Steven Lettieri

Can a weight loss of one pound a week be achieved with a 3500-kcal deficit? Commentary on a commonly accepted rule.

Despite theoretical evidence that the model commonly referred to as the 3500-kcal rule grossly overestimates actual weight loss, widespread application of the 3500-kcal formula continues to appear in textbooks, on respected government- and health-related websites, and scientific research publications. Here we demonstrate the risk of applying the 3500-kcal rule even as a convenient estimate by comparing predicted against actual weight loss in seven weight loss experiments conducted in confinement under total supervision or objectively measured energy intake. We offer three newly developed, downloadable applications housed in Microsoft Excel and Java, which simulates a rigorously validated, dynamic model of weight change. The first two tools available at http://www.pbrc.edu/sswcp, provide a convenient alternative method for providing patients with projected weight loss/gain estimates in response to changes in dietary intake. The second tool, which can be downloaded from the URL http://www.pbrc.edu/mswcp, projects estimated weight loss simultaneously for multiple subjects. This tool was developed to inform weight change experimental design and analysis. While complex dynamic models may not be directly tractable, the newly developed tools offer the opportunity to deliver dynamic model predictions as a convenient and significantly more accurate alternative to the 3500-kcal rule.

WESTPA: An Interoperable, Highly Scalable Software Package for Weighted Ensemble Simulation and Analysis

The weighted ensemble (WE) path sampling approach orchestrates an ensemble of parallel calculations with intermittent communication to enhance the sampling of rare events, such as molecular associations or conformational changes in proteins or peptides. Trajectories are replicated and pruned in a way that focuses computational effort on underexplored regions of configuration space while maintaining rigorous kinetics. To enable the simulation of rare events at any scale (e.g., atomistic, cellular), we have developed an open-source, interoperable, and highly scalable software package for the execution and analysis of WE simulations: WESTPA (The Weighted Ensemble Simulation Toolkit with Parallelization and Analysis). WESTPA scales to thousands of CPU cores and includes a suite of analysis tools that have been implemented in a massively parallel fashion. The software has been designed to interface conveniently with any dynamics engine and has already been used with a variety of molecular dynamics (e.g., GROMACS, NAMD, OpenMM, AMBER) and cell-modeling packages (e.g., BioNetGen, MCell). WESTPA has been in production use for over a year, and its utility has been demonstrated for a broad set of problems, ranging from atomically detailed host–guest associations to nonspatial chemical kinetics of cellular signaling networks. The following describes the design and features of WESTPA, including the facilities it provides for running WE simulations and storing and analyzing WE simulation data, as well as examples of input and output.

Effect of dietary adherence on the body weight plateau: a mathematical model incorporating intermittent compliance with energy intake prescription

BACKGROUND Clinical weight loss in individuals typically stabilizes at 6 mo. However, validated models of dynamic energy balance have consistently shown weight plateaus between 1 and 2 y. The cause for this discrepancy is unclear. OBJECTIVE We developed 2 mathematical models on the basis of the first law of thermodynamics to investigate plausible explanations for reaching an early weight plateau at 6 mo. DESIGN The first model was an energy-expenditure adaptation model and was applied to determine the degree of metabolic adaptation required to generate this plateau. The second model was an intermittent lack-of-adherence model formulated by using a randomly fluctuating energy intake term accounting for intermittent noncompliance in dietary intake to reach this plateau. To set model variables, validate models, and compare free-living weight-loss patterns to in-residence supervised programs, we applied the following 4 different studies: The US NHANES 1999-2004, Comprehensive Assessment of Long-term Effects of Reducing Intake of Energy (CALERIE) weight-loss study, the Bouchard Twin overfeeding study, and the Minnesota Starvation Experiment. RESULTS The metabolic adaptation model increased final weight but did not affect the predicted plateau time point. The intermittent lack-of-adherence model generated oscillating weight graphs that have been frequently observed in weight-loss studies. The model showed that a 6-mo weight-loss plateau can be attained despite what can be considered as high diet adherence. The model was programmed as a downloadable application. CONCLUSIONS An intermittent lack of diet adherence, not metabolic adaptation, is a major contributor to the frequently observed early weight-loss plateau. The new weight-loss prediction software, which incorporates an intermittent lack of adherence, can be used to guide and inform patients on realistic levels of adherence on the basis of patient lifestyle.

Simultaneous Computation of Dynamical and Equilibrium Information Using a Weighted Ensemble of Trajectories.

Equilibrium formally can be represented as an ensemble of uncoupled systems undergoing unbiased dynamics in which detailed balance is maintained. Many nonequilibrium processes can be described by suitable subsets of the equilibrium ensemble. Here, we employ the “weighted ensemble” (WE) simulation protocol [Huber and Kim, Biophys. J.1996, 70, 97–110] to generate equilibrium trajectory ensembles and extract nonequilibrium subsets for computing kinetic quantities. States do not need to be chosen in advance. The procedure formally allows estimation of kinetic rates between arbitrary states chosen after the simulation, along with their equilibrium populations. We also describe a related history-dependent matrix procedure for estimating equilibrium and nonequilibrium observables when phase space has been divided into arbitrary non-Markovian regions, whether in WE or ordinary simulation. In this proof-of-principle study, these methods are successfully applied and validated on two molecular systems: explicitly solvated methane association and the implicitly solvated Ala4 peptide. We comment on challenges remaining in WE calculations.

