Emergent Behaviors in Kinetically Controlled Dynamic Self-Assembly of Synthetic Molecular Systems.

Living systems are categorically a kinetic state of matter that exhibits complex functions and emergent behaviors. By contrast, synthetic systems are relatively simple and are typically controlled by the thermodynamic parameters. To understand this inherent difference between the biological and synthetic systems, novel approaches are of vital importance. In this regard, we have designed a three-component molecular system (a triad) by conjugating an amino acid with two functional molecules (naphthalenediimide and pyrene), which facilitates kinetically controlled self-assemblies. Herein, we describe three different molecular aggregation states of triads (entitled State I, State II, and State III) and also the dynamic pathway complexities associated with their transformations from one state to another. By meticulously employing the triads of different molecular aggregation states and the stereochemical information of the amino acid, we report emergent behaviors termed "supramolecular speciation" and "supramolecular regulation". Further, we present a hitherto unknown emergent property in a self-assembled state under the majority-rules experiment, which has been termed "super-nonlinearity". This work provides novel insights into complex synthetic systems having unprecedented functions and properties. Such emergent behaviors of synthetic triads that involve an interplay among complex interactions may find relevance in the context of prebiotic chemical evolution.

Introduction

Living cells embody an exclusive collection of self-assembled molecular entities that by themselves are nonliving in nature.[1−3] Nonetheless, through the delicate interplay of an interactive network of molecular ensembles, they exhibit emergent properties such as self-reproduction (self-replication/autocatalysis), self-maintenance (autoregulation), and Darwinian evolution.[4−22] Emergence is the process by which complex systems and patterns arise out of a multitude of relatively simple interactions. Emergent behaviors are often unpredictable and unprecedented and represent the advanced stages of the system’s evolution. In spite of our expertise to invariably synthesize almost all biomolecules in the laboratory, synthetic systems that can showcase emergent properties and complex lifelike functions as well as their underlying molecular mechanisms are relatively unknown. In this context, we present a kinetically controlled synthetic molecular system that exhibits emergent behaviors such as supramolecular speciation, supramolecular regulation, super-nonlinearity, and chiral denaturation.

Almost all synthetic molecular assemblies are thermodynamically controlled, whereas living systems are a kinetic state of matter that maintains a far-from-equilibrium state.[23−26] The kinetically controlled systems enable the regulation of their behavior depending on the changes in the surrounding medium.[27−38] Moreover, it is rather difficult to emulate such biomolecular systems with synthetic molecular systems (except analogues) because biomolecular systems possess highly specific biofunctions and unparalleled structure–property relationships.[39−42] In this scenario, it was envisioned that a modular system consisting of simple biomolecular auxiliaries and synthetic functional molecules would be a propitious design strategy to effectively engineer molecular assemblies and to provide better opportunities to emulate biological systems.[43−46] Amino acids are a particularly attractive pool of auxiliaries because of their extraordinary molecular recognition and stereoselective and sequence-specific self-assembling properties.[47] Remarkably, several billion years of evolution has enabled the amino acids to integrate chemical groups (either individually or in the form of peptides/proteins) that facilitate multiple interactions such as hydrogen bonding and hydrophilic, hydrophobic, and aromatic interactions rather synergistically via their compact size and positions. Thus, it was envisaged that by derivatizing functional abiotic molecules with amino acids, a wide variety of functional systems with novel properties and applications can be achieved. Befittingly, it was demonstrated that amino acid-appended functional molecules can be kinetically trapped in organic solvents of appropriate polarity (namely, acetonitrile and dimethyl sulfoxide), which, in turn, can be hydrophobically triggered to undergo spontaneous self-assembly in an aqueous environment or subjected to temporal assembly under solvophobic forces.[45,46,48]

