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Bulletin of Mathematical Biology Mar 2022We consider a continuum mathematical model of biological tissue formation inspired by recent experiments describing thin tissue growth in 3D-printed bioscaffolds. The...
We consider a continuum mathematical model of biological tissue formation inspired by recent experiments describing thin tissue growth in 3D-printed bioscaffolds. The continuum model, which we call the substrate model, involves a partial differential equation describing the density of tissue, [Formula: see text] that is coupled to the concentration of an immobile extracellular substrate, [Formula: see text]. Cell migration is modelled with a nonlinear diffusion term, where the diffusive flux is proportional to [Formula: see text], while a logistic growth term models cell proliferation. The extracellular substrate [Formula: see text] is produced by cells and undergoes linear decay. Preliminary numerical simulations show that this mathematical model is able to recapitulate key features of recent tissue growth experiments, including the formation of sharp fronts. To provide a deeper understanding of the model we analyse travelling wave solutions of the substrate model, showing that the model supports both sharp-fronted travelling wave solutions that move with a minimum wave speed, [Formula: see text], as well as smooth-fronted travelling wave solutions that move with a faster travelling wave speed, [Formula: see text]. We provide a geometric interpretation that explains the difference between smooth and sharp-fronted travelling wave solutions that is based on a slow manifold reduction of the desingularised three-dimensional phase space. In addition, we also develop and test a series of useful approximations that describe the shape of the travelling wave solutions in various limits. These approximations apply to both the sharp-fronted and smooth-fronted travelling wave solutions. Software to implement all calculations is available at GitHub .
Topics: Cell Movement; Diffusion; Mathematical Concepts; Models, Biological
PubMed: 35237899
DOI: 10.1007/s11538-022-01005-7 -
Methods in Enzymology 2021Biomolecular condensates are membrane-less sub-cellular compartments that perform a plethora of important functions in signaling and storage. The material properties of...
Biomolecular condensates are membrane-less sub-cellular compartments that perform a plethora of important functions in signaling and storage. The material properties of biomolecular condensates such as viscosity, surface tension, viscoelasticity, and macromolecular diffusion play important roles in regulating their biological functions. Aberrations in these properties have been implicated in various neurodegenerative disorders and certain types of cancer. Unraveling the molecular driving forces that control the fluid structure and dynamics of biomolecular condensates across different length- and time-scales necessitates the application of innovative biophysical methodologies. In this chapter, we discuss major experimental techniques that are widely used to study the material states and dynamics of biomolecular condensates as well as their practical and conceptual limitations. We end this chapter with a discussion on more advanced tools that are currently emerging to address the complex fluid dynamics of these condensates.
Topics: Diffusion; Macromolecular Substances; Viscosity
PubMed: 33453924
DOI: 10.1016/bs.mie.2020.06.009 -
Physica Medica : PM : An International... Nov 2022The aim of this study was to perform a quantitative quality assurance of diffusion-weighted MRI to assess the variability of the mean apparent diffusion coefficient...
PURPOSE
The aim of this study was to perform a quantitative quality assurance of diffusion-weighted MRI to assess the variability of the mean apparent diffusion coefficient (ADC) and other radiomic features across the scanners involved in the REGINA trial.
MATERIALS AND METHODS
The NIST/QIBA diffusion phantom was acquired on six 3 T scanners from five centres with a rectum-specific diffusion protocol. All sequences were repeated in each scan session without moving the phantom from the table. Linear interpolation to two isotropic voxel spacing (0.9 and 4 mm) was performed as well as the ComBat feature harmonisation method between scanners. The absolute accuracy error was evaluated for the mean ADC. Repeatability and reproducibility within-subject coefficients of variation (wCV) were computed for 142 radiomic features.
RESULTS
For the mean ADC, accuracy error ranged between 0.1 % and 8.5 %, repeatability was <1 % and reproducibility was <3 % for diffusivity range between 0.4 and 1.1x10mm/s. For the other radiomic features, wCV was below 10 % for 24 % and 15 % features for repeatability with resampling 0.9 mm and 4 mm, respectively, and 13 % and 11 % feature for reproducibility. ComBat method could improve significantly the wCV compared to reproducibility without ComBat (p-value < 0.001) but variation was still high for most of the features.
