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.

Can prospect theory explain risk-seeking behavior by terminally ill patients?

Patients with life-threatening conditions sometimes appear to make risky treatment decisions as their condition declines, contradicting the risk-averse behavior predicted by expected utility theory. Prospect theory accommodates such decisions by describing how individuals evaluate outcomes relative to a reference point and how they exhibit risk-seeking behavior over losses relative to that point. The authors show that a patient's reference point for his or her health is a key factor in determining which treatment option the patient selects, and they examine under what circumstances the more risky option is selected. The authors argue that patients' reference points may take time to adjust following a change in diagnosis, with implications for predicting under what circumstances a patient may select experimental or conventional therapies or select no treatment.

Can metaphors and analogies improve communication with seriously ill patients?

OBJECTIVE: It is not known how often physicians use metaphors and analogies, or whether they improve patients' perceptions of their physicians' ability to communicate effectively. Therefore, the objective of this study was to determine whether the use of metaphors and analogies in difficult conversations is associated with better patient ratings of their physicians' communication skills. DESIGN: Cross-sectional observational study of audio-recorded conversations between patients and physicians. SETTING: Three outpatient oncology practices. PATIENTS: Ninety-four patients with advanced cancer and 52 physicians. INTERVENTION: None. MAIN OUTCOME MEASURES: Conversations were reviewed and coded for the presence of metaphors and analogies. Patients also completed a 6-item rating of their physician's ability to communicate. RESULTS: In a sample of 101 conversations, coders identified 193 metaphors and 75 analogies. Metaphors appeared in approximately twice as many conversations as analogies did (65/101, 64% versus 31/101, 31%; sign test p < 0.001). Conversations also contained more metaphors than analogies (mean 1.6, range 0-11 versus mean 0.6, range 0-5; sign rank test p < 0.001). Physicians who used more metaphors elicited better patient ratings of communication (rho = 0.27; p = 0.006), as did physicians who used more analogies (Spearman rho = 0.34; p < 0.001). CONCLUSIONS: The use of metaphors and analogies may enhance physicians' ability to communicate.

Communication practices in physician decision-making for an unstable critically ill patient with end-stage cancer.

BACKGROUND: Shared decision-making has become the standard of care for most medical treatments. However, little is known about physician communication practices in the decision making for unstable critically ill patients with known end-stage disease. OBJECTIVE: To describe communication practices of physicians making treatment decisions for unstable critically ill patients with end-stage cancer, using the framework of shared decision-making. DESIGN: Analysis of audiotaped encounters between physicians and a standardized patient, in a high-fidelity simulation scenario, to identify best practice communication behaviors. The simulation depicted a 78-year-old man with metastatic gastric cancer, life-threatening hypoxia, and stable preferences to avoid intensive care unit (ICU) admission and intubation. Blinded coders assessed the encounters for verbal communication behaviors associated with handling emotions and discussion of end-of-life goals. We calculated a score for skill at handling emotions (0-6) and at discussing end of life goals (0-16). SUBJECTS: Twenty-seven hospital-based physicians. RESULTS: Independent variables included physician demographics and communication behaviors. We used treatment decisions (ICU admission and initiation of palliation) as a proxy for accurate identification of patient preferences. Eight physicians admitted the patient to the ICU, and 16 initiated palliation. Physicians varied, but on average demonstrated low skill at handling emotions (mean, 0.7) and moderate skill at discussing end-of-life goals (mean, 7.4). We found that skill at discussing end-of-life goals was associated with initiation of palliation (p = 0.04). CONCLUSIONS: It is possible to analyze the decision making of physicians managing unstable critically ill patients with end-stage cancer using the framework of shared decision-making.

Bayes and empirical-Bayes multiplicity adjustment in the variable-selection problem

This paper studies the multiplicity-correction effect of standard Bayesian variable-selection priors in linear regression. Our first goal is to clarify when, and how, multiplicity correction happens automatically in Bayesian analysis, and to distinguish this correction from the Bayesian Ockham's-razor effect. Our second goal is to contrast empirical-Bayes and fully Bayesian approaches to variable selection through examples, theoretical results and simulations. Considerable differences between the two approaches are found. In particular, we prove a theorem that characterizes a surprising aymptotic discrepancy between fully Bayes and empirical Bayes. This discrepancy arises from a different source than the failure to account for hyperparameter uncertainty in the empirical-Bayes estimate. Indeed, even at the extreme, when the empirical-Bayes estimate converges asymptotically to the true variable-inclusion probability, the potential for a serious difference remains. © Institute of Mathematical Statistics, 2010.

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.

Atherosclerosis: Viewing the problem from a different perspective including possible treatment options

This paper proposes that atherosclerosis is initiated by a signaling event that deposits calcium hydroxyapatite (Ca-HAP). This event is preceded by a loss of mechanical structure in the arterial wall. After Ca-HAP has been deposited, it is unlikely that it will be reabsorbed because the solubility product constant (K sp) is very small, and the large stores of Ca +2 and PO 4-3 in the bones oppose any attempts to dissolve Ca-HAP by decreasing the common ions. The hydroxide ion (OH -) of Ca-HAP can be displaced in nature by fluoride (F -) and carbonate (CO 3-2) ions, and it is proposed that anions associated with cholesterol ester hydrolysis and, in very small quantities, the enolate of 7-ketocholesterol could also displace the OH -of Ca-HAP, forming an ionic bond. The free energy of hydration of Ca-HAP at 310 K is most likely negative, and the ionic radii of the anions associated with the hydrolysis of cholesterol ester are compatible with the substitution. Furthermore, examination of the pathology of atherosclerotic lesions by Raman and NMR spectroscopy and confocal microscopy supports deposition of Ca-HAP associated with cholesterol. Investigating the affinity of intermediates of cholesterol hydrolysis for Ca-HAP compared to lipoproteins such as HDL, LDL, and VLDL using isothermic titration calorimetry could add proof of this concept and may lead to the development of a new class of medications targeted at the deposition of cholesterol within Ca-HAP. Treatment of acute ischemic events as a consequence of atherosclerosis with denitrogenation and oxygenation is discussed. © the author(s), publisher and licensee Libertas Academica Ltd.