Extracting Higher Central Charge from a Single Wave Function.

A (2+1)D topologically ordered phase may or may not have a gappable edge, even if its chiral central charge c_{-} is vanishing. Recently, it was discovered that a quantity regarded as a "higher" version of chiral central charge gives a further obstruction beyond c_{-} to gapping out the edge. In this Letter, we show that the higher central charges can be characterized by the expectation value of the partial rotation operator acting on the wave function of the topologically ordered state. This allows us to extract the higher central charge from a single wave function, which can be evaluated on a quantum computer. Our characterization of the higher central charge is analytically derived from the modular properties of edge conformal field theory, as well as the numerical results with the ν=1/2 bosonic Laughlin state and the non-Abelian gapped phase of the Kitaev honeycomb model, which corresponds to U(1)_{2} and Ising topological order, respectively. The Letter establishes a numerical method to obtain a set of obstructions to the gappable edge of (2+1)D bosonic topological order beyond c_{-}, which enables us to completely determine if a (2+1)D bosonic Abelian topological order has a gappable edge or not. We also point out that the expectation values of the partial rotation on a single wave function put a constraint on the low-energy spectrum of the bulk-boundary system of (2+1)D bosonic topological order, reminiscent of the Lieb-Schultz-Mattis-type theorems.

Clinical outcomes of endoscopic detachable snare ligation for colonic diverticular hemorrhage: Multicenter cohort study.

OBJECTIVES: The hemostatic mechanism of endoscopic detachable snare ligation (EDSL) for colonic diverticular hemorrhage (CDH) is similar to that of endoscopic band ligation, which is effective and safe. However, because reports on EDSL are scarce, we conducted a two-center cohort study to evaluate its effectiveness. METHODS: This study analyzed 283 patients with CDH treated with EDSL at two Japanese hospitals between July 2015 and November 2021. Patient characteristics and clinical outcomes were retrospectively evaluated. A Kaplan-Meier analysis was performed to evaluate the cumulative probability of rebleeding after EDSL. A Cox proportional hazards regression analysis was performed to compare the effects of complete and incomplete ligation on rebleeding. RESULTS: The initial hemostasis success and early rebleeding rates were 97.9% and 11.0%, respectively. The time to hemostasis after identification of the bleeding site and total procedure time were 9 min and 44 min, respectively. Red blood cell transfusion was required for 32.9% of patients. The median hospital length of stay after EDSL was 5 days. The complete ligation rate of the early rebleeding group was significantly lower than that of the group without early rebleeding (P < 0.01). The 1-year cumulative rebleeding rate with EDSL was 28.2%. Complete ligation was associated with decreased cumulative rebleeding after EDSL (P < 0.01). One patient experienced colonic diverticulitis; however, colonic perforation was not observed. CONCLUSION: Complete ligation is associated with reduced short-term and long-term rebleeding. EDSL could be valuable for CDH because of its low rebleeding rate and the absence of serious adverse events.

Complete Crystalline Topological Invariants from Partial Rotations in (2+1)D Invertible Fermionic States and Hofstadter's Butterfly.

The theory of topological phases of matter predicts invariants protected only by crystalline symmetry, yet it has been unclear how to extract these from microscopic calculations in general. Here, we show how to extract a set of many-body invariants {Θ_{o}^{±}}, where o is a high symmetry point, from partial rotations in (2+1)D invertible fermionic states. Our results apply in the presence of magnetic field and Chern number C≠0, in contrast to previous work. {Θ_{o}^{±}} together with C, chiral central charge c_{-}, and filling ν provide a complete many-body characterization of the topological state with symmetry group G=U(1)×_{ϕ}[Z^{2}⋊Z_{M}]. Moreover, all these many-body invariants can be obtained from a single bulk ground state, without inserting additional defects. We perform numerical computations on the square lattice Hofstadter model. Remarkably, these match calculations from conformal and topological field theory, where G-crossed modular S, T matrices of symmetry defects play a crucial role. Our results provide additional colorings of Hofstadter's butterfly, extending recently discovered colorings by the discrete shift and quantized charge polarization.

Anticoagulation against portal vein thrombosis reduces mortality and liver cirrhosis-related complications: A propensity score-matched study.

