Sudipto Muhuri

The experimental use of micropatterned quasi-one-dimensional substrates has emerged as a useful experimental tool to study the nature of cell-cell interactions and gain insight on collective behavior of cell colonies. Inspired by these experiments, we propose an active spin model to investigate the emergent properties of the cell assemblies. The lattice gas model incorporates the interplay of self-propulsion, polarity directional switching, intracellular attraction, and contact Inhibition Locomotion (CIL). In the absence of vacancies, which corresponds to a confluent cell packing on the substrate, the model reduces to an equilibrium spin model that can be solved exactly. In the presence of vacancies, the clustering is controlled by a dimensionless Peclét Number, Q-the ratio of magnitude of self-propulsion rate to directional switching rate of particles. In the absence of CIL interactions, we invoke a mapping to Katz-Lebowitz-Spohn model to determine an exact analytical form of the cluster size distribution in the limit Q≪1. In the limit of Q≫1, the cluster size distribution exhibits a universal scaling behavior (in an approximate sense), such that the distribution function can be expressed as a scaled function of Q, particle density, and CIL interaction strength. We characterize the phase behavior of the system in terms of contour plots of average cluster size. These measures exhibit a nonmonotonic dependence on CIL interaction strength, attractive interaction strength, and self-propulsion.

A theoretical study of cargo transport by dynein motors in an optical trap shows non-trivial transport behaviour due to the dynein catch bond. We compare our model with experimental data to estimate the force scale at which the catch bond sets in.

Dynein motors exhibit catch bonding, where the unbinding rate of the motors from microtubule filaments decreases with increasing opposing load. The implications of this catch bond on the transport properties of dynein-driven cargo are yet to be fully understood. In this context, optical trapping assays constitute an important means of accurately measuring the forces generated by molecular motor proteins. We investigate, using theory and stochastic simulations, the transport properties of cargo transported by catch bonded dynein molecular motors - both singly and in teams - in a harmonic potential, which mimics the variable force experienced by cargo in an optical trap. We estimate the biologically relevant measures of first passage time - the time during which the cargo remains bound to the microtubule and detachment force -the force at which the cargo unbinds from the microtubule, using both two-dimensional and one-dimensional force balance frameworks. Our results suggest that even for cargo transported by a single motor, catch bonding may play a role depending on the force scale which marks the onset of the catch bond. By comparing with experimental measurements on single dynein-driven transport, we estimate realistic bounds of this catch bond force scale. Generically, catch bonding results in increased persistent motion, and can also generate non-monotonic behaviour of first passage times. For cargo transported by multiple motors, emergent collective effects due to catch bonding can result in non-trivial re-entrant phenomena wherein average first passage times and detachment forces exhibit non-monotonic behaviour as a function of the stall force and the motor velocity.

Experiments performed using micro-patterned one dimensional collision assays have allowed a precise quantitative analysis of the collective manifestation of contact inhibition locomotion (CIL) wherein, individual migrating cells reorient their direction of motion when they come in contact with other cells. Inspired by these experiments, we present a discrete, minimal 1D Active spin model that mimics the CIL interaction between cells in one dimensional channels. We analyze the emergent collective behaviour of migrating cells in such confined geometries, as well as the sensitivity of the emergent patterns to driving forces that couple to cell motion. In the absence of vacancies, akin to dense cell packing, the translation dynamics is arrested and the model reduces to an equilibrium spin model which can be solved exactly. In the presence of vacancies, the interplay of activity-driven translation, cell polarity switching, and CIL results in an exponential steady cluster size distribution. We define a dimensionless Péclet number Q - the ratio of the translation rate and directional switching rate of particles in the absence of CIL. While the average cluster size increases monotonically as a function of Q, it exhibits a non-monotonic dependence on CIL strength, when the Q is sufficiently high. In the high Q limit, an analytical form of average cluster size can be obtained approximately by effectively mapping the system to an equivalent equilibrium process involving clusters of different sizes wherein the cluster size distribution is obtained by minimizing an effective Helmholtz free energy for the system. The resultant prediction of exponential dependence on CIL strength of the average cluster size and Q^{1/2} dependence of the average cluster size is borne out to reasonable accuracy as long as the CIL strength is not very large.

Experiments performed using micro-patterned one dimensional collision assays have allowed a precise quantitative analysis of the collective manifestation of contact inhibition locomotion (CIL) wherein, individual migrating cells reorient their directionof motion when they come in contact with other cells. Inspired by these experiments, we present a discrete, minimal 1D Active spin model that mimics the CIL interaction between cells in one dimensional channels. We analyze the emergent collective behaviour of migrating cells in such confined geometries, as well as the sensitivity of the emergent patterns to driving forces that couple to cell motion. In the absence of vacancies, akin to dense cell packing, the translation dynamics is arrested and the model reduces to an equilibrium spin model which can be solved exactly. In the presence of vacancies, the interplay of activity-driven translation, cell polarity switching, and CIL results in an exponential steady cluster size distribution. We define a dimensionless Péclet number Q - the ratio of the translation rate and directional switching rate of particles in the absence of CIL. While the average cluster size increases monotonically as a function of Q, it exhibits a non-monotonic dependence on CIL strength, when the Q is sufficiently high. In the high Q limit, an analytical form of average cluster size can be obtained approximately by effectively mapping the system to an equivalent equilibrium process involving clusters of different sizes wherein the cluster size distribution is obtained by minimizing an effective Helmholtz free energy for the system. The resultant prediction of exponential dependence on CIL strength of the average cluster size and Q^1/2 dependence of the average cluster size is borne out to reasonable accuracy as long as the CIL strength is not very large.

We study the cluster size distribution of particles for a two-species exclusion process which involves totally asymmetric transport process of two oppositely directed species with stochastic directional switching of the species on a 1D lattice. As a function of Q - the ratio of the translation rate and directional switching rate of particles, in the limit of Q → 0, the probability distribution of the cluster size is an exponentially decaying function of cluster size m and is exactly similar to the cluster size distribution of a TASEP. For Q >> 1, the model can be mapped to persistent exclusion process (PEP) and the average cluster size, 〈 m 〉 ∝ Q ^1/2 . We obtain an approximate expression for the average cluster size in this limit. For finite system size system of L lattice sites, for a particle number density ρ , the probability distribution of cluster sizes exhibits a distinct peak which corresponds to the formation of a single cluster of size m _s = ρL . However this peak vanishes in the thermodynamic limit L → ∞. Interestingly, the probability of this largest size cluster, P ( m _s ), exhibits scaling behaviour such that in terms of scaled variable Q ₁ ≡ Q / L ² ρ (1 − ρ ), data collapse is observed for the probability of this cluster. The statistical features related to clustering observed for this minimal model may also be relevant for understanding clustering characteristics in active particles systems in confined 1D geometry.