Nucleic acids(6, 7), peptides(2, 3, 8), and surfactants(9–11) can be designed to self-replicate via chemical templating(6, 7, 12–14) and liquid droplet division(9, 15, 16). Although conceptually exciting, the practicality of these findings is not apparent, because the produced molecules and particles remain largely disorganized. Additionally, the biological polymers and liquid colloids foundational for simplified replicas of dividing cells are structurally complicated and environmentally sensitive. Self-replicating inorganic colloids are technologically more attractive than organic molecules and particles because they possess structural simplicity and environmental robustness as well as multiple favorable optical, catalytic, and electrical properties, which are absent in organic particles and molecules. Mirroring some organic systems, the self-replication of particles via chemical templating has been modeled computationally(17–21), however, chemical pathways to their experimental realization are not apparent yet. Similarly, self-replication by colloidal division requires much higher (>10x) activation energy than organic systems because the cohesion energy of inorganic crystals, held together by strong interatomic bonds, is much higher than that of droplets held together by weak intermolecular interactions.
We hypothesized that thermodynamic barriers for self-replication can be reduced for nanoparticles (NPs). Photoinduced autocatalytic reduction of metal ions, for instance Ag+, in the vicinity of metal NPs can be used for the practical realization of NP self-replication. The newly formed particles can then induce nucleation of their own offspring. Furthermore, the strong van der Waals (vdW) attraction between mother (NPm) and daughter (NPd) nanoparticles with Hamaker constants(22) ~5x higher than those of organic substances (e.g., 25×10−20 J for gold vs. 5×10−20 J for hydrocarbons), should facilitate the self-assembly. Such a light-driven system appears to be experimentally plausible but fundamentally non-trivial. The first challenge is to drastically slow down the growth of NPm at specific size so that NPd start growing and reach similar sizes, before the local supply of Ag+ is exhausted. Second, 1-3 nm thick surfactant layers are typically required for the colloidal stability of NPs(23, 24). However, these layers create a barrier for electron ejection into the solvent, preventing generation of NPd and reducing vdW attraction between NPs. Surfactant-related challenges also include strong light scattering(9, 13), weak attenuation of electron beams, and competitive adsorption of long-chain molecules to solid surfaces. All these factors prevent the observation of nanoscale dynamics in real time and undermine the identification of chemical mechanisms.
Realization of the reaction cascade, where self-replication is followed by spontaneous organization into structures with partial order, creates a separate set of chemical challenges. Central among them is the irreversible agglomeration of particles into disorganized precipitates, which hinders both self-replication and the emergence of complex structures. Additionally, the shape, size, and composition of self-replicated particles are determined by the local conditions rather than the NPm as in surfactant-stabilized droplets(9, 13, 15, 16); thus, they strongly fluctuate through the system. These factors discourage self-organization of NPs into assemblies with distinct structural patterns.
Light-Driven Autocatalytic Self-Replication
All these challenges, combined with prior knowledge of NP interactions(25) and crystallization behavior (26–28) informed our choice to make nanoscale chemistry conducive to self-replication and the subsequent self-assembly of NPs. We investigated an open system based on silver NPs carrying citrate ions as surface ligands (Fig. 1A). These surface ligands are small and labile, creating a minimal redox barrier, yet sufficient to prevent the rapid growth of NPm. Excitation of the plasmonic states of metal NPs leads to electromagnetic hot spots, where electrons are photoejected into the surrounding media(29). Solvated electrons reduce Ag+ into solvated Ag0, which leads to the nucleation of NPd in the vicinity of the NPm (Fig. 1,and Supplementary Text 1). Specifically, a solution of 0.1 mM silver nitrate (AgNO3) and 3 mM sodium citrate dihydrate at pH of 10.3 was illuminated under 365 nm ultraviolet (UV) light with an intensity of 1.3 mW/cm2 (fig. S2 and Supplementary Text 2). The optical extinction peak between 400 and 420 nm followed nearly ideal S-shaped kinetic profiles (Fig. 1C, fig. S2), expected for self-replicating and autocatalytic systems(30–32). The lag time seen in Fig 1C corresponds to the slow emergence of few NPd initially, followed by a stage of explosive growth in the middle of the S-curve when the local concentration of Ag+ remains high. The final plateau in the S-curve is reached when Ag+ ions in solution (i.e., food) are depleted (33). The minimalism of this system is quite remarkable. Its simplicity also makes it robust for a wide range of physical conditions, which include illumination with photons and electrons of different energies. The system can also be realized under 1D, 2D, and 3D diffusion conditions to enable the spatial modulation of self-replication.
Using the high contrast of NPs in electron beams, transmission electron microscopy (TEM) was applied to determine the structural and temporal patterns of the NP product(s) (Figs. 1,2). Under conditions resulting in the S-shaped accumulation kinetics, irregularly shaped NPs gradually increased during the illumination (fig. S3). The peak wavelength shifts slightly from 417 nm (fig. S1A and Supplementary Text 3) to 402 nm due to increased charge density around the NPs (fig. S4)(34). Cryo-TEM images indicate the formation of 1.1-1.5 nm clusters of critical nuclei near the surface of NPm with an average diameter d ~ 8 nm(Fig. 1D, 60 min), confirming the mechanism of photoinduced autocatalytic nucleation (Fig. 1A). These clusters produced NPd (Figs.1, 2, fig. S7B) via interparticle exchange of Ag0 and catalytic reduction of Ag+.
