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PubMed1992

Refinement of the thrombin-bound structure of a hirudin peptide by a restrained electrostatically driven Monte Carlo method.

Energy refinement of the structure of a linear peptide, hirudin56-65, bound to thrombin was carried out using a conformational search method in combination with restrained minimization. Five conformations originated from nmr data and distance geometry calculations having a similar global folding pattern but quite different backbone conformations were used as the starting structures. As a result of this approach, a series of low-energy conformations compatible with a set of upper and lower bounds of interproton distances determined from transferred nuclear Overhauser effects were found. A comparison among the lowest energy conformations of each run showed that the combination of energy refinement plus distance constraints led to a very well-defined structure for both the backbone and the side chains of the last 7 residues of the polypeptide. Furthermore, the low-energy conformations generated with this technique contain a segment of 3(10)-helix involving the last 5 residues at the COOH terminal end.

Electrochemistry↗
PubMed2006

A Markov chain Monte Carlo method for estimating population mixing using Y-chromosome markers: mixing of the Han people in China.

We present a new approach for estimating mixing between populations based on non-recombining markers, specifically Y-chromosome microsatellites. A Markov chain Monte Carlo (MCMC) Bayesian statistical approach is used to calculate the posterior probability distribution of population parameters of interest, including the effective population size and the time to most recent common ancestor (MRCA). To test whether two populations are homogeneously mixed we introduce a "mixing" statistic defined for each coalescent event that weights the contribution of that ancestor's descendants to the two subpopulations, and an associated population "purity" statistic. Using simulated data with low levels of migration between two populations, we demonstrate that our method is more sensitive than other commonly used distance-based methods such as R(ST) and D(SW). To illustrate our method, we analysed mixing between 11 pre-defined Chinese ethnic/regional populations, using 5 microsatellite markers from the non-recombining region of the Y-chromosome (NRY), demonstrating a significant clustering of a subset of subpopulations with a high mutual relative degree of mixing (homogeneous mixing with support >0.99). Our analysis suggests that there is a strong correlation between effective population size and mixing with other subpopulations. Thus, despite considerable mixing between these groups, the purity statistic still identifies significant heterogeneity, suggesting that periods of historical isolation continue to leave a recoverable signal despite modern introgression.

Asian People↗
PubMed1999

Simulation of electron-proton coupling with a Monte Carlo method: application to cytochrome c3 using continuum electrostatics.

A new method is presented for simulating the simultaneous binding equilibrium of electrons and protons on protein molecules, which makes it possible to study the full equilibrium thermodynamics of redox and protonation processes, including electron-proton coupling. The simulations using this method reflect directly the pH and electrostatic potential of the environment, thus providing a much closer and realistic connection with experimental parameters than do usual methods. By ignoring the full binding equilibrium, calculations usually overlook the twofold effect that binding fluctuations have on the behavior of redox proteins: first, they affect the energy of the system by creating partially occupied sites; second, they affect its entropy by introducing an additional empty/occupied site disorder (here named occupational entropy). The proposed method is applied to cytochrome c3 of Desulfovibrio vulgaris Hildenborough to study its redox properties and electron-proton coupling (redox-Bohr effect), using a continuum electrostatic method based on the linear Poisson-Boltzmann equation. Unlike previous studies using other methods, the full reduction order of the four hemes at physiological pH is successfully predicted. The sites more strongly involved in the redox-Bohr effect are identified by analysis of their titration curves/surfaces and the shifts of their midpoint redox potentials and pKa values. Site-site couplings are analyzed using statistical correlations, a method much more realistic than the usual analysis based on direct interactions. The site found to be more strongly involved in the redox-Bohr effect is propionate D of heme I, in agreement with previous studies; other likely candidates are His67, the N-terminus, and propionate D of heme IV. Even though the present study is limited to equilibrium conditions, the possible role of binding fluctuations in the concerted transfer of protons and electrons under nonequilibrium conditions is also discussed. The occupational entropy contributions to midpoint redox potentials and pKa values are computed and shown to be significant.

Binding Sites↗
PubMed2005

Organ and effective dose conversion coefficients for radiographic examinations of the pediatric skull estimated by Monte Carlo methods.

