ABSTRACT
Bacterial ribosomes are composed of one-third protein and two-thirds RNA by mass. The predominance of RNA is often attributed to a primordial RNA world, but why exactly two-thirds remains a long-standing mystery. Here we present a quantitative analysis, based on the kinetics of ribosome self-replication, demonstrating that the 1â¶2 protein-to-RNA mass ratio uniquely maximizes cellular growth rates in E. coli. A previously unrecognized growth law, and an invariant of bacterial growth, also follow from our analysis. The growth law reveals that the ratio between the number of ribosomes and the number of polymerases making ribosomal RNA is proportional to the cellular doubling time. The invariant 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 are shown to be in excellent agreement with E. coli data despite having no fitting parameters. Our analysis can be readily extended to other bacteria once data become available.
Subject(s)
Escherichia coli Proteins/metabolism , Escherichia coli/growth & development , Escherichia coli/metabolism , Models, Biological , RNA, Bacterial/metabolism , RNA, Ribosomal/metabolism , Ribosomal Proteins/metabolism , Ribosomes/metabolism , Escherichia coli/genetics , Ribosomes/geneticsABSTRACT
Understanding and controlling polyelectrolyte adsorption onto carbon nanotubes is a fundamental challenge in nanotechnology. Polyelectrolytes have been shown to stabilize nanotube suspensions through adsorbing onto the nanotube surface, and polyelectrolyte-coated nanotubes are emerging as building blocks for complex and addressable self-assembly. Conventional wisdom suggests that polyelectrolyte adsorption onto nanotubes is driven by specific chemical or van der Waals interactions. We develop a simple mean-field model and show that ion-image attraction significantly effects adsorption onto conducting nanotubes at low salt concentrations. Our theory suggests a simple strategy to selectively and reversibly functionalize carbon nanotubes on the basis of their electronic structures, which in turn modify the ion-image attraction.
ABSTRACT
Motivated by colloidal lithography, we study the problem of characterizing periodic planar patterns formed by shadows of spheres. The set of patterns accessible to shadow lithography spanned by lattice types, tilt, and rotation angles is rich, but topological considerations of shadow overlap along simplex edges and faces lead us to just 4+1 distinct categories. These planar patterns are in one-to-one correspondence with a 4-valued index linked to Cayley-Menger determinants. The characterization is confirmed by a phase diagram which predicts surface patterns for any experimental geometry.