Herein, with an objective to systematically enhance the complexity of the molecular design and their interactions via a simplistic approach, naphthalenediimide (NDI) and pyrene were used as functional molecules that possess a wide variety of promising applications.[43,49,50] Interestingly, the complementary π-character of NDI (π-acidic) and pyrene (π-basic) had earlier enabled us to engineer the molecular assemblies via their π–π stacking interaction energies.[51] In the present work, pyrene–NDI–pyrene conjugates interlinked with alanine, phenylalanine, and isoleucine have been reported, which modulate self-assemblies of the derived triads via distinct stereochemical information (Figure ). Herein, we use the term “triad” to denote our molecular system having three components, namely, NDI, pyrene, and the amino acid. LL, DD, LD, and RAC are alanine-appended triads, whereas C1 and C2 are phenylalanine- and isoleucine-appended triads, respectively. LL, DD, and LD represent the stereochemistry of the alanine linker, whereas the RAC triad was synthesized using a racemic mixture of the alanine precursor. In contrast to the alanine-based triads, C1 and C2 serve as controls for the study, which demonstrates that minute structural mutations can also restrain the temporal assembly behavior as well as the emergent properties.

Figure 1

The generic molecular structure of amino acid-interlinked NDI and the pyrene-based triad. The stereochemistries of amino acids for the respective triads are tabled on the right side. Homochiral (LL & DD) and heterochiral (RAC & LD) molecules that are kinetically trapped in the dimeric/oligomeric state in N-methyl-2-pyrrolidone (NMP) undergo homogeneous/heterogeneous nucleation and successive elongation by supramolecular polymerization in aqueous NMP to ultimately form respective nanoarchitectures.

Results and Discussion

Dynamic Molecular Self-Assembly

Ultraviolet–visible (UV–vis) absorption spectra of the triads (LL/DD/RAC/LD) in NMP showed characteristic absorption bands in the region of 270–400 nm because of the π–π* transitions of NDI and pyrene (Figure S2).[43] The triads were hydrophobically triggered to undergo π–π stacking in aqueous NMP (having different volume percentages of water in NMP). Under the enhanced hydrophobic forces of water, a new broad absorption band (400–650 nm) was observed because of the intermolecular charge transfer interaction between NDI and pyrene moieties.[51] The triads were further probed using CD studies to understand the nature of their helical assembly. In aqueous NMP, LL showed the characteristic sigmoid-shaped temporal self-assembly (Figure a). The differences in the kinetic nature of the sigmoidal traces of LL in aqueous NMP reflect the effect of enhanced hydrophobic forces on their helical assemblies. The CD signals arising from the excitonic coupling of transition dipole moments of NDI and pyrene were found to have distinct spectral features as a function of solvent composition (Figure b,c). Notably, three main aggregation states could be described, namely, State I, State II, and State III. For up to 34% of the aqueous content in NMP, LL retained State I. With the successive increase in water content, transition from State I to State II (40% aqueous NMP) and, in turn, to State III (46% aqueous NMP) was observed. On the other hand, the DD enantiomer exhibited spectral features similar to those of LL, with some interesting variations (Figure d). Herein, the transition from State I to State II occurred at 30% of the aqueous content in NMP (Figure e), instead of 34%, as in the case of LL (Figure b). The transition from State I to State II was completed at 36% aqueous NMP, above which a transition to State III occurred (Figure e,f).

Figure 2

Time-dependent circular dichroism (CD) spectra of 200 μM solutions of (a) LL (monitored at 350 nm) and (d) DD (monitored at 360 nm) in aqueous NMP. The values represent the various volume percentages of water in NMP. The corresponding CD spectra in (b,c) and (e,f) display the distinct aggregation states of LL and DD, respectively.

Interestingly, an unprecedented sequential transition encompassing all three distinct aggregation states of DD in 36% aqueous NMP was observed (Figure a). Such automated aggregation pathway complexities involving transitions from State I to State III and, in turn, to State II occurring over a timescale of several minutes may be highlighted as one of the striking aspects of this molecular system.[52,53] The above-described molecular self-assembly behavior indicates four solvent compositions, namely, 30%, 36%, 40%, and 46% of the aqueous NMP (denoted as Sol30, Sol36, Sol40, and Sol46, respectively), wherein different combinations of the LL and DD aggregation states exist (Figure S3).

