diffusion coefficients calculations  (Molecular Dynamics Inc)

Journal: Discover Nano

Article Title: Impact of temporal resolution in single particle tracking analysis

doi: 10.1186/s11671-024-04029-1

Figure Lengend Snippet: Diffusivity distributions determined starting from exact tracks. Tracks simulated using different diffusion coefficients D S (as reported at the top of each graph) and time steps Δt (as reported in the legends) were analysed to extract the reported diffusivity (D) distributions as calculated from the first two points of the MSD function. Simulations were performed on a square area of 256 μm 2 with reflective boundaries at a density of 0.3 particles/μm 2 . The different temporal resolutions were obtained by appropriate sampling on the same simulated tracks, stopping at 500 time steps in each case. 385 tracks from 5 different simulations were analysed for each case

Article Snippet: MSD analysis and calculation of the short-term diffusion coefficient D were performed in MATLAB as previously described [ , , , ].

Techniques: Diffusion-based Assay, Sampling

Journal: Discover Nano

Article Title: Impact of temporal resolution in single particle tracking analysis

doi: 10.1186/s11671-024-04029-1

Figure Lengend Snippet: Single particle tracking experiment on p75 NTR receptors fluorescently labelled on the membrane of living SK-N-BE(2) neuroblastoma cells and comparison with simulated results. A Experimental images from the movies recorded by TIRF microscopy; on each image we report the integration time; frame time was 25 ms longer due to readout time. Images are shown in the same fixed grayscale; scale bar: 5 μm. B Corresponding measured diffusivity distributions. Mean particle density was 0.3 µm −2 . Data were obtained from 2180 to 3050 tracks for each case. C Diffusivity distribution derived from detection, tracking, and MSD analysis on simulated movies with integration, frame times as written in the legend. Particle density was 0.3 µm −2 , D S was 0.75 μm 2 /s (equal to D P for all curves but the red one for which it is 0.8 μm 2 /s). 385 tracks from 5 different simulations were used for each case. In both B and C 130-frames movies were analysed for each temporal resolution. We calculated the uncertainties in the distributions for both the experimental and simulation cases; some examples are reported in Fig.

Article Snippet: MSD analysis and calculation of the short-term diffusion coefficient D were performed in MATLAB as previously described [ , , , ].

Techniques: Single-particle Tracking, Membrane, Comparison, Microscopy, Derivative Assay

Journal: Computers in biology and medicine

Article Title: Mass release curves as the constitutive curves for modeling diffusive transport within biological tissue

doi: 10.1016/j.compbiomed.2016.06.026

Figure Lengend Snippet: Mass release curves at a point of a continuum determined computationally. (a) Composite medium and small (reference volume RV) around a point P. (b) Schematics of microstructure and FE model for diffusion, with boundary conditions. (c) Molecular dynamics (MD) schematics of calculation of the effective diffusion coefficient. (d) Mass release curves obtained using FE model of RV, normalized to the inlet/outlet surface area, in, say, [µg/µm2]. (e) Change of diffusion coefficient with the distance from solid surface for three concentrations (distance is of nanometer size; Dbulk is diffusion coefficient far from surface).

Article Snippet: From follows that the tangent to a mass release curve (normalized with respect to the area) geometrically determines the mass flux at a considered time, J i = ( dm dt ) i = tan α (2) and then, for a given gradient ( dc / dx ) i , D i = ( dm / dt ) i ( dc / dx ) i , no sum on i (3) Note that dm has dimension mass/(unit area) and dt is time (in seconds), hence tan α is the mass flux in eq. (2) , in, say [ μg / μm 2 s ]. fig ft0 fig mode=article f1 fig/graphic|fig/alternatives/graphic mode="anchored" m1 Open in a separate window caption a7 Mass release curves at a point of a continuum determined computationally. (a) Composite medium and small (reference volume RV) around a point P. (b) Schematics of microstructure and FE model for diffusion, with boundary conditions. (c) Molecular dynamics (MD) schematics of calculation of the effective diffusion coefficient. (d) Mass release curves obtained using FE model of RV, normalized to the inlet/outlet surface area, in, say, [ μg / μm 2 ]. (e) Change of diffusion coefficient with the distance from solid surface for three concentrations (distance is of nanometer size; D bulk is diffusion coefficient far from surface).

