A Monte Carlo method for the simulation of kinetie models

The purpose of this note is to illustrate the feasibility of simulating kinetic systems, such as commonly encountered in photosynthesis research, using the Monte Carlo (MC) method. In this approach, chemical events are considered at the molecular level where they occur randomly and the macroscopic kinetic evolution results from averaging a large number of such events. Their repeated simulation is easily accomplished using digital computing. It is shown that the MC approach is well suited to the capabilities and resources of modern microcomputers. A software package is briefly described and discussed, allowing a simple programming of any kinetic model system and its resolution. The execution is reasonably fast and accurate; it is not subject to such instabilities as found with the conventional analytical approach.Abbreviations MC Monte Carlo - RN random number - PSU photosynthetic unit Dedicated to Prof. L.N.M. Duysens on the occasion of his retirement.     

Optical parameters of embedded abnormalities in tissues as determined by Monte Carlo simulation

Photon propagation through tissue phantoms, made of heart, adipose, and spleen tissues was simulated by Monte Carlo procedure. To detect the presence of deep-seated abnormalities, phantoms of heart with adipose and spleen tissues embedded into it were created and simulations were performed to scan the tissue surface with a source and four detector model. Profiles drawn showed variation in parameters such as backscattered intensity in regions where adipose and spleen tissues were embedded. This study shows that depending on the type of embedded tissue the backscattered fraction as measured at 2 mm from the input fiber is altered. This is enhanced for adipose and decreased for spleen tissue. This is not only shown in scanned profiles on the surface but also in constructed images.     

Uncertainty analysis of penicillin V production using Monte Carlo simulation

Uncertainty and variability affect economic and environmental performance in the production of biotechnology and pharmaceutical products. However, commercial process simulation software typically provides analysis that assumes deterministic rather than stochastic process parameters and thus is not capable of dealing with the complexities created by variance that arise in the decision-making process. Using the production of penicillin V as a case study, this article shows how uncertainty can be quantified and evaluated. The first step is construction of a process model, as well as analysis of its cost structure and environmental impact. The second step is identification of uncertain variables and determination of their probability distributions based on available process and literature data. Finally, Monte Carlo simulations are run to see how these uncertainties propagate through the model and affect key economic and environmental outcomes. Thus, the overall variation of these objective functions are quantified, the technical, supply chain, and market parameters that contribute most to the existing variance are identified and the differences between economic and ecological evaluation are analyzed. In our case study analysis, we show that final penicillin and biomass concentrations in the fermenter have the highest contribution to variance for both unit production cost and environmental impact. The penicillin selling price dominates return on investment variance as well as the variance for other revenue-dependent parameters.     

Conformational free energy of alkylsilanes by nonequilibrium-pulling Monte Carlo simulation

The stationary phase in supercritical fluid chromatography includes alkylsilanes, bearing typically 18-carbon alkane chains, bonded to silica. The silanes are in contact with supercritical carbon dioxide. Interaction of the stationary phase with analytes from the mobile phase depends on conformation of the silanes, whether they form a collapsed layer between the silica and the carbon dioxide or are extended into the carbon dioxide. Although equilibrium conformation of alkylsilanes can be determined by equilibrium Monte Carlo (MC) simulation, that is hampered by slow relaxation of the chains. An alternative is to pull alkylsilanes from collapsed to extended conformations, then calculate free energy change from the Jarzynski equality. This work compares conformational results from equilibrium MC simulation to free energies from nonequilibrium pulling simulations. Because both equilibrium and nonequilibrium simulations are faster for shorter silanes, this work also compares results from 8-carbon and 18-carbon silanes. Free energies from nonequilibrium pulling predict that alkylsilanes tend to bend over and form a layer between silica and carbon dioxide. Results from equilibrium simulations are qualitatively consistent with results from nonequilibrium pulling. Longer-chain silanes have greater tendency to extend slightly into the carbon dioxide.     

