Wind as a Driver of Peat CO2 Dynamics in a Northern Bog.

Excess CO2 accumulated in soils is typically transported to the atmosphere through molecular diffusion along a concentration gradient. Because of the slow and constant nature of this process, a steady state between peat CO2 production and emissions is often established. However, in peatland ecosystems, high peat porosity could foster additional non-diffusive transport processes, whose dynamics may become important to peat CO2 storage, transport and emission. Based on a continuous record of in situ peat pore CO2 concentration within the unsaturated zone of a raised bog in southern Canada, we show that changes in wind speed create large diel fluctuations in peat pore CO2 store. Peat CO2 builds up overnight and is regularly flushed out the following morning. Persistently high wind speed during the day maintains the peat CO2 with concentrations close to that of the ambient air. At night, wind speed decreases and CO2 production overtakes the transport rate leading to the accumulation of CO2 in the peat. Our results indicate that the effective diffusion coefficient fluctuates based on wind speed and generally exceeds the estimated molecular diffusion coefficient. The balance between peat CO2 accumulation and transport is most dynamic within the range of 0-2 m s-1 wind speeds, which occurs over 75% of the growing season and dominates night-time measurements. Wind therefore drives considerable temporal dynamics in peat CO2 transport and storage, particularly over sub-daily timescales, such that peat CO2 emissions can only be directly related to biological production over longer timescales. Supplementary Information: The online version contains supplementary material available at 10.1007/s10021-024-00904-1.

On the generality of the finite element modeling physical fields in biological systems by the multiscale smeared concept (Kojic transport model).

The biomechanical and biochemical processes in the biological systems of living organisms are extremely complex. Advances in understanding these processes are mainly achieved by laboratory and clinical investigations, but in recent decades they are supported by computational modeling. Besides enormous efforts and achievements in this modeling, there still is a need for new methods that can be used in everyday research and medical practice. In this report, we give a view of the generality of the finite element methodology introduced by the first author and supported by his collaborators. It is based on the multiscale smeared physical fields, termed as Kojic Transport Model (KTM), published in several journal papers and summarized in a recent book (Kojic et al., 2022) [1]. We review relevant literature to demonstrate the distinctions and advantages of our methodology and indicate possible further applications. We refer to our published results by a selection of a few examples which include modeling of partitioning, blood flow, molecular transport within the pancreas, multiscale-multiphysics model of coupling electrical field and ion concentration, and a model of convective-diffusive transport within the lung parenchyma. Two new examples include a model of convective-diffusive transport within a growing tumor, and drug release from nanofibers with fiber degradation.

PFAS release from the subsurface and capillary fringe during managed aquifer recharge.

Managed aquifer recharge (MAR) is a sustainable way of harvesting groundwater in water-stressed urbanized areas, where reclaimed wastewater or stormwater is applied on a large basin to infiltrate water into the groundwater aquifer naturally. This process could rapidly fluctuate the water table and move the capillary fringe boundary, and the change in flow dynamic and associated geochemical changes could trigger the release of sequestered pollutants, including per- and polyfluoroalkyl substances (PFAS), also known as 'forever chemicals', from the subsurface and capillary fringe. Yet, the potential of PFAS release from the subsurface and capillary zone during recharge events when the water table rapidly fluctuates has not been evaluated. This study uses laboratory column experiments to simulate PFAS release from pre-contaminated subsurface and capillary fringe during groundwater table fluctuation. The results reveal that the groundwater level fluctuations during MAR increased the release of perfluorobutanesulfonic acid (PFBS) and perfluorooctanesulfonic acid (PFOS) from the capillary fringe, but the fraction released depended on PFAS type and their association with soil colloids. A higher proportion of PFOS in column effluent was found to be associated with particles, while a greater portion of released PFBS was in a free or dissolved state. The direction of water table fluctuation did not affect the release of PFAS in this study. A lack of change in the concentration of bromide, a conservative tracer, during flow interruption, indicates that diffusion of PFAS through reconnected pores during water table rise had an insignificant effect on PFAS release. Overall, this study provides insights into how PFAS can be released from the subsurface and capillary fringe during managed aquifer recharge when the groundwater level is expected to fluctuate quickly.

