Discovering universal temperature regulation dynamics in animals

TL;DR

The results suggest that a universal, environmentally sensitive core regulator could control body temperature across a diverse range of species -- a restructuring of the current understanding of the physiological organization across species.

Abstract

Hibernation is an adaptation to extreme environmental seasonality that has been studied for almost 200 years, but our understanding of the underlying physiological system remains lacking due to the partially observed nature of the system. During hibernation, small mammals, such as the Arctic ground squirrel, exhibit dramatic oscillations in body temperature, typically one of the only physiological states measured, of up to 40 $^{\circ}$C. These spikes are known as interbout arousals and typically occur 10-20 times throughout hibernation. The physiological process that drives interbout arousals is unknown, but two distinct macro-scale mechanisms have been hypothesized. Using model selection for partially observed systems and classical dynamical systems theory, we are able to differentiate between these two hypotheses using only body temperature data recorded from a free-ranging Arctic ground squirrel, and show that our model can capture the broad features of the observed seasonal physiological transitions. We then modify our discovered physiological model of Arctic ground squirrel to include neurally-encoded environmental information and find that we can qualitatively match body temperature data recorded from a wide range of species, including a bird, a shrew, and a bear, which also dynamically modulate body temperature. Our results suggest that a universal, environmentally sensitive core regulator could control body temperature across a diverse range of species -- a restructuring of our current understanding of the physiological organization across species. While the findings presented here are applicable to thermophysiology, the general modeling procedure is applicable to time series data collected from partially observed biological, chemical, physical, mechanical, and cosmic systems for which the goal is to elucidate the underlying mechanism or control structure.

Figures (9)

• Figure 1: The physiological mechanism driving the spiking behavior observed in the body temperature of the hibernating Arctic ground squirrel is unknown. Two distinct mechanistic hypotheses describe the dynamics of the hidden physiological mechanism. The distinguishing feature is whether the oscillation has a variable period (Torpor Arousal Clock Hypothesis) or a fixed period (Hourglass and Threshold Hypothesis, assuming a relatively constant metabolite decay rate and fixed physiological threshold shown in gray). Left: Body temperature recording of the Arctic ground squirrel during hibernation from chmura. Right: In the Torpor Arousal Clock Hypothesis, the hidden physiological driver of interbout arousals has a variable period that depends on the body temperature of the organism (see Figure 3 in malan). When the body temperature of the organism is high, the hidden physiological state is predicted to have a short period. When the body temperature of the organism is low, the hidden physiological state is predicted to have a long period. In the Hourglass and Threshold Hypothesis, the hidden physiological driver of interbout arousals has a constant period, assuming a constant metabolite decay rate and fixed physiological threshold (shown in gray) ruf2022.
• Figure 2: Model selection reveals a seven-term core model and possible higher-order terms that describe experimental observations of Arctic ground squirrel thermophysiology. (A) Inputs for model selection. Data: Body temperature recorded from a free-ranging Arctic ground squirrel chmura. Training data is shown in blue. Validation data is shown in orange. Dimension of the system: We compute the dimension of the system using time delay embedding. The system is two-dimensional. We show the phase space reconstruction of the system. Model library: we include monomials up to cubic order in our library. (B) Simplified schematic of the model selection algorithm (for more details, see dahsi). Sparse Pareto optimal models with a conserved core structure are shown in pink. (C) A term-size argument is applied to the 8-term model during an interbout arousal to further sparsify our nested family of models by an additional two terms. The terms below the dotted gray line are not needed for oscillation and are therefore placed into the "possible terms" category. (D) Functional form of the core model (black) and additional possible terms (pink and blue). Possible terms in pink emerge as structural variations from the three Pareto optimal models with conserved structure. The terms in blue are eliminated from the core model using the term-size argument.
• Figure 3: Model validation shows that the simplest model, Model 6, is a reasonable fit to the data. A (top and middle): $l^2$ norm and AIC for the entire nested family of models fit to the first two interbout arousals of the training data. A (bottom): Dynamic time warping values of the model ensemble computed on the validation data. B (top): The fit of Model 6 (blue) to the training data (dotted purple). B (bottom): Close up of the fits during the first interbout arousal for Model 6 (blue) and Model 9ABC (orange), data shown as a dotted purple line. C (top): Dynamics of Model 6 ($x(t)$ in blue, $y(t)$ in pink). The hidden state has a fixed period, lending support to the Hourglass and Threshold Hypothesis ruf2022. C (bottom): Introducing a scaling symmetry into the hidden state changes the biological interpretation. In this case, the physiological threshold acts on the difference between multiple metabolites rather than a single metabolite.
• Figure 4: The beginnings of a multi-scale, neuro-physiological understanding of seasonal physiology. A: We find the location of the supercritical Hopf bifurcation in $\omega$-$\nu$-$\zeta$-$\rho$ space and plot Eq. \ref{['h']} for $\zeta=0.001$ and $\rho=0.1$. This curve divides parameter space into two qualitatively different model behaviors associated with distinct thermoregulatory modes exhibited by the Arctic ground squirrel: a stable fixed point, which corresponds to a regulated body temperature exhibited by the squirrel in the summer, and oscillatory dynamics exhibited during hibernation. Seasonal thermoregulatory changes are associated with the system crossing the boundary that separates fixed point behavior and oscillatory dynamics. B: Biologically, $\nu(t)$ may correspond to a summary output of the circannual clock, a neural mechanism to track seasonal change and generate seasonal decisions. An example trajectory of $\nu(t)$ that allows Eqs. (\ref{['nd3']})-(\ref{['nd4']}) to qualitatively capture the body temperature dynamics observed throughout the annual cycle (see Figure \ref{['fig:0']}, Left). C: The full seasonal physiological dynamics of Eqs. (\ref{['nd3']})-(\ref{['nd4']}) as $\nu(t)$ varies as in B. Dimensionless body temperature, $\tilde{x}$, and the dimensionless unknown physiological state, $\tilde{y}$, are shown in blue and purple, respectively.
• Figure 5: We modify our discovered physiological model of Arctic ground squirrel to include environmental information and find that we can qualitatively match body temperature data recorded from a wide range of species, including a bird, an elephant shrew, and a bear, which also dynamically modulate body temperature. This suggests that a universal, environmentally sensitive mechanism could regulate body temperature across a diverse range of species. A: Photographs of an Arctic ground squirrel, an elephant shrew, a noisy miner, and a black bear. All images taken from Wikipedia. B: Temperature recordings from an Arctic ground squirrel chmura, an elephant shrew shrew, a noisy miner nm, and a black bear toien. C: Phase space reconstructions of underlying thermophysiological systems. These systems are 2-to 3-dimensional. D: Model simulations of body temperature across species (blue) qualitatively match the observed body temperature data in B. Inferred dynamics of a hidden physiological state (pink). E: Internally-encoded environmental information interacting with the core model for each species.