Kinetic Monte Carlo simulation for the void defects formation in Czochralski silicon growth

The quality of silicon wafers used as substrates for microelectronic devices is measured in terms of the type, size and density of defects formed during crystal growth process. The native point defects such as vacancies and self-interstitials diffuse, react and aggregate to form intrinsic defects in the silicon wafers. We investigated the point defect behaviour using the kinetic lattice Monte Carlo (KLMC) model. The KLMC method has been applied extensively in various forms to the study of microdefects in silicon wafers. The purpose of this paper is to demonstrate the phenomena of void defect formation. The size and density of void defects are usually affected by system temperature, vacancy–vacancy reaction and vacancy–impurity reaction. In this paper, we study the temperature effect and the vacancy concentration effect. The simulation results with various temperatures are well matched with our experimental data, and the relationship between temperature and vacancy density describes well the phenomena of void defect formation. This is the first time such KLMC simulation results have been reported.     

Kinetic Monte Carlo simulation for the striation distribution of void defects in Czochralski silicon growth

Unique crystal-originated pit (COP) distribution, similar to a striation pattern, is well matched with the oxygen profile in experimental analysis. It shows the strong relationship between oxygen concentration and COP distribution. In this paper, we study the generation of void defects and the relationship between interstitial oxygen and vacancy using the kinetic lattice Monte Carlo (KLMC) method. The KLMC method has been applied extensively in various forms to the study of micro-defects in silicon wafers. It explained well the formation of void defects such as vacancy–oxygen complex and vacancy–vacancy complex. The formation of clusters is strongly affected by oxygen concentration, which showed the relationship between COP distribution and oxygen concentration. The unique COP distribution could be correctly explained with KLMC results, and this kind of meso-scale results has not yet been reported.     

Monte Carlo simulation of damascene electroplating: effects of additives

The influence of additives on the filling process of via holes in damascene electroplating is investigated with use of a kinetic Monte Carlo method. The basic system is the solid-by-solid model for crystal growth which includes the vacancy formation during the growth of thin film. Three kinds of additives are included in the model to control the local surface growth rate. Inhibitors and levelers have the effect of preventing the deposition, while accelerators increase the local growth rate. Levelers are modeled to stick to the tips of the surface. We performed a series of simulations by changing the parameters which characterize the additives to see their influence on the filling mechanism. It is shown that void-free filling is possible by the combination of the effects of the additives.     

Monte Carlo Comparison of Multiple Comparison Procedures

Seven procedures of multiple comparisons: Tukey, Scheffé, Bonferroni, Studentized Maximum Modulus, Duncan, Newman-Keuls and F are compared with respect to the probability of the correct decision. Monte Carlo simulation shows that there is no the best procedure. AMS 1985 Subject Classification: 62 J 15.     

Monte Carlo simulation of protein folding in the presence of residue-specific binding sites

Ensemble growth Monte Carlo (EGMC) and dynamic Monte Carlo (DMC) simulations are used to study sequential folding and thermodynamic stability of hydrophobic-polar (HP) chains that fold to a compact structure. Molecularly imprinted cavities are modeled as hard walls having sites that are attractive to specific polar residues on the chain. Using EGMC simulation, we find that the folded conformation can be stabilized using a small number of carefully selected residue-specific sites while a random selection of surface-bound residues may only slightly contribute toward stabilizing the folded conformation, and in some cases may hinder the folding of the chain. DMC simulations of the surface-bound chain confirm increased stability of the folded conformation over a free chain. However, a different trend of the equilibrium population of folded chains as a function of residue-external site interactions is predicted with the two simulation methods.     

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.     

An approach to generate noncontact ACL-injury prone situations on a computer using kinematic data of non-injury situations and Monte Carlo simulation

ACL-injuries are one of the most common knee injuries in noncontact sports. Kinematic data of injury prone situations provide important information to study the underlying ACL-injury mechanisms. However, these data are rare. In this work an approach is presented to generate injury prone situations for noncontact ACL-injuries on a computer. The injury prone situations are generated by a musculoskeletal simulation model using kinematic data of a non-injury situation and the method of Monte Carlo simulation. The approach is successfully applied to generate injury prone landings in downhill ski racing. The characteristics of the obtained injury prone landings are consistent with video recordings of injury cases.     

