Machine learning (ML) is becoming an attractive tool in mutagenesis-based protein engineering because of its ability to design a variant library containing proteins with a desired function. However, it remains unclear how ML guides directed evolution in sequence space depending on the composition of training data. Here, we present a ML-guided directed evolution study of an enzyme to investigate the effects of a known “highly positive” variant (i.e., variant known to have high enzyme activity) in training data. We performed two separate series of ML-guided directed evolution of Sortase A with and without a known highly positive variant called 5M in training data. In each series, two rounds of ML were conducted: variants predicted by the initial round were experimentally evaluated and used as additional training data for the second-round of prediction. The improvements in enzyme activity were comparable between the two series, both achieving enzyme activity 2.2–2.5 times higher than 5M. Intriguingly, the sequences of the improved variants were largely different between the two series, indicating that ML guided the directed evolution to the distinct regions of sequence space depending on the presence/absence of the highly positive variant in the training data. This suggests that the sequence diversity of improved variants can be expanded not only by conventional ML using the whole training data but also by ML using a subset of the training data even when it lacks highly positive variants. In summary, this study demonstrates the importance of regulating the composition of training data in ML-guided directed evolution.

We have performed angle-resolved photoemission spectroscopy (ARPES) on Cu x (PbSe) 5 (Bi 2 Se 3 ) 6 (CPSBS; x = 1.47), a superconductor derived from a topological insulator heterostructure, to elucidate the electronic states relevant to the occurrence of possible unconventional superconductivity. Upon Cu intercalation into the parent compound (PbSe) 5 (Bi 2 Se 3 ) 6 , we observed a distinct energy shift of the bulk conduction band due to electron doping. Photonenergy dependent ARPES measurements of CPSBS revealed that the observed bulk band forms a cylindrical electronlike Fermi surface at the Brillouin-zone center. The two-dimensional nature of the bulk electronic states puts strong constraints on the possible topological character of the superconducting state in CPSBS. 75.70.Tj, 79.60 In this Rapid Communication, we report high-resolution ARPES study of PSBS (m = 2) and its Cu-intercalated counterpart, CPSBS. By utilizing a relatively long escape depth of photoelectrons excited by low-energy photons, we have succeeded in observing previously unidentified, intrinsic bulk band structure of the 2-QL Bi 2 Se 3 unit lying deeper beneath the surface. Our most important finding is that the near-E F bulk band responsible for the superconductivity shows a two-dimensional (2D) character, in contrast to the 3D character of bulk Bi 2 Se 3 . We discuss the implications of the present result in relation to the possible topological superconductivity in CPSBS.High-quality single crystals of a parent compound PSBS (m = 2) were grown by a modified Bridgman method using high purity elements Pb ( between the quantized bulk CB and the lower branch of the gapped Dirac-cone state in the topmost 2-QL Bi 2 Se 3 of PSBS in Fig. 1(a). Thus, bands A and B are attributed to the quantized bulk CB and the lower branch of the gapped Dirac-cone state, respectively. It is noted that bands A and B in Fig. 2(f) are shifted downward by ∼ 0.1 eV as compared to those in Fig. 1(a). This may be due to the weakened band-bending effect (i.e. weakened outof-plane potential gradient) at the second Bi 2 Se 3 unit, which may also explain the absence of a clear Rashba splitting for band A in Figs. 2(b) and 2(f). Also, the absence of the upper branch of gapped Dirac-cone state is likely due to overlapping by CB 1st with a dominant intensity.To elucidate the Fermi-surface topology in the 3D momentum space relevant to the possible unconventional superconductivity of CPSBS, we have performed hν-dependent ARPES measurements by focusing on band A (hereafter we call CB 2nd ). As one can see in the representative second-derivative intensity plots in Fig. 3(a), we commonly see CB 2nd and CB 1st over a wide hν range of 8.4-23 eV (note that 8.4-eV photons are most bulk sensitive).A direct comparison of the EDC at theΓ point in Fig. 3 Now we discuss the implications of our results in relation to topological superconductivity.The most important finding of the present study is that the unconventional superconduc- an intriguing platform to explore Majorana fermio...