Topical Delivery Systems Effectively Transport Analgesics to Areas of Localized Pain via Direct Diffusion.

Topical delivery systems (TDSs) enable the direct transport of analgesics into areas of localized pain and thus minimize the side effects of administration routes that rely on systemic drug distribution. For musculoskeletal pain, clinicians frequently prescribe topical products containing lidocaine or diclofenac. This study assessed whether drug delivery from a TDS into muscle tissue occurs mainly via direct diffusion or systemic transport. An investigational TDS containing 108 mg lidocaine (SP-103, 5.4% lidocaine), a commercially available TDS containing 36 mg lidocaine (ZTlido®, 1.8% lidocaine), and a topical pain relief gel (Pennsaid®, 2% diclofenac) were tested. Using open flow microperfusion (OFM), interstitial fluid from the dermis, subcutaneous adipose tissue (SAT), and muscle was continuously sampled to assess drug penetration in all tissue layers. Ex vivo and in vivo experiments showed a higher diffusive transport of lidocaine compared to diclofenac. The data showed a clear contribution of diffusive transport to lidocaine concentration, with SP-103 5.4% resulting in a significantly higher lidocaine concentration in muscle tissue than commercially available ZTlido® (p = 0.008). These results indicate that SP-103 5.4% is highly effective in delivering lidocaine into muscle tissue in areas of localized pain for the treatment of musculoskeletal pain disorders (e.g., lower back pain).

Characteristics of constrained turbulent transport in flux-driven toroidal plasmas.

We study the dynamics of turbulence transport subject to a constraint on the profile formation and relaxation, dominated by the ion temperature gradient modes, within the framework of adiabatic electron response using a flux-driven global gyro-kinetic toroidal code, GKNET. We observe exponentially constrained profiles, with two different scale lengths, that are spatially constant in each region in higher input power regimes. The profiles are smoothly connected in the knee region located at [Formula: see text] of the minor radius, outside which the gradient is steepened and shows a weak confinement improvement. Based on the probability density function analysis of heat flux eddies, the power law demonstrates a dependence on the eddy size S, as [Formula: see text], which distinguishes events into diffusive and non-diffusive parts including the validation of quasi-linear hypotheses. Radially localized avalanches and global bursts, which exhibit different spatial scales, play central roles in giving rise to constrained profiles on an equal footing. It is also found that the [Formula: see text] shear layers are initiated by the global bursts, which evolve downward on a slow time scale across the knee region and play a role in adjusting the profile by increasing the gradient. This article is part of a discussion meeting issue 'H-mode transition and pedestal studies in fusion plasmas'.

Multi-Scale Modeling and Simulation of Transport Processes in an Elastically Deformable Perforated Medium.

In this paper, we derive an effective model for transport processes in periodically perforated elastic media, taking into account, e.g., cyclic elastic deformations as they occur in lung tissue due to respiratory movement. The underlying microscopic problem couples the deformation of the domain with a diffusion process within a mixed Lagrangian/Eulerian formulation. After a transformation of the diffusion problem onto the fixed domain, we use the formal method of two-scale asymptotic expansion to derive the upscaled model, which is nonlinearly coupled through effective coefficients. The effective model is implemented and validated using an application-inspired model problem. Numerical solutions for both, cell problems and macroscopic equations, are investigated and interpreted. We use simulations to qualitatively determine the effect of the deformation on the transport process.

The influence of a transport process on the epidemic threshold.

By generating transient encounters between individuals beyond their immediate social environment, transport can have a profound impact on the spreading of an epidemic. In this work, we consider epidemic dynamics in the presence of the transport process that gives rise to a multiplex network model. In addition to a static layer, the (multiplex) epidemic network consists of a second dynamic layer in which any two individuals are connected for the time they occupy the same site during a random walk they perform on a separate transport network. We develop a mean-field description of the stochastic network model and study the influence the transport process has on the epidemic threshold. We show that any transport process generally lowers the epidemic threshold because of the additional connections it generates. In contrast, considering also random walks of fractional order that in some sense are a more realistic model of human mobility, we find that these non-local transport dynamics raise the epidemic threshold in comparison to a classical local random walk. We also test our model on a realistic transport network (the Munich U-Bahn network), and carefully compare mean-field solutions with stochastic trajectories in a range of scenarios.

