Fuel-Driven Dynamic Combinatorial Libraries

Article abstract of DOI:10.1021/jacs.1c01616

In dynamic combinatorial libraries, molecules react with each other reversibly to form intricate networks under thermodynamic control. In biological systems, chemical reaction networks operate under kinetic control by the transduction of chemical energy. We thus introduced the notion of energy transduction, via chemical reaction cycles, to a dynamic combinatorial library. In the library, monomers can be oligomerized, oligomers can be deoligomerized, and oligomers can recombine. Interestingly, we found that the dynamics of the library's components were dominated by transacylation, which is an equilibrium reaction. In contrast, the library's dynamics were dictated by fuel-driven activation, which is a nonequilibrium reaction. Finally, we found that self-assembly can play a large role in affecting the reaction's kinetics via feedback mechanisms. The interplay of the simultaneously operating reactions and feedback mechanisms can result in hysteresis effects in which the outcome of the competition for fuel depends on events that occurred in the past. In future work, we envision diversifying the library by modifying building blocks with catalytically active motifs and information-containing monomers.

Full text of DOI:10.1021/jacs.1c01616

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Article
Fuel-Driven Dynamic Combinatorial Libraries
Christine M. E. Kriebisch, Alexander M. Bergmann, and Job Boekhoven*
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ABSTRACT: In dynamic combinatorial libraries, molecules react
with each other reversibly to form intricate networks under
thermodynamic control. In biological systems, chemical reaction
networks operate under kinetic control by the transduction of
chemical energy. We thus introduced the notion of energy
transduction, via chemical reaction cycles, to a dynamic
combinatorial library. In the library, monomers can be
oligomerized, oligomers can be deoligomerized, and oligomers
can recombine. Interestingly, we found that the dynamics of the
library’s components were dominated by transacylation, which is
an equilibrium reaction. In contrast, the library’s dynamics were
dictated by fuel-driven activation, which is a nonequilibrium
reaction. Finally, we found that self-assembly can play a large role in affecting the reaction’s kinetics via feedback mechanisms. The
interplay of the simultaneously operating reactions and feedback mechanisms can result in hysteresis effects in which the outcome of
the competition for fuel depends on events that occurred in the past. In future work, we envision diversifying the library by
modifying building blocks with catalytically active motifs and information-containing monomers.
Moreover, several reaction cycles have been introduced that
lead to the formulation of preliminary design rules for such
structures under kinetic control.27−29 Despite these develop-
ments,27−29 only a few examples exist in which multiple
building blocks compete in a transient dynamic combinatorial
library.24,30,31 In such experiments, we may expect components
of thermodynamic and kinetic control that determine the
composition of the library. However, the interplay of kinetic
and thermodynamic control within dynamic combinatorial
libraries has not been demonstrated.
In this work, we used a well-understood chemically fueled
reaction cycle14 to drive oligomerization and deoligomerization
of building blocks, which are part of a dynamic combinatorial
library. The oligomerization (or activation) reaction creates
transient bonds between the library’s components at the
expense of a chemical fuel, whereas the deoligomerization
(deactivation) reaction destroys these bonds spontaneously. A
reversible equilibrium reaction scrambles the oligomers,
resulting in a dynamic combinatorial library under kinetic
control that results in recombination (Figure 1A). Excitingly,
we find that assembly drastically alters the distribution of the
oligomers in the library.
INTRODUCTION
■
In dynamic combinatorial libraries, molecules react with each
other reversibly under thermodynamic control.1,2 The resulting
library of dynamic interconverting building blocks can give rise
to exciting collective behavior, like the selection of molecules
that can replicate or even evolve within molecular reaction
networks.1,2 Understanding the rudimentary behavior of such
libraries is relevant to better understanding biology, which also
constitutes, at the most rudimentary levels, chemical reaction
networks.3 However, dynamic combinatorial libraries so far
have mostly focused on libraries under thermodynamic
control.1,2 In contrast, living systems are dissipative structures
that are sustained by the constant transduction of energy via
nonequilibrium chemical reactions.4−6 Therefore, reaction
networks of living systems are partly under dynamic kinetic
control.5,6 Models of the dynamic combinatorial chemistry in
living systems that are driven by the transduction of chemical
energy can increase our understanding of the role of
equilibrium and nonequilibrium reactions in biological systems
or at the origin of life (e.g., for RNA),7 which so far has been
studied mostly in or close to equilibrium.8−10 Indeed, studies
on out-of-equilibrium reaction networks in continuously
stirred tank reactors result in exciting behavior like oscillations
and bistability.11−13
Received: February 9, 2021
Published: May 12, 2021
Inspired by the kinetic control in biological structure
formation, synthetic analogues of such systems have been
developed. In these so-called chemically fueled assemblies,
energy-transducing chemical reaction cycles are regulating the
activation and deactivation of molecules for self-assembly.14−26
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Figure 1. Description of the chemically fueled reaction network. (A) Schematic representation of the concept of a transient dynamic combinatorial
library and all oligomers of the transient library. The increase in hydrophobicity decreases the solubility, making oligomers 4−6 more likely to
assemble. (B) Chemical reaction network that converts a chemical fuel (EDC) into waste (EDU) while building up a transient dynamic
combinatorial library. (C) Reversible equilibrium reaction, transacylation, that recombines the oligomers of the library. (D) Formation of the
unwanted side product N-acylisourea 1*. (E) Molecular structures of fuel (EDC) and waste (EDU).
