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Bulletin of Mathematical Biology Mar 2021This paper considers predator-prey systems in which the prey can move between source and sink patches. First, we give a complete analysis on global dynamics of the...
This paper considers predator-prey systems in which the prey can move between source and sink patches. First, we give a complete analysis on global dynamics of the model. Then, we show that when diffusion from the source to sink is not large, the species would coexist at a steady state; when the diffusion is large, the predator goes to extinction, while the prey persists in both patches at a steady state; when the diffusion is extremely large, both species go to extinction. It is derived that diffusion in the system could lead to results reversing those without diffusion. That is, diffusion could change species' coexistence if non-diffusing, to extinction of the predator, and even to extinction of both species. Furthermore, we show that intermediate diffusion to the sink could make the prey reach total abundance higher than if non-diffusing, larger or smaller diffusion rates are not favorable. The total abundance, as a function of diffusion rates, can be both hump-shaped and bowl-shaped, which extends previous theory. A novel finding of this work is that there exist diffusion scenarios which could drive the predator into extinction and make the prey reach the maximal abundance. Diffusion from the sink to source and asymmetry in diffusion could also lead to results reversing those without diffusion. Meanwhile, diffusion always leads to reduction of the predator's density. The results are biologically important in protection of endangered species.
Topics: Animals; Diffusion; Endangered Species; Food Chain; Models, Biological; Population Dynamics
PubMed: 33745081
DOI: 10.1007/s11538-021-00884-6 -
Langmuir : the ACS Journal of Surfaces... Jun 2020Human skin, the largest external organ of the body, provides a selective barrier to therapeutics applied topically. The molecules having specific chemical and physical...
Human skin, the largest external organ of the body, provides a selective barrier to therapeutics applied topically. The molecules having specific chemical and physical properties can only penetrate the deeper layer of the skin. However, the lag time for reaching a steady state in the deeper layer is generally of the order of hours. In order to deliver higher-molecular-weight, charged, and hydrophilic therapeutics in the deeper layer, the skin barrier must be breached. Electroporation is one of the methods used to breach the skin barrier for enhancement of drug permeation and reduction of lag time. However, the underlying mechanism responsible for the enhancement of drug permeation is not well understood. In this study, a multiscale model of skin electroporation is developed by connecting molecular phenomena to a macroscopic model. At the atomic scale, molecular dynamics simulations of the lipid matrix of the human stratum corneum (SC) were performed under the influence of an external electric field. The pores get formed during the electroporation process and the transport properties (diffusivity) of drug molecules are computed. The diffusion coefficient obtained during electroporation was found to be higher than passive diffusion. However, this alone could not explain the multifold increase in the drug flux on application of an electric field as observed in the experiments. Hence, a finite element method (FEM) model of the skin SC is also developed. The release of fentanyl through this model is compared with the available experimental results. Both experimental and simulated results of pore formation on application of an electric field and many folds' increase in drug flux are comparable. Once validated, the framework was used for the design of skin electroporation experiments (in silico) by changing the electric pulse parameters such as voltage, pulse duration, and number of pulses. This multiscale modeling framework provides valuable insight at the molecular and macroscopic levels to design the electroporation experiments. The framework can be utilized as a design tool for skin electroporation applications.
Topics: Diffusion; Electroporation; Epidermis; Humans; Molecular Dynamics Simulation; Skin
PubMed: 32475118
DOI: 10.1021/acs.langmuir.0c00500 -
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 -
Magnetic Resonance in Medicine Nov 2022While diffusion and T relaxation are intertwined, little or no correlation exists between diffusion and T relaxation of intracellular metabolites in the rodent brain, as...
PURPOSE
While diffusion and T relaxation are intertwined, little or no correlation exists between diffusion and T relaxation of intracellular metabolites in the rodent brain, as measured by diffusion-weighted MRS at different TEs. However, situation might be different for lactate, since it is present in both extracellular and intracellular spaces, which exhibit different diffusion properties and may also exhibit different T . Such a TE dependence would be crucial to account for when interpreting or modeling lactate diffusion. Here we propose to take advantage of a new diffusion sequence, where J-modulation of lactate is canceled even at long TE, thus retaining excellent signal, to assess potential T dependence on diffusion of lactate in the mouse brain.
