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Scientific Reports Jul 2023This paper deals with the mathematical modeling of bacterial co-aggregation and its numerical implementation in a FEM framework. Since the concept of co-aggregation...
This paper deals with the mathematical modeling of bacterial co-aggregation and its numerical implementation in a FEM framework. Since the concept of co-aggregation refers to the physical binding between cells of different microbial species, a system composed of two species is considered in the modeling framework. The extension of the model to an arbitrary number of species is straightforward. In addition to two-species (multi-species growth) dynamics, the transport of a nutritional substance and the extent of co-aggregation are introduced into the model as the third and fourth primary variables. A phase-field modeling approach is employed to describe the co-aggregation between the two species. The mathematical model is three-dimensional and fully based on the continuum description of the problem without any need for discrete agents which are the key elements of the individual-based modeling approach. It is shown that the use of a phase-field-based model is equivalent to a particular form of classical diffusion-reaction systems. Unlike the so-called mixture models, the evolution of each component of the multi-species system is captured thanks to the inherent capability of phase-field modeling in treating systems consisting of distinct multi-phases. The details of numerical implementation in a FEM framework are also presented. Indeed, a new multi-field user element is developed and implemented in ANSYS for this multiphysics problem. Predictions of the model are compared with the experimental observations. By that, the versatility and applicability of the model and the numerical tool are well established.
Topics: Diffusion; Physical Examination
PubMed: 37481628
DOI: 10.1038/s41598-023-38806-2 -
Biophysical Journal Jun 2021Cell migration, which can be significantly affected by intracellular signaling pathways and extracellular matrix, plays a crucial role in many physiological and...
Cell migration, which can be significantly affected by intracellular signaling pathways and extracellular matrix, plays a crucial role in many physiological and pathological processes. Cell migration is typically modeled as a persistent random walk, which depends on two critical motility parameters, i.e., migration speed and persistence time. It is generally very challenging to efficiently and accurately quantify the migration dynamics from noisy experimental data. Here, we introduce the normalized Shannon entropy (SE) based on the FPS of cellular velocity autocovariance function to quantify migration dynamics. The SE introduced here possesses a similar physical interpretation as the Gibbs entropy for thermal systems in that SE naturally reflects the degree of order or randomness of cellular migration, attaining the maximal value of unity for purely diffusive migration (i.e., SE = 1 for the most "random" dynamics) and the minimal value of 0 for purely ballistic dynamics (i.e., SE = 0 for the most "ordered" dynamics). We also find that SE is strongly correlated with the migration persistence but is less sensitive to the migration speed. Moreover, we introduce the time-varying SE based on the WPS of cellular dynamics and demonstrate its superior utility to characterize the time-dependent persistence of cell migration, which typically results from complex and time-varying intra- or extracellular mechanisms. We employ our approach to analyze experimental data of in vitro cell migration regulated by distinct intracellular and extracellular mechanisms, exhibiting a rich spectrum of dynamic characteristics. Our analysis indicates that the SE and wavelet transform (i.e., SE-based approach) offers a simple and efficient tool to quantify cell migration dynamics in complex microenvironment.
Topics: Cell Movement; Diffusion; Entropy; Extracellular Matrix
PubMed: 33940024
DOI: 10.1016/j.bpj.2021.04.026 -
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 -
Nanotechnology Oct 2019Nanofluidic devices have channel dimensions which come to within one order of magnitude of the Debye length of common aqueous solutions. Conventionally, external driving...
Nanofluidic devices have channel dimensions which come to within one order of magnitude of the Debye length of common aqueous solutions. Conventionally, external driving is used to create concentration polarization of ions and biomolecules in nanofluidic devices. Here we show that long-range ionic strength gradients intrinsic to all nanofluidic devices, even at equilibrium, also drive a drift of macromolecules. To demonstrate the effect, we confine long DNA to straight nanochannels of constant, rectangular cross-section (100 × 100 nm) which are connected to large microfluidic reservoirs. The motion of DNA is observed in absence of any driving. We find that at low ionic strengths, molecules in nanochannels migrate toward the nano-micro interface, while they are undergoing purely diffusive motion in high salt. Using numerical models, we demonstrate that the motion is consistent with the ionic strength gradient at the micro-nano interface even at equilibrium, and that the dominant cause of the drift is diffusophoresis.
Topics: DNA; Diffusion; Ions; Macromolecular Substances; Microfluidics; Nanotechnology; Osmolar Concentration
PubMed: 31300622
DOI: 10.1088/1361-6528/ab31f7 -
Journal of the Royal Society, Interface Nov 2022Budding allows virus replication and macromolecular secretion in cells through the formation of a membrane protrusion (bud) that evolves into an envelope. The largest...