Techniques: Diffusion-based Assay

Journal: Computers in biology and medicine

Article Title: Mass release curves as the constitutive curves for modeling diffusive transport within biological tissue

doi: 10.1016/j.compbiomed.2016.06.026

Figure Lengend Snippet: Mass release curve for diffusion of glucose molecules through porous medium with silica spheres as solids [47]. (a) Larger porosity. (b) Small porosity of 15% and complex geometry of pores. (c) Scaling functions for glucose-silica interaction; diffusion coefficient is D(h,c)=f Dbulk, where h is distance from solid surface and f is the scaling function. (d) Mass release curves for several porosities. (e) Equivalent diffusion coefficient in terms of concentration. Model size: 125,000 3D finite elements, 132,651 nodes.

Article Snippet: From follows that the tangent to a mass release curve (normalized with respect to the area) geometrically determines the mass flux at a considered time, J i = ( dm dt ) i = tan α (2) and then, for a given gradient ( dc / dx ) i , D i = ( dm / dt ) i ( dc / dx ) i , no sum on i (3) Note that dm has dimension mass/(unit area) and dt is time (in seconds), hence tan α is the mass flux in eq. (2) , in, say [ μg / μm 2 s ]. fig ft0 fig mode=article f1 fig/graphic|fig/alternatives/graphic mode="anchored" m1 Open in a separate window caption a7 Mass release curves at a point of a continuum determined computationally. (a) Composite medium and small (reference volume RV) around a point P. (b) Schematics of microstructure and FE model for diffusion, with boundary conditions. (c) Molecular dynamics (MD) schematics of calculation of the effective diffusion coefficient. (d) Mass release curves obtained using FE model of RV, normalized to the inlet/outlet surface area, in, say, [ μg / μm 2 ]. (e) Change of diffusion coefficient with the distance from solid surface for three concentrations (distance is of nanometer size; D bulk is diffusion coefficient far from surface).

Techniques: Diffusion-based Assay, Concentration Assay

Journal: Computers in biology and medicine

Article Title: Mass release curves as the constitutive curves for modeling diffusive transport within biological tissue

doi: 10.1016/j.compbiomed.2016.06.026

Figure Lengend Snippet: Agarose polymer gel model-2, with flux in x direction (AA) due to prescribed concentration difference between left and right boundary of the model (according to Ref. [47]). (a) Distribution of concentration at time t=1s, microstructural model; zero-values correspond to fibers. (b) Distribution of concentration and mass flux-x along line AA, microstructural (full line) and continuum (dashed) solution. (c) Distribution of concentration and mass flux-y along line BB, microstructural (full line) and continuum (dashed) solution. (d) Mass flux-x distribution at time t= 1s. Molecule of 6.25nm, linear dependence of bulk diffusion coefficient within gel.

Article Snippet: From follows that the tangent to a mass release curve (normalized with respect to the area) geometrically determines the mass flux at a considered time, J i = ( dm dt ) i = tan α (2) and then, for a given gradient ( dc / dx ) i , D i = ( dm / dt ) i ( dc / dx ) i , no sum on i (3) Note that dm has dimension mass/(unit area) and dt is time (in seconds), hence tan α is the mass flux in eq. (2) , in, say [ μg / μm 2 s ]. fig ft0 fig mode=article f1 fig/graphic|fig/alternatives/graphic mode="anchored" m1 Open in a separate window caption a7 Mass release curves at a point of a continuum determined computationally. (a) Composite medium and small (reference volume RV) around a point P. (b) Schematics of microstructure and FE model for diffusion, with boundary conditions. (c) Molecular dynamics (MD) schematics of calculation of the effective diffusion coefficient. (d) Mass release curves obtained using FE model of RV, normalized to the inlet/outlet surface area, in, say, [ μg / μm 2 ]. (e) Change of diffusion coefficient with the distance from solid surface for three concentrations (distance is of nanometer size; D bulk is diffusion coefficient far from surface).

