*4.5. Chemicals*

The 1,2-dioleoyl-sn-glycero-3-phosphocholine(DOPC), 1,2-dioleoyl-sn-glycero-3- phosphoetha-nolamine (DOPE), cardiolipin (CL) from bovine heart, arachidonic acid (AA), Triton X-114 octylpolyoxyethylene, dithiothreitol (DTT), bovine serum albumin (BSA), adenosine and guanosine triphosphate (ATP and GTP), sodium sulfate (Na2SO4), diammonium hydrogen phosphate ((NH4)2HPO4), 2-(N-morpholino)ethanesulfonic acid (MES), 2- Amino-2-(hydroxymethyl)propane-1,3-diol (Tris), ethylene glycol-bis(β-aminoethyl ether)- N,N,N,N-tetraacetic acid (EGTA), hexane, hexadecane and sodium dodecyl sulfate (SDS) were obtained from Sigma-Aldrich (Munich, Germany). Chloroform was from Merck KGaA (Darmstadt, Germany).

#### *4.6. Cloning, Mutation and Expression of mUCP2 and Reconstitution into Liposomes*

Mouse UCP2 (mUCP2) was cloned and expressed, as described previously [75,76]. In brief, the ORF of mUCP2 was inserted into the pET24a- expression plasmid. For expression of the protein the plasmid of wild type mUCP2 was transferred into *E. coli* cells (strain Rosetta) and grown to reach OD600nm between 0.3 and 0.5. The protein expression was then induced by adding 1 mM isopropyl-β-D-thiogalactopyranoside (IPTG). *E. coli* cells were incubated for 3 h before harvesting by centrifugation. Inclusion bodies (IB) containing the expressed proteins were collected by disruption of cells using a French press following centrifugation at 14,000× *g* [77].

In vitro site-directed mutagenesis was carried out on expression plasmids containing the cDNA of mUCP2 as templates. The mutation was introduced with a designed oligonucleotide to alter the R60 (CGT) to S (AGT) using Q5 site-directed mutagenesis kit (New England Biolabs GmbH, Frankfurt am Main, Germany) and confirmed by sequencing.

Recombinant mUCP2WT and mUCP2R60S were purified and refolded from inclusion bodies, and reconstituted into liposomes according to the previously described protocol [54]. In brief, mUCP3 were solubilized from IB using 2% sarcosyl and 1 mM DTT. 100 mg *E. coli* polar lipid (Avanti polar lipids, Alabaster, AL, USA), 300 μg Triton X-114, 75 μg octylpolyoxyethylene and 2 mM GTP were added to the solubilized mUCP2. Sarcosyl and GTP were removed by dialysis with the assay buffer (50 mM Na2SO4, 10 mM Tris, 10 mM MES

and 0.6 mM EGTA, pH 7.34). The sample was passed through a hydroxyapatite column (Bio-Rad, Laboratories, Inc., Feldkirchen, Germany) to remove decomposed proteins. Nonionic detergents were eliminated using Bio Beads (Bio-Rad, Germany). The purity of the recombinant proteins was verified by silver staining (Figure S10). The correct folding was proved by the activity assay—protein activation or inhibition.

#### *4.7. Measurements of Electrical Parameters of Membranes Reconstituted with mUCP2*

Planar lipid bilayers were formed from (proteo-) liposomes [78,79] made of 45:45:10 mol.% DOPC:DOPE:CL. Lipid concentration was 1.5 mg/mL and protein to lipid ratio— 4 μg per mg of lipid. Arachidonic acid (AA) at a concentration of 15 mol.% was directly added to the lipid phase before membrane formation. Buffer contained 50 mM Na2SO4, 10 mM Tris, 10 mM MES and 0.6 mM EGTA at pH = 7.34 and *T* = 306 K. Proper membrane formation was verified by measuring specific capacitance (C = 718 ± 34 nF/cm2) that was independent of protein, AA and ATP content. Current −voltage (I-U) measurements were performed with a patch-clamp amplifier (EPC 10 USB, HEKA Elektronik Dr Schulze GmbH, Lambrecht, Germany). Total membrane conductance at 0 mV was obtained from the slope of a linear fit of experimental data at applied voltages from −50 mV to +50 mV (Figure S7). ATP was dissolved in a buffer solution to a concentration of 400 mM and the stock solution pH was adjusted to 7.34. The volume of 3.75 μL of the stock solution was added to 750 μL buffer solution for a final concentration of 2 mM ATP. Incubation time was 30 min at *T* = 306 K. Data were analyzed using Sigma Plot (Systat Software GmbH, Erkrath, Germany).

**Supplementary Materials:** The following are available online at https://www.mdpi.com/1422-006 7/22/3/1214/s1. Figure S1: A schematic representation of UCP2 protein in the inner mitochondrial membrane, Figure S2: Time propagation of the secondary structure in simulations of UCP2 protein, Figure S3: Analysis of the EG motif in UCP2 and ANT structures, Figure S4: Time evolution of *z*-averaged water number density in simulations of UCP2 protein, Figure S5: Alignment of the primary sequences of UCP1, UCP2 and UCP3 proteins, Figure S6: Analysis of ATP binding in UCP2h, UCP2NMR and ANT structures, Figure S7: Experimental measurements of UCP2 conductance, Figure S8: Cylindrical region of UCP2 used for permeability calculations, Figure S9: Mean square displacements (MSDs) for diffusion coefficient calculations, Figure S10: Representative silverstaining of murine UCP2WT and UCP2R60S, Table S1: Number of water molecules passing through the membrane for UCP2h, UCP2NMR and ANT.

**Author Contributions:** Conceptualization, M.V.; Funding acquisition, E.E.P. and M.V.; Investigation, S.Š., Z.B., J.K. and M.V.; Project administration, M.V.; Resources, E.E.P. and M.V.; Supervision, E.E.P. and M.V.; Writing—original draft, S.Š. and M.V.; Writing—review & editing, S.Š., Z.B., J.K., E.E.P. and M.V. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was supported by the Croatian Science Foundation (Project No. IP-2019-04- 3804 to M.V.) and the Austrian Research Fund (FWF, P31559 to E.E.P.). We thank the computer cluster Isabella based in SRCE—the University of Zagreb, University Computing Centre for computational resources. M.V. was supported by the UOCHB Sabbatical visit program. Open Access was funded by the Austrian Science Fund (FWF).

**Institutional Review Board Statement:** Not Applicable.

**Informed Consent Statement:** Not Applicable.

**Data Availability Statement:** The datasets generated and/or analyzed during this study are available from the corresponding authors on reasonable request.

**Acknowledgments:** The authors thank the reviewers for their useful comments. We thank Sarah Bardakji (Vetmeduni Vienna, Austria) for excellent technical assistance.

**Conflicts of Interest:** The authors declare no conflict of interest.
