Phase separation is a physical mechanism by which two mixed liquids form distinct phases, just as the oil separates from water to form droplets. This phenomenon occurs in many different scenarios, ranging from biological systems to quantum matter. Strikingly, it has been recently shown that liquid-liquid phase separation regulates a multitude of biochemical processes in living cells by creating molecular condensates. These condensates operate as versatile biochemical hubs intervening in several aspects of cellular processes, promoting or damping biological reactions. 

An important example of such condensates is the transcription factors (TF), proteins that bind to specific DNA sequences to regulate gene transcription. By forming phase-separated TF condensates the cell could promote gene expression at will. Although there has been some progress in understanding this phenomenon, studying phase separation in living nuclei at the required spatial and temporal resolution is extremely challenging. For this reason, the biophysics of transcription factor (TF) condensation remains highly unexplored with most experiments so far being restricted to either fixed cells or to in-vitro settings.

In a joint collaboration between the groups of Miguel Beato at CRG, Maciej Lewenstein and Maria Garcia-Parajo at ICFO, we investigated the physics of TF condensates by combining single-molecule experiments with theory and simulations. Using cutting-edge single molecule approaches and machine learning algorithms we followed the diffusion, growth dynamics, and sizes of a particular type of TF condensates in living cells. We found that at a short times, condensates grow in a classical fashion as any phase-separated system. Intriguingly, at longer times, the condensates stopped growing and remained as nanoscale-sized droplets. By developing a theoretical model and performing extensive simulations, we demonstrated that condensate growth dynamics and nanoscale-size arrested growth is regulated by molecular escaping from condensates. This mechanism of stochastic escaping provides an exquisite control of condensate size in nonequilibrium systems such as living cells.

Since the irruption of metal halide perovskites (MHPs) in the field of photovoltaics (PV) about a decade ago, these semiconductor materials have been the focus of attention worldwide. They triggered an intense research activity among scientists striving for a steady increase in energy conversion efficiencies, which have recently reached values beyond 25%. MHPs are really attractive because they are produced and processed by scalable, low-cost, energy-saving solution-based methods like organic semiconductors but they exhibit optoelectronic properties rivaling those of their inorganic counterparts. The nature of the peculiar optoelectronic properties underlying such astounding performance is still controversial. The existence of ferroelectricity in MHPs and its alleged impact on photovoltaic activity have fueled an intense debate, in which unanimous consensus is still far from being reached.

The aim of this work is two-fold: On one hand, we finally settle the controversy about ferroelectricity by exposing the main experimental and theoretical facts and revising their interpretation from the alternative point of view of ferroelasticity. In particular, we aim to convey the message that a ferroelectric polarization cannot be sustained when the A-site cation dynamics is fully unleashed, in frank contrast to the formation of ferroelastic domains. On the other hand, we discuss the possible impact of the ferroic behavior of MHPs on the charge-carrier generation and transport, taking into account the magnitude of the observed effects in comparison with competing ones like polaron formation and ion migration.