Techniques: Polymer, Concentration Assay, Diffusion-based Assay

Journal: Computers in biology and medicine

Article Title: Mass release curves as the constitutive curves for modeling diffusive transport within biological tissue

doi: 10.1016/j.compbiomed.2016.06.026

Figure Lengend Snippet: Agarose polymer gel model-3. (a) Mass release curves. (b) Equivalent diffusion coefficient.

Article Snippet: From follows that the tangent to a mass release curve (normalized with respect to the area) geometrically determines the mass flux at a considered time, J i = ( dm dt ) i = tan α (2) and then, for a given gradient ( dc / dx ) i , D i = ( dm / dt ) i ( dc / dx ) i , no sum on i (3) Note that dm has dimension mass/(unit area) and dt is time (in seconds), hence tan α is the mass flux in eq. (2) , in, say [ μg / μm 2 s ]. fig ft0 fig mode=article f1 fig/graphic|fig/alternatives/graphic mode="anchored" m1 Open in a separate window caption a7 Mass release curves at a point of a continuum determined computationally. (a) Composite medium and small (reference volume RV) around a point P. (b) Schematics of microstructure and FE model for diffusion, with boundary conditions. (c) Molecular dynamics (MD) schematics of calculation of the effective diffusion coefficient. (d) Mass release curves obtained using FE model of RV, normalized to the inlet/outlet surface area, in, say, [ μg / μm 2 ]. (e) Change of diffusion coefficient with the distance from solid surface for three concentrations (distance is of nanometer size; D bulk is diffusion coefficient far from surface).

Techniques: Polymer, Diffusion-based Assay

Journal: Computers in biology and medicine

Article Title: Mass release curves as the constitutive curves for modeling diffusive transport within biological tissue

doi: 10.1016/j.compbiomed.2016.06.026

Figure Lengend Snippet: Reference volume for a typical composition of tissue. The domain includes extracellular space, cell membranes and cell interior. Boundary conditions: Concentrations at inlet outlet are increased from zero to 1M with small concentration gradient, while there is no flux though lateral surfaces. (a) Concentration field in the RV and graph of concentration along a line AB. (b) Mass release curve. (c) Diffusion coefficient for the equivalent homogenous continuum. Model size: 34,000 2D finite elements, 1684 fictitious 1D element, 34,281 nodes.

Article Snippet: From follows that the tangent to a mass release curve (normalized with respect to the area) geometrically determines the mass flux at a considered time, J i = ( dm dt ) i = tan α (2) and then, for a given gradient ( dc / dx ) i , D i = ( dm / dt ) i ( dc / dx ) i , no sum on i (3) Note that dm has dimension mass/(unit area) and dt is time (in seconds), hence tan α is the mass flux in eq. (2) , in, say [ μg / μm 2 s ]. fig ft0 fig mode=article f1 fig/graphic|fig/alternatives/graphic mode="anchored" m1 Open in a separate window caption a7 Mass release curves at a point of a continuum determined computationally. (a) Composite medium and small (reference volume RV) around a point P. (b) Schematics of microstructure and FE model for diffusion, with boundary conditions. (c) Molecular dynamics (MD) schematics of calculation of the effective diffusion coefficient. (d) Mass release curves obtained using FE model of RV, normalized to the inlet/outlet surface area, in, say, [ μg / μm 2 ]. (e) Change of diffusion coefficient with the distance from solid surface for three concentrations (distance is of nanometer size; D bulk is diffusion coefficient far from surface).

Techniques: Concentration Assay, Diffusion-based Assay

Journal: Computers in biology and medicine

Article Title: Mass release curves as the constitutive curves for modeling diffusive transport within biological tissue

doi: 10.1016/j.compbiomed.2016.06.026

Figure Lengend Snippet: Extracellular space of skin. (a) Fibrous structure according to [60]. (b) A simplified RV model. (c) Diffusion coefficient for free diffusion in the liquid (Dbulk) and equivalent diffusion coefficient. Model size: 125,000 3D finite elements, 132,651 nodes.

