge of their performance (optimality). As getting to the optimum is often subject to quantifiable constraints, we try to understand how these impacted living organisms and the molecules that make life possible.
​
We have previously utilized the above approach to show that proteins obey a universal equation of state that captures a delicate balance between stability and flexibility [Phys. Rev. Lett. 100, 208101, 2008; PLOS ONE 4(10), 2009]. In a different project, we took a similar approach to show that central features of the ribosome — the protein production factory of the cell — can be explained based on optimization for self-replication [Nature 547 (7663), 293, 2017]. Yet, a long-standing mystery remained unresolved. Why is the bacterial ribosome made up of a mix of protein and RNA in an almost perfect 1:2 mass ratio? Recently, we were able to show that this ratio is special because it allows bacterial cells to maximize their growth rate and thus gain an evolutionary advantage.
​
Ribosome composition maximizes cellular growth rates in E.coli
​
Two autocatalytic loops are required to describe ribosome production: One for ribosomal protein and one for ribosomal RNA. Ribosomal protein is synthesized directly by ribosomes, as illustrated by the blue autocatalytic loop in the figure below. Ribosomal RNA is synthesized by RNA polymerases (RNAPs), symbolized by the top left gray arrow. RNA polymerases, in turn, are made of protein that is synthesized by ribosomes (bottom left blue arrow). We obtained two bounds on the cellular growth rate based on the production of these ribosomal building blocks. The bounds assert that an excess of either protein or RNA in the ribosome causes cells to grow too slowly. An optimal mixture of protein and RNA is therefore required.
​
​
​
​
Combining predictions coming from our analysis with data gathered on the model organism E. coli, we showed that maximization of cellular growth rates is uniquely attained when RNA constitutes two-thirds of the ribosome mass [Phys. Rev. Lett. 125, 028103, 2020]. Furthermore, we demonstrated that E. coli in fact achieves the maximal growth rates permitted by the bounds, which allowed us to recast them in the form of a previously unrecognized growth law, and an invariant of bacterial growth. The growth law revealed that the ratio between the number of ribosomes and the number of polymerases making ribosomal RNA in the cell is proportional to the cellular doubling time. The invariant (first of its kind) is conserved across growth conditions and specifies how key microscopic parameters in the cell, such as transcription and translation rates, are coupled to cellular physiology. Quantitative predictions from the growth law and invariant were shown to be in excellent agreement with data despite having no fitting parameters. Our work was selected for suggested read by the editors of PRL and was further highlighted in Physics [Speed Limit for Cell Growth].
​
Growth laws and invariants from ribosome biogenesis in lower Eukarya
The approach described above is not limited to Bacteria, and have recently extended it to lower Eukarya [Phys. Rev. Research 3, 013020, 2021]. To this end, we developed a much-needed theoretical framework to quantitatively describe central aspects of eukaryotic cell physiology and growth. Starting from first principles, we derived three growth-laws and two invariants, which to our knowledge constitute the first set of mathematical relations describing Eukarya. We applied the relations to the model organism S. cerevisiae (baker’s yeast), showing them to be in excellent agreement with currently available data. Additional data collection is needed to verify several other predictions, offering a series of experimental follow-ups.
