Background: Information processing in the brain requires large amounts of metabolic energy, the spatial distribution of which is highly heterogeneous, reflecting the complex activity patterns in the mammalian brain.

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To establish the relationship between locomotory behavior and dynamics of neural circuits in the nematode C. elegans we combined molecular and theoretical approaches. In particular, we quantitatively analyzed the motion of C. elegans with defective synaptic GABA and acetylcholine transmission, defective muscle calcium signaling, and defective muscles and cuticle structures, and compared the data with our systems level circuit model. The major experimental findings are: (1) anterior-to-posterior gradients of body bending flex for almost all strains both for forward and backward motion, and for neuronal mutants, also analogous weak gradients of undulatory frequency, (2) existence of some form of neuromuscular (stretch receptor) feedback, (3) invariance of neuromuscular wavelength, (4) biphasic dependence of frequency on synaptic signaling, and (5) decrease of frequency with increase of the muscle time constant. Based on (1) we hypothesize that the Central Pattern Generator (CPG) is located in the head both for forward and backward motion. Points (1) and (2) are the starting assumptions for our theoretical model, whose dynamical patterns are qualitatively insensitive to the details of the CPG design if stretch receptor feedback is sufficiently strong and slow. The model reveals that stretch receptor coupling in the body wall is critical for generation of the neuromuscular wave. Our model agrees with our behavioral data (3), (4), and (5), and with other pertinent published data, e.g., that frequency is an increasing function of muscle gap-junction coupling.

There have been suggestions that heat caused by cerebral metabolic activity may constrain mammalian brain evolution, architecture, and function. This article investigates physical limits on brain wiring and corresponding changes in brain temperature that are imposed by thermodynamics of heat balance determined mainly by Na(+)/K(+)-ATPase, cerebral blood flow, and heat conduction. It is found that even moderate firing rates cause significant intracellular Na(+) build-up, and the ATP consumption rate associated with pumping out these ions grows nonlinearly with frequency. Surprisingly, the power dissipated by the Na(+)/K(+) pump depends biphasically on frequency, which can lead to the biphasic dependence of brain temperature on frequency as well. Both the total power of sodium pumps and brain temperature diverge for very small fiber diameters, indicating that too thin fibers are not beneficial for thermal balance. For very small brains blood flow is not a sufficient cooling mechanism deep in the brain. The theoretical lower bound on fiber diameter above which brain temperature is in the operational regime is strongly frequency dependent but finite due to synaptic depression. For normal neurophysiological conditions this bound is at least an order of magnitude smaller than average values of empirical fiber diameters, suggesting that neuroanatomy of the mammalian brains operates in the thermodynamically safe regime. Analytical formulas presented can be used to estimate average firing rates in mammals, and relate their changes to changes in brain temperature, which can have important practical applications. In general, activity in larger brains is found to be slower than in smaller brains.