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Larkin A, Kim JS, Kim N, Baek SH, Yamada S, Park K, Tai K, Yanagi Y, Park JH. Accuracy of artificial intelligence-assisted growth prediction in skeletal Class I preadolescent patients using serial lateral cephalograms for a 2-year growth interval. Orthod Craniofac Res 2024. [PMID: 38321788 DOI: 10.1111/ocr.12764] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 01/23/2024] [Indexed: 02/08/2024]
Abstract
OBJECTIVE To investigate the accuracy of artificial intelligence-assisted growth prediction using a convolutional neural network (CNN) algorithm and longitudinal lateral cephalograms (Lat-cephs). MATERIALS AND METHODS A total of 198 Japanese preadolescent children, who had skeletal Class I malocclusion and whose Lat-cephs were available at age 8 years (T0) and 10 years (T1), were allocated into the training, validation, and test phases (n = 161, n = 17, n = 20). Orthodontists and the CNN model identified 28 hard-tissue landmarks (HTL) and 19 soft-tissue landmarks (STL). The mean prediction error values were defined as 'excellent,' 'very good,' 'good,' 'acceptable,' and 'unsatisfactory' (criteria: 0.5 mm, 1.0 mm, 1.5 mm, and 2.0 mm, respectively). The degree of accurate prediction percentage (APP) was defined as 'very high,' 'high,' 'medium,' and 'low' (criteria: 90%, 70%, and 50%, respectively) according to the percentage of subjects that showed the error range within 1.5 mm. RESULTS All HTLs showed acceptable-to-excellent mean PE values, while the STLs Pog', Gn', and Me' showed unsatisfactory values, and the rest showed good-to-acceptable values. Regarding the degree of APP, HTLs Ba, ramus posterior, Pm, Pog, B-point, Me, and mandibular first molar root apex exhibited low APPs. The STLs labrale superius, lower embrasure, lower lip, point of lower profile, B', Pog,' Gn' and Me' also exhibited low APPs. The remainder of HTLs and STLs showed medium-to-very high APPs. CONCLUSION Despite the possibility of using the CNN model to predict growth, further studies are needed to improve the prediction accuracy in HTLs and STLs of the chin area.
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Tai K, Komatsu S, Sofue K, Kido M, Tanaka M, Kuramitsu K, Awazu M, Gon H, Tsugawa D, Yanagimoto H, Toyama H, Murakami S, Murakami T, Fukumoto T. Total tumour volume as a prognostic factor in patients with resectable colorectal cancer liver metastases. BJS Open 2020; 4:456-466. [PMID: 32277807 PMCID: PMC7260417 DOI: 10.1002/bjs5.50280] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/08/2020] [Accepted: 02/16/2020] [Indexed: 12/29/2022] Open
Abstract
Background Although total tumour volume (TTV) may have prognostic value for hepatic resection in certain solid cancers, its importance in colorectal liver metastases (CRLM) remains unexplored. This study investigated its prognostic value in patients with resectable
CRLM. Method This was a retrospective review of patients who underwent hepatic resection for CRLM between 2008 and 2017 in a single institution. TTV was measured from CT images using three‐dimensional construction software; cut‐off values were determined using receiver operating characteristic (ROC) curve analyses. Potential prognostic factors, overall survival (OS) and recurrence‐free survival (RFS) were determined using multivariable and Kaplan–Meier analyses. Results Some 94 patients were included. TTV cut‐off values for OS and RFS were 100 and 10 ml respectively. Right colonic primary tumours, primary lymph node metastasis and bilobar liver metastasis were included in the multivariable analysis of OS; a TTV of 100 ml or above was independently associated with poorer OS (hazard ratio (HR) 6·34, 95 per cent c.i. 2·08 to 17·90; P = 0·002). Right colonic primary tumours and primary lymph node metastasis were included in the RFS analysis; a TTV of 10 ml or more independently predicted poorer RFS (HR 1·90, 1·12 to 3·57; P = 0·017). The 5‐year OS rate for a TTV of 100 ml or more was 41 per cent, compared with 67 per cent for a TTV below 100 ml (P = 0·006). Corresponding RFS rates with TTV of 10 ml or more, or less than 10 ml, were 14 and 58 per cent respectively (P = 0·009). A TTV of at least 100 ml conferred a higher rate of unresectable initial recurrences (12 of 15, 80 per cent) after initial hepatic resection. Conclusion TTV was associated with RFS and OS after initial hepatic resection for CRLM; TTV of 100 ml or above was associated with a higher rate of unresectable recurrence.