Accelerating molecular Monte Carlo simulations using distance and orientation-dependent energy tables: tuning from atomistic accuracy to smoothed "coarse-grained" models.

Typically, the most time consuming part of any atomistic molecular simulation is the repeated calculation of distances, energies, and forces between pairs of atoms. However, many molecules contain nearly rigid multi‐atom groups such as rings and other conjugated moieties, whose rigidity can be exploited to significantly speed‐up computations. The availability of GB‐scale random‐access memory (RAM) offers the possibility of tabulation (precalculation) of distance‐ and orientation‐dependent interactions among such rigid molecular bodies. Here, we perform an investigation of this energy tabulation approach for a fluid of atomistic—but rigid—benzene molecules at standard temperature and density. In particular, using

Extending fragment-based free energy calculations with library monte carlo simulation: Annealing in interaction space

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Extending Fragment Based Free Energy Calculations with Library Based Monte Carlo Simulation: Annealing in Interaction Space

(1) GB of RAM, we construct an energy look‐up table, which encompasses the full range of allowed relative positions and orientations between a pair of whole molecules. We obtain a hardware‐dependent speed‐up of a factor of 24–50 as compared to an ordinary (“exact”) Monte Carlo simulation and find excellent agreement between energetic and structural properties. Second, we examine the somewhat reduced fidelity of results obtained using energy tables based on much less memory use. Third, the energy table serves as a convenient platform to explore potential energy smoothing techniques, akin to coarse‐graining. Simulations with smoothed tables exhibit near atomistic accuracy while increasing diffusivity. The combined speed‐up in sampling from tabulation and smoothing exceeds a factor of 100. For future applications, greater speed‐ups can be expected for larger rigid groups, such as those found in biomolecules.

Accelerating Molecular Monte Carlo Simulations using Distance and Orientation Dependent Energy Tables: Tuning from Atomistic Accuracy to Smoothed “Coarse-Grained” Models

Pre‐calculated libraries of molecular fragment configurations have previously been used as a basis for both equilibrium sampling (via library‐based Monte Carlo) and for obtaining absolute free energies using a polymer‐growth formalism. Here, we combine the two approaches to extend the size of systems for which free energies can be calculated. We study a series of all‐atom poly‐alanine systems in a simple dielectric solvent and find that precise free energies can be obtained rapidly. For instance, for 12 residues, less than an hour of single‐processor time is required. The combined approach is formally equivalent to the annealed importance sampling algorithm; instead of annealing by decreasing temperature, however, interactions among fragments are gradually added as the molecule is grown. We discuss implications for future binding affinity calculations in which a ligand is grown into a binding site.

Tunable, mixed-resolution modeling using library-based Monte Carlo and graphics processing units.

Pre-calculated libraries of molecular fragment configurations have previously been used as a basis for both equilibrium sampling (via librarybased Monte Carlo) and for obtaining absolute free energies using a polymergrowth formalism. Here, we combine the two approaches to extend the size of systems for which free energies can be calculated. We study a series of all-atom poly-alanine systems in a simple dielectric solvent and find that precise free energies can be obtained rapidly. For instance, for 12 residues, less than an hour of single-processor is required. The combined approach is formally equivalent to the annealed importance sampling algorithm; instead of annealing by decreasing temperature, however, interactions among fragments are gradually added as the molecule is grown. We discuss implications for future binding affinity calculations in which a ligand is grown into a binding site.

Characteristic and Minimal Polynomials of Linear Cellular Automata

Typically, the most time consuming part of any atomistic molecular simulation is due to the repeated calculation of distances, energies and forces between pairs of atoms. However, many molecules contain nearly rigid multi-atom groups such as rings and other conjugated moieties, whose rigidity can be exploited to significantly speed up computations. The availability of GB-scale random-access memory (RAM) offers the possibility of tabulation (pre-calculation) of distance and orientation-dependent interactions among such rigid molecular bodies. Here, we perform an investigation of this energy tabulation approach for a fluid of atomistic - but rigid - benzene molecules at standard temperature and density. In particular, using O(1) GB of RAM, we construct an energy look-up table which encompasses the full range of allowed relative positions and orientations between a pair of whole molecules. We obtain a hardware-dependent speed-up of a factor of 24-50 as compared to an ordinary (“exact”) Monte Carlo simulation and find excellent agreement between energetic and structural properties. Second, we examine the somewhat reduced fidelity of results obtained using energy tables based on much less memory use. Third, the energy table serves as a convenient platform to explore potential energy smoothing techniques, akin to coarse-graining. Simulations with smoothed tables exhibit near atomistic accuracy while increasing diffusivity. The combined speed-up in sampling from tabulation and smoothing exceeds a factor of 100. For future applications greater speed-ups can be expected for larger rigid groups, such as those found in biomolecules.