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At least 19 recordsLinked to original sources

Dissecting spatial patterning and signaling with directional diffusion in spatial multi-omics.

Spatial multi-omics sequencing enables the simultaneous profiling of transcriptomics, proteomics, and epigenomics at a spatial resolution, offering insights into complex tissue organization and molecular regulation. However, the effective integration of multiple omics modalities in a spatial context remains a major challenge. Here, we present SpaDDM, a spatial multi-omics integration framework based on directional diffusion models (DDMs), which supports spatial pattern identification, cross-omics alignment, and inter-and intracellular signaling flow analysis. SpaDDM employs DDM-based graph networks to learn omics-specific representations by jointly incorporating spatial coordinates and molecular measurements within each modality, followed by an attention mechanism to align features across modalities. We benchmarked SpaDDM on diverse spatial multi-omics datasets, including transcriptomics-epigenomics and transcriptomics-proteomics combinations across multiple tissues and species. SpaDDM consistently outperformed existing methods by more accurately deciphering spatial tissue patterns and effectively reducing the boundary noise between spatial regions. Moreover, the learned low-dimensional coembedded representations of individual cells serve as integral mediators for inferring the signaling flows that underlie spatial patterning. Finally, we demonstrated that SpaDDM alignment of complementary information across multi-omics layers facilitates cross-omics translation and significantly improves the prediction of cell state alignments.

Multiomics↗

Short-term cell/substrate contact dynamics of subconfluent endothelial cells following exposure to laminar flow.

The manner in which fluid stresses are transmitted from the apical to the basal surface of the endothelium will influence the dynamics of cell/substrate contacts. Such dynamics could be important in the design of synthetic vascular grafts to promote endothelial cell adhesion. To examine whether the initial response of cell/substrate contact sites to flow depends on the magnitude of the applied shear stress, subconfluent monolayers of endothelial cells were exposed to flow at 10, 20, and 30 dyn cm-2 wall shear stresses for 20 min. Cell/substrate contact sites were visualized with total internal reflection fluorescence microscopy. Flow induced a rapid fluctuation in the membrane topography, which was reflected in dynamic changes in cell/substrate contacts. Exposure to flow caused marked changes in contact area. Contact movement occurred normal and parallel to the direction of flow. Contact sites demonstrated significant variability in contact area at 30 dyn cm-2 during the experiment but no significant movement of the contact sites in flow direction after 20 min of flow. Mean square displacements of the contact center of mass were described in terms of a directed diffusion model. Prior to onset of flow, contact movement was random. Flow induced a significant convective component to contact movement for 300-600 s, followed by reestablishment of diffusive growth and movement of contacts. These results suggest that fluid stresses are rapidly transmitted from the apical to the basal surface of the cell via the cytoskeleton.

Animals↗

Photosynthesis of a Scots pine shoot: a comparison of two models of shoot photosynthesis in direct and diffuse radiation fields.

Two models of shoot photosynthesis, the needle surface element model (SEM) and needle volume element model (VEM), were tested against empirical data obtained from measurements of the photosynthetic response of twelve Scots pine (Pinus sylvestris L.) shoots in direct and diffuse radiation. The models assume that shoot photosynthesis is obtained as the integrated response of either all needle surface area elements (SEM) or all needle volume elements (VEM) of the shoot. The models differ in that needles are treated as optically black in SEM, whereas in VEM radiation penetrates into the needle. The photosynthetic response of a surface/volume element was described as a Blackman-type curve and the distributions of irradiance on the elements were derived by computer simulation, based on a model of shoot geometry. The parameters (initial slope and maximum rate) of the Blackman-curve of an element were estimated iteratively by the method of least squares, i.e., by minimizing the residual sum of squares of simulated and measured rates of shoot photosynthesis. The parameter estimation was done separately for direct and diffuse radiation, and the models were evaluated based on the notion that, for the "ideal" model, the estimated parameter values should be the same in direct and diffuse radiation. Both models produced shoot photosynthesis curves that agreed well with measurements, but there was a discrepancy in the estimated parameter values, indicating that differences in the photosynthetic response of shoots in direct and diffuse radiation could not be explained solely on the basis of the simulated irradiance distributions. The agreement was, however, much better for the volume element model, which accounts for penetration of radiation into the needles.

Journal Article↗

Localization properties of the anomalous diffusion phase in the directed trap model and in the Sinai diffusion with a bias.