METHODS
Using a frequency-selective diffusion-weighted spin-echo sequence that removes J-modulation at 1.3 ppm, thus preserving lactate signal even at long TE, we investigate the effect of TE between 50.9 and 110.9 ms (while keeping diffusion time constant) on apparent diffusivity and kurtosis in the mouse brain.
RESULTS
Regardless of the metabolites, no difference appears for the diffusion-weighted signal attenuation with increasing TE. For lactate, apparent diffusivity and kurtosis remain unchanged as TE increases.
CONCLUSION
No significant TE dependence of diffusivity and kurtosis is measured for lactate in the 50-110 ms TE range, confirming that potential T effects can be ignored when interpreting or modeling lactate diffusion.
Topics: Animals; Brain; Diffusion; Diffusion Magnetic Resonance Imaging; Lactic Acid; Mice
PubMed: 35906915
DOI: 10.1002/mrm.29395 -
Journal of the American Chemical Society Aug 2022
Editorial Summary of the Comment and Responses on "Following Molecular Mobility during Chemical Reactions: No Evidence for Active Propulsion" and "Molecular Diffusivity of Click Reaction Components: The Diffusion Enhancement Question".
Topics: Diffusion
PubMed: 35919984
DOI: 10.1021/jacs.2c05873 -
Journal of Chromatography. A Feb 2022The peak parking method was applied to evaluate the surface diffusivity D of polystyrenes dissolved in a THF/heptane mixture and transported through porous silica...
The peak parking method was applied to evaluate the surface diffusivity D of polystyrenes dissolved in a THF/heptane mixture and transported through porous silica materials with various morphologies. With this method, the overall effective diffusivity D is measured experimentally with coarse-grained models like Maxwell equation allowing one to infer the particle diffusivity D. Such particle diffusivity has two main contributions: in-pore diffusivity D and surface diffusivity D. The diffusion within the pores is determined experimentally using either non-adsorbing conditions or calculated from particle porosity, particle tortuosity, and hydrodynamic hindrance. The surface diffusion coefficient D is usually determined using models considering parallel diffusion in the pores and at the surface but this assumption is rather crude. In this paper, to address this problem, another approach is proposed using the Brownian motion of molecules in the pore space. These two approaches lead to similar equations relating the effective diffusion coefficient D, the in-pore diffusion D and surface diffusion D. The surface diffusion is analyzed as a function of the surface affinity of the probes considered here (polystyrenes of different molecular weights/lengths). Such surface affinity depends both on the probe chain length and surface chemistry of the host solid (the latter being characterized here through the silanol surface density). For short chain lengths, a non-monotonic change in the surface diffusion with affinity (i.e. retention factor) is observed in some cases. Yet, generally, as expected, surface diffusion decreases upon increasing the surface affinity. In contrast to short chain lengths, the longest chain lengths are less sensitive to the silanol surface density.
Topics: Diffusion; Molecular Weight; Polystyrenes; Porosity; Silicon Dioxide
PubMed: 35066296
DOI: 10.1016/j.chroma.2022.462823 -
Magnetic Resonance in Medicine Jan 2022Diffusion MRI provides a valuable tool for imaging tissue microstructure. However, due to the lack of related experimental methods and specially designed phantoms, no...
Assessment of the effects of mimicking tissue microstructural properties on apparent diffusion coefficient and apparent exchange rate in diffusion MRI via a series of specially designed phantoms.
PURPOSE
Diffusion MRI provides a valuable tool for imaging tissue microstructure. However, due to the lack of related experimental methods and specially designed phantoms, no experimental study has been conducted yet to quantitatively assess the effects of membrane permeability, intracellular volume fraction (IVF), and intracellular diffusivity on the apparent diffusion coefficient (ADC) obtained from diffusion weighted imaging (DWI), and the effects of membrane permeability on the apparent exchange rate (AXR) obtained from filter exchange imaging (FEXI).
METHODS
A series of phantoms with three adjustable parameters was designed to mimic tissue microstructural properties including membrane permeability, IVF, and intracellular diffusivity. Quantitative experiments were conducted to assess the effects of these properties on ADC and AXR. DWI scans were performed to obtain axial and radial ADC values. FEXI scans were performed to obtain AXR values.