Figure 3

(a) Time-dependent CD spectra of LL (200 μM) in 36% aqueous NMP, monitored at 360 nm. (b) Plot of T50 (time at which 50% aggregation occurs) for 200 μM solutions of LL and DD in aqueous NMP. (c) Time-dependent CD spectra of 200 μM solutions of LL and DD under the majority-rules experiment in Sol40, monitored at 280 nm. (d) The corresponding CD spectra of (c) for various stoichiometric ratios of LL and DD. (e) CD amplitudes measured at 280 and 490 nm for the majority-rules experiment in Sol40. The green and orange dotted lines respectively represent the typical “no amplification” and “conventional amplification” under the majority-rules experiment. (f) CD amplitudes for the majority-rules experiment in Sol30, Sol34, Sol40, and Sol46. Sol30 and Sol34 were monitored at 277 nm. Sol40 and Sol46 were monitored at 280 nm.

In Figure b, a plot of the solvent composition has been shown against the time at which 50% of aggregation occurs (termed T50) to illustrate the relative differences in the aggregation dynamics of LL and DD. Expectedly, RAC did not show any CD signals in NMP and aqueous NMP, suggesting the absence of any enantiomeric excesses to induce a biased helical assembly (Figure S4). In addition, LD also did not show any CD signals in NMP because of an opposing biasing effect of the L and D isomers. However, under enhanced hydrophobic forces, LD showed bisignated CD signals because of probable chiral symmetry breaking.

Majority-Rules Experiment

The existence of the distinct aggregation states of LL and DD led us to envisage the majority-rules experiment, wherein two enantiomers of different stoichiometric ratios are mixed together to enable interesting self-assembly behaviors.[54] In Sol30, both LL and DD existed independently in State I; here, the majority-rules experiment did not show any appreciable CD signal amplification, indicating fidelity behavior (Figure S5). Similarly, in Sol36, minimal CD signal amplification was observed, wherein LL and DD independently existed in State I and State II, respectively. However, in Sol40, mixtures of LL (that independently existed in State II) and DD (that independently existed in State III) displayed a hitherto unknown dynamic assembly behavior under the majority-rules condition. The sigmoidal time course for various stoichiometric ratios of the enantiomers LL and DD reflected unusual cooperativity (Figure c).[55] Further, the CD spectral features recorded after the temporal studies were remarkably different from those of LL or DD (Figure d). These distinguishable CD spectral features suggest the formation of distinct aggregation states for various stoichiometric ratios of LL and DD. The distinct CD spectral features indicate supramolecular speciation in terms of the helical organization, which involves the formation of respective heterogeneous nuclei and successive elongation by supramolecular polymerization.[17] This archetypal speciation at the supramolecular level involving structural reorganization (vide infra) of dynamically formed aggregates for various compositions of LL and DD represents the advanced stage of system’s evolution.

The plot of CD amplitude at 280 nm against the enantiomeric excesses clearly showed a set of nonlinear data points (Figure e). Typically, fidelity assembly behavior of enantiomers results in a linear plot, as represented by the dashed green line in Figure e. In the case of CD signal amplification due to majority rules, the best possible system would have data points along the dashed orange line as shown in Figure e.[54] Nonlinear plots under majority rules arise from the mixed stacking of minor and major enantiomers in a single column, giving rise to strong and weak CD signals at low and high enantiomeric excess values, respectively. Besides the experimental observation in molecular and macromolecular systems, theoretical validation of such conventional nonlinearity has been reported in the literature.[56] Surprisingly, data points in Figure e are well over the limits of conventional nonlinearity, and the nature of the resulting spectra is also quite distinct from that of LL or DD. To the best of our knowledge, this anomalous behavior is the first case of a novel emergent property in a molecularly self-assembled system and it has been specifically termed “super-nonlinearity.” Remarkably, a careful inspection revealed that the plot of CD amplitude at 480 nm (charge transfer band[57]) for various enantiomeric excesses was complementary to that at 280 nm (Figure e). Notably, the CD amplitude for a fixed concentration of specific molecular species (molar extinction coefficient) depends on the interchromophore distance and the angle between their transition dipole moments. Thus, the observed CD spectral changes strongly suggest that LL and DD undergo a significant structural reorganization at the supramolecular level for various stoichiometric ratios, thereby leading to the observed emergent property. Similarly, various stoichiometric ratios of LL (that independently existed in State III) and DD (that independently existed in State III) in Sol46 also displayed distinct CD spectral features (Figure S6). Once again, the plot of CD intensity against the enantiomeric excesses showed nonlinearity well over the conventional type. Thus, it is evident that the solvent compositions of Sol30, Sol36, Sol40, and Sol46 determine the nature of the supramolecular species (helical aggregates) formed by the mixture of LL and DD, thereby reflecting the solvophobic effect on their kinetic stability (Figure f). It is important to note that for a specific solvent composition (e.g., Sol40), the hydrophobic force imposed is fixed whereas the nature of the supramolecular species formed is distinct and therefore it reflects the formation of different kinetic species for various stoichiometric ratios of LL and DD.

