Latest Research Projects

• Mitotic waves

  Post-fertilisation, a single-celled oocyte becomes an early embryo in a process termed “cleavage”, consisting of several rounds of rapid mitotic cell divisions, partitioning the large volume of the oocyte into thousands of somatic-sized cells and specifying the blueprint for subsequent embryo developments. It has also been observed that the timings of the cell divisions exhibit travelling wave like behaviours, known as mitotic waves. The waves emanate from the animal pole, the top of the embryo when oriented with respect to gravity, and travels towards the vegetal pole at the bottom. There is evidence suggesting that the local cell division cycles have different natural frequencies depending on their positions along the animal-vegetal axis. Remarkably, preliminary data showed that the mitotic waves persist without cell membranes, albeit with subtly different characteristics: the wavefronts are much smoother and more regular in cytokinesis-defective embryos. We thus hypothesize that, the absence of cell membranes enhances the coupling between neighbouring cells. This also constitutes an ideal model system to study the interaction between temporal oscillations and spatial cytoplasmic self-organisation, introducing a novel class of active matter model with a wide range of applications in other oscillatory biological systems such as somitogenesis and seminiferous cycles.

• Towards a liquid-state theory for active matter

  In equilibrium, the collective behaviour of particles interacting via steep, short-ranged potentials is well captured by the virial expansion of the free energy at low density. Here, we extend this approach beyond equilibrium to the case of active matter with self-propelled particles. Given that active systems do not admit any free-energy description in general, our aim is to build the dynamics of the coarse-grained density from first principles without any equilibrium assumption. Starting from microscopic equations of motion, we obtain the hierarchy of density correlations, which we close with an ansatz for the two-point density valid in the dilute regime at small activity. This closure yields the nonlinear dynamics of the one-point density, with hydrodynamic coefficients depending explicitly on microscopic interactions, by analogy with the equilibrium virial expan- sion. This dynamics admits a spinodal instability for purely repulsive interactions, a signature of motility-induced phase separation. Therefore, although our approach should be restricted to dilute, weakly-active systems a priori, it actually captures the features of a broader class of active matter.

• Phase waves in spermatogenesis

  In the epithelium of mouse seminiferous tubules, the production of mature sperm from undifferentiated stem cells occurs in a periodic fashion, known as the “seminiferous cycle”. During such a cycle, Sertoli cells change their function in accordance with the differentiation of germ cells under the regulation of retinoic acid (RA) signalling. In addition, the intensity of RA signalling has been observed to exhibit travelling phase waves along the length of the seminiferous tubules. Yet, the physical base of the phase wave is not understood. In this work, we construct a time-delayed model for the local cyclic behaviour, incorporating the feedback mechanisms between the RA concentration and germ line differentiation. Having established that the local model gives rise to sustained cycles, we propose a Kuramoto-type minimal model for the spatio-temporal phase profile and show that phase wave is a natural consequence of the model.

• Extension of Model AB

  To expand upon the systematic study of active reaction-diffusion systems, we also consider that the diffusive dynamics can break time reversal symmetry in its own right. This happens only at higher order in the gradient expansion, but is the leading behaviour without reactions present. We incorporate the higher gradient terms into Model AB and show that for slow reaction rates the system can undergo a new type of hierarchical microphase separation, which we call ‘bubbly microphase separation’. In this state, small droplets of one fluid are continuously created and absorbed into large droplets, whose length-scales are controlled by the competing reactive and diffusive dynamics. For further details, see my paper on Model AB+.

• Entropy production of scalar Langevin systems

  Motivated by the distinct non-equilibrium nature of active systems, we introduce the entropy production rate (EPR) as a quantitative measure of time reversal symmetry breaking. It can be defined either at particle level or at the level of coarse-grained fields such as den- sity; the EPR for the latter quantifies the extent to which these coarse-grained fields behave irreversibly. In this work, we first develop a general method to compute the EPR of scalar Langevin field theories with additive noise (this large class includes the aforementioned Model AB). Treating the scalar field φ as the sole observable, we arrive at an expression for the EPR that is non-negative for every field configuration and is quadratic in the time-antisymmetric component of the dynamics. Our general expression is a function of the quasipotential, which determines the full probability distribution for configurations, and is not generally calculable. To alleviate this difficulty, we present a small-noise expansion of the EPR, which only re- quires knowledge of the deterministic (mean-field) solution for the scalar field in steady state, which generally is calculable, at least numerically. We demonstrate this calculation for the case of Model AB. We then present a similar EPR calculation for Model AB with the con- servative and non-conservative contributions viewed as separately observable quantities. The results are qualitatively different, confirming that the field-level EPR depends on the choice of coarse-grained information retained within the dynamical description. For further details, see my paper on entropy production rate.

• Model AB -- a canonical model for phase-separating non-equilibrium systems with chemical reactions

  Active matter, characterised by their ability to inject energy into the environment locally, forms an important class of non-equilibrium systems. Recently there has been a surge of interests in active systems with chemical reactions, fuelled in particular by studies in biomolecular condensates, or ‘membraneless organelles’, within cells. In contrast to their passive coun- terparts, such systems have conserved and non-conserved dynamics that do not, in general, derive from a shared free energy. This mismatch breaks time-reversal symmetry (TRS) and leads to new types of dynamical competition that are absent in or near equilibrium. We construct a canonical scalar field theory to describe such systems, with conserved and non- conserved dynamics obeying Model B and Model A respectively (in the Hohenberg-Halperin classification), chosen such that the two free energies involved are incompatible. The resulting minimal model is shown to capture the various phenomenologies reported previously for more complicated models with the same physical ingredients, including microphase separation, limit cycles and droplet splitting. For further details, see my paper on Model AB.

• Active matter in general

  I gave a talk on Active Matter at the Trinity Mathematics Society symposium a couple of months back. It’s meant to be a popular science type introduction for Maths undergrads.