Ranjan Mukhopadhyay

A Curvature-Mediated Mechanism for Localization of Lipids to Bacterial Poles

Subcellular protein localization is a universal feature of eukaryotic cells, and the ubiquity of protein localization in prokaryotic species is now acquiring greater appreciation. Though some targeting anchors are known, the origin of polar and division-site localization remains mysterious for a large fraction of bacterial proteins. Ultimately, the molecular components responsible for such symmetry breaking must employ a high degree of self-organization. Here we propose a novel physical mechanism, based on the two-dimensional curvature of the membrane, for spontaneous lipid targeting to the poles and division site of rod-shaped bacterial cells. If one of the membrane components has a large intrinsic curvature, the geometrical constraint of the plasma membrane by the more rigid bacterial cell wall naturally leads to lipid microphase separation. We find that the resulting clusters of high-curvature lipids are large enough to spontaneously and stably localize to the two cell poles. Recent evidence of localization of the phospholipid cardiolipin to the poles of bacterial cells suggests that polar targeting of some proteins may rely on the membranes differential lipid content. More generally, aggregates of lipids, proteins, or lipid-protein complexes may localize in response to features of cell geometry incapable of localizing individual molecules.

Cell shape and cell-wall organization in Gram-negative bacteria

In bacterial cells, the peptidoglycan cell wall is the stress-bearing structure that dictates cell shape. Although many molecular details of the composition and assembly of cell-wall components are known, how the network of peptidoglycan subunits is organized to give the cell shape during normal growth and how it is reorganized in response to damage or environmental forces have been relatively unexplored. In this work, we introduce a quantitative physical model of the bacterial cell wall that predicts the mechanical response of cell shape to peptidoglycan damage and perturbation in the rod-shaped Gram-negative bacterium Escherichia coli. To test these predictions, we use time-lapse imaging experiments to show that damage often manifests as a bulge on the sidewall, coupled to large-scale bending of the cylindrical cell wall around the bulge. Our physical model also suggests a surprising robustness of cell shape to peptidoglycan defects, helping explain the observed porosity of the cell wall and the ability of cells to grow and maintain their shape even under conditions that limit peptide crosslinking. Finally, we show that many common bacterial cell shapes can be realized within the same model via simple spatial patterning of peptidoglycan defects, suggesting that minor patterning changes could underlie the great diversity of shapes observed in the bacterial kingdom.

Lipid localization in bacterial cells through curvature-mediated microphase separation.

Although many proteins are known to localize in bacterial cells, for the most part our understanding of how such localization takes place is limited. Recent evidence that the phospholipid cardiolipin localizes to the poles of rod-shaped bacteria suggests that targeting of some proteins may rely on the heterogeneous distribution of membrane lipids. Membrane curvature has been proposed as a factor in the polar localization of high-intrinsic-curvature lipids, but the small size of lipids compared to the dimensions of the cell means that single molecules cannot stably localize. At the other extreme, phase separation of the membrane energetically favors a single domain of such lipids at one pole. We have proposed a physical mechanism in which osmotic pinning of the membrane to the cell wall naturally produces microphase separation, i.e., lipid domains of finite size, whose aggregate sensitivity to cell curvature can support spontaneous and stable localization to both poles. Here, we demonstrate that variations in the strength of pinning of the membrane to the cell wall can also act as a strong localization mechanism, in agreement with observations of cardiolipin relocalization from the poles to the septum during sporulation in the bacterium Bacillus subtilis. In addition, we rigorously determine the relationship between localization and the domain-size distribution including the effects of entropy, and quantify the strength of domain-domain interactions. Our model predicts a critical concentration of cardiolipin below which domains will not form and hence polar localization will not take place. This observation is consistent with recent experiments showing that in Escherichia coli cells with reduced cardiolipin concentrations, cardiolipin and the osmoregulatory protein ProP fail to localize to the poles.

Symmetries and elasticity of nematic gels.

