On Provable Algorithms for Determination of Continuous Protein Interdomain Motions from Residual Dipolar Couplings

Dynamics of biomolecules over various spatial and time scales are essential for biological functions such as molecular recognition, catalysis and signaling. However, reconstruction of biomolecular dynamics from experimental observables requires the determination of a conformational probability distribution. Unfortunately, these distributions cannot be fully constrained by the limited information from experiments, making the problem an ill-posed one in the terminology of Hadamard. The ill-posed nature of the problem comes from the fact that it has no unique solution. Multiple or even an infinite number of solutions may exist. To avoid the ill-posed nature, the problem needs to be regularized by making assumptions, which inevitably introduce biases into the result.

Here, I present two continuous probability density function approaches to solve an important inverse problem called the RDC trigonometric moment problem. By focusing on interdomain orientations we reduced the problem to determination of a distribution on the 3D rotational space from residual dipolar couplings (RDCs). We derived an analytical equation that relates alignment tensors of adjacent domains, which serves as the foundation of the two methods. In the first approach, the ill-posed nature of the problem was avoided by introducing a continuous distribution model, which enjoys a smoothness assumption. To find the optimal solution for the distribution, we also designed an efficient branch-and-bound algorithm that exploits the mathematical structure of the analytical solutions. The algorithm is guaranteed to find the distribution that best satisfies the analytical relationship. We observed good performance of the method when tested under various levels of experimental noise and when applied to two protein systems. The second approach avoids the use of any model by employing maximum entropy principles. This 'model-free' approach delivers the least biased result which presents our state of knowledge. In this approach, the solution is an exponential function of Lagrange multipliers. To determine the multipliers, a convex objective function is constructed. Consequently, the maximum entropy solution can be found easily by gradient descent methods. Both algorithms can be applied to biomolecular RDC data in general, including data from RNA and DNA molecules.

Missing data in randomized clinical trials for weight loss: scope of the problem, state of the field, and performance of statistical methods.

BACKGROUND: Dropouts and missing data are nearly-ubiquitous in obesity randomized controlled trails, threatening validity and generalizability of conclusions. Herein, we meta-analytically evaluate the extent of missing data, the frequency with which various analytic methods are employed to accommodate dropouts, and the performance of multiple statistical methods. METHODOLOGY/PRINCIPAL FINDINGS: We searched PubMed and Cochrane databases (2000-2006) for articles published in English and manually searched bibliographic references. Articles of pharmaceutical randomized controlled trials with weight loss or weight gain prevention as major endpoints were included. Two authors independently reviewed each publication for inclusion. 121 articles met the inclusion criteria. Two authors independently extracted treatment, sample size, drop-out rates, study duration, and statistical method used to handle missing data from all articles and resolved disagreements by consensus. In the meta-analysis, drop-out rates were substantial with the survival (non-dropout) rates being approximated by an exponential decay curve (e(-lambdat)) where lambda was estimated to be .0088 (95% bootstrap confidence interval: .0076 to .0100) and t represents time in weeks. The estimated drop-out rate at 1 year was 37%. Most studies used last observation carried forward as the primary analytic method to handle missing data. We also obtained 12 raw obesity randomized controlled trial datasets for empirical analyses. Analyses of raw randomized controlled trial data suggested that both mixed models and multiple imputation performed well, but that multiple imputation may be more robust when missing data are extensive. CONCLUSION/SIGNIFICANCE: Our analysis offers an equation for predictions of dropout rates useful for future study planning. Our raw data analyses suggests that multiple imputation is better than other methods for handling missing data in obesity randomized controlled trials, followed closely by mixed models. We suggest these methods supplant last observation carried forward as the primary method of analysis.

Transsynaptic Tracing from Peripheral Targets with Pseudorabies Virus Followed by Cholera Toxin and Biotinylated Dextran Amines Double Labeling.

Transsynaptic tracing has become a powerful tool used to analyze central efferents that regulate peripheral targets through multi-synaptic circuits. This approach has been most extensively used in the brain by utilizing the swine pathogen pseudorabies virus (PRV)(1). PRV does not infect great apes, including humans, so it is most commonly used in studies on small mammals, especially rodents. The pseudorabies strain PRV152 expresses the enhanced green fluorescent protein (eGFP) reporter gene and only crosses functional synapses retrogradely through the hierarchical sequence of synaptic connections away from the infection site(2,3). Other PRV strains have distinct microbiological properties and may be transported in both directions (PRV-Becker and PRV-Kaplan)(4,5). This protocol will deal exclusively with PRV152. By delivering the virus at a peripheral site, such as muscle, it is possible to limit the entry of the virus into the brain through a specific set of neurons. The resulting pattern of eGFP signal throughout the brain then resolves the neurons that are connected to the initially infected cells. As the distributed nature of transsynaptic tracing with pseudorabies virus makes interpreting specific connections within an identified network difficult, we present a sensitive and reliable method employing biotinylated dextran amines (BDA) and cholera toxin subunit b (CTb) for confirming the connections between cells identified using PRV152. Immunochemical detection of BDA and CTb with peroxidase and DAB (3, 3'-diaminobenzidine) was chosen because they are effective at revealing cellular processes including distal dendrites(6-11).

The accuracy and completeness for receipt of colorectal cancer care using Veterans Health Administration administrative data.

BACKGROUND: The National Comprehensive Cancer Network and the American Society of Clinical Oncology have established guidelines for the treatment and surveillance of colorectal cancer (CRC), respectively. Considering these guidelines, an accurate and efficient method is needed to measure receipt of care. METHODS: The accuracy and completeness of Veterans Health Administration (VA) administrative data were assessed by comparing them with data manually abstracted during the Colorectal Cancer Care Collaborative (C4) quality improvement initiative for 618 patients with stage I-III CRC. RESULTS: The VA administrative data contained gender, marital, and birth information for all patients but race information was missing for 62.1% of patients. The percent agreement for demographic variables ranged from 98.1-100%. The kappa statistic for receipt of treatments ranged from 0.21 to 0.60 and there was a 96.9% agreement for the date of surgical resection. The percentage of post-diagnosis surveillance events in C4 also in VA administrative data were 76.0% for colonoscopy, 84.6% for physician visit, and 26.3% for carcinoembryonic antigen (CEA) test. CONCLUSIONS: VA administrative data are accurate and complete for non-race demographic variables, receipt of CRC treatment, colonoscopy, and physician visits; but alternative data sources may be necessary to capture patient race and receipt of CEA tests.