Leakless Polymerase-Dependent Strand Displacement Systems

Remarkably, a single complex can produce an output signal that is sequence orthogonal to its input while guaranteeing an arbitrarily high energy barrier to leak. The intuition for this claim is depicted in Figure 3(a): if a signal domain has not yet been produced then it is only found sequestered in double-stranded regions of gates thus necessitating an energy barrier to leak proportional to fraying open an entire long domain (see Figure 3(b)).

The robustness of this architecture is possible due to the complete sequestration of output signal domains in double stranded regions of gates. This point can be subtle. It is the systematic composition of this motif, into larger gates and then into entire circuits or reaction networks, that maintain an invariant on the barrier to leak. While our focus in this paper is on the description of the architecture, in the complete absence of input, it is a straightforward exercise to arrive at the following result. (We introduce Join and Fork gates in Section 4.)

The simple translator motif can be extended into a multi-armed complex that remains inactive until a specific signal is present to “deprotect” the gate, at which point it becomes functionally identical to the original translator. This conditional gating strategy enables the system to remain dormant, sensing and collecting input signals without triggering downstream reactions until the final readout step. As shown in Figure 4, this approach is particularly well-suited for long-term applications such as environmental monitoring – where inputs may accumulate over days or weeks – and fuel strands, dNTPs and polymerase can be withheld from the reaction mixture until readout.

The PD-TMSD architecture supports engineered systems that require control of relative rate constants. As with TMSD, PD-TMSD reaction rate constants can be modulated by the careful design of toehold strengths and and the introduction of secondary structure features into the branch migration domain such as mismatch introduction and mismatch replacement [15].

Additionally, the rate of the polymerase extension portion of a PD-TMSD reaction can also be modulated via sequence design and choice of dNTP concentrations. It is common to design signal strands over a three-letter code, reserving a fourth nucleotide that could be used as a rare or missing base to introduce conditional behavior. For example, one or more complements to a rare dNTP could be incorporated into the template strand of a gate, as illustrated in Figure 1 part IV. By changing the available concentration of the rare dNTP, the rate at which the polymerase is able to progress through that region can be tuned.

To prevent any polymerization through gates containing the rare dNTP complement, the corresponding dNTP could be omitted entirely from the reaction mixture, effectively disabling the associated reaction pathways. If desired, these pathways can later be activated by simply spiking in the missing dNTP, restoring gate function and enabling polymerase extension. The use of a missing dNTP to precisely halt polymerization has been previously demonstrated as an effective control mechanism in other contexts [12, 10].

Figure 5(a) introduces a three-stranded Join gate, a natural extension of the translator architecture and similar in style to the activatable translator. This design implements a conditional logic where the output C is only produced when both inputs A and B are present, and avoids sequence overlap between the two inputs – a desirable property for scalable systems.

The gate operates as follows: input A first binds via TMSD to the exposed arm of the gate. This triggers polymerase-mediated extension, which displaces the protector strand. This displacement reveals a previously sequestered internal toehold, enabling input B to bind via TMSD, be extended by polymerase, and displace output C. In theory, this architecture realizes a leakless join operation, where both inputs are required sequentially for productive output.

However, in practice, we observed complications that undermine the theoretical leaklessness. Prior work [33] has shown that strand-displacing polymerases can exhibit template switching or “track jumping” in the absence of single-stranded binding proteins (SSBs), particularly when polymerizing through regions of secondary structure. In our gate, this behavior results in polymerase switching from the intended path to the adjacent duplex arm, producing spurious output C even without input A (Figure 5(b)). Thus, despite its appealing design, the gate is not functionally leakless under experimental conditions (data not shown).

To address the issue of track jumping, we added a specialized PD-TMSD translator gate (Figure 5(c)) for correct computation. In this design, input A binds the translator gate that produces an output strand which can remove the entire protecting strand on the three-stranded complex through TMSD. This eliminates the possibility of the polymerase choosing to follow an incorrect strand as the template. Following this deprotection event, an internal toehold is revealed that allows input B to bind and extend, resulting in the production of output C. Functionally, this gate resembles the activatable translator introduced in Section 3.2, where signal-dependent deprotection enables conditional activation, here utilized to implement join logic. This structural similarity highlights the modularity of the PD-TMSD motif and its adaptability to different computational tasks.

Figure 6(a) presents a leakless Fork gate that converts a single input X into two outputs, Y and Z. When input X binds to the fork gate via TMSD, it is extended by a polymerase, subsequently displacing two signal strands Y and Z. The overhang of the universal domain following signal Y has a free $3^{\prime }$ end; however, it is sufficiently long and a designed to mismatch with the template in order to prevent spurious initiation of polymerase extension. The Fork gate can be generalized to produce an arbitrary number of outputs by extending the template strand to accommodate additional bound signals to be released via PD-TMSD initiated by a single input.

