Stochastic particle unbinding modulates growth dynamics and size of transcription factor condensates in living cells.

Liquid-liquid phase separation (LLPS) is emerging as a key physical principle for biological organization inside living cells, forming condensates that play important regulatory roles. Inside living nuclei, transcription factor (TF) condensates regulate transcriptional initiation and amplify the transcriptional output of expressed genes. However, the biophysical parameters controlling TF condensation are still poorly understood. Here we applied a battery of single-molecule imaging, theory, and simulations to investigate the physical properties of TF condensates of the progesterone receptor (PR) in living cells. Analysis of individual PR trajectories at different ligand concentrations showed marked signatures of a ligand-tunable LLPS process. Using a machine learning architecture, we found that receptor diffusion within condensates follows fractional Brownian motion resulting from viscoelastic interactions with chromatin. Interestingly, condensate growth dynamics at shorter times is dominated by Brownian motion coalescence (BMC), followed by a growth plateau at longer timescales that result in nanoscale condensate sizes. To rationalize these observations, we extended on the BMC model by including the stochastic unbinding of particles within condensates. Our model reproduced the BMC behavior together with finite condensate sizes at the steady state, fully recapitulating our experimental data. Overall, our results are consistent with condensate growth dynamics being regulated by the escaping probability of PR molecules from condensates. The interplay between condensation assembly and molecular escaping maintains an optimum physical condensate size. Such phenomena must have implications for the biophysical regulation of other nuclear condensates and could also operate in multiple biological scenarios.

Learning how to find targets in the micro-world: the case of intermittent active Brownian particles.

Finding the best strategy to minimize the time needed to find a given target is a crucial task both in nature and in reaching decisive technological advances. By considering learning agents able to switch their dynamics between standard and active Brownian motion, here we focus on developing effective target-search behavioral policies for microswimmers navigating a homogeneous environment and searching for targets of unknown position. We exploit projective simulation, a reinforcement learning algorithm, to acquire an efficient stochastic policy represented by the probability of switching the phase, i.e. the navigation mode, in response to the type and the duration of the current phase. Our findings reveal that the target-search efficiency increases with the particle's self-propulsion during the active phase and that, while the optimal duration of the passive case decreases monotonically with the activity, the optimal duration of the active phase displays a non-monotonic behavior.

Inferring pointwise diffusion properties of single trajectories with deep learning.

To characterize the mechanisms governing the diffusion of particles in biological scenarios, it is essential to accurately determine their diffusive properties. To do so, we propose a machine-learning method to characterize diffusion processes with time-dependent properties at the experimental time resolution. Our approach operates at the single-trajectory level predicting the properties of interest, such as the diffusion coefficient or the anomalous diffusion exponent, at every time step of the trajectory. In this way, changes in the diffusive properties occurring along the trajectory emerge naturally in the prediction and thus allow the characterization without any prior knowledge or assumption about the system. We first benchmark the method on synthetic trajectories simulated under several conditions. We show that our approach can successfully characterize both abrupt and continuous changes in the diffusion coefficient or the anomalous diffusion exponent. Finally, we leverage the method to analyze experiments of single-molecule diffusion of two membrane proteins in living cells: the pathogen-recognition receptor DC-SIGN and the integrin α5ß1. The analysis allows us to characterize physical parameters and diffusive states with unprecedented accuracy, shedding new light on the underlying mechanisms.

Objective comparison of methods to decode anomalous diffusion.

Deviations from Brownian motion leading to anomalous diffusion are found in transport dynamics from quantum physics to life sciences. The characterization of anomalous diffusion from the measurement of an individual trajectory is a challenging task, which traditionally relies on calculating the trajectory mean squared displacement. However, this approach breaks down for cases of practical interest, e.g., short or noisy trajectories, heterogeneous behaviour, or non-ergodic processes. Recently, several new approaches have been proposed, mostly building on the ongoing machine-learning revolution. To perform an objective comparison of methods, we gathered the community and organized an open competition, the Anomalous Diffusion challenge (AnDi). Participating teams applied their algorithms to a commonly-defined dataset including diverse conditions. Although no single method performed best across all scenarios, machine-learning-based approaches achieved superior performance for all tasks. The discussion of the challenge results provides practical advice for users and a benchmark for developers.