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Journal of Mathematical Biology Jul 2023We examine the effect of human mobility on disease prevalence by studying the dependence of the total infected population at endemic equilibria with respect to...
We examine the effect of human mobility on disease prevalence by studying the dependence of the total infected population at endemic equilibria with respect to population diffusion rates of a diffusive epidemic model. For small diffusion rates, our results indicate that the total infected population size is strictly decreasing with respect to the ratio of the diffusion rate of the infected population over that of the susceptible population. Moreover, when the disease local reproductive function is spatially heterogeneous, we found that: (i) for large diffusion rate of the infected population, the total infected population size is strictly maximized at large diffusion rate of the susceptible population when the recovery rate is spatially homogeneous, while it is strictly maximized at intermediate diffusion rate of the susceptible population when the difference of the transmission and recovery rates are spatially homogeneous; (ii) for large diffusion rate of the susceptible population, the total infected population size is strictly maximized at intermediate diffusion rate of the infected population when the recovery rate is spatially homogeneous, while it is strictly minimized at large diffusion rate of the infected population when the difference of the transmission and recovery rates is spatially homogeneous. Numerical simulations are provided to complement the theoretical results. Our studies may provide some insight into the impact of human mobility on disease outbreaks and the severity of epidemics.
Topics: Humans; Prevalence; Population Density; Diffusion; Disease Outbreaks; Epidemics
PubMed: 37392280
DOI: 10.1007/s00285-023-01953-1 -
The Journal of Physical Chemistry. B Jul 2021We present here a model for multivalent diffusive transport whereby a central point-like hub is coupled to multiple feet, which bind to complementary sites on a...
We present here a model for multivalent diffusive transport whereby a central point-like hub is coupled to multiple feet, which bind to complementary sites on a two-dimensional landscape. The available number of binding interactions is dependent on the number of feet (multivalency) and on their allowed distance from the central hub (span). Using Monte Carlo simulations that implement the Gillespie algorithm, we simulate multivalent diffusive transport processes for 100 distinct walker designs. Informed by our simulation results, we derive an analytical expression for the diffusion coefficient of a general multivalent diffusive process as a function of multivalency, span, and dissociation constant . Our findings can be used to guide the experimental design of multivalent transporters, in particular, providing insight into how to overcome trade-offs between diffusivity and processivity.
Topics: Algorithms; Computer Simulation; Diffusion; Monte Carlo Method
PubMed: 34151560
DOI: 10.1021/acs.jpcb.1c02821 -
The Journal of General Physiology Oct 2023Osmosis is an important force in all living organisms, yet the molecular basis of osmosis is widely misunderstood as arising from diffusion of water across a membrane...
Osmosis is an important force in all living organisms, yet the molecular basis of osmosis is widely misunderstood as arising from diffusion of water across a membrane separating solutions of differing osmolarities, and hence different water concentrations. In 1923, Peter Debye proposed a physical model for a semipermeable membrane emphasizing the repulsive forces between solute molecules and membrane that prevent the solute from entering the membrane. His work was hardly noticed at the time and slipped out of view. We show that Debye's analysis of van 't Hoff's law for osmotic equilibrium also provides a consistent and plausible mechanism for osmotic flow. A difference in osmolyte concentrations in solutions separated by a semipermeable membrane leads to different pressures at the two water-membrane interfaces because the total repulsive force between solute molecules and the membrane is different at the two interfaces. Water is therefore driven through the membrane for exactly the same reason that pure water flows in response to an imposed hydrostatic pressure difference. In this paper, we present the Debye model in both equilibrium and flow conditions. We point out its applicability regardless of the nature of the membrane with examples ranging from the predominantly convective flow of water through synthetic membranes and capillary walls to the purely diffusive flow of independent water molecules through a lipid bilayer and the flow of a single-file column of water molecules in narrow protein channels.
Topics: Diffusion; Lipid Bilayers; Osmosis; Pressure; Water
PubMed: 37624228
DOI: 10.1085/jgp.202313332 -
Magnetic Resonance in Medicine Jun 2020To demonstrate how triple diffusion encoding (TDE) MRI can be applied to separately estimate the intra-axonal and extra-axonal diffusion tensors in white matter (WM).
