Recently we investigated the problem of chromosome alignment for recombination during meiosis (with Frank Jülicher, MPI-PKS and Iva Tolić, RBI). This distinct biological problem appeared to be linked to a gold-mine of statistical physics problems. We first could reduce the original problem to finding the conformation of pinned polymer loops under constant external force (see figure). This in turn can be formulated in the language of random walks and Brownian bridges. Surprisingly the found analytical solution relied on the Fermi-Dirac statistics. In order to study the relaxation dynamics of such polymer loops, we used the mapping to the particle system of asymmetric exclusion process (ASEP), which in turn can be solved by using the Bethe Ansatz methodology. Further analogy can be drawn to the single-file diffusion in the finite domain with reflecting boundaries. This work is in progress and it shows that very seemingly distant approaches of statistical physics can be used to analytically attack problems motivated by concrete biological questions.
Exactly solvable dynamics of forced polymer loops; W. Huang, Y.T. Lin, D. Froemberg, J. Shin, F. Jülicher, and V. Zaburdaev
New Journal of Physics, 20 113005 (2018)
Live cell X-ray imaging of autophagic vacuoles formation and chromatin dynamics in fission yeast;
N. Strelnikova, N. Sauter, M. Guizar-Sicairos, M. Göllner, A. Diaz, P. Delivani, M. Chacón, I. M. Tolić, V. Zaburdaev, and T. Pfohl,
Scientific Reports 7,13775 (2017)
Pulled Polymer Loops as a Model for the Alignment of Meiotic Chromosomes; Y.T. Lin, D. Frömberg, W. Huang, P. Delivani, M. Chacón, I. M. Tolić, F. Jülicher, and V. Zaburdaev, Phys. Rev. Lett. 115, 208102 (2015)