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Keall P, Nguyen D, O'Brien R, Hewson E, Ball H, Poulsen P, Booth J, Greer P, Hunter P, Wilton L, Bromley R, Kipritidis J, Eade T, Kneebone A, Hruby G, Moodie T, Hayden A, Turner S, Arumugam S, Sidhom M, Hardcastle N, Siva S, Tai K, Gebski V, Martin J. PO-0842 Real-Time tracking improves treatment: The TROG Stereo Prostate Ablative Radiotherapy with KIM trial. Radiother Oncol 2019. [DOI: 10.1016/s0167-8140(19)31262-9] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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Ogasawara A, Hihara T, Yabuno A, Shintani D, Ikeda Y, Tai K, Fujiwara K, Hasegawa K. Circulating tumor DNA is an independent prognostic factor in patients with early-stage epithelial ovarian cancer. Gynecol Oncol 2018. [DOI: 10.1016/j.ygyno.2018.04.392] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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Shintani D, Hihara T, Ogasawara A, Yabuno A, Fujiwara K, Tai K, Hasegawa K. Evaluation of circulating tumor DNA in patients with endometrial cancer harboring somatic PIK3CA or KRAS mutations: A potential high-risk factor for recurrence. Gynecol Oncol 2018. [DOI: 10.1016/j.ygyno.2018.04.082] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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Kim MJ, Park JH, Kojima Y, Tai K, Chae JM. A finite element analysis of the optimal bending angles in a running loop for mesial translation of a mandibular molar using indirect skeletal anchorage. Orthod Craniofac Res 2017; 21:63-70. [PMID: 29271058 DOI: 10.1111/ocr.12216] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 11/29/2017] [Indexed: 11/30/2022]
Abstract
OBJECTIVES To estimate the optimal bending angles in the running loop for mesial translation of a mandibular second molar using indirect skeletal anchorage and to clarify the mechanics of tipping and rotating the molar. METHODS A three-dimensional finite element model was developed for predicting tooth movement, and a mechanical model based on the beam theory was constructed for clarifying the force systems. RESULTS When using a running loop without bends, the molar tipped mesially 14.4° and lingually 0.6°, rotated counterclockwise 4.1°, and the incisors retracted 0.02 mm and intruded 0.05 mm. These angles were about the same as those estimated by the beam theory. When the amount of tip back and toe-in angles was 11.0°, mesial translation of the molar was achieved, and incisors retracted 0.10 mm and intruded 0.30 mm. CONCLUSIONS Mesial translation of a mandibular second molar without any significant movement of anterior teeth was achieved during protraction by controlling the tip back and toe-in angles and enhancing anterior anchorage with the combined use of a running loop and indirect skeletal anchorage.
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Garg A, Panda BN, Tai K. True stress measurement of nuclear fuel rod cladding material subjected to DSA regime. Neural Comput Appl 2017. [DOI: 10.1007/s00521-016-2298-4] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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Ogasawara A, Hihara T, Yabuno A, Shimoyokkaichi S, Shintani D, Ikeda Y, Tai K, Fujiwara K, Watanabe K, Hasegawa K. Evaluation of circulating tumor DNA in patients with ovarian cancer harboring somatic PIK3CA or KRAS mutations. Ann Oncol 2017. [DOI: 10.1093/annonc/mdx372.015] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022] Open
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Kimura T, Adachi Y, Matsuki M, Yamaguchi A, Ozawa Y, Okamoto K, Mitsuhashi K, Hoshi T, Tohyama O, Tai K, Ogo M, Matsui J, Funahashi Y. The antitumor activity of lenvatinib (LEN) in combination with everolimus (EVE) in human renal cell carcinoma (RCC) xenograft models is dependent on VEGFR and FGFR signaling. Ann Oncol 2016. [DOI: 10.1093/annonc/mdw362.06] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Hong J, Lee T, Tai K, Chen Y. 627 Involvement of TYRP1 in melanoma drug response to BRAF inhibitor. J Invest Dermatol 2016. [DOI: 10.1016/j.jid.2016.02.667] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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Garg A, Vijayaraghavan V, Wong C, Tai K, Sumithra K, Mahapatra S, Singru PM, Yao L. Application of artificial intelligence technique for modelling elastic properties of 2D nanoscale material. MOLECULAR SIMULATION 2014. [DOI: 10.1080/08927022.2014.951351] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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Garg A, Garg A, Tai K, Barontini S, Stokes A. A Computational Intelligence-Based Genetic Programming Approach for the Simulation of Soil Water Retention Curves. Transp Porous Media 2014. [DOI: 10.1007/s11242-014-0313-8] [Citation(s) in RCA: 34] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Tai K, Houlahan TJ, Eden JG, Dillon SJ. Integration of microplasma with transmission electron microscopy: Real-time observation of gold sputtering and island formation. Sci Rep 2013; 3:1325. [PMID: 23429577 PMCID: PMC3579186 DOI: 10.1038/srep01325] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2012] [Accepted: 01/18/2013] [Indexed: 11/16/2022] Open
