Design rules for reciprocal coupling in chemically fueled assembly

Biology regulates the function and assembly of proteins through non-equilibrium reaction cycles. Reciprocally, the assembly of proteins can influence the reaction rates of these cycles. Such reciprocal coupling between assembly and reaction cycle is a prerequisite for behavior like dynamic instabilities, treadmilling, pattern formation, and oscillations between morphologies. While assemblies regulated by chemical reaction cycles gained traction, the concept of reciprocal coupling is under-explored. In this work, we provide two molecular design strategies to tweak the degree of reciprocal coupling between the assembly and reaction cycle. The strategies involve spacing the chemically active site away from the assembly or burying it into the assembly. We envision that design strategies facilitate the creation of reciprocally coupled and, by extension, dynamic supramolecular materials in the future.


Introduction
Biological supramolecular structures like the nucleolus, the transmembrane ATPases, and the cytoskeleton are tightly regulated using non-equilibrium chemical reaction cycles, giving them unique properties like the capacity to heal or form patterns. [1][2][3] These reaction cycles are catalytic and convert molecules with high chemical potential into their lower chemical potential counterparts, like the enzymatic conversion of ATP to ADP.Upon doing so, the enzyme is temporarily activated for a function like assembling.Prototypical examples are the ATPdriven formation of actin laments or ATP-fueled ATPase pumps.5][6] Thus, the reaction cycle and assembly are reciprocally coupled (Scheme 1A).Again, actin assembly is a great example-ATP activates monomeric, globular actin (G-actin) for assembly into laments. 4Upon assembly, actin changes its conformation (F-actin), resulting in an increased ATP hydrolysis rate. 5ATP hydrolysis triggers disassembly.Thus, the reaction cycle activates and deactivates molecules for assembly.Vice versa, the assembly affects the kinetics of the reaction cycle by catalyzing hydrolysis-the assembly process and its reaction cycle are reciprocally coupled.In an extreme case of reciprocal coupling, a building block's activation can only occur in the non-assembled state, and its deactivation can only occur in the assembled state. 7In such a scenario, building blocks must assemble and disassemble to proceed through a reaction cycle.Such reciprocal coupling is a prerequisite for driven selfassembly and behavior like dynamic instabilities, treadmilling, pattern formation, and oscillations between morphologies.Even though reciprocal coupling is ubiquitous in biology, synthetic assemblies with similar dynamic behavior are underexplored.To create synthetic assemblies with similar dynamic behavior, we must understand mechanisms by which assembly and reaction cycle reciprocally affect each other.Moreover, we need design rules by which we can control the nature of feedback and the degree of reciprocal coupling interaction.
We recently found a chemically fueled peptide that forms bers that display reciprocal coupling between assembly and cycle (Scheme 1). 31In the chemical reaction cycle, an anionic dicarboxylate peptide (precursor) converts into a non-charged anhydride (product) (Scheme 1B) by reacting with a carbodiimide.The hydrophobization, upon converting to an anhydride, induces self-assembly into bers.Simultaneously, hydrolysis of the anhydride reinstates the negative charges on the precursor, which induces disassembly. 11Reciprocally, we demonstrated that the assembly into bers accelerates both the EDC-consuming activation of the peptide and the deactivation of the building block through hydrolysis (Scheme 1C). 31The underlying mechanism has to do with the organization of the active sites of the peptide, which affects their apparent pK a and thereby changes the reaction pathway.Peptides that do not assemble have a relatively low apparent pK a and, thus, a low degree of protonation.Organizing the peptides into bers increases the degree of protonation of the active sites, affecting whether the rate-determining step of the activation reaction proceeds via the slow stepwise or the fast concerted proton transfer pathway (Scheme 1C).Besides, the strength of hydrogen bonding also affects the deactivation rate.We hypothesized that the hydrogen bonding of a neighboring amide and the anhydride carbonyl's oxygen increases the carbonyl carbon's electrophilicity.Thereby, the anhydride hydrolysis is accelerated.
