-
Journal of Neuroscience Methods Jan 2021Diffusion encoding along multiple spatial directions per signal acquisition can be described in terms of a b-tensor. The benefit of tensor-valued diffusion encoding is... (Review)
Review
Diffusion encoding along multiple spatial directions per signal acquisition can be described in terms of a b-tensor. The benefit of tensor-valued diffusion encoding is that it unlocks the 'shape of the b-tensor' as a new encoding dimension. By modulating the b-tensor shape, we can control the sensitivity to microscopic diffusion anisotropy which can be used as a contrast mechanism; a feature that is inaccessible by conventional diffusion encoding. Since imaging methods based on tensor-valued diffusion encoding are finding an increasing number of applications we are prompted to highlight the challenge of designing the optimal gradient waveforms for any given application. In this review, we first establish the basic design objectives in creating field gradient waveforms for tensor-valued diffusion MRI. We also survey additional design considerations related to limitations imposed by hardware and physiology, potential confounding effects that cannot be captured by the b-tensor, and artifacts related to the diffusion encoding waveform. Throughout, we discuss the expected compromises and tradeoffs with an aim to establish a more complete understanding of gradient waveform design and its impact on accurate measurements and interpretations of data.
Topics: Anisotropy; Artifacts; Diffusion; Diffusion Magnetic Resonance Imaging; Diffusion Tensor Imaging
PubMed: 33242529
DOI: 10.1016/j.jneumeth.2020.109007 -
Journal of Theoretical Biology Jan 2021A new method to derive an essential integral kernel from any given reaction-diffusion network is proposed. Any network describing metabolites or signals with arbitrary...
A new method to derive an essential integral kernel from any given reaction-diffusion network is proposed. Any network describing metabolites or signals with arbitrary many factors can be reduced to a single or a simpler system of integro-differential equations called "effective equation" including the reduced integral kernel (called "effective kernel") in the convolution type. As one typical example, the Mexican hat shaped kernel is theoretically derived from two component activator-inhibitor systems. It is also shown that a three component system with quite different appearance from activator-inhibitor systems is reduced to an effective equation with the Mexican hat shaped kernel. It means that the two different systems have essentially the same effective equations and that they exhibit essentially the same spatial and temporal patterns. Thus, we can identify two different systems with the understanding in unified concept through the reduced effective kernels. Other two applications of this method are also given: Applications to pigment patterns on skins (two factors network with long range interaction) and waves of differentiation (called proneural waves) in visual systems on brains (four factors network with long range interaction). In the applications, we observe the reproduction of the same spatial and temporal patterns as those appearing in pre-existing models through the numerical simulations of the effective equations.
Topics: Computer Simulation; Diffusion; Models, Biological
PubMed: 33007272
DOI: 10.1016/j.jtbi.2020.110496 -
Annual Review of Biophysics May 2023Diffusion is a pervasive process present in a broad spectrum of cellular reactions. Its mathematical description has existed for nearly two centuries and permits the... (Review)
Review
Diffusion is a pervasive process present in a broad spectrum of cellular reactions. Its mathematical description has existed for nearly two centuries and permits the construction of simple rules for evaluating the characteristic timescales of diffusive processes and some of their determinants. Although the term diffusion originally referred to random motions in three-dimensional (3D) media, several biological diffusion processes in lower dimensions have been reported. One-dimensional (1D) diffusions have been reported, for example, for translocations of various proteins along DNA or protein (e.g., microtubule) lattices and translation of helical peptides along the coiled-coil interface. Two-dimensional (2D) diffusion has been shown for dynamics of proteins along membranes. The microscopic mechanisms of these 1-3D diffusions may vary significantly depending on the nature of the diffusing molecules, the substrate, and the interactions between them. In this review, we highlight some key examples of 1-3D biomolecular diffusion processes and illustrate the roles that electrostatic interactions and intrinsic disorder may play in modulating these processes.
Topics: Static Electricity; DNA; Diffusion; Microtubules; Motion
PubMed: 36750250
DOI: 10.1146/annurev-biophys-111622-091220 -
Nature Methods Jun 2022Label-free characterization of single biomolecules aims to complement fluorescence microscopy in situations where labeling compromises data interpretation, is...
