Arvind R. Subramaniam

Environmental perturbations lift the degeneracy of the genetic code to regulate protein levels in bacteria

The genetic code underlying protein synthesis is a canonical example of a degenerate biological system. Degeneracies in physical and biological systems can be lifted by external perturbations, thus allowing degenerate systems to exhibit a wide range of behaviors. Here we show that the degeneracy of the genetic code is lifted by environmental perturbations to regulate protein levels in living cells. By measuring protein synthesis rates from a synthetic reporter library in Escherichia coli, we find that environmental perturbations, such as reduction of cognate amino acid supply, lift the degeneracy of the genetic code by splitting codon families into a hierarchy of robust and sensitive synonymous codons. Rates of protein synthesis associated with robust codons are up to 100-fold higher than those associated with sensitive codons under these conditions. We find that the observed hierarchy between synonymous codons is not determined by usual rules associated with tRNA abundance and codon usage. Rather, competition among tRNA isoacceptors for aminoacylation underlies the robustness of protein synthesis. Remarkably, the hierarchy established using the synthetic library also explains the measured robustness of synthesis for endogenous proteins in E. coli. We further found that the same hierarchy is reflected in the fitness cost of synonymous mutations in amino acid biosynthesis genes and in the transcriptional control of σ-factor genes. Our study suggests that organisms can exploit degeneracy lifting as a general strategy to adapt protein synthesis to their environment.

A serine sensor for multicellularity in a bacterium.

We report the discovery of a simple environmental sensing mechanism for biofilm formation in the bacterium Bacillus subtilis that operates without the involvement of a dedicated RNA or protein. Certain serine codons, the four TCN codons, in the gene for the biofilm repressor SinR caused a lowering of SinR levels under biofilm-inducing conditions. Synonymous substitutions of these TCN codons with AGC or AGT impaired biofilm formation and gene expression. Conversely, switching AGC or AGT to TCN codons upregulated biofilm formation. Genome-wide ribosome profiling showed that ribosome density was higher at UCN codons than at AGC or AGU during biofilm formation. Serine starvation recapitulated the effect of biofilm-inducing conditions on ribosome occupancy and SinR production. As serine is one of the first amino acids to be exhausted at the end of exponential phase growth, reduced translation speed at serine codons may be exploited by other microbes in adapting to stationary phase. DOI: http://dx.doi.org/10.7554/eLife.01501.001

Entanglement entropy and multifractality at localization transitions

The von Neumann entanglement entropy is a useful measure to characterize a quantum phase transition. We investigate the nonanalyticity of this entropy at disorder-dominated quantum phase transitions in noninteracting electronic systems. At these critical points, the von Neumann entropy is determined by the single particle wave function intensity, which exhibits complex scale invariant fluctuations. We find that the concept of multifractality is naturally suited for studying von Neumann entropy of the critical wave functions. Our numerical simulations of the three dimensional Anderson localization transition and the integer quantum Hall plateau transition show that the entanglement at these transitions is well described using multifractal analysis.

Conformal invariance, multifractality, and finite-size scaling at Anderson localization transitions in two dimensions

We generalize universal relations between the multifractal exponent � 0 for the scaling of the typical wave function magnitude at a (Anderson) localization-delocalization transition in two dimensions and the corresponding critical finite size scaling (FSS) amplitudec of the typical localization length in quasi-one-dimensional (Q1D) geometry: (i) When open boundary conditions are imposed in the transverse direction of Q1D samples (strip geometry), we show that the corresponding critical FSS amplitudeo is universally related to the boundary multifractal exponents for the typical wave function amplitude along a straight boundary (surface). (ii) We further propose a generalization of these universal relations to those symmetry classes whose density of states vanishes at the transition. (iii) We verify our generalized relations (Eqs. (6) and (7)) numerically for the following four types of two-dimensional Anderson transitions: (a) the metal-to-(ordinary insulator) transition in the spin- orbit (symplectic) symmetry class, (b) the metal-to-(Z2 topological insulator) transition which is also in the spin-orbit (symplectic) class, (c) the integer quantum Hall plateau transition, and (d) the spin quantum Hall plateau transition. PACS numbers: 73.20.Fz, 05.45.Df, 72.15.Rn

Multifractality and conformal invariance at 2D metal-insulator transition in the spin-orbit symmetry class.