By adding a single additional translator gate that converts output Z back into input X, signal fanout can be transformed into a linear signal amplifier (Figure 6(b)). This implementation enables signal amplification using only one polymerase step per gate, and two per cycle, using a minimal set of components.

We introduce the “pas de deux” (PDD) gate.³³3In classical ballet, “pas de deux” (French for “step of two”) is a duet typically performed by a male and female dancer in concert. A grand pas de deux follows the structure of an entrée, a slow partnered adagio, individual solos for each dancer, and culminates in a fast virtuosic coda danced in unison. Like its namesake, it exhibits symmetry and elegant coordination of a pair as they act alone and then in a choreographed sequence to achieve their collective aim. Although the sequence of events in our system unfolds slightly out of order compared to a grand pas de deux, the underlying motifs remain the same. Each input first interacts with its respective gate, stripping off the protector strand via toehold-mediated strand exchange (TMSE) – this step mirrors the solo variations of male and female dancers, each showcasing their individual abilities. The combination of $3^{\prime }$ phosphate modifications on inputs and toeholds to prevent polymerization along with TMSE at this stage, render these reactions reversible. Only when both inputs are present can the two deprotected components of the gates come together – analogous to the adagio when dancers join in a coordinated, slow duet. In the final stage of the reaction, the polymerase is able to find and extend from the two free $3^{\prime }$ hydroxyl groups, displacing both output strands in a final, coordinated motion – this mirrors the coda where both dancers re-emerge with renewed energy, and the performance culminates in a dazzling, synchronized flourish.

To facilitate more efficient strand displacement by Klenow fragment (exo-) polymerase, we introduced intentional mismatches into the duplex regions downstream of input binding. Unlike more processive polymerases or those operating at elevated temperatures – where decreased duplex stability can aid in duplex unwinding – Klenow operates at relatively low temperatures (25–37°C) and lacks intrinsic helicase activity, making polymerase-mediated strand displacement more challenging. In natural systems, single-stranded binding proteins (SSBs) have been shown to enhance strand displacement activity by binding and stabilizing the displaced strand, preventing its rehybridization to the template, thus enabling continuous polymerase progression [18]. However, because our system uses single-stranded DNA as signal strands, the inclusion of SSBs is incompatible, as they would bind these functional signals and interfere with downstream reactions. In the absence of such stabilizing factors, the displaced strand can readily rehybridize to the template, creating a kinetic barrier to polymerase progression. By incorporating mismatches or bulges into the displaced strand, we reduce its hybridization stability and effectively slow the reverse reaction, lowering the energy barrier for forward strand displacement synthesis. A similar strategy has been observed in biological systems; for example, HIV-1 reverse transcriptase leverages single unpaired nucleotides or bulged structures within its RNA genome to promote strand displacement and enhance polymerase processivity through otherwise inhibitory duplex regions [13]. Consistent with this, Srinivas et al. (2013) showed that branch migration initiation can be a key rate-limiting step in strand displacement and that tuning the stability of the incumbent strand’s interactions with the template can modulate these interactions to favor forward displacement [29]. This design strategy provides a simple and effective means to improve polymerization kinetics in systems where traditional accessory proteins cannot be used.

While the majority of this paper focuses on systems built with the exonuclease-deficient Klenow fragment (Klenow exo$-$), our architecture is readily adaptable to polymerases that retain $3^{\prime }\to 5^{\prime }$ exonuclease activity, such as the full Klenow fragment polymerase. Before exploring the new behaviors this enables, we first address several important design considerations necessary for working with proofreading polymerases.

In systems using strand displacing polymerases with an exonuclease domain, all exposed $3^{\prime }$ overhangs – including toeholds – must be protected from degradation. This is typically achieved using phosphorothioate (PS) backbone modifications, which render the strand resistant to exonuclease activity. Once these protective modifications are in place, the exonuclease activity of the polymerase can be harnessed as a feature rather than a threat. In particular, we can exploit the gradual degradation of single-stranded overhangs by exonuclease activity.

As the polymerase chews back mismatched or unpaired regions from the $3^{\prime }$ end of a strand, it will eventually reveal a perfectly matched primer-template duplex. At this point, the enzyme can initiate extension. This delayed onset of polymerization effectively functions as a molecular timer, with the length of the single-stranded region acting as a programmable delay: the longer the overhang, the longer the delay before polymerization can proceed.

Timed delay elements are increasingly important in molecular systems that require sequential, transient, or conditional behavior. Prior work has demonstrated timer circuits and sequential release mechanisms using DNA strand displacement [6, 22, 14], as well as enzymatic timers for pulse generation and orthogonal delays [2, 3, 21]. However, many of these designs depend on auxiliary structures, multi-step cascades, or reaction-specific configurations, which can limit composability and generalizability. Our approach offers a simple and scalable alternative: delay elements based on a single enzyme and tunable overhangs. We use this principle to build a new class of timing-enabled molecular gates, that highlight how proofreading polymerases, when used strategically, can unlock compact and programmable temporal control in DNA-based molecular computation.