Sergeants-and-Soldiers Experiment

The triads were further subjected to a modified version of the sergeants-and-soldiers experiment, wherein increasing concentrations of the “soldier” (RAC or LD) was added to a fixed concentration of the “sergeant” (enantiomers LL or DD), with the anticipation of achieving stereoselective amplification behavior.[58] When LL (100 μM) was added to RAC in various stoichiometric ratios (25–100 μM) in Sol40, sigmoidal time courses were observed, indicating cooperativity (Figure a). Moreover, the corresponding CD spectra showed the transition from State I to State II upon addition of RAC to LL (Figure b). A similar behavior was observed in the experiment performed with DD upon addition of RAC to Sol40, except that the transition was from State III to State II (Figure S7). Further, the fate of the resulting aggregates, if a heterochiral LD replaced RAC, was investigated. Here as well, upon addition of LD, the cooperative process and the characteristic transition from State I to State II for LL and a transition from State III to State II for DD were observed (Figure S8). To probe the effect of solvent composition, if any, on the transition of aggregation states, additional studies were performed in Sol46. Interestingly, successive addition of RAC to LL or DD in Sol46 revealed the transition from State III to State II via a cooperative process (Figures c,d and S7). A similar transition from State III to State II via a cooperative process was also observed with the successive addition of LD to LL or DD in Sol46 (Figure S9). It should be noted that because of the relative differences in the self-assembly characteristics of LL and DD as a function of solvent composition (Figure b), typical sigmoidal curves having a lag phase are not observed in some cases. For such cases, by employing lower concentrations of the sergeant and soldier, typical sigmoidal curves can be obtained. From the above experiments, it is evident that irrespective of solvent compositions (Sol40/Sol46) and the stereochemistry (RAC/LD) of the moieties added to LL or DD, a transition from either State I or State III to State II occurred. This characteristic property of the molecular system to mitigate the formation of State II from various constraints (detailed above) is termed “supramolecular regulation.”

Figure 4

Time-dependent CD spectra of 100 μM solutions of LL upon addition of various stoichiometric ratios of RAC under a modified sergeants-and-soldiers experiment (monitored at 350 nm) in (a) Sol40 and (c) Sol46. The corresponding CD spectra of (a) and (c) are shown in (b) and (d), respectively. Temperature-dependent CD spectra of LL and DD for (e) State I, (f) State II, and (g) State III. (e) LL and DD (200 μM) in NMP monitored at 346 nm. (f) LL (125 μM) in Sol40 monitored at 350 nm; DD (125 μM) in Sol34 monitored at 350 nm. (g) LL (125 μM) in Sol46 monitored at 350 nm; DD (125 μM) in Sol40 monitored at 360 nm.

