José Guilherme Chaui-Berlinck

A critical understanding of the fractal model of metabolic scaling.

SUMMARY The exponent of the scaling of metabolic rate with body mass has been the subject of debate for more than a century. The argument is at two levels, one concerning questions of empirical support for the exponent and the other, how to derive it theoretically. At this second level, the exponent is usually treated as the outcome of an underlying physical burden and approached as the search for a natural law emerging within energetic and geometric constraints. Recently, a model relying on fractal geometry was proposed as a general explanation for the phenomenon. In the present study, a reanalysis of the fractal model is performed to verify its validity. All the conditions that allow for the connection between the geometric proposition and the allometric exponent are evaluated, as well as the energy loss minimization procedure put forward in the model. It is demonstrated that the minimization procedure is mathematically incorrect and ill-posed. Also, it is shown that none of the connecting conditions are fulfilled. Therefore, it is concluded that the fractal model lacks self-consistency and correct statement: it relies on strong assumptions of homogeneity in morpho-physiological features among organisms instead of demonstrating them, as claimed by its authors. It is proposed that empiricists and theoreticians should rather evaluate the frameworks for addressing metabolic scaling phenomena.

Thermogenesis in birds.

The article discusses the importance of avian skeletal muscle as a source for heat generation by means of both shivering and non-shivering. Non-shivering thermogenesis in birds is still a polemic issue. Recent evidence at the molecular/cellular level indicates, however, that this type of heat generation may also exist among birds. The involvement of the sarcoplasmic reticulum calcium ATPase in non-shivering thermogenesis is discussed in-depth.

Intraspecific relationships between resting and activity metabolism in anuran amphibians: influence of ecology and behavior.

The aerobic capacity model, as well as other models for the evolution of aerobic metabolism and the origin of endothermy, requires a mechanistic link between rates of resting and activity oxygen consumption (V̇o2 rest and V̇o2 act). The existence of such link is still controversial, but studies with anuran amphibians support a correlation between V̇o2 rest and V̇o2 act at both the intraspecific and interspecific levels. Because results at the intraspecific level are based only on a few species, we test for the generality of a link between these two metabolic variables in anurans by studying the intraspecific correlational patterns between mass‐independent V̇o2 rest and V̇o2 act in anurans. We focus on 21 Neotropical species from different geographical areas that include remarkable diversity in behavior and thermal ecology. Although uncorrelated, V̇o2 rest and V̇o2 act seem to be consistent among individuals. Diverse intraspecific phenotypic correlational trends were detected, indicating that the intraspecific relationships between V̇o2 rest and V̇o2 act might be very diverse in anurans. The three possible trends (positive, negative, and absent correlations) were observed and appeared to be predictable from ecological and behavioral variables that relate to evolutionary physiological shifts in anurans. Positive correlations between V̇o2 rest and V̇o2 act were more common in species with active lifestyles (e.g., intense vocal activity) and in species that call at low temperatures (e.g., winter or high‐elevation specialists).

Temperature effects on energy metabolism: a dynamic system analysis.

Q10 factors are widely used as indicators of the magnitude of temperature-induced changes in physico–chemical and physiological rates. However, there is a long–standing debate concerning the extent to which Q10 values can be used to derive conclusions about energy metabolism regulatory control. The main point of this disagreement is whether or not it is fair to use concepts derived from molecular theory in the integrative physiological responses of living organisms. We address this debate using a dynamic systems theory, and analyse the behaviour of a model at the organismal level. It is shown that typical Q10 values cannot be used unambiguously to deduce metabolic rate regulatory control. Analytical constraints emerge due to the more formal and precise equation used to compute Q10, derived from a reference system composed from the metabolic rate and the Q10. Such an equation has more than one unknown variable and thus is unsolvable. This problem disappears only if the Q10 is assumed to be a known parameter. Therefore, it is concluded that typical Q10 calculations are inappropriate for addressing questions about the regulatory control of a metabolism unless the Q10 values are considered to be true parameters whose values are known beforehand. We offer mathematical tools to analyse the regulatory control of a metabolism for those who are willing to accept such an assumption.

Global and partial synchronism in phase-locked loop networks

We analytically investigate the existence of global and partial synchronism in neural networks where each node is represented by a phase oscillator. Partial synchronism, which is important to pattern recognition, can be caused by increasing the natural frequency of an oscillator and restricting the frequencies of others in certain ranges.

