A Monte Carlo evaluation for effects of probable dimensional uncertainties of low dose rate brachytherapy seeds on dose

The aim of this study is to determine effects of size deviations of brachytherapy seeds on two dimensional dose distributions around the seed. Although many uncertainties are well known, the uncertainties which stem from geometric features of radiation sources are weakly considered and predicted. Neither TG-43 report which is not completely in common consensus, nor individual scientific MC and experimental studies include sufficient data for geometric uncertainties. Sizes of seed and its components can vary in a manufacturing deviation. This causes geometrical uncertainties, too. In this study, three seeds which have different geometrical properties were modeled using EGSnrc-Code Packages. Seeds were designed with all their details using the geometry package. 5% deviations of seed sizes were assumed. Modified seeds were derived from original seed by changing sizes by 5%. Normalizations of doses which were calculated from three kinds of brachytherapy seed and their derivations were found to be about 3%–20%. It was shown that manufacturing differences of brachytherapy seed cause considerable changes in dose distribution.     

Monte Carlo commissioning of radiotherapy LINAC—Introducing an improved methodology

PurposeMonte Carlo (MC) commissioning of medical linear accelerator (LINAC) is a time-consuming process involving a comparison between measured and simulated cross beam/lateral profiles and percentage depth doses (PDDs) for various field sizes. An agreement between these two data sets is sought by trial and error method while varying the incident electron beam parameters, such as electron beam energy or width, etc. This study aims to improve the efficiency of MC commissioning of a LINAC by assessing the feasibility of using a limited number of simulated PDDs.Materials and methodsUsing EGSnrc codes, a Varian Clinac 2100 unit has been commissioned for 6 MV photon beam, and a methodology has been proposed to identify the incident electron beam parameters in a speedier fashion. Impact of voxel size in 3-dimensions and cost functions used for comparison of the measured and simulated data have been investigated along with the role of interpolation.ResultsA voxel size of 1 × 1×0.5 cm³ has been identified as suitable for accurate and fast commissioning of the LIANC. The optimum number of simulated PDDs (required for further interpolation) has been found to be five.ConclusionThe present study suggests that PDDs alone at times can be insufficient for an unambiguous commissioning process and should be supported by including the lateral beam profiles in the process.     

All-Atom Monte Carlo Approach to Protein-Peptide Binding

We develop a procedure for exploring the free energy landscape of protein-peptide binding at atomic detail and apply it to PDZ domain-peptide interactions. The procedure involves soft constraints on receptor proteins providing limited chain flexibility, including backbone motions. Peptide chains are left fully flexible and kept in spatial proximity of the protein through periodic boundary conditions. By extensive Monte Carlo simulations, full representative conformational ensembles at temperatures where bound and unbound states coexist are obtained. To make this approach computationally feasible, we develop an effective all-atom energy function centering on hydrophobicity, hydrogen bonding, and electrostatic interactions. Our initial focus is a set of 11 PDZ domain-peptide pairs with experimentally determined complex structures. Minimum-energy conformations are found to be highly similar to the respective native structures in eight of the cases (all-atom peptide RMSDs < 6 Å). Having achieved that, we turn to a more complete characterization of the bound peptide state through a clustering scheme applied on the full ensembles of peptide structures. We find a significant diversity among bound peptide conformations for several PDZ domains, in particular involving the N terminal side of the peptide chains. Our computational model is then tested further on a set of nine PDZ domain-peptide pairs where the peptides are not originally present in the experimentally determined structures. We find a similar success rate in terms of the nativeness of minimum-energy conformations. Finally, we investigate the ability of our approach to capture variations in binding affinities for different peptide sequences. This is done in particular for a set of related sequences binding to the third PDZ domain of PSD-95 with encouraging results.     