Mechanism and Discussion

Concentration-dependent studies revealed that the transition from State I to State II could be achieved in Sol40 by increasing the concentration of LL from 100 to 200 μM (Figure S12). On the other hand, DD showed the existence of State III in the concentration range of 50–200 μM in Sol40. Further, the temperature-dependent CD studies showed that all of the three aggregation states (State I–III) of LL and DD were kinetically controlled aggregates.[55] State I was a kinetically trapped state because the aggregates did not melt even at 90 °C, whereas State II and State III exhibited chiral denaturation behavior, as described in an earlier report (Figure e–g).[46] The differences in the trajectories of the heating and cooling cycles of State II and State III indicated that the self-assembly was not under thermodynamic control. As the transitions from State III to State II are evident from sergeants-and-soldiers experiments and the temporal assembly of DD in Sol36 (Figure a), State III and State II were termed “kinetically controlled” (kinetically less stable) aggregates and “pseudo-thermodynamically-controlled” (kinetically more stable) aggregates, respectively, under these conditions. The aggregates formed under majority-rules and sergeants-and-soldiers experiments were also kinetic in nature and exhibited the characteristic chiral denaturation behavior (Figure S13).

Morphological studies provided additional evidence to support the existence of different aggregation states of this molecular system. The kinetically trapped State I (for both LL and DD) showed a spherical architecture of 1–4 μm diameter (Figure a,b). States II and III of LL and DD exhibited right-handed and left-handed helical nanofibers, respectively (Figure c–f). These helical nanofibers were of 10–25 nm width and 25–55 nm helical pitch. Also, there were no appreciable morphological differences between the respective States II and III of LL and DD. Expectedly, the aggregates formed under the majority-rules experiment by the cooperative assembly of LL and DD enantiomers resulted in nanobelts of 10–100 nm width (Figure g–i). On the other hand, RAC formed nanobelts that were several micrometers long and 10–100 nm wide; LD resulted in shorter nanobelts of similar lateral dimensions (Figure j,k). Interestingly, the aggregates formed from the mixture of LL (or DD) and RAC revealed nanobelt (15–100 nm width) architectures, whereas the aggregates formed from the mixture of LL (or DD) and LD showed spherical (15–200 nm diameter) agglomerates (Figures l,m and S19). Additionally, the formation of nonhelical (15–100 nm width) architectures of LL and DD after a heating–cooling cycle provided compelling evidence in favor of chiral denaturation (Figure n,o).

Figure 5

Field emission scanning electron microscopy (FESEM) images from 200 μM solutions of (a) LL in NMP, (b) DD in NMP, (c), LL in Sol40, (d) DD in Sol34, (e), LL in Sol46, (f) DD in Sol46, (g) 8:2 mixture of LL and DD in Sol40, (h) 5:5 mixture of LL and DD in Sol40, (i) 2:8 mixture of LL and DD in Sol40, (j) RAC in Sol40, (k) LD in Sol40, (l) 1:1 mixture of LL and RAC in Sol40, (m) 1:1 mixture of LL and LD in Sol40, (n) LL in Sol40 after a heating (to 90 °C) and cooling (to 20 °C) cycle, and (o) DD in Sol40 after a heating (to 90 °C) and cooling (to 20 °C) cycle.

The sigmoidal traces that evidently involve the nucleation–elongation-based supramolecular polymerization were further utilized to extract kinetic parameters (Figure and Supporting Information). With the aid of kinetic analysis carried out in MATLAB, we show that two kinetic models can perfectly fit our sigmoidal traces. The two-step and four-step kinetic models proposed in this work are the Finke–Watsky (F–W) two-step single-autocatalytic mechanism (two rate constants k1 and k2) and the four-step double-autocatalytic mechanism (four rate constants k1, k2, k3, and k4), respectively.[59,60] The F–W two-step model is widely used to analyze the kinetics of protein aggregation because it is the simplest kinetic model that can clearly deconvolute the nucleation and elongation steps.[59,61−63] Recently, a simulation study to understand the nucleation–elongation-based self-assembly kinetics of conjugated molecules was also described using the F–W two-step autocatalytic model.[64]

The concentration- and solvent composition-dependent kinetic traces of DD were found to follow the two-step kinetic mechanism. On the other hand, LL showed the two-step pathway at lower concentrations and low water content in aqueous NMP, while exhibiting the four-step mechanism at higher concentrations and high aqueous content in the solvent composition. For example, a 125 μM solution of LL in Sol40 revealed a two-step mechanism with k1 = 2.8095 × 10–07 and k2 = 3.1886 × 10–04, whereas the 200 μM solution of LL in Sol38 exhibited a four-step pathway with k1 = 1.545 × 10–09, k2 = 2.355 × 10–04, k3 = 4.065 × 10–05, and k4 = 4.306 × 10–05. The latter case of the four-step mechanism of LL could be ascribed to the formation of higher order aggregates under enhanced hydrophobic forces and at higher concentrations.

