2.8. Implementation of EE model based on Tb and thermal conductance

A model using equations (3), (4)) was constructed by optimizing the fit (minimizing the sum of squares) between the measured and predicted EE while fitting a constant conductance, k (‘optim’ function from the ‘base’ package in R). This was applied to ∼48 h of data (omitting <1 h before Ta reached its target), sampling every 120–140 s, for each mouse, combining light and dark phases (there were 1261 ± 12 intervals available per mouse for Ta 23–32 °C and 788 ± 23 for 35 °C; the first 12 h of data were omitted at 35 °C). The time constant (τ) in our system is 8.6 min. Parameters are summarized in Table S3 and below.

Cp, heat capacity, is estimated from the body weight and fat fraction (m_f) using 0.9100–0.5231 m_f cal/g BW/°C, without correction for the implanted E-Mitter [8,38]. Implanted E-mitters prevent measurement of body composition, so it was estimated from body weight using previously published male C57BL/6J data [32], m_f = 0.0140 ± 0.0015 ∗ BW – 0.218 ± 0.043, where BW is body weight, n = 28, r² = 0.762. For each mouse, the Ta changes were minimal, and Ta(n) was used for Ta(n+1).

This initial model held k constant (see 3.8). However, k was observed to be bimodally distributed, so the model was modified to fit two conductances, k_high for intervals with PA(n) > the median 24-h physical activity and k_low for intervals with PA(n) ≤ the median physical activity (see 3.8). While other ways of assigning between two conductances were explored, the median PA is biologically relevant and produced the greatest improvement in model fit.