We study the multifractality (MF) of critical wave functions at boundaries and corners at the metal-insulator transition (MIT) for noninteracting electrons in the two-dimensional (2D) spin-orbit (symplectic) universality class. We find that the MF exponents near a boundary are different from those in the bulk. The exponents at a corner are found to be directly related to those at a straight boundary through a relation arising from conformal invariance. This provides direct numerical evidence for conformal invariance at the 2D spin-orbit MIT. The presence of boundaries modifies the MF of the whole sample even in the thermodynamic limit.

Surface Criticality and Multifractality at Localization Transitions

We have synthesized the solid solution, Sr_2Fe_1+xMo_1-xO_6 with -1<= x<= 0.25, the composition x = 0 corresponding to the well-known double perovskite system Sr2FeMoO6. We report structural and magnetic properties of the above system, exhibiting systematic variations across the series. These results restrict the range of models that can explain magnetism in this family of compounds, providing an understanding of the magnetic structure.We develop the concept of surface multifractality for localization-delocalization (LD) transitions in disordered electronic systems. We point out that the critical behavior of various observables related to wave functions near a boundary at a LD transition is different from that in the bulk. We illustrate this point with a calculation of boundary critical and multifractal behavior at the 2D spin quantum Hall transition and in a 2D metal at scales below the localization length.

Kinetic modeling predicts a stimulatory role for ribosome collisions at elongation stall sites in bacteria

Ribosome stalling on mRNAs can decrease protein expression. To decipher ribosome kinetics at stall sites, we induced ribosome stalling at specific codons by starving the bacterium Escherichia coli for the cognate amino acid. We measured protein synthesis rates from a reporter library of over 100 variants that encoded systematic perturbations of translation initiation rate, the number of stall sites, and the distance between stall sites. Our measurements are quantitatively inconsistent with two widely-used kinetic models for stalled ribosomes: ribosome traffic jams that block initiation, and abortive (premature) termination of stalled ribosomes. Rather, our measurements support a model in which collision with a trailing ribosome causes abortive termination of the stalled ribosome. In our computational analysis, ribosome collisions selectively stimulate abortive termination without fine-tuning of kinetic rate parameters at ribosome stall sites. We propose that ribosome collisions serve as a robust timer for translational quality control pathways to recognize stalled ribosomes. DOI: http://dx.doi.org/10.7554/eLife.23629.001

Boundary criticality and multifractality at the two-dimensional spin quantum Hall transition

Multifractal scaling of critical wave functions at a disorder-driven Anderson localization transition is modified near boundaries of a sample. Here this effect is studied for the example of the spin quantum Hall plateau transition using the supersymmetry technique for disorder averaging. Upon mapping the spin quantum Hall transition to the classical percolation problem with reflecting boundaries, a number of multifractal exponents governing wave-function scaling near a boundary are obtained exactly. Moreover, additional exact boundary scaling exponents of the localization problem are extracted, and the problem is analyzed in other

Boundary multifractality in critical one-dimensional systems with long-range hopping

Boundary multifractality of electronic wave functions is studied analytically and numerically for the power-law random banded matrix (PRBM) model, describing a critical one-dimensional system with long-range hopping. The peculiarity of the Anderson localization transition in this model is the existence of a line of fixed points describing the critical system in the bulk. We demonstrate that the boundary critical theory of the PRBM model is not uniquely determined by the bulk properties. Instead, the boundary criticality is controlled by an additional parameter characterizing the hopping amplitudes of particles reflected by the boundary.

Corner multifractality for reflex angles and conformal invariance at 2D Anderson metal–insulator transition with spin–orbit scattering

Abstract We investigate boundary multifractality of critical wave functions at the Anderson metal–insulator transition in two-dimensional disordered non-interacting electron systems with spin–orbit scattering. We show numerically that multifractal exponents at a corner with an opening angle θ = 3 π / 2 are directly related to those near a straight boundary in the way dictated by conformal symmetry. This result extends our previous numerical results on corner multifractality obtained for θ π to θ > π , and gives further supporting evidence for conformal invariance at criticality. We also propose a refinement of the validity of the symmetry relation of A.D. Mirlin et al. [Phys. Rev. Lett. 97 (2006) 046803] for corners.