In this work, we demonstrate design strategies by which the degree of reciprocal coupling and its nature can be tuned (Fig. 1A).In one peptide, Ac-FAVD, the active site is attached to a non-assembling peptide (Fig. 1B).In one peptide design, Fmoc-AVG n D, the active site is attached to a peptide that stacks into bers.We space the chemical active site further from the peptide stack with a glycine spacer and an ethylene glycol spacer (Fig. 1C and D).Finally, we attach the active site to the selfassembling peptide but bury it inside the peptide stack and place it at a different position in the peptide sequence (Fig. 1E).We measure the reciprocal coupling between assembly and reaction kinetics for each design strategy.

Results and discussion
The degree of reciprocal coupling as a function of spacer length The internal ordering or rigidity of the chemically fueled bers results from stacking the hydrophobic Fmoc-group and b-sheet hydrogen bonds between the alanine and valine.To regulate the rigidity's effect on the apparent pK a of the carboxylates, which are the active site, we spaced it away from the peptide domain responsible for the ber's rigidity with a glycine linker.We designed the peptides Fmoc-AVG n D-OH (G n ) with n = 0, 1, 2, 3, i.e., G 0 , G 1 , G 2 , G 3 (Fig. 1C).We chose glycine (G) as a exible spacer because it lacks a side group, having the greatest freedom of rotation of the N-C a (phi, 4) and C a -C ′ (psi, j) and, thus, the lowest propensity to form b-sheets. 32,33 We dissolved the peptides G n at 2.5 mM in an aqueous buffer of 200 mM MES at pH 6.The addition of 50 mM 1-ethyl-3-(3dimethylaminopropyl)carbodiimide (EDC) initiated the reaction cycle and led to the formation of a dense network of bundled bers for all peptides (Fig. 2A).We determined the critical aggregation concentration of the peptides by a Nile red uorescence assay.We used Nile red's increased emission intensity as a proxy for ber formation.We added increasing amounts of peptide to a solution of 50 mM EDC and measured the uorescence intensity (Fig. S1A-D †).The peptide needed to get the rst evidence of assemblies was 0.5 mM.We then used the kinetic model (vide infra) to calculate the amount of anhydride around 0.2-0.3mM when 0.5 mM precursor is used.Thus, we conclude that the anhydride's critical aggregation concentration (CAC) of the G n peptides is below 0.3 mM.We studied the kinetics of the reaction cycle for G n by applying fuel and using a benzylamine quench 34 to stop the reaction cycle at predetermined time points.Benzylamine reacts with the anhydride (the activated peptide) to form the stable benzylamide, and the increase in pH stops the activation reaction.We monitored the concentration of fuel and benzylamide as a measure of the anhydride by high-performance liquid chromatography (HPLC) (Fig. 2B, C, S2A-C, G-I and S3-S7 †).The activated peptide was temporarily sustained and decayed as the system ran out of fuel.
To quantify the nature of feedback and the degree of reciprocal coupling between the bers and the reaction cycle, we used the non-assembling peptide Ac-FAVD-OH (Ac-FAVD, Ac = acetyl, F = phenylalanine) as a reference (Fig. S8A †).We observed that all G n consumed EDC faster than Ac-FAVD (Fig. 2B, S2A-C and S3-S7 †).Moreover, the anhydride of all G n peptides was hydrolyzed faster than Ac-FAVD (Fig. 2C, S2G-I and S3-S7 †).[35][36][37] The peptide without spacer G 0 showed the largest increase in the second-order rate constant of activation relative to Ac-FAVD, i.e., a factor of 4.3 (Fig. 2D and Table S3 †).In contrast, the acceleration of the activation decreased to 3.3/2.9/2.7 for G 1 , G 2 , G 3 compared to Ac-FAVD.Moreover, the rate constant of anhydride hydrolysis remained more or less constant with varying Gly spacer lengths and ranged between 2.1-2.2-foldacceleration compared to the non-assembling Ac-FAVD (Fig. 2D and Table S3 †).
