homeostasis, which is determined by the association with LDs and the local cellular needs.

\section{Materials and Methods}

\subsection{Mice}

Mitochondria were isolated from the interscapular BAT and both left and right epididymal white adipose fat pads from 12-wk-old male C57BL6/J mice (Jackson lab). Animals were fed standard chow (mouse diet 9F; PMI Nutrition International) and maintained under controlled conditions (19–22°C and a 14:10 h light–dark cycle) until euthanasia by isoflurane. All animal procedures were performed in accordance with the Guide for Care and Use of Laboratory Animals of the NIH and were approved by the Animal Subjects Committee of the University of California, Los Angeles Institutional Guidelines for Animal Care.

\subsection{PDM isolation}

PDM were isolated as previously described in detail \cite{Benador_2018, Ngo_2021} with some modifications. BAT was isolated from the inter-scapular BAT depot, and WAT was isolated from both perigonadal fat pads, also known as the epididymal fat from each mouse. BAT was homogenized using a glass–teflon dounce homogenizer, and WAT was homogenized using a glass–glass dounce homogenizer in Sucrose–HEPES–EGTA buffer supplemented with BSA (SHE + BSA: 250 mM sucrose, 5 mM HEPES, 2 mM EGTA, 1\% fatty acid-free BSA, pH 7.2). Homogenate was split into four equal parts to test protocol optimizations side-by-side. Homogenates were centrifuged at 1,000g for 10 min at 4°C. The supernatant was poured into a new tube and the fat layer was scraped into a second tube and resuspended in SHE + BSA buffer. Fat layers and supernatant were left either untreated or treated with Prot K at 2 \textmu g/ml for 15 min (Prot K, 25530-049 20 mg/ml; Invitrogen). All fat layers were incubated for 15 min at 4°C under constant rotation. For protocol including PMSF, 2 mM PMSF was added for an additional 20 min of incubation on ice while inverting the samples every 2 min (PMSF, 78830; Sigma-Aldrich). Then, all the samples were centrifuged again at 10,000g for 10 min at 4°C. The pellets were resuspended in SHE + BSA and centrifuged with the same settings once more. The pellets were then resuspended in SHE without BSA and again centrifuged with the same settings. Final pellets were resuspended in SHE without BSA and protein concentration was determined by BCA (Thermo Fisher Scientific).

\subsection{Isolation of peridroplet mitochondria from large and small lipid droplets}

Fat tissue was homogenized as described above for the PDM isolation. Homogenates were first sieved through a 630-\textmu m mesh (Genesee Scientific), and transferred into ice-cold tubes. Homogenates were then centrifuged at 500g for 3 min at 4°C which created a fat layer made up of the larger lipid droplets (LG-LD). The supernatant was carefully poured into a new tube and centrifuged at 2,000g for 10 min at 4°C which created a second fat layer consisting of smaller lipid droplets (SM-LD). The supernatant which contained the cytoplasmic mitochondria was transferred into a new tube by carefully pipetting underneath the fat layer. LG-LDs and SM-LDs were resuspended in SHE + BSA. LG-LDs were centrifuged again at 500g for 5 min at 4°C and SM-LGs were centrifuged at 2,000g for 10 min at 4°C. Both large and small LDs were resuspended in 1 ml SHE + BSA and incubated with Prot K as described above. All fractions including the supernatant containing the CM were centrifuged at 10,000g for 10 min at 4°C to pellet the mitochondria. Mitochondrial pellets were resuspended in SHE without BSA and spun one more time with the same conditions. Mitochondrial pellets were resuspended in SHE without BSA and protein concentrations were determined by BCA (Thermo Fisher Scientific).

\subsection{Isolated mitochondria respirometry}

Respirometry in isolated mitochondria was performed as previously described in detail \cite{Ngo_2021}. Briefly, isolated mitochondria were resuspended in a mitochondrial assay buffer (MAS; 100 mM KCl, 10 mM KH$_2$PO$_4$, 2 mM MgCl$_2$, 5 mM HEPES, 1 mM EGTA, 0.1\% BSA, 1 mM GDP, pH 7.2) and kept on ice. Two micrograms per well were loaded in a Seahorse XF96 microplate in 20 \textmu l volume containing substrates. The loaded plate was centrifuged at 2,000g for 5 min at 4°C and an additional 130 \textmu l of MAS buffer + substrate was added to each well. Substrate concentrations in the well were as follows: (i) 5 mM pyruvate + 5 mM malate + 4 mM ADP or (ii) 2 mM malate + 4 mM ADP. For pyruvate malate-dependent respiration, oligomycin was injected at port A (3.5 \textmu M), TMPD + ascorbic acid (0.5 + 1 mM) at port B and azide (50 mM) at port C. For palmitoyl-carnitine dependent respiration; 5 mM malate + 4 mM ADP + 40 \textmu M palmitoyl-carnitine was injected at port A, oligomycin was injected at port B (3.5 \textmu M), TMPD + ascorbic acid (0.5 + 1 mM) at port C and azide (50 mM) at port D. Mix and measure times were 0.5 and 4 min, respectively. A 2-min wait time was included for oligomycin-resistant respiration measurements.

To calculate the effects of Prot K on OCR, we measured state 3 or the capacity of coupled mitochondria to produce ATP in the presence of substrates and ADP, oligomycin-resistant leak and ATP-linked respiration, Complex IV-driven respiration, and non-mitochondrial oxygen consumption.

Fold changes in respiration were calculated from raw OCR values obtained in each experimental group, where respiration of treated mitochondria isolated on the same day and analyzed on the same plate were normalized to the untreated mitochondria to establish the effect of PK and PMSF treatment. The individual fold changes over untreated mitochondria obtained from independent experiments were then averaged, and represented in bar graphs. For each substrate (pyruvate malate or palmitoyl carnitine) and mitochondrial state (i.e., State 3, leak, ATP-linked, CoxIV), we calculated the fold change of each mitochondrial state between the mitochondria treated with PK and/or PMSF and compared it with the untreated CM or PDM of the group. For example for State 3, we set the CM untreated equal to 1 by dividing by the raw OCR value and then compared the raw OCR values of the 3 other groups with the CM untreated to calculate the fold change. For the comparison between CM Prot K and PDM Prot K as in Figs \ref{fig:figure_2} and \ref{fig:figure_3}, the fold