AIM: Portal vein thrombosis (PVT) is one of the common complications of liver cirrhosis. Although anticoagulation contributes to thrombus resolution and is considered the first-choice treatment, its impact on patients' prognosis is still controversial. This study aimed to clarify the benefit of anticoagulation on mortality, liver function, and the incidence of liver cirrhosis-related complications in cirrhotic PVT patients. METHODS: We conducted a multicenter retrospective review in which we included 78 eligible patients with PVT out of 439. After propensity score matching, 21 cirrhotic PVT patients were included in each one of the untreated control and anticoagulation groups. RESULTS: Overall survival was significantly improved in the anticoagulation group compared with the control group (p = 0.041), along with PVT size reduction (53.3% vs. 108.2%, p = 0.009). At the time of CT follow-up, the anticoagulation group showed a lower ALBI score (p = 0.037) and its prevalence of massive ascites was significantly lower (p = 0.043) compared with the control group. The incidence of overt encephalopathy was also lower in the anticoagulation group (p = 0.041). The cumulative incidence of bleeding events did not differ significantly between the two groups. CONCLUSIONS: Anticoagulation improves the survival of patients with cirrhotic PVT. Preserved liver function and reduced risks of cirrhosis-related complications under the treatment may have contributed to a better prognosis. Given its efficacy and safety, anticoagulation is worth initiating in patients with PVT.

Rotary catalysis of bovine mitochondrial F1-ATPase studied by single-molecule experiments.

The reaction scheme of rotary catalysis and the torque generation mechanism of bovine mitochondrial F1 (bMF1) were studied in single-molecule experiments. Under ATP-saturated concentrations, high-speed imaging of a single 40-nm gold bead attached to the γ subunit of bMF1 showed 2 types of intervening pauses during the rotation that were discriminated by short dwell and long dwell. Using ATPγS as a slowly hydrolyzing ATP derivative as well as using a functional mutant ßE188D with slowed ATP hydrolysis, the 2 pausing events were distinctively identified. Buffer-exchange experiments with a nonhydrolyzable analog (AMP-PNP) revealed that the long dwell corresponds to the catalytic dwell, that is, the waiting state for hydrolysis, while it remains elusive which catalytic state short pause represents. The angular position of catalytic dwell was determined to be at +80° from the ATP-binding angle, mostly consistent with other F1s. The position of short dwell was found at 50 to 60° from catalytic dwell, that is, +10 to 20° from the ATP-binding angle. This is a distinct difference from human mitochondrial F1, which also shows intervening dwell that probably corresponds to the short dwell of bMF1, at +65° from the binding pause. Furthermore, we conducted "stall-and-release" experiments with magnetic tweezers to reveal how the binding affinity and hydrolysis equilibrium are modulated by the γ rotation. Similar to thermophilic F1, bMF1 showed a strong exponential increase in ATP affinity, while the hydrolysis equilibrium did not change significantly. This indicates that the ATP binding process generates larger torque than the hydrolysis process.

Radiographic Splenic Artery Involvement Is a Poor Prognostic Factor in Upfront Surgery for Patients with Resectable Pancreatic Body and Tail Cancer.

PURPOSE: The prognostic impact of radiographic splenic vessel involvement in pancreatic cancer remains unclear. We evaluate its oncological significance in resectable pancreatic body/tail cancer. PATIENTS AND METHODS: We retrospectively review 102 cases of resectable pancreatic cancer and 51 of borderline resectable pancreatic cancer (BRPC) who underwent pancreatectomy for pancreatic body/tail cancer. Resectable pancreatic body/tail cancer was classified into one of three categories based on radiographic splenic vessel involvement. RESULTS: Among 102 cases of resectable pancreatic cancer, 37 (36.3%), 35 (34.3%), and 30 cases (29.4%) were classified as no splenic vessel involvement (Rnone), splenic vein involvement (RV), and splenic artery involvement (RA), respectively. Disease-free survival (DFS) among patients with Rnone, RV, RA, and BRPC was 58.5, 18.4, 10.8, and 9.2 months, respectively. Patients with RV and RA had significantly poorer DFS than patients with Rnone (P = 0.010, P < 0.001, respectively). Median survival among Rnone, RV, RA, and BRPC was 80.6, 23.4, 15.1, and 21.3 months, respectively. Patients with RV and RA had significantly poorer survival than patients with Rnone (P = 0.001, P < 0.001, respectively) and had short survival similar to that of those with BRPC. Multivariate Cox proportional hazard analysis detected preoperative CA19-9 ≥ 37 IU/L, radiologic splenic vein involvement, radiologic splenic artery involvement, intraoperative bleeding ≥ 500 ml, transfusion, positive washing cytology, and noncompletion of adjuvant therapy as independent prognostic factors. CONCLUSIONS: Radiographic splenic artery involvement is a poor prognostic factor in resectable pancreatic body/tail cancer and may have a role in stratification of treatment strategy.