Trends and errors in reverse osmosis membrane performance calculations stemming from test pressure and simplifying assumptions about concentration polarization and solute rejection.

A primary goal in the design of reverse osmosis (RO) membranes is to improve water-solute selectivity and water permeance. These transport properties are commonly calculated in the literature using the solution-diffusion model with selectivity (A/B, bar-1) defined as the ratio between water permeance (A, L.m-2.h-1.bar-1) and solute permeance (B, L.m-2.h-1). In calculating transport properties, researchers often use simplifying assumptions about concentration polarization (CP; i.e., assuming negligible CP or a certain extent of CP) and solute rejection (i.e., assuming solute rejection is approximately 1 to enable the explicit use of the CP modulus in solute permeance calculations). Although using these assumptions to calculate transport properties is common practice, we could not find a study that evaluated the errors associated with using them. The uncertainty in these errors could impede unequivocally identifying manufacturing approaches that break through the commonly plotted trade-off frontier between selectivity and water permeance (A/B vs. A); however, we did not find in the literature a study that quantified such errors. Accordingly, we aimed to: (1) quantify the error in transport properties (A, B, and A/B) calculated using common simplifying assumptions about CP and rejection; and (2) determine if using simplifying assumptions affects conclusions drawn about membrane performance or trends concerning the trade-off frontier. Results show that compared with the case where no simplifying assumptions were made, simplified calculations were least accurate at low pressures for water permeance (up to 78% overestimation) and high pressures for solute permeance (up to 188% overestimation). Accordingly, the corresponding selectivities were least accurate at low pressure (up to 111% overestimation) and high pressure (up to 66% underestimation), and conclusions drawn about membrane performance and trade-off trends were pressure-dependent. Importantly, even in the absence of simplifying assumptions, selectivity results were pressure-dependent, indicating the importance of standardizing test conditions for the continued use of current performance metrics (i.e., A/B and A). We propose a two-pressure approach-collecting data for A and B at a high and a low pressure, respectively-combined with simplifying assumptions for more accurate simplified estimations of selectivity (< 10% absolute error). Our work contributes to a better understanding of the effects of operating pressure and key simplifying assumptions commonly used in calculating RO membrane performance metrics and interpretation of corresponding results.

Dataset of reverse osmosis membrane transport properties calculated with and without assumptions about concentration polarization and solute rejection and the errors associated with each assumption.

The data shared in this work represent aspects of the performance of reverse osmosis membranes during filtration. We present pressure, permeate flux, and solute rejection data gathered during cross-flow filtration experiments, which were used to (i) model water and solute permeation through the membranes and (ii) calculate concentration polarization moduli and a suite of transport properties, including water permeance, solute permeance, and water-solute selectivity. Membrane transport properties were calculated with the different approaches commonly used to simplify transport property calculations. Typical calculations of these transport properties often use simplifying assumptions (e.g., negligible concentration polarization and solute rejection close to 100%). However, the extent of the errors associated with using simplifying assumptions in this context were not previously known or quantified. This publication and corresponding dataset pertain to figures presented in the accompanying work (Armstrong et al., 2022) [1].

Influence of Phase Transitions on Diffusive Molecular Transport Across Biological Membranes.

Phase transitions of lipid bilayer membranes should affect passive transport of molecules. While this hypothesis has been used to design drug-releasing thermosensitive liposomes, the effect has yet to be quantified. Herein, we use time-resolved second harmonic light scattering to measure transport of a molecular cation across membranes of unilamellar liposomes composed of the total lipid extract of E. coli from 9 °C to 36 °C, in which two distinct phase transitions (gel to liquid-disordered phase) have been identified. While the transport rate slowly increases with temperature as a diffusion process, dramatic jumps are observed at 14.7 °C and 27.6 °C, the known phase transitions. The transport rate constant measured as (7.3±0.8)×10-3  s-1 in the liquid-disordered phase at 36 °C is 35-times faster than (2.1±0.2)×10-4  s-1 of the gel phase at 9 °C. For the mixed-phase between these two phases, the measured rates are consistent with a structure of gel domains among a liquid-disordered bulk.