PURPOSE
To demonstrate how triple diffusion encoding (TDE) MRI can be applied to separately estimate the intra-axonal and extra-axonal diffusion tensors in white matter (WM).
METHODS
Using a TDE pulse sequence with an axially symmetric b-matrix, diffusion MRI data were acquired at 3T for 3 healthy adults with an axial b-value of 4000 s/mm , a radial b-value of 307 s/mm , and 64 diffusion encoding directions. This acquisition was then repeated with the radial b-value set to 0. A previously proposed theory was applied to these data in order to estimate the intra-axonal diffusivity and axonal water fraction for each WM voxel. Conventional single diffusion encoding data were also obtained with b-values of 1000 and 2000 s/mm , which provided additional information sufficient for determining both the intra-axonal and extra-axonal diffusion tensors.
RESULTS
From the TDE data, the average intra-axonal diffusivity in WM was found to be 2.24 ± 0.18 µm /ms, and the average axonal water fraction was found to be 0.60 ± 0.11. From the 2 diffusion tensors, average WM values were estimated for several compartment-specific diffusion parameters. In particular, the extra-axonal mean diffusivity was 1.09 ± 0.19 µm /ms, the intra-axonal fractional anisotropy was 0.50 ± 0.14, and the extra-axonal fractional anisotropy was 0.23 ± 0.13.
CONCLUSION
By using a simple TDE pulse sequence with an axially symmetric b-matrix, the diffusion tensors for the intra-axonal and extra-axonal spaces can be separately estimated in adult WM. This allows one to determine compartment-specific diffusion properties for these 2 water pools.
Topics: Adult; Anisotropy; Axons; Diffusion; Diffusion Magnetic Resonance Imaging; Diffusion Tensor Imaging; Humans; White Matter
PubMed: 31763730
DOI: 10.1002/mrm.28084 -
International Journal of Molecular... Nov 2023Using the framework of a continuous diffusion model based on the Smoluchowski equation, we analyze particle dynamics in the confinement of a transmembrane nanopore. We... (Review)
Review
Using the framework of a continuous diffusion model based on the Smoluchowski equation, we analyze particle dynamics in the confinement of a transmembrane nanopore. We briefly review existing analytical results to highlight consequences of interactions between the channel nanopore and the translocating particles. These interactions are described within a minimalistic approach by lumping together multiple physical forces acting on the particle in the pore into a one-dimensional potential of mean force. Such radical simplification allows us to obtain transparent analytical results, often in a simple algebraic form. While most of our findings are quite intuitive, some of them may seem unexpected and even surprising at first glance. The focus is on five examples: (i) attractive interactions between the particles and the nanopore create a potential well and thus cause the particles to spend more time in the pore but, nevertheless, increase their net flux; (ii) if the potential well-describing particle-pore interaction occupies only a part of the pore length, the mean translocation time is a non-monotonic function of the well length, first increasing and then decreasing with the length; (iii) when a rectangular potential well occupies the entire nanopore, the mean particle residence time in the pore is independent of the particle diffusivity inside the pore and depends only on its diffusivity in the bulk; (iv) although in the presence of a potential bias applied to the nanopore the "downhill" particle flux is higher than the "uphill" one, the mean translocation times and their distributions are identical, i.e., independent of the translocation direction; and (v) fast spontaneous gating affects nanopore selectivity when its characteristic time is comparable to that of the particle transport through the pore.
Topics: Nanopores; Diffusion
PubMed: 37958906
DOI: 10.3390/ijms242115923 -
ACS Nano Nov 2020Collective decision making by living cells is facilitated by exchange of diffusible signals where sender cells release a chemical signal that is interpreted by receiver...
