[论文解读] Programmable Control of Nucleation for Algorithmic Self-Assembly

Rebecca Schulman, Erik Winfree|CaltechAUTHORS (California Institute of Technology)|Jul 13, 2006

Advanced biosensing and bioanalysis techniques被引用 4

一句话总结

本文提出了一种可编程的成核控制机制，用于通过'锯齿形'tile集合实现算法化DNA自组装，该机制通过设计较大的动力学能垒来实现对非引导生长的指数级抑制。在最佳条件下，随着tile集合大小线性增加，虚假成核速率呈指数级降低，从而在数小时内实现大型结构的稳健、低误差生长，虚假晶体量低于1%。

ABSTRACT

Algorithmic self-assembly, a generalization of crystal growth processes, has been proposed as a mechanism for autonomous DNA computation and for bottom-up fabrication of complex nanostructures. A `program' for growing a desired structure consists of a set of molecular `tiles' designed to have specific binding interactions. A key challenge to making algorithmic self-assembly practical is designing tile set programs that make assembly robust to errors that occur during initiation and growth. One method for the controlled initiation of assembly, often seen in biology, is the use of a seed or catalyst molecule that reduces an otherwise large kinetic barrier to nucleation. Here we show how to program algorithmic self-assembly similarly, such that seeded assembly proceeds quickly but there is an arbitrarily large kinetic barrier to unseeded growth. We demonstrate this technique by introducing a family of tile sets for which we rigorously prove that, under the right physical conditions, linearly increasing the size of the tile set exponentially reduces the rate of spurious nucleation. Simulations of these `zig-zag' tile sets suggest that under plausible experimental conditions, it is possible to grow large seeded crystals in just a few hours such that less than 1 percent of crystals are spuriously nucleated. Simulation results also suggest that zig-zag tile sets could be used for detection of single DNA strands. Together with prior work showing that tile sets can be made robust to errors during properly initiated growth, this work demonstrates that growth of objects via algorithmic self-assembly can proceed both efficiently and with an arbitrarily low error rate, even in a model where local growth rules are probabilistic.

研究动机与目标

• 为解决算法化自组装中因非引导成核导致的错误启动问题，其中非引导成核可能干扰期望的生长过程。
• 设计tile集合，使生长快速且受引导，同时保持对非引导成核的任意大的动力学能垒。
• 通过理论分析和模拟证明，通过扩大tile集合大小可实现虚假成核速率的指数级降低。
• 在概率性局部生长规则下实现稳健、高保真度的算法化自组装。
• 探索在单分子DNA检测中利用受控成核动力学的应用。

提出的方法

• 引入具有特定结合亲和力的'锯齿形'tile集合，以促进受引导生长而非非引导成核。
• 采用基于成核理论的动力学模型，其中虚假成核速率取决于结合自由能（G_mc）和粘性末端相互作用能（G_se）。
• 使用凝聚函数将较长的组装体映射为较短的组装体，同时保持tile数和键数不变，以限制可能的虚假构型数量。
• 应用递归边界技术，证明在特定能量条件下，长度为l+2时的虚假成核事件数小于长度为l时的二分之一。
• 推导出一个条件：当G_se > ln(10)(k−2) + ln(4)时，随着tile集合大小k的增加，成核将实现指数级抑制。
• 通过模拟验证结果，表明在合理实验条件下，大型晶体中虚假成核率低于1%。

实验结果

研究问题

• RQ1 能否通过设计对非引导生长具有大动力学能垒的机制，使算法化自组装对虚假成核具有鲁棒性？
• RQ2 增大tile集合大小如何影响自组装结构中虚假成核的速率？
• RQ3 能否设计一种可编程的成核机制，使得受引导生长快速进行，而非引导生长被指数级抑制？
• RQ4 在概率性生长规则下，实现任意低错误率的算法化自组装需要何种物理条件？
• RQ5 此类系统能否通过受控成核实现对单个DNA链的高灵敏度检测？

主要发现

• 虚假成核速率随tile集合大小的线性增加而呈指数级降低，从而实现任意低错误率。
• 模拟结果表明，在合理条件下，受引导晶体可在数小时内生长至大尺寸，且虚假成核率低于1%。
• 通过tile集合设计构建大动力学能垒，成功实现对非引导成核的指数级抑制。
• 理论分析证明，在特定能量条件下，长度为l+2时的虚假成核事件数被限制为长度为l时的一半以下。
• 即使在概率性局部生长规则下，系统仍保持鲁棒性，支持通过自组装实现可靠的算法计算。
• 该方法因成核控制的高灵敏度，为单分子DNA检测提供了潜在应用前景。