Abstract
An in situ platform for characterizing plasma-materials interactions at the nanoscale in the transmission electron microscope (TEM) has been demonstrated. Integrating a DC microplasma device, having plane-parallel electrodes with a 25 nm thick Au film on both the cathode and anode and operating in 760 Torr of Ar, within a TEM provides real-time observation of Au sputtering and island formation with a spatial resolution of < 100 nm. Analyses of TEM and atomic force microscopy images show the growth of Au islands to proceed by a Stranski-Krastanov process at a rate that varies linearly with the discharge power and is approximately a factor of 3 larger than the predictions of a DC plasma sputtering model. The experiments reported here extend in situ TEM diagnostics to plasma-solid and plasma-liquid interactions.
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Tai K, Iwasaki H, Ikegaya S, Ueda T. P147 Minocycline reduces cytokine and chemokine production in lipopolysaccharide-stimulated THP-1 monocytic cells by inhibition of IκB kinase α/β. Int J Antimicrob Agents 2013. [DOI: 10.1016/s0924-8579(13)70391-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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Singh B, Tai K, Cook KR, Irving LR, Lucci A. Abstract P4-03-06: Selection of Rare and Novel Breast Cancer Cell Variants Based on Glutamine Metabolism. Cancer Res 2010. [DOI: 10.1158/0008-5472.sabcs10-p4-03-06] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Abstract
Background: Breast cancer is a heterogeneous disease composed of tumor cells that have different characteristics. Although there are several different ways to explain cellular heterogeneity, it is clear that only rare cancer cells out of the overall population succeed in metastasizing. The current approach of classifying subpopulations of cancer cells based on certain biomarkers derived from the bulk of primary tumor is unsatisfactory for identifying the rare cells that cause metastasis. The purpose of this study was to test a novel function-based, rather than biomarker-based, selection strategy using glutamine (Gln) metabolism (or Gln-dependence to be more specific) since it is a prominent feature of cancer cells. While the majority of cells present in metastatic breast cancer cell lines are predicted to be dependent on Gln and thus will die upon Gln withdrawal, we hypothesized that some rare cells would survive and grow without Gln as a nutrient, thus suggesting a simple robust selection method for “tumorigenic” cancer cells. Methods: We chose an aggressive inflammatory breast cancer cell line SUM149 and SUM149-FP76 cell line that was recently derived by “passaging” SUM149-Luc cells (luciferase transfected for imaging in mice) in nude mice in our laboratory, first selecting for growth subcutaneously and then in inguinal fat pad. Gln-independent variants were selected by growing cells in a medium without Gln, supplemented with dialyzed fetal bovine serum. We evaluated protein level of glutaminase (GLS), an enzyme that converts glutamine to glutamate and usually correlates with Gln addiction in cancer cells, by western blotting. Expression of COX-2, an enzyme associated with inflammation, metastasis, and with cellular hierarchy, was measured by western blotting and compared between parental and Gln-independent lines. Tests were repeated in triplicate and evaluated using paired T-test. Results: We were able to select rare variants (one in 35,000 cancer cells) from the SUM149 inflammatory breast cancer cell line that grow long-term in Gln-free medium. We found that Gln-independent variants produced a significantly lower level of GLS (1/5th) and a significantly higher level (5-fold) of COX-2 than did the parental cell line. To provide further support for a link between Gln metabolism and tumorigenesis, we were also able to select the rare Gln-independent variants from the SUM149-FP76 cell line. Further experiments involving siRNA-mediated COX-2 knockdown indicated that the high level of COX-2 protein present in Gln-independent variants was not a direct regulator of the reduced GLS level, but rather COX-2 may offer indirect selective advantage by influencing processes such as apoptosis and “developmental hierarchy”. Conclusions: Since COX-2 is very important in breast cancermetastasis, our results suggest the possibility of a strong link between a critical metabolic adaptation (decreased GLS to maintain a sufficient Gln pool) that may be essential for cell survival and growth, and metastatic ability (via increased COX-2) in cancer cells. Our study also revealed a deep connection between glutamine metabolism and metastasis that could be exploited for developing novel models of cancer cell function and for targeted therapy development against these cells.
