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# Evolution of dynamical networks enhances catalysis in a designer enzyme

## Abstract

Activation heat capacity is emerging as a crucial factor in enzyme thermoadaptation, as shown by the non-Arrhenius behaviour of many natural enzymes. However, its physical origin and relationship to the evolution of catalytic activity remain uncertain. Here we show that directed evolution of a computationally designed Kemp eliminase reshapes protein dynamics, which gives rise to an activation heat capacity absent in the original design. These changes buttress transition-state stabilization. Extensive molecular dynamics simulations show that evolution results in the closure of solvent-exposed loops and a better packing of the active site. Remarkably, this gives rise to a correlated dynamical network that involves the transition state and large parts of the protein. This network tightens the transition-state ensemble, which induces a negative activation heat capacity and non-linearity in the activity–temperature dependence. Our results have implications for understanding enzyme evolution and suggest that selectively targeting the conformational dynamics of the transition-state ensemble by design and evolution will expedite the creation of novel enzymes.

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## Data availability

Data that support the findings of this study are available within the paper and its Supplementary Information. Input files, MD trajectories, topologies and parameters relevant to this work are available at the University of Bristol data repository at https://doi.org/10.5523/bris.l6hm9j11yil92bh9rvh27i7ge.

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## Acknowledgements

H.A.B. and A.J.M. thank EPSRC (EP/M013219/1 and EP/M022609/1) and, along with J.L.R.A., the BBSRC (BB/R016445/1) for funding. H.A.B. thanks the Swiss National Science Foundation (Postdoc.Mobility fellowship) for support. M.W.v.d.K. thanks BBSRC for support (David Phillips Fellowship, BB/M026280/1). V.L.A. and A.J.M. thank the Marsden Fund of New Zealand (16-UOW-027). V.L.A. is a James Cook Research Fellow (Royal Society of New Zealand). D.H. thanks the Swiss National Science Foundation. This work was conducted using the computational facilities of the Advanced Computing Research Centre, University of Bristol. We thank R. Crean and S. Osuna for help with and providing a script to perform the shortest-path analysis.

## Author information

Authors

### Contributions

H.A.B., M.W.v.d.K. and A.J.M. devised the simulation and analysis. H.A.B. performed the simulations and analysis. H.A.B., J.L.R.A., D.H., V.L.A., M.W.v.d.K. and A.J.M. wrote the manuscript.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature Chemistry thanks Paolo Carloni, Vicent Moliner and Sílvia Osuna for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Extended data

### Extended Data Fig. 1 The emergent $${{{\Delta}C}}_{\mathrm{p}}^{\ddagger}$$ in the Kemp eliminase variants predominantly reflects effects on the chemical step.

a, In the activity-temperature dependence of 1A53-2.9, deviations from the linear Eyring behaviour are slightly more pronounced for kcat than kcat/KM. This indicates that the $${{{\Delta}C}}_{\mathrm{p}}^{\ddagger}$$ for kcat is of similar magnitude to that of kcat/KM, though no precise $${{{\Delta}C}}_{\mathrm{p}}^{\ddagger}$$ has been determined for kcat. Thus, the experimentally determined $${{{\Delta}C}}_{\mathrm{p}}^{\ddagger}$$ of −1.17 kJ∙mol−1K−1 for kcat/KM predominantly reflects thermodynamic differences between the TS and GS ensemble. b, Comparison of the activity-temperature profiles and CD melt curves of 1A53-2 (red) 1A53-2.5 (blue) and 1A53-2.9 (black) shows that the apparent $${{{\Delta}C}}_{\mathrm{p}}^{\ddagger}$$ is not due to thermal denaturation of the protein. The melting temperatures of all variants are high, and those of the evolved variants are significantly above their catalytic temperature optima. 1A53-2.5, which evolved an activation heat capacity, has an even higher melting temperature than 1A53-2 (82 °C vs. 75 °C). Also, long incubation of all variants at the highest experimental assay temperatures does not affect activity, which shows that there is no significant unfolding at this temperature on the timescale of the experiments. Of note: the Kemp elimination only involves a single deprotonation step. A change in mechanisms is neither likely, nor did we observe any kinetic signatures signalling rate-limiting substrate binding or product release (e.g. burst phases or hysteresis under single turnover conditions). All data presented in Extended Data Fig. 1 were extracted from Bunzel et al. JACS 2019.