uct is a dimer of the building block (2) and also carries two
carboxylates. This dimer also can be activated and react with
another monomer to yield a trimer (3), which can react further
(4...n, respectively, Figures 1B and S1). Alternatively, these
oligomers can be activated and react with other oligomers. In
both cases, EDC-driven oligomerization increases the average
length of the oligomer in the systems. In contrast, the
oligomeric components in the library are prone to deoligo-
merize via hydrolysis. Dimer 2 can be hydrolyzed to yield two
molecules of the original 1, whereas longer oligomers can be
deactivated into shorter oligomers, e.g., 4 can be hydrolyzed to
RESULTS AND DISCUSSION
■
We chose isophthalic acid (1) as a building block because it
carries two carboxylates under the used conditions (500 mM
MES-buffered water at pH 6) and can thus be converted into a
polyanhydride. Indeed, oligomerization of isophthalic acid to
polyanhydrides has been demonstrated.32,33 In our chemically
fueled reaction cycle, two of these building blocks are
condensed into their corresponding anhydride (2) at the
expense of a condensing agent (EDC, 1-ethyl-3-(3-
(dimethylamino)propyl)carbodiimide, Figure 1E). The prod-
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yield two molecules of 2. In all cases, deoligomerization via
hydrolysis leads to a decrease in the average oligomer length.
Finally, oligomers can transacylate, i.e., an anhydride is
attacked by a carboxylate of a monomer or another oligomer
to yield a new anhydride and carboxylate. For example,
oligomer 3 can be attacked by a monomer to yield two dimers
2. Or, dimer 2 can attack 4, yielding two trimers 3, which is
referred to as transacylation (Figure 1C).24,34,35 Transacylation
scrambles the oligomers but does not change the average
length of the library. We confirmed the presence of
transacylation experimentally (Supporting Notes, Figure S2,
and Table S1). Clearly, our chemically fueled library products
are governed by the kinetics of activation, deactivation, and
transacylation. Moreover, as the oligomer size increases, the
oligomer becomes increasingly more hydrophobic, and we find
that tetramers or higher can assemble (vide infra). Ultimately,
however, the system’s equilibrium state is the monomeric
isophthalic acid 1, i.e., if all fuel is depleted or no fuel is added,
the system reverts to monomers. It is noteworthy that an
unwanted side product, N-acylisourea, can be formed by the
rearrangement of the activated intermediate, O-acylisourea
(Figures 1D and S1).
We dissolved 300 mM 1 in 500 mM MES-buffered water at
pH 6 with 40 mM pyridine, which are also the reaction
conditions for all further experiments. We added a batch of 50
mM EDC and analyzed the emergence and evolution of the
library composition and the fuel by high-performance liquid
chromatography (HPLC) and mass spectrometry (Figure 2A
and Tables S3 and S4). Under the applied conditions, the pH
remained stable between pH 6.0 and 6.2 (Figure S3A). With a
much higher concentration of EDC (i.e., >150 mM), the pH
tended to noticeably increase as the cycle progressed. We
found that the fuel rapidly decayed and was fully consumed
after 16 min (Figure S4A), which resulted in five detectable
anhydride products (2−6, Figure 2A). The major component
was anhydride 2. In contrast, 3 had a roughly 23-fold lower
yield at 1 mM (Figure 2B). The concentrations of 4, 5, and 6
decreased further at 0.17, 0.02, and 0.0025 mM, respectively.