Control of metabolic rate is a hidden variable in the allometric scaling of homeotherms

SUMMARY The allometric scaling exponent of the relationship between standard metabolic rate (SMR) and body mass for homeotherms has a long history and has been subject to much debate. Provided the external and internal conditions required to measure SMR are met, it is tacitly assumed that the metabolic rate (B) converges to SMR. If SMR does indeed represent a local minimum, then short-term regulatory control mechanisms should not operate to sustain it. This is a hidden assumption in many published articles aiming to explain the scaling exponent in terms of physical and morphological constraints. This paper discusses the findings of a minimalist body temperature (Tb) control model in which short-term controlling operations, related to the difference between Tb and the set-point temperatures by specific gains and time delays in the control loops, are described by a system of differential equations of Tb, B and thermal conductance. We found that because the gains in the control loops tend to increase as body size decreases (i.e. changes in B and thermal conductance are speeded-up in small homeotherms), the equilibrium point of the system potentially changes from asymptotically stable to a centre, transforming B and Tb in oscillating variables. Under these specific circumstances the very concept of SMR no longer makes sense. A series of empirical reports of metabolic rate in very small homeotherms supports this theoretical prediction, because in these animals B seems not to converge to a SMR value. We conclude that the unrestricted use of allometric equations to relate metabolic rate to body size might be misleading because metabolic control itself experiences size effects that are overlooked in ordinary allometric analysis.

The oxygen gain of diving insects.

The gas gill of diving insects allows gas exchange with the surrounding water, thus extending diving time. Incompressible gas gills can potentially last indefinitely underwater, but compressible gas gills have a definite lifetime. Theoretical models of a dive event have reached opposite conclusions about the oxygen gain (G, the ratio between the duration of the diving event and the time that the initial oxygen content of the bubble would allow the insect to stay underwater). While some authors claim that G has a fixed value independently of the parameters of the dive (e.g. oxygen consumption rate) others claim the contrary. However, these claims are based on numerical solutions of the models. In this study we offer an analytical solution to the problem. The analysis of a model with constant area for gas exchange demonstrates that G cannot have a fixed value, for a fixed gain would imply in a P(O(2)) inside the bubble different from the one occurring as a result of physical constraints of the gas exchange process.

Temperature effects on a whole metabolic reaction cannot be inferred from its components

Changes in temperature affect the kinetic energy of the constituents of a system at the molecular level and have pervasive effects on the physiology of the whole organism. A mechanistic link between these levels of organization has been assumed and made explicit through the use of values of organismal Q10 to infer control of metabolic rate. To be valid this postulate requires linearity and independence of the isolated reaction steps, assumptions not accepted by all. We address this controversy by applying dynamic systems theory and metabolic control analysis to a metabolic pathway model. It is shown that temperature effects on isolated steps cannot rigorously be extrapolated to higher levels of organization.

The signal in total-body plethysmography: errors due to adiabatic-isothermic difference.

Total-body plethysmography is a technique often employed in comparative physiology studies because it avoids excessive handling of the animals. The pressure signal obtained is generated by an increase in internal energy of the gas phase of the system. Currently, this increase in internal energy is ascribed to heating (and water vapour saturation) of the inspired gas. The standard equation for computing tidal-volume implies that only temperature and saturation differences can be responsible for generating the ventilation signal. In this study, we were able to demonstrate that the difference between the external process of the thoracic expansion, which is adiabatic, and the internal process of it, which is isothermic, is an important factor of internal energy change in the total-body plethysmography method. In other words, organic tissues transfer heat to the entering gas but also to the present gas, in a way that keeps internal expansion an isothermic process. This extra amount of energy was never taken into account before. Therefore, experiments using such a technique to measure tidal-volume should be done using isothermic chambers. Moreover, due to uncertainties of the complementary measurements (ambient and lung temperatures, ambient water vapour saturation) needed to compute tidal-volume using total-body plethysmography, a minimal temperature difference about 15 degrees C between body and ambient should exist to keep uncertainties in tidal-volume values below 5%. However, this limit is not absolute, because it varies as a function of humidity and degree of uncertainty of the complementary measurements.

Respiratory physiology of high-altitude anurans: 55 years of research on altitude and oxygen.

In a 1951 paper, perhaps the first one addressing adjustments of respiratory physiology in high-elevation anurans, L.C. Stuart tested the hypothesis that hemoglobin values were higher in the high-elevation Bufo bocourti than in the low-elevation species Bufo marinus. We use Stuarts paper as a starting point for a historical review of the field that encompasses the past 55 years. We start with the early search for evidence of physiological adjustments that took place in the 1960s, move to the studies with Telmatobius that dominated the 1970s and the 1980s, continue with the contributions of experimental physiology that characterized the 1990s, and finish with the discovery of mechanisms enhancing hemoglobin oxygen affinity in high-elevation anurans (2000s). When analyzing the last mentioned topic, we highlight the contributions by the late Professor Carlos Monge, to whom we dedicate this paper. Finally, we discuss the current state of the field, and propose directions for further studies.