The objective of the present work was to provide precise effective and organ dose data for radiographic examinations of the skull performed on pediatric patients. To accomplish this, the MCNP4C2 transport code was utilized and 18 mathematical anthropomorphic phantoms, representing ages from a newborn child to a 17-year-old adolescent, were developed. Three common projections, anterior-posterior, posterior-anterior and lateral, were considered. The results consist of effective and organ radiation doses normalized to the entrance surface dose. Normalized data are presented for a wide range of peak kilovoltages and beam filtration values so that doses for any X-ray unit can be calculated. Both organ and effective dose values showed an inverse correlation with age. Good agreement was observed between the normalized effective doses produced in this study and values derived from calculations based on the National Radiological Protection Board coefficients for specific mathematical phantoms representing 1-, 5-, 10- and 15-year-old children. In the present work, dose data for nine mathematical phantoms representing 0-, 1-, 2-, 3-, 4-, 5-, 6-, 9- and 14-year-old pediatric patients were provided for estimation of organ and effective doses delivered to pediatric patients from radiographic examinations of the skull.

Adolescent↗
PubMed1989

Path analysis under generalized marital resemblance: evaluation of the assumptions underlying the mixed homogamy model by the Monte Carlo method.

Path analysis of nuclear family data has been widely applied to resolve genetic and environmental sources of familial resemblance. Here we report the results of a systematic evaluation of the effects of departures from five modeling assumptions often made when analyzing nuclear family data; i) the observed environmental index is unaffected by the genotype, ii) the basis of marital resemblance is correctly specified in the model, iii) there are no intergenerational differences in either the genetic or cultural heritability, iv) there is no genetic dominance, and v) there is no genotype by family environment interaction. "Deterministic simulations" identified various situations where model misspecification could lead to substantial bias in the estimation of the heritabilities. For these situations, "stochastic simulations" were performed to determine whether the "goodness-of-fit" test used in path analysis would correctly reject the misspecified model. In samples of 500 nuclear families, each comprising two parents and two children, the goodness-of-fit test was found to be sensitive to misspecifications of the source of marital resemblance and the existence of intergenerational differences in heritabilities, although reduced power would make the test less sensitive in smaller samples. The test was largely insensitive to misspecifications of possible genetic effects on the environmental index, and to the existence of multiplicative interaction between the genotype and familial environment. When genetic effects on the index are ignored, the genetic heritability (h2) is underestimated, the cultural heritability (c2) is overestimated, but h2+c2 remains unchanged. Neglecting the interaction was found to result in an overestimate of h2.

Consanguinity↗
PubMed2002

Optimisation of electron cone design in high energy radiotherapy using the Monte Carlo method.

Cylindrical solid-walled steel electron collimators are used at the Royal Adelaide Hospital with a Siemens KD2 Mevatron accelerator to produce circular fields 2-8 cm in diameter. The cones are used in contact with the patient's skin. A flat treatment field is required at the treatment depth and the beam should also satisfy the uniformity standards as specified by the International Electrotechnical Commission (IEC). However, the seven and eight centimetre diameter cones provided by the manufacturer did not meet these specifications. In particular, the maximum dose relative to the depth-dose maximum on the central axis exceeded 126% as compared with the IEC recommended value of 109%, when used with a 21 MeV electron beam. Cone modifications were previously investigated by others with the results demonstrating some improvement in the 'horn' (as it appears on surface dose profiles) but still not satisfying IEC requirements. In the present paper the EGS4 code was used to model the existing treatment head geometry and cones, as well as new suggested modifications to the cone. The results of the simulation for the existing cone geometry corresponded closely to previously obtained measurements. The suggested collimator modifications involved a plastic insert along the internal wall of the collimator. Variations of the insert width and height were simulated for a 21 MeV electron beam and the results plotted to indicate the optimal insert dimensions. A plastic insert with the dimensions taken from one of the best models was produced and tested. The measurements showed close agreement with the simulation results (for the 'horn' height, dose within 1% and radial position within 2 mm) and improvement of the "maximum ratio of absorbed dose" from 126% before modification to 108% with the plastic insert. The tested insert was also simulated for a 12 MeV electron beam, to see whether permanent fitting of such an insert would have a deleterious effect at lower energies. Neither penetration nor flatness was significantly compromised, with a small penalty being a slight increase in the central axis dose near the surface.