Collective decision making by living cells is facilitated by exchange of diffusible signals where sender cells release a chemical signal that is interpreted by receiver cells. A variety of nonliving artificial cell models have been developed in recent years that mimic various aspects of diffusion-based intercellular communication. However, localized secretion of diffusive signals from individual protocells, which is critical for mimicking biological sender-receiver systems, has remained challenging to control precisely. Here, we engineer light-responsive, DNA-encoded sender-receiver architectures, where protein-polymer microcapsules act as cell mimics and molecular communication occurs through diffusive DNA signals. We prepare spatial distributions of sender and receiver protocells using a microfluidic trapping array and set up a signaling gradient from a single sender cell using light, which activates surrounding receivers through DNA strand displacement. Our systematic analysis reveals how the effective signal range of a single sender is determined by various factors including the density and permeability of receivers, extracellular signal degradation, signal consumption, and catalytic regeneration. In addition, we construct a three-population configuration where two sender cells are embedded in a dense array of receivers that implement Boolean logic and investigate spatial integration of nonidentical input cues. The results offer a means for studying diffusion-based sender-receiver topologies and present a strategy to achieve the congruence of reaction-diffusion and positional information in chemical communication systems that have the potential to reconstitute collective cellular patterns.
Topics: Artificial Cells; Cell Communication; DNA; Diffusion; Signal Transduction
PubMed: 33078948
DOI: 10.1021/acsnano.0c07537 -
Advances in Colloid and Interface... Jan 2021In this review, we present a summary of computer simulation studies on solute diffusion in gels carried out in the last three decades. Special attention is paid to... (Review)
Review
In this review, we present a summary of computer simulation studies on solute diffusion in gels carried out in the last three decades. Special attention is paid to coarse-grained simulations in which the role of steric and electrostatic interactions on the particle diffusion can be evaluated. In addition, other important characteristics of particle diffusion in gels, such as the stiffness of the gel structure and hydrodynamic interactions, can be taken into account through coarse-grained simulations. Emphasis is placed on how simulation results help to test phenomenological models and to improve the interpretation interof experimental results. Finally, coarse-grained simulations have also been employed to study the diffusion controlled release of drugs from gels. We believe that scientific advances in this line will be useful to better understand the mechanisms that control the diffusive transport of molecules in a wide variety of biological systems.
Topics: Computer Simulation; Diffusion; Gels; Solutions; Static Electricity
PubMed: 33296722
DOI: 10.1016/j.cis.2020.102320 -
International Journal of Molecular... Oct 2022The mechanisms of transport of substances in the brain parenchyma have been a hot topic in scientific discussion in the past decade. This discussion was triggered by the... (Review)
Review
The mechanisms of transport of substances in the brain parenchyma have been a hot topic in scientific discussion in the past decade. This discussion was triggered by the proposed glymphatic hypothesis, which assumes a directed flow of cerebral fluid within the parenchyma, in contrast to the previous notion that diffusion is the main mechanism. However, when discussing the issue of "diffusion or non-diffusion", much less attention was given to the question that diffusion itself can have a different character. In our opinion, some of the recently published results do not fit into the traditional understanding of diffusion. In this regard, we outline the relevant new theoretical approaches on transport processes in complex random media such as concepts of diffusive diffusivity and time-dependent homogenization, which expands the understanding of the forms of transport of substances based on diffusion.
Topics: Extracellular Space; Brain; Diffusion; Biological Transport; Diffusion Magnetic Resonance Imaging
PubMed: 36293258
DOI: 10.3390/ijms232012401 -
Magnetic Resonance in Medicine Dec 2021Microstructure imaging seeks to noninvasively measure and map microscopic tissue features by pairing mathematical modeling with tailored MRI protocols. This article... (Review)
Review
Microstructure imaging seeks to noninvasively measure and map microscopic tissue features by pairing mathematical modeling with tailored MRI protocols. This article reviews an emerging paradigm that has the potential to provide a more detailed assessment of tissue microstructure-combined diffusion-relaxometry imaging. Combined diffusion-relaxometry acquisitions vary multiple MR contrast encodings-such as b-value, gradient direction, inversion time, and echo time-in a multidimensional acquisition space. When paired with suitable analysis techniques, this enables quantification of correlations and coupling between multiple MR parameters-such as diffusivity, , , and . This opens the possibility of disentangling multiple tissue compartments (within voxels) that are indistinguishable with single-contrast scans, enabling a new generation of microstructural maps with improved biological sensitivity and specificity.
Topics: Brain; Diffusion; Diffusion Magnetic Resonance Imaging; Magnetic Resonance Imaging; Models, Theoretical
PubMed: 34411331
DOI: 10.1002/mrm.28963 -
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