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Computers in Biology and Medicine Sep 2022We develop a lumped parameter model to describe and predict the mass release of (absorption from) an arbitrary shaped body of any dimension in a large environment....
We develop a lumped parameter model to describe and predict the mass release of (absorption from) an arbitrary shaped body of any dimension in a large environment. Through the one-to-one analogy between diffusion-dominated mass transfer systems and electrical circuits we provide exact solutions in terms of averaged concentrations and mass released. An estimate of the equivalent resistance and of the release time is also given, and shown to be inversely proportional to the diffusivity. The proposed electrical analogue approach allows a time constant to be defined and provides an easy extension to a multi-layer and multi-phase cases in planar and spherical geometries. The simulation results are compared with those obtained from the solution of the corresponding analytical, numerical and experimental solutions, showing a satisfactory accuracy and a good agreement.
Topics: Computer Simulation; Diffusion; Electricity; Mathematics
PubMed: 35834969
DOI: 10.1016/j.compbiomed.2022.105774 -
Proceedings of the National Academy of... Mar 2020Protein mobility at solid-liquid interfaces can affect the performance of applications such as bioseparations and biosensors by facilitating reorganization of adsorbed...
Protein mobility at solid-liquid interfaces can affect the performance of applications such as bioseparations and biosensors by facilitating reorganization of adsorbed protein, accelerating molecular recognition, and informing the fundamentals of adsorption. In the case of ion-exchange chromatographic beads with small, tortuous pores, where the existence of surface diffusion is often not recognized, slow mass transfer can result in lower resin capacity utilization. We demonstrate that accounting for and exploiting protein surface diffusion can alleviate the mass-transfer limitations on multiple significant length scales. Although the surface diffusivity has previously been shown to correlate with ionic strength (IS) and binding affinity, we show that the dependence is solely on the binding affinity, irrespective of pH, IS, and resin ligand density. Different surface diffusivities give rise to different protein distributions within the resin, as characterized using confocal microscopy and small-angle neutron scattering (length scales of micrometer and nanometer, respectively). The binding dependence of surface diffusion inspired a protein-loading approach in which the binding affinity, and hence the surface diffusivity, is modulated by varying IS. Such gradient loading increased the protein uptake efficiency by up to 43%, corroborating the importance of protein surface diffusion in protein transport in ion-exchange chromatography.
Topics: Diffusion; Ion Exchange Resins; Models, Chemical; Proteins
PubMed: 32179691
DOI: 10.1073/pnas.1921499117 -
Journal of Biological Physics Oct 2016We study in silico the influence of host tissue inhomogeneity on tumor cell proliferation and diffusion by simulating the mobility of a tumor on percolation clusters...
We study in silico the influence of host tissue inhomogeneity on tumor cell proliferation and diffusion by simulating the mobility of a tumor on percolation clusters with different homogeneities of surrounding tissues. The proliferation and diffusion of a tumor in an inhomogeneous tissue could be characterized in the framework of the percolation theory, which displays similar thresholds (0.54, 0.44, and 0.37, respectively) for tumor proliferation and diffusion in three kinds of lattices with 4, 6, and 8 connecting near neighbors. Our study reveals the existence of a critical transition concerning the survival and diffusion of tumor cells with leaping metastatic diffusion movement in the host tissues. Tumor cells usually flow in the direction of greater pressure variation during their diffusing and infiltrating to a further location in the host tissue. Some specific sites suitable for tumor invasion were observed on the percolation cluster and around these specific sites a tumor can develop into scattered tumors linked by some advantage tunnels that facilitate tumor invasion. We also investigate the manner that tissue inhomogeneity surrounding a tumor may influence the velocity of tumor diffusion and invasion. Our simulation suggested that invasion of a tumor is controlled by the homogeneity of the tumor microenvironment, which is basically consistent with the experimental report by Riching et al. as well as our clinical observation of medical imaging. Both simulation and clinical observation proved that tumor diffusion and invasion into the surrounding host tissue is positively correlated with the homogeneity of the tissue.
Topics: Cell Proliferation; Computer Simulation; Diffusion; Models, Biological; Monte Carlo Method; Neoplasm Invasiveness; Neoplasm Metastasis; Neoplasms
PubMed: 27678112
DOI: 10.1007/s10867-016-9427-2 -
Journal of the American Chemical Society Nov 2022A detailed velocity-resolved kinetics study of NH thermal desorption rates from (2 × 2) O/Pt(111) is presented. We find a large reduction in the NH desorption rate due...