A nematic liquid-crystal gel is a macroscopically homogeneous elastic medium with the rotational symmetry of a nematic liquid crystal. In this paper, we develop a general approach to the study of these gels that incorporates all underlying symmetries. After reviewing traditional elasticity and clarifying the role of broken rotational symmetries in both the reference space of points in the undistorted medium and the target space into which these points are mapped, we explore the unusual properties of nematic gels from a number of perspectives. We show how symmetries of nematic gels formed via spontaneous symmetry breaking from an isotropic gel enforce soft elastic response characterized by the vanishing of a shear modulus and the vanishing of stress up to a critical value of strain along certain directions. We also study the phase transition from isotropic to nematic gels. In addition to being fully consistent with approaches to nematic gels based on rubber elasticity, our description has the important advantages of being independent of a microscopic model, of emphasizing and clarifying the role of broken symmetries in determining elastic response, and of permitting easy incorporation of spatial variations, thermal fluctuations, and gel heterogeneity, thereby allowing a full statistical-mechanical treatment of these materials.

Exponential sensitivity of noise-driven switching in genetic networks

There is increasing experimental evidence that cells can utilize biochemical noise to switch probabilistically between distinct gene-expression states. In this paper, we demonstrate that such noise-driven switching is dominated by tails of probability distributions and is therefore exponentially sensitive to changes in physiological parameters such as transcription and translation rates. Exponential sensitivity limits the robustness of noise-driven switching, suggesting cells may use other mechanisms in order to switch reliably. We discuss our results in the context of competence in the bacterium Bacillus subtilis.

Optimal path to epigenetic switching.

We use large deviation methods to calculate rates of noise-induced transitions between states in multistable genetic networks. We analyze a synthetic biochemical circuit, the toggle switch, and compare the results to those obtained from a numerical solution of the master equation.

Fractional quantum Hall effect in an array of quantum wires.

We demonstrate the emergence of the quantum Hall (QH) hierarchy in a 2D model of coupled quantum wires in a perpendicular magnetic field. At commensurate values of the magnetic field, the system can develop instabilities to appropriate interwire electron hopping processes that drive the system into a variety of QH states. Some of the QH states are not included in the Haldane-Halperin hierarchy. In addition, we find operators allowed at any field that lead to novel crystals of Laughlin quasiparticles. We demonstrate that any QH state is the ground state of a Hamiltonian that we explicitly construct.

Self-organized periodicity of protein clusters in growing bacteria.

Chemotaxis receptors in E. coli form clusters at the cell poles and also laterally along the cell body, and this clustering plays an important role in signal transduction. Recently, experiments using fluorescence imaging have shown that, during cell growth, lateral clusters form at positions approximately periodically spaced along the cell body. In this Letter, we demonstrate within a lattice model that such spatial organization could arise spontaneously from a stochastic nucleation mechanism. The same mechanism may explain the recent observation of periodic aggregates of misfolded proteins in E. coli.

Sliding Luttinger liquid phases

We study systems of coupled spin-gapped and gapless Luttinger liquids. First, we establish the existence of a sliding Luttinger liquid phase for a system of weakly coupled parallel quantum wires, with and without disorder. It is shown that the coupling can stabilize a Luttinger liquid phase in the presence of disorder. We then extend our analysis to a system of crossed Luttinger liquids and establish the stability of a non-Fermiliquid state: the crossed sliding Luttinger liquid phase. In this phase the system exhibits a finite-temperature, long-wavelength, isotropic electric conductivity that diverges as a power law in temperature T as T!0. This two-dimensional system has many properties of a true isotropic Luttinger liquid, though at zero temperature it becomes anisotropic. An extension of this model to a three-dimensional stack exhibits a much higher in-plane conductivity than the conductivity in a perpendicular direction.

Semisoft nematic elastomers and nematics in crossed electric and magnetic fields.

Nematic elastomers with a locked-in anisotropy direction exhibit semisoft elastic response characterized by a plateau in the stress-strain curve in which stress does not change with strain. We calculate the global phase diagram for a minimal model, which is equivalent to one describing a nematic in crossed electric and magnetic fields, and show that semisoft behavior is associated with a broken symmetry biaxial phase and that it persists well into the supercritical regime. We also consider generalizations beyond the minimal model and find similar results.