We study the localization properties of the anomalous diffusion phase x approximately t(micro) with 0 0 and corresponds to the Golosov localization. For finite micro we thus generalize the usual real space renormalization method to allow for the spreading of the thermal packet over many renormalized valleys. Our construction allows one to compute exact series expansions in micro for all observables: to compute observables at order micro (n), it is sufficient to consider in each sample a spreading of the thermal packet onto at most (1+n) traps. So our approach provides a description of the structure of the thermal packet sample by sample, and a full statistical characterization of the important traps at a given order in micro. For the directed trap model, we show explicitly up to order micro(2) how to recover the exact expressions for the diffusion front, the thermal width, and the localization parameter Y2. We then use our method to derive exact results for the localization parameters Y(k) for arbitrary k, the correlation function of two particles, and the generating function of thermal cumulants. We then explain how these results apply to the Sinai diffusion with bias by deriving the quantitative mapping between the large-scale renormalized descriptions of the two models. Finally we study the internal structure of the effective "traps" for the Sinai model via path-integral methods.

Journal Article↗

Quantitative three-dimensional analysis and diffusion modeling of oligonucleotide concentrations after direct intraparenchymal brain infusion.

We compared quantitative experimental results on the diffusion of 35S-labeled phosphorothioate oligonucleotide (PS-ODN) after intraparenchymal infusion in rat brain, with the distributions predicted by Fick's second law of diffusion. Fischer 344 rats underwent identical intracerebral infusions of 36S-PS-ODN. After 0, 5, 11, 23, and 47 h, groups of animals were sacrificed and sequential brain cryosections subjected to autoradiography. The resulting experimental data were compared to the predicted distributions, for estimation of the apparent free diffusion coefficient, D*. Volumes of distribution and total content of 36 S-PS-ODN in the parenchyma were also computed, to monitor loss of total material. The values for D* were within the expected range for the 21-mer PS-ODN used, but a progressive decrease in D* over time was noted. The model requires D* to remain constant and, thus, does not adequately explain the spread of 35S-PS-ODN following infusion. The progressive slowing of spread over time suggests that at later time points, 35S-PS-ODN may be fixed by tissue binding or cellular uptake in the brain. Loss of material via vascular and CSF clearance may also contribute to the lack of fit. Our results highlight issues to be addressed in the modeling and experimental design of the intraparenchymal infusion process.

Algorithms↗

Single-particle tracking: models of directed transport.

Single-particle tracking techniques make it possible to measure motion of individual particles on the cell surface. In these experiments, individual trajectories are observed, so the data analysis must take into account the randomness of individual random walks. Methods of data analysis are discussed for models combining diffusion and directed motion. In the uniform flow model, a tracer simultaneously diffuses and undergoes directed motion. In the conveyor belt model, a tracer binds and unbinds to a uniform conveyor belt moving with constant velocity. If a tracer is bound, it moves at the velocity of the conveyor belt; if it is unbound, it diffuses freely. Trajectories are analyzed using parameters that measure the extent and asymmetry of the trajectory. A method of assessing the usefulness of such parameters is presented, and pitfalls in data analysis are discussed. Joint probability distributions of pairs of extent and asymmetry parameters are obtained for a pure random walk. These distributions can be used to show that a trajectory is not likely to have resulted from a pure random walk.

Biological Transport, Active↗

Diffusion dynamics of the Li+ ion on a model surface of amorphous carbon: a direct molecular orbital dynamics study.

Diffusion processes of the Li+ ion on a model surface of amorphous carbon (Li+C96H24 system) have been investigated by means of the direct molecular orbital (MO) dynamics method at the semiempirical AM1 level. The total energy and energy gradient on the full-dimensional AM1 potential energy surface were calculated at each time step in the dynamics calculation. The optimized structure, where Li+ is located in the center of the cluster, was used as the initial structure at time zero. The dynamics calculation was carried out in the temperature range 100-1000 K. The calculations showed that the Li+ ion vibrates around the equilibrium point below 200 K, while the Li+ ion moves on the surface above 250 K. At intermediate temperatures (300 K < T < 400 K), the ion moves on the surface and falls in the edge regions of the cluster. At higher temperatures (600 K < T), the Li+ ion transfers freely on the surface and edge regions. The diffusion pathway of the Li+ ion was discussed on the basis of theoretical results.

Journal Article↗

Human projected area factors for detailed direct and diffuse solar radiation analysis.

Projected area factors for individual segments of the standing and sedentary human body were modelled for both direct and diffuse solar radiation using detailed 3D geometry and radiation models. The local projected area factors with respect to direct short-wave radiation are a function of the solar azimuth angle (alpha) between 0 degrees < alpha<360 degrees and the solar altitude (beta) angles between -90 degrees < beta<+90 degrees . In case of diffuse solar radiation from the isotropic sky the local human projected area factors were modelled as a function of the ground albedo (rho) ranging between 0< rho<1. The model was validated against available experimental data and showed good general agreement with projected area factors measured for both the human body as a whole and for local quantities. Scientists can use the equations to predict the inhomogeneous irradiation and absorption of direct and diffuse solar radiation and UV-radiation at surfaces of the human body. In conjunction with detailed multi-node models of human thermoregulation the equations can be used to predict the physiological implications of solar radiation and outdoor weather conditions on humans.