Division of the pancreas at the neck reduces postoperative pancreatic fistula in laparoscopic distal pancreatectomy: Comparison of pancreatic division at the body.

BACKGROUND: objectives: During laparoscopic distal pancreatectomy (LDP), the optimal site for pancreatic division with consideration of postoperative pancreatic fistula (POPF) is unclear. We evaluate which site of pancreatic division, neck or body, has better outcomes after LDP. METHODS: This was a retrospective, observational study. LDP was performed in 102 consecutive patients between December 2009 and May 2020. After excluding 14 patients with pancreatic division at tail, 88 patients (pancreatic division at neck n = 46, at body n = 42) were included in this study. Short- and long-term outcomes after LDP were compared between pancreatic division at neck and body. RESULTS: The pancreatic transection site was thicker at body than at neck (17.5 vs. 11.9 mm, P < 0.001), although there were no significant differences of pancreatic texture and pancreatic duct size. The Grade B/C POPF rate was significantly higher when the pancreas was divided at body than when divided at neck (21.4 vs. 6.5%, P = 0.042). We found no significant differences between pancreatic division at neck and body in residual pancreatic volume (34.0 vs. 34.8 ml, P = 0.855), incidence of new-onset or worsening diabetes mellitus more than six months after LDP (P = 0.218), or body weight change (six-month: P = 0.116, one-year: P = 0.108, two-year: P = 0.195, tree-year: P = 0.131, four-year: P = 0.608, five-year: P = 0.408). CONCLUSION: This study suggests that the pancreatic division at neck might reduce the Grade B/C POPF incidence after LDP, compared to division at body. A potential reason is that the pancreas at body is thicker than that at neck. However, further large-scale studies are necessary to confirm our results.

Complete REtraction of the StomaCh using pEnrose draiN and liver reTractor (CRESCENT) during laparoscopic distal pancreatectomy.

PURPOSE: Laparoscopic distal pancreatectomy (LDP) is a well-accepted procedure for benign and malignant diseases of the pancreatic body and/or tail. To perform it safely, a wide operative field is crucial. For the maintenance of a good surgical field during LDP, we developed an original technique for stomach retraction: "Complete REtraction of the StomaCh using pEnrose draiN and liver reTractor, CRESCENT." METHODS: In CRESCENT technique, the body and antrum of the stomach are suspended by two Penrose drains, and the fundus and/or upper body of the stomach are retracted upward using a liver retractor. After complete retraction, the stomach is well attached to the abdominal wall and forms a crescent-like shape. Before we developed the CRESCENT technique, we pulled the antrum of the stomach laterally by suture and hanged the body of the stomach upward using a Penrose drain (control method). We evaluated perioperative outcomes of the 87 consecutive patients who underwent LDP and compared outcomes of CRESCENT technique (n = 24) and previously used technique as a control (n = 63). RESULTS: Operative time was significantly shorter in the CRESCENT technique than in control method (median, 234 vs. 303 min, P < 0.001). We found no significant differences in incidences of overall morbidity (16.7 vs. 20.6%, P = 0.677), including grade B/C postoperative pancreatic fistula (8.3 vs. 7.9%, P = 0.455), between CRESCENT technique and control method. There was no mortality by either method. CONCLUSIONS: Our original technique, CRESCENT, is a simple procedure in which the stomach is completely retracted during LDP.

Impact of Ninjin'Yoeito on Fatigue in Patients Receiving Nab-Paclitaxel Plus Gemcitabine Therapy: A Prospective, Single-Arm, Phase II Open Label, Nonrandomized, Historically-Controlled Study.

