Elements of future snowpack modeling – Part 2: A modular and extendable Eulerian–Lagrangian numerical scheme for coupled transport, phase changes and settling processes

A coupled treatment of transport processes, phase changes and mechanical settling is the core of any detailed snowpack model. A key concept underlying the majority of these models is the notion of layers as deforming material elements that carry the information on their physical state. Thereby an explicit numerical solution of the ice mass continuity equation can be circumvented, although with the downside of virtual no flexibility in implementing different coupling schemes for densification, phase changes and transport. As a remedy we consistently recast the numerical core of a snowpack model into an extendable Eulerian–Lagrangian framework for solving the coupled non-linear processes. In the proposed scheme, we explicitly solve the most general form of the ice mass balance using the method of characteristics, a Lagrangian method. The underlying coordinate transformation is employed to state a finite-difference formulation for the superimposed (vapor and heat) transport equations which are treated in their Eulerian form on a moving, spatially non-uniform grid that includes the snow surface as a free upper boundary. This formulation allows us to unify the different existing viewpoints of densification in snow or firn models in a flexible way and yields a stable coupling of the advection-dominated mechanical settling with the remaining equations. The flexibility of the scheme is demonstrated within several numerical experiments using a modular solver strategy. We focus on emerging heterogeneities in (two-layer) snowpacks, the coupling of (solid–vapor) phase changes with settling at layer interfaces and the impact of switching to a non-linear mechanical constitutive law. Lastly, we discuss the potential of the scheme for extensions like a dynamical equation for the surface mass balance or the coupling to liquid water flow.

A new seasonal frozen soil water-thermal coupled migration model and its numerical simulation

In this paper, a mathematical model based on spherical differential unit cell is proposed as a model for studying seasonal freeze-thaw soil space infinitesimal differential unit cell. From this model, the basic equations of permafrost moisture and heat flow motion are directly derived, then the linked equations form the permafrost water-heat coupled transport model. On this basis, the one-dimensional seasonal permafrost water-heat transport equation is derived. The model reduces the original spatial three-variable coordinate system (parallel hexahedron) into a coupled equation with a single spherical radius (R) as the independent variable, so the iterations of the numerical simulation algorithm is greatly reduced and the complexity is decreased. Finally, the model is used to simulate the seasonal freeze-thaw soil in the ShiHeZi region of Xinjiang, China. The principle of the simulation is to collect the soil temperature and humidity values of the region in layers and fixed-points using a homemade freeze-thaw soil sensor, after that we solve it by numerical calculation using MATLAB. The analysis results show that the maximum relative error of the model we proposed is 4.36, the minimum error is 0.98, and the average error is 2.515. The numerical simulation results are basically consistent with the measured data, then the proposed model is consistent with the matching states of permafrost moisture content and soil temperature in the region at different times. In addition, the experiments also demonstrate the reliability and accuracy of the model.

Microscopic Characterization of the Chloride Permeation Pathway in the Human Excitatory Amino Acid Transporter 1 (EAAT1)

Excitatory amino acid transporters (EAATs) are glutamate transporters that belong to the solute carrier 1A (SLC1A) family. They couple glutamate transport to the co-transport of three sodium (Na+) ions and one proton (H+) and the counter-transport of one potassium (K+) ion. In addition to this coupled transport, binding of substrate and Na+ ions to EAATs activates a thermodynamically uncoupled chloride (Cl-) conductance. Structures of SLC1A family members have revealed that these transporters use a twisting elevator mechanism of transport, where a mobile transport domain carries substrate and coupled ions across the membrane, while a static scaffold domain anchors the transporter in the membrane. We have recently demonstrated that the uncoupled Cl- conductance is activated by the formation of an aqueous pore at the domain interface during the transport cycle in archaeal GltPh. However, a pathway for the uncoupled Cl- conductance has not been reported for the EAATs and it is unclear if such a pathway is conserved. Here, we employ all-atom molecular dynamics (MD) simulations combined with enhanced sampling, free-energy calculations, and experimental mutagenesis to approximate large-scale conformational changes during the transport process and identified a Cl- conducting conformation in human EAAT1. We were able to extensively sample the large-scale structural transitions, allowing us to capture an intermediate conformation formed during the transport cycle with a continuous aqueous pore at the domain interface. The free-energy calculations performed for the conduction of Cl- and Na+ ions through the captured conformation, highlight the presence of two hydrophobic gates which control the selective movement of Cl- through the aqueous pathway. Overall, our findings provide insights into the mechanism by which a human glutamate transporter can support the dual functions of active transport and passive Cl- permeation and confirming the commonality of this mechanism in different members of the SLC1A family.

