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Concept: Monte Carlo method


Ultrafast video recording of spatiotemporal light distribution in a scattering medium has a significant impact in biomedicine. Although many simulation tools have been implemented to model light propagation in scattering media, existing experimental instruments still lack sufficient imaging speed to record transient light-scattering events in real time. We report single-shot ultrafast video recording of a light-induced photonic Mach cone propagating in an engineered scattering plate assembly. This dynamic light-scattering event was captured in a single camera exposure by lossless-encoding compressed ultrafast photography at 100 billion frames per second. Our experimental results are in excellent agreement with theoretical predictions by time-resolved Monte Carlo simulation. This technology holds great promise for next-generation biomedical imaging instrumentation.

Concepts: Optics, Simulation, Monte Carlo, Monte Carlo method, Monte Carlo methods in finance, Camera, Video, NTSC


Because of its optical and electrical properties, large surfaces, and compatibility with standard silicon processes, porous silicon is a very interesting material in photovoltaic and microelectromechanical systems technology. In some applications, porous silicon is annealed at high temperature and, consequently, the cylindrical pores that are generated by anodization or stain etching reorganize into randomly distributed closed sphere-like pores. Although the design of devices which involve this material needs an accurate evaluation of its mechanical properties, only few researchers have studied the mechanical properties of porous silicon, and no data are nowadays available on the mechanical properties of sintered porous silicon. In this work we propose a finite element model to estimate the mechanical properties of sintered meso-porous silicon. The model has been employed to study the dependence of the Young’s modulus and the shear modulus (upper and lower bounds) on the porosity for porosities between 0% to 40%. Interpolation functions for the Young’s modulus and shear modulus have been obtained, and the results show good agreement with the data reported for other porous media. A Monte Carlo simulation has also been employed to study the effect of the actual microstructure on the mechanical properties.

Concepts: Silicon, Materials science, Monte Carlo method, Porosity, Computer simulation, Young's modulus, Numerical analysis, Shear modulus


Explicit solvent molecular dynamics simulations have been used to complement preceding experimental and computational studies of folding of guanine quadruplexes (G-DNA). We initiate early stages of unfolding of several G-DNAs by simulating them under no-salt conditions and then try to fold them back using standard excess salt simulations. There is a significant difference between G-DNAs with all-anti parallel stranded stems and those with stems containing mixtures of syn and anti guanosines. The most natural rearrangement for all-anti stems is a vertical mutual slippage of the strands. This leads to stems with reduced numbers of tetrads during unfolding and a reduction of strand slippage during refolding. The presence of syn nucleotides prevents mutual strand slippage; therefore, the antiparallel and hybrid quadruplexes initiate unfolding via separation of the individual strands. The simulations confirm the capability of G-DNA molecules to adopt numerous stable locally and globally misfolded structures. The key point for a proper individual folding attempt appears to be correct prior distribution of syn and anti nucleotides in all four G-strands. The results suggest that at the level of individual molecules, G-DNA folding is an extremely multi-pathway process that is slowed by numerous misfolding arrangements stabilized on highly variable timescales.

Concepts: DNA, Molecular dynamics, Molecule, Protein folding, Computational chemistry, G-quadruplex, Monte Carlo method, Computer simulation


