Limit theorems for von Mises statistics of a measure preserving transformation

For a measure preserving transformation $T$ of a probability space $(X,\mathcal F,\mu)$ we investigate almost sure and distributional convergence of random variables of the form $$x \to \frac{1}{C_n} \sum_{i_1<n,...,i_d<n} f(T^{i_1}x,...,T^{i_d}x),\, n=1,2,...,$$ where $f$ (called the \emph{kernel}) is a function from $X^d$ to $\R$ and $C_1, C_2,...$ are appropriate normalizing constants. We observe that the above random variables are well defined and belong to $L_r(\mu)$ provided that the kernel is chosen from the projective tensor product $$L_p(X_1,\mathcal F_1, \mu_1) \otimes_{\pi}...\otimes_{\pi} L_p(X_d,\mathcal F_d, \mu_d)\subset L_p(\mu^d)$$ with $p=d\,r,\, r\ \in [1, \infty).$ We establish a form of the individual ergodic theorem for such sequences. Next, we give a martingale approximation argument to derive a central limit theorem in the non-degenerate case (in the sense of the classical Hoeffding's decomposition). Furthermore, for $d=2$ and a wide class of canonical kernels $f$ we also show that the convergence holds in distribution towards a quadratic form $\sum_{m=1}^{\infty} \lambda_m\eta^2_m$ in independent standard Gaussian variables $\eta_1, \eta_2,...$. Our results on the distributional convergence use a $T$--\,invariant filtration as a prerequisite and are derived from uni- and multivariate martingale approximations

Gα12 Activation in Podocytes Leads to Cumulative Changes in Glomerular Collagen Expression, Proteinuria and Glomerulosclerosis

Glomerulosclerosis is a common pathologic finding that often progresses to renal failure. The mechanisms of chronic kidney disease progression are not well-defined but may include activation of numerous vasoactive and inflammatory pathways. We hypothesized that podocytes are susceptible to filtered plasma components including hormones and growth factors that stimulate signaling pathways leading to glomerulosclerosis. Gα12 couples to numerous G-protein-coupled receptors (GPCR) and regulates multiple epithelial responses including proliferation, apoptosis, permeability and the actin cytoskeleton. Herein, we report that genetic activation of Gα12 in podocytes leads to time dependent increases in proteinuria and glomerulosclerosis. To mimic activation of Gα12-pathways, constitutively active Gα12(QL) was conditionally expressed in podocytes using Nphs2-Cre and LacZfloxed QLα12 transgenic mice. Some QLα12$^{LacZ+/Cre+}$ mice developed proteinuria at 4-6m, and most were proteinuric by 12m. Proteinuria increased with age, and by 12-14m many demonstrated glomerulosclerosis with ultrastructural changes including foot process fusion and both mesangial and subendothelial deposits. QLα12$^{LacZ+/Cre+}$ mice showed no changes in podocyte number, apoptosis, proliferation, or Rho/Src activation. Real-time PCR revealed no significant changes in Nphs1, Nphs2, Cd2ap, or Trpc6 expression, but Col4a2 message was increased in younger and older mice while Col4a5 was decreased in older mice. Confocal microscopy revealed disordered collagen IVα1/2 staining in older mice and loss of α5 without changes in other collagen IV subunits. Taken together, these studies suggest that Gα12 activation promotes glomerular injury without podocyte depletion through a novel mechanism regulating collagen (α)IV expression, and supports the notion that glomerular damage may accrue through persistent GPCR activation in podocytes

Identification, purification, and partial characterization of a novel Mr 28,000 integral membrane protein from erythrocytes and renal tubules

A novel Mr 28,000 integral membrane protein ("28kDa") was identified in human erythrocytes and found entirely associated with the Triton X-100 insoluble membrane skeletons. Antibodies to 28kDa reacted strongly on immunoblots with 28kDa and a diffuse region of Mr 35,000-60,000 ("HMW-28kDa"). Selective proteolytic digestions of membranes demonstrated that HMW-28kDa has an extracellular domain, and both 28kDa and HMW-28kDa have intracellular domains. 28kDa and HMW-28kDa were purified to homogeneity. Quantitative immunoblots indicate that each erythrocyte contains 120,000-160,000 copies of 28kDa. Two-dimensional iodopeptide maps of 28kDa and HMW-28kDa were nearly identical; peptide-N-glycosidase digestion of purified HMW-28kDa demonstrated that it is the N-glycosylated form of 28kDa. When concentrated, 28kDa formed a series of larger oligomers which were stable in sodium dodecyl sulfate. Of several nonerythroid tissues studied with anti-28kDa immunoblots, only kidney displayed immunoreactive 28kDa. Purified rat kidney 28kDa was nearly identical to rat erythrocyte 28kDa when compared by two-dimensional iodopeptide mapping. Immunohistochemical staining of human kidney with anti-28kDa demonstrated prominent staining over the apical brush borders of proximal convoluted tubules. A novel integral membrane protein has been purified from erythrocyte and kidney membranes. This new protein may play a role in linkage of the membrane skeleton to the lipid bilayer