### Extended Data Fig. 2 MD parameters and restraints.

a, Ground state and b, transition state distances (red) and charges (black) based on gas-phase calculations with 6-nitrobenzisoxazole and acetate. To prevent artificial rigidification of the transition state by introduction of a covalent bond between the ligand and catalytic residue,1 the transition state was simulated with the transferring proton residing either on the ligand (TS) or base (TS2). Both transition state models provided similar results, supporting the significance of our findings. *, Because Glu178 has only two γ-hydrogens, their charge is adjusted to the given value according to the corresponding three hydrogens in acetate. c, Similar to previous work,1 restraints were used to avoid drifting away from reactive conformations during the extended simulations. Weak harmonic restraints for the ligand-base distance δC-C (black, >5.0 Å, 5.0 kcal mol−1 Å−1) and the ligand-base dihedral angle ΨO-C-N-O (red, >±60°, 5.0 kcal mol−1 rad2) were added to keep the ligand in the active site. Furthermore, the χ2 dihedral angle of Trp110 ΦC-C-C-C (blue, 65° > ΦC-C-C-C > 155°, 5.0 kcal mol−1 rad−2) was restrained, preventing its indole sidechain from blocking the active site. To avoid biasing the $${{{\Delta}C}}_{\mathrm{p}}^{\ddagger}$$ calculations, the same restraints were added to all variants and ligands.

### Extended Data Fig. 3 MD trajectories.

Individual (light colours) and average (dark colours) trajectories of 1A53-2 and 1A53-2.5 with GS (red), TS (blue) and TS2 (grey) bound. a, Based on the r.m.s.d, the first 50 ns of each simulations were discarded to avoid biasing of the analysis to the starting structures (dotted lines). The ligand-base distance δC-C (b), and dihedral angle ΨO-C-N-O (c), remained within the weak harmonic constraints (dotted lines) for most of the simulations. For a definition of the restraints see Extended Data Fig. 2.

### Extended Data Fig. 4 Changes in energetic fluctuations give rise to an activation heat capacity $${{{\Delta}C}}_{\mathrm{p}}^{\ddagger}$$.

a, The energy distributions for 1A53-2 (TS: dark red; GS: light red) are almost identical, indicating a $${{{\Delta}C}}_{\mathrm{p}}^{\ddagger}$$ close to zero. Energetic fluctuations were calculated after removal of all but 10 water molecules, though removing these only slightly affected $${{{\Delta}C}}_{\mathrm{p}}^{\ddagger}$$. b, The distribution for 1A53-2.5 is narrower for the TS (dark blue) than for the GS (light blue) complex, resulting in a negative $${{{\Delta}C}}_{\mathrm{p}}^{\ddagger}$$. Distributions in (a) and (b) are normalized to a 50 ns moving average and plotted against a log scale to emphasize changes in variance. c, $${{{\Delta}C}}_{\mathrm{p}}^{\ddagger}$$ was calculated based on the difference in variance between the TS and GS ensemble for moving windows of various sizes, and converges after 50 ns to negative values for 1A53-2.5 (blue). For 1A53-2, $${{{\Delta}C}}_{\mathrm{p}}^{\ddagger}$$ does not significantly deviate from zero (red). Error bars were obtained by leave-one-out cross-validation. As expected, the statistical errors increase with larger window size, because slow conformational changes that are not exhaustively sampled begin to mix into the calculations, complicating the analysis1. Clearly, the energetic fluctuations in 1A53-2 and 1A53-2.5 are different, which gives rise to the dynamical network that tightens the TS ensemble in the evolved variant1. d + e, Heat capacities calculated under various conditions qualitatively agree well with each other. Heat capacities were calculated either dry (e), or with the 10 water molecules closest to Glu178 bound (d) based on the difference in energy variance of the transition and ground state for running windows with varying size (5 ns to 80 ns) for 1A53-2 (red) 1A53-2.5 (blue) for TS (filled circles) and TS2 (open circles).

### Extended Data Fig. 5 Structural fluctuations in 1A53-2 and 1A53-2.5.

Residues that rigidify (blue) or become more flexible (red) between a+b, GS and TS, and c+d, GS and TS2. In 1A53-2.5, rigidification is particularly evident in three solvent exposed loops (residues 53-65, 84-92, and 181-192), which is reproduced by clustering based on the whole protein backbone. These loops were thus employed to cluster the structures in an open and closed state (Extended Data Fig. 6).