The exponential decay of the concentration as a function of
oligomer length is because the product of one reaction is the
precursor for the next, e.g., 2 is required for the formation of 3,
which is required to form 4. We followed the further evolution
of the cycle. The concentrations of anhydrides 2−6 initially
rose and then collapsed (Figures 2C and S4B−E). It is
noteworthy that, as the cycle progressed, we found the
emergence of an unwanted side product, i.e., the N-acylisourea
1* of monomer 1. Its concentration was <2.5 mM after the
cycle was completed (Figures S4G and S1). The high
concentration of precursor (300 mM) ensures that, despite
the formation of 1*, a sufficient amount of 1 always is present.
Indeed, experiments with only 25 or 100 mM 1 yielded a loss
of 24% of 1 due to its conversion into N-acylisourea 1* (Figure
S3B). It is worth noting that, under these conditions, only
minimal amounts of the anhydrides formed hydrolyze during
the HPLC analysis (Figure S3C).
Figure 2. Response of the dynamic combinatorial library to a batch of
fuel. (A) HPLC chromatogram of the transient dynamic combina-
torial library made from 1, when fueling with 50 mM EDC after 4
min. (B) Maximum concentration of the library compounds 2−6,
plotted on a logarithmic scale when fueling with 50 mM EDC
(crosses). The data is an average of the maximum yields obtained in
the reaction cycle. The kinetic model was used to fit the maximum
yields (squares). (C) HPLC (markers, monitored at 290 nm) data of
3 when 1 was fueled with 50 mM EDC. The kinetic model was used
to fit the experimental data (lines). (D) Schematic representation of
example reactions for the build-up and breakdown of 3 by activation,
deactivation, and transacylation. (E, F) Reaction rates for the
formation and breakdown of 3 via activation, deactivation, or
transacylation.
the rate constant of the reaction of 1 with EDC, yielding the O-
acylisourea (k1). We assumed that this activation rate constant
is similar for all oligomer species. We then fitted the evolution
of the N-acylisourea 1* concentration to obtain the rate
constants of its formation (k3). Because the O-acylisourea was
never observed, we ensured that 1 or the oligomers rapidly
reacted toward the anhydride by choosing a high-rate constant
attack of the O-acylisourea by 1 or the oligomers (k2). We used
the evolution of the anhydrides to fit k4 and k5, which describe
the anhydride hydrolysis and the transacylation reaction rate
constants (Table S6). We considered that transacylation is
faster than hydrolysis in the presence of pyridine.24,34,35 The
fitted rate constant ensured that the kinetic model accurately
predicted the decay of the concentration of EDC and the
emergence of N-acylisourea 1* (Figure S4A and G). It also
captured the exponential decay of the maximum concentration
of each oligomer as a function of oligomer length (Figure 2B).
It is noteworthy that the model predicted the evolution
To quantitatively understand the kinetics that dominates the
evolution of the library, we wrote a kinetic model that predicts
the concentrations of fuel, 1, and anhydrides 2−6 in response
to the fuel (see the Supporting Information). The model also
predicts the concentration of N-acylisourea 1*. The kinetic
model considers the EDC-driven activation, anhydride
hydrolysis, and also transacylation between the oligomers.
We first fitted the EDC decay profile of the experiments to give
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accurately for various sizes of EDC batches (Figures S4 and
S5).
The kinetic model allows for extracting the individual
reaction rates that dominate the evolution of the oligomers.
For example, when we analyze the evolution of oligomer 3, we
find three possible pathways to its formation (Figure 2D), i.e.,
the fuel-driven activation (e.g., 1 + 2 yields 3), the
transacylation (e.g., 4 + 2 yields 3 + 3), or the deactivation
of longer oligomers (e.g., 4 yields 3 + 1). Similarly, we find
three possible pathways for the breakdown of oligomer 3, i.e.,
its spontaneous hydrolysis (deactivation), its transacylation
(scrambling), or its activation into a longer oligomer (Figure
2D). In the first few minutes, the fuel-driven activation governs
the formation of 3. However, we were surprised to find that,
within minutes, the formation of 3 is dominated by the
scrambling of other oligomers, e.g., the transacylation of two
dimers 2 resulting in a 3 and a monomer 1 (Figure 2E). Even
more surprising was that the breakdown kinetics of 3 is always
dominated by the kinetics of transacylation as opposed to the
deactivation via hydrolysis (Figure 2F). Specifically, the
reaction that leads to most of the loss of 3 is the transacylation
of 3, with 1 resulting in two molecules of 2. This loss via
transacylation can be explained by the high concentrations of
1. Taken together, our kinetic model can capture the kinetics
of the reaction cycle and reveals that the scrambling via
transacylation plays an important role in the dynamics of our
nonequilibrium system’s chemistry (Figure 2D). Even though
the activation and deactivation kinetics are dictated by
nonequilibrium chemical reactions, the transacylation, which
dominates the dynamics of the library, is an equilibrium
reaction.
