Namiko Mitarai

Wet granular materials

Most studies on granular physics have focused on dry granular media, with no liquids between the grains. However, in geology and many real world applications (e.g. food processing, pharmaceuticals, ceramics, civil engineering, construction, and many industrial applications), liquid is present between the grains. This produces inter-grain cohesion and drastically modifies the mechanical properties of the granular media (e.g. the surface angle can be larger than 90 degrees). Here we present a review of the mechanical properties of wet granular media, with particular emphasis on the effect of cohesion. We also list several open problems that might motivate future studies in this exciting but mostly unexplored field. Contents PAGE 1. Introduction 2  1.1. Granular physics and wet granular media 2  1.2. What is different from dry granular media? 3 2. Wet granular media: Grains with liquid and air 5  2.1. Cohesion between two spheres 5  2.1.1. Meniscus and suction 5  2.1.2. Liquid bridge between two spheres 6  2.2. Wet granular media with various liquid content 7  2.2.1. Four states of liquid content: pendular, funicular, capillary, and slurry state 7  2.2.2. Liquid content and suction 8  2.2.2.1. Measurement of suction in granular media 8  2.2.2.2. Relation between the liquid content and suction 10 3. Mechanical properties 12  3.1. Granular cohesion in the static and quasi-static regimes 12  3.1.1. Compaction of wet granular media 12  3.1.2. Angle of repose for small amounts of liquid 13  3.1.2.1. Experiments 13  3.1.2.2. Cohesion and angle of repose 14  3.1.3. Tensile, compression, and shear tests for intermediate and large liquid content 19  3.1.3.1. Test methods and Mohr circle 19  3.1.3.2. Tests in the pendular state 23  3.1.3.3. Tests with intermediate liquid content 24  3.1.3.4. Tests in soil mechanics: relatively large amounts of liquid 25  3.2. Dynamical behaviour 27  3.2.1. Dynamics in the pendular state 28  3.2.1.1. Avalanches in rotating drums 28  3.2.1.2. Vibrated wet granular media 29  3.2.1.3. Segregation 31  3.2.2. Shear experiments for various liquid content 32  3.2.3. Dynamics of wet granular media: practical applications 35  3.2.3.1. Agglomeration processing: grains bound by liquid 35  3.2.3.2. Geological events 35 4. Summary and open questions 35  4.1. Effect of the liquid content on quasi-static behaviour 35  4.2. Open problems 36  4.2.1. Jamming 37  4.2.2. Statistical mechanics approach 39  4.2.3. Arches and contact-force fluctuations 39  4.2.4. Simple experimental set-ups to study the dynamics of wet granular media 39  4.2.5. Numerical simulations 40  4.2.6. Mechanical properties of snow 40 5. Conclusion 41 Acknowledgements 41 References 41

Ribosome Collisions and Translation Efficiency: Optimization by Codon Usage and mRNA Destabilization

Individual mRNAs are translated by multiple ribosomes that initiate translation with an interval of a few seconds. The ribosome speed is codon dependent, and ribosome queuing has been suggested to explain specific data for translation of some mRNAs in vivo. By modeling the stochastic translation process as a traffic problem, we here analyze conditions and consequences of collisions and queuing. The model allowed us to determine the on-rate (0.8 to 1.1 initiations/s) and the time (1 s) the preceding ribosome occludes initiation for Escherichia coli lacZ mRNA in vivo. We find that ribosome collisions and queues are inevitable consequences of a stochastic translation mechanism that reduce the translation efficiency substantially on natural mRNAs. The cells minimize collisions by having its mRNAs being unstable and by a highly selected codon usage in the start of the mRNA. The cost of mRNA breakdown is offset by the concomitant increase in translation efficiency.

Efficient degradation and expression prioritization with small RNAs

We build a simple model for feedback systems involving small RNA (sRNA) molecules based on the iron metabolism system in the bacterium E. coli, and compare it with the corresponding system in H. pylori which uses purely transcriptional regulation. This reveals several unique features of sRNA-based regulation that could be exploited by cells. Firstly, we show that sRNA regulation can maintain a smaller turnover of target mRNAs than transcriptional regulation, without sacrificing the speed of response to external shocks. Secondly, we propose that a single sRNA can prioritize the usage of different target mRNAs. This suggests that sRNA regulation would be more common in more complex systems which need to co-regulate many mRNAs efficiently.

Dynamic features of gene expression control by small regulatory RNAs

Small regulatory RNAs (sRNAs) in eukaryotes and bacteria play an important role in the regulation of gene expression either by binding to regulatory proteins or directly to target mRNAs. Two of the best-characterized bacterial sRNAs, Spot42 and RyhB, form a complementary pair with the ribosome binding region of their target mRNAs, thereby inhibiting translation or promoting mRNA degradation. To investigate the steady-state and dynamic potential of such sRNAs, we examine the 2 key parameters characterizing sRNA regulation: the capacity to overexpress the sRNA relative to its target mRNA and the speed at which the target mRNA is irreversibly inactivated. We demonstrate different methods to determine these 2 key parameters, for Spot42 and RyhB, which combine biochemical and genetic experiments with computational analysis. We have developed a mathematical model that describes the functional properties of sRNAs with various characteristic parameters. We observed that Spot42 and RyhB function in distinctive parameter regimes, which result in divergent mechanisms.

