We are interested in the way chromatin organizes inside the nucleus, and in particular how cellular activities define chromatin conformation and how this can affect the transcriptional regulation. In this project the focus is loop extrusion, a process that has been proposed to control transcription, and consists in the activity of a molecular motor (cohesin) that extrudes loops in the chromosomes of mammalian cells. We want to discover how activities define chromosome shapes, and how shapes can encode for memory and affect cell behavior.
In this context, we are developing two simulation Python packages, polyFlux and simLoop, to perform theoretical studies and make predictions for experiments. The two packages play complementary roles in our simulation framework: simLoop is a flexible implementation of the Gillespie algorithm that can realize different dynamics of the cohesin proteins on DNA, while polyFlux is a powerful innovative numerical approach that performs polymer simulations using the Rouse model and predicts full probability distribution functions by solving the Einstein-Smoluchovsky equation for this stochastic process. A problem that has a solution in linear algebra calculations of large matrices. This tool is currently implemented to run on CPUs and GPUs, and has the ambition of outperform molecular simulations.
We propose an internship in Computational or Theoretical Physics to develop, test and utilize polyFlux in order to optimize it to its full potential. The student will chose and work towards one or more of the following objectives:
- Work on the eigenvalue problem for a real symmetric positive matrix. Study the general problem and devise optimisations to exploit additional information available.*
- Replace the implementation of the algorithm to use banded or sparse matrices instead of dense matrices. Possibly devising perturbation approaches.*†
- Expand the Rouse model by more general linear models. Currently the beta model is working and implemented, to introduce viscoelastic effects of the nucleoplasm and hydrodynamic interactions.†
- Introduce spherical confinement.†
We search an enthusiast intern driven by the curiosity for modelling biology, with theoretical/computational physics or applied mathematics backgrounds. Experience of Python and the Numpy package programming is required. The work will be supervised by Vittore Scolari and Antoine Coulon at the Institut Curie. The intern will experience a dynamic interdisciplinary research context by being included in the activities of the Nuclear Dynamics and Physico-Chemical units of Institut Curie.
* Objective that requires mostly computational skills
† Objective that requires mostly theoretical skills