Next, we tested the response of the system to larger batch
sizes of fuel, i.e., 75 and 100 mM. We were surprised to find
that the maximum concentrations of the anhydrides did not
decay exponentially with oligomer length as observed before
(Figure 3A). While 2 had by far the highest maximum
concentration, the maximum concentrations of oligomers 3, 4,
5, and 6 were similar at ∼2.5 mM and much higher compared
to the experiment with 50 mM fuel. The difference in the
kinetics of the chemical reaction cycle was likely due to the
oligomer’s ability to self-assemble because the samples
immediately turned turbid after the addition of the larger
batches of fuel (Figure 3B). Moreover, the turbidity was a
transient phenomenon, i.e., it decayed over 130 min, at which
point the original transparency was restored. We imaged the
rapid increase and subsequent decay of turbidity by time-lapse
photography and measured the gray value of the samples with
different batch sizes of EDC (Figure S6A and B). Fluorescence
microscopy with the hydrophobic dye Nile red showed that
micron-sized light-scattering particles were responsible for the
increased turbidity (Figure 3C). Furthermore, cryogenic
transmission electron microscopy (cryo-TEM) revealed a
fibrillar substructure in the irregular micron-sized assemblies
(Figure 3D). We measured the sample scattering rate by
dynamic light scattering (DLS), which is a more sensitive
measure of the presence of assemblies compared to the
turbidity assays. The addition of 75 or 100 mM fuel drastically
increased the scattering rate of our samples, whereas the
addition of 50 mM or less did not, further corroborating that
>50 mM fuel was needed to induce the formation of transient
assemblies (Figure S7).
Figure 3. Response of the dynamic combinatorial library to a large
batch of fuel. (A) Maximum concentrations of the library compounds
2−6, plotted on a logarithmic scale when fueling with 100 mM EDC
(crosses). The data is an average of the maximum yields obtained in
the reaction cycle. The kinetic model was used to fit the maximum
yields (squares). (B) Photographs of 1 at different time points. (C)
Micrograph of 1 and 25 μM Nile red, fueled with 75 mM EDC after 5
min. (D) Cryo-TEM micrograph of 1 fueled with 75 mM EDC after 2
min. (E, F) HPLC data (markers, monitored at 290 nm) of 3 and 6,
respectively, when 1 was fueled with 100 mM EDC. The kinetic
model was used to fit the experimental data (lines). (G) Schematic
representation of the feedback of assemblies on the deoligomerization
reactions and scrambling reactions of the transient dynamic
combinatorial library. Only oligomer 4 is shown in the scheme to
save space.
oligomers in the supernatant and pellet. We found that the
pellet contained mostly oligomers 4−6 (95 mol %) and only
minor fractions of 2 and 3 (5.0 mol %) (Figure S6C and D). In
contrast, the supernatant contained only 0.1 mM 4 but no 5 or
6. We conclude that library members 4−6 can assemble when
a larger amount of fuel is added and that assembly can change
the reaction kinetics, resulting in increasing yields of 4−6.
Because of the ill-defined morphology of the assemblies and
the huge polydispersity, we assume that all these library
members randomly coassemble as opposed to self-sorting into
individual assemblies.
We analyzed the evolution of the concentration of fuel and
anhydrides 2−6 when assemblies were present (Figures 3E, S8,
and S9). When 100 mM EDC was added, the fuel was entirely
consumed within 16 min (Figure S9A). The concentrations of
anhydrides 2−6 initially rose and then collapsed (Figures 3E
and F and S9B−D). However, we observed a large difference
in the deactivation kinetics of the oligomers that assembled
(4−6) compared to those that did not (2 and 3, Figure 3E and
F). For 100 mM EDC, we found that 2 and 3 peaked in the
first few minutes and then decayed with first-order kinetics
(Figures 3E and S10B). Moreover, at the time where the most
fuel was consumed, these anhydrides had also mostly decayed.
