| Vesicles containing SGLT1. Model of a unilamellar vesicle with SGLT1 incorporated in two different orientations. The inward-and outward facing configurations oriented towards the intra and extra luminal side are denoted as IN and OUT, respectively. In each transport cycle SGLT1 transports 2 Na + ions and one glucose molecule. The model takes into account passive permeation of osmotically active solutes (OS) (i.e., sucrose, glucose, and NMDG 0 ) and charged particles (CP) (i.e., Na + , K + , NMDG + , Cl − , and protons) as well as passive flux of water.

| Vesicles containing SGLT1. Model of a unilamellar vesicle with SGLT1 incorporated in two different orientations. The inward-and outward facing configurations oriented towards the intra and extra luminal side are denoted as IN and OUT, respectively. In each transport cycle SGLT1 transports 2 Na + ions and one glucose molecule. The model takes into account passive permeation of osmotically active solutes (OS) (i.e., sucrose, glucose, and NMDG 0 ) and charged particles (CP) (i.e., Na + , K + , NMDG + , Cl − , and protons) as well as passive flux of water.

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The reconstitution of secondary active transporters into liposomes shed light on their molecular transport mechanism. The latter are either symporters, antiporters or exchangers, which use the energy contained in the electrochemical gradient of ions to fuel concentrative uptake of their cognate substrate. In liposomal preparations, these gradients...

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... transition rates used in the model were adapted from Table S3 in Adelman et al. (2016) and they are listed in Table 3. When we incorporated the kinetic model of SGLT1 into the vesicle we also accounted for: 1) transporter orientation (IN and OUT) after insertion into the vesicular membrane (see Figure 9) and 2) for passive water flux through the transporter. We implemented the two orientations of the transporter by switching in the equations, which constitute the kinetic model the concentration terms (i.e., [Na] OUT and [glucose] OUT became [Na] IN and [glucose] IN and vice versa) (Parent et al., 1992). ...

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... Once the relation of the intensity and pH change is established, governing equations for solute transport or simplified versions can be used to fit the P s values similar to the procedure followed for calculating the permeability of water. The details of the procedure, including a complete mathematical description of the model system [211], and various important considerations concerning proton, weak acid/base, and ion permeabilities are available in SI Section 3. It is important to note however that the number of studies that used a comprehensive stopped flow-based analysis for quantifying solute permeabilities is low and the accuracy and sensitivity of some of these approaches are still under question. ...
... This approach was used to estimate passive Cl − permeability through peptide-appended hybrid [4] arene channels [13] and carbon nanotubes [212]. However, the accuracy of this approach under a wide range of experimental conditions needs to be established in comparison with a detailed modeling approach [211] described above for pH-sensitive dyes. ...
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