Investigating the dynamics of surface-immobilized DNA nanomachines

Surface-immobilization of molecules can have a profound influence on their structure, function and dynamics. Toehold-mediated strand displacement is often used in solution to drive synthetic nanomachines made from DNA, but the effects of surface-immobilization on the mechanism and kinetics of this reaction have not yet been fully elucidated. Here we show that the kinetics of strand displacement in surface-immobilized nanomachines are significantly different to those of the solution phase reaction, and we attribute this to the effects of intermolecular interactions within the DNA layer. We demonstrate that the dynamics of strand displacement can be manipulated by changing strand length, concentration and G/C content. By inserting mismatched bases it is also possible to tune the rates of the constituent displacement processes (toehold-binding and branch migration) independently, and information can be encoded in the time-dependence of the overall reaction. Our findings will facilitate the rational design of surface-immobilized dynamic DNA nanomachines, including computing devices and track-based motors

Programmable disorder in random DNA tilings

Scaling up the complexity and diversity of synthetic molecular structures will require strategies that exploit the inherent stochasticity of molecular systems in a controlled fashion. Here we demonstrate a framework for programming random DNA tilings and show how to control the properties of global patterns through simple, local rules. We constructed three general forms of planar network—random loops, mazes and trees—on the surface of self-assembled DNA origami arrays on the micrometre scale with nanometre resolution. Using simple molecular building blocks and robust experimental conditions, we demonstrate control of a wide range of properties of the random networks, including the branching rules, the growth directions, the proximity between adjacent networks and the size distribution. Much as combinatorial approaches for generating random one-dimensional chains of polymers have been used to revolutionize chemical synthesis and the selection of functional nucleic acids, our strategy extends these principles to random two-dimensional networks of molecules and creates new opportunities for fabricating more complex molecular devices that are organized by DNA nanostructures

Precise parameter synthesis for stochastic biochemical systems

We consider the problem of synthesising rate parameters for stochastic biochemical networks so that a given time-bounded CSL property is guaranteed to hold, or, in the case of quantitative properties, the probability of satisfying the property is maximised or minimised. Our method is based on extending CSL model checking and standard uniformisation to parametric models, in order to compute safe bounds on the satisfaction probability of the property. We develop synthesis algorithms that yield answers that are precise to within an arbitrarily small tolerance value. The algorithms combine the computation of probability bounds with the refinement and sampling of the parameter space. Our methods are precise and efficient, and improve on existing approximate techniques that employ discretisation and refinement. We evaluate the usefulness of the methods by synthesising rates for three biologically motivated case studies: infection control for a SIR epidemic model; reliability analysis of molecular computation by a DNA walker; and bistability in the gene regulation of the mammalian cell cycle

On Quantitative Modelling and Verification of DNA Walker Circuits Using Stochastic Petri Nets

Molecular programming is an emerging field concerned with building synthetic biomolecular computing devices at nanoscale, for example from DNA or RNA molecules. Many promising applications have been proposed, ranging from diagnostic biosensors and nanorobots to synthetic biology, but prohibitive complexity and imprecision of experimental observations makes reliability of molecular programs difficult to achieve. This paper advocates the development of design automation methodologies for molecular programming, highlighting the role of quantitative verification in this context. We focus on DNA 'walker' circuits, in which molecules can be programmed to traverse tracks placed on a DNA origami tile, taking appropriate decisions at junctions and reporting the outcome when reaching the end of the track. The behaviour of molecular walkers is inherently probabilistic and thus probabilistic model checking methods are needed for their analysis. We demonstrate how DNA walkers can be modelled using stochastic Petri nets, and apply statistical model checking using the tool Cosmos to analyse the reliability and performance characteristics of the designs. The results are compared and contrasted with those obtained for the PRISM model checker. The paper ends by summarising future research challenges in the field