Diffusion of molecules through nanopores under confinement: Time-scale bridging and crowding effects via Markov state model.

Passive transport of molecules through nanopores is characterized by the interaction of molecules with pore internal walls and by a general crowding effect due to the constricted size of the nanopore itself, which limits the presence of molecules in its interior. The molecule-pore interaction is treated within the diffusion approximation by introducing the potential of mean force and the local diffusion coefficient for a correct statistical description. The crowding effect can be handled within the Markov state model approximation. By combining the two methods, one can deal with complex free energy surfaces taking into account crowding effects. We recapitulate the equations bridging the two models to calculate passive currents assuming a limited occupancy of the nanopore in a wide range of molecular concentrations. Several simple models are analyzed to clarify the consequences of the model. Eventually, a biologically relevant case of transport of an antibiotic molecule through a bacterial porin is used to draw conclusions (i) on the effects of crowding on transport of small molecules through biological channels, and (ii) to demonstrate its importance for modelling of cellular transport.

Enhanced Diffusive Transport in Fluctuating Porous Media.

Mass transport within porous structures is a ubiquitous process in biological, geological, and technological systems. Despite the importance of these phenomena, there is no comprehensive theory that describes the complex and diverse transport behavior within porous environments. While the porous matrix itself is generally considered a static and passive participant, many porous environments are in fact dynamic, with fluctuating walls, pores that open and close, and dynamically changing cross-links. While diffusion has been measured in fluctuating structures, notably in model biological systems, it is rarely possible to isolate the effect of fluctuations because of the absence of control experiments involving an identical static counterpart, and it is generally impossible to observe the dynamics of the structure. Here we present a direct comparison of the diffusion of nanoparticles of various sizes within a trackable, fluctuating porous matrix and a geometrically equivalent static matrix, in conditions spanning a range of regimes from obstructed to highly confined. The experimental system comprised a close-packed layer of colloidal spheres that were either immobilized to a planar surface or allowed to fluctuate locally, within the space defined by their nearest neighbors. Interestingly, the effective long-time diffusion coefficient was approximately 35-65% greater in the fluctuating porous matrix than in the static one (depending on the size of the nanoparticle probes), regardless of the geometric regime. This was explained by considering the enhancing effects of matrix fluctuations on the short-time diffusion coefficient and cooperative "gate-opening" motions of matrix particles and nanoparticle probes.

Multi-region finite element modelling of drug release from hydrogel based ophthalmic lenses.

Understanding the way in which drug is released from drug carrying hydrogel based ophthalmic lenses aids in the development of efficient ophthalmic drug delivery. Various solute-polymer interactions affect solute diffusion within hydrogels as well as hydrogel-bulk partitioning. Additionally, surface modifications or coatings may add to resistance of mass transfer across the hydrogel interface. It is necessary to consider both interfacial resistances as well as the appropriate driving force when characterizing interface flux. Such a driving force is induced by a difference in concentration which deviates from equilibrium conditions. We present a Galerkin finite element approach for solute transport in hydrogels which accounts for diffusion within the gel, storage effects due to polymer-solute interaction, as well as partitioning and mass transfer resistance effects at the interface. The approach is formulated using a rotational symmetric model to account for realistic geometry. We show that although the resulting global system is not symmetric in the case of partitioning, it is similar to a symmetric negative semidefinite system. Thus, it has non-positive real eigenvalues and is coercive, ensuring the validity of the finite element formulation as well as the numerical stability of the implicit backward Euler time integration method employed. Two models demonstrating this approach are presented and verified with release experimental data. The first is the release of moxifloxacin from intraocular lenses (IOLs) plasma grafted with different polyacrylates. The second accounts for both loading as well as the release of diclofenac from disc shaped IOL material loaded for varied time periods and temperature.

Mathematical description data: Spin-resolved electron transport in nanoscale heterojunctions: Theory and applications.