The dopamine transporter counter-transports potassium to increase the uptake of dopamine

The dopamine transporter (DAT) facilitates dopamine reuptake from the extracellular space, and thereby terminates neurotransmission and refills cellular stores of dopamine. DAT belongs to the neurotransmitter:sodium symporter (NSS) family, which includes similar transporters for serotonin, norepinephrine, and GABA. A hallmark of NSS proteins is their ability to utilize the energy stored in the inward-directed Na+ gradient to drive the uphill transport of substrate. Decades ago, it was shown that the serotonin transporter also counter-transports K+, but investigations of K+-coupled transport in other NSSs have been inconclusive. Here, we show that the Drosophila dopamine transporter (dDAT) counter-transports K+. We found that ligand binding to both dDAT and human DAT is inhibited by K+ and that the conformational dynamics of dDAT in K+ is highly divergent from both the apo- and Na+-bound conformations. Furthermore, we found that K+ increased dopamine uptake by purified dDAT reconstituted in liposomes, and we visualized, in real-time, Na+ and K+ fluxes in single proteoliposomes using fluorescent ion indicators. Our results expand on the fundamentals of dopamine transport and prompt a reevaluation of the impact of K+ on other NSSs, including whether K+ counter-transport is a common mechanism for this pharmacologically important protein family.

Assessment of local and non–local turbulent flow components on turbulence–flame interaction

In the framework of turbulence-flame interaction, the flame is characterized by the gradient of a reactive scalar such as the progress variable, whereas the turbulence is represented by the vorticity and the strain rate. Quantitative assessment of this interaction is performed trough the study of the coupled transport between these quantities that are subject to the effects of heat release and chemical reactions. The present analysis aims at improving the understanding of the small scale turbulence – flame interaction properties, through the introduction of an additive decomposition of the strain rate and vorticity fields into their local and non-local components. The respective role of the local and non-local effects is studied for a broad range of Karlovitz numbers, by virtue of direct numerical simulations (DNS) of turbulent, premixed, lean, and statistically planar flames of methane-air. In the conditions of the present study, the alignment between flame front normals and the strain rate is found to be dominated by the local contribution from the strain rate tensor.

A 2D Numerical Simulation of Binary Alloy Solidification: Effect of Mesh Resolution on Formation of Channel Segregates

Mesh refinement is crucial for capturing the complex phenomena that governs the formation of channel segregates during binary alloy solidification. In this article, the influence of mesh size on the formation of channel segregates during the solidification of Sn-5wt%Pb alloy is numerically investigated. A solver is developed in OpenFOAM for solving the coupled transport equations of mass, momentum, energy and species. Subsequently, the simulations are performed for different mesh sizes to predict the flow field, temperature, species and solid fraction distribution including the morphology of channel segregates. From this study, it is observed that the mesh size significantly affects the morphology and the strength of channel segregates. For very fine mesh size, having sufficient number of grid point along their width, the formed channels are more continuous and the flow inside channels is resolved.

Asymmetric protonation of glutamate residues drives a preferred transport pathway in EmrE

EmrE is an Escherichia coli multidrug efflux pump and member of the small multidrug resistance (SMR) family that transports drugs as a homodimer by harnessing energy from the proton motive force. SMR family transporters contain a conserved glutamate residue in transmembrane 1 (Glu14 in EmrE) that is required for binding protons and drugs. Yet the mechanism underlying proton-coupled transport by the two glutamate residues in the dimer remains unresolved. Here, we used NMR spectroscopy to determine acid dissociation constants (pKa) for wild-type EmrE and heterodimers containing one or two Glu14 residues in the dimer. For wild-type EmrE, we measured chemical shifts of the carboxyl side chain of Glu14 using solid-state NMR in lipid bilayers and obtained unambiguous evidence on the existence of asymmetric protonation states. Subsequent measurements of pKa values for heterodimers with a single Glu14 residue showed no significant differences from heterodimers with two Glu14 residues, supporting a model where the two Glu14 residues have independent pKa values and are not electrostatically coupled. These insights support a transport pathway with well-defined protonation states in each monomer of the dimer, including a preferred cytoplasmic-facing state where Glu14 is deprotonated in monomer A and protonated in monomer B under pH conditions in the cytoplasm of E. coli. Our findings also lead to a model, hop-free exchange, which proposes how exchangers with conformation-dependent pKa values reduce proton leakage. This model is relevant to the SMR family and transporters comprised of inverted repeat domains.

Proton Coupling and the Multiscale Kinetic Mechanism of a Peptide Transporter

ABSTRACTThe proton electrochemical gradient drives substrate transport across the cell membrane via a diverse set of secondary active transporters. Proton coupled peptide transporters (POTs) are important for peptide transport in prokaryotes and eukaryotic cells, where they mediate the uptake of di- and tri-peptides in addition to drug and pro-drug molecules. Previously, we captured a POT transporter from Staphylococcus hominis, PepTSh, in a cytoplasm-facing, inward open state (Minhas et al., 2018). Biochemical experiments have further revealed several critical residues for proton coupled transport; however, the precise role played by these residues in coupling proton binding to conformational changes as well as the timescales for proton transfers have remained obscure. Here, we employed multiscale modeling, including classical molecular dynamics, reactive molecular dynamics, and enhanced free energy sampling to characterize proton coupling within this transporter. We show directly that proton binding to a glutamate on TM7 opens the extracellular gate. The inward proton flow is found to induce movement of the peptide towards the cytosol by varying the protonation state of a second conserved glutamate on TM10. We also show that proton movement between TM7 and TM10 is thermodynamically driven and kinetically permissible, revealing a mechanism for proton movement inside the transporter.