CONCLUSION
Our study provided the first investigation of feature selection for development of robust predictive models in the REGINA trial, demonstrating the added value of such a quality assurance process to select conventional and radiomic features in prospective multicentre trials.
Topics: Reproducibility of Results; Prospective Studies; Diffusion Magnetic Resonance Imaging; Phantoms, Imaging; Diffusion
PubMed: 36308999
DOI: 10.1016/j.ejmp.2022.10.009 -
Journal of the Royal Society, Interface Mar 2021A recent experiment (Sadoon AA, Wang Y. 2018 , 042411. (doi:10.1103/PhysRevE.98.042411)) has revealed that nucleoid-associated proteins (i.e. DNA-binding proteins)...
A recent experiment (Sadoon AA, Wang Y. 2018 , 042411. (doi:10.1103/PhysRevE.98.042411)) has revealed that nucleoid-associated proteins (i.e. DNA-binding proteins) exhibit highly heterogeneous diffusion processes in bacteria where not only the diffusion constant but also the anomalous diffusion exponent fluctuates for the various proteins. The distribution of displacements of such proteins is observed to take a -Gaussian form, which decays as a power law. Here, a statistical model is developed for the diffusive motion of the proteins within the bacterium, based on a superstatistics with two variables. This model hierarchically takes into account the joint fluctuations of both the anomalous diffusion exponents and the diffusion constants. A fractional Brownian motion is discussed as a possible local model. Good agreement with the experimental data is obtained.
Topics: Bacteria; Bacterial Proteins; Diffusion; Models, Statistical; Motion
PubMed: 33653112
DOI: 10.1098/rsif.2020.0927 -
Lab on a Chip Sep 2019Hydrogels allow for controlling the diffusion rate and amount of solute according to the hydrogel network and thus have found many applications in drug delivery,...
Hydrogels allow for controlling the diffusion rate and amount of solute according to the hydrogel network and thus have found many applications in drug delivery, biomaterials, toxicology, and tissue engineering. This paper describes a 3D-printed microfluidic chip for the straightforward partitioning of hydrogel barriers between microchannels. We use a previously-reported 3-channel architecture whereby the middle channel is filled with a hydrogel - acting like a porous barrier for diffusive transport - and the two side channels act as sink and source; the middle channel communicates with the side channels via orthogonal, small capillary channels that are also responsible for partitioning the hydrogel during filling. Our 3D-printed microfluidic chip is simple to fabricate by stereolithography (SL), inexpensive, reproducible, and convenient, so it is more adequate for transport studies than a microchip fabricated by photolithographic procedures. The chip was fabricated in a resin made of poly(ethylene glycol) diacrylate (PEG-DA) (MW = 258) (PEG-DA-258). The SL process allowed us to print high aspect ratio (37 : 1) capillary channels (27 μm-width and 1 mm-height) and enable the trapping of liquid-phase hydrogels in the hydrogel barrier middle channel. We studied the permeability of hydrogel barriers made of PEG-DA (MW = 700) (PEG-DA-700, 10% polymer content by wt. in water) - as a model of photopolymerizable barriers - and agarose (MW = 120 000, 2% polymer content by wt. in water) - as a model of thermally-gelled barriers. We measured the diffusion of fluorescein, 10k-dextran-Alexa 680 and BSA-Texas Red through these barriers. Fluorescein diffusion was observed through both 10% PEG-DA-700 and 2% agarose barriers while 10k-dextran-Alexa 680 and BSA-Texas Red diffused appreciably only through the 2% agarose hydrogel barrier. Our microfluidic chip facilitates the tuning of such barriers simply by altering the hydrogel materials. The straightforward trapping of selective barriers in 3D-printed microchannels should find wide applicability in drug delivery, tissue engineering, cell separation, and organ-on-a-chip platforms.
Topics: Diffusion; Hydrogels; Microfluidic Analytical Techniques; Polyethylene Glycols; Printing, Three-Dimensional
PubMed: 31502633
DOI: 10.1039/c9lc00535h -
Proceedings of the National Academy of... Sep 2022Understanding the physical principle that governs the stimuli-induced swelling and shrinking kinetics of hydrogels is indispensable for their applications. Here, we show...