Surprisingly, 4, 5, and 6 peaked at ∼9 min, which is close to
the point where almost all fuel was depleted. Moreover,
Ten minutes after the addition of fuel, we centrifuged the
reaction solution and measured the concentration of the
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beyond their peaks, their concentrations decayed much slower
as compared to 2 and 3 (Figures 3F and S9C and D). It is
noteworthy that the concentration of an unwanted side
product, i.e., the N-acylisourea 1* of monomer 1, was <6
mM after the cycle was completed (Figure S9E).
From the combined results, we can conclude that, due to
their ability to assemble, oligomers 4−6 are less reactive, likely
because they are shielded from water and less mobile in their
assemblies. These changes in the anhydride’s microenviron-
ment change their hydrolysis and transacylation rate constants.
We adjusted our kinetic model in order to capture the much
slower decays of 4, 5, and 6 due to their ability to assemble. In
brief, we decreased the rate constants of deactivation and
transacylation (k4 and k5) of those compounds until a good fit
of the decay profile to the HPLC data was obtained for all
oligomers (Figures 3E and F and S9, Table S6). Although the
decay profiles of 4−6 were captured by the decreased rate
constants of hydrolysis and transacylation, the yields of 3 and 4
remained overestimated, whereas the yields of 5 and 6 were
underestimated. Therefore, we increased the rate constant of
activation (k1) for oligomers 4 and 5 and obtained good fits.
Such an increase in the rate constant due to self-assembly
could be explained by a surface catalysis mechanism.
To further confirm the role of self-assembly in these
libraries, we carried out a seeding experiment. We first created
a solution with assemblies, spun down the assemblies, removed
the supernatant, and resuspended them in the buffer. A small
fraction of this solution was added to an experiment of 300
mM 1 fueled with 30 mM EDC. Without the seed in that
experiment, no 5 or 6 was observed (Figure S10). With the
seed, the maximum concentration of 5 was ∼0.3 mM.
Moreover, the concentration of 5 was almost double compared
to the amount of the added seed, demonstrating that new 5
was made. Only when the feedback mechanisms were taken
into account in our kinetic model could the evolution of 5 be
well-predicted in the described seeding experiment (Figure
S11).
Figure 4. Response of the dynamic combinatorial library to
continuous transduction of fuel. (A, C) Schematic experimental
setup of continuous fueled experiments in the absence (A) and
presence (C) of a seed. (B, D) HPLC (markers, monitored at 290
nm) data of 3 and 4 when 1 was continuously fueled with 100 mM
EDC/h in either the absence (B) or presence of a seed (D). The
kinetic model was used to fit the experimental data (lines).
From the combined data sets, we can make the following
observations. Our chemically fueled, dynamic combinatorial
library is governed by in-equilibrium and out-of-equilibrium
reaction kinetics, as exemplarily illustrated for part of the
library in Figure 3G. The fuel-driven activation reaction and
the spontaneous hydrolysis are of nonequilibrium nature. In
contrast, the transacylation reaction is an equilibrium reaction.
All these reactions are happening simultaneously at com-
parable rates, which makes the interpretation of the data nearly
impossible without the use of a kinetic model. Our kinetic
model shows that the reaction kinetics of the individual library
members are largely dominated by the in-equilibrium trans-
acylation, i.e., transacylation recombines the library compo-
nents while maintaining the average oligomer length. However,
the global and transient shift toward longer oligomer members
is driven by the fuel-consuming activation reactions (Figure
3G).
Our study has focused on the transient formation of a
dynamic combinatorial library in response to a batch of
chemical energy, which allowed us to write a kinetic model. To
mimic better the complexity of chemical reaction networks in
biology, we designed experiments that are regulated by the
continuous transduction of energy. A vial was continuously
fueled, via a microsyringe pump, with 100 mM h−1 EDC
(Figure 4A). It is noteworthy that the reactor was continuously
stirred and had no outlet ports, i.e., we used a continuously
stirred batch reactor. By the naked eye, we found that the
sample remained clear. HPLC analysis revealed that only
oligomers 2 and 3 were formed in measurable amounts and
were stable in a steady state over the course of the experiment
(Figure 4B). Our kinetic model could accurately predict the
evolution well (Figures 4B and S12).
