Provenance of life: Chemical autonomous agents surviving through associative learning

We present a benchmark study of autonomous, chemical agents exhibiting associative learning of an environmental feature. Associative learning systems have been widely studied in cognitive science and artificial intelligence but are most commonly implemented in highly complex or carefully engineered systems, such as animal brains, artificial neural networks, DNA computing systems, and gene regulatory networks, among others. The ability to encode environmental information and use it to make simple predictions is a benchmark of biological resilience and underpins a plethora of adaptive responses in the living hierarchy, spanning prey animal species anticipating the arrival of predators to epigenetic systems in microorganisms learning environmental correlations. Given the ubiquitous and essential presence of learning behaviors in the biosphere, we aimed to explore whether simple, nonliving dissipative structures could also exhibit associative learning. Inspired by previous modeling of associative learning in chemical networks, we simulated simple systems composed of long- and short-term memory chemical species that could encode the presence or absence of temporal correlations between two external species. The ability to learn this association was implemented in Gray-Scott reaction-diffusion spots, emergent chemical patterns that exhibit self-replication and homeostasis. With the novel ability of associative learning, we demonstrate that simple chemical patterns can exhibit a broad repertoire of lifelike behavior, paving the way for in vitro studies of autonomous chemical learning systems, with potential relevance to artificial life, origins of life, and systems chemistry. The experimental realization of these learning behaviors in protocell or coacervate systems could advance a new research direction in astrobiology, since our system significantly reduces the lower bound on the required complexity for autonomous chemical learning.

Figure 1

Dynamics of key compounds in learning task. Stimulus and toxin bolus deliveries in the learning task to be solved. Delivery period is $\mathcal{T}=1000$ and the time separation between stimulus and toxin occurrences is $\mathrm{\Delta }\mathcal{T}=400$. Stimulus boluses are always of unit concentration, while the magnitude of toxin boluses are controlled by the environmental parameter $\epsilon \left(t\right)$ (black line), which varies slowly over time. Both stimulus $S$ and toxin $T$ decay exponentially with a short characteristic time ${\tau }_S=0.2\mathcal{T}$.

Figure 2

Dynamics of system in the absence of a defense mechanism. Time evolution of the concentration of $B$ with toxin deliveries, in the absence of any defense network (network ${\mathcal{N}}_0$, see Table 1 for a summary of chemical equations used).

Figure 3

Concentration time series for the three networks. Top: Direct network ${\mathcal{N}}_D$ with $k_D=0.1$. Middle: Preemptive network ${\mathcal{N}}_P$ with $k_P=0.005$. Bottom: Associative learning network ${\mathcal{N}}_A$ with $k_A=0.006$ (see Table 1 for a summary of chemical equations used in each network).

Figure 4

Dynamics of environmental parameter and long-term memory. Time evolution of the environmental parameter $\epsilon \left(t\right)$ controlling toxin bolus concentration and long-term memory $L$ for the optimal associative learning network.

Figure 5

Long-term memory concentration as a low-pass filter. Environmental parameter $\epsilon \left(t\right)$ varies with a more complex time evolution (computed as the sum of three sine waves of random amplitude, frequency and phase). The long-term memory concentration acts like a low-pass filter on $\epsilon \left(t\right)$. It approximates $\epsilon \left(t\right)$ with a slight lag related to the long-term memory characteristic timescale, and also exhibits high frequency oscillations (appearing as the thick segment of the curve) due to the periodic bolus deliveries.

Figure 6

Performance variations as a function of reaction constant. Performance of the different networks, measured as the temporal average of the concentration of $B$, as each key network reaction constant is varied. (See Table 1 for a summary of chemical equations used in each network.)

Figure 7

Dynamics of uniform delivery system. Time series of the spatial average concentration of Gray Scott component $B$, Toxin $T$ and Antidote $N$, along with the number of RDSTs, in the case of uniform bolus delivery: (1) no network, (2) direct network, (3) preemptive network, (4) associative learning network (time series of toxin and antidote concentration have been filtered to remove high frequency oscillations). See Table 1 for a summary of chemical equations used in each network.

Figure 8

Dynamics of boundary delivery system. Time series of the spatial average concentration of Gray Scott component $B$, Toxin $T$ and Antidote $N$, along with the number of RDSTs, in the case of boundary diffusion bolus delivery: (1) no network, (2) direct network, (3) preemptive network, (4) associative learning network (time series of toxin and antidote concentration have been filtered to remove high frequency oscillations). See Table 1 for a summary of chemical equations used in each network.

Figure 9

Spatial behavior of uniform delivery system. Snapshots of the Gray-Scott $B$ component and long-term memory $L$ concentration at regular time intervals in the uniform delivery case, for the associative learning network ${\mathcal{N}}_A$. This sequence corresponds to the bottom panel of Fig. 7.

Figure 10

Spatial behavior of boundary delivery system. Snapshots of the Gray-Scott $B$ component and long-term memory $L$ concentration at regular time intervals in the boundary diffusion delivery case, for the associative learning network ${\mathcal{N}}_A$. This sequence corresponds to the bottom panel of Fig. 8.

Figure 11

Comparison between preemptive and associative concentration fields. Concentration map for preemptive and associative network in the boundary diffusion case, at the same time stamp ($t=3010$, after 10 toxin deliveries.) For the associative network (right), antidote production is located at the boundary, as dictated by long-term memory concentration. For the preemptive network (left), antidote is produced by all spots in comparable amounts.