Understanding the physical principle that governs the stimuli-induced swelling and shrinking kinetics of hydrogels is indispensable for their applications. Here, we show that the shrinking and swelling kinetics of self-healing hydrogels could be intrinsically asymmetric. The structure frustration, formed by the large difference in the heat and solvent diffusions, remarkably slows down the shrinking kinetics. The plateau modulus of viscoelastic gels is found to be a key parameter governing the formation of structure frustration and, in turn, the asymmetric swelling and shrinking kinetics. This work provides fundamental understandings on the temperature-triggered transient structure formation in self-healing hydrogels. Our findings will find broad use in diverse applications of self-healing hydrogels, where cooperative diffusion of water and gel network is involved. Our findings should also give insight into the molecular diffusion in biological systems that possess macromolecular crowding environments similar to self-healing hydrogels.
Topics: Diffusion; Hydrogels; Kinetics; Temperature; Water
PubMed: 36037384
DOI: 10.1073/pnas.2207422119 -
International Journal of Molecular... Sep 2022Self-balancing diffusion is a theoretical concept that restricts the introduction of extents of reactions. This concept is analyzed in detail for general mass- and...
Self-balancing diffusion is a theoretical concept that restricts the introduction of extents of reactions. This concept is analyzed in detail for general mass- and molar-based balances of reaction-diffusion mixtures, in relation to non-self-balancing cases, and with respect to its practical consequences. Self-balancing is a mathematical restriction on the divergences of diffusion fluxes. Fulfilling this condition enables the proper introduction of the extents of (independent) reactions that reduce the number of independent variables in thermodynamic descriptions. A note on a recent generalization of the concept of reaction and diffusion extents is also included. Even in the case of self-balancing diffusion, such extents do not directly replace reaction rates. Concentration changes caused by reactions (not by diffusion) are properly described by rates of independent reactions, which are instantaneous descriptors. If an overall descriptor is needed, the traditional extents of reactions can be used, bearing in mind that they include diffusion-caused changes. On the other hand, rates of independent reactions integrated with respect to time provide another overall, but reaction-only-related descriptor.
Topics: Diffusion; Kinetics; Thermodynamics
PubMed: 36142429
DOI: 10.3390/ijms231810511 -
Redox Biology Apr 2022Hydrogen peroxide is a major redox signaling molecule underlying a novel paradigm of cell function and communication. A role for HO as an intercellular signaling...
Hydrogen peroxide is a major redox signaling molecule underlying a novel paradigm of cell function and communication. A role for HO as an intercellular signaling molecule and neuromodulator in the brain has become increasingly apparent, with evidence showing this biological oxidant to regulate neuronal polarity, connectivity, synaptic transmission and tuning of neuronal networks. This notion is supported by its ability to diffuse in the extracellular space, from source of production to target. It is, thus, crucial to understand extracellular HO concentration dynamics in the living brain and the factors which shape its diffusion pattern and half-life. To address this issue, we have used a novel microsensor to measure HO concentration dynamics in the brain extracellular matrix both in an ex vivo model using rodent brain slices and in vivo. We found that exogenously applied HO is removed from the extracellular space with an average half-life of t = 2.2 s in vivo. We determined the in vivo effective diffusion coefficient of HO to be D* = 2.5 × 10 cm s. This allows it to diffuse over 100 μm in the extracellular space within its half-life. Considering this, we can tentatively place HO within the class of volume neurotransmitters, connecting all cell types within the complex network of brain tissue, regardless of whether they are physically connected. These quantitative details of HO diffusion and half-life in the brain allow us to interpret the physiology of the redox signal and lay the pavement to then address dysregulation in redox homeostasis associated with disease processes.
Topics: Brain; Diffusion; Hydrogen Peroxide; Oxidation-Reduction; Signal Transduction
PubMed: 35101799
DOI: 10.1016/j.redox.2022.102250 -
Biophysical Journal May 2020Single-particle tracking experiments have measured escape times of DNA-binding species diffusing in living cells: CRISPR-Cas9, TetR, and LacI. The observed distribution...