Absorption↗

Directed percolation in a two-dimensional stochastic fire-diffuse-fire model.

We establish, from extensive numerical experiments, that the two dimensional stochastic fire-diffuse-fire model belongs to the directed percolation universality class. This model is an idealized model of intracellular calcium release that retains both the discrete nature of calcium stores and the stochastic nature of release. It is formed from an array of noisy threshold elements that are coupled only by a diffusing signal. The model supports spontaneous release events that can merge to form spreading circular and spiral waves of activity. The critical level of noise required for the system to exhibit a nonequilibrium phase transition between propagating and nonpropagating waves is obtained by an examination of the local slope delta (t) of the survival probability Pi(t) proportional exp [-delta(t)] for a wave to propagate for a time t .

Action Potentials↗

Mechanisms for positional signalling by morphogen transport: a theoretical study.

Gradients of cellular activities are ubiquitous in embryonic development. It is widely believed that the inhomogeneous spatial distribution of a morphogen would be able to set up such gradients. But how then does the morphogen propagate in the first place? Straightforward molecular diffusion is often proposed as a possible mechanism. We first show that, surprisingly, the mere binding of the diffusing morphogen to its membrane receptors suffices to prevent the establishment of a concentration-based positional signalling system. Instead, a flat, saturated distribution of receptor-bound morphogen builds up. Because the distribution spreads gradually from the morphogen source, however, cells may still know their position if they are able to integrate the morphogen signal in time. The irregularities of diffusion in the complex extracellular medium would in fact be partially compensated for by such time summation. Another, non-exclusive possibility is that morphogen transport does not occur by simple diffusion only. We put forth a novel model of receptor-aided, directed diffusion that achieves a spatial distribution of morphogen. Our model is based, as an illustration, on the properties of members of the TGFbeta family of molecules. We show that two simple hypotheses regarding the kinetics of TGBbeta binding to its receptors suffice to establish a remarkable transfer mechanism whereby a morphogen such as activin could be both propagated along cell membranes, and transferred between cells that are in contact. The model predicts that morphogen propagation properties depend strongly on the closeness of cell-cell appositions, does not necessitate protein synthesis, accumulation or slow degradation (in contrast to the diffusion/time integration model), and that the morphogen is localised mostly on or close to cell membranes.

Animals↗

A pharmacokinetic model of styrene inhalation with the fugacity approach.

The physiologically based pharmacokinetic model of J. C. Ramsey and M. E. Andersen (1984, Toxicol. Appl. Pharmacol. 73, 159-175) of styrene inhalation in rats, with extrapolation to humans, was reformulated with the chemical equilibrium criterion of fugacity instead of concentration to describe compartment partitioning. Fugacity models have been used successfully to describe environmental partitioning processes which are similar in principle to pharmacokinetic processes. The fugacity and concentration models are mathematically equivalent and produce identical results. The use of fugacity provides direct insights into the relative chemical equilibrium partitioning status of compartments, thus facilitating interpretation of experimental and model data. It can help to elucidate dominant processes of transfer, reaction and accumulation, and the direction of diffusion. Certain model simplifications become apparent in which compartments which remain close to equilibrium may be grouped. Maximum steady-state tissue concentrations for a known exposure may be calculated readily. It is suggested that pharmacokinetic fugacity models can complement conventional concentration models and may facilitate linkage to fugacity models describing environmental sources, pathways, and exposure routes.

Adipose Tissue↗

Computational electrochemistry: finite element simulation of a disk electrode with ultrasonic acoustic streaming.

Computer simulations using the finite element method (FEM) are used to predict the correlation between the transport limiting current (I(lim)) and parameters such as diffusion coefficient, source to electrode separation, source power, and medium viscosity for a sonicated disk electrode in "face on" mode. The fluid dynamics and diffusion layer are modeled directly using FEM and predict that the electrode is uniformly accessible, I(lim) is proportional to the diffusion coefficient to the 2/3 power and I(lim) is proportional to the square root of the source power. Curves are also calculated relating I(lim) to the source to electrode separation and liquid viscosity.

Journal Article↗

Diffusion theory and drug use.