BACKGROUND: Ninjin'yoeito, a traditional Japanese herbal medicine, is used to prevent fatigue, loss of appetite, and coldness of limbs. Fatigue is an especially common issue during chemotherapy and can affect quality of life and the ability to complete scheduled treatment. OBJECTIVES: This prospective exploratory trial evaluates the efficacy of ninjin'yoeito for fatigue in patients undergoing nab-paclitaxel plus gemcitabine therapy for unresectable pancreatic cancer. The primary end point was evaluation of fatigue according to Functional Assessment of Chronic Illness Therapy-Fatigue score during 2 courses of nab-paclitaxel plus gemcitabine therapy. Secondary end points included evaluation of dose intensity, appetite loss using numerical rating scale, and peripheral neuropathy using a patient neurotoxicity questionnaire. METHODS: We compared data from this interventional trial with a prior observational trial without administration of ninjin'yoeito with identical definition of end points (UMIN000021758). Thirty patients were required by the study. RESULTS: Threshold mean of Functional Assessment of Chronic Illness Therapy-Fatigue score across 8 weeks during chemotherapy was under 5.3 (P = 0.002). Secondary end points did not reveal any specific patterns in appetite loss or degree of pain. No significant changes in patient neurotoxicity questionnaire concerning sensory/motor disorders were observed, but the mean (SD) incidence of patients with sensory disturbance was higher between the fifth and eighth weeks (8.8 [1.26]) than during the first and fourth weeks (4.8 [0.96]) (P = 0.003). Clinically significant adverse reactions of ninjin'yoeito were not observed. CONCLUSIONS: Ninjin'yoeito may be useful for improving the symptoms of fatigue caused by nab-paclitaxel plus gemcitabine in patients with unresectable pancreatic cancer. UMIN Clinical Trials Registry identifier: UMIN000025606. (Curr Ther Res Clin Exp. 2020; 81:XXX-XXX).

New horizons in cardiac innervation imaging: introduction of novel 18F-labeled PET tracers.

Cardiac sympathetic nervous activity can be uniquely visualized by non-invasive radionuclide imaging techniques due to the fast growing and widespread application of nuclear cardiology in the last few years. The norepinephrine analogue 123I-meta-iodobenzylguanidine (123I-MIBG) is a single photon emission computed tomography (SPECT) tracer for the clinical implementation of sympathetic nervous imaging for both diagnosis and prognosis of heart failure. Meanwhile, positron emission tomography (PET) imaging has become increasingly attractive because of its higher spatial and temporal resolution compared to SPECT, which allows regional functional and dynamic kinetic analysis. Nevertheless, wider use of cardiac sympathetic nervous PET imaging is still limited mainly due to the demand of costly on-site cyclotrons, which are required for the production of conventional 11C-labeled (radiological half-life, 20 min) PET tracers. Most recently, more promising 18F-labeled (half-life, 110 min) PET radiopharmaceuticals targeting sympathetic nervous system have been introduced. These tracers optimize PET imaging and, by using delivery networks, cost less to produce. In this article, the latest advances of sympathetic nervous imaging using 18F-labeled radiotracers along with their possible applications are reviewed.

Preclinical properties and human in vivo assessment of 123I-ABC577 as a novel SPECT agent for imaging amyloid-ß.

Non-invasive imaging of amyloid-ß in the brain, a hallmark of Alzheimer's disease, may support earlier and more accurate diagnosis of the disease. In this study, we assessed the novel single photon emission computed tomography tracer (123)I-ABC577 as a potential imaging biomarker for amyloid-ß in the brain. The radio-iodinated imidazopyridine derivative (123)I-ABC577 was designed as a candidate for a novel amyloid-ß imaging agent. The binding affinity of (123)I-ABC577 for amyloid-ß was evaluated by saturation binding assay and in vitro autoradiography using post-mortem Alzheimer's disease brain tissue. Biodistribution experiments using normal rats were performed to evaluate the biokinetics of (123)I-ABC577. Furthermore, to validate (123)I-ABC577 as a biomarker for Alzheimer's disease, we performed a clinical study to compare the brain uptake of (123)I-ABC577 in three patients with Alzheimer's disease and three healthy control subjects. (123)I-ABC577 binding was quantified by use of the standardized uptake value ratio, which was calculated for the cortex using the cerebellum as a reference region. Standardized uptake value ratio images were visually scored as positive or negative. As a result, (123)I-ABC577 showed high binding affinity for amyloid-ß and desirable pharmacokinetics in the preclinical studies. In the clinical study, (123)I-ABC577 was an effective marker for discriminating patients with Alzheimer's disease from healthy control subjects based on visual images or the ratio of cortical-to-cerebellar binding. In patients with Alzheimer's disease, (123)I-ABC577 demonstrated clear retention in cortical regions known to accumulate amyloid, such as the frontal cortex, temporal cortex, and posterior cingulate. In contrast, less, more diffuse, and non-specific uptake without localization to these key regions was observed in healthy controls. At 150 min after injection, the cortical standardized uptake value ratio increased by ∼ 60% in patients with Alzheimer's disease relative to healthy control subjects. Both healthy control subjects and patients with Alzheimer's disease showed minimal (123)I-ABC577 retention in the white matter. These observations indicate that (123)I-ABC577 may be a useful single photon emission computed tomography imaging maker to identify amyloid-ß in the human brain. The availability of an amyloid-ß tracer for single photon emission computed tomography might increase the accessibility of diagnostic imaging for Alzheimer's disease.