Many of the kinetic traces of majority-rules and sergeants-and-soldiers experiments were found to fit both two-step and four-step mechanisms, whereas for a few cases, the four-step model was found to be a better fit. The selection of two-step or four-step mechanism under the majority-rules and sergeants-and-soldiers experiments for a specific chemical composition is thought to depend on the kinetic stability of the heterogeneous nucleus, which can then facilitate the elongation via supramolecular polymerization (Figure ).

The majority-rules experiments carried out under different environmental constraints imposed by the solvent media, namely, Sol30, Sol36, Sol40, and Sol46, suggest that two kinetic systems may be necessary for the emergent properties, whereas the cooperativity between them appears to play the most crucial role (Figure S1). LL and DD independently exist in State II and State III in Sol40, respectively, whereas they both exist in State III in Sol46; therefore, the existence of distinct aggregation states is not necessary to achieve the emergent super-nonlinearity. It is to be noted that the spontaneous assembly of LL and DD, as in Sol46, can also lead to super-nonlinearity analogous to their temporal assembly in Sol40. Although LL was found to follow both two-step and four-step mechanisms, the concentrations of LL employed under the majority-rules and sergeants-and-soldiers experiments were not more than 100 μM. Hence, it is appropriate to conclude that two different types of kinetic mechanisms are also not necessary for anomalous self-assembly behaviors (Figure S12). In contrast, the present studies reveal that C1 and C2 do not show any temporal or unusual assembly behavior, possibly because of their bulky hydrophobic side chains that facilitate rapid aggregation in aqueous NMP and also engender additional hindrance for the interactions between the NDI and pyrene functionalities (Figure S4).

Experimental Section

Materials

1,4,5,8-Naphthalenetetracarboxylic acid dianhydride, 1-pyrenemethylamine hydrochloride, and N,N-diisopropylethylamine were obtained from Sigma-Aldrich. 1-Hydroxybenzotriazole, l-alanine, d-alanine, rac-alanine, l-phenylalanine, and l-isoleucine were obtained from Spectrochem Pvt. Ltd. (Mumbai, India). All other reagents and solvents were of reagent grade and used without further purification.

NMR Spectroscopy, Mass Spectrometry (MS), and Elemental Analysis

1H and 13C NMR spectra were recorded on a Bruker AV-400 spectrometer, with chemical shifts reported as ppm (in dimethylsulfoxide-d6 with tetramethylsilane as the internal standard). Mass spectra were obtained from a Shimadzu 2020 LC-MS spectrometer. Elemental analysis was carried out on a ThermoScientific FLASH 2000 Organic Element Analyzer.

Absorption Spectroscopy

UV–vis spectra were recorded on a Cary 5000 UV–vis–NIR spectrophotometer (Agilent Technologies). Solutions of the samples of appropriate concentrations were analyzed in a quartz cuvette of 1 mm path length.

CD Spectroscopy

CD measurements were carried out on a Jasco J-815 spectropolarimeter in a nitrogen atmosphere. The sensitivity, time constant, and scan rate were chosen appropriately. Solutions of the samples of appropriate concentrations were analyzed in a quartz cuvette of 1 mm path length. Temperature-dependent measurements were performed using a Peltier-type temperature controller (CDF-4265/15) in the range of 20–90 °C, with a ramp rate of 1–3 °C min–1. For temperature-dependent studies, once the molecular self-assembly of the triad (except State I of LL and DD) reached its saturation (maximum CD amplitude), it was subjected to heating with a specific ramp rate until it reached 90 °C, which was then maintained for 5 min at 90 °C and successively cooled at the same ramp rate to 20 °C. In the case of State I of LL and DD, their solution in NMP was directly used for the temperature-dependent studies, as described above.