RESULTS
Axial ADC values range from 1.148 μm /ms to 2.157 μm /ms, and radial ADC values range from 0.904 μm /ms to 2.067 μm /ms. Radial ADC decreased with a decrease in fiber permeability. Decreased axial and radial ADC values with increased intra-fiber volume fraction, and increased polyvinylpyrrolidone (PVP) concentration of the intra-fiber space were observed. AXR values range from 2.1 s to 4.9 s . AXR increases with fiber permeability.
CONCLUSION
The proposed phantoms can quantitatively evaluate the effects of mimicking tissue microstructural properties on ADC and AXR. This new phantom design provides a potential method for further understanding the biophysical mechanisms underlying the change in ADC and diffusion exchange.
Topics: Cell Membrane Permeability; Diffusion; Diffusion Magnetic Resonance Imaging; Phantoms, Imaging
PubMed: 34435698
DOI: 10.1002/mrm.28990 -
ELife Oct 2021Key processes of biological condensates are diffusion and material exchange with their environment. Experimentally, diffusive dynamics are typically probed via...
Key processes of biological condensates are diffusion and material exchange with their environment. Experimentally, diffusive dynamics are typically probed via fluorescent labels. However, to date, a physics-based, quantitative framework for the dynamics of labeled condensate components is lacking. Here, we derive the corresponding dynamic equations, building on the physics of phase separation, and quantitatively validate the related framework via experiments. We show that by using our framework, we can precisely determine diffusion coefficients inside liquid condensates via a spatio-temporal analysis of fluorescence recovery after photobleaching (FRAP) experiments. We showcase the accuracy and precision of our approach by considering space- and time-resolved data of protein condensates and two different polyelectrolyte-coacervate systems. Interestingly, our theory can also be used to determine a relationship between the diffusion coefficient in the dilute phase and the partition coefficient, without relying on fluorescence measurements in the dilute phase. This enables us to investigate the effect of salt addition on partitioning and bypasses recently described quenching artifacts in the dense phase. Our approach opens new avenues for theoretically describing molecule dynamics in condensates, measuring concentrations based on the dynamics of fluorescence intensities, and quantifying rates of biochemical reactions in liquid condensates.
Topics: Biomolecular Condensates; Diffusion; Fluorescence Recovery After Photobleaching; Polyelectrolytes; Proteins; Spatio-Temporal Analysis
PubMed: 34636323
DOI: 10.7554/eLife.68620 -
The Journal of Chemical Physics Jul 2021Single-particle tracking (SPT) experiments of lipids and membrane proteins provide a wealth of information about the properties of biomembranes. Careful analysis of SPT...
Single-particle tracking (SPT) experiments of lipids and membrane proteins provide a wealth of information about the properties of biomembranes. Careful analysis of SPT trajectories can reveal deviations from ideal Brownian behavior. Among others, this includes confinement effects and anomalous diffusion, which are manifestations of both the nanoscale structure of the underlying membrane and the structure of the diffuser. With the rapid increase in temporal and spatial resolution of experimental methods, a new aspect of the motion of the particle, namely, anisotropic diffusion, might become relevant. This aspect that so far received only little attention is the anisotropy of the diffusive motion and may soon provide an additional proxy to the structure and topology of biomembranes. Unfortunately, the theoretical framework for detecting and interpreting anisotropy effects is currently scattered and incomplete. Here, we provide a computational method to evaluate the degree of anisotropy directly from molecular dynamics simulations and also point out a way to compare the obtained results with those available from SPT experiments. In order to probe the effects of anisotropic diffusion, we performed coarse-grained molecular dynamics simulations of peripheral and integral membrane proteins in flat and curved bilayers. In agreement with the theoretical basis, our computational results indicate that anisotropy can persist up to the rotational relaxation time [τ=(2D)], after which isotropic diffusion is observed. Moreover, the underlying topology of the membrane bilayer can couple with the geometry of the particle, thus extending the spatiotemporal domain over which this type of motion can be detected.
Topics: Anisotropy; Diffusion; Membrane Proteins; Molecular Dynamics Simulation
PubMed: 34241397
DOI: 10.1063/5.0054973 -
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