Terpenoids and Phenylpropanoids in Ligularia duciformis, L. kongkalingensis, L. nelumbifolia, and L. limprichtii.

The diversity in root chemicals and evolutionally neutral DNA regions in the complex of Ligularia duciformis, L. kongkalingensis, and L. nelumbifolia (the d/k/n complex) was studied using eight samples collected in central and northern Sichuan Province of China. Cacalol (14) and epicacalone (15), rearranged eremophilanes, were isolated from the complex for the first time. Two new phenylpropanoids were also obtained. Seven of the eight samples produced phenylpropanoids and the other produced lupeol alone. Two of the seven samples also produced furanoeremophilanes or their derivatives and one produced oplopanes. The geographical distribution of the sesquiterpene-producing populations suggests that the production of sesquiterpenes evolved independently in separate regions. L. limprichtii collected in northern Sichuan was also analyzed and its chemical composition and the sequence of internal transcribed spacers (ITSs) in the ribosomal RNA gene cluster were found to be similar to that in the d/k/n complex and L. yunnanensis, which are morphologically similar.

Versatile In Situ Generated N-Boc-Imines: Application to Phase-Transfer-Catalyzed Asymmetric Mannich-Type Reactions.

The efficient construction of nitrogen-containing organic compounds is a major challenge in chemical synthesis. Imines are one of the most important classes of electrophiles for this transformation. However, both the available imines and applicable nucleophiles for them are quite limited given the existing preparative methods. Described herein are imine precursors which generate reactive imines with a wide variety of substituents under mild basic conditions. This approach enables the construction of various nitrogen-containing molecules which cannot be accessed by the traditional approach. The utility of the novel imine precursor was demonstrated in the asymmetric Mannich-type reaction under phase-transfer conditions.

Chiral Brønsted acid-catalyzed enantioselective addition of indoles to ketimines.

A highly enantioselective addition of indoles to a readily available ketimine was found to be catalyzed by a chiral phosphoric acid. This organocatalytic process represents a rare example of an addition reaction to a non-aromatic ketimine.

Engineering of IF1 -susceptive bacterial F1 -ATPase.

IF1 , an inhibitor protein of mitochondrial ATP synthase, suppresses ATP hydrolytic activity of F1 . One of the unique features of IF1 is the selective inhibition in mitochondrial F1 (MF1 ); it inhibits catalysis of MF1 but does not affect F1 with bacterial origin despite high sequence homology between MF1 and bacterial F1 . Here, we aimed to engineer thermophilic Bacillus F1 (TF1 ) to confer the susceptibility to IF1 for elucidating the molecular mechanism of selective inhibition of IF1 . We first examined the IF1 -susceptibility of hybrid F1 s, composed of each subunit originating from bovine MF1 (bMF1 ) or TF1 . It was clearly shown that only the hybrid with the ß subunit of mitochondrial origin has the IF1 -susceptibility. Based on structural analysis and sequence alignment of bMF1 and TF1 , the five non-conserved residues on the C-terminus of the ß subunit were identified as the candidate responsible for the IF1 -susceptibility. These residues in TF1 were substituted with the bMF1 residues. The resultant mutant TF1 showed evident IF1 -susceptibility. Reversely, we examined the bMF1 mutant with TF1 residues at the corresponding sites, which showed significant suppression of IF1 -susceptibility, confirming the critical role of these residues. We also tested additional three substitutions with bMF1 residues in α and γ subunits that further enhanced the IF1 -susceptibility, suggesting the additive role of these residues. We discuss the molecular mechanism by which IF1 specifically recognizes F1 with mitochondrial origin, based on the present result and the structure of F1 -IF1 complex. These findings would help the development of the inhibitors targeting bacterial F1 .

Synthesis of okicamelliaside, a glucoside of ellagic acid with potent anti-degranulation activity.

Okicamelliaside, a glucoside of ellagic acid with potent anti-degranulation activity, was synthesized from ellagic acid. The regioselectivity, solubility, and high reactivity of the intermediates throughout the synthesis were obtained by the complementary use of triisopropylsilyl (TIPS) and methoxyethoxymethyl (MEM) protective groups on the aglycone skeleton.