Computer Simulation↗
PubMed2006

Remedy for the fermion sign problem in the diffusion Monte Carlo method for few fermions with antisymmetric diffusion process.

We suggest an exact approach to help remedy the fermion sign problem in diffusion quantum Monte Carlo simulations. The approach is based on an explicit suppression of symmetric modes in the Schrödinger equation by means of a modified stochastic diffusion process (antisymmetric diffusion process). We introduce this algorithm and illustrate it on potential models in one dimension (1D) and show that there it solves the fermion sign problem exactly and converges to the lowest antisymmetric state of the system. Then, we discuss extensions of this approach to many-dimensional systems on examples of quantum oscillator in 2D-20D and a toy model of three and four fermions on harmonic strings in 2D and 3D. We show that in all these cases our method shows a performance comparable to that of a fixed-node approximation with an exact node.

Journal Article↗
PubMed1996

A general Monte Carlo method for mapping multiple quantitative trait loci.

In this paper we address the mapping of multiple quantitative trait loci (QTLs) in line crosses for which the genetic data are highly incomplete. Such complicated situations occur, for instance, when dominant markers are used or when unequally informative markers are used in experiments with outbred populations. We describe a general and flexible Monte Carlo expectation-maximization (Monte Carlo EM) algorithm for fitting multiple-QTL models to such data. Implementation of this algorithm is straightforward in standard statistical software, but computation may take much time. The method may be generalized to cope with more complex models for animal and human pedigrees. A practical example is presented, where a three-QTL model is adopted in an outbreeding situation with dominant markers. The example is concerned with the linkage between randomly amplified polymorphic DNA (RAPD) markers and QTLs for partial resistance to Fusarium oxysporum in lily.

Algorithms↗
PubMed2006

Seriation in paleontological data using markov chain Monte Carlo methods.

Given a collection of fossil sites with data about the taxa that occur in each site, the task in biochronology is to find good estimates for the ages or ordering of sites. We describe a full probabilistic model for fossil data. The parameters of the model are natural: the ordering of the sites, the origination and extinction times for each taxon, and the probabilities of different types of errors. We show that the posterior distributions of these parameters can be estimated reliably by using Markov chain Monte Carlo techniques. The posterior distributions of the model parameters can be used to answer many different questions about the data, including seriation (finding the best ordering of the sites) and outlier detection. We demonstrate the usefulness of the model and estimation method on synthetic data and on real data on large late Cenozoic mammals. As an example, for the sites with large number of occurrences of common genera, our methods give orderings, whose correlation with geochronologic ages is 0.95.

Animals↗
PubMed2003

Re-evaluation of the dose to the cyst wall in P-32 radiocolloid treatments of cystic brain tumors using the dose-point-kernel and Monte Carlo methods.

Intracavity instillation of beta-emitting colloid pharmaceuticals is a common technique used to treat cystic brain tumors. Most of the dosimetric calculations that have been reported in the literature for this problem are based on empirical formulas derived by Loevinger. Concentration of P-32 radiolabeled solution for the delivery of a prescribed dose (200 Gy to the cyst wall) has been published previously using this formalism in what we refer to as a standard nomogram. The calculations using the Loevinger formulas for calculating the P-32 activity necessary to achieve 200 Gy at the cyst wall is re-evaluated and compared to numerically computed results based on full Monte Carlo simulations (EGSnrc) and the dose-point-kernel (DPK) integration method. For cyst diameters greater than 1 cm, the new calculations agree well with previously published results (the standard nomogram) to within a few percents. However, for cyst diameters of less than 1 cm, it is shown that the standard nomogram results underestimate the therapeutic activity by a factor of approximately 3 for very small diameters (approximately 0.2 cm). New tables based on our calculations are presented and the sources of discrepancies are identified. It is concluded that the new set of data based on our calculations should replace the standard nomogram to administer accurately the target dose to the cyst wall for the smaller diameter cysts (< 1 cm).

Beta Particles↗
PubMed2006

Improved density of states Monte Carlo method based on recycling of rejected states.

In this paper a new algorithm is presented that improves the efficiency of Wang and Landau algorithm or density of states (DOS) Monte Carlo simulations by employing rejected states. The algorithm is shown to have a performance superior to that of the original Wang-Landau [F. Wang and D. P. Landau, Phys. Rev. Lett. 86, 2050 (2001)] algorithm and the more recent configurational temperature DOS algorithm. The performance of the method is illustrated in the context of results for the Lennard-Jones fluid.

