Tissue Hydrodynamics
Project | 01
Epithelial tissues mainly consist of two components: cells and interstitial fluid. A hydrodynamic continuum model of an epithelium with two components has been developed in https://www.pks.mpg.de/mpi-doc/julichergruppe/julicher/Tdwp2012.pdf. In a collaboration with F. Jülicher and J. Prost, I have extended this model to the case where cells can pump fluid through the epithelium. Consequently, we have used this model to describe the dynamics of the epithelial tissue and how this dynamics depends on the cellular pumping activity and on the rate at which external fluid is pumped through the tissue. We have then further generalized this model in order to account for a voltage drop across the epithelium. Recently, we have started to look at the dynamics of epithelia in different geometries: we are now comparing planar tissues with spherical tissues. In these models I have characterized the conditions for which epithelia develop a stable stationary state of finite thickness. Our theoretical results about the instantaneous velocity, the stress, the cell division rate and the apoptosis rate can be tested in in-vitro experiments of epithelial tissues.
In a future work I would like to study the thickness fluctuations of epithelia using linear response theory.
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Field induced cell proliferation and apoptosis in a thick epithelium, NS, Jacques Prost, Frank Jülicher, (2018) (soon to be submitted)
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Field induced lumen nucleation and oscillation in a spherical epithelium, Charlie Duclut, NS, Jacques Prost, Frank Jülicher, (2018) (manuscript under preparation)
Mechanosensing of cells
Project | 02
Caveolae are omega shaped invaginations in cell membranes formed by caveolin proteins and neck proteins. Caveloin proteins are a family of transmembrane proteins with an unusual hairpin like structure that serve as mechanoregulators of cell membrane tension. Equilibrium models of caveolae describe the formation of caveolae as a thermodynamic phase transition which affects the mechanical properties of the membrane https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1304058/. It is however not well understood what is the role of neck proteins in the formation of the omega shaped invaginations.
In order to investigate the role of the neck proteins in the regultion of the membrane tension and the formation of caveloae, I have developed, in collaboration with Pierre Sense, a continuum description of a membrane that contains neck proteins and caveolins. I have constructed the free energy of this system which incorporates the membrane-mediated interactions between neck proteins and caveolins. I have computed the phase diagram of this model, and I have used this phase diagram to describe the formation of caveolae as a function of the protein densities, the bending rigidity and the tension of the membrane.
These results can be compared with experimental data, which describes the formation of cavealae and membrane invaginations after an osmotic shock.
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Mechanosensing by caveolae in the presence of neck proteins, NS, Pierre Sens, (2018) (manuscript under preparation)
Giant fluctuations in polar ordered active particles
Project | 03
We consider a two-dimensional (2D) polar ordered active flock on a solid substrate, immersed in an isotropic bulk fluid. This may potentially model a mictrobule assay with motors in a fluid. We study the stability of the ordered phase and find that for proper choices of the model parameters, the long-range polar order indeed survives noises and fluctuations. We study the correlation function of the active particle concentrations and show that they display giant number fluctuations, observed in 2D dry polar flocks in earlier studies. Nonetheless, the mean number dependence of the giant number fluctuations in our case is different from the well-known results for 2D dry flocks. These differences are due to the hydrodynamic interactions mediated by the bulk fluid.