Article Snippet: From follows that the tangent to a mass release curve (normalized with respect to the area) geometrically determines the mass flux at a considered time, J i = ( dm dt ) i = tan α (2) and then, for a given gradient ( dc / dx ) i , D i = ( dm / dt ) i ( dc / dx ) i , no sum on i (3) Note that dm has dimension mass/(unit area) and dt is time (in seconds), hence tan α is the mass flux in eq. (2) , in, say [ μg / μm 2 s ]. fig ft0 fig mode=article f1 fig/graphic|fig/alternatives/graphic mode="anchored" m1 Open in a separate window caption a7 Mass release curves at a point of a continuum determined computationally. (a) Composite medium and small (reference volume RV) around a point P. (b) Schematics of microstructure and FE model for diffusion, with boundary conditions. (c) Molecular dynamics (MD) schematics of calculation of the effective diffusion coefficient. (d) Mass release curves obtained using FE model of RV, normalized to the inlet/outlet surface area, in, say, [ μg / μm 2 ]. (e) Change of diffusion coefficient with the distance from solid surface for three concentrations (distance is of nanometer size; D bulk is diffusion coefficient far from surface).

Techniques: Diffusion-based Assay

Journal: Computers in biology and medicine

Article Title: Mass release curves as the constitutive curves for modeling diffusive transport within biological tissue

doi: 10.1016/j.compbiomed.2016.06.026

Figure Lengend Snippet: (a) Collagen presence in reference volumes RV1-RV5. (b) Computed field of diffusion coefficient for protein. Model size: minimum size model RV1-48,474 2D elements, 952 fictitious 1D elements, 49,665 nodes; maximum size model RV2-196,048 2D elements, 3,846 fictitious 1D elements, 200,769 nodes.

Article Snippet: From follows that the tangent to a mass release curve (normalized with respect to the area) geometrically determines the mass flux at a considered time, J i = ( dm dt ) i = tan α (2) and then, for a given gradient ( dc / dx ) i , D i = ( dm / dt ) i ( dc / dx ) i , no sum on i (3) Note that dm has dimension mass/(unit area) and dt is time (in seconds), hence tan α is the mass flux in eq. (2) , in, say [ μg / μm 2 s ]. fig ft0 fig mode=article f1 fig/graphic|fig/alternatives/graphic mode="anchored" m1 Open in a separate window caption a7 Mass release curves at a point of a continuum determined computationally. (a) Composite medium and small (reference volume RV) around a point P. (b) Schematics of microstructure and FE model for diffusion, with boundary conditions. (c) Molecular dynamics (MD) schematics of calculation of the effective diffusion coefficient. (d) Mass release curves obtained using FE model of RV, normalized to the inlet/outlet surface area, in, say, [ μg / μm 2 ]. (e) Change of diffusion coefficient with the distance from solid surface for three concentrations (distance is of nanometer size; D bulk is diffusion coefficient far from surface).

Techniques: Diffusion-based Assay

Journal: Computers in biology and medicine

Article Title: Mass release curves as the constitutive curves for modeling diffusive transport within biological tissue

doi: 10.1016/j.compbiomed.2016.06.026

Figure Lengend Snippet: Diffusion coefficient [µm 2 /s] calculated from collagen content, and partitioning coefficient used for RV modeling. D 255 - diffusion in water-like media, aka nominal, and D 180 - diffusion across fibers.