For the assembly to accelerate the activation, two conditions must be fullled. 31First, the assembly is a co-assembly of activated and deactivated peptides, i.e., precursors and anhydrides.Second, the apparent pK a of the deactivated peptide is shied in the assembly compared to in solution.Indeed, we found by 1 H-NMR spectroscopy that the deactivated peptide co-assembled into the bers in all cases of G n (Fig. 2E, S9A-C and S10 †).Over the entire 90 minute chemical reaction cycle, most of the peptide was in the self-assembled state.Even though all the anhydride hydrolyzed back to its precursor aer 90 minutes, the precursor stayed trapped inside the assembled bers, indicating that the disassembly rate for all precursors is very slow.Because most of the peptide is in the assembly, we expect the coassembled peptide to be reactivated inside the ber.As the coassembled peptide is exposed to a different microenvironment than in solution, we expect a change in the apparent pK a of the active site and, thus, its reactivity.We determined the apparent pK a by titration.We found that for the non-assembling Ac-FAVD, the apparent pK a values were 4.2 and 2.2, which is in line with reference values for aspartic acid (Fig. S11A †). 40In contrast, for all G n , only a single apparent pK a value was found with a shi to higher values, i.e., 5.8 for G 0 , 5.6 for G 1 , 5.1 for G 2 , and 5.1 for G 3 (Fig. S11B-E †).
Our combined ndings conclude that the deactivated peptide is co-assembled with the activated peptide, and the change of its microenvironment compared to the nonassembled peptide changes the apparent pK a of the active site.However, the further active site is spaced away from the ber the smaller the change in apparent pK a .As the activation reaction is rate limited by a proton transfer, shiing the apparent pK a to a higher value increased the activation rate.Yet, the effect decreases with increasing glycine spacer.We hypothesize that more than two Gly-spacers do not lead to more conformational exibility of the aspartic acid headgroup.
We studied the inuence of the Gly spacers on the b-sheet interactions of the bers by Fourier-Transform Infrared spectroscopy (FT-IR).With FT-IR measurements, the b-sheet interactions are normally characterized in a range of 1625-1640 cm −1 . 41These bers showed two predominant peaks: the amide I band at 1630 cm −1 (carbonyl stretch vibration responsible for the b-sheet interactions) and the Fmoc-OCNH band at 1690 cm −1 (Fig. 2F, S12A and B †).The amide I band is sensitive to hydrogen bonding in the assembly, and it broadens towards higher wavenumbers with increasing glycine spacer length.This broadening indicates that the peptide assemblies are less ordered, i.e., the b-sheet interactions between peptides are decreased. 41Moreover, we used a ThT assay to measure the assembly's ability to bind ThT, which is a measure of the atness and, thus, the rigidity of the b-sheets of the assemblies. 42,43he maximum emission intensity of ThT decreased by introducing Gly-spacers, indicating a decreased degree of b-sheet atness and rigidity for G n (n = 1, 2, 3) assemblies (Fig. 2G,  S13A-D and S14A-D †).Cryogenic-Transmission Electron Microscopy (Cryo-TEM) studies showed that G 0 assembled into broad tapes with a width of 52 ± 11 nm whereas G n (n = 1, 2, 3) assembled into thin bers with a width of 7 ± 2 nm (Fig. 2H).The planar tape structure of G 0 indicates that the active aspartic acid headgroup is conformationally more constrained than in the thin ber assemblies of G n (n = 1, 2, 3).