Citation Information: Cancer Res 2010;70(24 Suppl):Abstract nr P4-03-06.
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Lamb D, Denham J, Joseph D, Tai K, Turner S, Matthews J, Woodhead D, Kumar M, Greer P, Steigler A. 2226. Int J Radiat Oncol Biol Phys 2006. [DOI: 10.1016/j.ijrobp.2006.07.632] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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Matsuda M, Tai K, Moore JE, Millar BC, Murayama O. Nucleotide sequence analysis of therecA gene and discrimination of the three isolates of urease-positive thermophilicCampylobacter (UPTC) isolated from seagulls (Larus spp.) in Northern Ireland. J Basic Microbiol 2005. [DOI: 10.1002/jobm.200410465] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
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Gore M, Brandenburg N, Tai K. Burden of illness in painful diabetic peripheral neuropathy (DPN): The patients’ perspectives. THE JOURNAL OF PAIN 2005. [DOI: 10.1016/j.jpain.2005.01.110] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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Matsuda M, Tai K, Moore JE, Millar BC, Murayama O. Nucleotide sequence analysis of the recA gene and discrimination of the three isolates of urease-positive thermophilic Campylobacter (UPTC) isolated from seagulls (Larus spp.) in Northern Ireland. J Basic Microbiol 2004; 44:215-9. [PMID: 15162395 DOI: 10.1002/jobm.200310346] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
Nucleotide sequencing after TA cloning of the amplicon of the almost-full length recA gene from three strains of UPTC (A1, A2, and A3) isolated from seagulls in Northern Ireland, the phenotypical and genotypical characteristics of which have been demonstrated to be indistinguishable, clarified nucleotide differences at three nucleotide positions among the three strains. In conclusion, the nucleotide sequences of the recA gene were found to discriminate among the three strains of UPTC, A1, A2, and A3, which are indistinguishable phenotypically and genotypically. Thus, the present study strongly suggests that nucleotide sequence data of the amplicon of a suitable gene or region could aid in discriminating among isolates of the UPTC group, which are indistinguishable phenotypically and genotypically.
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Gore M, Brandenburg N, Dukes E, Hoffman D, Snyder-Chavis A, Tai K. Clinical outcomes measurement. THE JOURNAL OF PAIN 2004. [DOI: 10.1016/j.jpain.2004.02.416] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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Abstract
Abstract
Computer simulation methods spanning several temporal and spatial scales are reviewed, focusing on their applications on the neuromuscular synapse. Quantum mechanics treats the enzymatic catalysis of neurotransmitters on the picometer scale. Molecular dynamics reveals conformational changes of the enzyme acetylcholinesterase for nanoseconds. Brownian dynamics follow the substrate molecule in its diffusion on the microsecond level. Methods such as finite elements describe the diffusion of neurotransmitters as a changing concentration continuum in the synapse. Promising directions for future research include integration of methods on several scales, and applying these methods to the acetylcholine receptor.
