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The α/β-hydrolase fold superfamily includes esterases and hydroxynitrile lyases which, despite catalyzing different reactions, share a Ser–His–Asp catalytic triad. We report a 1.99 Å resolution crystal structure of HNL6V, an engineered variant of hydroxynitrile lyase fromHevea brasiliensis(HbHNL) containing seven amino-acid substitutions (T11G, E79H, C81L, H103V, N104A, G176S and K236M). The structure reveals that HNL6V maintains the characteristic α/β-hydrolase fold while exhibiting systematic shifts in backbone and catalytic atom positions. Compared with wild-typeHbHNL, the C^αpositions in HNL6V differ by a mean of 0.2 ± 0.1 Å, representing a statistically significant displacement. Importantly, the catalytic triad and oxyanion-hole atoms have moved 0.2–0.8 Å closer to their corresponding positions in SABP2, although they remain 0.3–1.1 Å from fully achieving the configuration of SABP2. The substitutions also increase local flexibility, particularly in the lid domain covering the active site. This structural characterization demonstrates that targeted amino-acid substitutions can systematically shift catalytic geometries towards those of evolutionarily related enzymes. 

Hydroxynitrile lyase fromHevea brasiliensis(HbHNL) and the esterase SABP2 fromNicotiana tabacumshare the α/β-hydrolase fold, a Ser–His–Asp catalytic triad and 44% sequence identity, yet catalyze different reactions. Prior studies showed that three active-site substitutions inHbHNL conferred weak esterase activity. To investigate how regions beyond the active site influence catalytic efficiency and active-site geometry, we engineeredHbHNL variants with increasing numbers of substitutions to match SABP2. Variant HNL16 has all amino acids within 6.5 Å of the active site identical to SABP2, HNL40 those within 10 Å and HNL71 those within 14 Å. HNL16 exhibited poor esterase activity, whereas both HNL40 and HNL71 showed efficient esterase catalysis, demonstrating that residues beyond the immediate active site are critical for functional conversion. X-ray structures of HNL40 and HNL71 reveal a progressive shift in backbone positions toward those of SABP2, with r.m.s.d. values of 0.51 Å (HNL40) and 0.41 Å (HNL71) over the C^αatoms, and even smaller r.m.s.d.s within the active-site region. Both HNL40 and HNL71 show a restored oxyanion hole and an additional tunnel connecting the active site to the protein surface. This work demonstrates the essential role of distant, indirectly acting residues to catalysis in α/β-hydrolase enzymes. 

Abstract We begin with a treatment of the Caputo time‐fractional diffusion equation, by using the Laplace transform, to obtain a Volterra integro‐differential equation. We derive and utilize a numerical scheme that is derived in parallel to the L1‐method for the time variable and a standard fourth‐order approximation in the spatial variable. The main method derived in this article has a rate of convergence ofO(k^α + h⁴)foru(x,t) ∈ C^α([0,T];C⁶(Ω)),0 < α < 1, which improves previous regularity assumptions that requireC²[0,T]regularity in the time variable. We also present a novel alternative method for a first‐order approximation in time, under a regularity assumption ofu(x,t) ∈ C¹([0,T];C⁶(Ω)), while exhibiting order of convergence slightly more thanO(k)in time. This allows for a much wider class of functions to be analyzed which was previously not possible under the L1‐method. We present numerical examples demonstrating these results and discuss future improvements and implications by using these techniques.