1. DNA mechanics in a tight squeeze Confinement of biopolymers changes their response to a mechanical force. We have derived an exact formula for the force-extension curve when the molecule is confined to a surface. Mechanical properties of semi-flexible polymers like DNA and actin play a central role in a number of biological processes, such as transcriptional regulation and cell motility. Biopolymers in cells are short and can be thought of as fluctuating rods. Using field-theoretical methods we have derived formulae describing the extension and average shape of short biopolymers. The case of stretching DNA by an applied field is particularly interesting theoretically and for biotech applications having to do with sequencing. The computed average shape is in accordance with observations. Mechanical properties of biomolecules are probed by applying a force on a single molecule. Figure from Maier et al, Europhys. Lett. 2002 Average shape of DNA Complex fluids confined at the nanometer scale, B. Chakraborty, J. Kondev, C. Chamon, D. Reichman, Brandeis University, DMR 0403997

2. DNA Diffusion Diffusion of macromolecules when their motion is constrained by obstacles or reduced dimensionality is of importance to their function in the cell and for lab-on-a-chip devices. A number of experiments have used fluorescence techniques to study DNA diffusion on supported lipid bilayers. This is an interesting model system on which to observe directly the motion of a single DNA chain. We have constructed a theoretical model for calculating the diffusion constant D of the molecule and how it depends on the chain length N. DNA diffusion in a lipid bilayer We have identified two regimes of DNA diffusing on a lipid bilayer, depending on the amount of momentum dissipation perpendicular to the membrane. In one regime, which is realized in experiments by Maier et al., the DNA behaves as if its various segments are diffusing in an uncorrelated fashion. In the other regime the DNA behaves as if it is a rigid disk. We propose experiments to check predictions for this novel regime. Experiment by Maier et al Phys Rev Lett, 1999 D N D N Complex fluids confined at the nanometer scale, B. Chakraborty, J. Kondev, C. Chamon, D. Reichman, Brandeis University, DMR 0403997

3. Complex fluids confined at the nanometer scale B. Chakraborty, J. Kondev, C. Chamon, D. Reichman, Brandeis University DMR 0403997 Modeling microtubule dynamics Bounded growth Unbounded growth Distribution of microtubule lengths Microtubules are hollow cylindrical polymers which support the overall structure of cells and control fundamental cellular processes through a dynamical instability involving alternating polymerization and depolymerization. Paul Weinger, an undergraduate at Brandeis has been studying a simple model of microtubule dynamics in collaboration with Rajesh Ravindran (postdoctoral fellow) and Allison Ferguson (graduate student) This simple one-dimensional model exhibits a transition from a bounded to unbounded growth regime. As the phase boundary is approached the distribution of lengths and times of growth become broader and indicate a diverging length and time scale. The simple model is amenable to analytical treatment and can be extended to study the effect of cell boundaries on the dynamical instability Distribution of breakup times