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Swarming Bottom feeders: Flocking at solid-liquid interfaces, NS, Abhik Basu, John Toner (2018) (manuscript under preparation)
Phases of asymmetric tethered membranes
Project | 04
We develop the elastic theory for inversion-asymmetric tethered membranes and use it to identify and study their possible phases. Asymmetry in a tethered membrane causes spontaneous curvature, which in general depends upon the local in-plane dilation of the tethered network. This in turn leads to long-ranged interactions between the local mean and Gaussian curvatures, which is not present in symmetric tethered membranes. This interplay between asymmetry and Gaussian curvature leads to a new double-spiral phase not found in symmetric tethered membranes. At temperature T = 0, tethered membranes of arbitrarily large size are always rolled up tightly into a conjoined pair of Archimedes’ spirals. At finite T this spiral structure swells up significantly into algebraic spirals characterized by universal exponents which we calculate. These spirals have long range orientational order, and are the asymmetric analogs of statistically flat symmetric tethered membranes. We also find that sufficiently strong asymmetry can trigger a structural instability leading to crumpling of these membranes as well. This provides a new route to crumpling for asymmetric tethered membranes. We calculate the maximum linear extent Lc beyond which the membrane crumples, and calculate the universal dependence of Lc on the membrane parameters. By tuning the asymmetry parameter, Lc can be continuously varied, implying a scale-dependent crumpling. Our theory can be tested on controlled experiments on lipids with artificial deposits of spectrin filaments, in-vitro experiments on red blood cell membrane extracts, and on graphene coated on one side.
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Rolled up, or crumpled: phases of asymmetric tethered membranes, Tirthankar Banerjee, NS, Abhik Basu, John Toner (2018) (soon to be submitted)
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Statistical mechanics of asymmetric tethered membranes: spiral and crumpled phases, Tirthankar Banerjee, NS, Abhik Basu, John Toner (2018) (soon to be submitted)
Statistical mechanics of asymmetric inhomogeneous fluid membranes
Project | 05
An asymmetric inhomogeneous membrane can be a fluid or tethered membrane which is asymmetric under inversion of the mebrane and has some compositional degrees of freedom residing on it which gives rise to inhomogeneties. In an asymmetric inhomogeneous fluid membrane, we have studied the miscibility phase transition (MPT), from high temperature homogeneous phase to a low temperature inhomogeneous phase using Renormalization Group (RG) technique. The asymmetry comes from the fact that the free energy of the system is not invariant under the inversion of membrane height. We have found enhanced fluctuations for the membrane height field (modelled as a fluid membrane using the Mongue gauge), which is coupled
to the inhomogeneous degrees of freedom maintaining certain symmetries, which dictate the fluctuation properties. If the coupling is ignored our free energy dictates the universal properties of a symmetric membrane which follows a continuous phase transition with fluctuations dictated by 2D Ising universality class. In case of asymmetric membranes, we find that the phase transition can be of first order or second order in nature and connected via a tricritical point. In case of second order transition, we also get a nontrivial stable fixed point to which the RG flow lines are directed. The coupling of membrane height with the inhomogeneous degrees of freedom results in the effective bending rigidity of the membrane to be less than that of a pure fluid membrane and hence giving rise to a softer membrane. The degree of softness is found to be dependent on the coupling used.
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Phases and fluctuations in a model for asymmetric inhomogeneous fluid membranes, NS, Abhik Basu, Phys. Rev. E, 88(4), 042106, (2013)
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Phase transitions and membrane stiffness in a class of asymmetric heterogeneous fluid membranes, NS, Abhik Basu, J. Stat. Mech, (8), P08023, (2015)
Nonequilibrium steady states in totally asymmetric simple exclusion process on a ring
Project | 06
The totally asymmetric simple exclusion process is a nonequilibrium transport processes of particles hopping unidirectionally along a one-dimensional chain and with excluded volume interactions. The totally asymmetric simple exclusion process serves as a paradigmatic model for nonequilibrium systems that have particle-particle interactions. On a ring, the stationary state of the totally asymmetric simple exclusion process is known, and it is given by a homogeneous (flat) density profile. On the contrary, exclusion processes on a ring with defects exhibits an inhomogeneous density profile, as we have shown in https://journals.aps.org/pre/abstract/10.1103/PhysRevE.90.022109, http://iopscience.iop.org/article/10.1088/1742-5468/2015/01/P01024/meta. Interestingly, depending on the number of defects, the totally asymmetric exclusion process can exhibit either localized domain walls or delocalized domain walls. Moreover, we have found that the stronger defect screens the weaker ones; this is a universal feature in case of many point defects. An interesting question that remains is what happens to the density profiles and phases if there is an exchange of particles with a reservoir through the attachment and detachment of particles. This process serves as a model of motor proteins with finite processivity. Many efforts have already been made in this direction https://journals.aps.org/pre/abstract/10.1103/PhysRevE.92.022121. It would be interesting to extend our model of ring TASEP with symmetrically placed defects in a LK medium, where the paricle attachment/detachment is allowed. This is going to modify the defect induced phase transition found in by particle nonservation, giving rise to new phases. The competing dynamics of the point defects and the LK is expected to give us a rich phase diagram depending on the strength of the two defects and the attachment/detachment rate of the particles.