The influence of basic plan parameters on calculated small field output factors – A multicenter study

PurposeThe influence of basic plan parameters such as slice thickness, grid resolution, algorithm type and field size on calculated small field output factors (OFs) was evaluated in a multicentric study.Methods and materialsThree computational homogeneous water phantoms with slice thicknesses (ST) 1, 2 and 3 mm were shared among twenty-one centers to calculate OFs for 1x1, 2x2 and 3x3 cm² field sizes (FSs) (normalized to 10x10 cm² FS), with their own treatment planning system (TPS) and the energy clinically used for stereotactic body radiation therapy delivery. OFs were calculated for each combination of grid resolution (GR) (1, 2 and 3 mm) and ST and finally compared with the OFs measured for the TPS commissioning. A multivariate analysis was performed to test the effect of basic plan parameters on calculated OFs.ResultsA total of 509 data points were collected. Calculated OFs are slightly higher than measured ones. The multivariate analysis showed that Center, GR, algorithm type, and FS are predictive variables of the difference between calculated and measured OFs (p < 0.001). As FS decreases, the spread in the difference between calculated and measured OFs became larger when increasing the GR. Monte Carlo and Analytical Anisotropic Algorithms, presented a dependence on GR (p < 0.01), while Collapsed Cone Convolution and Acuros did not. The effect of the ST was found to be negligible.ConclusionsModern TPSs slightly overestimate the calculated small field OFs compared with measured ones. Grid resolution, algorithm, center number and field size influence the calculation of small field OFs.     

Atomistic simulations of the effects of polyglutamine chain length and solvent quality on conformational equilibria and spontaneous homodimerization

Aggregation of expanded polyglutamine tracts is associated with nine different neurodegenerative diseases, including Huntington's disease. Experiments and computer simulations have demonstrated that monomeric forms of polyglutamine molecules sample heterogeneous sets of collapsed structures in water. The current work focuses on a mechanistic characterization of polyglutamine homodimerization as a function of chain length and temperature. These studies were carried out using molecular simulations based on a recently developed continuum solvation model that was designed for studying conformational and binding equilibria of intrinsically disordered molecules such as polyglutamine systems. The main results are as follows: Polyglutamine molecules form disordered, collapsed globules in aqueous solution. These molecules spontaneously associate at conditions approaching those of typical in vitro experiments for chains of length N ≥ 15. The spontaneity of these homotypic associations increases with increasing chain length and decreases with increasing temperature. Similar and generic driving forces govern both collapse and spontaneous homodimerization of polyglutamine in aqueous milieus. Collapse and dimerization maximize self-interactions and reduce the interface between polyglutamine molecules and the surrounding solvent. Other than these generic considerations, there do not appear to be any specific structural requirements for either chain collapse or chain dimerization; that is, both collapse and dimerization are nonspecific in that disordered globules form disordered dimers. In fact, it is shown that the driving force for intermolecular associations is governed by spontaneous conformational fluctuations within monomeric polyglutamine. These results suggest that polyglutamine aggregation is unlikely to follow a homogeneous nucleation mechanism with the monomer as the critical nucleus. Instead, the results support the formation of disordered, non-β-sheet-like soluble molten oligomers as early intermediates—a proposal that is congruent with recent experimental data.     

Monte Carlo Simulation of Nonionic Surfactants at the Oil-Water Interface

Abstract

A Monte Carlo simulation method has been developed for modelling amphiphiles at an oil-water interface. Properties are calculated for the mixture water, benzene and tetraoxyethylene glycol dodecyl ether.     

Distance-scaled Force Biased Monte Carlo Simulation for Solutions containing a Strongly Interacting Solute

The force-biased extension of the Metropolis Monte Carlo method [1] improves convergence by sampling moves preferentially along the directions of force (and torque) [2]. For solvated systems it is particularly effective [3] when coupled with the preferential sampling scheme [4] that attempts to move solvents near the solute more frequently. However, in recent force-biased simulations of aqueous ionic solutions [5] some of the water molecules in the vicinity of the solute remained essentially stationary. Only significant reduction in the stepsize produced some accepted moves.     