The advantages of simple inorganic NPs were also utilized to investigate the dynamics and localization of NP products using nanoscale tracking analysis (NTA), which enabled the direct count of particles in the media. NTA data also revealed S-shaped kinetics (Fig. 1C) with an incubation period, followed by a rapid increase in NP count, and a final plateau, which confirmed the photoinduced autocatalytic generation of NPs.
Self-Assembly of Photogenerated NPs
Cryo-TEM images (Fig. 1 E, F, fig. s7, s8), zeta-potential distribution (fig. S5), NTA dark field microscopy videos, and photo snapshots (fig. S6, Movie S1), showed that self-replication is accompanied by the self-assembly of NPs into particle chains (Supplementary Texts 4, 5). The average quasi-steady-state NP size depends on the illumination conditions and can be varied from d equal to 6.6 nm ± 2.7 nm, 16.1 nm ± 2.2 nm, and 18.2 nm ± 2.1 after 30, 60, and 180 min of 365 nm illumination, respectively (fig. S3); illumination by a 130 e-/Å·s electron beam leads to chains with d =13.6 ± 3.5 nm. The NP chains, rather than disordered agglomerates, formed because of the spatially restricted attachment that originated from the propagating linear anisotropy. Starting from NP pairs, the energy barrier for NPs to approach the axial assembly is higher in the middle than at the apexes(5).
Constrains on Ag+ diffusion can strongly diminish the rate of NP nucleation and growth, which disrupts the formation of the chains. Indicative of the process robustness, conformal self-assembly of self-replicating NPs was also observed on surfaces, for example, on polyelectrolyte-functionalized(35) TEM grids floating on the surface of the growth solution (Fig. 1E, fig. S8,and Supplementary Text 6). The distances between the NPs in these samples were 0.5-0.9 nm (fig. S9), which is characteristic of the ejection of hot electrons that reduce the Ag+ ions in solution around the NPm(36–38), in agreement with schematics in Fig.1A.
Nanoscale videography using liquid-phase TEM (LP-TEM) demonstrated the rapid growth of intersecting NP chains following self-replication (Movie S2, Fig. 2, Supplementary Text 7). Movie S3 also shows that NPd can nucleate outside of the focus area, diffuse, and attach to a pre-formed chain from a different NPm. Chain length is diminished for non-replicating NP systems (fig. S10, Movie S4,and Supplementary Text 8) with predominant generation of individual NPs.
Electromagnetic field localized between mesoscale singularities can also restrict the location and growth direction of NP chains but without diminishing Ag+ diffusion, which creates additional opportunities for spatial organization of the newly formed NPs. Hedgehog particles (HPs) with zinc oxide (ZnO) spikes(39) produce hotspot singularities at the ends of their apexes (Fig. 3D-F). Additionally, 365 nm light generates high-field zones bridging them (Fig. 3F, inset). Consequently, NPs emerge preferentially on the apexes and produce bridges between the spikes. Furthermore, HPs stabilize the NP assemblies against fluidic distortions and capillary forces during drying (Fig. 3 and fig. S18).
Kinetics and Thermodynamics of the Self-Replicating NP Chains
We sought a quantitative theoretical description for the observed S-shaped kinetics (Fig. 1C, fig. S2) based on parameters that are experimentally accessible for the NP system. The standard Finke-Watzky model, successfully used for the standard description of NP growth in the past (28) unfortunately did not fit to the temporal trajectories as shown in figs. S11C, S12, S14 (Supplementary Text 9). We modified the Finke-Watzky model to account for the chemical reactions described by Eq. S3-S6, including two populations of exchangeable and non-exchangeable silver atoms located on the surface and in the cores of the NPs. A set of kinetic constants k1, k2, and k3 describe the rates of three light-driven redox reactions caused by the capture of photoejected electrons by Ag+ and NPs (Supplementary Text 10, fig. S1A). Our kinetic model resulted in high-confidence fits to the S-shape experimental curves under various illumination conditions (Figs. 3A, B, C). It also predicted S-shape curves for other chemical components, (i.e., Ag+ and Ag0, fig. S13) and trends for temporal derivatives of NP concentration, that is, d[NP]/dt, d2[NP]/dt2 and d3[NP]/dt3 (fig. S14). Using experimental data for three light intensities (i.e., 1.3, 8, and 17.2 mW/cm2) and additional checkpoints provided by the TEM images (fig. S15 and fig. S16), we obtained confident estimates for these parameters (Fig. 3, C-F and fig. S13, C-F). The calculated k1,k2, and k3 values (Table S1) matched well with the rate constants for the diffusion-controlled nucleation, growth, and agglomeration of transition-metal nanoclusters(40, 41). As expected from Eq. S1-S6, k1,k2, and k3, increased linearly with light intensity (Table S1, Fig. S17), which is typical for photoinduced reactions.