Focal degradation of extracellular matrix (ECM) is the first step in the invasion of cancer cells. MT1-MMP is a potent membrane proteinase employed by aggressive cancer cells. In our previous study, we reported that MT1-MMP was preferentially located at membrane protrusions called invadopodia, where MT1-MMP underwent quick turnover. Our computer simulation and experiments showed that this quick turnover was essential for the degradation of ECM at invadopodia (Hoshino, D., et al., (2012) PLoS Comp. Biol., 8: e1002479). Here we report on characterization and analysis of the ECM-degrading activity of MT1-MMP, aiming at elucidating a possible reason for its repetitive insertion in the ECM degradation. First, in our computational model, we found a very narrow transient peak in the activity of MT1-MMP followed by steady state activity. This transient activity was due to the inhibition by TIMP-2, and the steady state activity of MT1-MMP decreased dramatically at higher TIMP-2 concentrations. Second, we evaluated the role of the narrow transient activity in the ECM degradation. When the transient activity was forcibly suppressed in computer simulations, the ECM degradation was heavily suppressed, indicating the essential role of this transient peak in the ECM degradation. Third, we compared continuous and pulsatile turnover of MT1-MMP in the ECM degradation at invadopodia. The pulsatile insertion showed basically consistent results with the continuous insertion in the ECM degradation, and the ECM degrading efficacy depended heavily on the transient activity of MT1-MMP in both models. Unexpectedly, however, low-frequency/high-concentration insertion of MT1-MMP was more effective in ECM degradation than high-frequency/low-concentration pulsatile insertion even if the time-averaged amount of inserted MT1-MMP was the same. The present analysis and characterization of ECM degradation by MT1-MMP together with our previous report indicate a dynamic nature of MT1-MMP at invadopodia and the importance of its transient peak in the degradation of the ECM.

Concepts: Cell membrane, Thermodynamics, Computer graphics, Monte Carlo method, Computer simulation, Mathematical model, AnyLogic, Computational science


A single cell can form a colony, and ionizing irradiation has long been known to reduce such a cellular clonogenic potential. Analysis of abortive colonies unable to continue to grow should provide important information on the reproductive cell death (RCD) following irradiation. Our previous analysis with a branching process model showed that the RCD in normal human fibroblasts can persist over 16 generations following irradiation with low linear energy transfer (LET) γ-rays. Here we further set out to evaluate the RCD persistency in abortive colonies arising from normal human fibroblasts exposed to high-LET carbon ions (18.3 MeV/u, 108 keV/µm). We found that the abortive colony size distribution determined by biological experiments follows a linear relationship on the log-log plot, and that the Monte Carlo simulation using the RCD probability estimated from such a linear relationship well simulates the experimentally determined surviving fraction and the relative biological effectiveness (RBE). We identified the short-term phase and long-term phase for the persistent RCD following carbon-ion irradiation, which were similar to those previously identified following γ-irradiation. Taken together, our results suggest that subsequent secondary or tertiary colony formation would be invaluable for understanding the long-lasting RCD. All together, our framework for analysis with a branching process model and a colony formation assay is applicable to determination of cellular responses to low- and high-LET radiation, and suggests that the long-lasting RCD is a pivotal determinant of the surviving fraction and the RBE.

Concepts: Cell, Human, Ion, Sievert, Monte Carlo, Monte Carlo method, Monte Carlo methods in finance, Monaco


‘Omics analysis (transcriptomics, proteomics) quantifies changes in gene/protein expression, providing a snapshot of changes in biochemical pathways over time. Although tools such as modelling that are needed to investigate the relationships between genes/proteins already exist, they are rarely utilised. We consider the potential for using Structural Equation Modelling to investigate protein-protein interactions in a proposed Rubisco protein degradation pathway using previously published data from 2D electrophoresis and mass spectrometry proteome analysis. These informed the development of a prior model that hypothesised a pathway of Rubisco Large Subunit and Small Subunit degradation, producing both primary and secondary degradation products. While some of the putative pathways were confirmed by the modelling approach, the model also demonstrated features that had not been originally hypothesised. We used Bayesian analysis based on Markov Chain Monte Carlo simulation to generate output statistics suggesting that the model had replicated the variation in the observed data due to protein-protein interactions. This study represents an early step in the development of approaches that seek to enable the full utilisation of information regarding the dynamics of biochemical pathways contained within proteomics data. As these approaches gain attention, they will guide the design and conduct of experiments that enable 'Omics modelling to become a common place practice within molecular biology.