Budding allows virus replication and macromolecular secretion in cells through the formation of a membrane protrusion (bud) that evolves into an envelope. The largest energetic barrier to bud formation is membrane deflection and is trespassed primarily thanks to nucleocapsid-membrane adhesion. Transmembrane proteins (TPs), which later form the virus ligands, are the main promotors of adhesion and can accommodate membrane bending thanks to an induced spontaneous curvature. Adhesive TPs must diffuse across the membrane from remote regions to gather on the bud surface, thus, diffusivity controls the kinetics. This paper proposes a simple model to describe diffusion-mediated budding unravelling important size limitations and size-dependent kinetics. The predicted optimal virion radius, giving the fastest budding, is validated against experiments for coronavirus, HIV, flu and hepatitis. Assuming exponential replication of virions and hereditary size, the model can predict the size distribution of a virus population. This is verified against experiments for SARS-CoV-2. All the above comparisons rely on the premise that budding poses the tightest size constraint. This is true in most cases, as demonstrated in this paper, where the proposed model is extended to describe virus infection via receptor- and clathrin-mediated endocytosis, and via membrane fusion.
Topics: Humans; SARS-CoV-2; COVID-19; Virus Replication; Virion; Diffusion
PubMed: 36321373
DOI: 10.1098/rsif.2022.0525 -
Science Advances Jun 2023Two influential concepts in tissue patterning are Wolpert's positional information and Turing's self-organized reaction-diffusion (RD). The latter establishes the...
Two influential concepts in tissue patterning are Wolpert's positional information and Turing's self-organized reaction-diffusion (RD). The latter establishes the patterning of hair and feathers. Here, our morphological, genetic, and functional-by CRISPR-Cas9-mediated gene disruption-characterization of wild-type versus "scaleless" snakes reveals that the near-perfect hexagonal pattern of snake scales is established through interactions between RD in the skin and somitic positional information. First, we show that ventral scale development is guided by hypaxial somites and, second, that ventral scales and epaxial somites guide the sequential RD patterning of the dorsolateral scales. The RD intrinsic length scale evolved to match somite periodicity, ensuring the alignment of ribs and scales, both of which play a critical role in snake locomotion.
Topics: Animals; Somites; Diffusion; Feathers; Hair; Locomotion
PubMed: 37315141
DOI: 10.1126/sciadv.adf8834 -
Magnetic Resonance in Medicine Jul 2022Relationships between diffusion-weighted MRI signals and hepatocyte microstructure were investigated to inform liver diffusion MRI modeling, focusing on the following...
PURPOSE
Relationships between diffusion-weighted MRI signals and hepatocyte microstructure were investigated to inform liver diffusion MRI modeling, focusing on the following question: Can cell size and diffusivity be estimated at fixed diffusion time, realistic SNR, and negligible contribution from extracellular/extravascular water and exchange?
METHODS
Monte Carlo simulations were performed within synthetic hepatocytes for varying cell size/diffusivity / , and clinical protocols (single diffusion encoding; maximum b-value: {1000, 1500, 2000} s/mm ; 5 unique gradient duration/separation pairs; SNR = { , 100, 80, 40, 20}), accounting for heterogeneity in and perfusion contamination. Diffusion ( ) and kurtosis ( ) coefficients were calculated, and relationships between and were visualized. Functions mapping to were computed to predict unseen values, tested for their ability to classify discrete cell-size contrasts, and deployed on 9.4T ex vivo MRI-histology data of fixed mouse livers RESULTS: Relationships between and are complex and depend on the diffusion encoding. Functions mapping to captures salient characteristics of and dependencies. Mappings are not always accurate, but they enable just under 70% accuracy in a three-class cell-size classification task (for SNR = 20, = 1500 s/mm , = 20 ms, and = 75 ms). MRI detects cell-size contrasts in the mouse livers that are confirmed by histology, but overestimates the largest cell sizes.
CONCLUSION
Salient information about liver cell size and diffusivity may be retrieved from minimal diffusion encodings at fixed diffusion time, in experimental conditions and pathological scenarios for which extracellular, extravascular water and exchange are negligible.
Topics: Animals; Contrast Media; Diffusion; Diffusion Magnetic Resonance Imaging; Hepatocytes; Magnetic Resonance Imaging; Mice; Water
PubMed: 35181943
DOI: 10.1002/mrm.29174 -
Magnetic Resonance in Medicine Sep 2020To investigate diffusion-time dependency of diffusional kurtosis in the mouse brain using pulsed-gradient spin-echo (PGSE) and oscillating-gradient spin-echo (OGSE)...
PURPOSE
To investigate diffusion-time dependency of diffusional kurtosis in the mouse brain using pulsed-gradient spin-echo (PGSE) and oscillating-gradient spin-echo (OGSE) sequences.
