Controlling energy delivery with bistable nanostructures

Abstract

Countless biological processes are fueled by energy-rich molecules like ATP and GTP that supply energy with extreme efficiency. However, designing similar energy-delivery schemes from the bottom up, essential for the development of powered nanostructures and other {\it de novo} machinery, presents a significant challenge: how can an energy-rich structure be stable in solution yet still deliver this energy at precisely the right time? In this paper, we present a purely physical mechanism that solves this challenge, facilitating energy transfer akin to ATP hydrolysis, yet occurring between synthetic nanostructures without any biochemical interactions. This targeted energy delivery is achieved by exploiting a differentiable state-based model to balance the energy profiles that govern the structural transitions in the two nanostructures, creating a combined relaxation pathway with minimal barriers that facilitates energy delivery. We verify the effectiveness and robustness of this mechanism through Molecular Dynamics simulations, demonstrating that a bath of the high-energy structures can systematically and repeatedly drive the target structure out of equilibrium, enabling it to perform tasks. As the mechanism operates only through explicit physical forces without any biochemistry or internal state variables, our results present generic and far-reaching design principles, setting the stage for the next generation of synthetic nanomachines.

Figures (11)

• Figure 1: Generic scheme for energy delivery between bistable nanostructures. (A) Two nanostructures, called the "Machine" and "Source", that can undergo a conformational change that elongates the distance between binding sites at the ends of the structures. We model these structures as dimers, as shown. Although the individual transitions are slow, we show that there is a potentially fast combined pathway in which the dimers form a complex and transition together (purple). All transitions can in principle go in both directions, but we show the target direction only. (B) The energy of the Machine, $E_\mathrm{M}(m)$, and the Source, $E_\mathrm{S}(s)$, depend only on the dimer lengths, $m$ and $s$, respectively. As shown in the example energy profiles, each structure has a "charged" high-energy state and an "uncharged" low-energy state. The Machine and Source dimer ends bind to each other through an interaction energy $E_\text{int}(r)$, with strength $\epsilon$ and range $1/\alpha$.
• Figure 2: Sculpting a relaxation pathway for controlled energy delivery. The solid black curve in A and blue curves in B, D, F, and H show the energy profiles for the Machine and Source, respectively, discussed in the text. Starting with the generic energy profiles in A-B, we decrease the length of the closed Source state (D), increase the energy capacity of the Source (F), and increase the binding energy $\epsilon$ (H), all with other minor changes as discussed in the text. C, E, G, and I show the corresponding minimum energy $E_\mathrm{min}(m,s)$ for fixed $m$ and $s$. The green curve shows the desired mutual transition, the yellow curve shows the catalytic transition, the red curve shows the undesired separated transition of the Source being wasted, and the dashed black curve shows the Machine opening on its own, which is always thermodynamically unfavorable but shown in A and C for reference. Saddle points are indicated by stars and squares. The state labels in I refer to Fig. \ref{['fig:md_results']}.
• Figure 3: Example trajectory from a Molecular Dynamics simulation demonstrating the progression of the energy-delivery mechanism as discussed in the text. The time evolution of all four relevant lengths, Machine and Source lengths, $m$ and $s$, as well as the dimer-end separations $r_1$ and $r_2$, are shown for a single Machine cycle. We use the energy profiles shown in Fig. \ref{['fig:mechanism_explainer']}A and H with $\tau_\text{d}=1$ for this representative example.
• Figure 4: Transition network between meta-stable states in our model. The progression along the horizontal line corresponds to the desired mechanism including the catalytic and energy-delivery reactions highlighted by thick arrows. Transitions to the waste state are irreversible and undesirable. This network does not consider the recharging of the Source or the spontaneous discharging of the free Machine. The state labels refer to Fig. \ref{['fig:mechanism_explainer']}I and Fig. \ref{['fig:md_results']}.
• Figure 5: Measures of merit of the energy-delivery mechanism with different energy profiles. (A-C) Performance, power, and efficiency as functions of the dissociation timescale. We report mean values of ten long simulations with standard deviation of the mean when there are at least ten Machine cycles, see SM. (D-E) Energy profiles corresponding to the data in the top row with parameters listed in Table \ref{['tab:params']}. The green systems differ only in the maximum binding energy $\epsilon_0$. (F) Example MD trajectory connecting the closed-closed to the open-open complex in a system with constant binding energy $\epsilon=10\,k_\text{B}T$. The color scale is identical to Fig. \ref{['fig:mechanism_explainer']}.