Mathematical models of cellular signaling and supramolecular self-assembly

Synthetic biologists endeavor to predict how the increasing complexity of multi-step signaling cascades impacts the fidelity of molecular signaling, whereby cellular state information is often transmitted with proteins diffusing by a pseudo-one-dimensional stochastic process. We address this problem by using a one-dimensional drift-diffusion model to derive an approximate lower bound on the degree of facilitation needed to achieve single-bit informational efficiency in signaling cascades as a function of their length. We find that a universal curve of the Shannon-Hartley form describes the information transmitted by a signaling chain of arbitrary length and depends upon only a small number of physically measurable parameters. This enables our model to be used in conjunction with experimental measurements to aid in the selective design of biomolecular systems. Another important concept in the cellular world is molecular self-assembly. As manipulating the self-assembly of supramolecular and nanoscale constructs at the single-molecule level increasingly becomes the norm, new theoretical scaffolds must be erected to replace the classical thermodynamic and kinetics-based models. The models we propose use state probabilities as its fundamental objects and directly model the transition probabilities between the initial and final states of a trajectory. We leverage these probabilities in the context of molecular self-assembly to compute the overall likelihood that a specified experimental condition leads to a desired structural outcome. We also investigated a larger complex self-assembly system, the heterotypic interactions between amyloid-beta and fatty acids by an independent ensemble kinetic simulation using an underlying differential equation-based system which was validated by biophysical experiments