Article Snippet: From follows that the tangent to a mass release curve (normalized with respect to the area) geometrically determines the mass flux at a considered time, J i = ( dm dt ) i = tan α (2) and then, for a given gradient ( dc / dx ) i , D i = ( dm / dt ) i ( dc / dx ) i , no sum on i (3) Note that dm has dimension mass/(unit area) and dt is time (in seconds), hence tan α is the mass flux in eq. (2) , in, say [ μg / μm 2 s ]. fig ft0 fig mode=article f1 fig/graphic|fig/alternatives/graphic mode="anchored" m1 Open in a separate window caption a7 Mass release curves at a point of a continuum determined computationally. (a) Composite medium and small (reference volume RV) around a point P. (b) Schematics of microstructure and FE model for diffusion, with boundary conditions. (c) Molecular dynamics (MD) schematics of calculation of the effective diffusion coefficient. (d) Mass release curves obtained using FE model of RV, normalized to the inlet/outlet surface area, in, say, [ μg / μm 2 ]. (e) Change of diffusion coefficient with the distance from solid surface for three concentrations (distance is of nanometer size; D bulk is diffusion coefficient far from surface).

Techniques: Diffusion-based Assay, Membrane

Journal: Computers in biology and medicine

Article Title: Mass release curves as the constitutive curves for modeling diffusive transport within biological tissue

doi: 10.1016/j.compbiomed.2016.06.026

Figure Lengend Snippet: Equivalent diffusion coefficient for each RV obtained using mass release curves

Article Snippet: From follows that the tangent to a mass release curve (normalized with respect to the area) geometrically determines the mass flux at a considered time, J i = ( dm dt ) i = tan α (2) and then, for a given gradient ( dc / dx ) i , D i = ( dm / dt ) i ( dc / dx ) i , no sum on i (3) Note that dm has dimension mass/(unit area) and dt is time (in seconds), hence tan α is the mass flux in eq. (2) , in, say [ μg / μm 2 s ]. fig ft0 fig mode=article f1 fig/graphic|fig/alternatives/graphic mode="anchored" m1 Open in a separate window caption a7 Mass release curves at a point of a continuum determined computationally. (a) Composite medium and small (reference volume RV) around a point P. (b) Schematics of microstructure and FE model for diffusion, with boundary conditions. (c) Molecular dynamics (MD) schematics of calculation of the effective diffusion coefficient. (d) Mass release curves obtained using FE model of RV, normalized to the inlet/outlet surface area, in, say, [ μg / μm 2 ]. (e) Change of diffusion coefficient with the distance from solid surface for three concentrations (distance is of nanometer size; D bulk is diffusion coefficient far from surface).

Techniques: Diffusion-based Assay

Journal: Computers in biology and medicine

Article Title: Mass release curves as the constitutive curves for modeling diffusive transport within biological tissue

doi: 10.1016/j.compbiomed.2016.06.026

Figure Lengend Snippet: Diffusion coefficient field for protein molecule, in [µm2/s]. (a) X-direction (DXmax = 19.2, DXmin = 5.4). (b) Y-direction (DYmax = 17.5, DYmin = 8.7). Model size: 35,418 2D elements, 35,418 nodes.

Article Snippet: From follows that the tangent to a mass release curve (normalized with respect to the area) geometrically determines the mass flux at a considered time, J i = ( dm dt ) i = tan α (2) and then, for a given gradient ( dc / dx ) i , D i = ( dm / dt ) i ( dc / dx ) i , no sum on i (3) Note that dm has dimension mass/(unit area) and dt is time (in seconds), hence tan α is the mass flux in eq. (2) , in, say [ μg / μm 2 s ]. fig ft0 fig mode=article f1 fig/graphic|fig/alternatives/graphic mode="anchored" m1 Open in a separate window caption a7 Mass release curves at a point of a continuum determined computationally. (a) Composite medium and small (reference volume RV) around a point P. (b) Schematics of microstructure and FE model for diffusion, with boundary conditions. (c) Molecular dynamics (MD) schematics of calculation of the effective diffusion coefficient. (d) Mass release curves obtained using FE model of RV, normalized to the inlet/outlet surface area, in, say, [ μg / μm 2 ]. (e) Change of diffusion coefficient with the distance from solid surface for three concentrations (distance is of nanometer size; D bulk is diffusion coefficient far from surface).

Techniques: Diffusion-based Assay