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Nonequilibrium steady states in asymmetric exclusion processes on a ring with bottlenecks, NS, Abhik Basu, Phys. Rev. E, 90(2), 022109, (2014)
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Generic nonequilibrium steady states in an exclusion process on an inhomogeneous ring, Tirthankar Banerjee, NS, Abhik Basu, J. Stat. Mech, (1), P01024, (2015)
Universality in a class of active-to-absorbing phase transition models
Project | 07
In the broad area of active to absorbing phase transitions (AAPTs), we have studied how the fluctuating properties of a percolating field at the critical field of an AAPT belonging to the DP universality class, are affected by coupling to environmental fluctuations, with or without feedback. We have analyzed the crtitical behaviour of this coupled system using Renormalization Group (RG) technique, and found different fixed points, to which the flow lines can be directed. More specifically, the scaling behaviour of the system near the extinction point of the AAPT depends on the regime of the phase space in which it is located, and based on that, the system may exhibit strong dynamic scaling (when the system shows non-DP like scaling behaviour), or weak dynamic scaling when the system falls under the DP universality class.
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Active-to-absorbing-state phase transition in an evolving population with mutation, NS, Phys. Rev. E, 92(4), 042110, (2015)
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Active to absorbing state phase transition in the presence of a fluctuating environment: feedback and universality, NS, Abhik Basu, J. Stat. Mech, (8), P08016, (2014)
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Active-to-absorbing-state phase transition in the presence of fluctuating environments: Weak and strong dynamic scaling, NS, Abhik Basu, Phys. Rev. E, 86(2), 021122, (2012)
Fluctuations and instabilities in active gels
Project | 08
Active matter consists of systems driven out of equilibrium by an energy source, which breaks the fluctuation dissipation theorem. Hydrodynamic models for active systems is now an active field of research where collective behaviour of these systems can be determined using symmetries and conservation laws, which govern their dynamics. We have been interested in studying the hydrodynamics of cytoskeletal filaments in eukaryotic cells. A cortical layer of actin filaments has viscoelastic properties which can be modelled in a coarse grained continuum description using a viscoelastic active gel model. We used Onsager's principles to write down the linearised flux-force relations between the generalised fluxes and forces of the system using symmetries and conservation laws. The active particles can have a nematic symmetry (system invariant under inversion of orientation direction of the active particles), or a polar symmetry (not invariant under inversion of particle orientation), which dictates the final equations of motion for the system. We have written down the force balance equations maintaining the symmetries of the system and studied the dynamics and fluctuations of the linearised system and analysed the linear stability in two dimensions. It is found that the strength of the activity which is included as a paramter in the model dictates whether the system is stable or unstable depending on its signature, and there may also be propagating waves, giving rise to moving instabilities and pattern formation.
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Role of interfacial friction for flow instabilities in a thin polar-ordered active fluid layer, NS, Abhik Basu, Phys. Rev. E, 92(5), 052306, (2015)
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Generic instabilities in a fluid membrane coupled to a thin layer of ordered active polar fluid, NS, Abhik Basu, Eur. Phys. J. E, 36(8), 1-11, (2013)
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Instabilities and diffusion in a hydrodynamic model of a fluid membrane coupled to a thin active fluid layer, NS, Abhik Basu, Eur. Phys. J. E, 35(11), 1-14, (2012)
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Fluctuations and symmetries in two-dimensional active gels, NS, Abhik Basu, Eur. Phys. J. E, 34(4), 1-22, (2011)