Mobile shielding evaluation on the fetal dose during a breast radiotherapy using Monte Carlo simulation

PurposeEvaluation of the out-of-field dose is an important aspect in radiotherapy. Due to the fetus radiosensitivity, this evaluation becomes even more conclusive when the patient is pregnant. In this work, a linear accelerator Varian Clinac 2100c operating at 6 MV, a pregnant anthropomorphic phantom (Maria), and different shields added above the abdominal region of the phantom were used for the analysis based on MCNPX. Methods: The simulations were performed for the medial and lateral projections, using either an open field collimation (10×16 cm²) or a multileaf collimator. The added shields (M1 and M2) were designed based on models proposed by Stovall et al. [1], intending to reduce the deposited dose on the fetus and related structures. Results: The presence of the shields showed to be effective in reducing the doses on the fetus, amniotic sac, and placenta, for example. A reduction of about 43% was found in the dose on the fetus when M2 was added, using the open field collimation, in comparison with the situation with no shield, being the lateral projection the main responsible for the dose. The use of MLC significatively reduced the doses in different structures, including on the fetus and amniotic sac, for example, in comparison to the open field situation. A slight increment on the dose in organs such as the eyes, thyroid and brain was found in both collimation systems, due to the presence of the shields. The contribution of the leakage radiation from the tube head of the linear accelerator was found to be in the order of µGy, being reduced by the presence of the M2 shield. Conclusion: Using the shields showed to be an essential feature in order to reduce the dose not only on the fetus, but also in important structures responsible to its development.     

Dynamic Monte Carlo simulation of non-equilibrium Brownian diffusion of single-chain macromolecules

We performed dynamic Monte Carlo simulations of biased diffusion of 3D phantom single lattice polymer. We observed spontaneous deformation of polymer coil when the external driving forces exceed a critical strength. In addition, longer chains require lower critical strengths, at which their activated velocities deviate from Newtonian-fluid behaviours and merge into a master curve exhibiting shear-thinning followed with shear thickening. We attributed the cause of deformation to the random updating of monomers. The latter represents the dynamic heterogeneity along the real polymer chain, and raises a nonlinear asymmetric accumulation of local acceleration and then an internal tension between chain middle and chain end, as evidenced by our previous Brownian Dynamics simulations. Our results unravel a single-molecular-level source of nonlinear dynamics, which has been overlooked in current theoretical considerations on the basis of Rouse ideal-chain model.     

Monte Carlo simulation of intercalated carbon nanotubes

Monte Carlo simulations of the single- and double-walled carbon nanotubes (CNT) intercalated with different metals have been carried out. The interrelation between the length of a CNT, the number and type of metal atoms has also been established. This research is aimed at studying intercalated systems based on CNTs and d-metals such as Fe and Co. Factors influencing the stability of these composites have been determined theoretically by the Monte Carlo method with the Tersoff potential. The modeling of CNTs intercalated with metals by the Monte Carlo method has proved that there is a correlation between the length of a CNT and the number of endo-atoms of specific type. Thus, in the case of a metallic CNT (9,0) with length 17 bands (3.60 nm), in contrast to Co atoms, Fe atoms are extruded out of the CNT if the number of atoms in the CNT is not less than eight. Thus, this paper shows that a CNT of a certain size can be intercalated with no more than eight Fe atoms. The systems investigated are stabilized by coordination of 3d-atoms close to the CNT wall with a radius-vector of (0.18–0.20) nm. Another characteristic feature is that, within the temperature range of (400–700) K, small systems exhibit ground-state stabilization which is not characteristic of the higher ones. The behavior of Fe and Co endo-atoms between the walls of a double-walled carbon nanotube (DW CNT) is explained by a dominating van der Waals interaction between the Co atoms themselves, which is not true for the Fe atoms.     

Evaluating spatial constraints in cellular assembly processes using a Monte Carlo approach

Biomolecular behavior commonly involves complex sets of interacting components that are challenging to understand through solution-based chemical theories. Molecular assembly is especially intriguing in the cellular environment because of its links to cell structure in processes such as chemotaxis. We use a coarse-grained Monte Carlo simulation to elucidate the importance of spatial constraints in molecular assembly. We have performed a study of actin filament polymerization through this space-aware probabilistic lattice-based model. Quantitative results are compared with nonspatial models and show convergence over a wide parameter space, but marked divergence over realistic levels corresponding to macromolecular crowding inside cells and localized actin concentrations found at the leading edge during cell motility. These conclusions have direct implications for cell shape and structure, as well as tumor cell migration.     