Label-free characterization of single biomolecules aims to complement fluorescence microscopy in situations where labeling compromises data interpretation, is technically challenging or even impossible. However, existing methods require the investigated species to bind to a surface to be visible, thereby leaving a large fraction of analytes undetected. Here, we present nanofluidic scattering microscopy (NSM), which overcomes these limitations by enabling label-free, real-time imaging of single biomolecules diffusing inside a nanofluidic channel. NSM facilitates accurate determination of molecular weight from the measured optical contrast and of the hydrodynamic radius from the measured diffusivity, from which information about the conformational state can be inferred. Furthermore, we demonstrate its applicability to the analysis of a complex biofluid, using conditioned cell culture medium containing extracellular vesicles as an example. We foresee the application of NSM to monitor conformational changes, aggregation and interactions of single biomolecules, and to analyze single-cell secretomes.
Topics: Diffusion; Microscopy, Fluorescence; Nanoparticles; Nanotechnology
PubMed: 35637303
DOI: 10.1038/s41592-022-01491-6 -
Bulletin of Mathematical Biology Aug 2022Time delays, modelling the process of intracellular gene expression, have been shown to have important impacts on the dynamics of pattern formation in reaction-diffusion...
Time delays, modelling the process of intracellular gene expression, have been shown to have important impacts on the dynamics of pattern formation in reaction-diffusion systems. In particular, past work has shown that such time delays can shrink the Turing space, thereby inhibiting patterns from forming across large ranges of parameters. Such delays can also increase the time taken for pattern formation even when Turing instabilities occur. Here, we consider reaction-diffusion models incorporating fixed or distributed time delays, modelling the underlying stochastic nature of gene expression dynamics, and analyse these through a systematic linear instability analysis and numerical simulations for several sets of different reaction kinetics. We find that even complicated distribution kernels (skewed Gaussian probability density functions) have little impact on the reaction-diffusion dynamics compared to fixed delays with the same mean delay. We show that the location of the delay terms in the model can lead to changes in the size of the Turing space (increasing or decreasing) as the mean time delay, [Formula: see text], is increased. We show that the time to pattern formation from a perturbation of the homogeneous steady state scales linearly with [Formula: see text], and conjecture that this is a general impact of time delay on reaction-diffusion dynamics, independent of the form of the kinetics or location of the delayed terms. Finally, we show that while initial and boundary conditions can influence these dynamics, particularly the time-to-pattern, the effects of delay appear robust under variations of initial and boundary data. Overall, our results help clarify the role of gene expression time delays in reaction-diffusion patterning, and suggest clear directions for further work in studying more realistic models of pattern formation.
Topics: Diffusion; Gene Expression; Kinetics; Mathematical Concepts; Models, Biological
PubMed: 35934760
DOI: 10.1007/s11538-022-01052-0 -
Accounts of Chemical Research Mar 2022Organic semiconductors (OSs) are an exciting class of materials that have enabled disruptive technologies in this century including large-area electronics, flexible... (Review)
Review
Organic semiconductors (OSs) are an exciting class of materials that have enabled disruptive technologies in this century including large-area electronics, flexible displays, and inexpensive solar cells. All of these technologies rely on the motion of electrical charges within the material and the diffusivity of these charges critically determines their performance. In this respect, it is remarkable that the nature of the charge transport in these materials has puzzled the community for so many years, even for apparently simple systems such as molecular single crystals: some experiments would better fit an interpretation in terms of a localized particle picture, akin to molecular or biological electron transfer, while others are in better agreement with a wave-like interpretation, more akin to band transport in metals.Exciting recent progress in the theory and simulation of charge carrier transport in OSs has now led to a unified understanding of these disparate findings, and this Account will review one of these tools developed in our laboratory in some detail: direct charge carrier propagation by quantum-classical nonadiabatic molecular dynamics. One finds that even in defect-free crystals the charge carrier can either localize on a single molecule or substantially delocalize over a large number of molecules depending on the relative strength of electronic couplings between the molecules, reorganization, or charge trapping energy of the molecule and thermal fluctuations of electronic couplings and site energies, also known as electron-phonon couplings.Our simulations predict that in molecular OSs exhibiting some of the highest measured charge mobilities to date, the charge carrier forms "flickering" polarons, objects that are delocalized over 10-20 molecules on average and that constantly change their shape and extension under the influence of thermal disorder. The flickering polarons propagate through the OS by short (≈10 fs long) bursts of the wave function that lead to an expansion of the polaron to about twice its size, resulting in spatial displacement, carrier diffusion, charge mobility, and electrical conductivity. Arguably best termed "transient delocalization", this mechanistic scenario is very similar to the one assumed in transient localization theory and supports its assertions. We also review recent applications of our methodology to charge transport in disordered and nanocrystalline samples, which allows us to understand the influence of defects and grain boundaries on the charge propagation.Unfortunately, the energetically favorable packing structures of typical OSs, whether molecular or polymeric, places fundamental constraints on charge mobilities/electronic conductivity compared to inorganic semiconductors, which limits their range of applications. In this Account, we review the design rules that could pave the way for new very high-mobility OS materials and we argue that 2D covalent organic frameworks are one of the most promising candidates to satisfy them.We conclude that our nonadiabatic dynamics method is a powerful approach for predicting charge carrier transport in crystalline and disordered materials. We close with a brief outlook on extensions of the method to exciton transport, dissociation, and recombination. This will bring us a step closer to an understanding of the birth, survival, and annihiliation of charges at interfaces of optoelectronic devices.