To further improve the exibility of the spacer unit, we used an ethylene glycol spacer.We designed Fmoc-AV-ethylene glycol-D-OH, i.e., GY (Fig. 1D).We added 50 mM EDC to 2.5 mM GY in MES buffer at pH 6 to initiate the reaction cycle, which led to the formation of bers (Fig. S8B †).We determined the CAC to be around 0.2 mM (Fig. S1E †).The kinetic experiments showed that the activation was only 2.1-fold accelerated compared to Ac-FAVD.The anhydride hydrolysis rate constant was slightly by a 1.5-fold (Fig. 2D, Table S3, Fig. S2D, J, S4C, S7C and D †).Like G n , 1 H-NMR spectroscopy showed that the deactivated peptide co-assembled into the GY bers (Fig. S9D and S15 †).In the ber microenvironment, the apparent pK a shis to 4.7 (Fig. S11F †).Thus, compared to G n, the pK a -shi is lower, resulting in a lower acceleration of activation and deactivation.The FT-IR-spectra of GY showed next to the characteristic amide I band at 1630 cm −1 also a broad shoulder between 1640-1670 cm −1 (Fig. S12C †).This peak shape points to a random coil (1640-1650 cm −1 ) next to elements of b-sheet structures (1625-1640 cm −1 ), meaning that parts of the peptide assemblies are even less ordered than the G n peptides. 41e conclude that introducing Gly-spacers as well as an ethylene glycol-spacer between the peptide core Fmoc-AV and the active site introduces conformational exibility of the active aspartic acid headgroup and thus decreases the shi in the apparent pK a value of the carboxylates.This enables us to tune the acceleration of the activation reaction compared to G 0 .The higher the exibility of the Gly vs. ethylene glycol, the greater the effect on the conformational exibility of the active aspartic acid headgroup.The effect decreases and attens if we introduce more than one Gly-spacer.

Tuning the reciprocal coupling by burying the active site
We designed the peptides Fmoc-AVD(D)G-NH 2 (D(D) 1 ), Fmoc-AD(D)VG-NH 2 (D(D) 2 ), and Fmoc-D(D)AVG-NH 2 (D(D) 3 ) in which the active site, i.e., the aspartic acid, is placed at different positions in the Fmoc-AVG peptide sequence via an aspartic acid linker (Fig. 1E).Thus, the active site is branched away from the peptide chain and buried deeper into the ber's core with increasing number.We hypothesize that the buried and branched dicarboxylate group disrupts the strong p-p interactions of the Fmoc-group and the b-sheet hydrogen-bonding interactions of the AV segment, thereby inuencing the degree of reciprocal coupling.We dissolved 2.5 mM D(D) n in MES buffer at pH 6 and added 50 mM EDC to initiate the reaction cycle, which led to the formation of bers (Fig. 3A).We found the CAC of these peptides to be below 0.3 mM (Fig. S1F-H †).
We analyzed the evolution of the D(D) n reaction cycle by HPLC and compared it to the non-assembling Ac-FAVD (Fig. 3B, C showed that over the entire reaction cycle, the D(D) n bers were a co-assembly of activated and deactivated peptides (Fig. 3E, S9E, F and S19 †).As for the G n and GY peptides, most of the peptide is trapped inside the assembly, indicating a slow disassembly rate.Thus, we expect the co-assembled D(D) n peptide to be reactivated inside the ber as well.In the ber microenvironment, the apparent pK a changes, and thus the reactivity of the D(D) n peptides changes.The apparent pK a we measured for D(D) n in its assembled state is and 5.6 for D(D) 1 , 5.0 for D(D) 2 and 4.7 for D(D) 3 (Fig. S11G-I †).Thus, compared to the non-assembling Ac-FAVD, the apparent pK a shis 0.5-1.4 units higher (Fig. 3D).The further the branched active aspartic acid is spaced away from the Fmoc-ber core, the less buried the active site is and the higher the apparent pK a shi, and thus the greater acceleration of the activation reaction.Indeed, the acceleration of the activation reaction for D(D) n decreased from 2.0 to 0.99 from D(D) 1 to D(D) 3 .In stark contrast to the G n peptide series and the GY peptide, we found that the rate constant for activated D(D) n deactivation around 30% slower for D(D) 1 and D(D) 2 and 70% slower for D(D) 3 , respectively than for Ac-FAVD (Fig. 3C, D, S2K, L and S16-S18 †).We hypothesize that the hydrophobic ber core excludes water.Thus, the buried anhydride, especially in D(D) 3 , is protected from hydrolysis.In D(D) 1 and D(D) 2 bers, the active site is less buried, and thus the anhydride is less protected from hydrolysis.This is in line with confocal microscopy that shows a dense ber network for D(D) 1 and D(D) 2 while for D(D) 3 we observe more nucleation sites from which bers grow (Fig. 3A).