This paper examines the applicability of the diffusion model to drug use. A variety of studies that employ the diffusion model to examine drug-related behaviour, including the use of alcohol, tobacco and illicit drugs, are discussed. Studies include those that focus on "natural" or spontaneous diffusion and those in which diffusion of a drug or a drug-related intervention is planned. Most studies examined support the application of the diffusion model in the study of drug use. The model is particularly valuable when new substances are introduced to a population or subgroup. The addition of economic and other forms of availability as a determinant of adoption would increase the power of the model. Recommended directions for research are outlined. The diffusion model has been used successfully in the study of drug use for several decades. More rigorous designs would strengthen this type of research and provide direction for policymakers and those involved in public health and education.

Diffusion of Innovation↗

Directionality of stripes formed by anisotropic reaction-diffusion models.

Turing mechanism explains the formation of striped patterns in a uniform field in which two substances interact locally and diffuse randomly. In a twin paper, to explain the directionality of stripes on fish skin in closely related species, we studied the effect of anisotropic diffusion of the two substances on the direction of stripes, in the cases in which both substances have high diffusivity in the same direction. In this paper, we study the direction of stripes in more general situations in which the diffusive direction may differ between the two substances. We derive a formula for the direction of stripes, based on a heuristic argument of unstable modes of deviation from the uniform steady state. We confirm the accuracy of the formula by computer simulations. When the diffusive direction is different between two substances, the directions of stripes in the spatial pattern change smoothly with the magnitude of anisotropy of two substances. When the diffusive direction of the two substances is the same, the stripes are formed either parallel or perpendicular to the common diffusive direction, depending on the relative magnitude of the anisotropy. The transition between these two phases occurs sharply.

Animals↗

Direct Spectroscopic Measurement and Theoretical Modeling of the Diffusion of a Single Species in a Two-Phase Unstirred System

The diffusion of 8-hydroxyquinoline from an aqueous phase into an organic phase and vice versa has been measured using a static transfer cell. The total change in concentration in either phase can be accurately predicted by considering one-dimensional diffusion in the plane normal to the oil/water interface. It was found that any turbulent mixing that occurs during the initiation of the experiment dies out in the first few minutes. The relevance of this technique to the study of metal ion extraction from an aqueous phase into an organic phase is discussed.

Journal Article↗

Brownian molecular motors driven by rotation-translation coupling.

We investigated three models of Brownian motors which convert rotational diffusion into directed translational motion by switching on and off a potential. In the first model a spatially asymmetric potential generates directed translational motion by rectifying rotational diffusion. It behaves much like a conventional flashing ratchet. The second model utilizes both rotational diffusion and drift to generate translational motion without spatial asymmetry in the potential. This second model can be driven by a combination of a Brownian motor mechanism (diffusion driven) or by powerstroke (drift driven) depending on the chosen parameters. In the third model, elements of both the Brownian motor and powerstroke mechanisms are combined by switching between three distinct states. Relevance of the model to biological motor proteins is discussed.

Computer Simulation↗

Modeling intra-crown and intra-canopy interactions in red maple: assessment of light transfer on carbon dioxide and water vapor exchange.

Daily and seasonal net photosynthesis (Anet), transpiration (E), absorbed photosynthetically active radiation (Qa) and light-use efficiency (epsilonc) in a red maple container nursery were simulated with MAESTRA, a three-dimensional canopy model. Effects of canopy heterogeneity were simulated by imposing changes in crown spacing. The light transfer sub-model, a distribution model of incident, direct, diffuse and scattered radiation within MAESTRA, was validated against field measurements of light interception on an intra-crown scale. In the container nursery, we found that a fiber-optic-based method of integrating photosynthetically active radiation (Q) was more suitable for crown-layer light transfer measurements and adjustments than either orthogonal line or individual quantum sensor measurements. The model underestimated intercepted Q by 9.3, 18 and 11.1% for crown layers 1, 2 and 3, respectively; however, there were linear relationships between model estimates and observations made with each of the three measurement methods. We used the validated and parameterized light transfer model to assess intra-crown and intra-canopy light transfer on a layer, crown and canopy basis, and investigated effects of tree size ratio and tree spacing interactions on Anet, E, Qa and epsilonc in the container nursery. Heterogeneous crown and canopy photosynthesis were predicted to exceed values for a uniform canopy under space-limiting conditions. Tree size ratio had large effects on Anet, E, Qa and epsilonc when light to lower-canopy layers was limited by inadequate space between crowns. Increasing Qa at lower-crown layers had the largest impact on whole-crown and whole-canopy Anet, E, Qa and epsilonc. Increases in canopy productivity led to increased water use. Simulations of heterogeneous stands with adequate soil water indicated that light absorption is maximized under space-limiting conditions as a canopy crown moves toward heterogeneity. Nursery and plantation productivity per unit land area was optimized by tactical placement of trees of several sizes, but this was accompanied by increased canopy water use.

Acer↗