We also sought to determine the chemical reasons for consistent switching from the growth of NPm to the growth of NPd, which is the rapid drop in the chemical potential, μ, with the particle volume (Supplementary text 11). Thermodynamic estimates based the Gibbs−Thomson relation, surface tension (γ), and dependence of μ on particle size(28, 38, 42), calculate the average NP diameter to be d = 6.4 nm the transition from the rapid to slow growth of NPm, which is accompanied by the onset of the rapid growth of NPd. The comparison of this estimate with an experimental diameter d = 6.6 nm ± 2.7 nm of the self-replicated NPs after 30 minutes of illumination (Fig. 1C, fig. S3) reveals a nearly exact match. The same NP size of ~6 nm was observed in mother-daughter pairs when the rate of post-formation growth was diminished (fig. S10). Cryo-TEM data for the NPm also established a characteristic diameter of ~8 nm (Fig. 1E). Subsequent growth of the NPs into chains is associated with finite probability of plasmon localization on any NP in the chain and gradual oxidation of citrate, which leads to increased γ and thus particle size.
Self-organization into complex NP networks
Networks represent a nearly universal higher order structural motif in the domains of biology and technology. Illumination of the glass slides floating on the growth solution surface-functionalized with (PSS/PDDA)3PDDA bilayers(43) leads to the formation of multiple nanostructured colonies consisting of several hundreds of interconnected NPs localized in microscale patches. The NPs in these colonies produce neurite-like networks that radially spread from the central nucleation site (Fig. 4 D). Continuous conduction through the NP networks conformally grown on solid surfaces can be obtained via electroless metal deposition catalysed by the deposited particles (fig. S19 and Supplementary Text 12).
The NP networks may appear random, but they follow specific hierarchical patterns that combine both order and disorder(44) reflective of the self-replication mechanisms and patterns.The structural organization and morphological complexity of these NP networks was assessed (Fig. 4) using Graph Theory (GT) and Fractal Theory (FT). To highlight the non-randomness of the NP networks, we compared them to bacterial and fungal networks. Cell cultures of Streptococcus spp. biofilm grown on agar and R. stolonifera biofilms grown on Capsicum annuum L represented bacterial and fungal networks, respectively. Additional data sets on fungal networks were extracted from the literature; they included Aspergillus fumigates biofilm grown on a confluent layer of human bronchial epithelia cells(45),Trametes versicolor biofilm grown on wheat grain(46),Ganoderma lucidum biofilm grown on wood(47), and Aspergilus Niger 55890biofilm grown on agar(48) (fig. S21 and Table S1).
The GT parameters of average nodal degree (AD),average clustering coefficient (ACC),average nodal connectivity(ANC), and assortativity coefficient (AC) enabled a quantitative multiparameter comparison of the organizational patterns. Albeit not perfectly ordered, the values of ACC, ANC, and AC as well as their variability indicate that these networks are far from being random. For example, the absolute value of |AC| can be as high as 0.25-0.3 compared to AC = 0 for random networks. Similarly, ACC in random networks with a similar number of nodes is expected to be ~10-3, while for those for NPs and other networks (as shown in Fig. 4 I)exceed 10-2. Furthermore, the multiparameter assessment indicates that the networks produced by NPs are structurally identical to those produced by Streptococcus spp. (Fig. 4). However, they are distinctly different from the networks produced by fungi. For both bacteria and NPs, the networks are the product of self-replication followed by the attachment of NPd to NPm (replicate-and-attach mechanism). For fungi, the networks are the product of individual cell growth, resulting in their intersection (grow-and-intersect mechanism), which results in different structural patterns.
Applying FT, the average value of fractal dimension, df, for NP networks is 1.75 ± 0.041, which is similar to dendritic assemblies of NPs from previous studies (49). Bacterial and fungal networks display df values of 1.88 ± 0.040 and 1.85 ± 0.020. The fractal dimensions for all the different networks are surprisingly close, which make the comparative analysis using GT more accurate. The combination of GT and FT enables quantitative evaluation of their complexity based on the multifractal spectra, f(α), of their graph representations(50). The values for the Lipschitz-Hölder exponent, α, when f(α) reaches maximum are 1.41, 1.2, and 1.45 for NPs, Streptococcus spp., and R.stolonifera, respectively (fig. S23). Despite the NP simplicity, the complexity of resulting NP networks is at least as great as those produced by bacteria and fungi.
In conclusion, the photocatalytic properties of NPs provide a path to a self-replicating system that can be fully abiotic. Strong attractive vdW forces, combined with spatial restrictions on NP attachment, lead to self-organization of networked architectures. As a representation of the technological benefits of self-replication coupled with self-assembly, the conductive and other networks are produced under UV light with intensity that is ~30 times lower than that used in lithographic processes(51). A parallel can be made with energy-frugal biological systems that tap into abundant thermal energy to self-assemble cellular substructures with remarkable energy efficiency(52, 53). Also note that the emergence of partial order in NP systems with quantifiable similarities to biological patterns via non-biological mechanisms could potentially rationalise the curios forms of inorganic microstructures observed in meteorites and sediments previously misinterpreted as bacterial fossils (54).