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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

Inhibition of glyoxalase I by the enediol mimic S-(N-hydroxy-N-methylcarbamoyl)glutathione. The possible basis of a tumor-selective anticancer strategy.

In principle, competitive inhibitors of glyoxalase I that also serve as substrates for the thioester hydrolase glyoxalase II might function as tumor-selective anti-cancer agents, given the role of these enzymes in removing cytotoxic methylglyoxal from cells and the observation that glyoxalase II activity is abnormally low in some types of cancer cells. In support of the feasibility of this anticancer strategy, an inhibitor of this type has been synthesized by a thioester-interchange reaction between glutathione and N-hydroxy-N-methylcarbamate 4-chlorophenyl ester to give S-(N-hydroxy-N-methylcarbamoyl)glutathione (1). This compound was designed to be a tight-binding inhibitor of glyoxalase I, on the basis of its stereoelectronic similarity to the enediol(ate) intermediate that forms along the reaction pathway of this enzyme. Indeed, 1 is a competitive inhibitor of yeast glyoxalase I, with an inhibition constant (Ki = 68 microM) that is approximately 30-fold lower than that reported for S-D-lactoylglutathione and approximately 7-fold lower than the Km for glutathione-methylglyoxal thiohemiacetal. In addition, 1 is a substrate for bovine liver glyoxalase II, with a Km (0.48 mM) approximately equal to that of the normal substrate S-D-lactoyglutathione and a kcat approximately 2 x 10(-5)-fold that of the normal substrate. Membrane transport studies show that 1 can be delivered into human erythrocytes (used here as a model cell) either by direct diffusion of 1 across the cell membrane or by more rapid diffusion of the glycylethyl ester of 1 across the cell membrane, followed by the catalyzed hydrolysis of the ester to give 1.

Animals

Pattern Formation in a Spatial Public Goods Dilemma due to Diffusive or Directed Motion.

The costly provision of public goods serves as a model problem for the evolution of cooperative behavior, presenting a social dilemma between the collective benefits of shared resources and the individual incentive to free-ride in resource production. The spatial structure of populations can also impact cooperation over public goods, as diffusion of public goods and intentional motion of individuals towards regions with greater resources can interact with population and public goods dynamics to produce heterogeneous patterns in the spatial distribution of strategies and resources. In this paper, we build off a model introduced by Young and Belmonte for the reaction dynamics of interacting individuals and an explicit public good, deriving a system of PDEs that describes the spatial profiles of strategies and the public good in the presence of both diffusive motion of individuals and resources and chemotaxis-like directed motion of individuals in response to gradients in the concentration of public goods. Through linear stability analysis, we show that spatial patterns in strategic and public goods profiles can emerge due to either Turing instability with high defector diffusivity or a directed-motion instability through strong sensitivity of cooperators towards increasing resource concentration. We further explore the emergent spatial patterns with a mix of weakly nonlinear stability analysis and numerical simulation, showing that, for a wide range of reaction parameters, diffusion-driven instability appears to increase cooperation and public goods across the spatial domain, while directed motion of cooperators towards public goods tends to decrease cooperation and environmental quality across the environment.

Models, Biological

Ethanol diffuses across the gastric muscle wall.

Ethanol inhibits the electrical and mechanical activities of gastric smooth muscle, but only at concentrations higher than can be provided by serum delivery. We speculated that the ethanol concentration in the gastric wall may exceed plasma levels by direct diffusion across the mucosa and through the muscle layers. A model of acute ethanol ingestion was created by partitioning the stomachs of three dogs with a surgical stapling device and instilling carbon 14 (14C)-labeled ethanol into the proximal segments. The flux of ethanol was traced by counting 14C in serial sections of the gastric wall. A mucosa-to-serosa gradient of 14C activity was established. The data indicate that direct diffusion from the mucosal surface will produce dramatically higher concentrations of ethanol in gastric muscle than would be anticipated from serum levels alone.

Animals

Model for drug uptake by brain tumors: effects of osmotic treatment and of diffusion in brain.

A mathematical model describing drug uptake into brain tumors, directly from blood and indirectly from neighboring tissue, is presented. The model quantitatively describes uptake into tumor, brain surrounding tumor (BST), and normal brain and uptake following reversible osmotic blood-brain barrier (BBB) and blood-tumor barrier disruption. It employs published data on the time course for reclosure of the BBB following osmotic treatment and on the brain and tumor uptake of [14C]alpha-aminoisobutyric acid by Walker 256 carcinomas and C6 gliomas implanted into the rat brain. Constant infusion and bolus injection infusion schedules are considered. In untreated brain, the BST acts as a sink, reducing the integrated exposure of the adjacent tumor to the drug, whereas following osmotic treatment, tumor exposure to drug is enhanced, not only by increased delivery from blood but also by diffusion (and bulk flow) from neighboring brain. The model provides a quantitative framework for examining the efficacy of osmotic treatment to enhance chemotherapy of brain tumors.

