This project is inspired by this rather puzzling observation: small cells, such as bacteria, have signaling machinery that transmit signals diffusively in one or two steps, whereas relatively larger cells, such as eukaryotes, usually transmit signal through diffusion or drift through multiple intermediate steps. This observation led me to question whether the size of a cell and the mode of transport of the signal carriers influence the architecture of the signaling network that transmits the received signal.

Most biological reactions occur on 2D surfaces, where the peculiarities of diffusion lead to chemical reaction rates that depend nontrivially on the reactant concentrations. However, it is usually assumed that reaction rates are independent of concentration. It remains unclear whether or not such discrepancies lead to any nontrivial consequences. Seeking to better understand this question, my investigation finds that this concentration dependence indeed has a profound impact on the behavior of nonequilibrium chemical systems, an essential building block of all cell-signaling systems.

Ras is a small protein that regulates many important cellular functions, including cell proliferation, growth, and differentiation. Due to its ubiquity in cell-regulation, mutated Ras causes many diseases, including cancer. Despite significant efforts, there is still no universally effective drug against malfunctioning Ras. This failure partially stemmed from incomplete understanding of the interaction of Ras with other proteins, in particular the serine/threonine kinase Raf. In particular, it is unclear whether Ras dimerization is necessary for Ras-Raf interaction. In my investigations, I have distinguished the kinetic signatures of the presence or absence of Ras dimerization and have discovered how molecular and spatial heterogeneity lead to diversification of functions of these proteins. My discoveries offer a well-defined and well-characterized null hypothesis through which Ras-Raf interaction can be probed to its full extent.

Self-replication is the process through which an object of finite dimension creates a nearly identical replica of itself utilizing raw materials available in its surroundings. The most well-known example is cell-division. In this work we provide improved understanding of the necessary conditions required for self-replication and prescribe design rules to create self-replicators through coarse control of the reaction kinetics. One of the necessary conditions is the existence of certain structural motifs in the reaction network topology. Once that is ensured one can almost certainly get self-replicating molecules if the rate constants are broadly distributed. As we show, broad rate constant distribution is easily achievable through control of the interaction energies of the building blocks. Therefore, self-replicating materials can be made without detailed manipulation of the chemical kinetics.

Granular materials are the second most abundant materials in the world, sand being the most prominent example. A fascinating aspect of the granular materials is that they become rigid when they are packed in a box and sheared. This phenomenon is known as shear jamming and it happens due to percolation of forces through the grains, which collectively rearrange and create contacts with each other during the shearing process. In our work, we try to understand how the percolation of the forces makes the material rigid. Using the constraints that the granular materials must obey, we developed a geometrical description of the forces and studied the structure of the shapes that the forces create in this description. We find that the shapes, called "force tiling", are structurally rigid in the jammed phase, but not so in the non-rigid unjammed phase.

Fun fact: Force tiles were the logo of 2016 APS March Meeting.