Effects of Material Structure on Stress Relaxation Characteristics of Rapidly Solidified Al-Fe Alloy.

An Al-Fe alloy which was produced by hot extrusion of rapidly solidified powder is a possible solution to substitute copper-based electrical conductor material due to its high strength and high electrical conductivity. However, the stress relaxation characteristic-an essential parameter as a conductor material-and the effect of the material structure have not been reported, which was the aim of the present paper. An Al-5%Fe alloy was selected as the test material. The material structures were controlled by hot extrusion practice, annealing, and cold rolling. The Al-Fe intermetallic compound particles controlled the residual stress after the stress relaxation test via the Orowan mechanism. Decreasing the mean inter-particle distance reduces the electrical conductivity. The increase in the number of dislocations by the cold rolling increased strength at room temperature without changing electrical conductivity; however, it did not have a positive effect on the stress relaxation characteristics. The stress relaxation characteristics and the electrical conductivity of the Al-Fe alloy were superior to conventional C52100 H04 phosphor bronze when compared with the case of the same mass.

Effects of Hot Extrusion Temperature Conditions on the Hardness and Electrical Conductivity of Rapidly Solidified Al-Fe Alloys.

Rapidly solidified Al-Fe alloys produced by hot extrusion are a promising replacement for copper-based electrical conductors because of their light weight. However, the effects of the extrusion temperature conditions on the mechanical and electrical properties of extruded materials are unknown. The present work investigated the effects of billet preheating temperature, in situ temperature during extrusion, and additional heat treatment after extrusion on hardness and electrical conductivity. An air-jet atomized Al-2.3%Fe alloy powder was pre-sintered into cylindrical billets and then hot-extruded. The hardness of the extrudates decreased as the in situ temperature during extrusion increased above 650 K. The billet preheating temperature affected the in situ temperature during extrusion. Additional annealing after extrusion decreased the hardness. The cause of the decrease in hardness was coarsening of the grain of the aluminum matrix. The electrical conductivity increased with higher billet preheating temperatures before extrusion or additional annealing after extrusion; however, an in situ temperature rise for a few seconds during extrusion did not affect the conductivity. The increase in electrical conductivity was considered to be caused by a decrease in the amount of solute iron, which requires holding the material at a high temperature for longer than several minutes.

Molecular mechanism on forcible ejection of ATPase inhibitory factor 1 from mitochondrial ATP synthase.

IF1 is a natural inhibitor protein for mitochondrial FoF1 ATP synthase that blocks catalysis and rotation of the F1 by deeply inserting its N-terminal helices into F1. A unique feature of IF1 is condition-dependent inhibition; although IF1 inhibits ATP hydrolysis by F1, IF1 inhibition is relieved under ATP synthesis conditions. To elucidate this condition-dependent inhibition mechanism, we have performed single-molecule manipulation experiments on IF1-inhibited bovine mitochondrial F1 (bMF1). The results show that IF1-inhibited F1 is efficiently activated only when F1 is rotated in the clockwise (ATP synthesis) direction, but not in the counterclockwise direction. The observed rotational-direction-dependent activation explains the condition-dependent mechanism of IF1 inhibition. Investigation of mutant IF1 with N-terminal truncations shows that the interaction with the γ subunit at the N-terminal regions is crucial for rotational-direction-dependent ejection, and the middle long helix is responsible for the inhibition of F1.

Rotary properties of hybrid F1-ATPases consisting of subunits from different species.

F1-ATPase (F1) is an ATP-driven rotary motor protein ubiquitously found in many species as the catalytic portion of FoF1-ATP synthase. Despite the highly conserved amino acid sequence of the catalytic core subunits: α and ß, F1 shows diversity in the maximum catalytic turnover rate Vmax and the number of rotary steps per turn. To study the design principle of F1, we prepared eight hybrid F1s composed of subunits from two of three genuine F1s: thermophilic Bacillus PS3 (TF1), bovine mitochondria (bMF1), and Paracoccus denitrificans (PdF1), differing in the Vmax and the number of rotary steps. The Vmax of the hybrids can be well fitted by a quadratic model highlighting the dominant roles of ß and the couplings between α-ß. Although there exist no simple rules on which subunit dominantly determines the number of steps, our findings show that the stepping behavior is characterized by the combination of all subunits.