A detailed velocity-resolved kinetics study of NH thermal desorption rates from (2 × 2) O/Pt(111) is presented. We find a large reduction in the NH desorption rate due to adsorption of O-atoms on Pt(111). A physical model describing the interactions between adsorbed NH and O-atoms explains these observations. By fitting the model to the derived desorption rate constants, we find an NH stabilization on (2 × 2) O/Pt(111) of 0.147 eV compared to Pt(111) and a rotational barrier of 0.084 eV, which is not present on Pt(111). The model also quantitatively predicts the steric hindrance of NH diffusion on Pt(111) due to co-adsorbed O-atoms. The derived diffusion barrier of NH on (2 × 2) O/Pt(111) is 1.10 eV, which is 0.39 eV higher than that on pristine Pt(111). We find that Perdew Burke Ernzerhof (PBE) and revised Perdew Burke Ernzerhof (RPBE) exchange-correlation functionals are unable to reproduce the experimentally observed NH-O adsorbate-adsorbate interactions and NH binding energies at Pt(111) and (2 × 2) O/Pt(111), which indicates the importance of dispersion interactions for both systems.
Topics: Diffusion; Kinetics; Adsorption
PubMed: 36399044
DOI: 10.1021/jacs.2c10458 -
Journal of Biomechanical Engineering Jul 2023The cartilage endplates (CEPs) on the superior and inferior surfaces of the intervertebral disk (IVD), are the primary nutrient transport pathways between the disk and...
The cartilage endplates (CEPs) on the superior and inferior surfaces of the intervertebral disk (IVD), are the primary nutrient transport pathways between the disk and the vertebral body. Passive diffusion is responsible for transporting small nutrient and metabolite molecules through the avascular CEPs. The baseline solute diffusivities in healthy CEPs have been previously studied, however alterations in CEP diffusion associated with IVD degeneration remain unclear. This study aimed to quantitatively compare the solute diffusion in healthy and degenerated human CEPs using a fluorescence recovery after photobleaching (FRAP) approach. Seven healthy CEPs and 22 degenerated CEPs were collected from five fresh-frozen human cadaveric spines and 17 patients undergoing spine fusion surgery, respectively. The sodium fluorescein diffusivities in CEP radial and vertical directions were measured using the FRAP method. The CEP calcification level was evaluated by measuring the average X-ray attenuation. No difference was found in solute diffusivities between radial and axial directions in healthy and degenerated CEPs. Compared to healthy CEPs, the average solute diffusivity was 44% lower in degenerated CEPs (Healthy: 29.07 μm2/s (CI: 23.96-33.62 μm2/s); degenerated: 16.32 μm2/s (CI: 13.84-18.84 μm2/s), p < 0.001). The average solute diffusivity had an inverse relationship with the degree of CEP calcification as determined by the normalized X-ray attenuation values (ß = -22.19, R2 = 0.633; p < 0.001). This study suggests that solute diffusion through the disk and vertebral body interface is significantly hindered by CEP calcification, providing clues to help further understand the mechanism of IVD degeneration.
Topics: Humans; Cartilage; Intervertebral Disc; Intervertebral Disc Degeneration; Biological Transport; Diffusion; Calcinosis
PubMed: 36752723
DOI: 10.1115/1.4056871 -
Optics Letters Feb 2016This study uses a sub-diffusive light transport model to analyze fiber-optic measurements of reflectance spectra to recover endogenous tissue biomarkers and to correct...
This study uses a sub-diffusive light transport model to analyze fiber-optic measurements of reflectance spectra to recover endogenous tissue biomarkers and to correct raw fluorescence emissions for distortions from background optical properties. Measurements in tissue-simulating phantoms validated accurate recovery of the reduced scattering coefficient [(0.3-3.4 mm), error 10%], blood volume fraction [(1-3 vol%), error 7%], and a dimensionless metric of anisotropic scattering, γ, that is sensitive to submillimeter tissue ultrastructure [(1.29-2.06), error 11%]. In vivo sub-diffusive optical data acquired during clinical neurosurgeries characterize differences in microstructure (γ), perfusion (blood volume), and metabolism (PpIX fluorescence) between normal cortex and malignant tumor.
Topics: Brain; Brain Neoplasms; Diffusion; Humans; Light; Monte Carlo Method; Neurogenesis; Optical Phenomena; Phantoms, Imaging
PubMed: 26872187
DOI: 10.1364/OL.41.000781 -
Journal of Mathematical Biology Apr 2022We consider a reaction-diffusion system of densities of two types of particles, introduced by Hannezo et al. (Cell 171(1):242-255.e27, 2017). It is a simple model for a...
