Programming Complex Behavior in DNA-based Molecular Circuits and Robots

Introduction

Overview of DNA nanotechnology

Inspired by the replication fork and the Holliday structure, a critical intermediate in genetic recombination, Ned Seeman in 1982 theorized the ability to study such biologically relevant reactions using strand displacement mechanisms [19] that could be easily mimicked using synthetic DNA molecules. Specifically, the footbrace-mediated string displacement mechanism has been widely used to implement the aforementioned systems and continues to be extremely important in the field.

DNA as a computing substrate

The overall effective rate of the strand displacement reaction keff was first investigated by Yurke and Mills [28]. 25] to build a DNA strand displacement circuit composed of 82 single and partially double stranded DNA circuit components in a single test tube representing a four-bit square root digital logic circuit.

Figure 1.3: Overview of DNA strand displacement. a, Abstraction of contiguous DNA bases into functional DNA domains that act as a unit in hybridization, branch migration or dissociation represented by numbers, starred domains denote domains complimentary i

DNA as an engineering material

By changing the threshold value in the simulation to 0.7 ×, the simulation results agreed with the experimental results. If there is an error in the participating toehold or migration domain of the invading signal chain, or in the initial toehold domain of the gate molecule (ie, the toehold that binds to the invading signal chain), the forward rate is 100-fold slower and the reverse course remains the same.

Figure 1.4: Making DNA origami. a, M13 viral sca ff old is mixed with designed staple strands in 1 × TAE/12.5 mM Mg ++ and annealed to form target triangle structure designed in caDNAo

Systematic construction of DNA circuits

Circuit design

The compiler then generates an equivalent dual-rail circuit file consisting only of AND-OR gates [62]. Simulations were performed at 1×= 50 nM – the compiler recommended standard concentration for large scale purified seesaw circuits.

Figure 2.2: Automated circuit design steps using the Seesaw Compiler. A feedfor- feedfor-ward digital logic circuit is first translated into an equivalent duel-rail logic circuit, and then translated into an equivalent seesaw DNA circuit

Calibrating e ff ective concentrations

This measured concentration may be greater than the effective concentration of the species that can actively participate in the desired reaction. Signal restoration experiments were performed on additional components of the rule110-rule124 circuit, and the threshold-to-signal ratio β/α = 1.4 was consistent for different threshold and signaling molecules (Supplementary Figure 2.14).

Figure 2.4: Calibrating e ff ective concentrations. a, Simulations and b, experimental data of digital signal restoration

Identifying outliers

To find a universal solution that can be applied across the entire circuit, we measure the difference between the effective concentrations of unpurified gate species that caused the unbalanced wires. Therefore, our solution to the unbalanced wires challenge is to measure the difference between the effective concentrations of unpurified gate species that caused the unbalanced wires and adjust the nominal value.

Tuning circuit output

Applying this change in gate concentration, we observed that the ON trajectory was in an ideal state with high fluorescence (fig. 2.5b). This is done by evaluating the ON/OFF separation of the circuit output in fig.2.5b.

Figure 2.6: Tuning circuit output. Logic circuit diagram, seesaw circuit diagram, and experimental data of a two-layer logic circuit with a, two upstream OR gates connected to an downstream AND gate, and b, two upstream AND gates connected to an downstream

Systematic procedure

Ensure that ON trajectories are significantly faster than OFF trajectories and increase the nominal concentration of the threshold in the logic gate that produces the circuit output. Each of the circuit outputs is illustrated by an array of 7 x 8 cells, representative of eight generations of cellular automata on a starting configuration torus.

Figure 2.7: The rule 124 sub-circuit. a, Logic circuit diagram. b, Dual-rail circuit diagram

Model

The branch migration domain in the downstream chain of the gate molecule is considered error-free as it does not affect the rate of the reaction. A defect in the upper set or the branch migration domain in the lower set will not affect the rate of the reaction.

Figure 2.10: A model for unpurified seesaw circuits. a, Populations of signal, gate and threshold molecules without and with synthesis errors in the marked locations

Methods

Symmetrically, if there is an error in the participating domain of the crossing leg or of the branch migration of the signal bound to the gate molecule, or in the retention domain of the disconnection leg (i.e. the leg retention that was originally covered) , the backward rate is 100 times slower and the forward rate remains the same. The tri-molecular complex consists of (a) the robot;. b) robot-probe that hybridizes to origami via 20nt complementarity to the start site also occupying leg1; and (c) the robot-brake string, which keeps the robot locked in the starting position by occupying the footrest2 (fig.3.2d) The brake string also has a free holder to help actuate the robot. Robotx,y is the robot at an arbitrary location (x,y) and Robotx∗,y∗ is the robot at a neighboring location of (x,y). xstop, ystop) is the goal location.

Figure 2.12: Diagrams of the rule 110-124 circuit. a, Dual-rail circuit diagram. b, Seesaw circuit diagram.

A random walk module for DNA robots

Implementing random walking DNA robot on DNA origami

This design of the robot along with appropriate track design (explained in the next section) enables bidirectional walking mechanism. The space between the start and finish locations is covered by a strategic track layout for the robot. In our setup, the time it takes for the robot to reach its goal from the starting location is a function of the number of steps taken to reach the goal (n2) (Fig.3.1b).

Track design for the random walk

Addition of a large excess of the robotic trigger molecule removes the robotic inhibitor strand via a forward-biased tether-mediated strand displacement reaction. This reaction is monitored via fluorophore-quenching interaction between the robot and target using a fluorescence spectrophotometer. Distance between two tracks on the origami surface is 6 nm and switches s1 and s2 are calculated to ensure that the robot can achieve the necessary toe hold to move between track 1 and track 2.