All-atom Monte Carlo simulation of GCAA RNA folding

We report a detailed all-atom simulation of the folding of the GCAA RNA tetraloop. The GCAA tetraloop motif is a very common and thermodynamically stable secondary structure in natural RNAs. We use our simulation methods to study the folding behavior of a 12-base GCAA tetraloop structure with a four-base helix adjacent to the tetraloop proper. We implement an all-atom Monte Carlo (MC) simulation of RNA structural dynamics using a Go potential. Molecular dynamics (MD) simulation of RNA and protein has realistic energetics and sterics, but is extremely expensive in terms of computational time. By coarsely treating non-covalent energetics, but retaining all-atom sterics and entropic effects, all-atom MC techniques are a useful method for the study of protein and now RNA. We observe a sharp folding transition for this structure, and in simulations at room temperature the state histogram shows three distinct minima: an unfolded state (U), a more narrow intermediated state (I), and a narrow folded state (F). The intermediate consists primarily of structures with the GCAA loop and some helix hydrogen bonds formed. Repeated kinetic folding simulations reveal that the number of helix base-pairs forms a simple 1D reaction coordinate for the I-->N transition.     

Taboo-based Monte Carlo Search as a Method to Improve Sampling Efficiency

Abstract

Taboo-based Monte Carlo search which restricts the sampling of the region near an old configuration, is developed. In this procedure, Monte Carlo simulation and random search method are combined to improve the sampling efficiency. The feasibility of this method is tested on global optimization of a continuous model function, melting of the 256 Lennard-Jones particles at T? = 0.680 and ρ? = 0.850 and polypeptides (alanine dipeptide and Metenkephalin). From the comparison of results for the model function between our method and other methods, we find the increase of convergence rate and the high possibility of escaping from the local energy minima. The results of the Lennard-Jones solids and polypeptides show that the convergence property to reach the equilibrium state is better than that of others. It is also found that no significant bias in ensemble distribution is detected, though taboo-based Monte Carlo search does not sample the correct ensemble distribution owing to the restriction of the sampling of the region near an old configuration.     

Generation of clinical 177Lu SPECT/CT images based on Monte Carlo simulation with GATE

PurposePatient-specific dosimetry in MRT relies on quantitative imaging, pharmacokinetic assessment and absorbed dose calculation. The DosiTest project was initiated to evaluate the uncertainties associated with each step of the clinical dosimetry workflow through a virtual multicentric clinical trial. This work presents the generation of simulated clinical SPECT datasets based on GATE Monte Carlo modelling with its corresponding experimental CT image, which can subsequently be processed by commercial image workstations.MethodsThis study considers a therapy cycle of 6.85 GBq ¹⁷⁷Lu-labelled DOTATATE derived from an IAEA-Coordinated Research Project (E23005) on “Dosimetry in Radiopharmaceutical therapy for personalised patient treatment”. Patient images were acquired on a GE Infinia-Hawkeye 4 gamma camera using a medium energy (ME) collimator. Simulated SPECT projections were generated based on experimental time points and validated against experimental SPECT projections using flattened profiles and gamma index. The simulated projections were then incorporated into the patient SPECT/CT DICOM envelopes for processing and their reconstruction within a commercial image workstation.ResultsGamma index passing rate (2% − 1 pixel criteria) between 95 and 98% and average gamma between 0.28 and 0.35 among different time points revealed high similarity between simulated and experimental images. Image reconstruction of the simulated projections was successful on HERMES and Xeleris workstations, a major step forward for the initiation of a multicentric virtual clinical dosimetry trial based on simulated SPECT/CT images.ConclusionsRealistic ¹⁷⁷Lu patient SPECT projections were generated in GATE. These modelled datasets will be circulated to different clinical departments to perform dosimetry in order to assess the uncertainties in the entire dosimetric chain.