Aminoisobutyric Acids

Models for the active transport of cations...the steady-state analysis.

We summarise the progress that has been made in the analysis of active transport models, at the steady-state level. The two general classes of such model, counter-and co-transport, can be treated by a kinetic analysis which makes no assumptions as to the symmetry or asymmetry of the systems nor as to the presence of any particular rate-limiting steps. Precisely the same formalism is obeyed for primary active transport as for secondary active transport. Both are merely a generalisation of facilitated diffusion, in that they follow directly from accepted properties of carrier models. How affinities of such carriers for their substrates affect the efficiency of active transport is discussed and it is shown that in a number of cases, the affinity changes that the carrier demonstrates arise from inherent properties of the free carrier and not from any "high energy" properties of the chemical reactants. Methods of obtaining the kinetic parameters of the system from experimental data are reviewed, together with methods for testing and characterising the different transport models.

Binding Sites

Mechanisms for intracellular distribution of mRNA: in situ hybridization studies in muscle.

The intracellular distribution of mRNA in striated muscle fibers is highly ordered, as is the structural organization of the fibers' contractile apparatus. Results from in situ hybridization of muscle mRNA are reviewed in an attempt to discern the mechanisms involved in mRNA distribution and to determine its relationship to developmental, growth, and repair processes in muscle. Nonradioactively labeled complementary RNA probes allow anatomic localization of mRNA at the light and electron microscopic level. Myosin mRNA in striated muscle is concentrated around transcriptionally active nuclei, myosin mRNA is excluded by the myofibrillar mass, myosin mRNA distribution correlates with that of cytoskeletal elements, and myosin mRNA is concentrated in regions of rapid growth and repair. The even distribution of myosin mRNA along the length of myofibrils gives no indication of specific association with either the thick or thin filaments. Of the possible mechanisms directing mRNA distribution, results from in situ hybridization and other analyses support a restricted diffusion model. Diffusion of mRNA (and polysomes) is severely limited by the myofibrillar lattice. It is possible that myosin mRNA is also associated with a cytoskeletal element, which may direct the mRNA to specific intracellular locations and affect translational activity.

Animals

Preaggregative cell motion in Dictyostelium.

The motions of a large number (495) of preaggregative D. discoideum NC-4 cells in sparse fields are recorded on time-lapse film and analysed using a specially constructed computer graphics system. All films are produced under a standard set of conditions, so that the range of cell behaviours under given conditions can be characterized. The mean velocity of pre-aggregative D. discoideum NC-4 is 7.19 micrometers/min. The mean velocity time course has a significant early peak at about 3 h. The distribution of mean velocities is fairly broad with a long high velocity tail. A modified random walk model using the parameters diffusion constant and persistence time describes well the changes in cell direction with time. Persistence can be described as an exponentially distributed 'memory' of movement direction, with a mean of 4.89 min. High velocity cells never have long persistence times, and persistence time shows no relationship with age. A nearest neighbour model of cell spacing shows that cells are randomly (Poisson) distributed at low densities. Measurements of cell contacts are compared to a simple model of contact frequency based on the kinetic theory of gases to show that cells at low densities have an affinity for making collisions. The length of contact durations is indicative of some mechanical adhesion between cells, and cells in contact move significantly though not dramatically slower. A cross-correlation analysis shows that the various parameters of motion are significantly interrelated in numerous ways. Finally mutants and strains related to D. discoideum NC-4 exhibit a number of new behaviours, suggesting that motion is a distinctive characteristic of cell type.

Agglutination

Air quality in the vicinity of urban roads.

Motor vehicle emissions are a major source of CO, NOx and lead particulate concentrations to urban air quality. London urban Boroughs with high traffic densities are therefore a particular cause for concern. The air quality was monitored at an urban background site in the London Borough of Haringey for 2-years. The results of this study are assessed and their effect on human health is considered in the light of EC Directives and WHO guidelines. A desk top modelling technique based on Gaussian diffusion theory was used to predict the CO levels found at the background site. All predicted levels had a accuracy of better than 30%.

Air Pollution

In vitro magnesium absorption and the role of intestinal motility.

