I NTRODUCTION

In enzyme design projects, the catalytic efficiency of initial candidates are usually rather mod-est, along with a plethora of produced inactive designs that are usually discarded without further consideration. Experimental solutions to this problem often lie in directed evolution techniques, from which new sequence changes are introduced on active designs and selected based on in-creased target function and/or stability.[24,214,215] Rationalization on the molecular basis for such low catalytic efficiencies often falls to a secondary role, thus limiting our current understand-ing of protein chemistry. In this regard, computational methods offer the opportunity to bridge the gap between theory and experimental findings.

Despite their potential in the development of new catalysts, CED tools have nonetheless some inherent limitations. For example, candidate designs are often ranked based on ad hoc ap-proaches such as the one described in Chapter 2 for selection of the RD02 scaffold. Moreover, design flaws may be inaccessible by MM-based methods such as the one employed in Rosetta, where static representations of the systems in implicit solvent medium are done, often based on a single crystallographic structure.⁴⁰ This is because designs often differ significantly from their native counterparts in terms of their primary sequence and this can affect considerably their po-tential energy landscape, as represented in Scheme 6.1.

Scheme 6.1 – Representation of the potential energy landscape in the conformational space of backbone and side chains for native and enzyme designs.

Native enzymes have potential energy landscapes (black line) with well-defined global minima where active conformation is located (open circle). Sampled subspace during MD simulations may be limited to neigh-bouring regions (dashed regions). Designs present different potential energy landscapes due to introduced sequence changes (blue lines). Sampled subspace during MD simulations may be close to target active conformation (blue circle) in active designs (dashed green) but might drift considerably towards non-active conformations that correspond to new global minima (dashed red).

Indeed, as described in Chapter 2, new sequence variants are obtained by iterative repacking and energy minimization of native structure upon introduction of the AS of interest. During this

40 Dynamics of the scaffold were nonetheless approached to some extent by using as input NMR-derived structures.

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stage, backbone and AS side chain constrains are typically imposed and as a result the new sequence variant may correspond to shallow, local energy minima in the potential energy land-scape.⁴¹ Alternative backbone and side chain conformations corresponding to neighbour energy minima may become more stable and thus being preferentially adopted. This may impact greatly the solvent accessibility of AS residues and substrate binding-interaction energies. Moreover, interactions with solvent molecules may also dictate to a major extent the adoption of alternative conformations, and this is particularly relevant for RD peptides where a water molecule is ex-pected to act as the fourth ligand in the substrate-free forms.

Calculation of energy profiles along the reaction coordinate would require the employment of DFT methods, but these are computationally very demanding and therefore limited to sampling of short time-scales (ps-ns). As a result, a relatively static treatment of protein-substrate interac-tions needs to be imposed.[216,217] The compromise between a realistic treatment of chemical reactions in fast time-scales and proper sampling of protein conformational space in longer ones has been commonly opted in favour of the latter in comprehensive enzyme design projects, where structural integrity and unfavourable catalytic interactions can be probed in advance by taking into consideration the intrinsic dynamical properties of designs and their evolved variants.[218] These can be addressed either experimentally by nuclear magnetic resonance (NMR) spectroscopy or computationally by the employment of atomistic MM simulation methods, such as Molecular Dy-namics (MD). [219] In MD simulations both the biomolecule and solvent are explicitly described by force fields where particle interactions are described by simplified energy potentials. These can be integrated in time according to Newton’s second law of motion to obtain forces acting on particles and calculate the resulting accelerations, which are then used to calculate new velocities and positions at each time step. The result is a simulation trajectory of the entire atomic system, which yields the conformational space available for the biomolecule to be explored under the employed simulating conditions of pressure, temperature and solvent composition.

MD simulations in the ns time-scale have been employed to guide several enzyme design projects. For example, MD-derived geometric descriptors have been employed in the study of Kemp eliminases and used to discriminate between active and inactive designs.[216,220] The conformational space explored in such cases is nonetheless restricted to sampled time-scales and may fail to capture major conformational changes occurring in slower regimes (μs-ms).[221]

Regarding RD peptides, their inherent structural flexibility characterized in Chapter 4 begs the question whether the designs failed to maintain scaffold integrity or accurate AS pre-organization.

Given their reduced size, MD methods are suitable to probe whether major conformational rear-rangements occur in μs time-scales. While not a high-throughput method, recent hardware and software development have made investigations of protein dynamics in slow regimes increasingly

41 This was the case in Chapter 2, where AS geometries were constrained during the design stage to avoid disruption of the metal site. Repacking and energy minimization without constraints led Zn(II) binding residues to depart from the orientations imposed by the pseudo-covalent bonds with the metal ion in a tet-rahedral-like fashion, since the later was treated as part of the diAla(min) substrate model.

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accessible by simulation.[222,223] This allows to bridge the gap between simulation and experi-ments when addressing the structural features of protein scaffolds in solution. The current chapter explores this link by employing μs-long MD simulations of RD peptides in explicit solvent and compare the results with experimental findings obtained in previous chapters, together with addi-tional insights obtained by NMR spectroscopy.

Simulation of metal-containing systems such as native MPs and RD designs faces issues regarding the realistic treatment of protein-metal interactions. This is because metal ion chemistry is not adequately captured by all-atom force fields, where charge-transfer and ligand-field stabili-zation effects often play a crucial role in dictating coordination geometries and binding affinities.

Again, QM-based treatment of metal systems would be preferred but the small time-scales sam-pled preclude major scaffold reorganizations to be probed. Along with QM-based corrections of metal first- and second-coordination sphere interactions, “bonded” models are usually employed where the metal-protein bond is treated as a pseudo-covalent one. [224] This greatly limits sam-pling of ligand-exchange phenomena and usually non-bonded models are adopted instead. How-ever, such models also present challenges since the metal ion is treated as a charged sphere, therefore not taking into account the spatial orientation of electron orbitals involved in ligand co-ordination.⁴² In the case of RD peptides, unsuitability of these approaches is aggravated since folding is mediated by the Zn(II) binding. Ligand exchange phenomena and significant drift from defined TS coordination geometries is therefore expected in such cases. Attempts to overcome these limitations have been developed recently, such as the employment of polarizable force fields that mimic some of the charge-transfer and ligand stabilization effects associated with metal coordination by biomolecules. An example of this is the Drude oscillator model by introducing an auxiliary charged particle attached to each polarizable atom through a harmonic poten-tial.[225,226] This method has been successfully employed in protein folding simulations, but its currently limited to treatment of monovalent charged species and shorter simulation trajectories.

A robust method for simulation of metal-containing system is the Cationic Dummy Atom (CaDa) approach, where a non-bonded description of e.g. Zn(II) is made by the inclusion of charged virtual particles that mimic the orientations of unoccupied 4s4p³ orbitals of the closed 3d¹⁰system.[227,228] This approach has been adopted in several simulations of metalloproteins, including native Zn(II) metalloenzymes, and shown to reasonably capture the structural and elec-trostatic effects involved in metal-protein interactions, including ligand-exchange events.[229–

231] Therefore, in the current chapter the suitability of employing the tetrahedral Zn(II) CaDa variant was addressed for the MD simulation studies of native astacin, Sp1f2 peptide and RD designs.

42 A non-bonded model was used in Chapter 2 for the study of thermolysin. Discussion of method limita-tions are addressed in annex 1 therein.

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