Design and analysis for three level hierarchical structures with count response

In numerous intervention studies and education field trials, random assignment to treatment occurs in clusters rather than at the level of observation. This departure of random assignment of units may be due to logistics, political feasibility, or ecological validity. Data within the same cluster or grouping are often correlated. Application of traditional regression techniques, which assume independence between observations, to clustered data produce consistent parameter estimates. However such estimators are often inefficient as compared to methods which incorporate the clustered nature of the data into the estimation procedure (Neuhaus 1993).1 Multilevel models, also known as random effects or random components models, can be used to account for the clustering of data by estimating higher level, or group, as well as lower level, or individual variation. Designing a study, in which the unit of observation is nested within higher level groupings, requires the determination of sample sizes at each level. This study investigates the design and analysis of various sampling strategies for a 3-level repeated measures design on the parameter estimates when the outcome variable of interest follows a Poisson distribution. ^ Results study suggest that second order PQL estimation produces the least biased estimates in the 3-level multilevel Poisson model followed by first order PQL and then second and first order MQL. The MQL estimates of both fixed and random parameters are generally satisfactory when the level 2 and level 3 variation is less than 0.10. However, as the higher level error variance increases, the MQL estimates become increasingly biased. If convergence of the estimation algorithm is not obtained by PQL procedure and higher level error variance is large, the estimates may be significantly biased. In this case bias correction techniques such as bootstrapping should be considered as an alternative procedure. For larger sample sizes, those structures with 20 or more units sampled at levels with normally distributed random errors produced more stable estimates with less sampling variance than structures with an increased number of level 1 units. For small sample sizes, sampling fewer units at the level with Poisson variation produces less sampling variation, however this criterion is no longer important when sample sizes are large. ^ 1Neuhaus J (1993). “Estimation efficiency and Tests of Covariate Effects with Clustered Binary Data”. Biometrics , 49, 989–996^

Identification of a conserved cluster in the RH domain of GRK critical for activation by GPCRs

One of the most critical aspects of G Protein Coupled Receptors (GPCRs) regulation is their rapid and acute desensitization following agonist stimulation. Phosphorylation of these receptors by GPCR kinases (GRK) is a major mechanism of desensitization. Considerable evidence from studies of rhodopsin kinase and GRK2 suggests there is an allosteric docking site for the receptor distinct from the GRK catalytic site. While the agonist-activated GPCR appears crucial for GRK activation, the molecular details of this interaction remain unclear. Recent studies suggested an important role for the N- and C-termini and domains in the small lobe of the kinase domain in allosteric activation; however, neither the mechanism of action of that site nor the RH domain contributions have been elucidated. To search for the allosteric site, we first indentified evolutionarily conserved sites within the RH and kinase domains presumably deterministic of protein function employing evolutionary trace (ET) methodology and crystal structures of GRK6. Focusing on a conserved cluster centered on helices 3, 9, and 10 in the RH domain, key residues of GRK5 and 6 were targeted for mutagenesis and functional assays. We found that a number of double mutations within helices 3, 9, and 10 and the N-terminus markedly reduced (50–90%) the constitutive phosphorylation of the β-2 Adrenergic Receptor (β2AR) in intact cells and phosphorylation of light-activated rhodopsin (Rho*) in vitro as compared to wild type (WT) GRK5 or 6. Based on these results, we designed peptide mimetics of GRK5 helix 9 both computationally and through chemical modifications with the goal of both confirming the importance of helix 9 and developing a useful inhibitor to disrupt the GPCR-GRK interaction. Several peptides were found to block Rho* phosphorylation by GRK5 including the native helix 9 sequence, Peptide Builder designed-peptide preserving only the key ET residues, and chemically locked helices. Most peptidomimetics showed inhibition of GRK5 activity greater than 80 % with an IC50 of ∼ 30 µM. Alanine scanning of helix 9 has further revealed both essential and non-essential residues for inhibition. Importantly, substitution of Arg 169 by an alanine in the native helix 9-based peptide gave an almost complete inhibition at 30 µM with an IC50 of ∼ 10 µM. In summary we report a previously unrecognized crucial role for the RH domain of GRK5 and 6, and the subsequent identification of a lead peptide inhibitor of protein-protein interaction with potential for specific blockade of GPCR desensitization. ^