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Deon D, Ahmed S, Tai K, Scaletta N, Herrero C, Lee IH, Krause A, Ivashkiv LB. Cross-talk between IL-1 and IL-6 signaling pathways in rheumatoid arthritis synovial fibroblasts. JOURNAL OF IMMUNOLOGY (BALTIMORE, MD. : 1950) 2001; 167:5395-403. [PMID: 11673558 DOI: 10.4049/jimmunol.167.9.5395] [Citation(s) in RCA: 83] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/30/2023]
Abstract
The balance between pro- and anti-inflammatory cytokines plays an important role in determining the severity of inflammation in rheumatoid arthritis (RA). Antagonism between opposing cytokines at the level of signal transduction plays an important role in many other systems. We have begun to explore the possible contribution of signal transduction cross-talk to cytokine balance in RA by examining the effects of IL-1, a proinflammatory cytokine, on the signaling and action of IL-6, a pleiotropic cytokine that has both pro- and anti-inflammatory actions, in RA synovial fibroblasts. Pretreatment with IL-1 suppressed Janus kinase-STAT signaling by IL-6, modified patterns of gene activation, and blocked IL-6 induction of tissue inhibitor of metalloproteases 1 expression. These results suggest that proinflammatory cytokines may contribute to pathogenesis by modulating or blocking signal transduction by pleiotropic or anti-inflammatory cytokines. The mechanism of inhibition did not require de novo gene activation and did not depend upon tyrosine phosphatase activity, but, instead, was dependent on the p38 stress kinase. These results identify a molecular basis for IL-1 and IL-6 cross-talk in RA synoviocytes and suggest that, in addition to levels of cytokine expression, modulation of signal transduction also plays a role in regulating cytokine balance in RA.
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Tai K, Shen T, Börjesson U, Philippopoulos M, McCammon JA. Analysis of a 10-ns molecular dynamics simulation of mouse acetylcholinesterase. Biophys J 2001; 81:715-24. [PMID: 11463620 PMCID: PMC1301548 DOI: 10.1016/s0006-3495(01)75736-0] [Citation(s) in RCA: 126] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022] Open
Abstract
A 10-ns molecular dynamics simulation of mouse acetylcholinesterase was analyzed, with special attention paid to the fluctuation in the width of the gorge and opening events of the back door. The trajectory was first verified to ensure its stability. We defined the gorge proper radius as the measure for the extent of gorge opening. We developed an expression of an inter-atom distance representative of the gorge proper radius in terms of projections on the principal components. This revealed the fact that collective motions of many scales contribute to the opening behavior of the gorge. Covariance and correlation results identified the motions of the protein backbone as the gorge opens. In the back-door region, side-chain dihedral angles that define the opening were identified.
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Kikuchi K, Tagami K, Hibi S, Yoshimura H, Tokuhara N, Tai K, Hida T, Yamauchi T, Nagai M. Syntheses and evaluation of quinoline derivatives as novel retinoic acid receptor α antagonists. Bioorg Med Chem Lett 2001; 11:1215-8. [PMID: 11354380 DOI: 10.1016/s0960-894x(01)00177-9] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
Abstract
In the course of studies on novel retinoids, we have designed and synthesized a series of quinoline derivatives. One of them, 4-[5-[8-(1-methylethyl)-4-phenyl-2-quinolinyl]-1H-2-pyrrolyl]benzoic acid (12f) shows potent RARalpha-selective antagonistic activity.
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Shen TY, Tai K, McCammon JA. Statistical analysis of the fractal gating motions of the enzyme acetylcholinesterase. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 63:041902. [PMID: 11308872 DOI: 10.1103/physreve.63.041902] [Citation(s) in RCA: 21] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/15/2000] [Indexed: 05/23/2023]
Abstract
The enzyme acetylcholinesterase has an active site that is accessible only by a "gorge" or main channel from the surface, and perhaps by secondary channels such as the "back door." Molecular-dynamics simulations show that these channels are too narrow most of the time to admit substrate or other small molecules. Binding of substrates is therefore "gated" by structural fluctuations of the enzyme. Here, we analyze the fluctuations of these possible channels, as observed in the 10.8-ns trajectory of the simulation. The probability density function of the gorge proper radius (defined in the text) was calculated. A double-peak feature of the function was discovered and therefore two states with a threshold were identified. The relaxation (transition probability) functions of these two states were also calculated. The results revealed a power-law decay trend and an oscillation around it, which show properties of fractal dynamics with a "complex exponent." The cross correlation of potential energy versus proper radius was also investigated. We discuss possible physical models behind the fractal protein dynamics; the dynamic hierarchical model for glassy systems is evaluated in detail.
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