Magnesium (Mg) is known as an inhibitor of spontaneously contracting muscular tissues. To increase extracellular Mg in vivo, high doses of Mg must be given orally. Therefore, we investigated the effect of different doses of Mg given from the mucosal side of the small intestine of rats. According to the model of Trendelenburg, a system for the perfusion of isolated small intestine was developed, which allows the simultaneous recording of absorption and muscle contractions. Increasing doses of Mg were applied serosally or intraluminally. Intramulinal Mg did not affect intestinal motility. In contrast, increasing concentrations of serosal Mg resulted in a 50% inhibition of motility at 2.9 mmol/l Mg. This indicates no influence on intestinal motility of high doses of Mg acting from the mucosal side. In further studies, the addition of citric acid or taurocholic acid did not alter Mg absorption. Serosally applied amiloride (1 mmol/l) inhibited absorption, but also resulted in complete loss of motility. Since in this model passive diffusion is the most important mechanism of Mg transport, a direct influence of amiloride on Mg absorption can be excluded. From these data, we conclude that intestinal motility influences absorption--also of ions in aqueous solution--and should therefore be taken into account in absorption studies.

Amiloride

Pharmacokinetics of halothane in the dog. Comparison of theory and measurement in individuals.

After surgical preparation under pentobarbitone anaesthesia seven dogs of mean body weight 31 kg were ventilated with 1% halothane for 80 min. At 1, 2, 5, 10, 20, 40 and 80 min after the start of the halothane administration blood samples were taken from the femoral artery and pulmonary artery and from a cerebral, a renal and a femoral vein. At 80 min a biopsy sample of skeletal muscle (psoas) was taken. The halothane tension in all samples was determined by extraction into carbon tetrachloride followed by gas chromatographic analysis using chloroform as an internal standard. The measured tensions were compared with tensions computed from a multi-compartment model of the uptake and distribution of halothane in the body. The model was quantified by measurements, in each individual, of total body mass, the masses of the major organs and the solubility of halothane in the major organs and tissues; by measurements of blood volume and solubility in blood at the start and finish of the halothane administration; and by repeated measurements of alveolar ventilation, cardiac output and body temperature. For the original version of the model, the computed tensions deviated from the measured tensions to an extent greater than could be attributed to experimental error and in a manner which could be attributed to metabolism of halothane and probably to direct diffusion of halothane from well-perfused organs and lean tissues into fat. Direct experimental evidence of diffusion into perirenal fat was obtained in supplementary experiments. With the quantitation of the model distorted to mimic the processes of metabolism and diffusion, measured arterial tensions could be predicted with a mean error of -0.2 mm Hg (SD 0.6 mm Hg). The mean measured arterial tension was 3.5 mm Hg.

Animals

[The application of in vivo diffusion weighted magnetic resonance imaging to intracranial disorders].

We have developed a magnetic resonance (MR) spin echo method to obtain diffusion weighted imaging using motion-probing gradient (MPG) pulses in one or three orthogonal directions before and after a 180 degree pulse. Phantom models containing water and acetone, normal volunteers and patients with brain tumors, brain edema and infarction were examined. Experimental models of brain edema including triethyltin intoxication and cold injuries were also examined in Wistar rats. MRI was performed at a 1.0-T clinical machine or a 4.7-T experimental machine using spin echo pulse sequences with or without additional MPGs on one or three orthogonal axes. The one direction method was useful to define diffusion anisotropy of myelinated axonal fibers in white matter. Faster diffusion was detected in the white matter parallel to the direction of MPGs. On the other hand, slower diffusion was detected perpendicular to the direction of MPGs because the myelin sheath restricted water diffusion. The three orthogonal gradients method was useful to demonstrate the difference in the diffusion coefficients in various diseases due to its larger total gradient strength. The clear distinction between the cytotoxic edema, which revealed slower diffusion, and the vasogenic edema, which revealed faster diffusion, was demonstrated in the experimental models using diffusion weighted image. In the clinical cases, faster diffusion was demonstrated in the brain tumor and perifocal vasogenic edema, which was in agreement with the results in the experimental models of rats. Brain tumors such as low grade astrocytoma with microcysts and perifocal vasogenic edema have very wide extracellular space.(ABSTRACT TRUNCATED AT 250 WORDS)

Animals

The effect of convection on bidirectional peritoneal solute transport: predictions from a distributed model.