Figure 3.2: The random walk track design. a, Scheme of DNA origami surface with track layout for randomwalk

Rigidity of DNA origami as a testing ground for DNA robots

Using CanDo [73], the thermal fluctuations of the monolayer and bilayer structures were compared. The simulation indicated increased degree of structural fluctuations in the case of the single layer rectangle compared to the double layer square (Fig.3.3d,i). The maximum separation between the start and target location along the diagonal of the double-layered origami was 48 nm.

DNA sequence and its e ff ect on the rate of walking

The data suggests that the half-life of the reaction on the origami surface is 1/2 = 2.5 hours. To this end, we replaced the foot1*toe rest closer to the origami surface with the weaker foot2*toe rest, which makes the disassociation of the robot while moving from track-1 to track-2 quite energetically favorable. The blue trajectory in Figure 3.4d still shows about 60% of the total number of robots on the target.

Figure 3.4: E ff ect of track sequence on randomwalk. a, Schematic of double layer DNA origami showing robot-start location single step away from the goal location

Purity of DNA origami and its e ff ect on the reaction completion level 67

The data shows that 7.2% (time of 14 hours) of the robots reached the target through inter-origami interaction. The concentrations of the origami were not measured in the same comprehensive manner as in Figure 2. Therefore, we measured the concentration of the origami for all subsequent experiments, including the data in Figure 3.8b.

Figure 3.5: E ff ect of sample purification on randomwalk. a, Schematic representation of different track lengths on the surface of double layer origami for randomwalk

Model

The robot can perform multiple iterations of the cargo sorting task without requiring reloading of relevant components. Two different types of cargo and their respective measurements are distributed on the opposite edges of the origami, and the robot is fixed in the middle at start. The previous section established that load-target interaction on the origami without the robot is negligible.

A cargo-sorting DNA robot

A simple cargo-sorting algorithm

The robot, by identifying the type of cargo, chooses a specific path to the goal location based on the cargo type. Upon reaching the goal, the robot must recognize the goal location to unload the cargo. The robot then continues its exploration until it reaches the designated target location, and drops the payload at its target.

Molecular implementation of the algorithm

The corresponding types of target molecules are distributed on the opposite edge of the origami from the cargo and are separated. The DNA sequence of the cargo sorting robot is identical to the random walking robot, without the quencher molecule at the 3' end. The cargo binds to the robot via the hand and arm complimentary domains in an irreversible strand displacement reaction.

Figure 4.2: Mechanism of cargo-sorting. a, Schematic representation of cargo-sorting playground on DNA origami

Demonstration of the robot picking up cargos

The hand domain (h) on the robot initiates a beach displacement response that picks up the charge (Fig. 4.2d). When the robot reaches a payload molecule, the payload is picked up and is no longer in the extinguished state (as indicated by the star-like fluorescence signal on the robot). Each origami carries one copy of the robot, and in the absence of target locations, the picked up cargo cannot be dropped off and thus remains on the robot.

Figure 4.3: Domain level representation for cargo pickup. a, Basic mechanism of activating the robot using a robot trigger

Inhibition and activation mechanism of cargo destinations

Domain hand, arm is used for load pick-up by the robot, while it is also used by the target for load drop-off (in addition to c1/c2). The c1, c2 and hand domains on the target and robot trigger waste molecules can temporarily interfere with the sorting of cargo. Adding robot-trigger string and the goal-trigger strings disarms the robot and goals respectively in a reversible response.

Figure 4.5: Experimental protocol for cargo-sort sample preparation. Step 1: anneal origami with a 10-fold excess of the regular, track, robot start, cargo and goal staples, 11-fold excess of the cargo attacher strands, and 12-11-fold excess of the cargo

Negative control for cargo-sorting without a robot

Demonstration of the robot sorting cargos

On the origami testing ground for this experiment, cargo1-F and cargo2-F are scattered on one edge of the origami, while goal1-Q and goal2-Q are located on the other edge. In our design, the asymmetric distribution of the charge along the top edge of the origami (as seen in the schematic) was used to label the left and right edges of the nanostructure. The unblocking strands move the partially double-stranded targets from their attachment sites on the origami without charge.

Demonstration of distinct cargo-sorting tasks in parallel

If a robot or target on one type of origami picks up a fluorophore labeled charge on the other type of origami, no signal change will occur because the corresponding target has no quencher. Since both types of origami already have a robot, an additional robot moved from another origami should not affect the completion level of the desired cargo sort. The decrease in the sorted part of the load may be due to undesirable inter-origami interactions and can be reduced by reducing the concentration of origami in solution.

Figure 4.9: Sample preparation for AFM imaging. The asymmetry of cargo distribution is used as a reference for recognizing the orientation of origami in AFM images

Model

We then define the responses used for the robot's pick-up and delivery of cargo; Here kc is the fetch and delivery rate constant when the payload or target is a direct neighbor of the robot (i.e. d = dmin). For cargo pick-up and delivery, the robot may or may not be a direct neighbor of the cargo (or target).

Figure 4.11: Parallellism. a, Schematic representation of two different origami present in the same test tube

Methods

Since the robot is able to explore the entire two-dimensional surface of the nanostructure, cargo molecules can be randomly positioned and do not need to be assigned specific locations (as designed in our demonstration). Multiple robots can be made to perform the same task in parallel on a single substrate, which can reduce sorting time. Using these tools in Chapters 3 and 4, we demonstrated the sophisticated task of cargo sorting on a two-dimensional DNA origami by a DNA robot.

Figure 4.14: Double-layer square DNA origami design using caDNAo. A single M13 sca ff old strand is show in blue

Conclusions