Team:Duke/Modeling

Introduction

Synthetic biologists, in their goal of designing biological systems with novel functions, are particularly interested in design techniques for synthetic genetic networks, given the many emergent properties observed in natural gene circuits. The simplest of these gene circuits is the bistable toggle switch, in which mutually repressing genes create a system that can be tuned to make either gene dominant at will. Previous studies have shown that an essential criterion for the bistability of these systems is the cooperative action of the repressors. Several toggle switch systems, including the first switch pioneered by Collins, have been proposed to introduce cooperativity in the form of the cooperative binding of multiple repressor molecules. In this study, we consider alternative methods for generating cooperativity though molecular titration. Analogous to chemical titration, molecular titration generates a nonlinear “all-or-nothing” response with a “sink” of buffer molecules that sequester and inactivate repressor molecules at low concentration of repressor. A naturally occurring example of this is protein sequestration, and a previous study has constructed a synthetic circuit with proteins using this principle and demonstrated an ultrasensitive response in yeast. We propose to look at novel forms of molecular titration that involve the widely used dCas9 system in an attempt to construct new building blocks for synthetic circuits. In particular, instead of having a protein and its sequestering protein as a buffer, we wish to use small RNA molecules (anti gRNAs) and decoy binding sites on a plasmid that are complementary to the gRNA component of the dcas9 system to suppress the activity of the cas9 complex and act as a buffer against repression. In this study, we will model the properties of this system by considering how its equilibrium conditions vary with respect to total gRNA concentration and we hope to demonstrate this system’s ability to exhibit an ultrasensitive response under biologically reasonable conditions and to characterize its behavior in general over a wide range of parameters.

Methods

The approach we took in modeling our systems is based on Buchler’s approach in modeling molecular titration in a system consisting of a generic repressor and its buffering molecule (1). Their model considers the equilibrium concentration of the active repressor. Taking the total concentration of the other molecules in the system as constants, it is possible to calculate this concentration as a function of the total concentration of repressor. This function is obtained as a solution to a system of equations involving the equilibrium expression for the sequestering reaction in addition to the mass balance equations for each component of the system. The resulting system of equations can be solved as a quadratic polynomial in terms of the concentration of active repressor, giving an explicit expression for this equilibrium concentration in terms of the dissociation constants and the total concentrations of each component in the system. Modeling Paper