Topics: Diffusion; Electronics; Electrons; Molecular Dynamics Simulation; Semiconductors
PubMed: 35196456
DOI: 10.1021/acs.accounts.1c00675 -
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 -
Journal of the Royal Society, Interface Feb 2024We link continuum models of reaction-diffusion systems that exhibit diffusion-driven instability to constraints on the particle-scale interactions underpinning this...
We link continuum models of reaction-diffusion systems that exhibit diffusion-driven instability to constraints on the particle-scale interactions underpinning this instability. While innumerable biological, chemical and physical patterns have been studied through the lens of Alan Turing's reaction-diffusion pattern-forming mechanism, the connections between models of pattern formation and the nature of the particle interactions generating them have been relatively understudied in comparison with the substantial efforts that have been focused on understanding proposed continuum systems. To derive the necessary reactant combinations for the most parsimonious reaction schemes, we analyse the emergent continuum models in terms of possible generating elementary reaction schemes. This analysis results in the complete list of such schemes containing the fewest reactions; these are the simplest possible hypothetical mass-action models for a pattern-forming system of two interacting species.
Topics: Models, Biological; Diffusion
PubMed: 38412962
DOI: 10.1098/rsif.2023.0490 -
Nature Communications Nov 2022Control over vesicle size during nanoscale liposome synthesis is critical for defining the pharmaceutical properties of liposomal nanomedicines. Microfluidic...
Control over vesicle size during nanoscale liposome synthesis is critical for defining the pharmaceutical properties of liposomal nanomedicines. Microfluidic technologies capable of size-tunable liposome generation have been widely explored, but scaling these microfluidic platforms for high production throughput without sacrificing size control has proven challenging. Here we describe a microfluidic-enabled process in which highly vortical flow is established around an axisymmetric stream of solvated lipids, simultaneously focusing the lipids while inducing rapid convective and diffusive mixing through application of the vortical flow field. By adjusting the individual buffer and lipid flow rates within the system, the microfluidic vortex focusing technique is capable of generating liposomes with precisely controlled size and low size variance, and may be operated up to the laminar flow limit for high throughput vesicle production. The reliable formation of liposomes as small as 27 nm and mass production rates over 20 g/h is demonstrated, offering a path toward production-scale liposome synthesis using a single continuous-flow vortex focusing device.
Topics: Liposomes; Microfluidics; Diffusion; Lipids
PubMed: 36384946
DOI: 10.1038/s41467-022-34750-3 -
The Journal of Physical Chemistry. B Jun 2021The thermal motion of charged proteins causes randomly fluctuating electric fields inside cells. According to the fluctuation-dissipation theorem, there is an additional...
The thermal motion of charged proteins causes randomly fluctuating electric fields inside cells. According to the fluctuation-dissipation theorem, there is an additional friction force associated with such fluctuations. However, the impact of these fluctuations on the diffusion and dynamics of proteins in the cytoplasm is unclear. Here, we provide an order-of-magnitude estimate of this effect by treating electric field fluctuations within a generalized Langevin equation model with a time-dependent friction memory kernel. We find that electric friction is generally negligible compared to solvent friction. However, a significant slowdown of protein diffusion and dynamics is expected for biomolecules with high net charges such as intrinsically disordered proteins and RNA. The results show that direct contacts between biomolecules in a cell are not necessarily required to alter their dynamics.
Topics: Diffusion; Friction; Intrinsically Disordered Proteins; Motion; Solvents
PubMed: 34081479
DOI: 10.1021/acs.jpcb.1c02783