### Extended Data Fig. 6 Cluster analysis reveals an open-closed equilibrium.

Average structures of the a, 1A53-2 and b, 1A53-2.5 ensembles in the open (light blue) and closed (dark blue) state in complex with the TS. Distance-based clustering was performed using the k-means algorithm based on the three solvent exposed loops (bold tubes, residues 53-65, 84-92, and 181-192). Loop closure is indicated by the Cα distance of residues 58 and 188 (spheres). c + d, Histograms and e + f, distributions of the open (light colours) and closed (dark colours) states bound to GS (red), TS (blue) and TS2 (grey). g + h, Loop closure decreases the radius of gyration which is smallest in the closed TS of 1A53-2.5 (blue line). i + j, The open and closed state interconvert on the timescale of the simulation. Error bars represent the standard deviation of 10 independent simulations.

### Extended Data Fig. 7 Principal component analysis reproduces the two state model.

Principal component analysis of the mobile loops (residues 53-65, 84-92, and 181-192) was performed for the a, GS (red), b, TS (blue), and c, TS2 (grey) ensembles of 1A53-2 (left) and 1A53-2.5 (right). The histogram of the first principal component after partition of the trajectory according to the cluster analysis (Extended Data Fig. 6) into open (light) and closed (dark) states reproduces the two-state model.

### Extended Data Fig. 8 Local structural effects at the active site.

a+b, The distance-distribution of the ten water molecules closest to the Oε of Glu178 is shown for the GS (red), TS (blue), and TS2 (grey) in the closed (dark colours) and open (light colours) state. The active site becomes less hydrated in the transition states compared to the ground state for both enzymes. Furthermore, the A157Y mutation in 1A53-2.5 displaces a water molecule in the evolved variant at approximately 3 Å. Remarkably, loop closure expels water from the active site in 1A53-2.5 (arrows) which was not observed for 1A53-2. The c+d, SASA of the ligand and e+f, RMSF of the ligand and base are furthermore lower in 1A53-2.5 than 1A53-2, indicating tighter packing of the ligand. Error bars represent the standard deviation of 10 independent simulations.

### Extended Data Fig. 9 Emerging dynamical networks in 1A53-2 and 1A53-2.5.

Only dynamical changes between the same states are comparable. The comparison of 1A53-2 with 1A53-2.5 is either performed between GS to TS (left) or between GS to TS2 (right). a, Backbone movements become highly correlated in the closed TS ensemble of 1A53-2.5, indicating the presence of global vibrations comprising most of the protein. b, Cross correlations that increase between GS and TS by ≥20% are indicated as lines on the structures. c, Based on the cross-correlations, shortest path maps were calculated2. These show that evolution introduced a communication network in 1A53-2.5 that originates from the TS and comprises large parts of the closed state. The size of the edge (black sticks) and vertices (blue spheres: protein, orange sphere: ligand) indicate the increasing weight of the network between GS and TS.

### Extended Data Fig. 10 QM/MM modelling of the Kemp eliminases.

Free energy surfaces of 1A53-2 (top) and 1A53-2.5 (bottom) at the a, PM6/CHARMM36, b, AM1/CHARMM36 and the c, PM6/AMBERff99SB level of theory. The ligand as well as the carboxylate of Glu178 were part of the QM region during umbrella sampling of the C-H and N-O bonds. The transition state (black dot) reproduces the asynchronous Kemp elimination with C-H cleavage preceding N-O cleavage observed for similar systems.3-5 PM6/CHARMM36 gave activation energies of 101 kJ∙mol-1 and 90 kJ∙mol-1, which reproduce the improvements achieved during evolution (86 and 68 kJ∙mol-1 for kcat). Similarly, simulations with AM1/CHARMM36 preserved that trend, but gave higher energies (117 and 105 kJ∙mol-1). In contrast, simulations with PM6/AMBERff99SB resulted in an inverse trend for the activation energies (111 and 116 kJ∙mol-1). This observation for AMBERff99SB mimics the classical MD, in which the ligand was expelled from the active site within 100 ns.

## Supplementary information

### Supplementary Information

Supplementary Methods.

### Supplementary Table 1

Variances and $${{{\Delta}C}}_{\mathrm{p}}^{\ddagger}$$ of 1A53-2.

### Supplementary Table 2

Variances and $${{{\Delta}C}}_{\mathrm{p}}^{\ddagger}$$ for 1A53-2.5.

## Rights and permissions

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Bunzel, H.A., Anderson, J.L.R., Hilvert, D. et al. Evolution of dynamical networks enhances catalysis in a designer enzyme. Nat. Chem. 13, 1017–1022 (2021). https://doi.org/10.1038/s41557-021-00763-6

• Accepted:

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• DOI: https://doi.org/10.1038/s41557-021-00763-6

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