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Electro-optic materials contain chromophores with a dipole moment. These dipoles align with an electric field and this imparts useful properties to the material. Two dipoles tend to align in an anti-parallel fashion, however, and achieving high chromophore density while preventing such a cancellation is an important goal. During this reporting period we have carried out Monte Carlo simulations to investigate the electro-optic (EO) properties of randomly branched polymers, using the computer programs developed in previous period. We have also used an analogy between randomly branched polymers and the bacterial nucleoid to study the distribution of ribosomes in E. coli.

We have investigated a variety of polymer models and chromophore distributions. For polymer models we considered freely-jointed tangent sphere chains and united atom models with torsional and bond angle interactions. In each case we considered two cases, i.e., quenched and annealed branching structures, where the connectivity of polymers is fixed or allowed to change, respectively. We incorporated dipoles into the polymer molecules and investigated their alignment in response to an external field. Furthermore we investigated two methods of chromophore incorporation where the chromophores are attached as side groups, or are part of the polymer backbone.

We investigated the dependence of the EO coefficient r on the chromophore number density (for different chromophore dipole moments (ranging from 6 D to 14 D, and external poling fields F, ranging from 100 V/(m to 600 V/(m. The EO coefficient can be computed from the chromophore orientational distribution function for an ensemble of interacting chromophores in the presence of an applied electric poling field.

The EO activity is sensitive to the nature of the branching and the nature of chromophore attachment. Systems with annealed branching structure with chromophores attached as side-groups have the largest EO activity of the cases tested. The chemical structure does not play a significant role as long as the chromophores are attached as side-groups. This observation can help guide the development of improved polymeric EO materials. We are preparing a manuscript on this work which we will submit to the journal Macromolecules.

We have also studied the behavior of freely-jointed hyperbranched polymer chains confined within a cylinder, which is a model for the behavior of the nucleoid in E. coli. cells. In E. coli, the nucleoid is the (ring-like) DNA that is twisted into a plectonemic conformation. The topology is very similar to a hyper-branched polymer, and we are in a position to study the conformations of the nucleoid and the diffusion of proteins inside the cell.

Our main interest is the distribution of ribosomes within the cell. It has been found, experimentally, that the ribosomes segregate to the periphery of the cell. Although various hypotheses have been proposed, the driving force for this segregation remains an open question. We model the nucleoid as a freely-jointed hyper-branched polymer where the "beads" can be either hard spheres or carry an additional charge. The ribosomes are spheres (neutral or charged) that can exist either as monomers or as clumps.

We perform simulations of the entire E. coli cell where only the nucleoid and ribosomes are incorporated explicitly. The beads of the nucleoid have a diameter 40 nm, the number of beads is 4000, and the "bond" length is 200 nm. The ribosomes have a diameter of 20 nm, and 8000 ribosomes are included. The E. coli cell is constructed as a spherocylinder whose cylindrical region has length 1.0 mm and end-caps have radius 0.5 mm.

We find that the un-perturbed (in free space) dimension of the nucleoid is much larger than that of the cell. When the nucleoid is confined within the cell, it essentially fills space. The number of tri-functional nodes is relatively insensitive to the length of the cell, but the chain expands in the axial direction as the cell becomes longer.

Our results show that in all cases ribosomes tend to segregate to the cytoplasmic periphery. This segregation is purely entropic and arises from the volume excluded by the nucleoid to the ribosomes. For monomeric ribosomes, this segregation is modest with a concentration of ribosomes at the periphery about 5-10% higher than in the interior of the cell. This is smaller than what is observed in experiment.

The segregation of the ribosomes becomes more significant if the ribosomes form strands. In real cells the ribosomes are attached to mRNA forming chain-like clumps with approximately 10 ribosomes attached to each mRNA strand. Our calculations show that when these clumps are formed, they segregate readily to the periphery of the cell.

The results suggest that the structure of ribosomes plays an important role in their distribution inside the E. coli cell. During translation the ribosomes are attached to the mRNA and entropic effects drive the entire assembly to the periphery of the cell. This is physiologically important because the proteins synthesized are primarily required near the membrane to which the ribosome-mRNA complex have segregated.

The main conclusion of our simulations is that the driving forces for ribosome segregation and nucleoid compaction could be solely from entropic effects arising from the excluded volume effect of the nucleoid and the physical structure of ribosomes.