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Natural biological branching processes can form tree-like structures at all scales and, moreover, can perform various functions to achieve specific goals; these include receiving stimuli, performing two-way communication along their branches, and dynamically reforming (extending or retracting branches). They underlie many biological systems with considerable diversity, frequency, and geometric complexity; these include networks of neurons, organ tissue, mycorrhizal fungal networks, plant growth, foraging networks, etc. This paper presents a biomimetic DNA tile assembly model (Y-STAM) to implement dynamic branching processes. The Y-STAM is a relatively compact mathematical model providing a design space where complex, biomimetic branch-like growth and behaviour can emerge from the appropriate parametrization of the model. We also introduce a class of augmented models (Y-STAM⁺) that provide time- and space-dependent modulations of tile glue strengths, which enable further diverse behaviours that are not possible in the Y-STAM; these additional behaviours include refinement of network assemblies, obstacle avoidance, and programmable growth patterns. We perform and discuss extensive simulations of the Y-STAM and the Y-STAM⁺. We envision that these models could be applied at the mesoscale and the molecular scale to dynamically assemble branching DNA nanostructures and offer insights into complex biological self-assembly processes. 

DNA computing has emerged as a promising alternative to achieve programmable behaviors in chemistry by repurposing the nucleic acid molecules into chemical hardware upon which synthetic chemical programs can be executed. These chemical programs are capable of simulating diverse behaviors, including boolean logic computation, oscillations, and nanorobotics. Chemical environments such as the cell are marked by uncertainty and are prone to random fluctuations. For this reason, potential DNA-based molecular devices that aim to be deployed into such environments should be capable of adapting to the stochasticity inherent in them. In keeping with this goal, a new subfield has emerged within DNA computing, focusing on developing approaches that embed learning and inference into chemical reaction systems. If realized in biochemical contexts, such molecular machines can engender novel applications in fields such as biotechnology, synthetic biology, and medicine. Therefore, it would be beneficial to review how different ideas were conceived, how the progress has been so far, and what the emerging ideas are in this nascent field of ‘molecular-scale learning’. 

Heuristic algorithms can generalize the design process of stiff and round capsule-like nanostructures made from DNA. 

Structural DNA nanotechnology is a pioneering biotechnology that presents the opportunity to engineer DNA-based hardware that will mediate a profound interface to the nanoscale. To date, an enormous library of shaped 3D DNA nanostructures have been designed and assembled. Moreover, recent research has demonstrated DNA nanostructures that are not only static but can exhibit specific dynamic motion. DNA nanostructures have thus garnered significant research interest as a template for pursuing shape and motion-dependent nanoscale phenomena. Potential applications have been explored in many interdisciplinary areas spanning medicine, biosensing, nanofabrication, plasmonics, single-molecule chemistry, and facilitating biophysical studies. In this review, we begin with a brief overview of general and versatile design techniques for 3D DNA nanostructures as well as some techniques and studies that have focused on improving the stability of DNA nanostructures in diverse environments, which is pivotal for its reliable utilization in downstream applications. Our main focus will be to compile a wide body of existing research on applications of 3D DNA nanostructures that demonstrably rely on the versatility of their mechanical design. Furthermore, we frame reviewed applications into three primary categories, namely encapsulation, surface templating, and nanomechanics, that we propose to be archetypal shape- or motion-related functions of DNA nanostructures found in nanoscience applications. Our intent is to identify core concepts that may define and motivate specific directions of progress in this field as we conclude the review with some perspectives on the future.