Single-particle tracking experiments have measured escape times of DNA-binding species diffusing in living cells: CRISPR-Cas9, TetR, and LacI. The observed distribution is a truncated power law. Working backward from the experimental results, the observed distribution appears inconsistent with a Gaussian distribution of binding energies. Working forward, the observed distribution leads to transient anomalous subdiffusion, in which diffusion is anomalous at short times and normal at long times, here only mildly anomalous. Monte Carlo simulations are used to characterize the time-dependent diffusion coefficient D(t) in terms of the anomalous exponent α, the crossover time t, and the limits D(0) and D(∞) and to relate these quantities to the escape time distribution. The simplest interpretations identify the escape time as the actual binding time to DNA or the period of one-dimensional diffusion on DNA in the standard model combining one-dimensional and three-dimensional search, but a more complicated interpretation may be required. The model has several implications for cell biophysics. 1) The initial anomalous regime represents the search of the DNA-binding species for its target DNA sequence. 2) Non-target DNA sites have a significant effect on search kinetics. False positives in bioinformatic searches of the genome are potentially rate-determining in vivo. For simple binding, the search would be speeded if false-positive sequences were eliminated from the genome. 3) Both binding and obstruction affect diffusion. Obstruction ought to be measured directly, using as the primary probe the DNA-binding species with the binding site inactivated and eGFP as a calibration standard among laboratories and cell types. 4) Overexpression of the DNA-binding species reduces anomalous subdiffusion because the deepest binding sites are occupied and unavailable. 5) The model provides a coarse-grained phenomenological description of diffusion of a DNA-binding species, useful in larger-scale modeling of kinetics, FCS, and FRAP.
Topics: Biophysical Phenomena; Cell Nucleus; Diffusion; Kinetics; Monte Carlo Method
PubMed: 32294478
DOI: 10.1016/j.bpj.2020.03.015 -
ACS Biomaterials Science & Engineering Sep 2021Synthetic hydrogels formed from poly(ethylene glycol) (PEG) are widely used to study how cells interact with their extracellular matrix. These -like 3D environments...
Synthetic hydrogels formed from poly(ethylene glycol) (PEG) are widely used to study how cells interact with their extracellular matrix. These -like 3D environments provide a basis for tissue engineering and cell therapies but also for research into fundamental biological questions and disease modeling. The physical properties of PEG hydrogels can be modulated to provide mechanical cues to encapsulated cells; however, the impact of changing hydrogel stiffness on the diffusivity of solutes to and from encapsulated cells has received only limited attention. This is particularly true in selectively cross-linked "tetra-PEG" hydrogels, whose design limits network inhomogeneities. Here, we used a combination of theoretical calculations, predictive modeling, and experimental measurements of hydrogel swelling, rheological behavior, and diffusion kinetics to characterize tetra-PEG hydrogels' permissiveness to the diffusion of molecules of biologically relevant size as we changed polymer concentration, and thus hydrogel mechanical strength. Our models predict that hydrogel mesh size has little effect on the diffusivity of model molecules and instead predicts that diffusion rates are more highly dependent on solute size. Indeed, our model predicts that changes in hydrogel mesh size only begin to have a non-negligible impact on the concentration of a solute that diffuses out of hydrogels for the smallest mesh sizes and largest diffusing solutes. Experimental measurements characterizing the diffusion of fluorescein isothiocyanate (FITC)-labeled dextran molecules of known size aligned well with modeling predictions and suggest that doubling the polymer concentration from 2.5% (w/v) to 5% produces stiffer gels with faster gelling kinetics without affecting the diffusivity of solutes of biologically relevant size but that 10% hydrogels can slow their diffusion. Our findings provide confidence that the stiffness of tetra-PEG hydrogels can be modulated over a physiological range without significantly impacting the transport rates of solutes to and from encapsulated cells.
Topics: Biocompatible Materials; Diffusion; Hydrogels; Polyethylene Glycols; Tissue Engineering
PubMed: 34151570
DOI: 10.1021/acsbiomaterials.0c01723