This study demonstrates a mathematical description of a point-like nanocontact model, which is developed to simulate electron transport through a nanoconstriction between magnetic or non-magnetic contact sides. The theory represents a solution to the quasi-(semi)-classical transport equations for charge current, which takes into account second-order derivatives of the related quasi-classical Green functions along the transport direction. The theoretical approach also enables the creation of an I-V model for a heterojunction with embedded objects, where the initial condition, a conduction band minimum profile of the system, is well-defined. The presented spin-resolved current approach covers a complete range of the scales including quantum, ballistic, quasi-ballistic (intermediate), and diffusive classical transport conditions, with a smooth transition between them without residual terms or any empirical variables. The main benefit of the mathematical solution is its novel methodology, which is an alternative candidate to the well-known Boltzmann technique.

Overcoming negatively charged tissue barriers: Drug delivery using cationic peptides and proteins.

Negatively charged tissues are ubiquitous in the human body and are associated with a number of common diseases yet remain an outstanding challenge for targeted drug delivery. While the anionic proteoglycans are critical for tissue structure and function, they make tissue matrix dense, conferring a high negative fixed charge density (FCD) that makes drug penetration through the tissue deep zones and drug delivery to resident cells extremely challenging. The high negative FCD of these tissues is now being utilized by taking advantage of electrostatic interactions to create positively charged multi-stage delivery methods that can sequentially penetrate through the full thickness of tissues, create a drug depot and target cells. After decades of work on attempting delivery using strong binding interactions, significant advances have recently been made using weak and reversible electrostatic interactions, a characteristic now considered essential to drug penetration and retention in negatively charged tissues. Here we discuss these advances using examples of negatively charged tissues (cartilage, meniscus, tendons and ligaments, nucleus pulposus, vitreous of eye, mucin, skin), and delve into how each of their structures, tissue matrix compositions and high negative FCDs create barriers to drug entry and explore how charge interactions are being used to overcome these barriers. We review work on tissue targeting cationic peptide and protein-based drug delivery, compare and contrast drug delivery designs, and also present examples of technologies that are entering clinical trials. We also present strategies on further enhancing drug retention within diseased tissues of lower FCD by using synergistic effects of short-range binding interactions like hydrophobic and H-bonds that stabilize long-range charge interactions. As electrostatic interactions are incorporated into design of drug delivery materials and used as a strategy to create properties that are reversible, tunable and dynamic, bio-electroceuticals are becoming an exciting new direction of research and clinical work.

Josephson Effect and Charge Distribution in Thin Bi2 Te3 Topological Insulators.

Thin layers of topological insulator materials are quasi-2D systems featuring a complex interplay between quantum confinement and topological band structure. To understand the role of the spatial distribution of carriers in electrical transport, the Josephson effect, magnetotransport, and weak anti-localization are studied in bottom-gated thin Bi2 Te3 topological insulator films. The experimental carrier densities are compared to a model based on the solutions of the self-consistent Schrödinger-Poisson equations and they are in excellent agreement. The modeling allows for a quantitative interpretation of the weak antilocalization correction to the conduction and of the critical current of Josephson junctions with weak links made from such films without any ad hoc assumptions.

Cartilage penetrating cationic peptide carriers for applications in drug delivery to avascular negatively charged tissues.

Drug delivery to avascular, negatively charged tissues like cartilage remains a challenge. The constant turnover of synovial fluid results in short residence time of administered drugs in the joint space and the dense negatively charged matrix of cartilage hinders their diffusive transport. Drugs are, therefore, unable to reach their cell and matrix targets in sufficient doses, and fail to elicit relevant biological response, which has led to unsuccessful clinical trials. The high negative fixed charge density (FCD) of cartilage, however, can be used to convert cartilage from a barrier to drug entry into a depot by making drugs positively charged. Here we design cartilage penetrating and binding cationic peptide carriers (CPCs) with varying net charge, spatial distribution and hydrophobicity to deliver large-sized therapeutics and investigate their electro-diffusive transport in healthy and arthritic cartilage. We showed that CPC uptake increased with increasing net charge up to +14 but dropped as charge increased further due to stronger binding interactions that hindered CPC penetrability and uptake showing that weak-reversible binding is key to enable their penetration through full tissue thickness. Even after 90% GAG depletion, while CPC +14 uptake reduced by over 50% but still had a significantly high value of 148× showing that intra-tissue long-range charge-based binding is further stabilized by short-range H-bond and hydrophobic interactions. The work presents an approach for rational design of cationic carriers based on tissue FCD and properties of macromolecules to be delivered. These design rules can be extended to drug delivery for other avascular, negatively charged tissues. STATEMENT OF SIGNIFICANCE: Osteoarthritis (OA) remains an untreatable disease partly due to short joint residence time of drugs and a lack of delivery methods that can effectively target the dense, avascular, highly negatively charged cartilage tissue. In this study, we designed cartilage penetrating and binding cationic peptide carriers (CPCs) that, due to their optimal charge provide adequate electrical driving force to rapidly transport OA drugs into cartilage and reach their cell and matrix targets in therapeutic doses before drugs exit the joint space. This way cartilage is converted from being a barrier to drug entry into a drug depot that can provide sustained drug release for several weeks. This study also investigates synergistic effects of short-range H-bond and hydrophobic interactions in combination with long-range electrostatic interactions on intra-cartilage solute transport. The work provides rules for rational design of cartilage penetrating charge-based carriers depending on the net charge of tissue (normal versus arthritic), macromolecule to be delivered and whether the application is in drug delivery or tissue imaging.

