Traditional bulk measurements yield only 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 that span several orders of magnitude. This phenomenon arises from slow conformational changes in single enzymes, as well as size, shape, and surface restructuring in inorganic nanoparticles. To map these chaotic, real-time behaviors, our lab developed a unique self-consistent pathway approach and a discrete-state stochastic framework using chemical master equations. This allows us to mathematically predict reaction-time distributions, directly linking deep molecular mechanisms to real-world experimental data

Polymer translocation is fundamental to numerous biological processes and remains a major focus of theoretical, experimental, and simulation research. While pore-driven translocation relies on an electric field acting within the channel, end-pulled translocation involves pulling the polymer using optical or magnetic tweezers. Because driven translocation is a distinct far-from-equilibrium phenomenon, quasi-equilibrium approximations fail to capture its dynamics. To address this, we develop a rigorous theoretical framework for end-pulled translocation using isoflux tension propagation (IFTP) theory. We then extend this model to analyze the translocation of folded polymers, which directly informs the behavior of double-stranded DNA in solid-state nanopores. We benchmark our theory using extensive coarse-grained, bead-spring molecular dynamics (MD) simulations. Additionally, we employ these MD simulations to investigate how polymer-pore interactions influence translocation under varying environmental conditions, including pore mutations, pH shifts, and salt concentration gradients.

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 proteins on the DNA chain, a phenomenon called facilitated diffusion. Despite many experimental and simulation studies, a complete understanding of the target search process is yet to be achieved. One 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 affects 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 and 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 in investigating the role of DNA conformations in the protein-DNA recognition process and understanding 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 find potential applications in many practical fields; these materials hold incredible potential for cutting-edge fields like biomedicine, drug and gene delivery, and tissue engineering.  Amphiphilic block polyelectrolytes—which contain both charged and neutral blocks—can shift their shapes between micelles, lamellae, and vesicles. These structures are incredibly sensitive, changing their morphology in response to tiny shifts in pH, temperature, salt concentration, and counterion valency. Computer simulations are a powerful tool for investigating the conformational behaviors of PEs. Predicting these shifts using all-atom simulations is computationally impossible at large scales. To solve this, our lab uses coarse-grained molecular dynamics (MD) simulations. We model how diblock polyelectrolyte copolymers respond to changing environments, allowing us to map their unique self-assembly pathways and discover fascinating properties like reentrant micelle behaviors in multivalent salt solutions.