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Two-sample testing is a fundamental problem in statistics. While many powerful nonparametric methods exist for both the univariate and multivariate context, it is comparatively less common to see a framework for determining which data features lead to rejection of the null. In this paper, we propose a new nonparametric two-sample test named AUGUST, which incorporates a framework for interpretation while maintaining power comparable to existing methods. AUGUST tests for inequality in distribution up to a predetermined resolution using symmetry statistics from binary expansion. Designed for univariate and low to moderate-dimensional multivariate data, this construction allows us to understand distributional differences as a combination of fundamental orthogonal signals. Asymptotic theory for the test statistic facilitates p-value computation and power analysis, and an efficient algorithm enables computation on large data sets. In empirical studies, we show that our test has power comparable to that of popular existing methods, as well as greater power in some circumstances. We illustrate the interpretability of our method using NBA shooting data. 

Ephrin type-A receptor 2 (EphA2) is a receptor tyrosine kinase that initiates both ligand-dependent tumor-suppressive and ligand-independent oncogenic signaling. We used time-resolved, live-cell fluorescence spectroscopy to show that the ligand-free EphA2 assembles into multimers driven by two types of intermolecular interactions in the ectodomain. The first type entails extended symmetric interactions required for ligand-induced receptor clustering and tumor-suppressive signaling that inhibits activity of the oncogenic extracellular signal–regulated kinase (ERK) and protein kinase B (AKT) protein kinases and suppresses cell migration. The second type is an asymmetric interaction between the amino terminus and the membrane proximal domain of the neighboring receptors, which supports oncogenic signaling and promotes migration in vitro and tumor invasiveness in vivo. Our results identify the molecular interactions that drive the formation of the EphA2 multimeric signaling clusters and reveal the pivotal role of EphA2 assembly in dictating its opposing functions in oncogenesis. 

Oncogenic mutations within the epidermal growth factor receptor (EGFR) are found in 15 to 30% of all non–small-cell lung carcinomas. The term exon 19 deletion (ex19del) is collectively used to refer to more than 20 distinct genomic alterations within exon 19 that comprise the most common EGFR mutation subtype in lung cancer. Despite this heterogeneity, clinical treatment decisions are made irrespective of which EGFR ex19del variant is present within the tumor, and there is a paucity of information regarding how individual ex19del variants influence protein structure and function. Herein, we identified allele-specific functional differences among ex19del variants attributable to recurring sequence and structure motifs. We built all-atom structural models of 60 ex19del variants identified in patients and combined molecular dynamics simulations with biochemical and biophysical experiments to analyze three ex19del mutations (E746_A750, E746_S752 > V, and L747_A750 > P). We demonstrate that sequence variation in ex19del alters oncogenic cell growth, dimerization propensity, enzyme kinetics, and tyrosine kinase inhibitor (TKI) sensitivity. We show that in contrast to E746_A750 and E746_S752 > V, the L747_A750 > P variant forms highly active ligand-independent dimers. Enzyme kinetic analysis and TKI inhibition experiments suggest that E746_S752 > V and L747_A750 > P display reduced TKI sensitivity due to decreased adenosine 5′-triphosphate K m . Through these analyses, we propose an expanded framework for interpreting ex19del variants and considerations for therapeutic intervention. 

Abstract The application of Co_2‐xRh_xP nanoparticles as electrocatalysts for the hydrogen evolution reaction (HER) and overall water splitting in basic media is reported. The experimental design seeks to dilute rhodium with earth‐abundant cobalt as a means to lower the cost of the material and achieve catalytic synergism, as reported for related bimetallic phosphides. The HER activity of Co_2‐xRh_xP is found to be composition‐dependent, with the rhodium‐rich compositions being more active as compared to their cobalt‐rich counterparts, with overpotentials (η) at 10 mA/cm²_geometricof 58.1–63.9 mV vs. 82.1–188.1 mV, respectively. In contrast, Co‐rich Co_2‐xRh_xP nanoparticles are active for the oxygen evolution reaction (OER) process in basic media, with η= 290 mV for x=0.25. A full water electrolysis cell was created using the most active compositions for OER and HER as the anode and cathode, respectively, generating an overall η= 390 mV. Notably, the cell became more active over a 50 h stability test, increasing by 2 mV/cm²_geometricat a constant applied voltage of 1.62 V vs NHE. This enhanced activity correlates with nanoscale phase segregation of Rh in the anode. Thus, the lower overpotential achieved for Co_1.75Rh_0.25P relative to Co₂P, and the augmented activity over time in the former, may be a consequence of restructuring of the anode driven by Rh phase‐segregation. The augmentation in activity at the anode more than compensates for small losses at the cathode. 

Abstract Mechanistic understanding of oncogenic variants facilitates the development and optimization of treatment strategies. We recently identified in-frame, tandem duplication ofEGFRexons 18 - 25, which causes EGFR Kinase Domain Duplication (EGFR-KDD). Here, we characterize the prevalence ofERBBfamily KDDs across multiple human cancers and evaluate the functional biochemistry of EGFR-KDD as it relates to pathogenesis and potential therapeutic intervention. We provide computational and experimental evidence that EGFR-KDD functions by forming asymmetric EGF-independent intra-molecular and EGF-dependent inter-molecular dimers. Time-resolved fluorescence microscopy and co-immunoprecipitation reveals EGFR-KDD can form ligand-dependent inter-molecular homo- and hetero-dimers/multimers. Furthermore, we show that inhibition of EGFR-KDD activity is maximally achieved by blocking both intra- and inter-molecular dimerization. Collectively, our findings define a previously unrecognized model of EGFR dimerization, providing important insights for the understanding of EGFR activation mechanisms and informing personalized treatment of patients with tumors harboring EGFR-KDD. Finally, we establishERBBKDDs as recurrent oncogenic events in multiple cancers. 

Abstract The constituent parts of a quantum computer are inherently vulnerable to errors. To this end, we have developed quantum error-correcting codes to protect quantum information from noise. However, discovering codes that are capable of a universal set of computational operations with the minimal cost in quantum resources remains an important and ongoing challenge. One proposal of significant recent interest is the gauge color code. Notably, this code may offer a reduced resource cost over other well-studied fault-tolerant architectures by using a new method, known as gauge fixing, for performing the non-Clifford operations that are essential for universal quantum computation. Here we examine the gauge color code when it is subject to noise. Specifically, we make use of single-shot error correction to develop a simple decoding algorithm for the gauge color code, and we numerically analyse its performance. Remarkably, we find threshold error rates comparable to those of other leading proposals. Our results thus provide the first steps of a comparative study between the gauge color code and other promising computational architectures.