In the FTIR-spectra, the D(D) 3 amide I band peaked at 1633 cm −1 and showed a broad shoulder between 1640-1670 cm −1 (Fig. 3F).This peak shape points to the presence of bsheet structures (1625-1640 cm −1 ) next to elements of a random coil (1640-1650 cm −1 ), meaning that parts of the peptide assemblies are less ordered. 41Going from D(D) 1 to D(D) 3, the broad shoulder increases, indicating less-ordered assemblies (Fig. 3F, S12D and E †).The maximum emission intensity of ThT for D(D) 1 is almost equal to G 0 as the aspartic acid branch does not disrupt the Fmoc-p-p interactions and the hydrogenbonding interactions of alanine and valine.However, for D(D) n (n = 2, 3) assemblies, the signal was lower than G 0 .In D(D) 2 the aspartic acid branch is placed between alanine and valine and we hypothesize it disrupts the hydrogen bonding.In D(D) 3 , the aspartic acid branch disrupts the b-sheet hydrogenbonding interactions of the AV-segment and the Fmoc-p-p interactions (Fig. 3G, S13A, E-G, S14A and E-G †).Cryo-TEM shows that D(D) 3 assembled into thin bers with a width of 6 ± 1 nm (Fig. 3H).The combined dataset of FT-IR, ThT, and Cryo-TEM reveals weaker intermolecular interaction of D(D) n compared to G 0 (FT-IR), yielding less rigid assemblies.Moreover, the more the branched active aspartic acid is placed in the ber core, D(D) 1 vs. D(D) 3 , the less rigid are the assemblies.These ndings corroborate our hypothesis that the buried dicarboxylate disrupts the strong p-p interactions of the Fmocgroup and the b-sheet hydrogen-bonding interactions of the peptide sequence AVG.

Molecular design tunes the nature and degree of reciprocal coupling
We establish the following design rules to regulate the reciprocal coupling between assembly and cycle.Molecular designs that yield high internal order in the assembly carried over to the active sites result in pK a shi which changes the kinetics of the activation.This organization also yields a higher deactivation (Fig. 4).Spacing the active site away from the ordered assembly with a exible linker decreases the effect (Fig. 4 and 2).Moreover, molecular designs in which the active site is buried in the hydrophobic ber core, excludes it from water, and thus protects it from hydrolysis resulting in a strong deceleration of the deactivation reaction (Fig. 4 and 3).

Conclusions
We studied two molecular design strategies to tune the nature of feedback and the degree of reciprocal coupling between the assembly and reaction cycle in chemically fueled peptide assemblies (bers).The reciprocal coupling couples to the internal structure, i.e. the rigidity of the peptide assembly, which we can tune with molecular design.We show that we can tune the propensity of the peptide to form b-sheet hydrogen bonding by spacing the chemically active site away from the peptide core or burying it in the peptide core responsible for the ber rigidity.These design strategies enable us to tune the degree and nature of feedback.Thus, our ndings allow us to establish heuristic design rules for controlling the degree and nature of reciprocal feedback.We envision that these design rules can be exploited in future work to create synthetic assemblies with kinetic asymmetry and tunable dynamic behavior like pattern formation, oscillations in morphology, and motility, as seen in living systems.