A distributed model of the peritoneum has been proposed as an alternative to the standard membrane model for describing peritoneal solute transport. The effect of convection on bidirectional peritoneal solute transport is studied theoretically using the distributed model. Approximate analytical and exact numerical solutions to the distributed model yield predictions similar to those when using a membrane model of peritoneal solute transport. Difficulties in interpretation of the membrane transport parameters may arise, however, when interstitial tissue, not the capillary wall, is the dominant diffusive solute transport resistance. Under such conditions the effect of convection on peritoneal solute transport is dependent on the transport direction. Moreover, predictions from the distributed model are similar to those for a membrane model containing two transport barriers in series. Thus, both the distributed model and a membrane model containing two serial transport barriers equivalently describe the effect of convection on bidirectional peritoneal solute transport.

Animals

Recovering membrane interaction kinetics of single molecules from 3D tracking data.

Interactions between cytosolic biomolecules and the bacterial inner membrane are fundamental to many cellular processes, yet directly measuring their binding kinetics in living cells remains challenging. Conventional 2D single-molecule tracking analyses can be insufficient, particularly when membrane association does not markedly alter the diffusion rate. Here, we present a method to recover membrane interaction kinetics from 3D single-molecule trajectories in rod-shaped bacteria. Using simulated 3D tracking data, we identify membrane-associated motion by quantifying how well short trajectory segments follow the circular curvature of the cell membrane. The resulting measure is further analyzed using a hidden Markov modeling framework, enabling robust discrimination between cytosolic and membrane-bound states and capturing the dynamics of state transitions without requiring diffusion-rate changes or direct colocalization with membrane markers. This work establishes a general framework for extracting membrane interaction kinetics from 3D single-molecule tracking data in live bacteria and highlights the value of realistic microscopy simulations for quantitative interpretation and systematic bias assessment.

Kinetics

Paracrine control of photomembrane removal.

Photomembrane turnover in vertebrate photoreceptors is regulated by light. Rod outer segments (ROS) shed membrane filled tips at light onset, during the coexistence of two light modulated processes: a dark priming factor and a light induction event. Transduction of these two signals is not direct but appears to involve the neural retina and diffusible paracrine molecules. I propose a model wherein three paracrines control this ROS tip shedding. Melatonin, a lipid soluble dark priming molecule, is synthesized in the dark by all photoreceptor cells, diffusing freely and separating the ROS disk membranes. A second paracrine, dopamine is released from the inner retina whenever light is absorbed by the 502 nm-cones, inhibiting melatonin synthesis. Third, a proposed trophic paracrine, "rostrophin", is released in the dark from internal horizontal cells, and stabilizes the photomembrane. Shedding occurs as rostrophin decreases in the presence melatonin; briefly at light onset or continuously in red or dim white light.

Animals

Determination of glucose diffusion coefficients in biofilms with micro-electrodes.

A glucose micro-electrode was developed for direct measurements inside biofilms, and applied for the determination of effective diffusion coefficients in a model system of agar beads containing immobilized yeast cells. Two methods were used, one based on concentration gradients present at the liquid/solid interface of an active biofilm under steady-state conditions, the other based on the rate of glucose redistribution in an inactivated biofilm under transient-state conditions. Additional measurements with pH and oxygen micro-electrodes were performed and thus allowed for in-situ correction of the glucose electrode signal. From the micro-electrode measurements in the model system it was concluded that the glucose micro-sensor is a useful tool with which to obtain effective diffusion coefficients in biofilms.

Agar

Numerical determination of intestinal membrane diffusing constants by a gradient method.

Optimisation problems arising in the identification of kinetic parameters of intestinal membranes are here considered. The dynamic behaviour of the membrane is described by means of a linear compartmental model. Using optimisation techniques of a gradient type, the intestinal kinetic parameters are identified, minimising a quadratic criterion between experimental data of D-histidine transport and model prediction. Numerical results are reported and their physiological implications discussed. The quantitative assessment of the asymmetry of diffusion constants with respect to diffusion direction seems to be an important result of this work.

Biological Transport

[Asymptotic solution of the model of the erythrocyte shape as an autowave process].

An asymptotic solution was plotted for a model of erythrocyte forms assuming that the biomembrane is anisotropic and of "small" thickness. This leads to small non-linearity and low diffusion, therefore the solution is unrelaxational. The model was investigated qualitatively assuming that the liquid current directed inside the spheric membrane induces its "distension", while that directed outside-its "crumpling". In the spherical system of coordinates the lines of solution level at theta = const are circumferences, while at phi-const-trochoids (Pascal coil, for example). Trochoids rotation areas show stomacyte and discocyte forms. Several hypotheses based on the analysis performed are advanced.

Erythrocyte Membrane