METHODS
3D PGSE and OGSE kurtosis tensor data were acquired from ex vivo brains of adult, cuprizone-treated, and age-matched control mice with diffusion-time (t ) ~ 20 ms and frequency (f) = 70 Hz, respectively. Further, 2D acquisitions were performed at multiple times/frequencies ranging from f = 140 Hz to t = 30 ms with b-values up to 4000 s/mm . Monte Carlo simulations were used to investigate the coupled effects of varying restriction size and permeability on time/frequency-dependence of kurtosis with both diffusion-encoding schemes. Simulations and experiments were further performed to investigate the effect of varying number of cycles in OGSE waveforms.
RESULTS
Kurtosis and diffusivity maps exhibited significant region-specific changes with diffusion time/frequency across both gray and white matter areas. PGSE- and OGSE-based kurtosis maps showed reversed contrast between gray matter regions in the cerebellar and cerebral cortex. Localized time/frequency-dependent changes in kurtosis tensor metrics were found in the splenium of the corpus callosum in cuprizone-treated mouse brains, corresponding to regional demyelination seen with histological assessment. Monte Carlo simulations showed that kurtosis estimates with pulsed- and oscillating-gradient waveforms differ in their sensitivity to exchange. Both simulations and experiments showed dependence of kurtosis on number of cycles in OGSE waveforms for non-zero permeability.
CONCLUSION
The results show significant time/frequency-dependency of diffusional kurtosis in the mouse brain, which can provide sensitivity to probe intrinsic cellular heterogeneity and pathological alterations in gray and white matter.
Topics: Animals; Brain; Corpus Callosum; Diffusion; Diffusion Magnetic Resonance Imaging; Mice; White Matter
PubMed: 32022313
DOI: 10.1002/mrm.28189 -
Biophysical Journal Jun 2020Protein diffusion in lower-dimensional spaces is used for various cellular functions. For example, sliding on DNA is essential for proteins searching for their target...
Protein diffusion in lower-dimensional spaces is used for various cellular functions. For example, sliding on DNA is essential for proteins searching for their target sites, and protein diffusion on microtubules is important for proper cell division and neuronal development. On the one hand, these linear diffusion processes are mediated by long-range electrostatic interactions between positively charged proteins and negatively charged biopolymers and have similar characteristic diffusion coefficients. On the other hand, DNA and microtubules have different structural properties. Here, using computational approaches, we studied the mechanism of protein diffusion along DNA and microtubules by exploring the diffusion of both protein types on both biopolymers. We found that DNA-binding and microtubule-binding proteins can diffuse on each other's substrates; however, the adopted diffusion mechanism depends on the molecular properties of the diffusing proteins and the biopolymers. On the protein side, only DNA-binding proteins can perform rotation-coupled diffusion along DNA, with this being due to their higher net charge and its spatial organization at the DNA recognition helix. By contrast, the lower net charge on microtubule-binding proteins enables them to diffuse more quickly than DNA-binding proteins on both biopolymers. On the biopolymer side, microtubules possess intrinsically disordered, negatively charged C-terminal tails that interact with microtubule-binding proteins, thus supporting their diffusion. Thus, although both DNA-binding and microtubule-binding proteins can diffuse on the negatively charged biopolymers, the unique molecular features of the biopolymers and of their natural substrates are essential for function.
Topics: Biopolymers; DNA; Diffusion; Microtubules; Protein Binding; Static Electricity
PubMed: 32492371
DOI: 10.1016/j.bpj.2020.05.004 -
Angewandte Chemie (International Ed. in... Mar 2022Numerous key biological processes rely on the concept of multivalency, where ligands achieve stable binding only upon engaging multiple receptors. These processes, like... (Review)
Review
Numerous key biological processes rely on the concept of multivalency, where ligands achieve stable binding only upon engaging multiple receptors. These processes, like viral entry or immune synapse formation, occur on the diffusive cellular membrane. One crucial, yet underexplored aspect of multivalent binding is the mobility of coupled receptors. Here, we discuss the consequences of mobility in multivalent processes from four perspectives: (I) The facilitation of receptor recruitment by the multivalent ligand due to their diffusivity prior to binding. (II) The effects of receptor preassembly, which allows their local accumulation. (III) The consequences of changes in mobility upon the formation of receptor/ligand complex. (IV) The changes in the diffusivity of lipid environment surrounding engaged receptors. We demonstrate how understanding mobility is essential for fully unravelling the principles of multivalent membrane processes, leading to further development in studies on receptor interactions, and guide the design of new generations of multivalent ligands.
Topics: Cell Membrane; Diffusion; Ligands; Lipids
PubMed: 34982497
DOI: 10.1002/anie.202114167