Field Emission Scanning Electron Microscopy

FESEM images were acquired using an FEI Nova nanoSEM-600 equipped with a field emission gun operating at 5–10 kV. The samples were prepared by drop-casting 200 μM solutions onto a Si(111) substrate.

Transmission Electron Microscopy (TEM)

TEM images were acquired using a JEOL, JEM 3010 instrument operating at 300 kV. The samples were prepared by drop-casting 200 μM solutions on a 200-mesh holey carbon-supported copper grid.

Self-Assembly Protocol for the Triads

An appropriate volume of the triad was transferred from a freshly prepared 2 mM stock solution in NMP to a sample vial. The triad was then diluted with NMP to a required concentration. The diluted triad was then added to an appropriate volume of water using an Eppendorf micropipette to induce self-assembly under the influence of hydrophobic force. Given the kinetic nature of the self-assembly, the molecular aggregation was dependent on temperature, mechanical agitation, and freshness of the triad stock solution. Thus, the samples were prepared from fresh stock solutions, and the measurements were carried out at 20–25 °C unless otherwise mentioned. To maintain uniformity, the aqueous solution of the triad upon addition of water was gently mixed using the Eppendorf micropipette itself and no vigorous mixing/agitation or sonication was employed. The mixing was done by drawing up and dispensing the solution of the triad in the sample vial thrice using the Eppendorf micropipette. The resulting triad in aqueous NMP was then used for further studies. For the majority-rules and sergeants-and-soldiers experiments, the triads taken from the respective stock solutions were mixed in a vial, which was then diluted with NMP. The mixture of triads in NMP was then added to water, and a similar procedure was followed as described above.

Kinetic Analysis

The kinetic traces of the triads were fitted to two-step (single-autocatalytic) and four-step (double-autocatalytic) models that are respectively known in the literature as the Finke–Watzky two-step model and four-step double-autocatalytic model.[59,60] We employed MATLAB to deduce the rate constants k1, k2, k3, and k4. Starting with an initial estimate, fminsearch was used to find the minimum values because it offers an unconstrained nonlinear optimization for a multivariable function. Given the stiffness of the mathematical problem, thousands of data points, and several orders of magnitude of the solution values (computationally obtained range 10–12–103), ordinary differential equation (ODE) solver ode15s was used to minimize the computation cost as well as to speed up the computational analysis. Additionally, absolute tolerance (AbsTol) and relative tolerance (RelTol) were both set at 1 × 10–06.

The two-step and four-step mechanisms are as follows

A—Monomer or kinetically trapped state

B—Aggregated nucleus

C—Higher-order aggregate

k1—Rate constant for nucleation

k2/k3/k4—Rate constant for growth

t—Time

The two-step mechanism was fitted using the following equation

The four-step mechanism was fitted using the following equations

Conclusions

In conclusion, we showed that the three-component modular system comprising biomolecules (amino acid) and functional molecules (NDI and pyrene) is an effective strategy to tailor molecular self-assembly and to emulate biological systems. By modulating the solvophobic interactions, the triads LL and DD were self-assembled into three different aggregation states, namely, State I, State II, and State III. A sequential transition involving all three different aggregation states of DD that occurred over a timescale of a few minutes is the most-striking dynamic pathway complexity ever observed in a molecularly self-assembled system. Remarkably, emergent behaviors such as supramolecular speciation, supramolecular regulation, and super-nonlinearity have been presented for the first time in a synthetic system. By employing various experiments and techniques, the mechanisms involved during the supramolecular speciation, super-nonlinearity, supramolecular regulation, and chiral denaturation were delineated, which illustrate the effects occurring at the molecular, supramolecular, and microscopic levels. Such efforts are likely to offer novel insights into protein (mis)folding, biochemical signaling, autoregulatory mechanisms, and several other biochemical processes. This report is expected to inspire novel designs to construct complex lifelike emergent ensembles via systems chemistry and/or synthetic biology approaches in the near future.