Programming discrete distributions with chemical reaction networks

Golgi compartments enable controlled biomolecular assembly using promiscuous enzymes

The synthesis of eukaryotic glycans - branched sugar oligomers attached to cell-surface proteins and lipids - is organized like a factory assembly line. Specific enzymes within successive compartments of the Golgi apparatus determine where new monomer building blocks are linked to the growing oligomer. These enzymes act promiscuously and stochastically, causing microheterogeneity (molecule-to-molecule variability) in the final oligomer products. However, this variability is tightly controlled: a given eukaryotic protein type is typically associated with a narrow, specific glycan oligomer profile. Here, we use ideas from the mathematical theory of self-assembly to enumerate the enzymatic causes of oligomer variability and show how to eliminate each cause. We rigorously demonstrate that cells can specifically synthesize a larger repertoire of glycan oligomers by partitioning promiscuous enzymes across multiple Golgi compartments. This places limits on biomolecular assembly: glycan microheterogeneity becomes unavoidable when the number of compartments is limited, or enzymes are excessively promiscuous.

Noise control for molecular computing

Synthetic biology is a growing interdisciplinary field, with far-reaching applications, which aims to design biochemical systems that behave in a desired manner. With the advancement in nucleic-acid-based technology in general, and strand-displacement DNA computing in particular, a large class of abstract biochemical networks may be physically realized using nucleic acids. Methods for systematic design of the abstract systems with prescribed behaviours have been predominantly developed at the (less-detailed) deterministic level. However, stochastic effects, neglected at the deterministic level, are increasingly found to play an important role in biochemistry. In such circumstances, methods for controlling the intrinsic noise in the system are necessary for a successful network design at the (more-detailed) stochastic level. To bridge the gap, the noise-control algorithm for designing biochemical networks is developed in this paper. The algorithm structurally modifies any given reaction network under mass-action kinetics, in such a way that (i) controllable state-dependent noise is introduced into the stochastic dynamics, while (ii) the deterministic dynamics are preserved. The capabilities of the algorithm are demonstrated on a production-decay reaction system, and on an exotic system displaying bistability. For the production-decay system, it is shown that the algorithm may be used to redesign the network to achieve noise-induced multistability. For the exotic system, the algorithm is used to redesign the network to control the stochastic switching, and achieve noise-induced oscillations.