We consider a reaction-diffusion system of densities of two types of particles, introduced by Hannezo et al. (Cell 171(1):242-255.e27, 2017). It is a simple model for a growth process: active, branching particles form the growing boundary layer of an otherwise static tissue, represented by inactive particles. The active particles diffuse, branch and become irreversibly inactive upon collision with a particle of arbitrary type. In absence of active particles, this system is in a steady state, without any a priori restriction on the amount of remaining inactive particles. Thus, while related to the well-studied FKPP-equation, this system features a game-changing continuum of steady state solutions, where each corresponds to a possible outcome of the growth process. However, simulations indicate that this system self-organizes: traveling fronts with fixed shape arise under a wide range of initial data. In the present work, we describe all positive and bounded traveling wave solutions, and obtain necessary and sufficient conditions for their existence. We find a surprisingly simple symmetry in the pairs of steady states which are joined via heteroclinic wave orbits. Our approach is constructive: we first prove the existence of almost constant solutions and then extend our results via a continuity argument along the continuum of limiting points.
Topics: Computer Simulation; Diffusion; Models, Biological
PubMed: 35482091
DOI: 10.1007/s00285-022-01753-z -
Biophysical Journal Nov 2015The efficient treatment of many ocular diseases depends on the rapid diffusive distribution of solutes such as drugs or drug delivery vehicles through the vitreous...
The efficient treatment of many ocular diseases depends on the rapid diffusive distribution of solutes such as drugs or drug delivery vehicles through the vitreous humor. However, this multicomponent hydrogel possesses selective permeability properties, which allow for the diffusion of certain molecules and particles, whereas others are immobilized. In this study, we perform an interspecies comparison showing that the selective permeability properties of the vitreous are conserved across several mammalian species. We identify the polyanionic glycosaminoglycans hyaluronic acid and heparan sulfate as two key macromolecules that establish this selective permeability. We show that electrostatic interactions between the polyanionic macromolecules and diffusing solutes can be weakened by charge screening or enzymatic glycosaminoglycan digestion. Furthermore, molecule penetration into the vitreous is also charge-dependent and only efficient as long as the net charge of the molecule does not exceed a certain threshold.
Topics: Animals; Cattle; Diffusion; Heparitin Sulfate; Humans; Hyaluronic Acid; Permeability; Sheep; Swine; Vitreous Body
PubMed: 26588575
DOI: 10.1016/j.bpj.2015.10.002 -
Journal of the American Chemical Society Oct 2022The kinetics of chemical reactions are determined by the law of mass action, which has been successfully applied to homogeneous, dilute mixtures. At nondilute...
The kinetics of chemical reactions are determined by the law of mass action, which has been successfully applied to homogeneous, dilute mixtures. At nondilute conditions, interactions among the components can give rise to coexisting phases, which can significantly alter the kinetics of chemical reactions. Here, we derive a theory for chemical reactions in coexisting phases at phase equilibrium. We show that phase equilibrium couples the rates of chemical reactions of components with their diffusive exchanges between the phases. Strikingly, the chemical relaxation kinetics can be represented as a flow along the phase equilibrium line in the phase diagram. A key finding of our theory is that differences in reaction rates between coexisting phases stem solely from phase-dependent reaction rate coefficients. Our theory is key to interpreting how concentration levels of reactive components in condensed phases control chemical reaction rates in synthetic and biological systems.
Topics: Kinetics; Diffusion
PubMed: 36241174
DOI: 10.1021/jacs.2c06265 -
Journal of the Royal Society, Interface Mar 2023How memory shapes animals' movement paths is a topic of growing interest in ecology, with connections to planning for conservation and climate change. Empirical studies...
How memory shapes animals' movement paths is a topic of growing interest in ecology, with connections to planning for conservation and climate change. Empirical studies suggest that memory has both temporal and spatial components, and can include both attractive and aversive elements. Here, we introduce reinforced diffusions (the continuous time counterpart of reinforced random walks) as a modelling framework for understanding the role that memory plays in determining animal movements. This framework includes reinforcement via functions of time before present and of distance away from a current location. Focusing on the interplay between memory and central place attraction (a component of home ranging behaviour), we explore patterns of space usage that result from the reinforced diffusion. Our efforts identify three qualitatively different behaviours: bounded wandering behaviour that does not collapse spatially, collapse to a very small area, and, most intriguingly, convergence to a cycle. Subsequent applications show how reinforced diffusion can create movement trajectories emulating the learning of movement routes by homing pigeons and consolidation of ant travel paths. The mathematically explicit manner with which assumptions about the structure of memory can be stated and subsequently explored provides linkages to biological concepts like an animal's 'immediate surroundings' and memory decay.
Topics: Animals; Ecology; Learning; Diffusion; Movement; Models, Biological
PubMed: 36987616
DOI: 10.1098/rsif.2022.0700