This wordle briefly summarizes my current research interests. Mostly, it involves creating experimentally consistent theories on problems in Biophysics. As of now, I deal with problems related to Cancer and Molecular Motors.

1) Cancer

1.1) Motility of Tumor Cells (active matter)

• Collective migration dominates many phenomena, from cell movement in living systems to abiotic self-propelling particles. Focusing on the early stages of tumor evolution, we enunciate the principle involved in cell dynamics and highlight their implications in understanding similar behavior in seemingly unrelated soft glassy materials and possibly chemokine-induced migration of CD8+ T cells. We performed simulations of tumor invasion using a minimal three-dimensional model, accounting for cell elasticity and adhesive cell-cell interactions as well as cell birth and death to establish that cell growth rate-dependent tumor expansion results in the emergence of distinct topological niches. Cells at the periphery move with higher velocity perpendicular to the tumor boundary, while motion of interior cells is slower and isotropic. The mean square displacement, Δ(t), of cells exhibits glassy behavior at times comparable to the cell cycle time, while exhibiting super-diffusive behavior, Δ(t)=t^a (α>1), at longer times. We derive the value of α =1.33 using a field theoretic approach based on stochastic quantization. In the process we establish the universality of super-diffusion in a class of seemingly unrelated non-equilibrium systems. Super diffusion at long times arises only if there is an imbalance between cell birth and death rates. Our findings for the collective migration, which also suggests that tumor evolution occurs in a polarized manner, are in quantitative agreement with in vitro experiments. Although set in the context of tumor invasion the findings should also hold in describing collective motion in growing cells and in active systems where creation and annihilation of particles play a role.

Under Review: Abdul N Malmi-Kakkada, Xin Li, Himadri Samanta, Sumit Sinha and D. Thirumalai, “Cell growth rate dictates the onset of glass to fluid-like transition and long-time super-diffusion in an evolving cell colony.”, Phys. Rev. X 8, 021025. (2018)

1.2) Intra-Tumor Heterogeneity

• Due to advent of multi-region sequencing technologies, it is now well established that there is widespread intra-tumor heterogeneity (ITH) both genetically and phenotypically. Due to ITH, traditional biopsy techniques, where limited subsample of tumor cells are investigated, seem redundant. To address this problem of extensive ITH, we develop a 3-D cellular automata model for tumor evolution and characterize the evolution under two regimes: Branched and Big Bang. The characterization of tumor evolution is based on 3 parameters: initial birth probability (α_o), mutation rate (μ) and fitness (s_d). Using the mentioned parameters as coordinates, we illustrate cancer evolution phase diagram where we demarcate Branched and Big Bang cancer evolution. Then, we develop a quantitative measure to estimate the ITH and also the mean clone size. We conclude that on an average, ITH is higher in Branched evolution and sub-clone size is larger in Big Bang evolution.

Under Preparation: Sumit Sinha, Xin Li, Abdul N Malmi-Kakkada and D. Thirumalai, “Intra-tumor heterogeneity under various evolution modes in cancer.”

1.3) Role of E-Cadherin

• The physical mechanism behind the role of cell-cell adhesion on proliferation, invasion and drug resistance as of yet unclear. Many questions such as how do the forces exerted by the cells on another influence their overall growth and proliferation are still unclear. In this work, we present results pointing to a biphasic dependence between proliferation and cell-cell adhesion. The existence of biphasic dependence of cell migration on attachment to the extracellular matrix is well known. However, such a biphasic relationship depending on cell-cell adhesion has not been proposed as of yet to our knowledge. Here, we report that increasing cell-cell adhesion from low levels causes the tumor proliferative capacity to increase. As cell-cell adhesion is increased, however, beyond an optimal level, proliferation is seen to markedly decrease. We identify an intermediate level of adhesion whereby invasiveness and proliferation are maximized as more generally biphasic relationships give clues towards optimality in terms of control of biological processes. We provide a physical picture of the role of cell-cell adhesion in the context of development, cancer metastasis and invasion consistent with a theoretical biophysical model for cell proliferation taking into account cell-cell adhesion forces and critical pressure experienced by cells.

Under Preparation: Abdul N Malmi-Kakkada, Xin Li, Sumit Sinha and D. Thirumalai, “Differential E-cadherin expression drives nonlinear proliferation behavior influenced by optimal cell packing within tissues.”

2) Molecular Motors

2.1) Traffic like model of RNA Polymerase

• In this work, we studied the flux of totally asymmetric simple exclusion processes (TASEPs) on twin co-axial square tracks. In this biologically motivated model the particles in each track act as mobile bottlenecks against the movement of the particles in the other although the particles are not allowed to move out of their respective tracks. So far as the outer track is concerned, the particles on the inner track act as bottlenecks only over a set of fixed segments of the outer track, in contrast to site-associated and particle-associated quenched randomness in the earlier models of disordered TASEP. In a special limiting situation, the movement of particles in the outer track mimics a TASEP with a “point-like” immobile (i.e. quenched) defect where phase segregation of the particles is known to take place. The length of the inner track as well as the strength and number density of the mobile bottlenecks moving on it are the control parameters that determine the nature of spatiotemporal organization of particles on the outer track. Variation of these control parameters allows variation of the width of the phase-coexistence region on the flux–density plane of the outer track. Some of these phenomena are likely to survive even in the future extensions intended for studying traffic-like collective phenomena of polymerase motors on double-stranded DNA.

Publication: Sumit Sinha and Debashish Chowdhury. "TASEP on parallel tracks: Effects of mobile bottlenecks in fixed segments.", Physica A: Statistical Mechanics and its Applications, 430, 254-262. (2015)