Programming active-molecule dynamics via intramolecular nonreciprocity

Abstract

The dynamics of a self-propelled particle are typically hard-wired by its microscopic construction, limiting the range of behaviors accessible without redesigning the particle itself. Here we show that intramolecular nonreciprocity provides a minimal and versatile mechanism to overcome this constraint. We construct active molecules from short chains of two species of self-propelled particles whose propulsion directions are coupled nonreciprocally according to a prescribed internal sequence. At the single-molecule level, homogeneous sequences exhibit standard persistent random-walk dynamics, whereas heterogeneous sequences produce distinct trajectories inaccessible to either constituent species alone. At the collective level, using motility-induced phase separation (MIPS) as a representative example, we find that modifying the internal sequence shifts the MIPS onset by multiple orders of magnitude in propulsion strength, without altering particle-level interactions. These results demonstrate that intramolecular nonreciprocity among a small set of active components enables sequence-level programmability from single-molecule dynamics to emergent collective behavior, providing a minimal mechanism to encode and control active-matter dynamics across scales.

Figures (4)

• Figure 1: (a) Illustration of the nonreciprocal coupling between the propulsion orientations of two bonded particles at $g=-1$. Red and light blue denote $A$ and $B$ particles. White semicircles and gray arrows indicate the instantaneous self-propulsion directions; for each particle, the orientation angle $\theta$ is measured relative to a fixed reference direction (dashed line). (b–d) Representative center-of-mass trajectories of molecular sequences at $g=-1$, shown over a time window of duration $\Delta t = 100$. Trajectories are shifted in time to start at $t=0$ and translated so that the initial position is at $x=0$. (b) Trajectories of the [A], [A–A], and [A–A–A] sequences. For clarity, trajectories are vertically shifted to different y positions. (c) Trajectory of the [A-B] sequence. (d) Two representative trajectories of the [B–A–B] sequence. The inset shows a long-time trajectory, with the starting and ending points of the two representative segments indicated by different symbols.
• Figure 2: Angular dynamics of a [B–A–B] molecule. (a–d) Time evolution of the orientation angles $\theta_i(t)$ for an initial condition $(\theta_1,\theta_2,\theta_3)=(0.3,0,\pi)$, shown for (a) $g=-3$, (b) $g=-2$, (c) $g=1$, and (d) $g=-1$. (e,f) In the oscillatory regime $-2<g<0$, oscillation frequency $\omega$ (e) and phase offset $\phi_0$ (f), defined in Eq. (\ref{['eq:nonreciprocal']}), as functions of $g$.
• Figure 3: (a) Mean-squared displacement (MSD) for four three-particle molecular sequences. Gray dashed curves are given by Eq. (\ref{['eq:msd_theory']}), using the effective parameters extracted from the autocorrelation in (b). For [B–A–B], data are shown up to $t=2\times10^{5}$ because resolving its rapid orientational fluctuations requires a smaller integration time step (see SM, Sec. V). (b) Autocorrelation of the net propulsion force, $C_{\mathbf{F}_{\mathrm{net}}}(t)$ [Eq. (\ref{['eq:corre']})], for the same sequences. Gray dashed lines are exponential fits; the gray dotted line indicates $C_{\mathbf{F}_{\mathrm{net}}}(t)=0$.
• Figure 4: (a) Average fraction of molecules in the largest cluster, $\bar{\alpha}$ [Eq. (\ref{['eq:alpha']})], as a function of propulsion strength $F_{0}$ for monomeric [A] molecules ($N=43{,}200$). The gray dashed line marks the threshold $\alpha_{\mathrm{th}}=0.6$. (b) Representative snapshots corresponding to the orange open circles in (a). (c) $\bar{\alpha}$ versus $F_{0}$ for four trimer sequences ($N=14{,}400$).