BBulk measurements only yield ensemble-averaged properties, masking the dynamic, individual behaviors of molecules. Single-molecule (SM) techniques overcome this limitation by exposing environmental heterogeneity and stochastic dynamics. In single-molecule fluorescence spectroscopy (SMFS), strongly fluorogenic substrates reveal "dynamic disorder"—temporal reaction rate fluctuations spanning several orders of magnitude. This phenomenon stems from slow conformational changes in single enzymes, and from size, shape, and surface restructuring in nanoparticles (NPs). To quantify these mechanisms, we developed a self-consistent pathway approach and a discrete-state stochastic framework using chemical master equations. This allows us to derive the probability distribution function (PDF) of stochastic reaction times across diverse catalytic systems, directly linking theoretical molecular mechanisms to experimental observables.

Polymer translocation plays a crucial role in many biological processes and has been a subject of several theoretical, experimental, and simulation studies. Translocation can be pore-driven case where an electric field acts on the monomers inside the pore. On the other hand, in the end-pulled case the polymer is pulled through a nanopore by either an optical or a magnetic tweezers. Previous studies indicate  that driven translocation processes are far-from-equilibrium phenomena and the quasi-equilibrium approximation does not hold during the translocation process. We develop a proper theoretical treatment of the end-pulled translocation based on the iso flux tension propagation theory and then generalizing this theory  to study the translocation dynamics of a pulled folded polymer through a nanopore that is relevant in understanding the translocation of double-strand DNA using solid state nanopores. We have performed extensive MD simulations of a coarse-grained bead-spring model to benchmark the theory. In the context of pore driven translocation, we explore the role of the polymer -pore interaction on the translocation induced by pore mutations, pH changes and salt concentration gradient using coarse grained molecular dynamics simulations.

One of the most critical aspects of protein-DNA interactions is the ability of protein molecules to find and recognize the targets on DNA . Theoretical studies supported by single molecule experiments indicate that the search process is a combination of three-dimensional motion of proteins in the bulk and one-dimensional sliding of protein on the DNA chain, a phenomenon called facilitated diffusion. Despite many experimental and simulation studies the complete understanding of the target search process is yet to be achieved. Onr major challenge is posed by the cellular environment, which is densely crowded by the presence of other proteins and macromolecules and an in-depth study is required to understand how cellular crowding affect the target search dynamics.We are interested in developing discrete state stochastic models that can mimic the cellular environment and calculate the target search time as a consequence of this crowded environment. Different aspects of cellular crowding such as inert and interacting crowders, static and mobile crowders are being incorporated in our theory. the impact of DNA conformation on the same is less explored. Apart from macromolecular crowding, we are also interested  to investigate the role of DNA conformations on the protein-DNA recognition process and also understand the target search dynamics in quorum sensing cells. 

Block copolymers composed of more than two kinds of chemically distinct polymers self-assemble into aggregates of different morphologies and finds potential applications in many practical fields, such as biomedicine, biomaterials, drug and gene delivery, tissue engineering and so on. Amphiphilic block polyelectrolytes, composed of charged hydrophilic blocks and neutral hydrophobic blocks  are capable of self-assembling into a diverse array of morphologies including micelles, lamellae, and vesicles. The self-assembled structures of block polyelectrolytes can undergo morphological transitions in response to minor changes in valency of counterions, temperature, pH, salt concentration, electric and magnetic fields. Computer simulations are a powerful tool for investigating the conformational behaviors of PEs . Due to the high computational cost, all-atom simulations are not suitable to simulate such large system sizes and long-time scales that are relevant to such systems. We use coarse-grained molecular dynamics simulations to investigate the different conformational  properties of diblock polyelectrolyte copolymers and their response to changes in salt concentration, counterion valency,  at different charge fractions. The self-assembly behaviors of diblock PEs in multivalent salt solutions and the reentrant behavior of the assembled micelles are investigated by molecular dynamics (MD) simulations.