Concepts: Protein, Molecular biology, Proteomics, Proteome, Monte Carlo method, Protein subunit, Markov chain Monte Carlo, Bayesian inference


We perform Monte Carlo simulations to determine the critical temperatures of Ising Ferromagnets (IFM) on different types of two-dimensional proximity graphs, in which the distribution of their underlying node sets has been changed systematically by means of a parameter σ. This allows us to interpolate between regular grids and proximity graphs based on complete random placement of nodes. Each edge of the planar proximity graphs carries a weighted ferromagnetic coupling. The coupling strengths are determined via the Euclidean distances between coupled spins. The simulations are carried out on graphs with N = 16(2) to N = 128(2) nodes utilising the Wolff cluster algorithm and parallel tempering method in a wide temperature range around the critical point to measure the Binder cumulant in order to obtain the critical temperature for different values of σ. Interestingly, the critical temperatures depend partially non-monotonously on the disorder parameter σ, corresponding to a non-monotonous change of the graph structure. For completeness, we further verify using finite-size scaling methods that the IFM on proximity graphs is for all values of the disorder in the same universality class as the IFM on the two-dimensional square lattice.

Concepts: Temperature, Thermodynamics, Monte Carlo method, Graph theory, Critical point, Boiling point, Critical phenomena, Renormalization group


The extent to which leaf-lobing influences the interception of direct solar radiation by individual plants was studied by means of computer simulations. The morphology, size and orientation ofAmbrosia artemisiifolia L. leaves were measured and used to construct a prototypeAmbrosia plant upon which a computer simulation was based. The leaf geometries of this simulation were then varied, and daily integrated irradiances (DII) were calculated for each variant plant simulation. Data indicate that lobedAmbrosia leaves do not confer an advantage to light-interception based upon values of DII. Simulated plants identical in all respects to the prototype, but with simple, elliptic leaves, had equivalent DII values to the prototype. Simulations with leaves in which gaps between lobes were “filledin” had reduced light-interception efficiencies compared to the prototype and to a simulation with elliptic-leaves. Lightinterception was maximized when leaves on distal nodes wereAmbrosia-like and leaves on proximal nodes were elliptic. The data are interpreted to indicate that lobingperse is not functionally advantageous to light-interception; however, gradients of leaf-lobing along the length of shoots may be very significant in terms of overall light interception.

Concepts: Photosynthesis, Computer graphics, Monte Carlo method, Computer simulation, Fern, Plant morphology, Mathematical model, AnyLogic


How rare are magic squares? So far, the exact number of magic squares of order n is only known for n ≤ 5. For larger squares, we need statistical approaches for estimating the number. For this purpose, we formulated the problem as a combinatorial optimization problem and applied the Multicanonical Monte Carlo method (MMC), which has been developed in the field of computational statistical physics. Among all the possible arrangements of the numbers 1; 2, …, n2 in an n × n square, the probability of finding a magic square decreases faster than the exponential of n. We estimated the number of magic squares for n ≤ 30. The number of magic squares for n = 30 was estimated to be 6.56(29) × 102056 and the corresponding probability is as small as 10-212. Thus the MMC is effective for counting very rare configurations.

Concepts: Statistics, Mathematics, Probability theory, Monte Carlo, Monte Carlo method, Optimization, Applied mathematics, Combinatorial optimization


Anisakiasis is an emerging zoonosis caused by the fish parasitic nematode Anisakis. Spain appears to have the highest reported incidence in Europe and marinated anchovies are recognised as the main food vehicle. Using data on fishery landings, fish infection rates and consumption habits of the Spanish population from questionnaires, we developed a quantitative risk assessment (QRA) model for the anchovy value chain. Spaniards were estimated to consume on average 0.66 Anisakis per untreated (non-frozen) raw or marinated anchovy meal. A dose-response relationship was generated and the probability of anisakiasis was calculated to be 9.56 × 10(-5) per meal, and the number of annual anisakiasis cases requiring medical attention was predicted between 7,700 and 8,320. Monte Carlo simulations estimated post-mortem migration of Anisakis from viscera to flesh increases the disease burden by >1000% whilst an education campaign to freeze anchovy before consumption may reduce cases by 80%. However, most of the questionnaire respondents who ate untreated meals knew how to prevent Anisakis infection. The QRA suggests that previously reported figures of 500 anisakiasis per year in Europe is a considerable underestimate. The QRA tool can be used by policy makers and informs industry, health professionals and consumers about this underdiagnosed zoonosis.

Concepts: Parasites, Monte Carlo, Monte Carlo method, Monte Carlo methods in finance, Spain, Computer simulation, Risk assessment, Monaco