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Intermolecular interactions in random copolymer systems depend on the copolymer composition as being observed as a miscibility window in the random copolymer blends. The copolymer composition dependencies of the Flory‐Huggins χ parameter and the heats of mixing ▵HM(∞) at infinite dilution were studied for the solutions of poly(methyl methacrylate‐ran‐n‐butyl methacrylate) (MMAnBMA) in cyclohexanone (CHN). The copolymer composition dependencies of χ obtained from osmotic pressures and of ▵HM(∞) measured with a microcalorimeter were concave curves. This suggests that the random copolymers MMAnBMA interact with CHN more attractively than do the homopolymers PMMA and PnBMA. This is caused by the repulsion effect between the MMA and nBMA segments. The equation‐of‐state theory extended to the random copolymer systems by us reproduced fairly well these thermodynamic properties. The χ parameter for the PMMA/PnBMA blends was calculated using the equation‐of‐state theory with the MMA/nBMA intersegmental parameters employed for the above random copolymer solutions in CHN. The χ value calculated thus was in satisfactory agreement with that obtained from the random copolymer solutions using the Flory‐Huggins theory extended to multicomponent systems. © 1996 John Wiley & Sons, Inc.

Three-dimensional topological insulators (3D-TIs) possess a specific topological order of electronic bands, resulting in gapless surface states via bulk-edge correspondence.Exotic phenomena have been realized in ferromagnetic TIs, such as the quantum anomalous Hall (QAH) effect with a chiral edge conduction and a quantized value of the Hall resistance Ryx. Here, we report on the emergence of distinct topological phases in paramagnetic Fe-doped (Bi,Sb)2Se3 heterostructures with varying structure architecture, doping, and magnetic and electric fields. Starting from a 3D-TI, a two-dimensional insulator appears at layer thicknesses below a critical value, which turns into an Anderson insulator for Fe concentrations sufficiently large to produce localization by magnetic disorder. With applying a magnetic field, a topological transition from the Anderson insulator to the QAH state occurs, which is driven by the formation of an exchange gap owing to a giant Zeeman splitting and reduced magnetic disorder. Topological phase diagram of (Bi,Sb)2Se3 allows exploration of intricate interplay of topological protection, magnetic disorder, and exchange splitting.The Zeeman exceeding hy forms a non-trivial exchange gap with one-dimensional chiraledge channel as shown in Figs. 1(e) and 1(f), with gap size proportional to the magnetic field. In Fig. 1(f), red (blue) thick curve shows the chiral edge mode at one (the other) edge. With a minor contribution of the ordinary Hall effect under magnetic field owing to Fermi energy (EF) locating in the gap, the magnetic-field-induced anomalous Hall effect plays a critical role for the quantization of the Hall conductivity. This study demonstrates the presence of TPTs between 3D-TI, a two-dimensional (2D) insulator, and QAH phases in paramagnetic Fe-doped Bi2Se3-based heterostructures by controlling Fe doping and layer thickness and by application of external magnetic and electric fields. The tetradymite compound Bi2Se3 is a representative 3D-TI, in which a large bulk band gap (approximately 300 meV) hosts gapless surface states [35]. Using angleresolved photoemission spectroscopy (ARPES) of surface states, 50 meV gap formation was detected in paramagnetic Fe-doped bulk Bi2Se3; it was assigned to breakage of the time-reversal symmetry by exchange interactions [36]. Effects of magnetic impurities upon topological surface states were also studied by in-situ deposition of Fe atoms [37-39]. It was found that Fe acts as donor [37,38] if deposited at room temperature but as an acceptor if deposited at 8 K [38]. A question on whether the presence of a Fe surface layer 6 opens a gap or not in the topological states was also examined experimentally and theoretically [37-39].According to one theoretical proposal, Fe-doped Bi2Se3-based heterostructures are a preferred platform for observing the emergence of QAH phase [17]. Nevertheless, no QAH effect has yet been observed in magnetically doped Bi2Se3-based films, probably because of the absence or weakness of the ferromagnetic ordering, and associat...

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