Comparison between fixed and Gaussian steplength in Monte Carlo simulations for diffusion processes

Barlett, V. Ruiz; Hoyuelos, Miguel; Mártin, H. O.

doi:10.1016/j.jcp.2011.01.041

Cited by 3 publications

(5 citation statements)

References 13 publications

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“…In a previous work [17], we have shown that the fixed steplength method exactly reproduces first and second order moments in homogeneous systems, and that the scaled error in higher order moments behaves as t −1 for t large.…”

Section: Discussionmentioning

confidence: 80%

“…On the other hand, also in the homogeneous case, the fixed steplength choice has some important good features. It produces exact results in the evaluation of first and second order moments [17] (scaled errors in higher order moments behave as t −1 for t large). And, more importantly, it keeps these good features when the diffusion coefficient is non homogeneous, in contrast with the Gaussian steplength.…”

Section: Discrete Description For MC Simulationmentioning

confidence: 99%

“…In Ref. [17], we proposed a different solution. We considered a discrete probability distribution for particle jumps at fixed distances to the left and right in a 1D lattice.…”

Section: Introductionmentioning

confidence: 99%

“…In Ref. [17], we illustrated the method with a constant gradient diffusion coefficient. Here, we apply it to the 1D model for diffusion of calcium ions in the neuromuscular junction of the crayfish [15] and compare the results with the ones obtained from MC simulation with Gaussian steplength and from numerical integration of the diffusion equation.…”

Section: Introductionmentioning

confidence: 99%

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Monte Carlo simulation with fixed steplength for diffusion processes in nonhomogeneous media

Barlett

Hoyuelos

Mártin

2013

Journal of Computational Physics

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Monte Carlo simulation is one of the most important tools in the study of diffusion processes. For constant diffusion coefficients, an appropriate Gaussian distribution of particle's steplengths can generate exact results, when compared with integration of the diffusion equation. It is important to notice that the same method is completely erroneous when applied to nonhomogeneous diffusion coefficients. A simple alternative, jumping at fixed steplegths with appropriate transition probabilities, produces correct results. Here, a model for diffusion of calcium ions in the neuromuscular junction of the crayfish is used as a test to compare Monte Carlo simulation with fixed and Gaussian steplegth.

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Section: Discussionmentioning

confidence: 80%

Section: Discrete Description For MC Simulationmentioning

confidence: 99%

“…In Ref. [17], we proposed a different solution. We considered a discrete probability distribution for particle jumps at fixed distances to the left and right in a 1D lattice.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Monte Carlo simulation with fixed steplength for diffusion processes in nonhomogeneous media

Barlett

Hoyuelos

Mártin

2013

Journal of Computational Physics

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“…To account for the diffusion of aggregates, a Monte Carlo simulation was used, in which two random numbers were generated from a uniform distribution and transformed to a Gaussian distribution using the Box-Muller method in an ImageJ macro [51]. For a constant diffusion coefficient and fixed time step, a Gaussian step-length distribution is known to exactly simulate normal diffusion [52]. For a simulated pixel size of 0.125 µm and one frame per second, this corresponds to the slow diffusion of the aggregates with a diffusion constant of D = 0.004 µm 2 /s, which is comparable to experimental findings for diffusion of small eGFP-mtHtt aggregates in cells [11].…”

Section: Outline Of the Dmd Methods Applied To Fluorescence Microscop...mentioning

confidence: 99%

Dynamic Mode Decomposition of Fluorescence Loss in Photobleaching Microscopy Data for Model-Free Analysis of Protein Transport and Aggregation in Living Cells

Wüstner

2022

Sensors

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The phase separation and aggregation of proteins are hallmarks of many neurodegenerative diseases. These processes can be studied in living cells using fluorescent protein constructs and quantitative live-cell imaging techniques, such as fluorescence recovery after photobleaching (FRAP) or the related fluorescence loss in photobleaching (FLIP). While the acquisition of FLIP images is straightforward on most commercial confocal microscope systems, the analysis and computational modeling of such data is challenging. Here, a novel model-free method is presented, which resolves complex spatiotemporal fluorescence-loss kinetics based on dynamic-mode decomposition (DMD) of FLIP live-cell image sequences. It is shown that the DMD of synthetic and experimental FLIP image series (DMD-FLIP) allows for the unequivocal discrimination of subcellular compartments, such as nuclei, cytoplasm, and protein condensates based on their differing transport and therefore fluorescence loss kinetics. By decomposing fluorescence-loss kinetics into distinct dynamic modes, DMD-FLIP will enable researchers to study protein dynamics at each time scale individually. Furthermore, it is shown that DMD-FLIP is very efficient in denoising confocal time series data. Thus, DMD-FLIP is an easy-to-use method for the model-free detection of barriers to protein diffusion, of phase-separated protein assemblies, and of insoluble protein aggregates. It should, therefore, find wide application in the analysis of protein transport and aggregation, in particular in relation to neurodegenerative diseases and the formation of protein condensates in living cells.

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Multiscale modeling of solute diffusion in triblock copolymer membranes

Cooper

Howard

Kadulkar

et al. 2023

The Journal of Chemical Physics

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We develop a multiscale simulation model for diffusion of solutes through porous triblock copolymer membranes. The approach combines two techniques: self-consistent field theory (SCFT) to predict the structure of the self-assembled, solvated membrane and on-lattice kinetic Monte Carlo (kMC) simulations to model diffusion of solutes. Solvation is simulated in SCFT by constraining the glassy membrane matrix while relaxing the brush-like membrane pore coating against the solvent. The kMC simulations capture the resulting solute spatial distribution and concentration-dependent local diffusivity in the polymer-coated pores; we parameterize the latter using particle-based simulations. We apply our approach to simulate solute diffusion through nonequilibrium morphologies of a model triblock copolymer, and we correlate diffusivity with structural descriptors of the morphologies. We also compare the model’s predictions to alternative approaches based on simple lattice random walks and find our multiscale model to be more robust and systematic to parameterize. Our multiscale modeling approach is general and can be readily extended in the future to other chemistries, morphologies, and models for the local solute diffusivity and interactions with the membrane.

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Comparison between fixed and Gaussian steplength in Monte Carlo simulations for diffusion processes

Cited by 3 publications

References 13 publications

Monte Carlo simulation with fixed steplength for diffusion processes in nonhomogeneous media

Monte Carlo simulation with fixed steplength for diffusion processes in nonhomogeneous media

Dynamic Mode Decomposition of Fluorescence Loss in Photobleaching Microscopy Data for Model-Free Analysis of Protein Transport and Aggregation in Living Cells

Multiscale modeling of solute diffusion in triblock copolymer membranes

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