Journal Article↗
PubMed2000

Population pharmacokinetic analysis of amikacin and validation on neonates using Monte Carlo method.

AIM: To make programs for population pharmacokinetic analysis and to assess the ability of this method in pharmacokinetic parameter estimation and in the prediction of serum concentrations. METHODS: Data of amikacin as a model drug were collected from 42 neonates with 142 serum samples. A one-compartment open model was used to describe the kinetics of amikacin after the intravenous infusion. Following Sheiner's idea of population pharmacokinetics, we made the programs to evaluate population parameter and individual parameter. The target function minimality was obtained from Monte Carlo algorithm. The validation of the population analysis was performed using classic pharmacokinetic program 3p87 for antithesis. The predictability of the developed method was evaluated by computing precision and accuracy of serum concentration predicted using the parameter estimates. RESULTS: The stability of our self-made program was good. The population parameters obtained from this approach were in conformity with those from 3p87, and the interindividual variability was relatively small. For the learning sample and the validation sample, predicted and observed concentrations were all close with correlation coefficient 0.995 and 0.990, respectively. Most of predicted errors were found < +/- 1 mg/L, and RMSD and BIAS were 0.58 and -0.07 for the validation sample, respectively. The choice of blood sampling time was an important factor for the predictive performance. An early sampling time after the infusion was observed to be the best sampling time. CONCLUSION: The estimation program of population parameter and individual parameter made by us ran stably, and allowed us to use sparse data to estimate population pharmacokinetic parameters. It provided accurate estimates of these parameters and satisfactory ability of serum concentration prediction. Therefore, it can be used for the population pharmacokinetic analysis and individualization of dosage regimen.

Amikacin↗
PubMed2006

Validity of the classical monte carlo method to model the magnetic properties of a large transition-metal cluster: Mn19.

The susceptibility of the large transition-metal cluster [Mn19O12(MOE)14(MOEH)10].MOEH (MOE = OC2H2O-CH3) has been fitted through classical Monte Carlo simulation, and an estimation of the exchange coupling constants has been done. With these results, it has been possible to perform a full-matrix diagonalization of the cluster core, which was used to provide information on the nature of the low-lying levels.

Journal Article↗
PubMed1996

Extraction of molecular edges on the average difference map by a Monte-Carlo method.

A method giving a low-resolution image of the molecules in the unit cell has been described, which was based only on the observed structure factors. An operator, called the average difference operator (ADO), was introduced in reciprocal space to flatten the electron densities everywhere but the regions on either side of the molecular envelope in real space. The observed structure factors were first modified by ADO, then a Monte-Carlo condensing protocol [Subbiah (1991). Science, 252, 128-133; (1993). Acta Cryst. D49, 108-119] was employed to stimulate the modified electron-density map at low resolution. It was found that molecular edges could be extracted, especially when there was relatively large solvent content in the unit cell.

Journal Article↗
PubMed2001

The utilization of classical spin Monte Carlo methods to simulate the magnetic behavior of extended three-dimensional cubic networks incorporating M(II) ions with an S = 5/2 ground state spin.

The numerical simulations of the magnetic properties of extended three-dimensional networks containing M(II) ions with an S = 5/2 ground-state spin have been carried out within the framework of the isotropic Heisenberg model. Analytical expressions fitting the numerical simulations for the primitive cubic, diamond, together with (10-3) cubic networks have all been derived. With these empirical formulas in hands, we can now extract the interaction between the magnetic ions from the experimental data for these networks. In the case of the primitive cubic network, these expressions are directly compared with those from the high-temperature expansions of the partition function. A fit of the experimental data for three complexes, namely [(N(CH(3))(4)][Mn(N(3))] 1, [Mn(CN(4))](n)() 2, and [Fe(II)(bipy)(3)][Mn(II)(2)(ox)(3)] 3, has been carried out. The best fits were those obtained using the following parameters, J = -3.5 cm(-)(1), g = 2.01 (1); J = -8.3 cm(-)(1), g = 1.95 (2); and J = -2.0 cm(-)(1), g = 1.95 (3).

Journal Article↗