Material barriers to diffusive and stochastic transport.

We seek transport barriers and transport enhancers as material surfaces across which the transport of diffusive tracers is minimal or maximal in a general, unsteady flow. We find that such surfaces are extremizers of a universal, nondimensional transport functional whose leading-order term in the diffusivity can be computed directly from the flow velocity. The most observable (uniform) transport extremizers are explicitly computable as null surfaces of an objective transport tensor. Even in the limit of vanishing diffusivity, these surfaces differ from all previously identified coherent structures for purely advective fluid transport. Our results extend directly to stochastic velocity fields and hence enable transport barrier and enhancer detection under uncertainties.

Fractal analysis of lateral movement in biomembranes.

Lateral movement of a molecule in a biomembrane containing small compartments (0.23-µm diameter) and large ones (0.75 µm) is analyzed using a fractal description of its walk. The early time dependence of the mean square displacement varies from linear due to the contribution of ballistic motion. In small compartments, walking molecules do not have sufficient time or space to develop an asymptotic relation and the diffusion coefficient deduced from the experimental records is lower than that measured without restrictions. The model makes it possible to deduce the molecule step parameters, namely the step length and time, from data concerning confined and unrestricted diffusion coefficients. This is also possible using experimental results for sub-diffusive transport. The transition from normal to anomalous diffusion does not affect the molecule step parameters. The experimental literature data on molecular trajectories recorded at a high time resolution appear to confirm the modeled value of the mean free path length of DOPE for Brownian and anomalous diffusion. Although the step length and time give the proper values of diffusion coefficient, the DOPE speed calculated as their quotient is several orders of magnitude lower than the thermal speed. This is interpreted as a result of intermolecular interactions, as confirmed by lateral diffusion of other molecules in different membranes. The molecule step parameters are then utilized to analyze the problem of multiple visits in small compartments. The modeling of the diffusion exponent results in a smooth transition to normal diffusion on entering a large compartment, as observed in experiments.

Significantly High Thermal Rectification in an Asymmetric Polymer Molecule Driven by Diffusive versus Ballistic Transport.

Tapered bottlebrush polymers have novel nanoscale polymer architecture. Using nonequilibrium molecular dynamics simulations, we showed that these polymers have the unique ability to generate thermal rectification in a single polymer molecule and offer an exceptional platform for unveiling different heat conduction regimes. In sharp contrast to all other reported asymmetric nanostructures, we observed that the heat current from the wide end to the narrow end (the forward direction) in tapered bottlebrush polymers is smaller than that in the opposite direction (the backward direction). We found that a more disordered to less disordered structural transition within tapered bottlebrush polymers is essential for generating nonlinearity in heat conduction for thermal rectification. Moreover, the thermal rectification ratio increased with device length, reaching as high as ∼70% with a device length of 28.5 nm. This large thermal rectification with strong length dependence uncovered an unprecedented phenomenon-diffusive thermal transport in the forward direction and ballistic thermal transport in the backward direction. This is the first observation of radically different transport mechanisms when heat flow direction changes in the same system. The fundamentally new knowledge gained from this study can guide exciting research into nanoscale organic thermal diodes.