Building the Components for a Biomolecular Computer

Abstract

We propose a new method for amorphous bio-compatible computing using deoxyribozyme logic gates [1] in which oligonucleotides act as enzymes on other oligonucleotides, yielding oligonucleotide products. Moreover, these reactions can be controlled by inputs that are also oligonucleotides. We interpret these reactions as logic gates, and the concentrations of chemical species as signals. Since these reactions are homogeneous, i.e., they use oligonucleotides as both inputs and outputs, we can compose them to construct complex logic circuits. Thus, our system for chemical computation offers functionality similar to conventional electronic circuits with the potential for deployment inside of living cells. Previously, this technology was demonstrated in closed-system batch reactions, which limited its computational ability to simple feed-forward circuits. In this work, we go beyond closed systems, and show how to use thermodynamically open reactors to build biomolecular circuits with feedback. The behavior of an open chemical system is determined both by its chemical reaction network and by the influx and efflux of chemical species. This motivates a change in design process from that used with closed systems. Rather than focusing solely on the stoichiometry of the chemical reactions, we must carefully examine their kinetics. Systems of differential equations and the theory of dynamical systems become the appropriate tools for designing and analyzing such systems. Using these tools, we present an inverter. Next, by introducing feedback into the reaction network, we construct devices with a sense of state. We show how a combination of analytical approximation techniques and numerical methods allows us to tune the dynamics of these systems. We demonstrate a flip-flop which exhibits behavior similar to the RS flip-flop of electronic computation. It has two states in which the concentration of one oligonucleotide is high and the other is low or vice versa. We describe how to control the state of the flip-flop by varying the concentration of the substrates. Moreover, there are large regions of parameter space in which this behavior is robust, and we show how to tune the influx rates as a function of the chemical reaction rates in a way that ensures bistability.