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.X. C. is grateful for the nancial support from the China Scholarship Council.B. A. K. K. is grateful for a Kekulé-Stipendium by the Verbandes der Chemischen Industrie.We are grateful for using the TEM infrastructure of the Dietz Lab and the TUM EM Core Facility.We thank Dr Héctor Soria-Carrera for his assistance with the gures.

Fig. 1
Fig. 1 Molecular design strategies to control reciprocal coupling and the nature of feedback.(A) Schematic representation of the design strategies.Either the active site is spaced away or buried in the stack compared to the original design (left).(B-E) Molecular design of precursor to regulate reciprocal coupling in chemically fueled assemblies.(B) The non-assembling compound as a reference.Spacing the aspartic acid away from the peptide core Fmoc-AV with (C) Gly-spacers and (D) an ethylene glycol segment.(E) Bury the aspartic acid in the peptide core by changing its position in the peptide sequence.

Fig. 3
Fig. 3 The self-assembly and kinetic behaviour of D(D) n compared to Ac-FAVD.(A) Confocal micrographs of D(D) n 10 minutes after fueling with EDC.HPLC (markers) and kinetic model data (lines) as a function of time of (B) the EDC consumption for D(D) 3 and Ac-FAVD and (C) the anhydride concentration of Ac-FAVD and D(D) 3 after fueling with EDC n = 3. (D) The influence of the branched linker on (1) the shift of apparent pK a of D(D) n to Ac-FAVD; (2) the activation and deactivation reaction rate (k 1 , k 4 ) of D(D) n compared to Ac-FAVD.(E) The components of the chemically fueled fibers as a function of time determined by 1 H-NMR spectroscopy.Experiments were done in duplicate.(F) FT-IR spectra of D(D) 3 fueled with EDC at 3 min.Fmoc-OCNH band at 1681 cm −1 and amide I band at 1630 cm −1 (typical bsheet).The blue box highlights the broad shoulder between 1640-1670 cm −1 .(G) Maximal ThT emission (a.u.) at 485 nm after excitation at 440 nm when 2.5 mM G 0 /D(D) n is fueled with 10 mM EDC, n = 3. (H) Cryo-TEM micrographs of 2.5 mM D(D) 3 fueled with 25 mM EDC at 2 min.Scale bar 100 nm.

Fig. 2
Fig. 2 The self-assembly and kinetic behavior of G n and GY-peptide compared to Ac-FAVD.(A) Confocal micrographs of 2.5 mM G n 10 minutes after fueling with 50 mM EDC. HPLC (markers) and kinetic model data (lines) as a function of time of (B) the EDC consumption for G 0 and Ac-FAVD, (C) the anhydride concentration of G 0 and Ac-FAVD after fueling with EDC, n = 3. (D) The influence of Gly's number and an ethylene glycol spacer (GY) on (1) the shift of apparent pK a of G n /GY to Ac-FAVD (2) the activation and deactivation reaction rate (k 1 , k 4 ) of G n / GY compared to Ac-FAVD.(E) The components of the chemically fueled fibers as a function of time determined by 1 H-NMR spectroscopy.Experiments were done in duplicate.(F) FT-IR spectra of G 0 and G 3 fueled with EDC at 3 min.Fmoc-OCNH band at 1687/1686 cm −1 and amide I band at 1633/1634 cm −1 (typical b-sheet).The blue box highlights the broad shoulder between 1640-1670 cm −1 .(G) Maximal ThT emission (a.u.) at 485 nm after excitation at 440 nm when 2.5 mM G n is fueled with 10 mM EDC, n = 3. (H) Cryo-TEM micrographs of 2.5 mM G n fueled with 25 mM EDC at 2 min.Scale bar 100 nm.
Fig. 4 Simplified scheme of molecular design tailoring the nature of feedback and the reciprocal coupling strength between assembly and reaction cycle.(A) Strategy of spacing away the active site.(B) Strategy of burying the active site.