Probing protein fold space with a simplified model

We probe the stability and near-native energy landscape of protein fold space using powerful conformational sampling methods together with simple reduced models and statistical potentials. Fold space is represented by a set of 280 protein domains spanning all topological classes and having a wide range of lengths (33-300 residues) amino acid composition and number of secondary structural elements. The degrees of freedom are taken as the loop torsion angles. This choice preserves the native secondary structure but allows the tertiary structure to change. The proteins are represented by three-point per residue, three-dimensional models with statistical potentials derived from a knowledge-based study of known protein structures. When this space is sampled by a combination of parallel tempering and equi-energy Monte Carlo, we find that the three-point model captures the known stability of protein native structures with stable energy basins that are near-native (all α: 4.77 Å, all β: 2.93 Å, α/β: 3.09 Å, α+β: 4.89 Å on average and within 6 Å for 71.41%, 92.85%, 94.29% and 64.28% for all-α, all-β, α/β and α+β, classes, respectively). Denatured structures also occur and these have interesting structural properties that shed light on the different landscape characteristics of α and β folds. We find that α/β proteins with alternating α and β segments (such as the β-barrel) are more stable than proteins in other fold classes.     

Test of the Inverse Monte Carlo Method for the Calculation of Interatomic Potential Energies in Atomic Liquids

Abstract

The principle purpose of this paper is to demonstrate the use of the Inverse Monte Carlo technique for calculating pair interaction energies in monoatomic liquids from a given equilibrium property. This method is based on the mathematical relation between transition probability and pair potential given by the fundamental equation of the “importance sampling” Monte Carlo method. In order to have well defined conditions for the test of the Inverse Monte Carlo method a Metropolis Monte Carlo simulation of a Lennard Jones liquid is carried out to give the equilibrium pair correlation function determined by the assumed potential. Because an equilibrium configuration is prerequisite for an Inverse Monte Carlo simulation a model system is generated reproducing the pair correlation function, which has been calculated by the Metropolis Monte Carlo simulation and therefore representing the system in thermal equilibrium. This configuration is used to simulate virtual atom displacements. The resulting changes in atom distribution for each single simulation step are inserted in a set of non-linear equations defining the transition probability for the virtual change of configuration. The solution of the set of equations for pair interaction energies yields the Lennard Jones potential by which the equilibrium configuration has been determined.     

Bayesian phylogeny analysis via stochastic approximation Monte Carlo

Monte Carlo methods have received much attention in the recent literature of phylogeny analysis. However, the conventional Markov chain Monte Carlo algorithms, such as the Metropolis–Hastings algorithm, tend to get trapped in a local mode in simulating from the posterior distribution of phylogenetic trees, rendering the inference ineffective. In this paper, we apply an advanced Monte Carlo algorithm, the stochastic approximation Monte Carlo algorithm, to Bayesian phylogeny analysis. Our method is compared with two popular Bayesian phylogeny software, BAMBE and MrBayes, on simulated and real datasets. The numerical results indicate that our method outperforms BAMBE and MrBayes. Among the three methods, SAMC produces the consensus trees which have the highest similarity to the true trees, and the model parameter estimates which have the smallest mean square errors, but costs the least CPU time.     

Folding small proteins via annealing stochastic approximation Monte Carlo

Recently, the stochastic approximation Monte Carlo algorithm has been proposed by Liang et al. (2007) as a general-purpose stochastic optimization and simulation algorithm. An annealing version of this algorithm was developed for real small protein folding problems. The numerical results indicate that it outperforms simulated annealing and conventional Monte Carlo algorithms as a stochastic optimization algorithm. We also propose one method for the use of secondary structures in protein folding. The predicted protein structures are rather close to the true structures.     

A Monte Carlo Study of the Relative Stability of Protein Helical Forms

We present simulation results on a simple model to describe the hydrogen bonding in proteins with helical structures. The approximation distinguishes between ! helices, where each amino acid interacts with another one located four residues apart, 3 10 structures, where the number of amino acids in between is three, and the ? arrangement, in which that number is five. We found that the main features of the system are determined by the most stable structure (the ! helix) and that the other type of hydrogen bonds appears just below the denaturation temperature of the peptide. The probability of finding a 3 10 -type bond is greater at the beginning or at the end of the peptide chain, irrespectively of its length, while in short peptides the existence of those bonds increases appreciably the denaturation temperature, promoting stability. On the other hand, the temperature of denaturation decreases with the length of the peptide to reach a value independent of the number of amino acid residues.