Given the ability of our assemblies to exert negative feedback
on their deactivation reactions, we were curious to see whether
their presence could affect steady states; e.g., could the
presence of a higher number of oligomers, as a seed, increase
their likelihood of survival (Figure 4C)? Thus, we formed the
seeds by the addition of a batch of 75 mM fuel to the solution
of monomer 1. We then waited 20 min to ensure that all EDC
had converted to EDU and the major components in the vial
were 4, 5, and 6, i.e., a seed of longer oligomers (Figure 4C).
Then, we started to continuously fuel the system with 100 mM
h−1 EDC (Figure 4C). We found that the concentrations of
longer oligomers 4−6 decreased until a steady-state level was
reached. That steady state was much higher compared to the
experiment without seeds in which 4, 5, and 6 were not
detected (Figures 4D and S13). Moreover, when we performed
a similar experiment with 100 mM fuel as a spike, we observed
very similar behavior (Figures S13 and S14). It is noteworthy
that our kinetic model predicted the experimentally observed
evolution of the concentration profiles of all oligomers. Taken
together, the presence of the assembly as a seed initiates the
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feedback mechanisms, which helps the survival of longer
oligomers. Because of the feedback mechanisms, the outcome
of the experiment on whether assemblies are present depends
on the history of the sample. Such behavior is ubiquitous in
biology and is used for decision-making, but synthetic
counterparts are rare.11,36
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Notes
The authors declare no competing financial interest.
ACKNOWLEDGMENTS
■
This research was funded by the Volkswagen Foundation via
the Life? program and was conducted within the Max Planck
School Matter to Life supported by the German Federal
Ministry of Education and Research (BMBF) in collaboration
with the Max Planck Society. J.B. is gratefull for support by the
European Research Council (ERC starting Grant 852187) and
the Deutsche Forschungsgemeinschaft (DFG, German Re-
search Foundation) − Project-ID 364653263 − TRR 235.
Cryo-TEM measurements were performed using infrastructure
contributed by the Dietz Lab and the TUM EM Core Facility.
We acknowledge the technical support provided by Fabian
Kohler.
CONCLUSION
■
Previous work on chemically fueled systems has mainly
focused on how chemical reactions regulate the self-assembly
behavior of one molecule. Because of the molecular design of
the precursor in this work, the product of one cycle is the
precursor for the next. This dynamic combinatorial library
approach opens the door to emergent mechanisms in which
sequences can be selectively up- or down- concentrated. In the
system we described, monomers can be oligomerized,
oligomers can be deoligomerized, and oligomers can trans-
acylate. Surprisingly, we found that the dynamics of the
individual components of the library were dominated by
transacylation, which is an equilibrium reaction. In contrast,
the dynamics of the entire library were dictated by fuel-driven
activation, which is a nonequilibrium reaction. Finally, we find
that self-assembly can play a large role in affecting the kinetics
of the reactions via feedback mechanisms. The interplay of the
simultaneously operating reactions and feedback mechanisms
can result in hysteresis effects in which the outcome of the
competition for fuel depends on events that occurred in the
past, i.e., via the presence of seeds. In future work, we envision
diversifying the library by modifying building blocks with
catalytically active motifs. In such mixtures, we expect
coassembly, self-sorting, and perhaps even hybridization of
the oligomers to result in feedback mechanisms by which
information-containing sequences can be spontaneously
selected from a pool of simple building blocks when supplied
with chemical energy.
ABBREVIATIONS
■
Cryo-TEM, cryogenic transmission electron microscopy; EDC,
1-ethyl-3-(3-(dimethylamino)propyl)carbodiimide; ESI-MS,
electrospray ionization−mass spectrometry; HPLC, high-
performance liquid chromatography; MES, 2-(N-morpholino)-
ethanesulfonic acid
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ASSOCIATED CONTENT
* Supporting Information
The Supporting Information is available free of charge at
https://pubs.acs.org/doi/10.1021/jacs.1c01616.
■
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Materials and methods description; additional data on
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AUTHOR INFORMATION
Corresponding Author
Job Boekhoven − Department of Chemistry, Technical
University of Munich, 85748 Garching, Germany; Institute
for Advanced Study, Technical University of Munich, 85748
Garching, Germany; orcid.org/0000-0002-9126-2430;
Email: job.boekhoven@tum.de
■
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Spontaneous advent of genetic diversity in RNA populations through
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Christine M. E. Kriebisch − Department of Chemistry,
Technical University of Munich, 85748 Garching, Germany
Alexander M. Bergmann − Department of Chemistry,
Technical University of Munich, 85748 Garching, Germany
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