Domains Necessary for G␣ 12 Binding and Stimulation of Protein Phosphatase-2A (PP2A): Is G␣ 12 a Novel Regulatory Subunit of PP2A?

ABSTRACT Many cellular signaling pathways share regulation by protein phosphatase-2A (PP2A), a widely expressed serine/threonine phosphatase, and the heterotrimeric G protein G␣ 12 . PP2A activity is altered in carcinogenesis and in some neurodegenerative diseases. We have identified binding of G␣ 12 with the A␣ subunit of PP2A, a trimeric enzyme composed of A (scaffolding), B (regulatory), and C (catalytic) subunits and demonstrated that G␣ 12 stimulated phosphatase activity (J Biol Chem 279: [54983][54984][54985][54986] 2004). We now show in substrate-velocity analysis using purified PP2A that V max was stimulated 3-to 4-fold by glutathione transferase (GST)-G␣ 12 with little effect on K m values. To identify the binding domains mediating the A␣-G␣ 12 interaction, an extensive mutational analysis was performed. Well-characterized mutations of A␣ were expressed in vitro and tested for binding to GST-G␣ 12 in pull-down assays. G␣ 12 binds to A␣ along repeats 7 to 10, and PP2A B subunits are not necessary for binding. To identify where A␣ binds to G␣ 12 , a series of 61 G␣ 12 mutants were engineered to contain the sequence Asn-Ala-Ala-Ile-Arg-Ser (NAAIRS) in place of 6 consecutive amino acids. Mutant G␣ 12 proteins were individually expressed in human embryonic kidney cells and analyzed for interaction with GST or GST-A␣ in pull-down assays. The A␣ binding sites were localized to regions near the N and C termini of G␣ 12 . The expression of constitutively activated G␣ 12 (QL␣ 12 ) in Madin Darby canine kidney cells stimulated PP2A activity as determined by decreased phosphorylation of tyrosine 307 on the catalytic subunit. Based on crystal structures of G␣ 12 and PP2A A␣, a model describing the binding surfaces and potential mechanisms of G␣ 12 -mediated PP2A activation is presented

Assessing Student Mindset, Interest, Participation, and Rapport in the Post-Pandemic Public Speaking Classroom: Effects of Modality Change and Communication Growth Mindset

The COVID-19 pandemic created an exigency for educators to reevaluate their approaches to the classroom with one major dimension being course modality. This study uses the Instructional Beliefs Model to examine the impacts of course modality (i.e., hybrid versus face-to-face formats) and students’ communication growth mindset on student engagement in the foundational public speaking course. Consistent with pre-COVID-19 findings, the results indicated that modality does not significantly impact student engagement, with one exception: higher cognitive interest scores were reported among students in the hybrid modality. Communication growth mindset associated positively with all student engagement variables examined: student interest–emotional, student interest–cognitive, participation, and class rapport. The findings offer tentative optimism about the promise of blended public speaking course modalities, and evidence for the necessity of mindset intervention to maximize student success

Isolation of proteins related to the Rh polypeptides from nonhuman erythrocytes.

It is thought that the Rh antigens may be important in maintaining normal erythrocyte membrane integrity. Despite their name, Rh antigens are serologically present only on human erythrocytes. Rh structural polymorphisms are known to reside within a family of nonglycosylated Mr 32,000 integral membrane proteins that can be purified by hydroxylapatite chromatography. Mr 32,000 integral membrane proteins were purified similarly from erythrocyte membrane vesicles prepared from rhesus monkeys, cows, cats, and rats, but could not be purified from human Rhmod erythrocytes, a rare syndrome lacking Rh antigens. The purified Mr 32,000 polypeptides were labeled with 125I, digested with chymotrypsin, and found to be 30-60% identical to human Rh polypeptides when compared by two-dimensional iodopeptide mapping. The physiologic function of the Rh polypeptides remains to be identified; however, the existence of related proteins in nonhuman erythrocytes supports the concept that the Rh polypeptides are erythrocyte membrane components of fundamental significance