Conditional cooperativity in toxin–antitoxin regulation prevents random toxin activation and promotes fast translational recovery

Many toxin–antitoxin (TA) loci are known to strongly repress their own transcription. This auto-inhibition is often called ‘conditional cooperativity’ as it relies on cooperative binding of TA complexes to operator DNA that occurs only when toxins are in a proper stoichiometric relationship with antitoxins. There has recently been an explosion of interest in TA systems due to their role in bacterial persistence, however the role of conditional cooperativity is still unclear. We reveal the biological function of conditional cooperativity by constructing a mathematical model of the well studied TA system, relBE of Escherichia coli. We show that the model with the in vivo and in vitro established parameters reproduces experimentally observed response to nutritional stress. We further demonstrate that conditional cooperativity stabilizes the level of antitoxin in rapidly growing cells such that random induction of relBE is minimized. At the same time it enables quick removal of free toxin when the starvation is terminated.

Collisional granular flow as a micropolar fluid.

We show that a micropolar fluid model successfully describes collisional granular flows on a slope. A micropolar fluid is the fluid with internal structures in which coupling between the spin of each particle and the macroscopic velocity field is taken into account. It is a hydrodynamical framework suitable for granular systems which consists of particles with macroscopic size. We demonstrate that the model equations can quantitatively reproduce the velocity and the angular velocity profiles obtained from the numerical simulation of the collisional granular flow on a slope using a simple estimate for the parameters in the theory.

Bagnold scaling, density plateau, and kinetic theory analysis of dense granular flow

We investigate the bulk rheology of dense granular flow down a rough slope, where the density profile has been found to show a plateau except for the boundary layers in simulations [Silbert et al., Phys. Rev. E 64, 051302 (2001)]. It is demonstrated that both the Bagnold scaling and the framework of kinetic theory are applicable in the bulk, which allows us to extract the constitutive relations from simulation data. The detailed comparison of our data with the kinetic theory shows quantitative agreement for the normal and shear stresses, but there exists a slight discrepancy in the energy dissipation, which causes a rather large disagreement in the kinetic theory analysis of the flow.

Spatiotemporal structure of traffic flow in a system with an open boundary

The spatiotemporal structure of a traffic flow pattern is investigated under the open boundary condition using the optimal velocity model. The parameter region where the uniform solution is convectively unstable is determined. It is found that a localized perturbation triggers a linearly unstable oscillatory solution out of the linearly unstable uniform state, and it is shown that the oscillatory solution is also convectively stabilized. It is demonstrated that the observed traffic pattern near an on-ramp can be interpreted as the noise sustained structure in the open flow system.

Conditional cooperativity of toxin - antitoxin regulation can mediate bistability between growth and dormancy.

Many toxin-antitoxin operons are regulated by the toxin/antitoxin ratio by mechanisms collectively coined “conditional cooperativity”. Toxin and antitoxin form heteromers with different stoichiometric ratios, and the complex with the intermediate ratio works best as a transcription repressor. This allows transcription at low toxin level, strong repression at intermediate toxin level, and then again transcription at high toxin level. Such regulation has two interesting features; firstly, it provides a non-monotonous response to the concentration of one of the proteins, and secondly, it opens for ultra-sensitivity mediated by the sequestration of the functioning heteromers. We explore possible functions of conditional regulation in simple feedback motifs, and show that it can provide bistability for a wide range of parameters. We then demonstrate that the conditional cooperativity in toxin-antitoxin systems combined with the growth-inhibition activity of free toxin can mediate bistability between a growing state and a dormant state.

Velocity correlations in dense granular shear flows: effects on energy dissipation and normal stress.

We study the effect of precollisional velocity correlations on granular shear flow by molecular dynamics simulations of an inelastic hard sphere system. Comparison of the simulations with kinetic theory reveals that the theory overestimates both the energy dissipation rate and the normal stress in the dense flow region. We find that the relative normal velocity of colliding particles is smaller than that expected from random collisions, and the discrepancies in the dissipation and the normal stress can be adjusted by introducing the idea of the collisional temperature, from which we conclude that the velocity correlation neglected in the kinetic theory is responsible for the discrepancies. Our analysis of the distributions of the precollisional velocity suggests that the correlation grows through multiple inelastic collisions during the time scale of the inverse of the shear rate. As for the shear stress, the discrepancy is also found in the dense region, but it depends strongly on the particle inelasticity.