M1/M2 internship : Signature of out-of-equilibrium dynamics in a partially observed system

M1/M2 internship : Signature of out-of-equilibrium dynamics in a partially observed system

There are numerous challenges in statistically testing whether a dynamic system displays out-of-equilibrium dynamics from experimental recordings.  Commonly, we have access to only some, but not all, relevant degrees of freedom of the dynamic system, which increases the difficulty of the already challenging inference task. For example, we can record the motion of a fluorescent particle in a cell but do not have direct access to the dynamics of the cellular structures with which it interacts. Inspired by the developments of Battle et al.¹, we aim to show that a statistical signature of out-of-equilibrium dynamics can be detected in a partially observed system.  
Focusing on the classic dumbbell with two coupled particles driven by Brownian noise at different temperatures, the intern will develop a spectral Bayesian^2–4 approach to reliably detect out-of-equilibrium dynamics from the trajectory of a single particle⁵. We will study the statistical properties of this inference and discuss future extensions.

References

1. Battle, C. et al. Broken detailed balance at mesoscopic scales in active biological systems. Science 352, 604–607 (2016).

2. Serov, A. S. et al. Statistical Tests for Force Inference in Heterogeneous Environments. Sci Rep 10, 3783 (2020).

3. Laurent, F. et al. TRamWAy: mapping physical properties of individual biomolecule random motion in large-scale single-particle tracking experiments. Bioinformatics 38, 3149–3150 (2022).

4. Beheiry, M. E., Dahan, M. & Masson, J.-B. InferenceMAP: mapping of single-molecule dynamics with Bayesian inference. Nat Methods 12, 594–595 (2015).

5. Vestergaard, C. L. Optimizing Experimental Parameters for Tracking of Diffusing Particles. Phys. Rev. E 94, 1–17 (2016).

Scientific or technical background required for work program

The successful intern should have one of the following backgrounds:

• statistical or condensed matter physics, applied mathematics, 
• or statistics. 

Some fluency in Python and large-scale simulations is expected.